Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

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Effect of the material-hardening mode on the springback

Effect of the material-hardening mode on the springbacksimulation accuracy of V-free bendingXuechun Li a,*,Yuying Yang a ,Yongzhi Wang a ,Jun Bao a ,Shunping Li baSchool of Material Science and Engineering,Harbin Institute of Technology,435,Hei Longjiang,Harbin 150001,ChinabNorthwestern Polytechnical University,Xi’an,Shanxi 710072,ChinaReceived 2January 2001AbstractLower springback simulation accuracy is a common problem for large complex sheet metal parts with FE software.The springback of V-free bending is studied in this paper by using a self-developed 2D elasto-plastic ﬁnite element program.A linear-hardening model and an elasto-plastic power-exponent hardening model of the material are adopted in this study.The change of the material’s Young’s modulus with plastic deformation is also considered.The results show that the material-hardening mode directly affects the springback simulation accuracy,and the greater the veracity of the hardening mode,the greater the springback accuracy.#2002Published by Elsevier Science B.V .Keywords:Springback simulation;Hardening model;Young’s modulus1.IntroductionSpringback is severe during the unloading phase of bending and greatly affects the forming accuracy of the bent parts.To exactly and effectively forecast the springback is the basis of achieving a steady and precise shape of the formed part.Springback is related to many factors such as tooling geometry,material properties,friction and so on.Springback is so complicated that it is hard to simulate ually very low precision can be found in ﬁnite element codes for springback simulation [1].Springback is caused by the release of internal stress during the unloading phase in sheet metal forming,so factors affecting the stress calculation accuracy will affect the springback calculation.It is indicated that the ﬁnite element dimensions and the material’s hardening model have greater effects on the stress calculation.The material’s hardening model,viz the material’s stress–strain relationship,expresses the basic properties of the material during plastic deformation.It is important to cor-rectly select and reasonably pre-digest the stress–strain curve to enhance the accuracy of the springback simulation of bending with FE codes [2,3].It is common knowledge that Young’s modulus is an important parameter in a plastic-hardening model.The lit-erature shows that the value of Young’s modulus of cold-rolled plate varies when it is undergoing plastic deformation,therefore,to consider the change of Young’s modulus of the material can increase the springback simulation accuracy [4–6].In this paper,the springback of V-free bending is studied with three materials:LY12(M),LF21(M)and SPCC,and the change of the material’s Young’s modulus with plastic deformation is considered in a self-developed 2D elasto-plastic ﬁnite element code to study the effects of the materi-al’s hardening mode on springback accuracy.2.Material-hardening modelGenerally,when a sheet metal begins to deform plasti-cally,the stress–strain relationship is very complicated and hard to express.For the convenience of actual application,some material-hardening models and relevant empirical equations have been put forward for different metal materi-als.Among them,the linear-hardening model and the elasto-plastic power-exponent hardening model are two frequently used models for simulation analysis.The linear-hardening model is as follows:s ¼E e ðe <e S Þs s þE T e ðe !e S Þ (1)where e S is the strain at the yield point,E the Young’s modulus (elastic modulus),E T the tangent modulus after yielding,s s the yield stress,s the true stress and e the truestrain.Journal of Materials Processing Technology 123(2002)209–211*Corresponding author.Tel.:þ86-451-6415776;fax:þ86-451-6415776.E-mail address:youlf@ (X.Li).0924-0136/02/$–see front matter #2002Published by Elsevier Science B.V .PII:S 0924-0136(02)00055-9The elasto-plastic power-exponent hardening model has the form:s ¼E e ðe <e S ÞK e n ðe !e S Þ(2)where K and n represents the hardening coef ﬁcient and the hardening exponent,respectively.The change of Young ’s modulus with plastic deforming can be expressed as [7]:E ¼E 0ð1þe p Þmwhere E 0is the initial Young ’s modulus and e p the equivalent plastic strain.Through the tensile test,the basic property parameters for three materials:LY12(M),LF21(M)and SPCC,were obtained,as shown in Table 1.And the Young ’s modulus –plastic strain relationships for the materials are shown in Fig.1.3.FEM for the springback simulation of V-free bending The static implicit algorithm is adopted in the FE code to simulate the V-free bending process.The counter node contact force at the end of forming phase is used as the initial acting force for springback calculation.Then an iteration algorithm begins until all the node contact forces becomes 0.The tooling dimensions for V-free bending are shown in Fig.2.In the developed FE code,an elasto-plastic algorithm is used in the loading phase and an elastic algo-rithm in springback,and the four nodes isoparametric plane element is adopted.Also,the change of Young ’s modulus with plastic deformation is considered.4.Results and analysisIn V-free bending simulation,different hardening modes result in different stress ﬁelds at the end of bending forming,viz the initial acting force for springback calculation will be different.In the simulation,the material ’s hardening mod-ulus H 0must be calculated to form a constitutive matrix,which can be expressed as:H 0¼d s d e p(3)or H 0¼EE T E ÀE T(4)where E T is the slope of the stress –strain curve after yielding,namely E T ¼d s d e(5)Table 1Basic property parameters Materials s (MPa)E 0(GPa)E T (MPa)K (MPa)n mLY12(M)91.4170.089386.668356.2250.206À0.0855LF21(M)60.0067.339148.15164.1170.183À0.1068SPCC 246.05159.048553.339551.6470.226À0.0351Fig.1.The change of Young ’s modulus with plasticdeformation.Fig.2.Tooling diagram:(1)punch;(2)blank;(3)die.Fig.3.Bending angle vs.springback angle for three materials without considering the change of Young ’s modulus with plastic deformation.BISO —linear-hardening model,MISO —elasto-plastic power-exponent hardening model.210X.Li et al./Journal of Materials Processing Technology 123(2002)209–211It is obvious that the stress obtained with the elasto-plastic power-exponent hardening model is more accurate than that with the linear-hardening model.As a result,the initial acting force for springback calculation is more accurate with the use of the elasto-plastic power-exponent hardening model.Fig.3is the relationship between the bending angle in the forming phase and the springback angle in the springback phase under the two material-hardening models.The bend-ing angle is the supplementary angle of the bent part ’s included angle.The ﬁgure shows that the springback calcu-lated with the elasto-plastic power-exponent hardening model is closer to the experiment results than that with the linear-hardening model.Figs.4–6show the relationships between the bending angle in the forming phase and the springback angle in the springback phase for the three materials,with the elasto-plastic power-exponent hardening model including the change of Young ’s modulus with plastic deformation.It has been proven by the experimental results that the value of Young ’s modulus changes along with plastic deformation,so considering the change of Young ’s modulus in the FE code can describe the deforming state of the material more truly,and the springback calculated is closer to the experiment value.5.Conclusions1.The material ’s hardening model directly affects the accuracy of springback calculation.The greater the veracity of the hardening model,the greater the springback accuracy.The springback calculated with the elasto-plastic power-exponent hardening model agrees better with experimental results than that calculated with the linear-hardening model.2.Young ’s modulus has a great effect on springback simulation ing the change of Young ’s modulus with plastic deformation can enhance the accuracy of springback simulation.References[1] D.B.Zhu,Newest progress on the springback ’s study of plate forming,J.Plas.Eng.1(2000)11–17.[2]Z.T.Zhang,D.Lee,Development of a new model for plane strainbending and springback analysis,J.Mater.Eng.Perform.4(3)(1995)291–300.[3]Z.T.Zhang,S.J.Hu,Stress and residual stress distributions in planestrain bending,Int.J.Mech.Sci.40(6)(1998)533–543.[4] A.Makinouchi,H.Ogawa,Use the ITAS-2D Program to Calculate theSpringback with Considering the Change in Young ’s Modulus due to Plastic Deformation,Unite Report Conference of Plastic Deformation,No.43,Tokyo,1992,pp.755–756.[5]L.J.Devin,A.H.Streppl,A process model for air bending,J.Mater.Process.Technol.57(1996)48–54.[6]S.Shima,M.Yang,A study of accuracy in an intelligent V-bendingprocess for sheet metals,Material 44(500)(1995)578–583.[7]X.C.Li,Y .Y .Yang,Discuss on the relationship between the Young ’smodulus and plastic deformation,J.Harbin Inst.Technol.32(5)(2000)54–56.Fig.4.Bending angle vs.springback angle for materialSPCC.Fig.5.Bending angle vs.springback angle for materialLY12(M).Fig.6.Bending angle vs.springback angle for material LF21(M).X.Li et al./Journal of Materials Processing Technology 123(2002)209–211211。

Effects of endurance on bone mass and mechanical properties in intact and ovariectomized rat

JOURNAL OF BONE AND MINERAL RESEARCH Volume 8, Number 8, 1993 M a r y Ann Liebert, Inc., Publishers
Effects of Endurance Exercise on Bone Mass and Mechanical Properties in Intact and Ovariectomized Rats
E.I. BARENGOLTS,' D. J. CURRY ,' M.S. BAPNA,' and S.C. KUKREJA'
ABSTRACT Exercise may play a role in the prevention of bone fractures in postmenopausal osteoporosis. The effects of endurance exercise on bone properties were assessed in 9-month-old sham-operated (SH) and ovariectomized (OVX) rats. The rats were either kept sedentary (SED) or were exercised (EX) on a rodent treadmill at 21 m/ minute, 7% grade, 40 minutes/day, 4 days/week for 3 months. Bone mineral (by ash weight), morphometry, and biomechanical properties (by three-point bending) were evaluated after excision of bones at sacrifice. Ovariectomy resulted in a loss of bone mineral in femur, tibia, and fourth lumbar vertebra (U), but biomechanical (force, deformation, stress, strain, and modulus of elasticity) and morphometric (length, cortial and medullary area, and moment of inertia) properties of femur were maintained. The ash weight of femur and tibia, but not L4, as well as femur yield and maximum force and moment of inertia, were improved in OVX-EX rats compared to OVX-SED animals. In SH rats exercise had no influence on ash weight of any of the three bones or femur morphometric properties, yet femur maximum force and plastic deformation were significantly enhanced compared to SH-SED rats. The results of the present study suggest that endurance exercise has beneficial effects on the bone mineral as well as biomechanical properties (femur yield and maximum force) during early stages after ovariectomy and improves the bending strength of the intact femur without an effect on bone mineral in sham-operated rats.

On the Effect of the Internal Friction of Fluids on the Motion of Pendulums

ON THE EFFECT OF THE INTERNAL FRICTION OF FLUIDS ON THE MOTION OF PENDULUMSSir George Gabriel Stokes[Read December 9, 1850.][From the Transactions of the Cambridge Philosophical Society, Vol. IX. p. [8]Reprinted in Mathematical and Physical Papers, Sir George Gabriel Stokes and Sir J. Larmor, Vol. 3, 1880-1905]T HE great importance of the results obtained by means of the pendulum has induced philosophers to devote so much attention to the subject, and to perform the experiments with such a scrupulous regard to accuracy in every particular, that pendulum observations may justly be ranked among those most distinguished by modern exactness. It is unnecessary here to enumerate the different methods which have been employed, and the several corrections which must be made, in order to deduce from the actual observations the result which would correspond to the ideal case of a simple pendulum performing indefinitely small oscillations in vacuum. There is only one of these corrections which bears on the subject of the present paper, namely, the correction usually termed the reduction to a vacuum. On account of the inconvenience and expense attending experiments in a vacuum apparatus, the observations are usually made in air, and it then becomes necessary to apply a small correction, in order to reduce the observed result to what would have been observed had the pendulum been swung in a vacuum. The most obvious effect of the air consists in a diminution of the moving force, and consequent increase in the time of vibration, arising from the buoyancy of the fluid. The correction for buoyancy is easily calculated from the first principles of hydrostatics, and formed for a considerable time the only correction which it was thought necessary to make for reduction to a vacuum. But in the year 1828 Bessel, in a very important memoir in which he determined by a new method the length of the seconds' pendulum, pointed out from theoretical considerations the necessity of taking account of the inertia of the air as well as of its buoyancy. The numerical calculation of the effect of the inertia forms a problem of hydrodynamics which Bessel did not attack; but he concluded from general principles that a fluid, or at any rate a fluid of small density, has no other effect on the time of very small vibrations of a pendulum than that it diminishes its gravity and increases its moment of inertia. In the case of a body of which the dimensions are small compared with the length of the suspending wire, Bessel represented the increase of inertia by that of a mass equal to k times the mass of the fluid displaced, which must be supposed to be added to the inertia of the body itself. This factor k be determined experimentally for a sphere a little more than two inches in diameter, swung in air and in water. The result for air, obtained in a rather indirect way, was k = 0.9459, which value Bessel in a subsequent paper increased to 0.956. A brass sphere of the above size having been swung in water with two different lengths of wire in succession gave two values of k, differing a little from each other, and equal to only about two-thirds of the value obtained for air.The attention of the scientific world having been called to the subject by the publication of Bessel's memoir, fresh researches both theoretical and experimental soon appeared. In order to examine the effect of the air by a more direct method than that employed by Bessel, a large vacuum apparatus was erected at the expense of the Board of Longitude, and by means of this apparatus Captain (now Colonel) Sabine determined the effect of the air on the time of vibration of a particular invariable pendulum. The results of the experiments are contained in a memoir read before the Royal Society in March 1829, and printed in the Philosophical Transactions for that year. The mean of eight very consistent experiments gave 1.655 as the factor by which for that pendulum the old correction for buoyancy must be multiplied in order to give the whole correction on account of the air. A very remarkable fact was discovered in the course of these experiments. While the effects of air at the atmospheric pressure and under a pressure of about half an atmosphere were found to be as nearly as possible proportional to the densities, it was found that the effect of hydrogen at the atmospheric pressure was much greater, compared with the effect of air, than corresponded with its density. In fact, it appeared that the ratio of the effects of hydrogen and air on the times of vibration was about 1 to 5 1/4, while the ratio of the densities is only about 1 to 13. In speaking of this result Colonel Sabine remarks, "The difference of this ratio from that shewn by experiment is greater than can well be ascribed to accidental error in the experiment, particularly as repetition produced results almost identical. May it not indicate an inherent property in the elastic fluids, analogous to that of viscidity in liquids, of resistance to the motion of bodies passing through them, independently of their density ? a property, in such case,possessed by air and hydrogen gas in very different degrees; since it would appear from the experiments that the ratio of the resistance of hydrogen gas to that of air is more than double the ratio following from their densities. Should the existence of such a distinct property of resistance, varying in the different elastic fluids, be confirmed by experiments now in progress with other gases, an apparatus more suitable than the present to investigate the ratio in which it is possessed by them, could scarcely be devised: and the pendulum, in addition to its many important and useful purposes in general physics, may find an application for its very delicate, but, with due precaution, not more delicate than certain, determinations, in the domain of chemistry." Colonel Sabine has informed me that the experiments here alluded to were interrupted by a cause which need not now be mentioned, but that as far as they went they confirmed the result of the experiments with hydrogen, and pointed out the existence of a specific action in different gases, quite distinct from mere variations of density.Our knowledge on the subject of the effect of air on the time of vibration of pendulums has received a most valuable addition from the labours of the late Mr Baily, who erected a vacuum apparatus at his own house, with which he performed many hundreds of careful experiments on a great variety of pendulums. The experiments are described in a paper read before the Royal Society on the 31st of May 1832. The result for each pendulum is expressed by the value of n, the factor by which the old correction for buoyancy must be multiplied in order to give the whole effect of the air as deduced from observation. Four spheres, not quite 1 1/2 inch in diameter, gave as a mean n = 1.864, while three spheres, a little more than 2 inches in diameter, gave only 1.748. The latter were nearly of the same size as those with which Bessel, by a different method, had obtained k = 0.946 or 0.956, which corresponds to n = 1.946 or 1.956. Among the "Additional Experiments " in the latter part of Baily's paper, is a set in which the pendulums consisted of plain cylindrical rods. With these pendulums it was found that n regularly increased, though according to an unknown law, as the diameter of the rod decreased. While a brass tube 1 1/2 inch in diameter gave n equal to about 2.3, a thin rod or thick wire only 0.072 inch in diameter gave for n a value as great as 7.530.Mathematicians in the meanwhile were not idle, and several memoirs appeared about this time, of which the object was to determine from hydrodynamics the effect of a fluid on the motion of a pendulum. The first of these came from the pen of the celebrated Poisson. It was read before the French Academy on the 22nd of August 1831, and is printed in the 11th Volume of the Memoirs. In this paper, Poisson considers the case of a sphere suspended by a fine wire, and oscillating in the air, or in any gas. He employs the ordinary equations of motion of an elastic fluid, simplified by neglecting the terms which involve the square of the velocity; but in the end, in adapting his solution to practice, be neglects, as insensible, the terms by which alone the action of an elastic differs from that of an incompressible fluid, so that the result thus simplified is equally applicable to fluids of both classes. He finds that when insensible quantities are neglected n = 1.5, so that the mass which we must suppose added to that of the pendulum is equal to half the mass of the fluid displaced. This result does not greatly differ from the results obtained experimentally by Bessel in the case of spheres oscillating in water, but differs materially from the result he bad obtained for air. It agrees pretty closely with some experiments which bad been performed about fifty years before by Dubuat, who bad in fact anticipated Bessel in shewing that the time of vibration of a pendulum vibrating in a fluid would be affected by the inertia of the fluid as well as by its density. Dubuat's labours on this subject had been altogether overlooked by those who were engaged in pendulum experiments; probably because such persons were not likely to seek in a treatise on hydraulics for information connected with the subject of their researches. Dubuat had, in fact, rather applied the pendulum to hydrodynamics than hydrodynamics to the pendulum.In the Philosophical Magazine for September 1833, p. 185, is a short paper by Professor Challis, on the subject of the resistance to a ball pendulum, After referring to a former paper, in which he had shewn that no sensible error would be committed in a problem of this nature by neglecting the compressibility of the fluid even if it be elastic, Professor Challis, adopting a particular hypothesis respecting the motion, obtains 2 for the value of the factor n for such a pendulum. This mode of solution, which is adopted in several subsequent papers, has given rise to a controversy between Professor Challis and the Astronomer Royal, who maintains the justice of Poisson's result.In a paper read before the Royal Society of Edinburgh on the 16th of December 1833, and printed in the 13th Volume of the Society's Transactions, Green has determined from the common equations of fluid motion the resistance to an ellipsoid performing small oscillations without rotation. The result is expressed by a definite integral; but when two of the principal axes of the ellipsoid become equal, the integral admits of expression in finite terms, by means of circular or logarithmic functions. When the ellipsoid becomes a sphere, Green's result reduces itself to Poisson's.In a memoir read before the Royal Academy of Turin on the 18th of January 1835, and printed in the 37th Volume of the memoirs of the Academy, M. Plana has entered at great length into the theory of the resistance of fluids to pendulums. This memoir contains, however, rather a detailed examination of various points connected with the theory, than the determination of the resistance for any new form of pendulum. The author first treats the case of an incompressible fluid, and then shews that the result would be sensibly the same in the case of an elastic fluid. In the case of a ball pendulum, the only one in which a complete solution of the problem is effected, M. Plana's result agrees with Poisson's.In a paper read before the Cambridge Philosophical Society on the 29th of May 1843, and printed in the 8th Volume of the Transactions, p. 105*, 1 have determined the resistance to a ball pendulum oscillating within a concentric spherical envelope, and have pointed out the source of an error into which Poisson had fallen, in concluding that such an envelope would have no effect . When the radius of the envelope becomes infinite, the solution agrees with that which Poisson had obtained for the case of an unlimited mass of fluid. I have also investigated the increase of resistance due to the confinement of the fluid by a distant rigid plane. The same paper contains likewise the calculation of the resistance to a long cylinder oscillating in a mass of fluid either unlimited, or confined by a cylindrical envelope, having the same axis as the cylinder in its position of equilibrium. In the case of an unconfined mass of fluid, it appeared that the effect of inertia was the same as if a mass equal to that of the fluid displaced were distributed along the axis of the cylinder, so that n = 2 in the case of a pendulum consisting of a long cylindrical rod. This nearly agrees with Baily's result for the long 1 ½-inch tube ; but, on comparing it with the results obtained with the cylindrical rods, we observe the same sort of discrepancy between theory and observation as was noticed in the case of spheres. The discrepancy is, however, far more striking in the present case, as might naturally have been expected, after what had been observed with spheres, on account of the far smaller diameter of the solids employed.* [Ante, Vol. 1. p. 179.]A few years ago Professor Thomson communicated to me a very beautiful and powerful method which he had applied to the theory of electricity, which depended on the consideration of what he called electrical images. The same method, I found, applied, with a certain modification, to some interesting problems relating to ball pendulums. It enabled me to calculate the resistance to a sphere oscillating in presence of a fixed sphere, or within a spherical envelope, or the resistance to a pair of spheres either in contact, or connected by a narrow rod, the direction of oscillation being, in all these cases, that of the line joining the centres of the spheres. The effect of a rigid plane perpendicular to the direction of motion is of course included as a particular case. The method even applies, as Professor Thomson pointed out to me, to the uncouth solid bounded by the exterior segments of two intersecting spheres, provided the exterior angle of intersection be a submultiple of two right angles. A set of corresponding problems, in which the spheres are replaced by long cylinders, may be solved in a similar manner. These results were mentioned at the meeting of the British Association at Oxford in 1847, and are noticed in the volume of reports for that year, but they have not yet been published in detail.The preceding are all the investigations that have fallen under my notice, of which the object was to calculate from hydrodynamics the resistance to a body of given form oscillating as a pendulum. They all proceed on the ordinary equations of the motion of fluids. They all fail to account for one leading feature of the experimental results, namely, the increase of the factor n with a decrease in the dimensions of the body. They recognize no distinction between the action of different fluids, except what arises from their difference of density.In a conversation with Dr Robinson about seven or eight years ago on the subject of the application of theory to pendulums, he noticed the discrepancy which existed between the results of theory and experiment relating to a ball pendulum, and expressed to me his conviction that the discrepancy in question arose from the adoption of the ordinary theory of fluid motion, in which the pressure is supposed to be equal in all directions. He also described to me a remarkable experiment of Sir James South's which be had witnessed. This experiment has not been published, but Sir James South has kindly allowed me to mention it. When a pendulum is in motion, one would naturally have supposed that the air near the moving body glided past the surface, or the surface past it, which comes to the same thing if the relative motion only be considered, with a velocity comparable with the absolute velocity of the surface itself. But on attaching a piece of gold leaf to the bottom of a pendulum, so as to stick out in a direction perpendicular to the surface, and then setting the pendulum in motion, Sir James South found that the gold leaf retained its perpendicular position just as if the pendulum had been at rest ; and it was not till the gold leaf carried by the pendulum had been removed to some distance from the surface, that it began to lag behind. Thisexperiment shews clearly the existence of a tangential action between the pendulum and the air, and between one layer of air and another. The existence of a similar action in water is clearly exhibited in some experiments of Coulomb's which will be mentioned in the second part of this paper, and indeed might be concluded from several very ordinary phenomena, Moreover Dubuat, in discussing the results of his experiments on the oscillations of spheres in water, notices a slight increase in the effect of the water corresponding to an increase in the time of vibration, and expressly attributes it to the viscosity of the fluid.Having afterwards occupied myself with the theory of the friction of fluids, and arrived at general equations of motion, the same in essential points as those which had been previously obtained in a totally different manner by others, of which, however, I was not at the time aware, I was desirous of applying, if possible, these equations to the calculation of the motion of some kind of pendulum. The difficulty of the problem is of course materially increased by the introduction of internal friction, but as I felt great confidence in the essential parts of the theory, I thought that labour would not be ill-bestowed on the subject. I first tried a long cylinder, because the solution of the problem appeared likely to be simpler than in the case of a sphere. But after having proceeded a good way towards the result, I was stopped by a difficulty relating to the determination of the arbitrary constants, which appeared as the coefficients of certain infinite series by which the integral of a certain differential equation was expressed. Having failed in the case of a cylinder, I tried a sphere, and presently found that the corresponding differential equation admitted of integration in finite terms, so that the solution of the problem could be completely effected. The result, I found, agreed very well with Baily's experiments, when the numerical value of a certain constant was properly assumed ; but the subject was laid aside for some time. Having afterwards attacked a definite integral to which Mr Airy bad been led in considering the theory of the illumination in the neighbourhood of a caustic, I found that the method which I had employed in the case of this integral* would apply to the problem of the resistance to a cylinder, and it enabled me to get over the difficulty with which I bad before been baffled. I immediately completed the numerical calculation, so far as was requisite to compare the formulae with Baily's experiments on cylindrical rods, and found a remarkably close agreement between theory and observation. These results were mentioned at the meeting of the British Association at Swansea in 1848, and are briefly described in the volume of reports for that year.The present paper is chiefly devoted to the solution of the problem in the two cases of a sphere and of a long cylinder, and to a comparison of the results with the experiments of Baily and others. Expressions are deduced for the effect of a fluid both on the time and on the arc of vibration of a pendulum consisting either of a sphere, or of a cylindrical rod, or of a combination of a sphere and a rod. These expressions contain only one disposable constant, which has a very simple physical meaning, and which I propose to call the index of friction of the fluid. This constant we may conceive determined by one observation, giving the effect of the fluid either on the time or on the arc of vibration of any one pendulum of one of the above forms, and then the theory ought to predict the effect both on the time and on the arc of vibration of all such pendulums. The agreement of theory with the experiments of Baily on the time of vibration is remarkably close. Even the rate of decrease of the are of vibration, which it formed no part of Baily's object to observe, except so far as was necessary for making the small correction for reduction to indefinitely small vibrations, agrees with the result calculated from theory as nearly a& could reasonably be expected under the circumstances.* [Ante, Vol. II. p. 328.]It follows from theory that with a given sphere or cylindrical rod the factor n increases with the time of vibration. This accounts in a good measure for the circumstance that Bessel obtained so large a value of k for air, as is shewn at length in the present paper; though it unquestionably arose in a great degree from the increase of resistance due to the close proximity of a rigid plane to the swinging ball.I have deduced the value of the index of friction of water from some experiments of Coulomb's on the decrement of the are of oscillation of disks, oscillating in water in their own plane by the torsion of a wire. When the numerical value thus obtained is substituted in the expression for the time of vibration of a sphere, the result agrees almost exactly with Bessel's experiments with a sphere swung in water.The present paper contains one or two applications of the theory of internal friction to problems which are of some interest, but which do not relate to pendulums. The resistance to a sphere moving uniformly in a fluid may be obtained as a limiting case of the resistance to a ball pendulum, provided the circumstances be such that the square of the velocity may be neglected. The resistance thus determined proves to be proportional, for a given fluid and a given velocity, not to the surface, but to the radius of the sphere; and therefore the accelerating force of theresistance increases much more rapidly, as the radius of the sphere decreases, than if the resistance varied as the surface, as would follow from the common theory. Accordingly, the resistance to a minute globule of water falling through the air with its terminal velocity depends almost wholly on the internal friction of air. Since the index of friction of air is known from pendulum experiments, we may easily calculate the terminal velocity of a globule of given size, neglecting the part of the resistance which depends upon the square of the velocity. The terminal velocity thus obtained is so small in the case of small globules such as those of which we may conceive a cloud to be composed, that the apparent suspension of the clouds does not seem to present any difficulty. Had the resistance been determined from the common theory, it would have been necessary to suppose the globules much more minute, in order to account in this way for the phenomenon. Since in the case of minute globules falling with their terminal velocity the part of the resistance depending upon the square of the velocity, as determined by the common theory, is quite insignificant compared with the part which depends on the internal friction of the air, it follows that were the pressure equal in all directions in air in the state of motion, the quantity of water which would remain suspended in the state of cloud would be enormously diminished. The pendulum thus, in addition to its other uses, affords us some interesting information relating to the department of meteorology.The fifth section of the first part of the present paper contains an investigation of the effect of the internal friction of water in causing a series of oscillatory waves to subside. It appears from the result that in the case of the long swells of the ocean the effect of friction is insignificant, while in the case of the ripples raised by the wind on a small pool, the motion subsides very rapidly when the disturbing force ceases to act.PART I.ANALYTICAL INVESTIGATION.SECTION I.Adaptation of the general equations to the case of the fluid surrounding a body which oscillates as a pendulum. General laws which follow from the form of the equations. Solution of the equations in the case of an oscillating plane.1. IN a paper "On the Theories of the Internal Friction of Fluids in Motion, &c.*,'' which the society did me the honour to publish in the 8th Volume of their Transactions, I have arrived at the following equations for calculating the motion of a fluid when the internal friction of the fluid itself is taken into account, and consequently the pressure not supposed equal in all directions: with two more equations which may be written down from symmetry. In these equations u, v, w, are the components of the velocity along the rectangular axes of x, y, z; X, Y, Z are the components of the accelerating force ; p is the pressure, t the time, ρ the density, and µ a certain constant depending on the nature of the fluid.The three equations of which (1) is the type are not the general equations of motion which apply to a heterogeneous fluid when internal friction is taken into account, which are those numbered 10 in my former paper, but are applicable to a homogeneous incompressible fluid, or to a homogeneous elastic fluid subject to small variations of density, such as those which accompany sonorous vibrations. It must be understood to be included in the term homogeneous that the temperature is uniform throughout the mass, except so far as it may be raised or lowered by sudden condensation or rarefaction in the case of an elastic fluid. The general equations contain the differential coefficients of the quantity µwith respect to x, y, and z; but the equations of the form (1) are in their present shape even more general than is required for the purposes of the present paper.* [Ante. Vol. I. p. 75.]These equations agree in the main with those which had been previously obtained, on different principles, by Navier, by Poisson, and by M. de Saint-Venant, as I have elsewhere observed*. The differences depend only on the coefficient of the last term, and this term vanishes in the case of an incompressible fluid, to which Navier bad confined his investigations.The equations such as (1) in their present shape are rather complicated, but in applying them to the case of a pendulum they may be a good deal simplified without the neglect of any quantities which it would be important to retain. In the first place the motion is supposed very small, on which account it will be allowable to neglect the terms which involve the square of the velocity. In the second place, the nature of the motion that we have got to deal with is such that the compressibility of the fluid has very little influence on the result, so that we may treat the fluid as incompressible, and consequently omit the last terms in the equations. Lastly, the forces X, Y, Z are in the present case the components of the force of gravity, and if we writeFor p, we may omit the terms X, Y, Z.If z' be measured vertically downwards from a horizontal plane drawn in the neighbourhood of the pendulum, and if g be the force of gravity, ∫ (Xdx + Ydy + Zdz) = gx', the arbitrary constant, or arbitrary function of the time if it should be found necessary to suppose it to be such, being included in Π. The part of the whole force acting on the pendulum which depends on the terms Π+ gρ z'is simply a force equal to the weight of the fluid displaced, and acting vertically upwards through the centre of gravity of the volume.* Report on recent researches in Hydrodynamics. Report of the British Association for 1846, p. 16. [Ante, Vol. I.p. 182.]When simplified in the manner just explained, the equations such as (1) becomewhich, with the equation of continuity,are the only equations which have to be satisfied at all points of the fluid, and at all instants of time.In applying equations (2) to a particular pendulum experiment, we may suppose µconstant ; but in order to compare experiments made in summer with experiments made in winter, or experiments made under a high barometer with experiments made under a low, it will be requisite to regard µ as a quantity which may vary with the temperature and pressure of the fluid. As far as the result of a single experiment*, which has been already mentioned, performed with a single elastic fluid, namely air, justifies us in drawing such a general conclusion, we may assert that for a given fluid at a given temperature µ varies as ρ +.2. For the formation of the equations such as (1), 1 must refer to my former paper; but it will be possible, in a few words, to enable the reader to form a clear idea of the meaning of the constant µ.Conceive the fluid to move in planes parallel to the plane of xy, the motion taking place in a direction parallel to the axis of y. The motion will evidently consist of a sort of continuous sliding, and the differential coefficient。

Effect of low-calorie parenteral nutrition on the incidence and severity of hyperglycemia

Effect of low-calorie parenteral nutrition on the incidence and severity of hyperglycemia in surgical patients:A randomized,controlled trialChristine L.Ahrens,PharmD;Jeffrey F.Barletta,PharmD;Salmaan Kanji,PharmD;James G.Tyburski,MD;Robert F.Wilson,MD;James J.Janisse,PhD;John W.Devlin,PharmDMalnutrition is a frequent occurrence in hospitalized patients and has been asso-ciated with increased mor-bidity,prolonged hospital stay,and ele-vated healthcare costs (1).Surgical patients,in particular,are at increased risk for becoming malnourished because of the hypermetabolic state that is often encountered in the postoperative period.This hypermetabolic state can rapidly lead to an exhaustion of energy reserves,can impair wound healing,and can result in organ dysfunction.The preferred method of providing nutritional support to these patients is via the enteral route;however,many surgical patients cannot be adequately fed enterally,and thus par-enteral nutrition (PN)must be used (1).The deﬁnition of adequate nutritional support is complicated by the limited number of grade-A recommendations and the lack of well-designed clinical trials to assist clinicians with their decisions (1).These trials suffer from a lack of statisti-cal power,inclusion of heterogeneous groups,and use of inappropriate clinical end points.In fact,only 17%of the rec-ommendations in recent guidelines from the American Society for Parenteral and Enteral Nutrition are considered grade A (1).This issue is further complicated by the lack of a practical method for deter-mining individual caloric requirements.Although several methods exist to esti-mate energy expenditure and caloric re-quirements,there are limitations to each of these strategies that hinder their ap-plicability to clinical practice.Clinicians therefore frequently prescribe PN for sur-gical patients by utilizing an empirical goal of 25–30nonprotein kilocalories (NPC)/kg/day (2).A concern with using an empirical ca-loric goal is that many patients may be overfed.Recent surveys reveal that pa-tients frequently have a caloric intake that far exceeds that which is actually required (1,3).Overfeeding,particularly through provision of excessive carbohy-drate calories,may lead to a number of deleterious effects such as hyperglyce-mia,infection,hepatic steatosis,and hy-percapnia (4–9).In a study evaluating the importance of glucose control in criti-cally ill surgical patients,maintenance of tight glycemic control (blood glucose,Ͻ110mg/dL)was associated with lower mortality,a shorter duration of both me-chanical ventilation and intensive care unit (ICU)stay,fewer episodes of renal impairment and septicemia,and a de-From the Department of Pharmacy (CLA),The Cleveland Clinic Foundation,Cleveland,OH;Depart-ment of Pharmacy (JFB),Spectrum Health,Grand Rap-ids,MI;Department of Pharmacy (SK),The Ottawa Hospital,Ottawa,ON,Canada;Department of Surgery (JGT,RFW),Detroit Receiving Hospital;College of Med-icine (JGT,RFW,JJJ),Wayne State University,Detroit,MI;and Northeastern University College of Pharmacy (JWD),Boston,MA.The authors have no ﬁnancial interests to disclose.Presented at the Society of Critical Care Medicine,32nd Critical Care Congress,San Antonio,TX,January 2003.Copyright ©2005by the Society of Critical Care Medicine and Lippincott Williams &Wilkins DOI:10.1097/M.0000186746.64572.8AObjective:To determine the effect of a low-calorie parenteral nutrition (PN)regimen on the incidence and severity of hypergly-cemia and insulin requirements.Design:Prospective,randomized,clinical trial.Setting:Urban,university-afﬁliated,level-I trauma center.Patients:Consecutive surgical patients requiring PN.Interventions:Patients were randomized to receive either a low-calorie PN formulation (20nonprotein kilocalories per kg per day)or a standard PN formulation (30nonprotein kilocalo-ries per kg per day).Lipid-derived calories were standardized to 1000kilocalories three times weekly for all patients;con-sequently,the number of calories varied only by the amount of carbohydrate administered.Protein requirements were individ-ualized on the basis of estimated metabolic stress.Hypergly-cemia was deﬁned as a blood glucose level >200mg/dL.Measurements and Main Results:Forty patients were evalu-ated (low-calorie PN,n ؍20;standard PN,n ؍20).Demograph-ics of the two groups were similar.The incidence of hyperglyce-mic events was signiﬁcantly lower in the low-calorie group (0%[0–0.5]vs.33.1%[0–58.4];p ؍.001].Additionally,the severity of hyperglycemia was also lower in the low-calorie group (mean glucose area under the curve ؍118؎22[mg·hr]/dL vs.172؎44[mg·hr]/dL;p <.001).This resulted in lower average daily insulin requirements (0[0–0]units vs.10.9[0–25.6]units;p <.001.).The only predictor of hyperglycemia was a dextrose ad-ministration rate >4mg/kg/min.Conclusions:Administration of a low-calorie PN formulation resulted in fewer and less-severe hyperglycemic events and lower insulin requirements.PN regimens should not exceed a dextrose administration rate of 4mg/kg/min to avoid hyperglycemic events.(Crit Care Med 2005;33:2507–2512)K EY W ORDS :hyperglycemia;parenteral nutrition;surgery;criti-cally ill;randomizedcreased need for red blood cell transfu-sions(6).The effect of a low-calorie PN regimen on the incidence of hyperglycemia has been recently investigated(10).In this study,no difference in the incidence of hyperglycemia was found between pa-tients receiving a PN formulation provid-ing1000kcal/day and patients receiving a control PN formulation providing20–25 kcal/kg/day.Major limitations of thisstudy include that the amount of calories actually administered to each group(14 kcal/kg/day and17kcal/kg/day)was sub-stantially lower than the caloric goals ad-vocated in published consensus guide-lines(1).In addition,the difference between the amounts of calories deliv-ered to each group was quite small and not clinically signiﬁcant.Recent clinical trials have demon-strated the impact of normoglycemia on morbidity and mortality,including the detrimental effects of excessive insulin administration(6,11,12)Since the pub-lication of these landmark trials,many institutions have adopted intensive insu-lin protocols in order to maintain normo-glycemia.Since overfeeding can lead to hyperglycemia,an alternative method for maintaining normoglycemia can be through providing low-calorie PN,when PN is indicated.Recognizing that no low-calorie PN regimen has been thoroughly evaluated previously,we chose to deter-mine the effect of a low-calorie PN regi-men(20NPC/kg/day)vs.a standard PN regimen(30NPC/kg/day)on the inci-dence and severity of hyperglycemia and insulin requirements in surgical patients. In addition,we identiﬁed risk factors as-sociated with the development of hyper-glycemia.MATERIALS AND METHODS This prospective,randomized study was approved by the Wayne State University Hu-man Investigation Committee,and informed consent was obtained from all patients.Con-secutive surgical patients admitted to Detroit Receiving Hospital who required PN(on the basis of either a contraindication or an intol-erance to EN)were considered for enrollment. To be included,patients had to beՆ18yrs of age and have an order to receive PN via a central catheter.Patients were excluded if they had a baseline blood glucose levelϾ200mg/ dL,were expected to receive PN therapy for fewer than4days,were severely underweight (Ͻ75%ideal body weight[IBW])or morbidly obese(greater than two times their IBW),were currently receiving corticosteroid therapy,had an admitting diagnosis of a burn,werereceiving PN on admission,or were not able toprovide informed consent.Patients were randomly assigned by meansof a computer-generated random-numbers ta-ble to receive either a low-calorie PN formu-lation(20NPC/kg/day)or a standard PN for-mulation(30NPC/kg/day).Clinicians wereblinded to which caloric group patients wererandomized to,with the exception of the crit-ical care pharmacist who calculated the PNformula.At our institution,a multiple-bottlesystem is used where lipids are administeredseparately.Lipids were thereby standardizedto500mL of a20%lipid emulsion providing1000kcal,three times weekly.The amount ofprotein prescribed was determined accordingto the estimated level of metabolic stress.Pa-tients who were mildly stressed(e.g.,unable toeat but with no other medical problems)re-ceived1.2to1.4g/kg/day of protein,those whowere moderately stressed(e.g.,by general sur-gery,pancreatitis,or intraabdominal disease)received1.5to1.7g/kg/day,and those whowere severely stressed(e.g.,by trauma-relatedsurgery,pelvic fracture,or head injury)re-ceived1.8to2.2g/kg/day.Those patients withhepatic failure(Childs-Pugh class B or C)orrenal failure(creatinine clearanceϽ10mL/min)received0.7to1.0g/kg/day and1.0to1.4g/kg/day,respectively.IBW was used for all calculations unlessthe actual body weight(ABW)was less thanthe ideal.In an attempt to better account forlean body mass in obese patients,an adjustedbody weight(AdBW)was used if ABW wasgreater than130%of IBW.Adjusted bodyweight was calculated with the following for-mula:AdBWϭIBWϩ0.4(ABW-IBW).All PN was initiated at a dosage of40mL/hr.After4hrs,if the blood glucose level wasϽ200mg/dL,the PN was advanced to thecalculated goal rate.All patients received astandardized insulin sliding scale for acutehyperglycemic events(Table1).Insulin wasadded to the PN if more than half of the bloodglucose values for a particular day wereϾ200mg/dL.Data collection continued until eitheroral feeds or tube feeds providedϾ500kcal/day.The primary outcomes assessed in thisstudy were the incidence and severity of hy-perglycemia and the daily insulin require-ments while patients were receiving PN.Hy-perglycemia was deﬁned as a blood glucoselevelՆ200mg/dL and was evaluated every4hrs with a bedside measurement(Accu-Chek,Boehringer Mannheim,Gaithersburg,MD),and blood glucose concentrations were deter-mined daily by means of a routine chemistrypanel.The incidence of hyperglycemia wascalculated as the number of assessments yield-ing a blood glucose levelՆ200mg/dL,dividedby the total number of assessments.Severityof hyperglycemia was assessed by graphingblood glucose levels over time and measuringthe area under the curve(AUC)for bothgroups.Serum albumin,prealbumin,andtransferrin values were used as measurementsof nutritional status and were determined atboth initiation and termination of PN admin-istration.A sample-size analysis revealed that26patients would be necessary to detect anabsolute difference in glucose AUC of50mg·hr/dL with80%power(pϭ.05).As a secondary objective,the incidence ofnew-onset infection was assessed using estab-lished criteria(13–18).Additionally,in an at-tempt to characterize the economics of low-calorie PN,speciﬁcally for critically illpatients,hospital charges were compared be-tween groups.Hospital charges includedcharges for a hospital room,diagnostic ser-vices,medications,nursing services,and di-rect expenses.When appropriate,transformations and/orwinsorizing was used to handle extreme(meanϮ3SD)parisons amonggroups for continuous variables were analyzedwith the Student’s t-test and the Mann-Whitney U-test.Associations between pairs ofdichotomous data were analyzed with Pear-son’s chi-square and Fisher’s exact tests.Glu-cose AUC was calculated according to the trap-ezoidal rule and then normalized for thelength of stay.For all analyses,a p valueՅ.05was considered statistically signiﬁcant.A literature review on MEDLINE for theyears1966–2003was conducted to identifypotential confounders for hyperglycemia.These confounders included age,diabetes,in-fection,critical illness,pancreatitis,and glu-cose oxidation rate.Confounders associatedwith hyperglycemia at pϽ.10were includedin a logistic regression model.Confounderswere retained if their probability level wasϽ.05and were expressed as odds ratios with95%conﬁdence intervals.To compare the hospital charges betweenthe two ICU patient groups,an analysis ofcovariance was performed with the admittingAcute Physiology and Chronic Health Evalua-tion(APACHE II)score as the covariate.Be-cause of the large amount of positive skew,asquare-root transformation was applied tonormalize the distribution of the data.Statis-tical analyses were performed with SPSS soft-Table1.Insulin sliding scaleBlood glucose(mg/dL)Regular insulindose(units)60–2000201–2503251–3006301–3509Ͻ60orϾ350Call physicianware(10.0.05,SPSS,Chicago,IL)and S-PLUS software(S-PLUS 6.1.,Insightful,Basing-stoke,Hampshire,UK;S software,Lucent Technologies,Seattle,WA).RESULTSAn equal number of patients were ran-domized between treatment groups(nϭ20for low-calorie PN;nϭ20for stan-dard PN).Baseline demographics were well-matched between groups,with the exception that the standard group had a higher serum creatinine level(1.0[0.8–1.5]mg/dL vs.0.9[0.7–1.1]mg/dL;pϭ.043)and a lower calculated creatinine clearance(77[43–107]mL/min vs.99 [83–127]mL/min;pϭ.045;Table2). One patient,in the standard group,had acute renal failure.The most common admitting diagnosis was pancreatitis(nϭ12),followed by trauma(nϭ10)and obstruction(nϭ10;Table3).The amounts of macronutrients ad-ministered are described in Table4.As expected,the number of kilocalories ad-ministered was different between the two groups,but the amount of protein ad-ministered and the duration of PN ther-apy were similar.Fewer hyperglycemic events occurred in the low-calorie group than in the stan-dard group(Table5).Additionally,the severity of hyperglycemia was lower in the low-calorie group.The mean glucose AUC was118Ϯ22(mg·hr)/dL and172Ϯ44(mg·hr)/dL for the low-calorie and standard groups,respectively(pϽ.001). As a more conservative test,the median group difference in glucose AUC wascompared with the Mann-Whitney U-test.This test was also signiﬁcant(pϽ.001).Average blood glucose values across timeand their95%conﬁdence intervals foreach group during PN are shown in Fig-ure1.Subsequently,less insulin was ad-ministered to the low-calorie group(0[0–0]vs.10.9[0–25.6];pϽ.001).Theincidence of infection was not differentbetween the groups.Analysis of potential risk factors forhyperglycemia revealed that patients whoreceived PN exceeding a dextrose admin-istration rate of4mg/kg/min were morelikely to become hyperglycemic(74%vs.29%;pϭ.004;Table6).The odds ratiowas7.00,with a95%conﬁdence intervalof1.74–28.17.No other risk factors sig-niﬁcantly predicted hyperglycemia.The changes in serum protein mark-ers during PN therapy(i.e.,albumin,pre-albumin,and transferrin)varied witheach group(Table7).In the low-caloriegroup,the change in serum albuminfrom initiation to termination of PN ad-ministration was greater than that ob-served in the standard-calorie group(pϭ.003).After controlling for length of timebetween initiation and termination,wenoted that the differential change in se-rum albumin remained signiﬁcant.Aninterestingﬁnding was a slight decreasein serum albumin in the standard-caloricgroup.Charge and APACHE II data for allcritically ill patients were evaluated(nϭ8,low-calorie group;nϭ10,standard-calorie group).After controlling forAPACHE II scores,we noted that themean hospital charges for ICU patientsreceiving low-calorie PN in the trans-formed scale was401.77,compared with479.53for standard PN,with a differenceof77.76and a95%conﬁdence intervalfor the difference ofϪ69.34to224.86.Transforming back to original units(squaring the results),we found that themean for the low-calorie and standard PNpatients was$161,419.13and$229,949.02,respectively,with a differ-ence of$6,046.62and a95%conﬁdenceinterval of$Ϫ4,808.04to$50,562.47.Itshould be noted that the square of thedifference($6,046.62)is not the same asthe difference of the squared means($161,419.13minus$229,949.02),and itis the square of the difference that shouldbe interpreted in these data.DISCUSSIONTheﬁndings of our investigation dem-onstrate that a low-calorie PN regimen of20NPC/kg/day is associated with fewerand less-severe episodes of hyperglycemiaand subsequently lower insulin require-ments than one of30NPC/kg/day.Wechose to quantify hyperglycemia in thestudy patients by both the number andthe severity of each hyperglycemic event,in order to avoid overemphasizing a sin-gle hyperglycemic event that may not beclinically signiﬁcant.This low-calorie PNformulation led not only to fewer bloodglucose valuesϾ200mg/dL but also tofewer blood glucose valuesϾ300mg/dLandϾ400mg/dL.The importance of maintaining tightglycemic control has been previouslydocumented in a study of1,548criticallyill surgical patients(6).Intensive insulintherapy(i.e.,insulin titrated to maintainglucose values between80and110mg/dL)was associated with a signiﬁcant re-duction in mortality(4.6%vs.8.0%;pϭ.04),with the greatest mortality beneﬁtfor those with multiple-organ failure/sepsis.This trial also demonstrated thattight glycemic control was associatedwith a reduction in the number of blood-stream infections,the number of epi-sodes of acute renal failure necessitatingdialysis,the median number of red-celltransfusions,and the incidence of criti-cal-illness polyneuropathy.The durationsof ventilatory support and ICU stay werealso signiﬁcantly reduced for those pa-tients who stayed in the ICU forϾ5daysand received intensive insulin therapy.Table2.Demographics and baseline characteristics of the low-calorie vs.standard-calorie groupCharacteristic Low-Calorie(nϭ20)Standard(nϭ20)pValueAge,yrs a45.3Ϯ17.253.1Ϯ17.9.170b Male,n(%)15(75)16(80) 1.000c Baseline albumin,g/dL a 2.57Ϯ0.71 2.32Ϯ0.71.263b Baseline prealbumin,mg/dL d9.2(6.5–16.7)9.2(4.8–13.3).273e Baseline transferrin,mg/dL d163(115–198)129(85–198).161e Baseline glucose,mg/dL d,i103.5(86.0–128.5)108.5(92.5–116.0).766e Baseline white blood cells,k/cumm d8.2(6.5–14.6)9.0(7.9–13.0).612e Baseline creatinine,mg/dL d0.9(0.7–1.1) 1.0(0.8–1.5).043e Creatinine clearance,mL/min d,f99(83–127)77(43–107).045e Actual body weight,kg d67.5(59.8–74.0)71(65.0–81.8).431e Ideal body weight,kg d68.5(63.8–77.9)67.2(61.1–78.8).914e Patients with diabetes,n32 1.000c ICU patients,n810.525g APACHE II score h20.1Ϯ9.118.6Ϯ11.1.759b Mechanical ventilation,n88 1.000g ICU,intensive care unit;APACHE,Acute Physiology and Chronic Health Evaluation.a MeanϮSD;b Student’s t-test;c Fisher’s exact test;d median(interquartile range);e Mann-Whitney U-test;f creatinine clearance,calculated according to Cockroft-Gault;g Pearson’s␹2;h nϭ18;i to convert the values for glucose to millimoles per liter,multiply by0.05551.A follow-up study by the same authors (19),which included the same patient database,assessed whether these beneﬁts were primarily related to blood glucose control or to the effect of insulin itself.It was concluded that lowering blood glu-cose levels rather than the amount of insulin administered was related to the beneﬁcial effect seen with morbidity and mortality.An interesting ﬁnding was that nutrition support was standardized to de-liver 20–30NPC/kg/day.Although mor-bidity and mortality were not affected by method of nutritional support (parenteral vs.enteral),it is unknown how the re-sults of the study were affected by the amount of nutritional support adminis-tered.These ﬁndings were supported in a third study,evaluating the relationship between glucose control,insulin admin-istration,and outcome for 523critically ill patients (12).In this trial,insulin ad-ministration was positively associated with mortality,a ﬁnding suggesting again that blood glucose control rather than insulin administration was respon-sible for any beneﬁt seen in mortality.Additionally,improved survival was noted when blood glucose values were below arange of 145to 200mg/dL.This trial emphasizes not only the importance of tight glycemic control but also the detri-mental effects of insulin administration.Another study highlighted the associ-ation between hyperglycemia and mortal-ity in a mixed population of critically ill patients (11).This trial reported in-creased blood glucose as an independent risk factor for mortality.In fact,the mean blood glucose value was 138mg/dL for those patients who survived,compared with 172mg/dL for those who did not (p Ͻ.001).Even though this difference may appear insigniﬁcant in clinical practice,the impact on outcome is sizeable.Thus,any intervention,such as low-calorie PN,that may reduce or prevent the occur-rence of hyperglycemia and the adminis-tration of insulin should be strongly con-sidered by clinicians.Along with beneﬁts in glucose control and insulin administration,we observed an absolute difference of 9days in length of mechanical ventilation,10days in length of stay,and 10days of ICU length of stay.These differences were not statis-tically signiﬁcant,however.It would be expected that these differences might be associated with lower hospital charges,particularly for ICU patients.We observed a difference of $6,047for ICU patients in favor of low-calorie PN,although the conﬁdence interval was wide and did cross one.The lack of statistical signiﬁ-cance for this outcome may be due to the small sample size;we calculated 108pa-tients would be required for adequate power (power ϭ0.8)to detect an effect of this magnitude.Future studies using larger sample sizes are needed to evaluate potential economic beneﬁts of low-calorie PN.In contrast to the results of our eval-uation,one recent study failed to show any beneﬁcial effects of a hypocaloric PN regimen (Ͻ1000kcal/day)on the inci-dence of hyperglycemia (10).This out-come is most likely due to the low num-ber of calories (14kcal/kg/day and 17kcal/kg/day)that were actually received by the experimental and control groups.In this study,20%of nondiabetic patients who were randomized to receive a hy-pocaloric regimen became hyperglyce-mic,compared with 26%who received a control formulation (p value not signiﬁ-cant).In our study,20%of patients re-ceiving 20NPC/kg/day became hypergly-cemic;however,this increased to 70%when patients received 30NPC/kg/day,a goal commonly targeted for surgical pa-tients today.Several risk factors for developing hy-perglycemia in the absence of diabetes have been identiﬁed and include pancre-atitis,age,rate of dextrose administra-tion,infection,and critical illness (20).In our trial,dextrose administration that ex-ceeded 4mg/kg/min was the only predic-tor of hyperglycemia.This ﬁnding is sim-ilar to that of Guenst and Nelson (21),who evaluated 140critically ill patients receiving PN.They observed a respiratory quotient (the ratio of carbon dioxide pro-duced to oxygen consumed)that ex-ceeded 1.00in 73%of patients who re-ceived dextrose at a dosage of Ͼ4mg/kg/min.Although it is important to provide an adequate number of calories,dextrose administration rates should not exceed 4mg/kg/min.This would be consistent with the caloric amounts suggested in recent recommendations (22).As part of routine care,serum protein markers (albumin,prealbumin,and transferrin)were evaluated to ensure that the patients were receiving adequate nu-trition support.These protein markers were not adversely affected by the use of a low-calorie PN formulation.Recognizing the limitations of albumin as a marker forTable 4.Description of administered nutritionLow-calorie (n ϭ20)Standard (n ϭ20)p Value Nonprotein calories/kg a 20.0(20.0–20.2)30.3(30.0–31.4)Ͻ.001b Proteins,g/kg c 1.61Ϯ0.13 1.53Ϯ0.26.210d Dextrose,g a 255(214–310)458(430–559)Ͻ.001b Lipid calories e1000,3ϫweekly 1000,3ϫweekly %Calories as lipid a 31.6(27.6–35.3)21.6(18.1–23.0)Ͻ.001b Total calories/kg a26.6(26.2–27.5)37.0(36.0–38.4)Ͻ.001b Dextrose administration rate mg/kg/min a2.82(2.65–2.98) 4.90(4.79–5.07)Ͻ.001b Duration of parenteral nutrition,days a6(4–10)7(5–10).388b Time to provision of any nutrition,days a 6(3–7)5(2–6).267b Time to PN,days a6(3–7)6(5–9).446baMedian (interquartile range);b Mann-Whitney U test;c mean ϮSD ;dStudent’s t -test;e all patientsreceived the same amount of lipids.Table 3.Admitting diagnosis for patients in the low-calorie vs.standard parenteral nutrition groupDiagnosis Low-calorie (n ϭ20)Standard (n ϭ20)Refractory pancreatitis 66TraumaPenetrating 42Blunt 31Obstruction Small bowel 23Colonic mass 23Other35nutritional progress,we thought it inter-esting that a decrease in serum albumin concentration was observed only in pa-tients receiving the standard PN formu-lation.One article recently demonstrated an association between hyperglycemia and an increased rate of muscle protein catabolism (23).Although the mecha-nism is unclear,it has been postulated that the increase in insulin resistance seen with continued hyperglycemia and the dual effect of insulin on both glucose and muscle protein metabolism may pro-vide a link between hyperglycemia and muscle protein metabolism.Future trials are warranted in this area.Our trial did have some limitations,one being that the ratio of calories ad-ministered as dextrose and lipids was not standardized.At our institution,lipids are routinely administered separately from dextrose and amino acids.To standardize this ratio would have resulted in partial administration of a 500-mL vial of lipid emulsion,which is not practical.These patients,however,did receive between 20%and 30%of their calories as lipids,which is consistent with general recom-mendations.A second limitation is that our study did not have adequate power to detect a difference between groups in clinical outcomes such as infection,length of stay,length of mechanical ven-tilation,and hospital charges.Future re-search is needed in this area.Finally,only 45%of these patients were in the ICU.It is therefore unclear whether these results could be extrapolated to critically ill pa-tients,in whom the effects of stress and gluconeogenesis may be more profound.In conclusion,administration of a low-calorie PN formulation consisting of 20NPC/kg/day led to fewer and less-severe hyperglycemic events and lower insulin requirements.Furthermore,byFigure 1.Average blood glucose values across time for each group during parenteral nutrition.Glucose curves begin with the blood glucose value 4hrs after initiation of administration of low-calorie vs.standard-calorie parenteral nutrition.Table 5.Study outcomes per parenteral nutrition groupVariableLow-calorie (n ϭ20)Standard (n ϭ20)p Value No.of glucose assessments per patient,median (interquartile range)34(24–52)40(30–51).424a Incidence of glucose events Ն200mg/dL,median (interquartile range)0%(0–0.5)33.1%(0–58.4).001a Incidence of glucose values Ն300mg/dL,median (interquartile range)0%(0–0)5%(0–13.8)Ͻ.001a Incidence of glucose values Ն400mg/dL,median (interquartile range)0%(0–0)0%(0–1.5).019a Insulin,units/day,median (interquartile range)0(0–0)10.9(0–25.6)Ͻ.001a New-onset infection (n)52.407b Hyperglycemic patients (n)514.001c Hypoglycemic patients (n)321.000b Days in hospital,median (interquartile range)15(11–26)25(15–39).116a Days in ICU,median (interquartile range)14(10–21)24(10–37).422a Length of mechanical ventilation,days,median (interquartile range)10(4–15)19(4–35).399aaMann-Whitney U-test;b Fisher’s exact test;c Pearson’s ␹2.Table 6.Univariate risk factor analysis of hyperglycemic patientsVariableNo.of patients with a hyperglycemic event(n ϭ19)No.of patients with no hyperglycemic event (n ϭ21)p Value Dextrose administration,Ͼ4mg/kg/min 146.004a Critical illness 108.356a Pancreatitis 75.369a Infection 25.412b Age Ͼ45yrs 1110.516a Diabetes231.000baPearson’s ␹2;b Fisher’s exact test.Table 7.Affect of parenteral nutrition on nutritional markersMarker Low-calorieStandardBaseline FinalBaseline Final Albumin (g/dL)a2.4Ϯ0.7 2.7Ϯ0.5b,c 2.3Ϯ0.6 2.1Ϯ0.7d Prealbumin (mg/dL)11.6Ϯ7.913.7Ϯ5.8c 9.6Ϯ5.312.7Ϯ5.7b,d Transferrin (mg/dL)159Ϯ64179Ϯ57b,c134Ϯ60139Ϯ60baStudent’s t -test,comparison between groups (low-calorie and standard)on the difference from baseline to ﬁnal,p Ͻ.05;b Student’s t -test,comparison within each group from baseline to ﬁnal,p Ͻ.05;c (n ϭ16);d (n ϭ18).。

Influence of geography on language competition

a r X i v :0807.3100v 2 [p h y s i c s .s o c -p h ] 22 J u l 2008Inﬂuence of geography on language competitionMarco Patriarca 1,2,∗and Els Heinsalu 1,2,†1National Institute of Chemical Physics and Biophysics,R¨a vala 10,15042Tallinn,Estonia2Institute of Physics,University of Tartu,T¨a he 4,Tartu 51010,Estonia(Dated:July 22,2008)Competition between languages or cultural traits diﬀusing in the same geographical area is studied combining the language competition model of Abrams and Strogatz and a human dispersal model on an inhomogeneous substrate.Also,the eﬀect of population growth is discussed.It is shown through numerical experiments that the ﬁnal conﬁguration of the surviving language can be strongly aﬀected by geographical and historical factors.These factors are not related to the dynamics of culture transmission,but rather to initial population distributions as well as geographical boundaries and inhomogeneities,which modulate the diﬀusion process.PACS numbers:89.65.Ef 87.23.Ge 89.65.-s 89.75.-kKeywords:language competition;culture diﬀusion;reaction-diﬀusion;I.INTRODUCTIONCurrently,statistical mechanics and stochastic models are employed to study a wide range of topics,not only in physical sciences,but also in interdisciplinary applica-tions in biology as well as in social and historical sciences.Examples include applications to ﬁnancial time series [1],population dynamics [2],and archeology [3].Recently,also various problems in linguistics have been approached using methods imported from the theory of complex sys-tems and statistical mechanics;see Refs.[4,5,6]for an overview.In the evolution and dispersal of biological species the importance of geography is well known [7].The goal of the present paper is to study how purely geographical and historical constraints can aﬀect the dynamics of diﬀerent languages or cultural traits competing in a region.Pre-viously the inﬂuence of geography on language dynamics has been investigated e.g.in Refs.[8,9,10,11].We start from the Abrams-Strogatz (AS)model [12]of two ﬁxed competing languages.The term “ﬁxed”refers to the fact that the evolution of language is neglected on the time scale considered,so that the model is for-mally similar to a model of population dynamics of two biological species.By “competing”one means that at any time speakers can switch to the other language,as a consequence of the interaction between speakers of lan-guage 1and 2.In order to take into account population growth,dispersal,and the eﬀect of geographical inhomo-geneities,we introduce in Sec.II a more general model.This model is then applied to some (idealized)examples concerning the inﬂuence of initial conditions (Sec.III),boundary conditions (Sec.IV),and geographical barriers (Secs.V and VI).These examples show how extending a 0-dimensional (i.e.homogeneous)model of a culture transmission to physical space gives rise to new,unex-dt =R (N 1,N 2)=s 1τN a 2N 1,dN 2τN a1N 2+s22around the value a=1.3for diﬀerent languages,as found in Ref.[12];in this article the value a=1.3is assumed. In the analogy with a population dynamics model it should be noticed that the reaction term R(N1,N2)in Eqs.(1)contains a positive and a negative contribution, depending on both populations N1and N2,which repre-sent an advantage and disadvantage due to the encounter with an individual of the other“species”.In other words, speakers of population1and2behave symmetrically to each other as prey and predator at the same time[2]. While this situation is not usual in biology,it can be jus-tiﬁed for the interaction between two cultural traits[12]. The analysis shows that the AS model has one unstable and two stable equilibrium points.The latter ones corre-spond to one of the languages surviving and the other one disappearing.Whichﬁnal state will be reached depends on the initial populations N i(t0),the status parameters s i,as well as on the value of a.The critical values of parameters deﬁning the unstable equilibrium point can be obtained from Eqs.(1)setting the rate term R equal to zero,N∗1s2 1/(a−1).(2)When the ratio N∗1/N∗2is larger than the right hand side of condition(2)at some time t=t′,then R(N1(t),N2(t))>0at any later time t>t′and N2→0 for t→∞,while N1→N′≡N1(t′)+N2(t′).The opposite takes place if N∗1/N∗2is smaller than the right hand side.B.Generalized modelPopulation and culture spreading may be aﬀected by a wide range of geographical factors,due to physical barri-ers such as water boundaries and mountains or e.g.geo-physical features such as type of ground and spatial dis-tribution of resources[7].While the underlying mech-anisms determining the inﬂuence of such geographical factors are in general complex,in aﬁrst approximation their overall eﬀect can be described statistically.In fact, dispersal of human populations in an geographical envi-ronment recalls the diﬀusion of Brownian particles modu-lated by an externalﬁeld or an inhomogeneous substrate. For example,human dispersal in neolithic Europe[13] and during the early colonization of South-America[14] has been studied using advection-diﬀusion equations with a logistic term taking into account population growth (i.e.,employing the so-called Fisher equation).In order to extend the AS model to take into account the geographical inhomogeneities,we merge it with the two-dimensional geographical model of human dispersal and growth proposed in Refs.[13,14].The corresponding evolution equations read,∂f1K ,∂f2K ,(3) with the reaction term given byR(f1,f2)=k(s1f a1f2−s2f a2f1).(4) The quantity f i=f i(x,y,t)represents the population density of speakers of language i,while the constant k in Eq.(4)is an eﬀective rate constant and s i still rep-resents the status of language i.In Eqs.(3)population movement is described by the advection term containing the external forceﬁeld F(x,y)=(F x(x,y),F y(x,y))and by the diﬀusion term with the diﬀusion coeﬃcients D= D(x,y,).In general F and D are related;their explicit form depends on the problem considered.One possibil-ity is to set F(x,y)=0and describe the inhomogeneous character of the substrate through a space-dependent dif-fusion coeﬃcient D(x,y)[13,14].In the model systems studied below we ascribe the inhomogeneous character of dispersal to the external force,F=F(x,y),while D is kept constant.For illustrative purposes and in analogy with Brownian motion,the forceﬁeld is expressed as the gradient of a potential,F(x,y)=−∇U(x,y).The logistic terms with Malthus rateαand carrying capacity K in Eqs.(3)take into account the population growth. According to Eqs.(3),populations1and2disperse in-dependently,whereas the densities f1and f2are coupled only through the reaction term R and through the logistic terms,which introduce a negative competitive coupling proportional to−f1f2.Also,it should be noticed that Eqs.(3)describe two populations with identical disper-sal and growth properties,diﬀering only in the way how the respective language interact,according to the term R given by Eq.(4).As a consequence,the total population density f=f1+f2follows a diﬀusion-advection-growth process without culture transmission,obtained by sum-ming Eqs.(3),∂fK .(5) In order to solve Eqs.(3)numerically,one can ap-proximate the derivatives through the correspondingﬁ-nite diﬀerences,replacing the problem in the continuous time and space variables(t,x,y)with the one on a lat-tice(k,m,n)deﬁned by the discrete variables t k=kδt, x m=mδx,and y n=nδy,respectively,where k,m, n are integers,whileδt,δx,δy are the lattice steps.By using the explicit Euler integration scheme[15],for con-3 FIG.1:Comparison of the evolution of population densities f1(x,y,t)and f2(x,y,t)(columns1and2)for two languages with status s1=1−s2=0.55for diﬀerent widths of the initial distribution f2(x,y,0).The initial distributions f i(x,y,0)are given byEq.(7).Example A:a more localized initial distribution f2(x,y,0)withσ1=1.75.Example B:a more spread f2(x,y,0)withσ1=3.All other parameters are the same,see text for details.stant D one obtains from(3)theﬁnite-diﬀerence equa-tionsδk f iδx−δn(F y f i)δx2+δ2n f iK ,i=1,2.(6)Here the term+R corresponds to i=1and−R to i= 2.The time diﬀerence operatorδk,when applied to a generic functionφ(k,m,n),givesδkφ(k,m,n)=φ(k+1,m,n)−φ(k,m,n).As for the x-diﬀerence operators,δm is deﬁned as δmφ(k,m,n)=[φ(k,m+1,n)−φ(k,m−1,n)]/2, while the second diﬀerence operatorδ2m asδ2mφ(k,m,n)=φ(k,m+1,n)+φ(k,m−1,n)−2φ(k,m,n);analogous deﬁnitions apply to the y-diﬀerence operators δn andδ2n.If theﬁnite-diﬀerence equations(6)are used to solve numerically the continuous problem,suitable constraints have to be imposed on the values of the steps δt,δx,δy in order to limit the numerical integration er-ror[15].One can also consider Eqs.(6)as a general lattice model of dispersal,growth,and cultural interaction of two populations,with no reference to the continuous equations(3).Such a discrete model is employed in the examples presented in the forthcoming sections,even if for convenience we will refer also to the corresponding continuous limit represented by Eqs.(3).III.INFLUENCE OF INITIAL CONDITIONS The minimal spatial version of the AS model is ob-tained when taking in Eqs.(3)the diﬀusion coeﬃcient40.20.40.60.810100200300400500600700N 1 = 1 - N 2t N 1 = N 2 = 0.5N 1*≈ 0.3387A (σ2 = 1.75)B (σ2 = 3.00)FIG.2:Time evolution of the total population N 1(t )=1−N 2(t )with a status s 1=0.55=1−s 2for the examples A (continuous line)and B (dotted line)of Fig.1.The criticalfraction N ∗1=0.3387given by the AS model for the survival of language 1and the line corresponding to N 1=N 2are also drawn.D equal to a constant,and neglecting the growth and advection terms.Similarly to the original AS model,it admits two stable equilibrium solutions,corresponding to one of the two languages surviving and the other one disappearing,as can be shown by linear stability analy-sis.Depending on the initial conditions,there exist also unstable equilibrium solutions.In the presence of a local spatial noise the unstable solutions are washed out by the random ﬂuctuations [10].However,the minimal spatial model (with no noise)presents also some new eﬀects re-spect to the corresponding homogeneous version.In this section we discuss some examples related to the inﬂuence of initial conditions.A.Cultural interaction and dispersal withoutgrowthDiﬀerently from a homogeneous model,such as the AS model,described by ordinary diﬀerential equations,in the spatial model the evolution in time and space depends on the form of the initial population densities f i (r ,t 0)(c.f.Sec.II A).While this is a standard mathematical property,it has a relevant meaning in terms of geographi-cal and historical conditions.We consider the discretized Eqs.(6)on a square lattice with reﬂecting boundary con-ditions,assuming F =0(no advection)and α=0(no growth).Here and in the other simulations units are cho-sen to have a constant diﬀusion coeﬃcient D =1.Such a model represents a simpliﬁed version of a region that is isolated and geographically homogeneous.We use a lattice of size 50×50with ∆x =∆y =1;the time step is ∆t =0.01and the reaction constant k =2000.In order to check the consistency of the minimal spa-tial model,we have veriﬁed the AS model predictions by choosing uniform initial conditions,f i (x,y,t 0)=const.In this case the diﬀusion terms in Eqs.(3)or (6)are zero and the distributions remain uniform at any time t ;this is the only case in which integrating over the space coordinates exactly gives back the AS model (1).Uni-form initial conditions for f 1and f 2represent a historical moment when the populations 1and 2were broadly dis-tributed across the territory.Population 1is observed to disappear whenever the initial density ratio f 1/f 2islower than the critical value N ∗1/N ∗2given by condition (2).In the non-uniform case,we have found for various val-ues of parameters that a broader initial distribution rep-resents a disadvantage when population growth is negli-gible (α≈0).We illustrate this eﬀect for two languages with status s 1=0.55and s 2=1−s 1=0.45(s 1>s 2)and equal initial total population sizes N 1(t 0)=N 2(t 0)=1/2.Since α=0,the total number of speakers is conserved and for simplicity we normalize it to one,N 1(t )+N 2(t )=1.Thus N i (t )represents here the fraction of speakers of the i -th language at time t .With such parameters and ini-tial conditions,language 1would be clearly favored in the uniform case (or in the AS model)while language 2would disappear.However,this does not necessarily happen when space dimensions are taken into account.Let us investigate the situation when populations 1and 2are initially distributed according to Gaussian densities,f i (x,y,t 0)=N i (t 0)2σ2i,(7)with i =1,2,x i =y i =25,i.e.,the average positions are located in the center of the simulation area (see Fig.1top).We remark that,given the symmetry of the ini-tial conﬁguration,using reﬂecting or periodic boundary conditions leads to perfectly equivalent results.For pop-ulation 1we assume σ1=10in both examples A and B,whereas for population 2we assign σ2=1.75in example A and σ2=3in example B.The particular initial con-ﬁgurations assumed can be interpreted from a historical point of view as the sudden appearance of a high pop-ulation density of speakers 2in the center (of mass)of population 1[21].One is then interested in predicting the ﬁnal conﬁguration,i.e.,which language will even-tually prevail.Surprisingly,even when the two initial population sizes are equal,it is not the language with a higher status which necessarily survives.This situation is illustrated by example A in Fig.1.In this case,the ini-tial population distribution,with σ2=1.75,is suﬃciently narrow and the associated high population density fa-vors the 1→2reaction,see the function R (f 1,f 2)given by Eq.(4).Eventually language 1disappears despite its higher status and the same initial population.Start-ing from a wider initial density of population 2,σ2=3,while all other parameters maintain the same values as in example A,the opposite ﬁnal conﬁguration is recovered,i.e.,it is population 2which now disappears (see example B in Fig.1).In Fig.2we compare the total populations N 1(t )≡1−N 2(t )for the same examples A and B of Fig.1.As one can notice,the total population N 1of example B be-comes smaller than N 2immediately at t >t 0=0and5 FIG.3:Comparison of the evolution of population densities f1(x,y,t)and f2(x,y,t)(columns1and2)for two languages with status s1=1−s2=0.55for diﬀerent widths of the initial distribution f1(x,y,t0).All other parameters are the same,see text.Example C:initial distribution f1(x,y,t0)localized within a radius R1=15.Example D:uniform initial distribution f1(x,y,t0)=const.remains smaller until t≈400;however,eventually pop-ulation1prevails.This is possible since language1hasa higher status,s1>s2.The snapshot at time t≈100 in Fig.1shows that population densities have becomealmost uniform by that time,so that one can use the AS model to estimate the critical ratio for the survival oflanguage1.From Eq.(2),one obtains N∗1/N∗2≈0.5122 for s1=1−s2=0.55,corresponding to a critical fractionN∗1≈0.3387.In Fig.2,in the example B,the surviving population N1(t)>N∗1at any time t,while in the ex-ample A N1(t)crosses the line N1=N∗1,beginning its irreversible decrease.B.Cultural interaction and dispersal with growthIn this subsection we show that taking into account population growth,for suﬃciently large values ofα,a larger initial spreading can lead to the survival of the lan-guage,on the contrary to the situation with no growth,considered above.In Fig.3we present two illustrative examples,C and D,which diﬀer from each other with respect to the initial spread of population1. Performing the numerical simulations,we have used a 100×100simulation area with∆x=∆y=0.5and periodic boundary conditions.The time step is∆t=0.001and the reaction constant k=1000.Regarding the growth term, a rateα=0.03and a carrying capacity K=0.1have been used.The initial densities have been chosen of the form f i(x,y,t0)= N i,r i(x,y)<R i,2N i(x−x i)2+(y−y i)2is the distance between position(x,y)and the average position(x i,y i) of the population density f i.The average positions have been chosen in the middle of the simulation area, x i=y i=25.The function(8)deﬁnes a population localized around(x i,y i)within a radius R i with con-stant density f i=N i,smoothly decreasing to zero for610-210-1110102103020406080100120140N it CN 1N 210-210-111010210320406080100120140N itDN 1N 2FIG.4:Time evolution of the total populations N 1(t )and N 2(t )corresponding to the examples C (left)and D (right)of Fig.3.r i (x,y )>R i on a scale σi .We have ensured that the density (8)is nowhere larger than the carrying capac-ity,f i (x,y,t 0)≤K .In both examples C and D,pop-ulation 2starts from the same initial density (8)with N 2=0.0163647,R 2=4,and σ2=2.Instead,for popu-lation 1two diﬀerent initial conditions are used.In ex-ample C it is given by the density (8),with parameters N 1=0.0020048,R 1=10,and σ1=3;In example D,the parameters are N 1=0.000548599,R 1=25and σ1=10;with such large values of R 1and σ1,the initial density f 1in example D is practically uniform.The parameters N 1and N 2have been chosen in order to have the same total initial populations in both examples C and D,namely,N 1(t 0)=1.36and N 2(t 0)=2.64.From Fig.3one observes that,diﬀerently from what happens in examples A and B (Fig.1),increasing the ini-tial spread of a population density favors its survival:a more localized initial density f 1(example C in Fig.3)is observed to disappear,while a uniform initial condition for f 1(example D in Fig.3)leads to its survival.This can be traced back to the fact that in example D a higher growth of population 1takes place in the peripheral re-gions,where the population density f 2is negligible.The time evolution of the total population N 1(t )and N 2(t )for examples C and D are depicted in Fig.4.IV.INFLUENCE OF BOUNDARYCONDITIONSAs shown for instance in the study of the three-state voter model in Ref.[11],boundary conditions can have a crucial inﬂuence on the competition process between cul-tural traits.Here we investigate the problem of language competition comparing the inﬂuence of reﬂecting and pe-riodic boundary ing reﬂecting boundaries one can model a geographical area which is isolated,i.e.,it is not possible to enter or leave it.Periodic boundaries are a numerically convenient way to simulate an open re-gion in the middle of a much larger accessible area.We found that if the growth rate is negligible (α≈0)the vicinity of reﬂecting boundary conditions favors the sur-vival of a language.For high growth rates,the eﬀect of diﬀerent boundaries is less appreciable.Here we present the results for the case with no growth (α=0).In Fig.5we compare the time evolutions of population densities f i (x,y,t )for two languages in the presence of reﬂecting and periodic boundaries.For the language status,the values s 1=0.55and s 2=0.45have been assigned.In both examples the initial distributions f i (x,y,t 0)are as-sumed to have the Gaussian shape deﬁned by Eqs.(7),with x 1=20,y 1=30,σ1=3,for population 1,and x 2=45,y 2=5,σ2=1,for population 2;the normaliza-tion constants are N 1(t 0)=0.37and N 2(t 0)=0.63.The size of the simulation area is 50×50with ∆x =∆y =1,the time step is ∆t =0.01,and the reaction constant k =1000.From Eq.(2)one obtains,for s 1=1−s 2=0.55,that the critical fraction ensuring survival of language 1is N ∗1≈0.36(N ∗2=1−N ∗1≈0.64).Thus,the initial popu-lation fractions N 1=0.37and N 2=0.63used here would give a slight advantage to population 1in the uniform case.Instead,as one can see from Fig.5,language 1dis-appears with reﬂecting boundary conditions (Fig.5,left),while it prevails if periodic boundary conditions are used (Fig.5,right).This eﬀect is due to the fact that re-ﬂecting boundaries bounce back a part of population 2located near the boundary increasing the corresponding density f 2.With open or periodic boundaries,population 2would spread and its density f 2decrease.This in turn would lower the term representing the 2→1language switching rate in the function R (f 1,f 2).Instead,a higher density f 2favors the switching of speakers 1to language 2.In Fig.6the total populations N 1(t )=1−N 2(t )for the two examples with reﬂecting and periodic boundary conditions are plotted.V.GEOGRAPHICAL BARRIERIn real situations the coexistence of more than one language in neighboring areas for long times is often ob-served [17].Some models,such as the AS model,describe situations in which after a relatively short time only one of the competing languages survives.Survival of diﬀerent7FIG.5:Comparison of the evolution of population densities f 1(x,y,t )and f 2(x,y,t )(columns 1and 2respectively)with language status s 1=0.45=1−s 2for reﬂecting (RBC,left part)and periodic (PBC,right part)boundary conditions,while all other parameters are the same.See text for details.0.20.40.60.810500100015002000N 1 = 1 - N 2tN 1 = N 2 = 0.5N 1*≈ 0.36reflecting b.c.periodic b.c.FIG.6:Time evolution of the total population N 1(t )=1−N 2(t )for the examples RBC and PBC of Fig.5.languages in the same area was shown in Ref.[18]to be possible when population growth is taken into account.Another mechanism was suggested in Ref.[19],based on the similarity of the competing languages.In the frame-work of the bit-string language evolution model,the in-ﬂuence of a barrier on language diﬀusion and evolution was considered by Schulze and Stauﬀer,who showed that two diﬀerent languages can exist on opposite sides of thebarrier [5,9].In the present paper we concentrate on the role of purely geographical factors.The scheme employed is dif-ferent from that of Ref.[8],where the coexistence of two languages in neighboring regions was made possible by a barrier (geographical boundary or political border)af-fecting the form of the switching rate R (f 1,f 2).Instead,the mechanism described in the examples presented in Secs.V and VI below is based on the presence of a geo-graphical barrier which inﬂuences solely population dis-persal,while the cultural interaction remains the same as in the AS model.As a ﬁrst example of geographical inhomogeneity,we consider a barrier,representing e.g.a mountain chain,which divides the accessible area into two regions.For the sake of simplicity we model the problem in one di-mension.We assume that the populations of speakers of language 1and 2are initially localized on the opposite sides of the barrier,as depicted in Fig.7top.We are in-terested in the inﬂuence of the barrier on the asymptotic state.In order to answer this question,we have evolved the population densities f i (x,t )according to Eqs.(3),where ∇=∂/∂x ;we do not take into account popula-tion growth (α=0).Numerical integration is performed8f iUf iR × 1080102030f iR × 107xFIG.7:Evolution of the speaker population density f 1(x,t )(continuous line,left axis)and f 2(x,t )(dashed line,left axis)in the presence of a barrier U (x ),drawn at t =0(top,gray area,right axis).Language 1is favored both in status (s 1=0.6=1−s 2)and initial population [N 1(t 0)=0.8=1−N 2(t 0)].At times t =10(middle)and t =3000(bottom)also the local reaction rate R (f 1(x,t ),f 2(x,t ))is depicted (dashed-dotted line,right axis).In the asymptotic state (bottom)both lan-guages survive,being localized on the opposite sides of the barrier.See text for further details.through the Crank-Nicolson method [15],assuming re-ﬂecting boundary conditions.A space step ∆x =0.05,a time step δt =0.001,and a reaction constant k =200,are used.The barrier is modeled through the force ﬁeld F =F (x )=−∂U (x )/∂x ,where the potential U (x ),de-picted in Fig.7top at t =t 0=0(gray area),is U (x )=U 0√FIG.10:Evolution of population density f1(x,y,t)(left column)and f2(x,y,t)(right column).Notice the temporary presence of population1on(the central)island B at t≈60.Despite the lower status of language2,geographical inhomogeneities favor its immigration to the central island B.See text for the details.to guess.In the presence of the potential barrier(9)theevolution of the population densities is shown in Fig.7: both languages survive in the asymptotic limit on the op-posite sides of the barrier.The time evolution of the total populations N i(t)is shown in Fig.8.The survival of lan-guage2on the right side of the barrier can be explained as follows:the potential barrier modulates diﬀusion to-ward both the directions and in particular it decreases theﬂux of population1from the left toward the rightregion.This in turn causes the term k s1f a1(x,t)f2(x,t) in the reaction rate(4)to remain very small in the rightregion,so that the local2→1language switching rate is negligible respect to that of the complementary process1→2.The survival of both languages observed in the exam-ple discussed above can be ascribed to the interplay be-tween historical conditions(initial localization of the twospeakers communities on opposite sides of the barrier) and geographical constraints(presence of the barrier).InFig.7center and bottom also the switching rate R(f1,f2)is depicted with a dash-dotted line.The largest values of |R|are located close to the barrier borders,where speak-ers coming from the other side meet the local speakers and switch to the local language.In Fig.8one can alsonotice that the asymptotic total population values are equal N1(t→∞)=N2(t→∞)=1/2,as a consequence of the identical dispersal properties assumed for the two populations and the symmetrical geometry of the system.VI.IMMIGRATION TO AN ISLANDLet us now see,what happens if we consider the spread-ing of two languages toward the same initially empty re-gion.To make an example,we study two islands A and C,initially colonized by populations speaking language1and2,nguage1has a higher status s1=1−s2=0.6.Between the two islands A and C is located a third island B,which is empty.For simplicity, we choose for the islands a circular shape with identi-cal radius R;the centers of the islands are located on a line.The situation is illustrated in Fig.9top.The sys-tem has been studied on a rectangular simulation area of sides L x=35and L y=11.The population densities were evolved through the explicit Euler algorithm(6)on a350×110lattice with stepsδx=δy=0.1,using a time stepδt=0.001and a rate constant k=2000. Speakers can freely diﬀuse inside the islands,but have to overcome a barrier in order to cross the sea and reach other islands.The eﬀective potential U(x,y)modeling the barrier due to the sea also deﬁnes the island shapes; it is depicted in the lower part of Fig.9and is given by U(x,y)= U0exp −[r j(x,y)−R]2/2σ2U ,r j<R,U0,otherwise.(11)Here j=A,B,C labels the islands and r j=r j(x,y)=0.40.50.6N iN 1 (total)N 2 (total)0.10.20.30.40.50500100015002000N itN 1 (A)N 1 (B)N 2 (B)N 2 (C)FIG.11:Time evolution of the speaker community 1(con-tinuous line)and 2(dotted line)for the three island example.Top:total populations.Bottom:partial population 1on is-land A and B and partial population 2on island B and C (the partial populations not shown are negligible).Notice that both populations 1and 2are present on the central is-land B until t ≈100.populations on islands A and C have been assigned the same value N 1(t 0)=N 2(t 0)=1/2.The population den-sities f i (x,y,t 0)have the same Gaussian shape (7)with σ1=σ2=2and average coordinates x i and y i coinciding with the center coordinates of the respective nguage 1,with the higher status s 1=0.55,would be favored in the absence of barriers.We would like to know if on island B eventually prevails language 1or 2.It is clear that if the central island B is located symmetrically between islands A and C then it is language 1that in the end will prevail (also on island A)due to its higher status.Population 2may still survive on island C,where it was initially dominating,if the sea represents a large enough barrier,due to the eﬀect described in the previous section which would transform islands C into a refugium.If not,language 1may prevail ﬁnally also on island C.On the other hand,if it is easier to cross the B-C rather than the A-B channel,e.g.if island B is closer to island C than to A,then language 2may spread ﬁrst on island B and then maintain its superiority thanks to the barrier due to the presence of the A-B channel.We have studiedthe problem for various values of the distance d BC be-tween island B and C,while keeping constant the other distance d AB .The example illustrated in Figs.10and 11corresponds to a value d AB =3and to a much smaller distance d BC =0.25between islands B and C.Figure 10shows how populations 1and 2disperse over the neigh-boring island starting from their initial locations.Due to the geographical asymmetry favoring dispersal of popu-lation 2,there is a much larger ﬂow of population 2from island B to C than population 1from island A to B.This in turn leads to a rapid spreading of language 2on island B.Once language 2,with a lower status,dominates on island B,the wide sea barrier between island A and B will maintain the advantage gained by language 2.Fig-ures 10and 11also show a small presence of language 1on the central island B limited to a short time interval.VII.CONCLUSIONDispersal in space and time of two languages or cul-tural traits competing in the same geographical area has been studied through an extended language competition model based on the one proposed by Abrams and Stro-gatz.We have discussed how initial and boundary con-ditions,as well as geographical inhomogeneities,have a relevant (even drastic)meaning for language spreading and competition.We have observed various examples where a language,which in the corresponding homogeneous model would disappear,actually ly,in a homogeneous model (without space dimensions),for given values of the parameters,the evolution of a population is determined by the total initial population.In the diﬀusion model studied here,the same total population of speakers,ini-tially distributed in space in diﬀerent ways,may evolve toward opposite asymptotic scenarios.Another result of our investigation shows that,when growth is negligible,a language,whose dispersal is more aﬀected by the geo-graphical boundaries,is favored respect to the case when no limiting boundaries are present.In the presence of geographical inhomogeneities,modeled as potential en-ergy barriers,languages can survive in diﬀerent regions,despite the possibly lower status and smaller initial pop-ulations.The eﬀects discussed in the present paper are purely geographical,in the sense that they are related to the diﬀusion processes and to the modulation of diﬀusion due to inhomogeneities of the background.They inﬂu-ence culture spreading only indirectly and are not due to a change in the cultural interaction law,diﬀerently from the model introduced in Ref.[8].The diﬀusion model and the highly idealized examples presented in this paper are intended as a ﬁrst step toward a quantitative description of the space-time diﬀusion of language and cultural traits.Our study will hopefully be useful in solving some of the many challenging problems regarding language diversity [17].At the same time,a more detailed understanding of the mechanisms underly-。

EFFECT OF PITTING CORROSION ON ULTIMATE STRENGTH AND BUCKLING STRENGTH OF PLATES – A REVIEW

Digest Journal of Nanomaterials and Biostructures Vol. 4, No. 4, December 2009, p. 783-788 EFFECT OF PITTING CORROSION ON ULTIMATE STRENGTH AND BUCKLING STRENGTH OF PLATES – A REVIEWA. ADHITHYA PLATO SIDHARTH *118, 6th cross, Tanthai Periyar Nagar, Pondicherry-5, IndiaThe plate structures have become a great importance of study due to their wide use in fieldof marine and offshore structure. Moreover, in several structural engineering applications,the thickness of the plate used has a variable thickness mainly resulted from metal surfacelosses due to corrosion .Out of all deteriorating factors, the main focus is on corrosionbecause they have large effect on strength, serviceability, stability of the offshore steelstructures. And there is an abreast development in the FE analysis technique used to studythe corrosion effect on the plates. The dominant technique adopted in most of the papersconsidered is non-linear analysis using software like ANSYS, ABAQUS and fewdeveloped their own finite element algorithm. In this paper, a literature review is made onlocalized corrosion. The main attention is given to localized corrosion such as pittingwhich varies the thickness non-uniformly in the structural plate region effect and its effecton the ultimate and buckling strength of thin plates is studied.(Received November 3, 2009; accepted November 17, 2009)Keywords: Pitting corrosion, Buckling dtrength1 IntroductionCorrosion can be defined as the degradation of a material due to a reaction with its environment. Degradation implies deterioration of physical properties of the material. This can be a weakening of the material due to a loss of cross-sectional area, it can be the shattering of a metal due to hydrogen embrittlement, or it can be the cracking of a metal due to sunlight exposure. The corrosion is dominant in marine and offshore structures because of the well known fact that the sea water is an aggressive corrosive environment. And moreover it is a good electrolyte and contains corrosive salts. This means that corrosion in marine structures, which are generally fabricated from various grades of steel and low alloy steel, is often very severe, not only under sustained immersed condition but also under general exposure to atmospheric conditions. The forms of corrosion can be grouped into general corrosion, localized corrosion and mechanical corrosion. Localized corrosion is the accelerated attack of a passive metal in a corrosive environment at discrete sites where the otherwise protective passive film has broken down. Common forms of localized corrosion include pitting on a boldly exposed surface, corrosion in a creviced region shielded from the bulk environment, inter-granular corrosion of an alloy with a susceptible grain boundary region, exfoliation corrosion, filiform corrosion, stray current corrosion that occurs when sources of direct current are connected to gate structures. The third type is mechanical corrosion which includes erosion, fretting and cavitation corrosion. In the general corrosion, the thickness of the plate varies uniformly and in localized corrosion, the thickness varies non-uniformly. Clearly either general or localized corrosion will reduce the residual strength of ageing ship structures. For general corrosion, the ultimate strength of the corroded plate can be assessed based on the thickness. Until now, there is still no acknowledged method to assess the ultimate strength of the plate with pitting corrosion.The method of ultimate strength assessment for the pitted plate has been developed from the effective thickness method to the method in which many factors have been considered to represent the characteristics of pitting corrosion. However, for pitting corrosion,784the corrosion form is complicated and the thickness of the whole plate is not uniform. Improperly maintained ageing ship structure could finally lead to disastrous casualties in rough seas and heavy weather. Thus it is important to assess the ultimate strength of ageing ship structure properly. To estimate the strength, there has been significant development of computer hardware and finite element analysis (FEA) software. The finite element analysis method has now become the most common, powerful and flexible tool in rational structural analysis and makes it possible to predict the strength of complex structures more accurately than existing classical theoretical methods. People have paid increasing attention to the corrosion caused structural damage in recent half century. Corrosion-caused thickness loss makes the ultimate and buckling strength of typical thin-walled ship structural plates degraded significantly. In this paper, the various procedures adopted by researchers to study corrosion were reviewed. Especially localized corrosion and its effect on plates are studied in depth.2. Pitting corrosion and its formationCertain conditions, such as low concentrations of oxygen or high concentrations of species such as chloride which compete as anions, can interfere with a given alloy's ability to re-form a passivating film. In the worst case, almost all of the surface will remain protected, but tiny local fluctuations will degrade the oxide film in a few critical points. Corrosion at these points will be greatly amplified, and can cause corrosion pits of several types, depending upon conditions. While the corrosion pits only nucleate under fairly extreme circumstances, they can continue to grow even when conditions return to normal, since the interior of a pit is naturally deprived of oxygen and locally the pH decreases to very low values and the corrosion rate increases due to an auto-catalytic process. In extreme cases, the sharp tips of extremely long and narrow can cause stress concentration to the point that otherwise tough alloys can shatter, or a thin film pierced by an invisibly small hole can hide a thumb sized pit from view. These problems are especially dangerous because they are difficult to detect before a part or structure fails. Pitting remains among the most common and damaging forms of corrosion in passivated alloys, but it can be prevented by control of the alloy's environment, which often includes ensuring that the material is exposed to oxygen uniformly (i.e., eliminating crevices)3. Strength assessment techniques for pitting corrosionHadi Amlashi and Torgeir Moan [1] studied the strength assessment of the stiffened plates used in offshore and marine structures, which are subjected to biaxial compression loading. They studied this effect by both FE analysis and Numerical method. For this study, they considered 2m x 0.5m x 0.01m stiffened plate and a four noded quadrilateral shell element. Especially, they investigated the effect of DOP (Degree of Pitting) and depth of pits on the ultimate strength of these plates. And it can be found from the table that as the level of DOP and the depth of pit increases there is reduction in the ultimate strength. A brief study on the variation of Residual stress due to pitting corrosion was made.To determine the effect of pitting corrosion on ultimate strength, a new FEA algorithm was developed by A.U.Ibekwe et al [2] who investigated the corroded plates using Finite Element Analysis. In their study, they modeled the varying thickness profile as 3rd degree polynomial. They divided the plate into rows and columns and importantly, the varying thickness was measured randomly along the length. The least square method was used to fit a curve through data points obtained for each row. From the polynomial curve, the equivalent thickness of elements was obtained as simple averages of its corresponding boundary edges. Then they developed finite element algorithm using Visual Basic 6.0 (programming language) by employing triangular elements. That analysis was carried out using input data, that fully described the idealized structure and its loading and boundary conditions built up in various subroutines. Finally, they compared the result obtained from the newly developed finite element algorithm and the analytical formula i.e., Navier solution and the error was found to be less than 2%.785 Ibrahim A. Assakkaf and Jaime F. Cárdenas-García [3] proposed a reliability design of the doubler plates which are dominantly found in ship structures. A doubler plate is nothing but a plate that is added to top of the defective area and welded around the plate’s perimeter. Critical buckling strength of damaged column structure was estimated thorough Finite-difference and finite-element analysis and further evaluation was made on the buckling strength of the unstiffened panel- doubler plate structure by placing the doubler plate at different locations within the unstiffened panel. They studied the effect of doubler location on the critical buckling strength of unstiffened plate (doubler on one side only).Then, they adopted, the LRFD (Load and Resistance Factor Design) approach is called a Level 1 reliability method. Usually, Level 1 reliability methods utilize partial safety factors (PSF) that are reliability based; but the methods do not require explicit use of the probabilistic description of the variables. They determined partial safety factors for a uniaxially loaded and damaged unstiffened panel with doubler plate, to satisfy the requirements of the LRFD general design formats for ship hull structural components as given by limit state 1 and limit state 2.Ok, Pu and Incecik [4] studied on assessing the effects of localized pitting corrosion which concentrates at one or several possibly large area on the ultimate strength of unstiffened plates by over 256 nonlinear finite element analyses of panels with various locations and sizes of pitting corrosion. The multi-variable regression method was applied to derive new formulae to predict ultimate strength of unstiffened plates with localized corrosion. Higher strength steel of 1m x 1m plate with a yield stress of 355 N / mm2 was used for this study. Five different B/t ratios (41.7, 45.5, 50.0, 55.6, and 62.5) have been chosen by changing plate thickness.Fig. 1. Finite element analysis modeling detail for pitting corrosion The location of pitting corrosion was assumed to start at aft bay (aft end) and the sizes of pitting corrosion have four different length values (0.25L, 0.5L, 0.75L, 1.0L), in which L is the total length of the plate. The depths of pits are classified into two cases (0.25t and 0.5t). For simplifying the finite element analyses the area of pitting corrosion is assumed to have rectangular shape with single side or both sides corroded pattern as illustrated. The results indicated that the length, breadth and depth of pit corrosion have weakening effects on the ultimate strength of the plates while plate slenderness has only marginal effect on strength reduction. Transverse location of pit corrosion is also an important factor determining the amount of strength reduction. When corrosion spreads transversely on both edges, it has the most deteriorating effect on strength. It was also found out that the proposed formulae can accurately predict the ultimate strength of unstiffened plate with localized corrosion.Diadola et al [5] proposed that an initial determination of the acceptability of a plate panel with pitting can be made on the basis of the pit depths. They proposed that individual pits with a depth less than 50% of the residual thickness can be repaired by epoxy and individual pits with a depth greater than 50% of the residual thickness may be welded if at least 6.5 mm of material remains at bottom of pit, the distance between adjacent pits is at least 76 mm, the maximum786diameter of any welded pit does not exceed 305 mm and the total cross sectional area lost in any section of the pitted plate should not be more than 15%.Paik and Thayamballi [6] analyzed the ultimate strength of ship panels with pitting corrosion under axial compressive loads using ANSYS. The rectangular was used to model the shape of pits. The results indicated that one isolated small corrosion pit located anywhere in the plate may not reduce the plate ultimate compressive strength to any significant extent. However, such a pit does affect post-ultimate strength behavior for the plate. Subsequently, Paik, Lee and Ko [7] proposed a new parameter, i.e. the smallest cross-sectional area, to represent the ultimate strength reduction characteristics due to pitting corrosion. It was proved that the proposed parameter-based approach is more useful than the traditional approach based on effective thickness in terms of the accuracy of ultimate strength predictions of pitted plates.Dunbar, Pegg et al. [8] investigated the effect of localized corrosion in stiffened plates by finite element analyses. A stiffened plate was divided into four main sections, each of which was further divided into four sub-sections in longitudinal direction and three sub-sections in the transverse direction. 10%, 50% and 75% by volume of the initial plate thickness over local sub-section were applied and it was found that 10% of corrosion has little effect on the ultimate strength of stiffened plate. Corrosion at higher levels (50% and 75% volume) caused local buckling at the corroded region, which affected the global collapse mode of the stiffened panel and the ultimate load was decreased as the corrosion location was closer to the centre of the panel span.Nakai et al.[9,10] discussed the structural integrity of hold frames of aged bulk carriers and shapes of corrosion pits observed on hold frames of bulk carriers. They found that the shape of the corrosion pits is a circular cone and the ratio of the diameter to the depth is in the range between 8 to 1 and 10 to 1. A series of actual test with structural models and finite element analyses have been carried out to investigate the effects of pitting corrosion on collapse behaviour and lateral distortional buckling behaviour. The ultimate load of the structural models with regular pittings on the web under the compression load was found to be almost the same as that of the structural models whose web has uniform corrosion corresponding to the average thickness loss.Flaks [11] in his study on Correlation of pitting corrosion of aluminum plates and reduction of load-bearing capacity under tension, described a mathematical method for assessing the influence of pits on the ultimate strength of aluminum plates under tensile loads. A coefficient which accounts for the loss of tensile strength, yield strength and hardness under tension was derived from experimental testing of naturally corroded aluminum plates.TSCF [12] carried out experimental and theoretical investigations on the strength of steel plating with pit corrosion and under bending. Based on the insights developed by the experimental and theoretical study, they suggested an equivalent plate thickness formula for bending capacity assessment of a pitted plate, which is a function of many parameters such as bending stiffness, mass, boundary condition and dimensions of the plate as well as features of pitting damage.P. A. Slater et al [13] conducted nonlinear FE buckling analysis on the corroded plates. These plates that are affected by corrosion reduce their overall thickness making them susceptible to buckling-related failures. The uniaxial buckling of simply supported square plates is studied for several corrosion patterns. The mechanics of buckling load variations by corrosion was discussed in detail. The spatial location of the corrosion patch appears to have a significant effect on the buckling strength. It was noted that the case of uniform corrosion is not the most detrimental case, rather corrosion confined in a corner or central area appears to be more critical. The finite element method is employed for computing buckling loads of corroded plates with different boundary conditions. Numerical results are presented in the form of generic plots of buckling load versus volumetric metal loss for several corrosion patterns considered in the paper.Paik et al.,[14]present paper is to investigate the ultimate strength characteristics of steel plate elements with pit corrosion wastage and under in-plane shear loads. A series of the ANSYS nonlinear finite element analyses for plate elements under in-plane shear loads are carried out, varying the degree of pit corrosion intensity and the plate geometric properties. For this study they considered, a simply supported rectangular plate with pit corrosion and under edge shear, as considered in the present study. They varied the DOP and depth of pit and studied their effect on ultimate strength. The distribution of pits is regular, i.e., with the same distance between individual787 pits and random pits were also taken into consideration. They concluded that the ultimate strength of a plate element was significantly decreased due to pit corrosion. The ultimate strength of a plate element with pit corrosion and under edge shear is determined by the DOP (degree of pit corrosion intensity). But, in the case of a pitted plate element under axial compressive loads, the ultimate strength is governed by the most corroded (pitted) plate section. They also developed the plate ultimate strength design formulae that can be utilized for the ultimate limit state based reliability or risk assessment of plated structures with pit corrosion wastage.SSC-443 [15] formulated design guidelines for doubler plate repairs of ship structures with criteria such as buckling, and fatigue. In the buckling analysis, they considred The scope of this analysis considered the effect of (i)doubler to base plate thickness ratio, (ii) corrosion feature location with respect to stiffener, and (iii) doubler plate versus corrosion feature geometry. For studying thiese effect through FE analysis they considered a constant corrosion feature width (152.4, 457.2 and 762 mm), aspect ratios of 4, 2, 1 and 0.5 were considered. Based on the design considerations, the doubler edge distances of 25.4, 50.8, 101.6 and 254 mm were considered and doubler thickness was assumed to be 100%, 75% and 50% of the stiffened panel thickness. At first corroded and uncorroded stiffened plates without doubler were studied, and found that corroded plates have lesser critical buckling strength than the uncorroded plates. Then, the effect of varying doubler thickness on the critical buckling load was studied. They also investigated the combined effect of doubler thickness and dimensions of corroded features.4. ConclusionIn this survey, it can be studied that the pitting corrosion reduces the ultimate strength of the plate. The main factors which reduce the ultimate strength of the plates are the pitting corrosion width, depth, length, DOP. The other factor is the location of the pit because the presence of the corrosion patterns in the edges results in deteriorating effect on load carrying capacity. And in this review it was found that FE analysis was a suitable method adopted by all researchers for the determination of ultimate strength. Likewise the ultimate strength, the buckling strength also depends on the width, depth, and length of the corroded feature. In the study, it was noted that presence of doublers on the plates has considerable effect on the buckling strength of the plate. Usually for larger doubler thickness, the buckling strength tends to increase. When the thickness of the doubler is less than the thickness of corrosion feature on the plate, the buckling strength is reduced.References[1] Hadi Amlashi and Torgeir Moan, 2005, ’On the strength assessment of the stiffened platesused under biaxial compression’, OMAE, Greece.[2] A.U. Ibekwe, I. E. Douglas and S. Odi-Owei, , Journal of Engineering and Applied Sciences,2(11), 1661-1668 (2007).[3] Yan Zhang, Yi Huang and Gang Liu, 2008, ‘A Study on Assessment of Ultimate Strength of Ship Structural Plate with Pitting Corrosion Damnification’, Proceedings of the EighthISOPE Pacific/Asia Offshore Mechanics Symposium, Bangkok, Thailand[4] Ibrahim A. Assakkaf and Jaime F. Cárdenas-García, 2003, ‘ Reliability based design of thedoubler plates for ship structures’, Proceedings of the Fourth International Symposium onUncertainity Modeling and Analysis.[5] D. Ok, Y. Pu and A. Incecik, , Computation of ultimate strength of locally corrodedunstiffened plates under uniaxial compression. Marine Structures, 20(1-2), 100 (2007).[6] Daidola, J.C., et al., 1997,Residual strength assessment of pitted plate panels. Ship Structure Committee, SSC-394.[7] Paik JK, Thayamballi AK, , Ultimate strength of ageing ships. Journal of Engineering forthe Mari-time Environment, 216(M1), 57 (2002).[8] Jeom Kee Paik, Jae Myung Lee and Man Ju Ko ,,Ultimate shear strength of plateelements with pit corrosion wastage,Thin-Walled Structures, 42(8), 1161 (2004).788[9] Nakai, T., H. Matsushita, and N. Yamamoto, , Effect of pitting corrosion on localstrength of hold frames of the bulk carriers (2nd report)-Lateral distortional buckling and local face buckling. Marine Structures. 17, 612 (2004).[10] Nakai, T., H. Matsushita, and N. Yamamoto, 2005,Pitting corrosion and its inluence onlocal strength of hull structural members. in 24th International Conference on Offshore Mechanics and Arctic Engineering.. Halkidiki, Greece[11] Dunbar, T.E., et al., , A computational investigation of the effects of localizedcorrosion on plates and stiffened panels. Marine Structures, 17(5), 385 (2004).[12] TSCF, 1984,Experimental and theoretical investigation of the strength of corroded hull Elements, Tanker Structure Co-operative Forum, Project 300, Report No. 84-3438. [13] Flaks, V.Y., Correlation of pitting corrosion of aluminium plates and reduction ofload- bearing capacity under tension. Fiziko-Khimicheskaya Mekhanika Materialov,14(1), 89 (1978).[14] Jeom Kee Paik, Jae Myung Lee, Man Ju Ko, 2004,Ultimate shear strength of plateElements with pit corrosion wastage, Thin-Walled Structures, 42: 1161–1176[15] Ssc-443,2005, Design Guidelines For Doubler Plate Repairs Of Ship Structures,NTIS # PB2005,Ship Structure Committee.。

Effects of culture conditions on ligninolytic enzymes and protease production

Journal of Environmental Sciences 20(2008)94–100E ﬀects of culture conditions on ligninolytic enzymes and protease productionby Phanerochaete chrysosporium in airXIONG Xiaoping,WEN Xianghua ∗,BAI Yanan,QIAN YiState Key Joint Laboratory of Environmental Simulation and Pollution Control,Department of Environmental Science and Engineering,Tsinghua University,Beijing 100084,China.E-mail:xxp02@Received 21March 2007;revised 22April 2007;accepted 28April 2007AbstractThe production of ligninolytic enzymes and protease by Phanerochaete chrysosporium was investigated under di ﬀerent culture conditions.Di ﬀerent amounts of medium were employed in free and immobilized culture,together with two kinds of medium with di ﬀerent C /N ratios.Little lignin peroxidase (LiP)(<2U /L)was detected in free culture with nitrogen-limited medium (C /N ratio:56/2.2,in mmol /L),while manganese peroxidase (MnP)maximum activity was 231and 240U /L in 50and 100ml medium culture,respectively.Immobilized culture with 50ml nitrogen-limited medium gave the highest MnP and LiP production with the maximum values of 410and 721U /L separately on the day 5;however,ﬂasks containing 100ml nitrogen-limited medium only produced less MnP with a peak value of 290U /paratively,carbon-limited medium (C /N ratio:28/44,in mmol /L)was adopted in culture but produced little MnP and LiP.Medium type had the greatest impact on protease rge amount of protease was produced due to glucose limitation.Culture type and medium volume inﬂuence protease activity corporately by a ﬀecting oxygen supply.The results implied shallow immobilized culture was a possible way to gain high production of ligninolytic enzymes.Key words :protease;culture conditions;ligninolytic enzymes;Phanerochaete chrysosporiumIntroductionThe white rot fungus Phanerochaete chrysosporium has been extensively studied because of its powerful ligni-nolytic enzymes.These enzymes,mainly including lignin peroxidase (LiP)and manganese peroxidase (MnP),are secreted during the secondary metabolism triggered by carbon,nitrogen or sulfur limitation (Je ﬀries et al .,1981;Tien and Kirk,1983,1988).They have been demonstrated to play a crucial role in lignin degradation and showed great potential in paper industry.At the same time,more and more researches have revealed that the ligninolytic enzymes are nonspeciﬁc enzymes and can assist in the degradation of a wide variety of recalcitrant organic pol-lutants,such as polycyclic aromatic hydrocarbons (PAHs),pesticide and dyes,as has been reviewed by Cameron et al .(2000).This raised the interest of study in ligninolytic enzymes production.To realize application of ligninolytic enzymes,a large production of the biocatalysts at low cost is needed (Ca-baleiro et al .,2002).However,most laboratory studies have been conducted in pure oxygen or in an oxygen-enriched environment (Dosoretz et al .,1990a;Zhen and Yu,1998),which increased the production cost.An ef-fective synthesis of ligninolytic enzymes in air would imply lower cost and greater feasibility essential for their*Corresponding author.E-mail:xhwen@.large scale production (Yu et al .,2006).So far,successful culture of P .chrysosporium with high ligninolytic enzymes production in air has rarely been reported.On the other hand,signiﬁcant losses of enzyme activity occurred during all cultivations,which prevent enzymes accumulation in crude fermentation product.The simultaneous secretion of proteolytic enzymes (protease)could have caused the low stability of produced peroxidases although di ﬀerent viewpoints still exist (Cabaleiro et al .,2001,2002;Chung et al .,2005;Dass et al .,1995;Dosoretz et al .,1990b,c;Jimenez et al .,2003;Pascal et al .,1993).Further study about protease production and its relationship with ligni-nolytic enzymes production in di ﬀerent culture conditions is needed to assist in directing fermentation process design.In the present report,the fermentation was carried out in batches under air atmosphere.Di ﬀerent volumes of both carbon-limited and nitrogen-limited medium were tested in both free and immobilized cultures.Protease and ligninolytic enzymes were measured during the whole fer-mentation ter,the e ﬀects of culture conditions,including culture type (free or immobilized),medium species (carbon-limited or nitrogen-limited)and volumes,on protease production,as well as the relationship between protease and ligninolytic enzymes,were discussed based on the results.No.1Eﬀects of culture conditions on ligninolytic enzymes and protease production by Phanerochaete chrysosporium in air951Materials and methods1.1StrainPhanerochaete chrysosporium strain BKM-F-1767 (ATCC24725)was maintained at37°C on PDA plates. 1.2CarriersPolyurethane foam cubes of5-mm per side(Dongfang Polyurethane Foam Co.,Beijing,China)were employed as the support in immobilized cultures.Prior to use,they were treated by boiling for10min and washing thoroughly three times with distilled water.After that,the carriers were dried at room temperature overnight and autoclaved at121°C for20min(Couto et al.,2002a).1.3Culture conditionsThe nitrogen-limited medium was prepared based on that described by Tien and Kirk(1988)with10g/L glucose as carbon source,except that the dimethylsuccinate was replaced by20mmol/L acetate buﬀer(pH4.5).Veratryl alcohol1.5mmol/L was introduced at the beginning of cul-tures and no surfactant was added(Couto and Ratto,1998). Seven-day-old spores were harvested in sterilized water,ﬁltered through glass-wool and adjusted to absorbance of0.5at650nm.This spore suspension(about2.5×106 spores/ml)was used for inoculation(Urek and Pazarlioglu, 2004).In carbon-limited medium,C/N ratio was altered from 56/2.2(in mmol/L nitrogen-limited medium)to28/44(in mmol/L)(Yu et al.,2005)and the other components were the same.1.3.1Free culturesTwo series of medium volume(100ml,50ml)were adopted in250-ml Erlenmeyerﬂasks,100-ml and50-ml. When100ml medium was added,4ml spore suspension (maintained before)was used for inoculum and half of that was added in theﬂasks with50ml medium.Cultures were incubated in air at37°C in a rotary shaker with an agitation speed of160r/min.1.3.2Immobilized culturesIn immobilized culture,1.8g carriers were added in 250-ml Erlenmeyerﬂask containing100ml medium.After addition,the carriers were in critical immerged status. Comparably,0.9g carriers were added inﬂask containing 50ml medium.The inoculum size was the same as that adopted in free culture.1.4Analytical methodsLignin peroxidase(LiP)activity was measured as de-scribed by Tien and Kirk(1988),with one unit deﬁned as1µmol veratryl alcohol oxidized to veratraldehyde per minute.Manganese peroxidase(MnP)activity was measured spectrophotometrically by the method of Paszczynski et al. (1988),using Mn2+as the substrate.One unit was deﬁned as the amount of enzyme that oxidized1µmol Mn2+per minute.Protease activity was measured with azocoll(Sigma Chemical Co.,USA)as the substrate in50mmol/L acetate buﬀer,as described by Dosoretz et al.(1990b). Nitrogen ammonium content was determined by the phenol-hypochlorite method at625nm as described by Weatherburn(1967),using ammonium sulfate as a stan-dard.Reducing sugars were determined by dinitrosalicylic acid method at540nm as described by Ghose(1987), using D-glucose as a standard.2Results2.1Free cultures2.1.1Cultured with diﬀerent volumes of N-limitedmediumIn the250-ml Erlenmeyerﬂasks with50or100ml nitrogen-limited medium,hyphal pellets were formed since the day2.After the pellets grew up to about5mm in diameter,spurs began to appear and MnP activity emerged in the medium ever since.Diﬀerent volumes of medium inﬂasks led to diﬀerent nutrition consumption rates(Fig.1).On one hand,am-monium nitrogen was totally consumed in2d when50 ml medium was added,but it was depleted on day3in cultures with100ml medium.On the other hand,faster average glucose consumption rate was found in50ml-medium cultures,which are0.407and0.845g/(L·d)during the primary metabolism phase(0–4d)and secondary metabolism phase(5–9d).In100ml-medium culture, glucose consumption rates are0.337and0.810g/(L·d) during these two phases.In these two cultures,protease activity curves were approximately the same with maximum value of around 2.4U/ml on the day6.However,the time when MnP ar-rived its maximum and its peak value were quite diﬀerent. Fermented with50ml medium,MnP activity was detected since the day3and peaked on the day4with a value of 231U/L.It sharply decreased after that.While in culture containing100ml medium,MnP appeared since the day4 and reached its maximum value of240U/L on the day7. Very few LiP activities were detected in these two culture systems(less than2U/L).In both cultures,after the peak MnP activity the medium became more and more viscous because of the secretion of extracellular polysaccharide and the hyphal pellets began to disaggregate.2.1.2Cultured with diﬀerent volumes of C-limitedmediumIn C-limited medium free cultures,hyphal pellets also formed since the day2,but they persisted for a longer time compared to those in N-limited medium free culture mentioned above.Ammonium nitrogen all reached its minimum on the day4and kept stable thereafter,but glucose was depleted more rapidly when50ml medium was employed(Fig.2).In spite of diﬀerent volumes added in theﬂasks,protease96XIONG Xiaoping et al.V ol.20Fig.1Glucose,ammonium nitrogen concentration and MnP,LiP,protease activity curves during the free culture with N-limited medium (C /N ratio is 56/2.2,in mmol /L).In 250-ml Erlenmeyer ﬂask,100ml (a)and 50ml (b)medium were added,respectively.Fig.2Glucose,ammonium nitrogen concentration and MnP,LiP,protease activity curves during the free culture with C-limited medium (C /N ratio is 28/44,in mmol /L).In 250-ml Erlenmeyer ﬂask,100ml (a)and 50ml (b)medium were added,respectively.activity curves showed the same trend during the culture.When P .chrysosporium entered the secondary metabolism period,protease activity began to increase (Fig.2),which ﬁnally arrived maximum (10U /ml for 100ml medium culture and 7U /ml for 50ml medium culture)when glucose concentration in the culture broth was low (less than 1g /L).MnP and LiP activities were low no matter 50ml or 100ml medium was added in culture.MnP activity was less than 10U /L and LiP was less than 2U /L.2.2Immobilized cultures2.2.1Cultured with di ﬀerent volumes of N-limitedmediumSince the immersion status of the support in the medium had e ﬀect on ligninolytic enzymes production (Yu et al .,No.1E ﬀects of culture conditions on ligninolytic enzymes and protease production by Phanerochaete chrysosporium in air 972005),in 50and 100ml nitrogen-limited medium,0.9and 1.8g polyurethane foam carriers were added,respectively.This made both of these two culture systems in critical immersed conditions.Fewer mediums in the ﬂask promoted ammonium nitro-gen and glucose consumption by fungus.In 50ml-medium system ammonium nitrogen was depleted on the day 1while it cost 2d for complete nitrogen consumption in 100ml-medium system.Glucose disappeared at a rate of 1.372g /(L ·d)during the whole fermentation process in 50ml-medium ﬂask,which is faster than the rate of 0.911g /(L ·d)in 100ml-medium ﬂask (Fig.3).Comparing results got in free and immobilized cultures,we can see that immobilization greatly improved nutrition take-in speed.Di ﬀerence was also found in MnP,LiP and protease activity in these two systems.Maximum MnP activity of 410U /L was reached on the day 5in ﬂasks containing 50ml medium,while in 100ml-medium culture,321U /L MnP was produced on the day 10.MnP in the latter system was more stable compared to former MnP activity,although its peak value was less.The highest LiP activity was attained in culture system with 50ml medium.On the day 5,it reached 721U /L.However,the other system did not produce LiP at all.Protease activity curve in 50ml-medium system showed 2peaks (1.43U /ml on the day 2,and 0.8U /ml on the day 8),which were nominated primary protease peak and secondary protease peak in time sequence (Rothschild et al .,1999).Actually it was very low compared to that in 100ml-medium system.In the 100ml medium system,protease activity was higher than 3U /ml since the day 3.The viscosity of the culture broth gradually increased with the culture age for extracellular polysaccharide pro-duction as happened in free culture.2.2.2Cultured with di ﬀerent volumes of C-limitedmediumIn the immobilized culture,carbon-limited medium was also employed to replace nitrogen-limited medium.As an e ﬀect of immobilization,nutrition disappeared quickly in the medium.Glucose was depleted on the day 2and ammonium nitrogen reached its minimum at the same time in both systems (Fig.4).Under these culture conditions,ligninolytic enzymes productions were comparatively low.In 50ml-medium ﬂasks the maximum MnP activity of 33U /L was achieved and maximum LiP was 37U /L.Less MnP and LiP were produced in 100ml-medium culture,their maximum was 22U /L and 3.1U /L,respectively (Fig.4).With carbon-limited medium,the culture broth kept clear from the beginning till the end of the culture.3Discussion3.1Ligninolytic enzymes productionTo promote ligninolytic enzymes production in large scale,harvesting these products during fermentation in air is undoubtedly of great signiﬁcance.MnP formation was generally less a ﬀected by oxygen level (Rothschild et al .,1999)and its production can be easily achieved in ﬂasks or reactors with commonly used nitrogen-limited medium when exposed to air (Couto et al .,2001).This viewpoint is also demonstrated in the present research because of high MnP activity in all cultures with nitrogen-limited medium.However,LiP was seldom produced with the same medium without pure oxygen exposure (Rothschild et al .,1999;Couto et al .,2002b).In this report,the inﬂu-ences of medium type,culture type and mediumvolumeFig.3Glucose,ammonium nitrogen concentration and MnP,LiP,protease activity curves during the immobilized culture with N-limited medium (C /N ratio is 56/2.2,in mmol /L).In 250-ml Erlenmeyer ﬂask;(a)100ml medium and 1.8g polyurethane carriers;(b)50ml medium and 0.9g polyurethane carriers were added,respectively.98XIONG Xiaoping et al.V ol.20 Fig.4Glucose,ammonium nitrogen concentration and MnP,LiP,protease activity curves during the immobilized culture with C-limited medium(C/N ratio is28/44,in mmol/L).In250-ml Erlenmeyerﬂask,(a)100ml medium and1.8g polyurethane carriers,(b)50ml medium and0.9g polyurethane carriers were added,respectively.on ligninolytic production were studied.Meanwhile,by employing shallow immobilized culture we synchronously got high level of MnP and LiP production in air with nitrogen-limited medium.When diﬀerent amounts of medium were employed in cultures,the transfer of oxygen from the air to biomass could be inﬂuenced(Couto et al.,2000).As the oxygen transfer speed may be the main limitation for fungus growth in liquid culture,the metabolite including ligni-nolytic enzymes and its deactivators could be released at diﬀerent time.In our result,the free culture with50 ml nitrogen-limited medium gave maximum MnP activity earlier and MnP activity decreased more quickly(Fig.1). Zhang(1999)reported similar phenomenon for LiP when 50and90ml medium were employed separately in250-ml ﬂasks.In immobilized culture,the polyurethane foam helped the fungus stretch out its hypha.This made it easier to assimilate nutrition and secret metabolites compared to the structure of fungal pellets.Actually,ammonium nitrogen and glucose consumption rates were higher when fungus hyphal was immobilized under all culture conditions in our experiment.Higher MnP activity was attained with the favor of carriers in both50and100ml nitrogen-limited medium.What is more,much LiP was produced in immobilized50ml-medium culture(Fig.3).On the other hand,immobilization can eﬀectively reduce the shear stress which is reported to have inverse eﬀect on LiP production and stability.The only high LiP production in immobilized50ml-medium culture reconﬁrmed the crucial importance of shear stress control and oxygen supply during LiP production process.The results also implied that culture under shallow immobilized conditions was a possible way to gain high activity of ligninolytic enzymes in air.Nitrogen-limited medium seems to be a better substrate because in these cultures higher ligninolytic enzymes production was achieved.However,because of the exces-sive glucose,production of polysaccharide during the late fermentation period made the broth viscous(Rothschild et al.,1999).It could hamper the diﬀusion of oxygen and other nutrient,production and secretion of ligninolytic en-zymes would be inhibited in succession.In order to make ligninolytic enzymes production more stable or realize its accumulation in nitrogen-limited culture,measures should be taken to avoid the inﬂuence of polysaccharide.3.2Protease productionSince protease is a factor which may inﬂuence ligninolytic enzymes stability during the culture of P. chrysosporium,studying the eﬀect of culture conditions on protease production is helpful to direct fermentation process aiming at stable enzymes production.Of all the three factors involved in this research,medium type has the greatest eﬀect on protease production.In all culture conditions when medium type was the only diﬀerence,protease production was always higher in C-limited system than that in N-limited system.The highest protease activity was achieved in immobilized culture with 100ml C-limited medium inﬂask.In addition,protease curves were about the same with the same medium in free culture.This result implies P.chrysosporium secreted more protease in response to glucose starvation although both glucose and ammonium limitation could stimulate protease secretion.Another common feature for C-limited system is that theNo.1Eﬀects of culture conditions on ligninolytic enzymes and protease production by Phanerochaete chrysosporium in air99protease maximum appeared when glucose was complete-ly consumed and all protease curves have no obvious peaks for primary and secondary protease.So far as we know, there is no report about protease production when cultured with C-limited medium.In free culture with N-limited medium and pure oxygenﬂushing,Dosoretz et al.(1990b) tried three kinds of initial glucose concentration.Their results showed that when glucose was depleted protease concentration increased,which was regarded as secondary protease.However,Dass et al.(1995)employed a medium containing excessive nitrogen source in their research and they suggested protease produced during the whole process was primary protease.So,we cannot determine which type the protease secreted in C-limited system belongs.The culture type and medium volume might act corpo-rately because they both can inﬂuence oxygen supply to biomass which was reported to be a factor for protease secretion(Dosoretz et al.,1990b;Zhen and Yu,1998). Immobilization favored biomass growth,which also in-creased nutrition,including glucose,ammonium nitrogen and oxygen consumption rate,as well as oxygen demand. Fewer medium inﬂask means more eﬀective oxygen transfer with the same shaking speed.In immobilized culture,more oxygen is needed and100ml medium system cannot meet this requirement.Fungus was in status of oxygen starvation(measured DO concentration was about 0.2mg/L)and subsequently secreted more protease(Figs.3 and4).Less diﬀerence in free cultures with50ml medium and100ml medium was found because less oxygen was needed(Figs.1and2).The protease in immobilized culture with50ml N-limited medium had the lowest activity(1.4U/ml)in our experiment,which is also the lowest in all the re-ports we have found.Dosoretz et al.(1990b)measured the primary and secondary protease maximum activity in submerged liquid culture,which was about6U/ml. This could have been caused by pure oxygenﬂushing as increased oxygenation simultaneously increased protease activity(Dosoretz et al.,1990b).This also can explain why protease was above20U/ml in solid-state culture (Cabaleiro et al.,2002).Another comparatively low pro-tease activity(3.5U/ml)was observed in free culture of P.chrysosporium under air atmosphere.These results indicate that protease production can be minimized with proper culture conditions in air.3.3Relationship between protease and ligninolytic en-zymesAlthough the culture conditions aﬀected both ligninolyt-ic enzymes and protease production,relationship between protease and ligninolytic enzymes was discussed in many research reports.Protease wasﬁrstly found to cause LiP degradation by Dosoretz et al.(1990b,c)and secondary protease was used in his experiment.Another research proved that the primary protease could totally denatured LiP(Pascal et al., 1993).In our result,high LiP production was only realized in the immobilized culture with50ml N-limited medium, where the lowest primary and secondary protease activity was detected.This indicated that protease produced during the culture is an important factor which reduces LiP production and it needs to be regulated to achieve higher LiP production in P.chrysosporium fermentation.It is reported that protease could be inhibited with addition of substances,such as PMSF(phenyl methane-sulfongl ﬂuoride)and glucose(Dosoretz et al.,1990b)and conse-quently ligninolytic enzymes could be reproduced in the culture(Yu et al.,2005).Our experimental results proved that protease secretion could be controlled by adopting proper culture conditions,which subsequently led to high LiP production.The relationship between protease and MnP is more complicated.Cabaleiro et al.(2001)presented the view-point that MnP activity is inhibited by extracellular protease with the fact that MnP was more stable when protease activity was inhibited.However,recently another viewpoint came up that theﬁrst peak of extracellular protease helped MnP secretion by participating in hy-phal autolysis steps,while the protease produced during late idiophase would play a role in the decline of MnP (Jimenez et al.,2003).Although the MnP and protease were reversely correlated in some cultures(e.g.Fig.1b), MnP still increased when protease activity was high(e.g. Fig.1a).It implies that protease isn’t a main factor for MnP production and stability.AcknowledgementsThis work was supported by the National Natural Sci-ence Foundation of China(No.50478010). ReferencesCabaleiro D R,Rodriguez S,Sanroman A,Longo M A,2001.Characterisation of deactivating agents and their inﬂuence on the stability of manganese-dependent peroxidase from Phanerochaete chrysosporium.J Chem Technol Biot,76(8): 867–872.Cabaleiro D R,Couto S R,Sanroman A,Longo M A,2002.Comparison between the protease production ability of ligninolytic fungi cultivated in solid state media.Process Biochemistry,37(9):1017–1023.Cameron M D,Timofeevski S,Aust S D,2000.Enzymology of Phanerochaete chrysosporium with respect to the degra-dation of recalcitrant compounds and xenobiotics.Appl Microbiol Biotechnol,54(6):751–758.Chung E,Oh J,Hwang S,Ahn I S,Yoon Y J,2005.Enhanced production of manganese peroxidase from immobilized Phanerochaete chrysosporium due to the increased autol-ysis of chlamydospore-like cells.Biotechnol Lett,27(7): 477–481.Couto S R,Ratto M,1998.Eﬀect of veratryl alcohol and manganese(IV)oxide on ligninolytic activity in semi solid cultures of Phanerochaete chrysosporium.Biodegradation, 9(2):143–150.Couto S R,Rivela I,Munoz M R,Sanroman A,2000.Stim-ulation of ligninolytic enzyme production and the ability to decolourise Poly R-478in semi-solid-state cultures of Phanerochaete chrysosporium.Bioresource Technol,74(2): 159–164.Couto S R,Ratto M,Dominguez A,Sanroman A,2001.Strategies for improving ligninolytic enzyme activities100XIONG Xiaoping et al.V ol.20in semi-solid-state bioreactors.Process Biochem,36(10): 995–999.Couto S R,Barreiro M,Rivela I,Longo M A,2002a.Perfor-mance of a solid-state immersion bioreactor for ligninolytic enzyme production:evaluation of diﬀerent operational vari-ables.Process Biochem,38(2):219–227.Couto S R,Feijoo G,Moreira M T,Lema J M,2002b.Evaluation of the environmental conditions for the continuous produc-tion of lignin peroxidase by Phanerochaete chrysosporium inﬁxed-bed bioreactors.Biotechnol Lett,24(10):791–794. Dass S B,Dosoretz C G,Reddy C A,Grethlein H E,1995.Extracellular proteases produced by the wood-degrading fungus Phanerochaete chrysosporium under ligninolytic and non-ligninolytic conditions.Arch Microbid,163(4): 254–258.Dosoretz C,Chen H C,Grethlein H E,1990a.Eﬀect of oxygena-tion conditions on submerged cultures of Phanerochaete chrysosporium.Appl Microbiol Biotechnol,34:131–137. Dosoretz C G,Chen H C,Grethlein H E,1990b.Eﬀect of environmental conditions on extracellular protease activity in ligninolytic cultures of Phanerochaete chrysosporium.Appl Environ Microbiol,56(2):395–400.Dosoretz C G,Dass S B,Reddy C A,Grethlein H E,1990c.Protease-mediated degradation of lignin peroxidase in liq-uid culture of Phanerochaete chrysosporium.Appl Environ Microbiol,56(11):3429–3434.Ghose T K,1987.Measurement of cellulose activities.Pure Applied Chemistry,59:257–268.Jeﬀries T W,Choi S,Kirk T K,1981.Nutritional regulation of lignin degradation by Phanerochaete chrysosporium.Appl Environ Microbiol,42:290–296.Jimenez-Tobon G,Kurzatkowski W,Rozbicka B,Solecka J,Poc-si I,Pennickx M J,2003.In situ localization of manganese peroxidase production in mycelial pellets of Phanerochaete chrysosporium.Microbiol-SGM,149:3121–3127.Pascal B,Mich`e le A,Marcel A,1993.Inﬂuence of primary and secondary proteases produced by free or immobilized cells of the white-rot fungus Phanerochaete chrysosporium on lignin peroxidase activity.J Biotechnol,30(3):271–282. 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一种高强钛合金疲劳裂纹扩展行为

引用格式：王欢，辛社伟，郭萍，等. 一种高强钛合金疲劳裂纹扩展行为[J ]. 航空材料学报，2024，44(2)：176-183.WANG Huan ，XIN Shewei ，GUO Ping ，et al. Fatigue crack propagation behavior of high strength titanium alloy [J ].Journal of Aeronautical Materials ，2024，44(2)：176-183.一种高强钛合金疲劳裂纹扩展行为王欢, 辛社伟, 郭萍, 强菲, 张磊, 乔忠立, 赵永庆*（西北有色金属研究院，西安 710016）¯101112¯1010¯101¯210摘要：高强Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe （Ti-5321）合金是顺应我国新一代飞机对高性能钛合金的需求设计而开发的一种新型高强损伤容限型钛合金。

以Ti-5321合金为研究对象，构造等轴组织（EM ）、网篮组织（BW ）和细网篮组织（F-BW ）三种典型组织，研究拉伸及疲劳裂纹扩展行为，利用光学显微镜（OM ）和扫描电镜（SEM ）观察组织和断口，揭示高强钛合金Paris 及失稳扩展区的疲劳裂纹扩展机制。

结果表明：三种组织试样的抗拉强度均在1200 MPa 以上，且整个裂纹扩展阶段均表现出优异的疲劳裂纹扩展抗力；细网篮组织疲劳裂纹扩展抗力最高，等轴组织疲劳裂纹扩展抗力最低；Paris 区及失稳扩展区疲劳裂纹主要以穿过初生α相和沿着初生α相两种方式进行扩展，裂纹扩展方式与α相的晶体学取向密切相关，裂纹倾向于穿过有利于（）<>锥滑移的α丛域，绕过有利于（）<>柱滑移的α丛域。

关键词：Ti-5321合金；细网篮组织；断口形貌；疲劳裂纹扩展机制doi ：10.11868/j.issn.1005-5053.2023.000154中图分类号：TG146.2+3 文献标识码：A 文章编号：1005-5053(2024)02-0176-08Fatigue crack propagation behavior of high strength titanium alloyWANG Huan, XIN Shewei, GUO Ping, QIANG Fei, ZHANG Lei, QIAO Zhongli, ZHAO Yongqing*（Northwest Institute for Nonferrous Metal Research ，Xi’an 710016，China ）¯101112¯1010¯101¯210Abstract: High strength Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe （Ti-5321） alloy is a new type of high strength tolerance titanium alloy designed and developed to meet the demand of high performance titanium alloy for new generation aircraft in China. Ti-5321 alloy with equiaxed microstructure （EM ），basket-weave microstructure （BW ） and fine basket-weave microstructure （F-BW ）was obtained by forging and heat treatment ，and the tensile properties and fatigue crack growth behavior were studied. Fatigue crack propagation mechanisms in Paris and unstable propagation regimes were revealed by analyzing the microstructures and fracture morphology using optical microscopy (OM) and scanning electron microscopy (SEM). The results show that the samples with EM ，BW and F-BW exhibit the excellent fatigue crack propagation resistance with the tensile strength of 1200 MPa. The sample with F-BW presents the highest fatigue crack propagation resistance in Paris and rapid growth regimes ，while the sample with EM presents the lowest fatigue crack propagation resistance. In F-BW ， the crack mainly propagates through and along α phase. Crack tends to propagate across colony oriented for （）<> pyramidal slip and propagates along colony oriented for （）<>prismatic planes.Key words: Ti-5321 alloy ；fine basket-weave microstructure ；fracture morphology ；fatigue crack growth mechanism钛合金因具有较好的综合力学性能、耐腐蚀以及易加工等优良性能，在航空领域应用广泛[1]。

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Waves

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Wavesand Associated Differential Ground MotionJ.P.N ARAYAN 1Abstract—This paper presents the effects of impedance con-trast (IC)across the basin edge,velocity contrast between the basin and underlying bedrock,Poisson’s ratio and soil thickness on the characteristics of basin-transduced Rayleigh (BTR)waves and associated differential ground motion (DGM).Analysis of simu-lated results for a two-dimensional (2D)basin revealed complex mode transformation of Rayleigh waves after entering the basin.Excellent correlation of frequencies corresponding to different spectral ratio peaks in ellipticity curves of BTR waves and spectral ampliﬁcation peaks was obtained.However,such correlation was not observed between values of peaks in ellipticity curves and spectral ampliﬁcation at the corresponding frequencies.An increase of spectral ampliﬁcation with IC was obtained.The largest spectral ampliﬁcation was more than twice the IC in the horizontal component and more than the IC in the vertical component in the case of large and same impedance contrast for P-and S-waves.It was concluded that the frequency corresponding to the largest spectral ampliﬁcation was greater than the fundamental frequency of soil by around 14%and 44%in the vertical and horizontal components,respectively.Spectral ampliﬁcation of the vertical component was negligible when soil thickness was less than around 15–20times the S-wave wavelength in the basin.The largest values of peak ground displacement (PGD)and peak differential ground motion (PDGM)were obtained very near the basin edge,and their values with offset from the edge were strongly dependent on the IC across the basin edge,Poisson’s ratio,velocity contrast between the basin and underlying bedrock (dispersion),damping and soil thickness.The obtained value of PDGM for a span of 50m in the horizontal and vertical components due to the BTR wave was of the order of 0.75910-3and 1.32910-3for unit amplitude (1.0cm)in the horizontal component of the Rayleigh wave at rock very near the basin edge.Key words:Basin-transduced surface wave,complex mode transformation,spectral ampliﬁcation of surface waves,differential ground motion,2D ﬁnite-difference simulation.1.IntroductionWhen high-frequency surface waves,caused by shallow-focal-depth earthquakes,enter a basin,part of their energy is reﬂected back while the rest is transmitted into the basin.Kawase (1993,2002)called such types of surface waves inside the basin as basin-transduced surface waves.In the basin,near the edge,complex transformation from one mode of surface wave from the surrounding rock to different modes in the basin takes place.The existence of basin-transduced surface wave was reported by H ANKS (1975),who showed a series of wavelets recorded during the San Fernando,California earth-quake of 1971.The duration of displacement records was short in rocky region but quite long and dispersed in the Los Angeles basin.V IDALE and H ELMBERGER (1988)subsequently simulated these low-frequency basin-transduced surface waves in the San Fernando and Los Angeles basins.S ATO et al.(1999)repro-duced results of displacement records observed at Tokyo during the Kanto earthquake of 1923and conﬁrmed the recording of basin-transduced surface waves based on three-dimensional (3D)ﬁnite-differ-ence simulations.O ZEL and T SUTOMU (2004)also reported long-period (about 2.0s)basin-transduced surface waves in the Adapazari basin during the Izmit,Turkey earthquake of 1999based on strong and weak motion records.The characteristics of the Rayleigh wave (R-wave)response of crust have been studied in detail for sources at various depths with different focal mechanisms (P ANZA et al.,1973,1975).Recently,K UMAR (2008)studied the effects of focal depth on the spectral content of R-waves gen-erated in a homogeneous half-space.1Department of Earthquake Engineering,Indian Instituteof Technology Roorkee,Roorkee 247667,India.E-mail:jaypnfeq@iitr.ernet.inPure Appl.Geophys.167(2010),1485–1510Ó2010Birkha¨user /Springer Basel AG DOI 10.1007/s00024-010-0131-zPure and Applied GeophysicsSpatial variability in ground motion(SVGM) refers to differences in amplitude and phase of seismic motions over extended areas.SVGM is caused by earthquake focal mechanism(radiation pattern),rupture directivity,non-vertical propagation of body waves,surface waves,relative surface fault motion,waves arriving from different azimuths and local site effects.In earthquake engineering,sto-chastic models are being used for the long back to asses and to incorporate the effects of SVGM into earthquake-resistant designs.The role of local site effects in SVGM may surpass the contribution of other factors listed above under certain conditions. Differential ground motion(DGM)caused by sur-face waves strongly depends on their frequency content and amplitude.If the wavelength of surface waves is comparable to the spatial extent of struc-tures,then DGM developed by surface waves has an important effect on the response of infrastructures such as pipelines,bridges and communication transmission systems,which extend over long dis-tances parallel to the ground and whose supports may undergo various motions during an earthquake. DGM induces signiﬁcant additional stresses in such structures compared with when the motions at the supports are considered to be identical.R OMANELLI et al.(2004)computed the SVGM caused due to lateral heterogeneity and concluded that it may cause an increase of more than one unit in the seismic intensity experienced by bridges(the structure con-sidered in that analysis)with respect to the average intensity affecting the area.Another important cause of DGM is surface waves generated at basin edges and underground ridges(B ARD and B OUCHON, 1980a,b;M OCZO and B ARD,1993;P ITARKA et al., 1998;G RAVES et al.,1998;N ARAYAN,2003,2005; N ARAYAN and S INGH,2006;N ARAYAN and R AM, 2006).Recently,H ALLIER et al.(2008)studied the effects of basin edges on ground motion character-istics and concluded that the basin-edge effect contributed to the occurrence of a damage belt in a frequency band wider than previously reported dur-ing the Hyogo-Ken Nanbu earthquake of1995.In this paper,effects of impedance contrast(IC) across the basin edge,velocity contrast between the basin and underlying bedrock,Poisson’s ratio of soil and soil thickness on the complex mode transformation of R-waves,spectral ampliﬁcation of basin-transduced Rayleigh waves,reﬂection of R-waves from the basin edge and conversion of R-waves into body waves are studied in detail.The spectral ampliﬁcation of BTR waves was obtained by taking the spectral ratio of the undamped computed response in the basin and at rock very near the basin edge.This is practicable since there is no divergence effect in2D simulation of surface waves.The dif-ferential ground motion caused by BTR waves near the basin edge was computed for different values of IC,Poisson’s ratio,span and soil thickness for unit amplitude(1.0cm)in the horizontal R-wave com-ponent at rock very near the basin edge.The basin-edge slope was taken as90°to study the effects of soil thickness on the reﬂectivity of R-waves and peak differential ground motion(PDGM).A second-order accurate in time and fourth-order accurate in space(2, 4)staggered-grid P-SV waveﬁnite-difference(FD) algorithm with variable grid size was used for the BTR wave simulations(N ARAYAN and K UMAR,2008; K UMAR,2008).2.Salient Aspects of the Applied Computer ProgramThe staggered-gridﬁnite-difference method is one of the most useful numerical methods to simu-late ground motion characteristics(M ADARIAGA, 1976;V IRIEUX,1986;L EVANDER,1988;L UO and S CHUSTER,1990;G RAVES,1996;P ITARKA,1999; O HMINATO and C HOUET,1997;N ARAYAN,2001a,b; M OCZO et al.2002;N ARAYAN and K UMAR,2008). K RISTEK et al.(2002)reported that the stress imag-ing technique used as the free surface boundary condition(L EVANDER,1988;G RAVES,1996)causes dispersion of Rayleigh waves in a homogeneous media and requires ten grid points per shortest wavelength.Recently,N ARAYAN and K UMAR(2008) have developed a vertical grid-size reduction(VGR) stress imaging technique in order to avoid the soil thickness discrepancy arising due to the combination of the staggered grid and the stress imaging tech-nique,and to avoid the signiﬁcant dispersion of Rayleigh waves in a homogeneous half-space.The elastodynamic wave equations for P-SV wave propagation in heterogeneous media are1486J.P.Narayan Pure Appl.Geophys.q o2Uo t¼o r xxo xþo r xzo z;ð1Þq o2Wo t¼o r xzo xþo r zzo z:ð2ÞThe stress–strain relationships arer xx¼ðkþ2lÞo Uo xþko Wo z;ð3Þr zz¼ðkþ2lÞo Wo zþko Uo x;ð4Þr xz¼lo Uo zþo Wo x;ð5Þwhere U and W are the components of particle dis-placement in the horizontal and vertical directions. r xx,r zz and r xz are the stress components,q is densityand k and l are the Lame´constants.oo x ;oo zand o2o t2arethe differential operators.Figure1shows the staggering technique,where normal stress components and Lame´parameters are deﬁned at the nodes.The shear stress component and the modulus of rigidity are deﬁned at the centre of the grid.Horizontal and vertical components of particle displacement and the density are deﬁned midway between the two adjacent grid points in the horizontal and vertical directions,respectively.The effective values of the modulus of rigidity and the density were obtained using harmonic and arithmetic means, respectively(Z AHRADNIK and P RIOLO,1995;M OCZO et al.,2002).Both sponge(I SRAELI and O RSZAG,1981) and A1absorbing(C LAYTON and E NGQUIST,1977) boundary conditions were implemented at the model edges to avoid edge reﬂections(K UMAR and N ARAYAN, 2008).A time-domain attenuation operator based on an approximate technique was used for modelling of spatially varying viscoelastic media(Z AHRADNIK et al.,1990a,b;G RAVES,1996;O PRSAL et al.,2005; O PRSAL and F AH,2007;N ARAYAN and K UMAR,2008).A dominant frequency(f0)in the middle of the desired frequency band was chosen as a reference frequency.The attenuation operator(A)used in the simulation and applied at a grid point(i,l)for duration D t,the time step,isA i;l¼expÀp f0D tQi;l!;ð6Þwhere Q S is the S-wave quality factor.The aim of this work is to simulate BTR waves,which will be more or less affected by the S-wave quality factor. As it is difﬁcult to distinguish P-and S-waves in ﬁnite-difference time-domain calculations,Q S was used in the attenuation operator.Q S was taken as 10%of the S-wave velocity at the grid nodes (O LSEN,2000).The attenuation operator was applied to displacementﬁelds at both the updated and present time after iteration,since effectively both the updated and the present displacementﬁelds have propagated during each iteration.The attenuation operator was not applied to the stress components, since they were computed using the updated dis-placementﬁeld,for which the attenuation operator had already been applied(N ARAYAN and K UMAR, 2008).In order to avoid the need for large amounts of computational memory and time,variable grid size with a continuous grid mesh was used(P ITARKA, 1999;N ARAYAN,2005;N ARAYAN and S INGH,2006; N ARAYAN and R AM,2006;N ARAYAN and K UMAR, 2008).2.1.VGR Stress Imaging TechniqueIn the applied FD algorithm,free surface is collocated with grid nodes where the horizontal component of the particle displacement is deﬁned (Fig.1).Effectively the layer interface lies one-half of the vertical grid size above the deﬁned layer interface for the horizontal component(N ARAYAN and K UMAR,2008).Similarly,the effective interface between theﬁrst soil layer and the vacuum/air will lie one-half of the vertical grid size above the free surface for the horizontal component of particle displacement.In the case of the VGR stress imaging technique,the vertical grid size above the free surface is reduced during the explicit computation of the free surface boundary condition(N ARAYAN and K UMAR, 2008).If the vertical grid size above the free surface tends to zero,then the interface between theﬁrst soil layer and the vacuum/air almost coincides with theVol.167,(2010)Basin-Transduced Rayleigh Waves1487free surface.In the following paragraphs,the proce-dure for computation of the required displacement and stress components above the free surface is brieﬂy described.To compute the particle displacement at the free surface and one-half and one grid size below the free surface,the stress components r zz ,r xx and r xz are required above the free surface (Fig.1b).The stress components r zz and r xz above the free surface can be obtained using the stress imaging technique (L EVANDER ,1988;G RAVES ,1996).r zz ðÞi ;l ¼0¼0;ð7Þr zz ðÞi ;l À1¼Àr zz ðÞi ;l þ1;ð8Þr xz ðÞi þ12;l À12¼Àr xz ðÞi þ12;l þ12;ð9Þr xz ðÞi þ12;l À32¼Àr xz ðÞi þ12;l þ32:ð10ÞLet us assume that the vertical grid size above the free surface is reduced by a factor of K compared with the vertical grid size just below the free surface [whereK ¼D Z below the free surfaceD Z above the free surface is the vertical grid size reduc-tion factor (VGRF)].During the computation of r xx and r zz at l =0and l ?1and of r xz at l ?1/2,the required components of particle displacement above the free surface W i ;l À1;W i ;l À3and U i þ1;l À1were obtained with the help of Eqs.4,5,7,8and 9using second-order FD approximations (G RAVES ,1996).ZZ XXand Lame´parameters are deﬁned at grid nodes,and shear stress components and modulus of rigidity are deﬁned at the centre of the grid and b extendedgrid points above the free surface1488J.P.Narayan Pure Appl.Geophys.W n þ1i ;l À12¼W n þ1i ;l þ12þk k þ2li ;l ¼0D Z i ;l D X i À1;l ¼0þD X i ;l ¼0Â1Kþ1 U n þ1i þ12;l ¼0ÀU n þ1i À12;l ¼0h i ;ð11ÞU n þ1i þ12;l À1¼U n þ1i þ12;l ¼0þD Z i ;l ¼0K D X i ;l ¼0ÂW n þ1i þ1;l À12ÀW n þ1i ;l À12þW n þ1i þ1;l þ12ÀW n þ1i ;l þ12h i þ1U n þ1i þ12;l þ1ÀU n þ1i þ12;l ¼0h i ;ð12ÞW n þ1i ;l À32¼W n þ1i ;l À12þk k þ2li ;l ¼02D Z i ;l K D X i À1;l þD X i ;lÀÁÂU n þ1i þ12;l À1ÀU n þ1i À12;l À1þU n þ1i þ12;l þ1ÀU n þ1i À12;l þ1h i þ1K W n þ1i ;l þ32ÀW n þ1i ;l þ12h i :ð13ÞFurthermore,it was assumed that,in the VGRstress imaging technique,the stress components at l ?1/2,l ?1or l ?3/2ﬁrst linearly reduce to zero up to the free surface and then linearly increase up to l -1/2,l -1or l -3/2above the free surface.Under this assumption,if the grid size above the free surface is reduced by K ,then the stress components above the free surface at l -1/2,l -1or l -3/2will be ðr xz Þi þ12;l À12K ;ðr zz Þi ;l À1K and ðr xz Þi þ12;l À32K;respectively.When the VGRF is equal to 1.0,the VGR stress imaging technique is equivalent to the well-known stress imaging technique.2.2.Rayleigh-Wave DispersionIn order to show the efﬁciency of the VGR stress imaging technique to avoid signiﬁcant dispersion of R-waves,seismic responses of a homogeneous half-space model were computed using both the stress imaging technique (L EVANDER ,1988;G RAVES ,1996)and the VGR stress imaging technique (N ARAYAN and K UMAR ,2008).The model parameters of P-wave and S-wave velocity,density and quality factor were taken as 3,117.7and 1,800m/s,2.5g/cc and 180,respec-tively.The response was computed at four epicentral distances,9.0,18.0,27.0and 36.0km,using a source at a focal depth of 2.0km.A Ricker wavelet with dominant frequency of 1Hz and bandwidth of 0–3Hz was used as a point source excitation function.Thegrid size in both the horizontal and vertical directions was 100m (six grid points per shortest wavelength).Figure 2shows a comparison of the responses com-puted using the stress imaging technique (dotted line)and the VGR stress imaging technique (solid line).The ﬁrst arrival in the response is the P-wave,whose amplitude is very small compared with the other two seismic phases.The P-wave is only visible in the trace recorded at epicentral distance of 9km.The second arrival is the evanescent P-wave caused by the SV-wave incident at the free surface at the critical angle.The evanescent P-wave is propagating along the free surface.The third arrival is the Rayleigh wave mainly caused by the incident SV-wave since the source was dominated by SV-wave.The arrival time of the evanescent P-wave is the same at different epicentral distances for both the stress imaging technique and the VGR stress imaging technique,which means,in the case of a body wave propagating along the free surface,that there is no dispersion for both free surface boundary conditions.However,there is dissimilarity in the arrival time of the Rayleigh wave (third arrival).The arrival time of the Rayleigh wave in the case of the stress imaging technique (dotted line)is greater than that in the case of the VGR stress imaging technique (solid line),and this difference in arrival time increases with distance travelled.So,it can be inferred that the increase of difference in Rayleigh-wave arrival time with distance travelled may be due to Rayleigh-wave dispersion in the computed response when using the stress imaging technique.In order to verify that there is no signiﬁcant Rayleigh-wave dispersion in the case of the VGR stress imaging technique,seismic responses were computed using different VGRF values.Figure 3a shows the response computed at 27km epicentral distance using different VGRFs.Again,there is no effect of VGRF on the arrival time of the evanescent P-wave.However,the travel time of the Rayleigh wave is strongly affected by the value of VGRF used.There is reduction of arrival time (dispersion)of the Rayleigh wave with increasing VGRF.So,it can be inferred that the delay in arrival time is largest in the case of the response computed using the stress imaging technique (VGRF =1)and it is theoretically negligible in the case of inﬁnite (107)VGRF.The dispersion also causes change of the wavelet shape.Vol.167,(2010)Basin-Transduced Rayleigh Waves 1489In order to further conﬁrm that the VGR stress imaging technique is Rayleigh wave dispersion free, the seismic responses computed at epicentral dis-tances of18.0and36.0km using the stress imaging technique(VGRF=1)and the VGR stress imaging technique(VGRF=107)were used to plot the path of particle motion during Rayleigh wave propagation. The seismic response in time windows of10–14and 22–26s corresponding to epicentral distances of18 and36km were used to plot the elliptical path of the particle motion.Figure3b and c depicts plots of the path of particle motion at epicentral distance of 18km(solid line)and36km(dotted line)using the stress imaging technique and the VGR stress imaging technique,respectively.Analysis of Fig.3b and c reveals a change of shape of the path of the particle motion in the case of the stress imaging technique. The preserved shape of the path of particle motion with distance travelled in the case of the VGR stress imaging technique further conﬁrms that the VGR stress imaging technique is free from any signiﬁcant Rayleigh-wave dispersion.3.Effects of Impedance Contrast(IC)on BTR WavesSeismic responses of a basin-edge model were computed to study the effects of impedance contrast (IC)on the characteristics of BTR waves and spatial variability in ground motion near the basin edge.The IC across the basin edge was varied by changing the velocity in the basin while keeping the density con-stant(velocity-dependent IC),and vice versa,since IC may not only affect the transmission of Rayleigh waves in the basin but also the dispersion of BTR waves due to the velocity contrast between the basin and underlying bedrock.The Poisson’s ratio in soil and rock was similar in order to avoid the effects of Poisson’s ratio on the characteristics of BTR waves. For this purpose,a basin with strong lateral discon-tinuity(SLD)with edge slope of90°was incorporated in a homogeneous half-space(Fig.4a). The positive X-coordinate was pointing north,and the positive Z-coordinate was pointing downward.The left edge of the basin was4.8km north of the epi-centre and the right edge of the basin was open.Soil thickness in the basin was taken as100m.The parameters for four velocity-dependent IC models (MVC1–MVC4)keeping soil density constant are presented in Table1.Similarly,the parameters for another four density-dependent IC models(MDC1–MDC4)keeping soil velocity constant are given in Table2.P-and S-wave velocities,density and quality factor for the basement were taken as3,117.7and 1,800m/s,2.5g/cc and180,respectively.The hori-zontal grid size from the left edge of the modelwas40m up to8.0km,10m from4.0km to16.8km and40m thereafter.The vertical grid size from the top of the model was10m up to180and40m thereafter.The time step was taken as0.0022s. Seismic response was computed at60equidistant (200m apart)receiver points extending from the epicentre to11.8km north of it.A Ricker wavelet with 2.0Hz dominant frequency was used as the excitation function.Figure4b shows the spectra of the horizontal and vertical components of the R-wave recorded at the tenth receiver using a source at a depth of150m.The R-wave has considerable spectral amplitude in the frequency bandwidth of1.0–5.0Hz,with a dominant frequency around2.75Hz.Figure5depicts the hor-izontal and vertical component of the damped seismic response of the basin-edge velocity-dependent IC models(MVC1–MVC4).Only the R-wave is visible in the traces recorded on rock(traces1–25).The traces recorded in the basin(traces26–60)show complex mode transformation of the R-wave after entering the basin.The amplitude of the R-waveisFigure 4a andb show the vertically exaggerated basin-edge model and spectra of Rayleigh waves recorded at the tenth receiver,respectivelyTable 1P-wave velocity (V p ),S-wave velocity (V S ),density,quality factor,Poisson’s ratio,impedance contrast and largest spectral ampliﬁcation forconsidered basin soils,corresponding to various velocity-dependent IC models (MVC1–MVC4)IC modelV p (m/s)V s (m/s)Density (g/cm 3)Quality factor Poisson’s ratio SV/P-waves IC Largest spectral ampliﬁcation H-comp V-comp MVC11,342.34775.0 2.077.50.25 2.90 4.29 3.76MVC21,039.23600.0 2.060.00.25 3.757.67 5.76MVC3866.02500.0 2.050.00.25 4.5010.09 6.67MVC4736.09425.02.042.50.255.2911.116.921492J.P.Narayan Pure Appl.Geophys.greater in the vertical component compared with the horizontal component in traces recorded at rock. Based on analysis of Fig.5,it seems that different modes of BTR wave have developed.The earlier arrivals of BTR wave are less dispersed and have greater amplitude in the horizontal than the vertical component.On the other hand,the later arrivals of BTR wave are highly dispersed and have more amplitude in the vertical than in the horizontal component.Furthermore,the earlier arrivals of BTR wave are less affected by the velocity contrast between the basin and underlying bedrock as com-pared with the later arrivals of BTR wave.3.1.Effects of IC on BTR-Wave AmpliﬁcationDamped seismic responses of basin-edge models (MVC1–MVC4)were used to quantify the effects of IC across the basin edge and the velocity contrast between the basin and underlying bedrock on peak ground displacement(PGD).Figure6a shows the PGD in each trace recorded on the free surface from 600m south to4.0km north of basin edge.The PGD in the vertical component is governed by the later arrivals of BTR waves.Similarly,the PGD in the horizontal component is governed by the earlier arrivals of BTR waves.The largest value of PGD was obtained at a distance of around200and400m north of basin edge in the vertical and horizontal compo-nents,respectively.It can be inferred that the distance of occurrence of the largest value of PGD is somewhat wavelength/mode dependent.The PGD was proportional to IC,except for model MVC4 where it has reduced.Furthermore,for an offset of more than1.5km from the basin edge,the PGD is decreasing with increasing IC in both components,due to the combined effects of soil damping and BTR-wave dispersion.Furthermore,the rate of decrease of PGD with offset is lesser in the horizontal component,since it is governed by the earlier arrivals of BTR waves.This means that the PGD in the basin is governed by the IC across the basin edge,velocity contrast between the basin and underlying bedrock (BTR-wave dispersion)and the damping.It can also be inferred that the maximum amplitude ampliﬁca-tion of BTR waves is of the order of3.3,in model MVC3.In order to determine the effects of velocity-dependent IC on the spectral ampliﬁcation of BTR waves,undamped seismic responses of basin-edge models(MVC1–MVC4)were computed(Table1). Figure7a shows a comparison of BTR-wave ampli-tude recorded at the30th receiver.There is only minor variation in maximum BTR-wave amplitude, but there is drastic increase of BTR-wave duration with increasing IC.This may be due to increasing Rayleigh-wave dispersion with increasing velocity contrast between the basin and underlying bedrock. The BTR-wave spectra shown in Fig.7b are highly complex compared with the R-wave spectra shown in Fig.4b.The BTR-wave spectral ampliﬁcation,shown in Fig.7c,was computed by taking the ratio of BTR-wave and R-wave spectra recorded at the30th and 10th receivers,respectively.This approach for com-putation of Rayleigh-wave spectral ampliﬁcation seems reasonable,since R-wave propagation is1D in nature in2D simulations and there is no decrease of energy of R-waves or BTR waves due to divergence.There is a shift of the frequency corre-sponding to the largest spectral ampliﬁcation towards lower values with increasing IC.The largest spectral ampliﬁcation factor is increasing with IC in bothTable2P-wave velocity(V p),S-wave velocity(V S),density,quality factor,Poisson’s ratio,impedance contrast and largest spectral ampliﬁcation for considered basin soils,corresponding to various velocity-dependent IC models(MDC1–MDC4)IC models V p(m/s)V s(m/s)Density(g/cm3)Quality factor Poisson’s ratio SV/P-wave IC Largest spectral ampliﬁcationH-comp V-comp MDC1736.09425.0 1.9042.50.25 5.5711.937.05MDC2736.09425.0 2.0042.50.25 5.2911.11 6.92MDC3736.09425.0 2.1542.50.25 4.9210.72 6.70MDC4736.09425.0 2.3042.50.25 4.6010.37 6.46Vol.167,(2010)Basin-Transduced Rayleigh Waves1493components,but more so in the horizontal compo-nent.In order to determine the relationship between the different spectral ampliﬁcation peaks in the horizontal and vertical components and the peaks in the ellipticity curves,BTR-wave H/V and V/H ratios were computed (Fig.7d).A comparison of Fig.7c and d shows that there is good correlation between the frequencies corresponding to different spectral ampliﬁcation peaks in the horizontal and vertical components with the H/V and V/H ratio peaks,respectively.However,such correlation between values of peaks in spectral ampliﬁcation and the ellipticity curves was not obtained,as for the IC across the basin edge.On the other hand,excellent correlation between IC and the values of spectral ampliﬁcation corresponding to the ﬁrst few peaks in the lower frequency range was obtained (Table 1).The average spectral ampliﬁcation is not governed by the IC.In order to determine the relation between the frequency corresponding to the largest spectral ampliﬁcation and the fundamental frequency of basin soil,a graph was plotted of spectral ampliﬁcation versus k S-wave /S TH (k S-wave :S-wave wavelength in soil;S TH :soil thickness).The analysis of Fig.7e shows that the largest spectral ampliﬁcation occurs at a particular value of k S-wave /S TH (3.45and 2.25in the horizontal and vertical components,respectively).Similarly,to quantify the effects of density-dependent IC on the spectral ampliﬁcation of BTR wave,undamped seismic responses ofbasin-edgeFigure 5Damped seismic response of basin-edge model for different impedance contrast (MVC1–MVC4)1494J.P.Narayan Pure Appl.Geophys.。

The effect of porosity on the strength of foamed concrete

The effect of porosity on the strength of foamed concreteE.P.Kearsley a,P.J.Wainwright b,*a Department of Civil Engineering,University Pretoria,Pretoria0001,South Africab Department of Civil Engineering,University of Leeds,Leeds LS29JT,UKReceived14August2001;accepted20August2001AbstractA study has been undertaken to investigate the effects of replacing large volumes of cement on the properties of foamed concrete(up to 75%by weight)with both classified and unclassified fly ash.This is the third paper in a series;it investigates the relationship between porosity and compressive strength and presents mathematical models that have been developed to describe this relationship.The compressive strength of the foamed concrete was shown to be a function of porosity and age,and a multiplicative model(such as the equation derived by Balshin)was found to best fit the results at all ages up to1year.In addition,it was concluded that the equation derived by Hoff could effectively be used to predict the compressive strength of foamed concrete mixtures containing high percentages of ash.D2002Elsevier Science Ltd.All rights reserved.Keywords:Foamed concrete;Porosity;Compressive strength;Fly ash1.IntroductionThis is the third paper in a series reporting on the results of an investigation into the effects on the properties of foamed concrete of replacing large volumes of the cement with both a classified(pfa)and unclassified(pozz-fill)fly ash.The first paper[1]reported on the effects on the compressive strength,while the second[2]on the relation-ship between porosity and permeability.This third paper investigates the relationship between porosity and compres-sive strength and presents mathematical models that have been developed to describe this relationship.The main aim of this part of this study was to investigate what effects the addition of the foam had on porosity and its relationship with strength.The strength and porosity of foamed concretes with different casting densities were compared to those of cement pastes with different water/cement ratios.Different percentages of both pfa and unclassified ash were used to establish the effect of ash content on the strength–porosity relationship.2.BackgroundWhen concrete is fully compacted,the strength is taken to be inversely proportional to the water/cement ratio (Abrams rule)[3].In1896,Rene´Fe´ret formulated the following rule to relate the strength of concrete to the volumes of water,cement and air in the mixture(Eq.(1)): f c¼Kccþwþa2ð1Þwhere:f c=concrete compressive strength(MPa);c,w, a=absolute volumetric proportions of cement,water and air;K=a constant.The strength of concrete is influenced by the volume of all voids in the concrete(entrapped air,capillary pores,gel pores and entrained air)and a number of functions,includ-ing the following,have been proposed to express this strength–porosity relationship[4,5](Eqs.(2)–(5)):f c¼f c;0ð1ÀpÞnðBalshinÞð2Þf c¼f c;0eÀk;pðRyshkevitchÞð3Þf c¼k s lnp0pðSchillerÞð4Þ*Corresponding author.Tel.:+44-113-233-2294;fax:+44-113-233-2265.E-mail address:p.j.wainwright@(P.J.Wainwright).Cement and Concrete Research32(2002)233–2390008-8846/02/$–see front matter D2002Elsevier Science Ltd.All rights reserved.PII:S0008-8846(01)00665-2f c¼f c;0Àk H pðHasselmannÞð5Þwhere:f c=compressive strength of concrete with porosity p;f c,0=compressive strength at zero porosity;p=porosity (volume of voids expressed as a fraction of the total concrete volume);n=a coefficient,which need not be constant; p0=porosity at zero strength;k r,k s,k H=empirical constants.Ro¨ßler and Odler[4]determined the relationship between porosity and strength for a series of cement pastes with different water/cement ratios after different periods of hydration.They concluded for porosities between5%and 28%that although all four of the strength–porosity equa-tions shown above could be used,the relation between compressive strength and porosity can best be expressed in the form of a linear plot.Fagerlund[5]stated that it often seems as if one equation fits experimental data for porosities below a certain limiting porosity and another for porosities above this limit.At high porosities,it is normally necessary to use an equation,which indicates a critical porosity while these equations are too insensitive to change for use with low porosities.An equation that takes into consideration the effect of high as well as low porosity will include a critical porosity as well as a stress concentration factor.After studying aerated concrete manufactured at factories in China,Baozhen and Erda[6]concluded that the com-pressive strength decreases as the porosity increases with the same relationship as indicated in the strength–porosity equation derived by Balshin(Eq.(2)).It was found that n varied from1to2.2in different ranges of porosity,indicat-ing that the strength of mixtures with low porosity was influenced more by small changes in porosity than the strength of mixtures with higher porosity.Hengst and Tressler[7]concluded that the dominant parameter in controlling the strength of a foamed Portland cement at a given bulk density is the flaw size,which correlates with the pore size.Hoff[8]conducted research on the porosity–strength relationship of cellular concrete and concluded that there is a single strength–porosity relationship for given cement and this relationship can be expressed in terms of water/ cement ratio and density.Hoff[8]expressed the theoretical porosity of cellular concrete containing only water,cement and foam as the volume of voids as a fraction of the total volume.He used an average value of0.2for the ratio of the water bound by hydration to cement(by weight)and derived the following equation:n¼1Àd cð1þ0:20p cÞð1þkÞp c g wð6Þwhere:n=theoretical porosity;d c=concrete density; p c=specific gravity of the cement;g w=unit weight of water;k=water/cement ratio(by weight).In the design of foamed concrete,the use of the space occupied by the evaporable water plus the air void space as the total void space in the concrete permits the determina-tion of a single strength–porosity relationship for a given cement.The strength of cellular concrete in relation to any given cement can,according to Hoff,be expressed using the following equation:s ys0¼d c1þkb1þ0:2pcp c g wbð7Þwhere:s y=compressive strength;s0=theoretical paste strength at zero porosity;k=water/cement ratio(by weight); p c=specific gravity of the cement;d c=concrete density;g w=unit weight of water;b=empirical constant.This equation does,however,only hold true for foamed concrete containing only air,water and cement.Adjustment will be required if additional components,such as fillers,are used.Hoff evaluated bag-cured samples manufactured using different cements with water/cement ratios varying from 0.66to1.06and casting densities varying from320to1000 kg/m3.The analysis produced values of s0=245MPa and b=2.7with a correlation coefficient of.95for cement with a Blaine fineness of between4500and4650cm2/g.3.Experimental procedure3.1.Mix compositionsFoamed concrete is produced under controlled condi-tions from cement,filler,water and a liquid chemical that is diluted with water and aerated to form the foaming agent.The foaming agent used was‘‘Foamtech,’’consist-ing of hydrolyzed proteins and manufactured in South Africa.The foaming agent was diluted with water in a ratio of1:40(by volume),and then aerated to a density of 70kg/m3.The cement used in this investigation was rapid hard-ening Portland cement(RHPC)from Pretoria Portland Cement(PPC),Hercules,Pretoria.Both the fly ashes used were obtained from the Lethabo power station in South Africa.One was a graded ash(pfa),which was screened to remove some of the larger particles(thus reducing the particles larger than45m m in diameter to less than 12.5%),and the second was an unclassified ash(pozz-fill). The chemical properties of all three binders are shown in Table1.The compositions by mass of the different mixtures cast are shown in Table2;a total of27mixes were made as summarised below:Cement pastes with water/cement ratios of0.3,0.4and0.6;Paste mixtures in which50%,66.7%and75%of the cement(by weight)was replaced with pfa and pozz-fill (ash/cement ratios of1,2and3).The water/binder ratio was kept constant at approximately0.3;andE.P.Kearsley,P.J.Wainwright/Cement and Concrete Research32(2002)233–239 234Foamed concrete mixtures of different casting den-sities(1000,1250and1500kg/m3)with differ-ent percentages of ash replacement(50%,66.7% and75%).More details relating to the materials used and casting procedure can be found in the previous publications[1,9]pressive strengthThe compressive strength of foamed concrete was deter-mined from100-mm cubes,which were cast in steel moulds,demoulded after24±2h,wrapped in polythene and kept in a constant temperature room at22±2°C up to the day of testing.The compressive strengths recorded are the average of three cubes.The cement paste cubes wereTable1Binder propertiesOxides RHPC fromPPC Hercules(%)Processed fly ash(pfa)fromLethabo(%)Pozz-fill fromLethabo(%)CaO61.7 4.7 5.0 SiO221.253.954.8 Al2O3 4.633.531.7 Fe2O3 1.8 3.7 3.8 Na2O0.10.70.8 K2O0.70.70.8 MgO 4.3 1.3 1.11 SO3 2.00.10.3 CO2 2.6Free CaO 1.2Loss on ignition0.80.8 Blaine surface area(m2/kg)431350280 Particles>45m m(%)839 Calculated surface area(m2/kg)408540 Table2Mix proportions and hardened concrete propertiesMix number Typeof ashTarget density(kg/m3)a/c w/c w/binderCompressive strength(365days)(MPa)Measured porosity(365days)(%)Dry density(kg/m3)Saturated density(kg/m3)1none full00.300.3085.428.21958.32057.52none full00.400.4078.931.01817.31968.53none full00.600.6046.737.21450.31753.04pfa full10.600.3080.329.81751.01920.05pfa full20.860.2981.527.01715.51889.56pfa full3 1.170.2958.130.61570.81819.07pfa150010.600.3039.543.31287.31530.58pfa150020.860.2935.643.61273.31509.59pfa15003 1.170.2936.143.11274.31531.510pfa125010.600.3019.848.41055.81304.511pfa125020.860.2918.452.51023.51254.012pfa12503 1.170.2919.149.51040.81318.513pfa100010.600.309.259.3833.01079.014pfa100020.860.298.662.6820.81064.515pfa10003 1.170.297.161.9810.01111.016poz full10.600.3093.431.71695.51871.517poz full20.860.2978.731.61561.01800.018poz full3 1.170.2963.133.21524.51789.019poz150010.600.3037.043.01341.51545.520poz150020.860.2941.341.11327.01537.521poz15003 1.170.2938.838.21308.51560.522poz125010.600.3019.850.01058.01303.023poz125020.860.2919.851.11055.01281.024poz12503 1.170.2917.648.31014.01280.525poz100010.600.297.058.7823.51097.526poz100020.860.297.560.6849.51088.027poz10003 1.170.29 5.862.6772.51023.5E.P.Kearsley,P.J.Wainwright/Cement and Concrete Research32(2002)233–239235crushed on a standard cube press,but as the foamed concrete strengths were relatively low,these cubes were crushed on a more sensitive machine with a50-MPa capacity and recorded to the nearest0.1MPa.Cubes were crushed after7,28,56,84,168,270and365days.3.1.2.PorosityThe porosity of the foamed concrete was determined using the Vacuum Saturation Apparatus as developed by Cabrera and Lynsdale[10]at the University of Leeds[11]. Porosity measurements were conducted on slices of68-mm diameter cores that were drilled out of the centre of a100-mm cube.The slices were dried at100±5°C until constant weight had been achieved and were then placed in a desiccator under vacuum for at least3h,where after the desiccator was filled with de-aired,distilled water.The porosity was calculated using the following formula[10] (Eq.(8)):P¼ðW satÀW dryÞðW satÀW watÞÂ100ð8Þwhere:P=vacuum saturation porosity(%);W sat=weight in air of saturated sample;W wat=weight in water of saturated sample;W dry=weight of oven-dried sample.4.ResultsDetails of mix proportions and selected hardened con-crete results are shown in Table2.The porosity of the foamed concrete is the sum of the air voids and the voids in the paste.The relationship between dry density and porosity is shown in Fig.1from which it can be seen that porosity is largely dependent on dry density and not on ash type or ash content.The porosities vary between29%(for cement paste with a water/cement ratio of0.3)and67%(for foamed concrete with a casting density of1000kg/m3and a pfa/ cement ratio of3).The lowest porosity,at29%,was measured for the cement paste with a water/cement ratio of0.3containing no ash.The cement paste with a water/ cement ratio of0.6had a porosity of40%,which is virtually the same as the porosity of the foamed concrete mixtures with a casting density of1500kg/m3and an ash/cement ratio of3.4.1.Effect of porosity on compressive strengthThe relationship between measured porosity and the compressive strength(after1year)of foamed concrete is shown in Fig.2.From this graph,it can be seen that the relationship is not significantly influenced by the use of pfa or pozz-fill.Mixtures with an ash/cement ratio of2seem to yield marginally higher strengths for a given porosity and mixtures with no ash or an ash/cement ratio of3seem to yield marginally lower strengths for a given porosity.These differences are,however,only small and it can be concluded that for the results available,the volume of ash used does not significantly influence the porosity–strength relation-ship of foamed concrete.Ro¨ßler and Odler[4]used four expressions that had been derived by other workers to express the relationship between porosity and compressive strength of porous solids. They determined the optimum values of the constant terms and sought the equation that best expressed the existing relationship between strength and total porosity for their set of Portland cement pastes.The same procedure was used to determine whether these equations could be used to express the relation between porosity and strength of the author’sfoamedFig.1.Porosity as a function of dry density.E.P.Kearsley,P.J.Wainwright/Cement and Concrete Research32(2002)233–239236concrete mixtures with high ash contents.The results in Table3indicate that for the1-year results,any one of the four equations can be fitted,resulting in a relatively strong relationship between the compressive strength and the porosity of the foamed concrete.While Ro¨ßler and Odler [4]concluded that the linear relation(Hasselmann)fits their results best,the author’s results are best fitted to an exponential function(Ryshkevitch).The solid line in Fig.2 fits the exponential function(f c=981eÀ7.43p)as shown in Table3.The porosities of the cement pastes analysed by Ro¨ßler and Odler were below0.3(30%),while the porosities of the authors’foamed concrete samples were as high as0.66(66%).From Fig.2,it can be seen that a linear function would fit the foamed concrete mixtures with lower porosities(say below0.4)and these results do therefore seem to concur with the conclusions drawn by Ro¨ßler and Odler.The multiplicative model(Balshin),fitted as shown in Table3,has a power of3.6,which is much higher than the values of up to 2.2calculated for aerated concrete by Baozhen and Erda[6].The fact that the authors’investiga-tion contains data with a larger spectrum of porosities as well as higher strengths could explain this difference.For the foamed concrete mixtures used in this investigation,the strength–porosity equation fitted using an exponential func-tion best explains this relationship with a high correlation coefficient of.967.All the authors’foamed concrete strengths and porosities used to fit these functions were,however,measured1year after casting.The compressive strength of the mixtures increased significantly between28and365days,while based on literature reviewed[12,13],it was assumed that the change in porosity during this period would be negli-gible.The equations as fitted can therefore only be valid for the1-year results and another factor will have to be added to the equation,taking time since casting into account.When the equations shown in Table3are fitted for strengths at different ages,the equation derived by Balshin gives the best result for the combination of all ages.The effect of age can be taken into account by taking the equation as derived by Balshin(Eq.(2))and expanding it to use a variable strength at zero porosity(changing s0to a function of time instead of using the fixed value of321that was derived for the1-year strengths).Fitting a multiplicative model through linear regression results in the following:f c¼39:6ðlnðtÞÞ1:174ð1ÀpÞ3:6ð9Þwhere:f c=compressive strength of foamed concrete(MPa); t=time since casting(days);p=mature porosity(measured after365days).The R2statistic indicates that this model,as fitted, explains89.6%of the variability in compressive strength.A correlation coefficient of.946indicates a relativelystrongFig.2.Effect of porosity on compressive strength at1year.Table3Equations for the strength–porosity relationship of foamed concreteAuthors’foamed concreteEquation Equation fitted by Ro¨ßler and Odler Equation fitted R2Correlation coefficient Balshin s c=540(1Àp)14.47f c=321(1Àp)3.6.926.962Ryshkevitch s c=636eÀ17.04p f c=981eÀ7.43p.936.967Schiller s c=81.5Ln(0.31/p)f c=109.5Ln(0.66/p).89.943Hasselmann s c=158À601p f c=147À226p.848.921E.P.Kearsley,P.J.Wainwright/Cement and Concrete Research32(2002)233–239237relationship between these variables.The relation between the compressive strength as predicted using Eq.(9)and the actual measured values can be seen in Fig.3.Although the equation predicts the strengths reasonably accurately at low values,the compressive strength is underestimated at higher strengths (between 50and 80MPa).Although from Eq.(9)it is possible to obtain a fairly accurate assessment of the compressive strength of the foamed concrete at any age,it does require a measurement of porosity to be made in order to solve the equation.Porosity is a property rarely measured outside the labora-tory,and a model for predicting strength that requires a knowledge of more easily measured properties may be of more use to the concrete producers.Using the equations derived by Hoff [8](see Eqs.(6)and (7)),a theoretical porosity can be calculated for any mixture provided the dry density,water/cement ratio and cement specific gravity are known.The equations though were derived for foamed concrete mixtures made only with cement and may not therefore be valid for the authors’mixtures made with high volumes of ash.Eq.(6)was used to calculate the theoretical porosity for each mix,where k was assumed to be equivalent to the water/binder (cemen-t +ash)ratio.The binder specific gravity (p c )was calculated by dividing the total binder (cement +ash)weight by the total binder volume.In calculating the volumes of cement and ash,relative densities of 3.14and 2.2,respectively,were used.The points in Fig.4have been plotted using the calculated porosity and measured compressive strength for each ing multiple regression analysis on Eq.(7),the line of best fit was derived,which is the solid line shown in Fig.4.The values of the s 0and b used to derive this line were 188MPa and 3.1,respectively.In Hoff’s original work,he used a variety of different cements and derived a range of values of s 0and b from 115to 290MPa and 2.7to 3.0,respectively,depending on the cement type.It is interesting to note that the values obtained by the authors lie almost within the ranges quoted by Hoff,whichsuggestsFig.3.Predicted versus measuredstrengths.pressive strength–theoretical porosity relation at 365days.E.P .Kearsley,P .J.Wainwright /Cement and Concrete Research 32(2002)233–239238that his equation may well be valid for mixtures containing fly ash.However,looking more closely at Fig.4,two things are evident:The two data points furthest from the line of best fit are for mixtures with water/binder ratios of0.40and0.60 compared with0.30for all the other mixtures.This would suggest that the relationship is only valid for a given water/binder ratio.The variability about the fitted line for mixtures without foam(at water/binder ratio0.3)is greater than for all the foamed concrete mixes.This might suggest that the equation is only valid for foamed concrete.However,the R2statistic indicates that the model,as fitted,explains92.3%of the variability in compressive strength,and the correlation coefficient equals.961,indicat-ing a relatively strong relationship between theoretical porosity and compressive strength.It can be concluded that the equation as derived by Hoff can effectively be used to predict the compressive strength of foamed concrete mix-tures containing high percentages of ash.5.ConclusionsPorosity is largely dependent on dry density and not on ash type or content.The compressive strength of foamed concrete was shown to be a function of porosity and age.A multiplicative model(such as the equation derived by Balshin)best fits the results at all ages of this investigation.The effect of ash/cement ratio has not yet been established and an attempt should be made to establish whether there are optimum ash contents at different ages and porosities.The equation as derived by Hoff can effectively be used to predict the compressive strength of foamed concrete mixtures containing high percentages of ash. References[1]E.P.Kearsley,P.J.Wainwright,The effect of high fly ash content onthe compressive strength of foamed concrete,Cem.Concr.Res.31 (2001)105–112.[2]E.P.Kearsley,P.J.Wainwright,Porosity and permeability of foamedconcrete,Cem.Concr.Res.31(2001)805–812.[3]A.M.Neville,Properties of Concrete,4th ed.,Longman,Essex,Eng-land,1995.[4]M.Ro¨ßler,I.Odler,Investigations on the relationship between poros-ity,structure and strength of hydrated Portland cement pastes:I.Effect of porosity,Cem.Concr.Res.15(1985)320–330.[5]G.Fagerlund,Strength and porosity of concrete,Proc.Int.RILEMSymp.Pore Structure,Prague(1973)D51–D73(Part2).[6]S.Baozhen,S.Erda,Relation between properties of aerated con-crete and its porosity and hydrates.Pore structure and materials properties,Proc.Int.RILEM Congress,Versailles,France(1987) 232–237(September).[7]R.R.Hengst,R.E.Tressler,Fracture of foamed Portland cements,Cem.Concr.Res.13(1983)127–134.[8]G.C.Hoff,Porosity–strength considerations for cellular concrete,Cem.Concr.Res.2(1972)91–100.[9]E.P.Kearsley,The effect of high volumes of ungraded fly ash on theproperties of foamed concrete,PhD Thesis,Department of Civil En-gineering,University of Leeds,UK,1999.[10]J.G.Cabrera,C.J.Lynsdale,A new gas permeameter for measuringthe permeability of mortar and concrete,Mag.Concr.Res.40(144) (1988)177–182.[11]B.A.Gaafar,The effect of environmental curing conditions on the gasand water permeability of concrete,PhD Thesis,University of Leeds, Leeds,UK,1995.[12]P.J.Wainwright,J.G.Cabrera,A.M.Alamri,Performance propertiesof pozzolanic mortars cured in hot dry environments.Concrete in hot climates,Proc.Third Int.RILEM Conf.,E&FN Spon,Torquay, England(1992)115–128.[13]K.E.Hassan,J.G.Cabrera,Y.M.Bajracharya,The influence of fly ashcontent and curing temperature on the properties of high performance concrete.Deterioration and repair of reinforced concrete in the Ara-bian Gulf,5th Int.Conf.,Bahrain vol.1,(1997)345–365.E.P.Kearsley,P.J.Wainwright/Cement and Concrete Research32(2002)233–239239。

The Effect of Body Position on GER in Premature Infants-Corvaglia-2007

The Effect of Body Positioning on Gastroesophageal Reﬂux in Premature Infants:Evaluation by Combined Impedance and pH MonitoringL UIGI C ORVAGLIA,MD,R AFFAELLA R OTATORI,MD,M ARIANNA F ERLINI,MD,A RIANNA A CETI,MD,G INA A NCORA,MD,AND G IACOMO F ALDELLA,MDObjective To evaluate the pattern of acid and nonacid gastroesophageal reﬂux(GER)in different body positions in preterm infants with reﬂux symptoms by a combined multichannel intraluminal impedance(MII)–pH monitoring,which identiﬁes both acid and nonacid GER.Study design Premature infants with frequent regurgitation and postprandial desaturation(n؍22)underwent a24-hour recording of MII-pH.In a within-subjects design,reﬂux indexes were analyzed with the infants in4different positions:supine (S),prone(P),on the right side(RS),and on the left side(LS).Results All infants were analyzed for20hours.The mean number of recorded GER episodes was109.7.The mean esophageal exposure to acid and nonacid GER was lower in positions P(4.4%and0.3%,respectively)and LS(7.5%and0.7%, respectively)than in positions RS(21.4%and1.2%,respectively)and S(17.6%and1.3%,respectively).The number of postprandial nonacid GER episodes decreased but the number of acid GER episodes increased over time.The LS position showed the lowest esophageal acid exposure(0.8%)in the early postprandial period,and the P position showed the lowest esophageal acid exposure(5.1%)in the late postprandial period.Conclusion Placing premature infants in the prone or left lateral position in the postprandial period is a simple intervention to limit GER.(J Pediatr2007;151:591-6)G astroesophageal reﬂux(GER)is common in premature infants.Because it may be linked to serious clinical conse-quences,it is cause for concern in neonatologists and parents and necessitates prolongation of hospitalization.1,2As in term infants,3a conservative approach based on postural treatment has been suggested in preterm infants with GER.1 However,few studies have been performed to investigate the best body position for this approach to GER treatment in premature infants,and results are not ing pH monitoring,Ewer et al4found that prone and left lateral positioning was more effective in preventing GER.Omari et al,5using combined manometry and multichannel intraluminal impedance (MII)recording in preterm infants asymptomatic for GER,found that left lateral positioning was more advantageous than right lateral positioning.These authors analyzed the mechanisms triggering GER and observed an increased number of transient lower esophageal sphincter relaxations(TLESRs)in the right lateral position,despite a gastricemptying rate twice that in the left lateral position.Despite these importantﬁndings,thisstudy was unable to differentiate acid and nonacid GER.5The effect of positioning is predictable based on previous work,but it is importantto describe this effect using the current state-of-the-art methods for GER measurement.Consequently,the aim of our study was to evaluate the affect of body position on GERin symptomatic premature infants using combining intraluminal impedance and pHmonitoring.MII is based on the intraluminal electrical impedance changes occurring duringthe passage of a bolus through the esophagus.It is measured by electrodes incorpo-rated along a catheter.Impedance is decreased if the bolus is liquid and is increasedif it is air.The direction of the bolus is determined by evaluating changes inintraluminal impedance at various levels over time.6MII can detect gas,mixed,andBEI Bolus exposure indexGER Gastroesophageal reﬂuxLES Lower esophageal sphincterLS Left sideMACT Mean acidic clearing timeMII Multichannel intraluminal impedance P ProneRIpH Reﬂux indexRS Right sideS SupineTLESR Transient lower esophageal sphincterrelaxationSee editorial,p560andrelated article,p585From the Institute of Preventive Pediatricsand Neonatology,St.Orsola Malpighi Gen-eral Hospital,University of Bologna,Bolo-gna,Italy(L.C.,R.R.,M.F.,A.A.,G.A.,G.F.).Submitted for publication Feb1,2007;lastrevision received Apr27,2007;acceptedJun6,2007.Reprint requests:Luigi Corvaglia,MD,Istitutodi Pediatria Preventiva e Neonatologia,ViaMassarenti11,40138Bologna,Italy.E-mail:luicorva@almadns.unibo.it.0022-3476/$-see front matterCopyright©2007Mosby Inc.All rightsreserved.10.1016/j.jpeds.2007.06.014591liquid GER episodes but cannot differentiate acid and non-acid episodes;for this reason,it is essential to combine MII and pH monitoring to evaluate the role of acid and nonacid GER episodes.METHODSA total of22(16male)symptomatic premature infants with a median gestational age at birth of31weeks(range,24 to32weeks)and a median birth weight of1220g(range,630 to2250g)were enrolled in the study at a median age of29 days(range,12to83days)and a median weight of1747g (range,1150to3215g).The infants exhibited frequent re-gurgitation and postprandial desaturation;in addition,7in-fants had postprandial apnea,4had failure to thrive,1had bradycardia,and1had both postprandial apnea and brady-cardia.All were otherwise healthy at the time of examination. None had malformation or major gastrointestinal problems or was taking drugs inﬂuencing gastrointestinal motility or gas-tric acidity.Seven infants were fed extracted human milk fortiﬁed with3%FM85(Nestlé,Vevey,Switzerland),3were fed a standard preterm formula,and the remaining12re-ceived both.All22infants tolerated at least100ml/kg per day of milk.The effect of postural intervention on GER was eval-uated in a within-subjects design,taking for each subject measurement of GER in different postural conditions.In a within-subjects design,the same subjects are tested in each condition;therefore,differences among subjects can be sep-arated from error,increasing the power of signiﬁcance tests.A possible drawback of this method is the“carry-over”effect—a persistent effect in a subsequent treatment period from treat-ment in the previous period.In our study,this could be represented by the effect on GER of each position on the subsequent position.To limit this effect,we randomly as-signed to each enrolled infant a different sequence of the possible postural combinations.Postural InterventionIn the24-hour examination,4positions—supine(S), prone(P),right side(RS),and left side(LS)—were studied. Each position was maintained for6hours,except for2 periods of30minutes each for feeding.The order of different positions was assigned randomly and was not known by the data analysts.Each infant received8meals(1every3hours) through a feeding bottle or an orogastric tube,inserted and removed at each meal.This approach allowed us to include2 meals and2150-minute postprandial periods in each body position.GER MonitoringEach patient underwent a24-hour,continuous,simul-taneous measurement of intraesophageal pH and multichan-nel electrical impedance.The system was calibrated before each measurement using pH buffer solutions of pH4.0and pH7.0.A single-use combined MII–pH probe(Comfortec MII-pH,2.1mm in diameter;Sandhill Scientiﬁc,Highlands Ranch,CO)was used.Theﬂexible catheter contained seven impedance electrodes representing6bipolar impedance chan-nels and1antimony electrode for pH detection.The distance between each impedance electrode was1.5cm,except for the distal couple spaced at2cm.The pH sensor was located1cm above the distal impedance ring,in the middle of the most distal impedance-measurement segment.The catheter was inserted through a nostril without sedation and placed under ﬂuoroscopic guidance.The tip wasﬁxed1to1.5cm above the gastroesophageal junction.Before removal,the position of the catheter was compared with the initial position by checking the depth mark on the catheter,to exclude possible displace-ment.Data were acquired on a portable Sleuth system(San-dhill Scientiﬁc),stored at the end of each test in a personal computer,and analyzed by BioVIEW Analysis software,ver-sion5.0.9(Sandhill Scientiﬁc)and by direct visual evaluation of each event.During each GER episode,we recorded the minimum pH value;the height(in cm),calculated by the distance from the lower esophageal sphincter(LES)of the most proximal electrode that detected the reﬂux;and the duration(in sec-onds),deﬁned as the time between the onset of GER and the recovery of50%of the initial impedance value,measured at the level of the distal impedance bipolar channel(ie,1.5cm). To be detected as MII-GER,the bolus,moving in a retro-grade direction,had to contact at least3impedance elec-trodes,reaching a height of at least4to4.5cm above the gastroesophageal junction.An MII-GER episode was de-ﬁned as acid(aMII-GER)if the pH wasϽ4and as nonacid (NaMII-GER)if the pH wasՆ4.7The total percentage of time with a MII-GER in the esophagus was indicated as bolus exposure index(BEI)and further separated into acid (aMII-GER-BEI)and nonacid(NaMII-GER-BEI)reﬂux indexes.The number of all acid GERs,including those detected only by pH electrode and those detected by MII as well,was classiﬁed as pH-acid-GER.The total percent time of esoph-ageal exposure to a pHϽ4was designated as the reﬂux index (RIpH).This latter measurement substantially represents a traditional pH monitoring and includes periods of acid esophageal exposure associated with retrograde movement detected by MII and periods with acid esophageal exposure not associated with retrograde movement detected by MII. The mean time(in seconds)required for pH to return to4 after a GER episode was designated the mean acidic clear-ing time(MACT).Because the features of GER change during postpran-dial hours,8we further analyzed and compared GER indexes measured during theﬁrst75postprandial minutes(ﬁrst pe-riod)with those measured during the second75postprandial minutes(second period).The study design was approved by the hospital’s Insti-tutional Ethics Committee.Written informed consent was obtained from a parent of each infant enrolled in the study.592Corvaglia et al The Journal of Pediatrics•December2007Statistical AnalysisAll statistical analyses were performed with SPSS13.0 for Windows(SPSS Inc,Chicago IL).Normal distribution wasﬁrst evaluated by the Kolmogorov-Smirnov test.Reﬂux variables in each position were analyzed using generalized likelihood model repeated-measures design(1within-subjects factor)and Bonferroni post hoc pairwise comparison;differ-ences between theﬁrst and second postprandial periods were tested by paired-sample t tests.A P valueϽ.05was consid-ered statistically signiﬁcant.RESULTSThe test was well tolerated by all of the patients,and their clinical status remained stable.No probe position changes were detected during any examination.We analyzed a total of176postprandial periods(44periods for each position),with a mean duration of149minutes(range,145to 157minutes).RIpH measurements in the22patients are given in Table I.During the20-hour monitoring(24hours minus4 feeding hours),the mean total number of recorded GER episodes was109.7(5.5per hour).The mean numbers of aMII-GER,NaMII-GER,and pH-acid-GER episodes were 11.7,35.9,and73.7,respectively,with corresponding mean percent times of esophageal exposure to reﬂux of0.3%,0.9%, and12.7%.Effect of Position on the Physical Compositionof ReﬂuxateGER episodes wereﬁrst analyzed regarding physical composition of the reﬂuxate.In each position,most of the GER reﬂuxate was liquid,although some was gaseous or mixed.Liquid reﬂuxate was signiﬁcantly less frequent in the LS and P positions compared with the RS and S positions (PϽ.01)(Table I).There were no signiﬁcant differences among positions regarding gaseous and mixed episodes. Effect of Position on Impedance-Detected andpH-Detected ReﬂuxWhen values were analyzed by different positions,we observed a reduction of each type of MII-pH–detected GER in the LS and P positions compared with the RS and S positions(Figures1and2).In particular,acid exposure time (RIpH)and MACT were signiﬁcantly lower in both the P and LS positions compared with the S and RS positions.We found no difference between the P and LS positions.The P position exhibited signiﬁcantly fewer Na-MII-GER episodes than the other3positions.Table I.Reﬂux parameters measured in the22patientsTotal Left side Right side Supine Prone PLiquid GER(n)40.5(20.5)0-877.9(4.8)0-2013.6(8.8)0-3015.9(9.7)0-393.1(2.6)0-10LS vs RS:.012LS vs S:.002P vs RS,S,LS:.001Gaseous GER(n) 4.8(5.2)0-191.7(2.1)0-81.1(1.4)0-50.9(1.2)0-41.1(2)0-8NSMixed GER(n)7.4(5.9)0-222.3(2.6)0-112.5(2.9)0-131.7(1.9)0-70.8(1.4)0-6NSaMII-GER(n)11.7(9.1)1-351.9(2.1)0-84.2(4.4)0-184.3(3.5)0-121.1(1.2)0-3P vs S:.001P vs RS:.019LS vs S:.029NaMII-GER(n)35.9(22)2-918.3(5.8)0-2111.9(8.9)0-3612.9(9.1)1-352.8(2.6)0-8P vs RS,S,LS:.001pH-acid-GER(n)73.7(44.3)3-14917.9(15.7)0-5627.1(18.1)3-6621.9(15.3)0-566.8(5.3)0-17P vs S,RS:.001P vs LS:.006aMII-GER-BEI(%)0.3(0.2)0-0.70.2(0.3)0-10.5(0.5)0-1.70.5(0.5)0-1.70.1(0.1)0-0.4P vs RS:.001P vs S:.006RS vs LS:.015NaMII-GER-BEI(%)0.9(0.5)0-1.80.7(0.6)0-2.11.2(0.9)0-2.61.3(1)0.11-3.30.3(0.3)0-1P vs S,RS:.0001LS vs S:.011RipH(%)12.7(10.5)1.6-37.97.5(8.2)0-32.221.4(19.4)0.4-68.417.6(16.1)0-48.64.4(5.8)0-19.8P vs RS:.001P vs S:.002LS vs RS:.004LS vs S:.014MACT(sec)119.8(116.1)26.4-582.693.2(143.9)0-701.8176.4(245.6)26.4-1216.9162.7(103)17.1-282.994.9(91.1)0-257.1P vs S:.016LS vs RS:.021Mean MII-GER height(cm)3.5(1.2)1.8-7.23.9(1.7)1.7-93.4(1.2)1.5-73.8(1.3)1.7-7.33(1.4)0-7NSNS,not signiﬁcant.Values are expressed as mean(standard deviation)and range.The Effect of Body Positioning on Gastroesophageal Reﬂux in Premature Infants:Evaluation by Combined Impedanceand pH Monitoring593Improvement in all GER indexes in the P and LS positions was seen in all patients except 1,who showed better GER indexes in the S and RS positions than in the P and LS positions.In this patient,an upper radiograph study with a barium swallow performed after MII-pH monitoring dem-onstrated a gastric malrotation.We decided not to exclude this patient from the analysis,because the inclusion criteria were fulﬁlled,and the diagnosis of malrotation was made after the MII-pH monitoring had been performed.Moreover,we veriﬁed that the exclusion of this patient would not have affected the global results;in fact,in an analysis performed excluding this patient,all statistical signiﬁcances did not vary (data not showed).Inﬂuence of Position on the Height of GER EpisodesNo difference among positions was found in mean height reached by GER episodes.Changes in the Composition of Postprandial Reﬂuxate Over TimeComparison of the 2postprandial periods (Table II )revealed that acid GER indexes (RIpH and aMII-GER-BEI)were signiﬁcantly higher in the second postprandial period than in the ﬁrst postprandial period in all of the positions studied except P.In the ﬁrst postprandial period,the P and LS positions were associated with a signiﬁcantly lower RIpH compared with the S and RS positions (P Ͻ.01).RIpH was the lowest in the LS position (with 12of the 22patients having a RipH of 0%),signiﬁcantly lower than in the P position (LS ϭ0.8%vs P ϭ3.6%;P Ͻ.05)(Figure 3;available at ).During the second postprandial period,the P position was associated with strongly reduced esophageal acid exposure compared with the other 3positions (P Ͻ.01).RIpH was lower in the LS than in the S and RS position (P Ͻ.01);however,RIpH was signiﬁcantly higher in the LS position than in the P position (14.3%vs 5%;P ϭ.016).In the ﬁrst postprandial period,Na-MII-GER-BEI was signiﬁcantly lower in the P position compared with the RS and S positions (P Ͻ.05);in the second postprandial period,Na-MII-GER-BEI was signiﬁcantly lower in the P position compared withall of the other positions (P Ͻ.01)(Figure 4;available at ).DISCUSSIONIn this study,we found fewer GER episodes when infants were placed in the LS and P positions compared with the RS and S positions.Body position had no inﬂuence on the proximal extent of MII-detected GER episodes.In each body position,we noticed a decrease in the number of postprandial nonacid GER episodes and an increase in the number of postprandial acid GER episodes over time.GER is common in preterm infants;the almost ﬁxed lying position promotes the entry of liquid gastric contents into the esophagus when TLESR occurs.Additional risk factors associated with preterm birth include high total ﬂuid enteral intake,frequent handling by nurses,and the use of permanent feeding tubes.9A study in asymptomatic preterm neonates found a median of 71reﬂux episodes in 24hours.10Although GER is asymptomatic in most preterm infants,in some it may cause such symptoms as desaturation,regurgitation,and bradycar-dia or can lead to such complications as apnea,recurrent desaturation and/or aspiration,difﬁculties in oral feeding,vomiting,and failure to thrive.1Although acid reﬂux episodes are considered more likely associated with symptoms in pre-term infants,11recent studies indicate that nonacid reﬂux can produce these symptoms as well.12For preterm infants with symptomatic GER,a stepwise approach,based mainly on conservative interventions,is the best therapeutic choice.Drugs should be the last option,considering that cisapride was withdrawn from the market because of its possible cardiac side effects,13and treatment with gastric acid inhibitors is not without risk.14,15In a previous study,we found no reduction of GER from thickening human milk with precooked starch.16More-over,a possible relationship between milk thickening and the development of necrotizing enterocolitis has been described in 2preterm infants.17Few studies have evaluated the inﬂuence of body posi-tion on acid GER in preterm newborns,and,to the best of our knowledge,none have investigated the inﬂuence of body position on nonacid GER.Omari et al 5evaluated the inci-dence of GER in 10newborns with mild prematurity and without GER symptoms using a combined MII and manom-etry catheter and found an advantage of LS over RS position-ing in terms of a reduced number of GER episodes.Although that study provided important data concerning GER patho-logical mechanisms,the presence of a trans-LES catheter could have increased the number of GER episodes,and the absence of a pH sensor did not allow the authors to differ-entiate acid and nonacid episodes.Another study conﬁrmed these ﬁndings in 18premature babies with GER symptoms using pH monitoring and comparing the P position with the RS and LS positions.4But that study evaluated only acid episodes with no information about the S position,the most frequently used position in both term and in pretermnew-Figure 1.RIpH in different body positions (—,median;---,95th percentile).594Corvaglia et alThe Journal of Pediatrics •December 2007borns.Recognizing that nonacid reﬂux episodes are common in premature infants,we believe that combined MII-pH monitoring is the most appropriate method for evaluating GER in preterm newborns.In our study,RIpH was mostly measured only by a pH electrode (placed 1.5to 2cm above the diaphragm),not by MII (with the most distal 2electrodes placed at about 4.5cm above diaphragm).Thus,GER episodes were detected in 2different esophageal sites 3cm apart;this distance is partic-ularly relevant considering the total esophageal length of about 6to 10cm.For this reason,we can state that in symptomatic preterm infants,most GER occurs in the distal half of the esophagus.Even in adults,a 6-fold increase in acid exposure (mean RipH,11.7%vs 1.8%)was found between the more distal and proximal pH measurements.18Our data are not comparable with those from previous studies,due to methodological differences.Wenzl,6Skopnik et al,19and others reported that most GER episodes reached the proximal esophagus because they considered as GER episodes only those detectable by both MII and pH probes.In comparison,we also considered numerous short-segment ep-isodes detected only by the pH probe.Omari et al 11charac-terized most GER episodes as nonacid,because they ﬁrst detected all GER episodes by manometry just above the LES and then classiﬁed them as acid or nonacid by a pH electrode.In contrast,we were able to detect GER episodes just above the LES only by the pH probe.We found that the P and LS positions signiﬁcantly decreased the number of acid and nonacid GER episodes compared with the S and RS positions.The effect of theLSFigure 2.aMII-BEI and NaMII-BEI in different body positions (—,median;---,95th percentile).(aMII-BEI:P vs RS P ϭ.001,P vs S ϭP ϭ.006,RS vs LS P ϭ.015;NaMII-BEI:P vs RS P ϭ.0001,P vs S ϭP ϭ.0001,RS vs LS P ϭ.011.)Table II.Variation of acid and nonacid GER during postprandial periodsRIpHP aMII-GER-BEI P NaMII-GER-BEI P Left sideFirst period 0.8(1.5)0-5.5.0010(0.1)0-0.3.031.2(1)0-3.7.0001Second period 14.3(16)0-64.40.2(0.5)0-20.2(0.2)0-0.6Right side First period 9.9(21)0-92.1.0010.3(0.5)0-2.2.01 2.2(1.7)0-5.2.0001Second period 32.9(26.1)0.7-84.30.8(0.9)0-2.50.2(0.3)0-0.8SupineFirst period 5.4(13.4)0-54.9.00010.1(0.2)0-0.6.0001 2.2(1.7)0.2-5.5.0001Second period 29.7(25.6)0-72.60.9(0.9)0-3.10.4(0.8)0-3.1ProneFirst period 3.6(8.7)0-37.3NS 0(0.1)0-0.4.040.7(0.6)0-2.0.0001Second period 5.1(7.3)0-33.70.1(0.2)0-0.90(0.1)0-0.5TotalFirst period 4.9(9.3)0-34.3.00010.1(0.1)0-0.5.001 1.6(0.9)0.1-3.5.0001Second period20.5(14.3)0.2-47.80.5(0.4)0-1.40.21(0.3)0-1.0Values are expressed as mean (standard deviation)and range.The Effect of Body Positioning on Gastroesophageal Reﬂux in Premature Infants:Evaluation by Combined Impedance and pH Monitoring595position in reducing GER is due mainly to a functional factor—reduced TLESR episodes—by laying the gastric con-tents on the gastric body and greater curvature,which to-gether act as a reservoir.5The effect of the P position is related mainly to an anatomic factor.In this position,the LES is above the gastric body,far from the gastric contents;4 thus,when a TLESR occurs,the gastric contents are farther from the LES and are less likely to go back into the esoph-agus.Our separate analysis of the incidence of acid and non-acid GER episodes and the relationship with different body positions in theﬁrst and second postprandial periods revealed that in theﬁrst period,the degree of acid esophageal exposure was4-fold higher in the P position compared with the LS position(percent time,3.6%vs0.8%;PϽ.05).In dyspeptic adults,after meals in upright position,a pocket of unbuffered acid juice forms near the gastroesophageal junction;it seems to escape the buffering effects of meals,remaining highly acid compared with the body of the stomach.20The presence of a similar pocket in preterm infants lying in the P position could explain the higher esophageal acid exposure in the P position than in the LS position during theﬁrst postprandial period. In contrast,in the second postprandial period,esophageal acid exposure was higher in the LS position than in the P position(Pϭ.016).Theseﬁndings suggest that acid exposure can be optimally reduced by keeping the newborn on the left side during the early postprandial period and in the prone position thereafter.In conclusion,our study suggests that placing prema-ture infants in a prone or left lateral position during the postprandial period is a simple intervention to limit GER. Ourﬁndings do not provide any information on clinical improvement,because the study was not designed to monitor the effect of postural intervention on GER symptoms.Fur-ther studies are needed to evaluate the effective correlation between postural intervention and improvement of GER symptoms.REFERENCES1.Poets CF.Gastroesophageal reﬂux:a critical review of its role in preterm infants. Pediatrics2004;113:128-32.2.Frakaloss G,Burke G,Sanders MR.Impact of gastroesophageal reﬂux on growth and hospital stay in premature infants.J Pediatr Gastroenterol Nutr 1998;26:146-50.3.Tobin JM,McCloud P,Cameron DJS.Posture and gastro-oesophageal reﬂux:a case for left lateral positioning.Arch Dis Child1997;76:254-8.4.Ewer AK,James ME,Tobin JM.Prone and left lateral positioning reduce gastro-oesophageal reﬂux in preterm infants.Arch Dis Child Fetal Neonatal Ed 1999;81:F201-5.5.Omari TI,Rommel N,Staunton E,Lontis R,Goodchild L,Haslam RR,et al. Paradoxical impact of body positioning on gastroesophageal reﬂux and gastric emptying in the premature neonate.J Pediatr2004;145:194-200.6.Wenzl TG.Investigating esophageal reﬂux with the intraluminal impedance technique.J Pediatr Gastroenterol Nutr2002;34:261-8.7.Sifrim D,Castell D,Dent J,Kahrilas PJ.Gastro-esophageal reﬂux monitoring: review and consensus report on detection and deﬁnitions of acid,nonacid,and gas reﬂux. Gut2004;53:1024-31.8.Wildi SM,Tutuian R,Castell DO.The inﬂuence of rapid food intake on postprandial reﬂux:studies in healthy volunteers.Am J Gastroenterol2004;99:1645-51.9.Peter CS,Wiechers C,Bohnhorst B,Silny J,Poets C.Inﬂuence of nasogastric tubes on gastroesophageal reﬂux in preterm infants:a multiple intraluminal impedance study.J Pediatr2002;14:277-9.10.Lòpez-Alonso M,Moya MJ,Cabo JA,Ribas J,Macias MdC,Silny J,et al. Twenty-four-hour esophageal impedance-pH monitoring in healthy preterm neonates: rate and characteristics of acidic,weakly acidic,and weakly alkaline gastroesophageal reﬂux.Pediatrics2006;118:e299-308.11.Omari TI,Barnett CP,Benninga MA,Lontis R,Goodchild L,Haslam RR,et al. Mechanism of gastro-oesophageal reﬂux in preterm and term infants with reﬂux disease. Gut2002;51:475-9.12.Wenzl TG,Silny J,Schenke S,Peschgens T,Heimann G,Skopnik H.Gastro-esophageal reﬂux and respiratory phenomena in infants:status of the intraluminal impedance technique.J Pediatr Gastroenterol Nutr1999;28:423-8.13.Corvaglia L,Faldella G,Rotatori R,Lanari M,Capretti MG,Salvioli GP. Intrauterine growth retardation is a risk factor for cisapride-induced QT prolongation in preterm infants.Cardiovasc Drug Ther2004;18:371-5.14.Guillet R,Stoll BJ,Cotten CM,Gantz M,McDonald S,Poole WK,Phelps DL, National Institute of Child Health and Human Development Research Network. Association of H2-blocker therapy and higher incidence of necrotizing enterocolitis in very low birth weight infants.Pediatrics2006;117:e137-42.15.Canani RB,Cirillo P,Roggero P,Romano C,Malamisura B,Terrin G,et al, Working Group on Intestinal Infections of the Italian Society of Pediatric Gastroen-terology,Hepatology and Nutrition.Therapy with gastric acidity inhibitors increases the risk of acute gastroenteritis and community-acquired pneumonia in children.Pediatrics 2006;117:e817-20.16.Corvaglia L,Ferlini M,Rotatori R,Paoletti V,Alessandroni R,Cocchi G,et al. Starch thickening of human milk is ineffective in reducing the gastroesophageal reﬂux in preterm infants:a crossover study using intraluminal impedance.J Pediatr2006; 148:265-8.17.Clarke P,Robinson MJ.Thickening milk feeds may cause necrotizing enteroco-litis.Arch Dis Child Fetal Neonatal Ed2004;89:F280.18.Fletcher J,Wirz A,Henry E,McColl KEL.Studies of acid exposure immediately above the gastro-oesophageal squamocolumnar junction:evidence of short segment reﬂux.Gut2004;53:168-73.19.Skopnik H,Silny J,Heiber O,Schulz J,Rau G,Heimann G.Gastroesophageal reﬂux in infants:evaluation of a new intraluminal impedance technique.J Pediatr Gastroenterol Nutr1996;23:591-8.20.Fletcher J,Wirz A,Young J,Vallance R,McColl KEL.Unbuffered highly acidic gastric juice exists at the esophageal junction after a meal.Gastroenterology2001; 121:775-83.596Corvaglia et al The Journal of Pediatrics•December2007。

Effects of Design Features on Rigid Pavement Performance(外文文献)

Effects of Design Features on Rigid Pavement PerformanceThe performance of rigid pavements is affected by a variety of design features, including slab thickness, base type, joint spacing, reinforcement, joint orientation, load trans fer, dowel bar coatings, longitudinal joint design, joint sealant, tied concrete shoulders ,and subdrainage . A study was made by ERES Consultants, Inc. under FHWA contract on the effects of these features on rigid pavement performance . Ninety-five pavemen tsections located in four major climatic regions were thoroughly evaluated . The following conclusions, which provide some revealing insights into pavement performance, are abstracted from the report (Smith et al., 1990a).Slab Thickness The effect of slab thickness on pavement performance was significant.It was found that increasing slab thickness reduced transverse and longitudinal cracking in all cases. This effect was much more pronounced for thinner slabs than fo rthicker slabs . It was not possible to compare the performance of the thinner slabs and the thicker slabs directly, because the thick slabs were all constructed directly on th esubgrade and the thinner slabs were all constructed on a base course .Increasing the thickness of slab did not appear to reduce joint spalling or join tfaulting . Thick slabs placed directly on the subgrade, especially in wet climates an dexposed to heavy traffic, faulted as much as thin slabs constructed on a base course .Base Type Base types, including base/slab interface friction, base stiffness, base erodibility, and base permeability, seemed to have a great effect on the performance of jointed concrete pavements . The major performance indicators, which were affected by variations in base type, were transverse and longitudinal cracking, joint spalling, and faulting .The worst performing base type, consisted of the cement-treated or soil cement bases, which tended to exhibit excessive pumping, faulting, and cracking. This is most likely due to the impervious nature of the base, which traps moisture and yet can brea- k down and contribute to the movement of fines beneath the slab .The use of lean concrete bases generally produced poor performance . Large curl -ing and warping stresses have been associated with slabs constructed over lean concrete bases. These stresses result in considerable transverse and longitudinal cracking of the slab . The poor performance of these bases can also be attributed to a bathtub design, in which moisture is trapped within the pavement cross section .Dense-graded asphalt-treated base courses ranged in performance from very poor to good. The fact that these types of bases were often constructed as a bathtub designcontributed to their poor performance . This improper design often resulted in severe cracking, faulting, and pumping.The construction of thicker slabs directly on the subgrade with no base resulted in a pavement that performed marginally. These pavements were especially susceptible to faulting, even under low traffic levels.Pavements constructed over aggregate bases had varied performance, but were generally in the fair to very good category. In general, the more open-graded the aggregate,the better the performance . An advantage of aggregate bases is that they contribute the least to the high curling and warping stresses in the slab . Even though aggregate bases are not open-graded, they are more permeable and have a lower friction factor than stabilized bases .The best bases in terms of pavement performance were the permeable bases . Typical base courses have permeabilities ranging from 0 to less than 1 ft/day (0 .3 m/day) ; good permeable bases have permeabilities up to 1000 ft/day (305 m/day) . Specific areas of concern were the high corner deflections and the low load transfer exhibited by the permeable bases . These can affect their long-term performance, so the use of dowel bars might be required . An unexpected benefit of using permeable bases was the reduction in "D" cracking on pavements susceptible to this type of distress .Slab Length For JPCP, the length of slabs investigated ranged from 7 .75 to 30 ft(2.4to9.1m). It was found that reducing the slab length decreased both the magnitude of the joint faulting and the amount of transverse cracking. On pavements with random joint spacings, slabs with joint spacings greater than 18 ft (5 .5 m) experienced more transverse cracking than did the shorter slabs .For JRCP, the length of slabs investigated ranged from 21 to 78 ft (6 .4 to 23 .9 m) .Generally, shorter joint spacings performed better, as measured by the deteriorated transverse cracks, joint faulting, and joint spalling . However, several JRCP with long joint spacings performed quite well . In particular, the long jointed pavements in New Jersey, which were constructed with expansion joints, displayed excellent performance .An examination of the stiffness of foundation was made through the use of the radius of relative stiffness, f . Generally speaking, when the ratio L/E, where L is the length of slab, was greater than 5, transverse cracking occurred more frequently . This factor was further examined for different base types . It was found that stiffer base courses required shorter joint spacings to reduce or eliminate transverse cracking .Reinforcement The amount of steel reinforcement appeared to have an effect in con -trolling the amount of deteriorated transverse cracking . Pavement sections with less than 0.1% reinforcing steel often displayed significant deteriorated transverse cracking.A minimum of 0 .1% reinforcing steel is therefore recommended, with larger amounts required for more severe climate and longer slabs.Joint Orientation Conventional wisdom has it that skewed joints prevent the application of two wheel loads to the joint at the same time and thus can reduce load-associated distresses . The results from the limited sample size in this study were ambiguous, but all of the nondoweled sections with skewed joints had a lower PSR than similar designs with perpendicular joints . The available data provide no definite conclusions on the effectiveness of skewing transverse joints for nondoweled slabs . Skewed joints are not believed to provide any benefit to doweled slabs.Load Transfer Dowel bars were found to be effective in reducing the amount of joint faulting when compared with nondoweled sections of comparable designs. The diameter of dowels had an effect on performance, because larger diameter bars provided better load transfer and control of faulting under heavy traffic than did smaller dowels.It appeared that a minimum dowel diameter of 1 .25 in . (32 mm) was necessary to provide good performance .Nondoweled JPCP slabs generally developed significant faulting, regardless of pavement design or climate . This effect was somewhat mitigated by the use of permeable bases. However, the sections in this group had a much lower number of accumulated ESAL, so no definite conclusions can be drawn yet .Dowel Bar Coatings Corrosion-resistant coatings are needed to protect dowels from the adverse effects of moisture and deicing chemicals .While most of the sections in this study did not contain corrosion-resistant dowel bars, those that did generally exhibited enhanced performance. Very little deteriorated transverse cracking was identified on these sections. In fact, one section in New Jersey with stainless steel-clad dowel bars was performing satisfactorily after 36 years of service .Longitudinal Joint Design The longitudinal joint design was found to be a critical design element.Both inadequate forming techniques and insufficient depths of joint can contribute to the development of longitudinal cracking . There was evidence of the ad vantage of sawing the joints over the use of inserts . The depth of longitudinal joints is generally recommended to be one-third of the actual, not designed, slab thickness, but might have to be greater when stabilized bases are used .Joint Sealant Joint sealing appeared to have a beneficial effect on performance . This was particularly true in harsh climates with excessive amounts of moisture . Preformed compression sealants were shown to perform well for more than 15 years under heavy traffic.Except where "D" cracking occurred, pavement sections containing preformed sealants generally exhibited little joint spalling and were in good overall conditions.Rubberized asphalt joint sealants showed good performance for 5 to 7 years.Tied Concrete Shoulders It is generally believed that tied concrete shoulders can reduce edge stresses and corner deflections by providing more lateral supports to the mainline pavement, thus improving pavement performance . Surprisingly, this study showed that, although tied concrete shoulders performed better than asphalt shoulders,many of the tied shoulders were not designed properly and actually contributed to poor performance of the mainline pavement . The tiebars were spaced too far apart ,sometimes at a spacing of 40 in . (1016 mm), and were not strategically located near slab corners to provide adequate support . In some cases, tied concrete shoulders were constructed over a stabilized dense-graded base in a bathtub design, resulting in the poor performance of mainline pavement.Subdrainage The provision of positive subdrainage, either in the form of longitudinal edge drains or the combination of a drainage layer and edge drains, generally reduced the amount of faulting and spalling related to "D" cracking . With few exceptions, the load-associated distresses, especially faulting and transverse cracking, decreased as the drainage characteristics improved . The overall pavement performance can be improved by using an open-graded base or restricting the percentage of fines . A filter layer must be placed below the permeable base, and regular maintenance of the outlets must be provided .。

The effects of Ag content and dendrite spacing on the

Considering the silver addition to a PbeCaeSn alloy, Prengaman [4] reported that Ag increases both the corrosion and creep resistances, improving considerably grid processing and battery performance and durability at high temperature service.
both the Ag alloying and the scale of secondary dendritic arm, l2, have important roles on the electrochemical corrosion behavior. The current density decreased with the increase in l2. The increase in
Journal of Power Sources 238 (2013) 324e335
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Journal of Power Sources
journal homepage: /locate/jpowsour
silver content provoked only a slightly improvement in the corrosion resistance and its addition to a Pb alloy should meticulously be analyzed considering the ratio anode/cathode areas. Although the addition of silver increases considerably the ﬁnal cost of PbeAg alloys, these alloys can be used as alternative materials for the manufacture of lead-acid battery components.

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