锤击成桩重锤低击轻锤重击桩头冲击力贯入度

1Hammer ’s Impact Force on Pile and Pile ’s PenetrationJi-Cheng WangInstitute of Architectural Engineering, Ningbo University of Technology, Ningbo, Zhejiang,China Jianlin YuCollege of Civil Engineering and Architecture, Zhejiang University, Hangzhou, ChinaMa ShiguoNingbo Urban Construction Investment Holding Company Limited, Ningbo, Zhejiang, ChinaXiaonan GongCollege of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China Address correspondence to Ji-Cheng Wang, No. 201, Fenghua Road, Jiangbei District, Ningbo, Zhejiang 315211, China. E-mail: wjc1818@Color versions of one or more of the figures in the article can be found online at /wifa.AbstractMethods of energy and momentum conservation, vibration theories, and model tests are employed to research into impact force of hammer on pile and pile ’s penetration Analytical formula of impact force of hammer on pile is obtained. Comparison of results from the three methods finds that the analytical formula proposed by this paper conforms well to practical situations. Research resultsD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 2015Marine Georesources & Geotechnology To cite this article:Ji-Cheng Wang, Jianlin Yu, Shiguo Ma & Xiaonan Gong (2015): Hammer's Impact Force on Pile and Pile'sPenetration, Marine Georesources & Geotechnology, DOI: 10.1080/1064119X.2015.1016637To link to this article: /10.1080/1064119X.2015.1016637 Accepted author version posted online: 28 May 2015.2show that, If hammer ’s impact energy remains unchanged, Penetration increases with the increase of hammer weight and cushion stiffness; Impact force the pile head receives degrades with the increase of hammer weight but increases with the increase of cushion stiffness; Impact time decreases with the increase of cushion stiffness but increases with the increase of hammer weight. Model test shows that, compared with cotton cloth cushion, elastic cushion ’s advantages lie in that relatively small pile head impact force can achieve big pile penetration, and cotton cloth is gradually compacted with the increase of blow counts, hence impact force the pile head receives tends to increase gradually.KeywordsINTRODUCTIONHammer piling is simple and economical, and has a great penetrability, hence is widely used. However, hammer ’s impact force on pile is usually very big, thus causing damage to pile head. Besides, hammer weight selection is generally empirical. Hammer ’s impact force on pile is usually calculated through pile driving formula, which are deduced from laws of energy and momentum conservation together with empirical parameters as energy utilization efficiency, coefficient of restitution, etc., such as the widely used Hiley (1925) Formula. Smith ’s (1960) model used lumped mass as hammer, and used weightless spring as anvil cushion. Helmet and cap cushion were all regarded as part of the pile. Wave equation analysis was used to simulate dynamic response of pile driving (Smith 1960). Rausche, Goble, and Likins (1985) proposed a pile driving dynamic model which was more complex than Smith ’s (Rausche, Goble, and Likins 1985). Deeks and Randolph (1990, 1991, 1993) built a model comprising piling hammer, anvil cushion, and helmet which was directly attached to pile top and proposed analytical solutions to this modelD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20153considering anvil cushion ’s elasticity and viscoelasticity (Randolph, Banerjee, and Buttefield 1991; Deeks and Randolph 1993, 1995). Koten (1991) researched into a simple hammering model comprising piling hammer and anvil cushion (Koten 1991). Take, Valsangkar, and Randolph (1999) analyzed interaction of piling hammer, anvil cushion, helmet, and cap cushion. The paper used lumped masses for the ram and anvil, a spring for the anvil cushion, and another spring for the cap cushion on the top of a pile. Pile and soil interaction was not considered. Take analyzed blow stress wave on pile top by using mass-spring-dashpot model and numerical computation method (Take, Valsangkar, and Randolph 1999). Runfu and Qing (2000) simplified pile to onedimensional rod and analyzed it by using stress wave solution and proposed a stress solution of pile (Runfu and Qing 2000). Based on one dimensional stress wave theory, Shifang et al. (2003) researched into impact force and penetration by building an interaction model of hammer, pile, and soil and obtained analytical solutions of pile end displacement and velocity (Shifang, Renpeng, and Yunmin 2004). Hehua, Yongjian, and Huaizhong (2004) used different lumped mass for piling hammer and helmet, and parallel spring and dashpot for anvil cushion, and spring for cap cushion, and dashpot for pile, and established an equilibrium equation, and then used the Laplace Transform to deduce analytical solutions of hammering force (Hehua, Yongjian, and Huaizhong 2004; Yongjian et al. 2005). Liyun and Pu'an (1994) carried out a simulation piling test of small diameter steel pipe pile and concluded that disc spring could improve piling efficiency (Liyun and Pu'an 1994). Renpeng et al.(2001) monitored pile body stress in piling and obtained relationships among blow count, pile length, and pile body ’s maximal stress (Renpeng et al. 2001). Peng-kong and Subrahmanyam (2003) researched into pile driving formula considering pile length factor by using one dimensional wave equation (Peng-kong and Subrahmanyam 2003). Based on Hiley Formula, So and Ng (2010) researched into impact compression behaviors of high-capacity long piles (SoD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20154and Ng 2010). With examples, Middendorp and van Weel (1986) attested that under most conditions, simple models could provide force and velocity response curve which was accurate enough (Middendorp and van Weel 1986; Middendorp 2004). This article simplifies the systemm S viz. hammer and pile stick together to move downward after collision. Here H P v v v c . Upon receiving kinetic energy, pile overcomes soil ’s frictional resistance and sinks, then:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201552H P 1()2W m m v c (2)According to momentum conservation, we have:0H P ()H m v m m v c (3)H P(7)In which S Plastic is penetration when complete plastic impact occurs between pile and hammer. From Eq. (7) we have:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20156H0P PlasticHP1m E m S m f m(8)It can be seen from Eq. (8) that if hammer ’s kinetic energy 20H 012E m v remainsp Then energy utilization efficiency is:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20157H 2P PP 220HH 0P 142112m m v m W E m m v m K§· ¨¸©¹ (11)Relationship between energy utilization efficiency K and m H /m p is illustrated in Figure 2.s Relationship between penetration S Elastic and m H /m p is illustrated in Figure 2. It can be seen that just as energy utilization efficiency K , if hammer ’s initial kinetic energy remains unchanged, when m H <m p , penetration S Elastic increases significantly with the increase of m H . When m H =m p ,D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20158penetration is the biggest, and 0Elastic E S f. When m H >m p , penetration S Elastic degrades gradually with the increase of m H . It can also be seen that when m H =3m p , penetration is 034E f, be it usingAssume elastic cushion stiffness coefficient is k H . Pile will not sink if anvil cushion ’s thrust for pile is smaller than soil ’s frictional resistance to pile f . This part of hammer ’s energy is transferred to cushion ’s compression energy, hence:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201592LossH 122f E fx k (17)In which x is compressed length of cushion under the effect of energy loss E Loss . Energy utilization efficiencyS s 2H 2H 0f k m v (22)Viz. when cushion stiffness 2H 2H 0f k m v , hammer ’s all kinetic energy is transferred to cushion ’s compression potential energy and will not cause pile to sink.D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201510When Soil's Resistance to Pile Is Very BigWhen pile receives very big resistance during sinking process and penetration is very small and is negligible, foundation soil ’s stiffness can be seen as P k f , then the system comprising hammer,sinking. When hammer ’s velocity v H equals to pile ’s velocity v P (assume H P v v v c ), cushion is compressed to the thinnest, hence cushion receives the biggest pressure. ThenH 0H P ()m v m m v c (26)D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201511We can obtain:H 0H P m v v m m c(27)The whole system ’s kinetic energyFrom Eqs. (25) and (32), we have:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201512max,P max,P 01k k F F f ! (33)It can be seen from Eq. (33) that max,P max,P 0k k F F f!, and the bigger m H /m p is, the bigger thedifference between max,P k F f and max,P 0k F will be.Actually, foundation soil ’s stiffness k P falls between 0 and f , and the maximal impact force F max the pile head receives satisfies the following Eq.:max,P 0max max,P k k F F F f(34)ANALYSES BASED ON VIBRATION THEORIESTheoretical Analysis of Impact Force Pile Head ReceivesLiteratures (Deeks and Randolph 1993; Take, Valsangkar, and Randolph 1999; So and Ng 2010) reveal that, compared with impact force, gravity of hammer and pile is very small and can be negligible. Compared with anvil cushion and foundation soil, hammer and pile have relatively great stiffness and can be approximately seen as rigid bodies. These literatures (Deeks and Randolph 1993; Take, Valsangkar, and Randolph 1999; So and Ng 2010) also show that hammer exerts the biggest impact force on pile at initial stage of hammering. At this stage, pile and its surrounding soil take relatively small sinking and no relative displacement occurs. Hence vertical downward sinking deformation is mainly elastic deformation. This is illustrated in Figures1(c) and 1(d). Then it can be assumed that soil ’s resistance and pile ’s sinkage display a direct ratio. Select the equilibrium position of hammer and pile as origin of coordinates, and select the displacements x H and x P of hammer and pile which deviate from the equilibrium position as coordinates, just as illustrated in Figure 4(c). When vibration occurs with the system, the forcesD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201513the hammer and the pile receive are illustrated in Figure 4(d). Establish force equations of the system:P P P P H H P H H H H P ()()m x k x k x x m x x x ­®¯k P P H H P x k x k (x Eqs. (36) is a second-order linear homogeneous differential equation set. To make it­®¯x P P bx x P x H dx 22()0()0b A cB dA d B Z Z ­ °® °¯ (41)D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201514Eqs. (41) are a linear equation set of vibration amplitudes A and B . When vibration occurswith the system, the equation set has non-zero solutions, and determinant of coefficient of the equation set must be 0, viz.:b d §¨¸©¹2 1Z 22212b b d c c Z J ª° «°«°¬¯(46)Kinematic equations of vibration (first principal vibration) corresponding to first natural frequency 1Z is:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201515(1)P 111(1)H 111sin()sin()x A t x B t Z T Z T ­ °® °¯ (47)Kinematic equations of vibration (second principal vibration) corresponding to second natural frequency 2Z is:(2)P 222(2)H 222sin()sin()x A t x B t Z T Z T ­ °® °¯ (48)With theories of differential equations, general solution of free vibration differential Eq. (38) can be obtained from Eqs. (47) and (48):P 111222H 11112222sin()sin()sin()sin()x A t A t x A t A t Z T Z T J Z T J Z T ­®¯ (49)Eqs. (49) include four undetermined constants A 1, A 2, T 1, and T 2.When t = 0, the distances of hammer and pile from equilibrium position are all 0, viz. x P = 0, x H = 0. Substitute them into Eqs. (49), we have:1122111222sin sin 0sin sin 0A A A A T T J T J T ­®¯ (50)Take the derivative of Eq. (49) with t , we have:11222211122222cos()cos()cos()cos()t A t t A t Z Z T Z Z T Z J Z T Z J Z T ­®¯11xP A c11x H A (51)When t = 0, hammer ’s velocity x v H 0, pile ’s velocity x 0P . Substitute them into Eqs. (51), we have:111222*********cos cos 0cos cos A A A A v Z T Z T Z J T Z J T ­®¯ (52)From Eqs. (50) and (52), we can obtain:0012121122120,,()()v v A A T T Z J J Z J J(53)Substitute Eqs. (53) into Eqs. (49), we have motion equations of hammer and pile:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 20151600P 121122121020H 12112212sin sin ()()sin sin ()()v v x t t v v x t t Z Z Z J J Z J J J J Z Z Z J J Z J J ­° °®° ° ¯ (54)It can be noted that if soil ’s frictional resistance to pile is very small and is negligible, thenP k x 11Jx H J H H x m H H H § ¨©x m 1 and Z 2. Again, substitute it into Eqs. (46), we have J 1 and J 2. Substitute Z 1, Z 2, J 1, and J 2 into second equation of Eqs. (54), we have:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 2015171020H 1201112212sin sin sin ()()v v x t t tJ J Z Z Z Z J J Z J J(58)Take the second derivative of Eq. (58), we have:H m kx H k mx H H k Hmax x n1t P P 02sin F tZ (63)The maximal value of Eq. (63) is:D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201518max 0max,P 0k F F (64)The conclusion is the same as the conclusion drawn from Eq. (32). When 222t n SZ S(nis nonnegative integer), Eq. (64) is true. Hammer separates from pile after collision, hence 2t ZD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201519Assume m P = 1.56 kg, k H = k P = 3.6×105 N/m. Hammer ’s initial energy 08N mE remains unchanged, Change hammer weight and fall height. Hammer ’s impact force on pile can be calculated with Eq. (57), as illustrated in Figure 7.As mentioned above, negative impact force means hammer separates from cushion. It can be seen from Figure 7 that, for identical hammer impact energy, the bigger the hammer weight is, the smaller the hammer ’s impact force on pile will be, and the longer the impact time will last. When m H >m P (1.56 kg), viz. hammer weight is bigger than pile weight, hammer ’s impact force onpile remains bigger than 0.ANALYSES BASED ON MODEL TESTEquipment parts of the model test are shown in Figure 8(a), and assembly drawing is illustrated in Figure 8(b). Loose uniform sand, void ratio is 0.8㸪relative density D r = 45%㸪dry unit weight is 14.5 kN/m 3, pile ’s lower end just touches soil surface. Lift hammer to a certain height, and let it fall down freely and hit spring, then the pile will sink.Elastic Cushion TestHammer ’s initial energy is 08N m E , and m H = 1.04 kg, and m P = 1.56 kg, and spring stiffness k H = 3.6×105 N/m. An accelerometer attached to hammer is used to measure hammer ’s acceleration when hitting spring. Hammer ’s actual impact force on spring is indirectly measured, as illustrated in Figure 9. Because soil ’s stiffness coefficient k P is unknown, here let k P = 0, 180, 360, 540, 720, 900, 1260, 1440, 2000, 4000 kN/m and infinitely great. Substitute these values into Eq. (57), hammer ’s impact force on pile can be achieved, as illustrated in Figure 9. It can be seen that measured impact force is approximate to theoretical value. Especially when k P = 360 kN/m,D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201520the maximal impact force measured is nearly identical with theoretical value. From Eqs. (62) and (63), it can be calculated that the times when maximal impact forces occur is 0.00204 s and 0.00262 s respectively, as illustrated in Figure 9. It can be seen that the bigger the foundation soil ’s stiffness coefficient k P is, the later the maximal impact force will come, and the bigger the impact force will be.Keep hammer ’s impact energy unchanged, but change hammer weight. Measure the values of hammer ’s maximal impact force on pile, pile ’s penetration, and maximal acceleration of soilsurface ’s vertical vibration at 0.2 m horizontally from pile, as illustrated in Figure 10. Let k P = 360 kN/m, Hammer ’s maximal impact force on pile calculated with Eq. (57) is also illustrated in Figure 10. It can be seen that maximal impact force measured is approximate to theoretical value, and the force degrades with the increase of hammer weight, which shows that “heavy hammer and low drop ” can reduce impact force on pile head and lower probability of pile head damages. It can also be seen that with the increase of hammer weight, pile ’s penetration also increases, especially when hammer weight is very small. Increasing hammer weight can significantly increase pile ’s penetration, which conforms to the conclusions drawn by using energy and momentum conservation method, as illustrated in Figure 2. However, it can be seen from Figure 2 that, when m H /m p > 1, penetration will degrade with the increase of hammer weight, which is different from the conclusions drawn by using methods of vibration theories and model test. This is because energy and momentum conservation method assumes that hammer separates from pile after collision. However, the actual case is not the same as assumed, as can be seen from Figure 7. When hammer weight is bigger than pile weight, the two do not separate after collision, and impact force is bigger than 0 all along, which means that, when hammer weight is bigger than pile weight, assumption of energy and momentum conservation method is unreasonable. It canD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201521also be seen from Figure 10 that vibration of soil surface from 0.2 m of pile starts to weaken with the increase of hammer weight, which means that the lost energy causing soil surface ’s vibration degrades, and energy utilization efficiency is improved. Penetration of “heavy hammer and low drop” is bigger than that of “light hammer and high drop”.Hammer ’s initial energy 08N m E , and m H = 1.04kg, and m P = 1.56kg. Change spring ’s stiffness. Hammer ’s maximal impact force on pile, pile ’s penetration, and spring ’s maximal compression are measured, as illustrated in Figure 11. Let k P =3.6×105 N/m. The maximal impactforce calculated with Eq. (57) is illustrated in Figure 11. It can be seen that with the increase of spring stiffness, hammer ’s impact force on spring and pile ’s penetration also increase, but spring ’s maximal compression degrades. This is even more evident especially when spring has a relatively small stiffness. The conclusion conforms to the conclusion drawn from Eq. (17). It can also be seen that when spring has a relatively big stiffness, theoretical value of hammer ’s maximal impact force on pile is bigger than measured value, and the bigger the spring stiffness is, the bigger the differences between these two values will be. For example, if H k o f , from Eq. (57) we know that F o f , viz. if there is no cushion, impact force will be infinitely great, which does not conform to reality. This is because Eq. (57) assumes that hammer and pile are all rigid bodies while actuallythey are not. When spring stiffness is very big, impact force will be very big. In this case, elastic deformation of hammer and pile cannot be neglected.Plastic Cushion TestAbsolute plastic materials do not exist. Moreover, materials with strong plastic properties present great difficulty in practical engineering use, hence elastic cushion or elastic-plastic cushion (such as plank) is widely used in engineering. Cotton cloth is used as cushion in this model test.D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201522The cotton cloth has a thickness of 50 mm and is fastened to the tray of pile. Hammer ’s initial energy is 08N m E . Hammer ’s maximal impact force on pile and pile ’s penetration, when given different hammer weights, are illustrated in Figure 10. It can be seen that, with the increase of hammer weight, the maximal impact force the pile head receives will degrade, but penetration will increase. The conclusion conforms to the conclusion when using elastic cushion. It can also be seen that the maximal impact force when using plastic cushion is bigger than that of when using elastic cushion, but penetration is smaller all along. It shows that relatively small impact force canachieve relatively great penetration when using elastic cushion, hence energy utilization efficiency is higher. Hammer weight is 1.04 kg, other factors are the same as the factors mentioned above. Repeat hammering test. Relationship between the maximal impact force and blow counts is illustrated in Figure 12. It can be seen that, compared with using spring as cushion, pile receives a greater maximal impact force when using cotton cloth as cushion. With the increase of blow counts, the maximal impact force increases with cotton cloth being gradually compacted. The increase of impact force is especially significant at the beginning of hammering when cotton cloth is significantly compacted. However, spring takes no significant changes, and impact forceremains almost unchanged. In practical engineering, with the increase of blow counts, plank as cushion is gradually compacted and becomes hardened, and its color turns black. The plank may even get scorched due to hammering, thus losing its protecting function for pile head. In this case, the plank needs to be changed or replaced with elastic cushion.CONCLUSIONSThe following conclusions can be drawn from this study.D o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201523 (1) If hammer ’s impact energy remains unchanged, penetration increases with the increaseof hammer weight and cushion stiffness; the impact force the pile head receivesdegrades with the increase of hammer weight, but increases with the increase ofcushion stiffness.(2) The time the pile head receives impact force degrades with the increase of elasticcushion stiffness, but increases with the increase of hammer weight. When hammerweight increases to a certain weight, hammer will not rebound and depart from pilehead.(3) Hammer ’s impact force on pile increases with the increase of foundation soil ’s stiffness.(4) Compared with elastic-plastic cushions such as planks, elastic cushion can achievegreater penetration with relatively small pile head impact force, hence protectinghead from being damaged. Cotton cloth cushion gradually gets compacted with theincrease of blow counts, and impact force the pile head receives increasesgradually.(5) When foundation soil ’s stiffness is 0 or infinitely great, the analytic formula of maximalimpact force the pile head receives obtained by using energy and momentumconservation method is the same as that of using method of vibration theories. Themaximal impact force and impact force changes over time obtained from methodof vibration theories coincides well with those of using model test method.(6) Energy and momentum conservation method assumes that hammer separates from pileafter collision when using elastic cushion, but the actual conditions as proved byusing methods of vibration theories and model test are not the case. When hammerD o w n l o a d e d b y [J i c h e n g W A N G ] a t 21:22 29 M a y 201524weight is bigger than pile weight, hammer does not separate from pile aftercollision. Penetration achieved by using energy and momentum conservationmethod is inaccurate.(7) When cushion stiffness is relatively small, theoretical value obtained by using methodof vibration theories coincides well with the value measured by using model testmethod. However, when cushion stiffness is very big, the maximal impact forceobtained by using method of vibration theories has certain difference with the valuemeasured by using model test method. This difference tends to increase with the increase of cushion stiffness. This is because vibration theories assume that hammer and pile are all rigid bodies, but when cushion stiffness is relatively big, impact force is also big. In this case, the deformation that occurs to hammer and pile cannot be neglected, hence differences exist with rigid body assumption. References Deeks, A. J., and M. F. Randolph. 1993. Analytical modelling of hammer impact for pile driving. International Journal for Numerical and Analytical Methods in Geomechanics 17 (5):279–302. doi:10.1002/nag.1610170502Deeks, A. J., and M. F. Randolph. 1995. A simple model for inelastic footing response to transientloading. 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