白垩土的蠕变实验

Experimental Investigation on the Time Dependent Behaviour of a Multiphase ChalkGrégoire Priol1,Vincenzo De Gennaro2,Pierre Delage2,and Thibaut Servant21Geotechnical Department,NTNU,Trondheim,Norwaygregoire.priol@ntnu.no2Ecole Nationale des Ponts et Chaussées,Paris(CERMES,Institut Navier),6–8 av.B.Pascal,F–77455Marne–la–Vallée cedex2,Francevincenzo.degennaro@enpc.fr,pierre.delage@enpc.fr,servantt@eleves.enpc.frSummary.A series of high pressure oedometer compression tests were carried out on samples of Lixhe chalk(Belgium)containing various porefluids:water,air(dry sample),oil(Soltrol)and oil/water under a controlled suction of200kPa.Strain curves with respect to time of tests carried out under a constant load were exam-ined in a purpose of investigating the time dependent behaviour of chalk.A simple empirical exponential law able to account for the combined effects of stress and suction is proposed.Experiments show that it provides satisfactory results to pre-dict a feature of multiphase chalk behaviour that is important in the study of the behaviour of oilfields.Key words:chalk,multiphase,creep,water weakening,suction,collapse IntroductionInvestigations carried out on multiphase chalk(i.e.chalk that contains vari-ous non miscible porefluids)as for example oil reservoir chalk(with gas,oil and water)or unsaturated chalk(with air and water)have evidenced a typ-ical water weakening effect under water infiltration.Water weakening leads to:(i)instantaneous deformation(collapse)under constant load,(ii)strength reduction and(iii)increasing compressibility(see among others:Masson1973, Schroeder et al.1998,Gutierrez et al.2000,Lord et al.2002,De Gennaro et al. 2004).Research on oilfield chalks has shown that important physico-chemical interactions exist between water,oil and chalk involving collapse and time dependent behaviour(e.g.Newman1983,Hellmann et al.2002,Risnes et al.2005).Delage et al.(1996)first suggested the reliability of the mechanical framework commonly used for unsaturated soils to study the coupled mechan-ical response of multiphase chalks provided oil is considered as a non wetting162G.Priol et al.fluid(like air in unsaturated soils).Instantaneous collapse during water injec-tion in oil reservoir chalk was thus considered as a typical case of collapse dueto wetting under constant load(Pasachalk2001,2004).In this paper,results from oedometer tests performed on a chalk saturatedwith various porefluids(oil,water and air)are presented.Particular atten-tion has been paid to the time dependent behaviour of chalk that has beeninvestigated by running creep tests.The effect of suction on the time depen-dent behaviour of chalk is investigated and the relevance of a simple empiricalcreep law accounting for suction effects is demonstrated.Tested Material and Experimental TechniquesThe chalk specimens used in this study come from blocks of an outcrop chalkextracted near Lixhe(CBR quarry,Belgium).This chalk originates from thesame geological unit as some oil reservoir chalks of the North Sea(Ekofisk).Lixhe chalk is composed of almost pure calcite(with less than1%of silica)with an average porosity n∼=43%.Oedometer tests were carried out on chalk specimens that were saturated with water and/or Soltrol170(PhillipsPetroleum Company).Soltrol is a non polar organic liquid not miscible towater used as an oil analog.Oil–water–chalk interaction is believed to bemainly dependent on the capillary effects in the water menisci that are locatedin the small intergranular spaces close to grain contacts.By defining the twopressures u o and u w as the oil and water pressures respectively,the oil/watersuction(called suction in the following)is defined as s=u o−u w(to compare to the air–water suction in unsaturated soil s=u a−u w,being u a the air pressure).Four standard step loading oedometer tests have been performed on sam-ples of38mm diameter and20mm high with total tests duration ranging fromsix months to more than one year.Tests were respectively performed on a wa-ter saturated sample,an oil saturated sample,a dry sample and the last testwas carried out under controlled suction using the osmotic technique(Kassiffand Ben Shalom1971,Delage et al.1992,Dineen and Burland1995).Thedry sample was obtained after a heating period of24hours at105◦C.Basedon the retention properties of Lixhe chalk a suction of200kPa was selected,corresponding to a degree of water saturation S rw of about30%.Void Ratio–Time RelationshipIn saturated soils,compression strains in oedometer tests are due to both porepressure dissipation and creep(respectively primary and secondary consolida-tion).In a multiphase chalk with two porefluids,compression affects the porepressures and strain stabilisation corresponds with suction equilibration un-der the applied mean net stress(σ v=σv−u o).In saturated soils,there is stillInvestigation on the Time Dependent Behaviour of a Multiphase Chalk 163020*********TIME (d a y s )8818 Fig.1.(a )Consolidation curves under a suction equal to 200kPa;(b )Analysis of the void ratio-time relationship during consolidationno agreement how to distinguish the effect of viscous strain to that of excess pore pressure dissipation during primary consolidation (Mesri and Choi 1985,Leroueil 2006).Results from compression tests on two chalks (De Gennaro et al.2005,Priol 2005)showed that neither Casagrande’s nor Taylor’s methods were helpful to identify any primary consolidation.Indeed,it seems likely that the low compressibility of the soil skeleton due to intergranular bonding ef-fect together with the relatively high chalk permeability (about 10−8m/s)are sufficient to prevent excess pore pressure generation (given that the amount of the applied total load instantaneously transferred to pore water pressure decreases when the drained bulk modulus increases,Biot 1941).Indeed,the results of the suction controlled oedometer test (s =200kPa)presented in Fig.1a show that,from the early beginning of the test,the curves giving the time dependent strain look very similar to creep curves.Hence,the time dependent volumetric strain of chalk should be essentially due to creep with the solid skeleton continuously settling under zero excess pore pressure.This result should obviously be confirmed by pore pressure measurements during initial loading.The examination of a typical consolidation curve is presented in Fig.1b in terms of normalised void ratio e/e o plotted as a function of the elapsed time in a linear scale.This allows defining the following evolution law:e e oi =βi t αi (1)where e oi is the void ratio at the beginning of loading stage i .βi represents the instantaneous strain whereas αi controls the shape of the curve in Fig.2,the164G.Priol et al.Fig. 2.(a)Compression curves of Lixhe chalk at various saturation states;(b) Influence of stress level and suction on the creep coefficientαhigherαi the larger the time dependent strain.Typical values ofαi are be-tween0(no time dependency)and0.02.Note that equation(1)bears strong similitude with the common interpretation in term of creep coefficient Cαe when using a logarithmic time scale(Cαe=Δe/Δlog t).As shown in Fig.1b, the interpolation given by equation(1)satisfactorilyfits the experimental data.This was verified,with minor exceptions,for all the analysed consolida-tion curves.The creep strain rate evolution law presented in dotted line in Fig.1b has been obtained by deriving equation(1)with respect to time.Good agreement is als observed with experimental data.This allows identifying the creep rate at each creep phase(right axis in Fig.1b).Stress-Void Ratio RelationshipIn the absence of any apparent pore pressure dissipation phase,it was neces-sary to adopt a strain criterion to define the stress strain curves.In the case of isochronous time dependent behaviour(i.e.only dependent of the loading duration t c),the strain after a loading duration t c can be adopted(Bjerrum 1967).In the alternative case of isotach behaviour(i.e.only dependent on the strain rate˙ε),the strain adopted corresponds to a given creep rate(˙εc) (Šuklje1957in Leroueil2006).This second approach was adopted here with ˙εc=10−10s−1.This value was chosen based on the accuracy limit of the LVDT used to measure the vertical displacement.The values of e determined at each loading stage with this approach correspond to given couples ofαi andβi values.Investigation on the Time Dependent Behaviour of a Multiphase Chalk165 The compression curves obtained are presented in Fig.2a.Like in unsat-urated soils,the higher the suction(i.e.the lower the degree of saturation in water S rw),the higher the yield stress,in good agreement with the wa-ter weakening effect.In contrast to unsaturated soils,the plastic compression modulus appears to be slightly suction dependent.Note however that it is smaller in the case of the dry sample.This shows that thefluid chemistry and the chalk wettability tofluids(oil,water,air)influence the mechanical behaviour.Creep EvolutionSince relation(1)is valid for all the saturation states,theαi andβi coeffi-cients have been assessed at all the loading stages of the four tests of Fig.2a. The values of the creep coefficientsαi are plotted with respect to the corre-sponding applied vertical stress in Fig.2b.A careful examination of the plots (between5and10MPa)shows that they are bilinear with a change in slope that approximately corresponds with the yield stress observed in Fig.2a(not shown here in more detail for lack of space).Above5MPa,αi increases with increased stress and decreased suction,starting from a fully water saturated state(s=0and S rw=100%),passing through a partially saturated state (s=200kPa and S rw=30%)up to a dry state.This is again consistent with the water weakening effects discussed in the previous sections.Relatively few creep tests on unsaturated materials have been presented in the literature.Similar effects of suction and stress on creep were also doc-umented from oedometer tests carried out on a partially saturated rockfill (Alonso et al.2005).However,the generalization of thesefindings to all pos-sible stress states is an open issue.The effect of water injection in a chalk sample saturated with oil under a constant vertical stress of19.8MPa is shown in Fig.2b.This situation is somewhat similar to that prevailing during waterflooding,a technique of enhanced oil recovery used in the North Sea.The sample was injected under a10kPa water pressure and it exhibited a collapse that occurred within a few hours.A more pronounced creep characterised by aαi coefficient of0.0164was then observed.Starting from the oil saturated plot of Fig.2b with aαi value of 0.0047at point A,the path followed in this diagram leads to point B(0.0164). It is observed that point B is located close to the s=200kPa line.This is related to the residual saturation in oil(S ro=30%)that probably has an effect on the macroscopic creep behaviour of the chalk through the physics of the intergrains bonds.In other words,there is apparently a difference between two samples at zero suction between a fully saturated sample and a sample with a residual oil content.Hysteresis effects may also play a role in this difference.166G.Priol et al.ConclusionThe experimental data presented in this paper were aimed at showing some effects of suction on the compressibility and on the time dependent behaviour of a sample used as a model of a multiphase oil reservoir chalk.Some simi-larities with the behaviour of unsaturated soils have been observed,the non wettingfluid in chalk being oil as compared to air in unsaturated soils.Chalk strength is increased by increasing the suction level,i.e.by decreasing the water content.Time dependent strains have been related to the changes in water saturation by means of the oil–water suction.Some aspects of the wa-ter weakening effect in chalk,including time effects,have been considered in a more comprehensive framework based on the use of the oil-water suction as an independent stress variable capable to account for thefluid-rock interactions. AcknowledgementsThe work carried out was conducted in relation with the European Project Pasachalk2(EC contract ENK6–2000–00089)in the framework of thefirst author’s PhD thesis that was supported by a grant from Ecole des ponts,Paris. 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