PORE PRESSURE CHARACTERISTICS IN ISOTROPIC
Journal of Marine Science and Technology, Vol. 24, No. 1, pp. 19-25 (2016 )DOI: 10.6119/JMST-016-0125-319PORE PRESSURE CHARACTERISTICS INISOTROPIC CONSOLIDATED SATURATED CLAYUNDER UNLOADING CONDITIONSShu-Wang Yan1, Jing-Jing Zhang1, Ying-Hui Tian1, 2, and Li-Qiang Sun1Key words: saturated soft clay, uplift, negative excess pore pressure,modified Cambridge model, triaxial extension test.ABSTRACTWhen foundations, such as caissons, spudcans, and mudmats, are pulled out from the saturated soft clay foundation,negative excess pore pressure will develop in the interfacebetween the base and the soil. This phenomenon will significantly increase the uplift force. Therefore, estimating thedeveloped negative excess pore pressure in the interfaceunder unloading conditions is important. The developmentof excess pore pressure was investigated based on the triaxialextension test under isotropic consolidation condition. Themethod of using the modified Cambridge model to predictthe excess pore pressure was programmed and has beenproven to be feasible. By associating Henkel’s theory in p-qspace, the generation mechanism of negative pore pressurewas revealed. The research indicates that excess pore pressure is initially negative and then becomes positive in triaxialextension test under isotropic consolidation. The generatedexcess pore pressure can be divided into two parts. The firstpart generated from the change in the mean total stress isnegative, whereas the second part generated from the changein deviatoric stress is positive. However, these two parts areunbalanced. Research results provide theoretical basis forthe development of excess pore pressure in soft clay toanalyze the pull-out of structure and the excavation offoundation pit.I. INTRODUCTIONAfter completing construction, certain offshore foundationsPaper submitted 09/29/15; revised 10/26/15; accepted 01/25/16. Author forcorrespondence: Li-Qiang Sun (e-mail: slq0532@126.com).1State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University, Tianjin 300072, China.2Center for offshore foundation systems, The University of Western Australia,Perth 6009, Australia.must be decommissioned and removed from the seabed tocomply with environmental regulations. In the removal procedure, suction develops at the interface between the foundation base and the underlying clay soil. In the extraction test ofspudcans, the increase in base suction is established to be thekey contributor for the larger breakout force (Purawana et al.,2005). On soft soil, removing mudmats during maintenanceor decommissioning is difficult and costly because of thesignificant suction that develops at the mudmat–soil interface(Chen et al., 2012; Li et al., 2014). Suction is an importantpart of uplift capacity. Therefore, the suction generationmechanism and the calculation method for the uplift analysisof bottom-supported foundation in saturated soft clay aresignificant for offshore design guidelines.The change of pore water pressure is determined by theexternal load. Skempton (1954) proposed the relationshipbetween excess pore pressure and total pressure in the axisymmetric stress situation, and this theory is widely used inthe engineering calculation. Pore pressure coefficient can beeasily determined through triaxial test. However, on the onehand, pore pressure coefficient A is constantly changing as soilstress state varies, which is inconvenience in practical application. On the other hand, this theory disregarded the influence of the intermediate principal stress. Henkel (1966)proposed a pore pressure calculation method generalized togeneral three-dimensional stress state. This method has a fewadvantages, such as considering the shear dilatancy and definite physical meaning. Zhou (2002) presented a method topredict excess pore pressure in triaxial extension test usingmodified Cambridge model, but the negative pore pressure isignored when analyzing pore pressure characteristics. Triaxialcompression and tension tests were first modeled by Li et al.(2015) to develop a rigorous understanding of the pore pressure responses, but lack test evidence.In the present study, the development of excess pore pressure was investigated based on the triaxial extension test insaturated clay under isotropic consolidation condition. Themodified Cambridge model was used to simulate triaxial extension test to find a method to predict pore pressure. Thegeneration mechanism of negative excess pore pressure wasthen analyzed based on Henkel’s theory.
Journal of Marine Science and Technology, Vol. 24, No. 1 (2016 )20Table 1. Parameters of Tianjin soft clay.Displacement sensorParameterPressure sensorCell pressure controllerRubberpistonTriaxialspecimenBack pressure controllerVolumetric apparatusBaseFig. 1. Stress path triaxial apparatus.Valueplastic index, Ip23.7Liquid limit, wL %46.5Specific gravity, Gs2.73Coefficient of consolidation cv/(m2/year)42.5Coefficient of permeability, k/(m/s)3.0 10-8Void ratio at p0 1 kPa on critical state line, e01.22Elasticity modulus E/MPa11Poisson's ratio, 0.3Slope of normally consolidated line in e – ln p0 space, λ0.15Slope of swelling and recompression line in e – ln p00.03space, κSlope of critical state line in p -q space, M0.658II. TRIAXIAL EXTENSION TESTAccording to the unloading path, triaxial extension test isdivided into relief triaxial extension (RTE), common triaxialextension, and average stress p for constant triaxial extension(Zhang and Yan, 2004). When foundation is extracted, thebottom soil of foundation is in the unloading state in whichcell pressure is constant and the vertical stress is reduced. Thequestion of foundation extraction can be approximatelyequivalent to RTE.1. Test ApparatusFig. 1. shows the sketch of the stress path triaxial apparatus,which is composed of a cell pressure controller, a back pressure controller, and a triaxial test chamber. The back pressurecontroller is connected to a volumetric apparatus that is usedto measure volume deformation. The triaxial specimen is installed in the triaxial test chamber. The top of the triaxialspecimen is fixed through the rubber piston connecting loading cap and loading rod, whereas the bottom can be activatedby adjusting the rigidity base. In addition, the apparatus isequipped with the displacement sensor and pressure sensor onthe upper portion of the chamber, which are used to measurethe axial deformation and axial deviatoric stress.2. Sample PropertiesThe soft clay used in this study was constituted from clay inTianjin Binhai New Area. Undisturbed soil sample wascoated by iron bucket and was then sealed with wax to preventmoisture loss. The properties of the soft clay have been determined by geo-technical testing, and are listed in Table 1.3. Test ProcedureIsotropic consolidation pressures are 100, 200, and 300 kPa,and the test is subject to SL237-1999 Specification of Soil Test(China, 1999). The test steps are as follows:1) Soil Sample PreparationAccording to the Specification of Soil Test and the requirements of stress path triaxial apparatus, triaxial specimen sizeof 7 cm in diameter and 14 cm in height is determined. Undisturbed soil sample is cut into specified size, and the weightquality of triaxial specimen is used to measure the density.2) Soil Sample SaturationSaturation process is divided into two steps. The first stepis vacuum saturation conducted in airtight container. Qualitycan be repeatedly weighed after this step to evaluate the uniformity of soil sample. Triaxial specimen is then installed intriaxial test chamber, and the method of back pressure saturation is adopted to fully saturate and detect saturability simultaneously. A 95% saturation is used as back pressure saturatedtermination condition.3) Isotropic ConsolidationCell pressure and back pressure are slowly applied on thetriaxial specimen. These pressures are made equal to theconsolidation pressure, also called the effective cell pressure.Under current stress state, saturated soil samples will be isotropically consolidated, while excess pore pressure dissipatesover time. The degree of consolidation reaches 97%, whichdenotes the end of consolidation.4) RTERTE is applied using strain control, and unloading shearstrain rate is 0.05%/min. The test records are shown in Table 2.III. THEORETICAL PREDICTION METHODCambridge model is based on a large number of experiments in the normal consolidation of clay and weakover-consolidated clay, including isotropic consolidation andexpansion test and the triaxial drained and undrained tests ofdifferent consolidation pressures. Roscoe and Burland (1968)have modified Cambridge model and is referred to as themodified Cam clay (denoted as MCC hereafter) constitutivemodel, in which yield surface is modified to oval. In the present study, MCC constitutive model was used to simulate RTE
S.-W. Yan et al.: Pore Pressure in Clay under Unloading Conditions21Table 2. Test records.Test numberConsolidationpressure P0 /kpaDensity /(kg m-3)SaturationSr /%Consolidationtime T/hDegree ofconsolidation Ut /%Unloading ratev 5.197.999.198.60.050.050.05and predict excess pore pressure. This task is conducted tosolve the effective stress path such that pore pressure can becalculated according to the principle of effective stress.Completely undrained situation is assumed, 2 3; and thestrain of each computing step in the direction of 1 is known.volumetric strain increment and plastic shear strain incrementcan be calculated.Elastic deformation can be determined by the Hooke’s law.The constitutive relation is expressed asp dp K ( d v d v ) p dq 3G ( d s d s )1. Theoretical ArithmeticThe equation of Modified Cambridge model yield surface is22 p q p f p , q, pc 0 pc pc Mpc (1)where K bulk modulus; G shear modulus; s shearingstrain.Eq. (1) is formulated using total differentiation and is takeninto Eq. (4). Therefore, d can be calculated aswhere p effective mean principal stress; q generalizedshear stress; pc hardening parameter; M slope of criticalstate line, ( 6sin /(3 sin ), where effective internalfriction angle, the denominator of triaxial compression takingminus sign, take plus triaxial extension).For brevity, p and q are expressed as f fdq dp q 1 pd 2H p f f 2 p q (2)Hp where η shear compression ratio, η q /p ; o 1/2[1 (η/M)2].Hardening rule is 1 eo p v pc exp (3)where pv plastic volumetric strain; eo initial void ratio; slope of normally consolidated line, and k slope of swellingand recompression line.If the associated flow rule is adopted, then the plastic potential function is equal to the yield surface function. Theplastic potential flow theory is expressed asd vp d f p fd d qps(4)(5)where plastic shear strain. If d is known, then plasticps(7)wherep o pcq o pc(6)1 e0 pc 1 k 2 m21 o 2 o ; 241 1 m o 2 o 2 .2 M Take Eq. (7) into Eq. (4) and Eq. (5). Plastic body strain increment and the plastic shear strain increment can be expressed as1 p d v H ( dp n p dqnq ) n pP d p 1 ( dp n dqn ) npqq sHP wherenp f p 2 f f p q 2 1 1 o ; 2 m (8)
Journal of Marine Science and Technology, Vol. 24, No. 1 (2016 )nq f q2 f f p q 22 01 1 o .m M -140-260p’/ kPa180 240300360Critical state lineM 0.658p0 100 kPa Testp0 200 kPa Testp0 300 kPa TestFig. 2. Critical state of triaxial extension test.(9) f f p p 22 f f p q f f q q 22 f f p q According to the principle of effective stress, pore pressureincrement is expressed asdu dp dp 120-80-200Take Eq. (8) into constitutive equation Eq. (6). Thus,3Gnq d s ( Kn p ) dp H p Kn 2p 3Gnq2 3Gnq d s dq 3G (d s H Kn 2 3Gn 2 nq )ppq 60-20q/ kPa22(10)where p total mean stress and du excess pore pressureincrement.2. Realization ProcessUnder completely undrained conditions, the total volumestrain is zero. The shear strain increment is expressed as 222 12[ d 1 d 2 d 2 d 3 d 3 d 1 ] 2 d s 3 d d d 023 1(11)If 2 3, then d 2 d 3. Therefore, d s d 1, whichmeans the generalized shear strain increment is equal to theprincipal strain increment.According to 2.1, excess pore pressure increment can becalculated, if each calculation step strain increment d s isknown. The specific steps are as follows:(1) Determine the Cambridge model parameters M, , k, andsoil property parameters eo, K, G;(2) Assume an initial condition q 0, p p0 (the consolidationpressure noted by p0), dε 0, total strain s, total steps N;(3) In every calculating step, the strain increment d s per stepequals to s /N. Then, dq, dp can be calculated using Eq. (9);(4) Isotropic consolidation soil is in the initial yield surface atfirst, and then the stress state under unloading is constantly changing along with yield surface affected byhardening rule. To ensure stress points on the yield surface in the entire calculation process, stress has beenamended along the yield surface normal direction (Gao etal., 2010). Correction formula is as follows:(12)where p modified variable effective mean stress and q modified variable deviatoric stress.(5) Considering the correction formula of stress, calculatepore pressure increment du, cumulative excess porepressure u, deviatoric stress q, effective mean stress p ,and total mean stress p;(6) In every calculation step, conduct cycle steps (3) to (5)until n N.IV. COMPARISON OF TEST AND THEORYAccording to triaxial extension test, the development ofexcess pore pressure under unloading condition was obtained.The modified Cambridge model was used to simulate triaxialtests and to confirm the feasibility of pore pressure predictionmethod. To easily distinguish the extension test and the compression test in the coordinate system, the generalized shearstress q in the compression test is represented in positive halfshaft, whereas in negative half shaft in the extension test.1. Stress PathThree triaxial extension tests were consolidated in pressures 100, 200, and 300 kPa. Effective stress paths were plotin p-q space, in which the critical state line can be determined,as shown in Fig. 2. The critical state line slope is the Cambridge parameter M, which is 0.658.Effective stress path of the test and theory are compared, asshown in Fig. 3. This figure shows that the values of both testand theory are very close. In other words, the two curves ofeffective stress path coincide basically. Shear stress predictedby modified Cambridge model is slightly lower than that of the
S.-W. Yan et al.: Pore Pressure in Clay under Unloading Conditions2040p’/ kPa6080100120p0 100 kPa Theoryp0 100 kPa Testp0 200 kPa Theoryp0 200 kPa Testp0 300 kPa Theoryp0 300 kPa Testq / kPa-2030-4025Inicial yeild surface20Critical state line-6015p0 100 kPaTheory(a) Consolidation pressure at p0 100 kPa10p0 100 kPa Test-8050p’/ kPa004080120160200240-5-4-3-2Axial strain εs /%-10-5Nomalisted pore pressure Δu/p0 /%0023Fig. 4. Development of excess pore pressure.q / kPa-40-80Inicial yeild surfaceCritical state line-120p0 200 kPaTheory(b) Consolidation pressure at p0 200 kPap0 200 kPa Test-160p’/ kPa0060120180240300360q / kPa-60-120-180-240Inicial yeild surfaceCritical state linep0 300 kPaTheory(c) Consolidation pressure at p0 300 kPap0 300 kPa TestFig. 3. Effective stress path test of triaxial extension test.test, but the error is within 4%. In theoretical predictionmethod, the excess pore pressure equals to the differencebetween total stress and effective stress. Hence, the closer thetheoretical stress path compared with experimental, the moreaccurate the predicted excess pore pressure.2. Development of Excess Pore PressureTo facilitate the analysis of the development of pore pressure under different consolidation pressures, excess porepressure was normally processed. The comparison of excesspore pressure between triaxial extension test and theoreticalprediction with axial strain is shown in Fig. 4. The development of pore pressure is consistent and close in test and theory,and the predicted error is within 6.3%. Excess pore pressure isnegative in the early unloading and increases with the development of the strain. The negative pore pressure increases to amaximum, and then decreases gradually and develops positivevalue after zero. Finally, the pore pressure achieves the positive maximum number and stops.As shown in Fig. 4, under consolidation pressures of 100,200, and 300 kPa, the maximum values of negative porepressure are 2, 5, and 7.5 kPa in the test results, respectively.The maximum negative value increases with varying consolidation pressure. Meanwhile, its corresponding strain valuealso increases. Notably, the theoretical prediction methodproposed in this study can also predict this rule.The comparison of the test and theoretical calculation onstress path and the development of the pore pressure indicatethat this prediction method is feasible in uplift question offoundation.V. GENERATION MECHANISM OF POREPRESSURE IN TENSIONBoth test and theory results demonstrate that excess porepressure is negative in the early unloading state, and thengradually becomes positive with the development of axialstrain. Combining with the modified Cambridge model(Roscoe and Burland, 1968) and Henkel pore pressure theory(Henkel and Wade, 1966), this change rule and the generationmechanism of excess pore pressure in unloading state can beexplained.In p-q space, p and q can be noted by principal stress 1, 2, 3: p 1 2 3 / 3 1222[ 1 - 2 2 - 3 3 - 1 ]1/ 2 q 2 (13)When 2 3, the generalized shear stress is given by q 1 – 3 . When isotropic consolidation has been completed,
Journal of Marine Science and Technology, Vol. 24, No. 1 (2016 )240.6Final yeild surfaceTotal stressEffective stress0.4Critical state line6 sin ϕ′M 3 - sin ϕ′q/p00.2Inicial yeild surface0.0ACritical state line6 sin ϕ′M 3 sin ϕ′-0.2B-0.4-0.60.0CompressionΔu ΔuqΔupC0.20.40.60.8pʹ/p0 or p/p01.0Tension1.21.4the critical state line, that is, the damage state points. In p-qspace, total stress and effective stress value difference is excess pore pressure, noted by u. The excess pore pressuresgenerated from the change in the mean total stress ( up) can bedetermined by Eq. (17), whereas that generated from thechange in deviatoric (or shear) stress ( uq) can be calculatedby Eq. (18). In tension, up is negative, whereas Δuq is positive. Hence, these parts partially cancel each other. Thiscancellation results in the generation of negative excess porepressures in section AB of tension ( up uq), but positiveexcess pore pressures in section BC of tension ( up uq).This observation suggests the generation mechanism of negative pore pressure and why excess pore pressure changes fromnegative to positive in this study.Fig. 5. Generation mechanism of pore pressure in tension state.VI. LIMITATIONS OF THE STUDYq 3( p p0 )(14)which means that q 0 and p p0, axial unloading test isconducted in undrained conditions along with constant cellpressure. The total stress path can be expressed asAccording to Henkel and Wade (1968), the generated excess pore pressures can be divided into two parts: the first partis generated from the change in the mean total stress, and thesecond part is generated from the change in deviatoric (orshear) stress. Henkel’s theory is as follows: u a12 1 2 3 0 [ 1 2 33 2 3 3 1 ]1/ 222(15)Taking formula (13) into the formula (15) obtains u p aq u p uq(16)where p excess pore pressure generated from the change inthe mean total stress, noted by up ; a q excess pore pressuregenerated from deviatoric stress, noted by uq.Considering u p p p0(17)According to the principle of effective stress u p – p , uq p0 p (18)Fig. 5 presents the total and effective stress paths for triaxialcompression and tension from the initial isotropic conditions.Point A denotes the stress state after the completion of isotropic consolidation, wherein the shear stress is zero. Point Bis the intersection of effective stress path and total stress path,whereas point C is the intersection of effective stress path andMany Centrifuge model tests only obtain negative porepressure under unloading state (Purawana et al., 2005; Chen etal., 2012; Li et al., 2014a; Liu et al., 2015). In this paper, theprocess of pore pressure existed from negative to positive.The present study focuses on the isotropic consolidation state,whereas the stress state of natural foundation is for K0 consolidation. This phenomenon maybe influenced the differenceof these tests. Several parameters including uplift velocity,loading history, and soil degree of consolidation influence theexcess pore pressure variation (Gourvenec et al., 2009; Li etal., 2014b; Li et al., 2014c). However, a more advanced research is necessary to realistically simulate the stress state andto explore the influencing parameters of excess pore pressure.VII. CONCLUSIONSThis paper presents the results from triaxial extension test atthe initial isotropic conditions and focuses on the developmentof excess pore pressure with strain. Furthermore, modifiedCambridge model was used to simulate RTE and to predictexcess pore pressure. Hence, the feasibility of this predictionmethod has been confirmed through comparing theory prediction results and test results. Based on Henkel’s theory, thegeneration mechanism of negative pore pressure was determined and the change of pore pressure from negative to positive was revealed. The following conclusions are drawn:(a) In unloading condition, the shear stress generates positivepore pressure, whereas the contribution of the total meanstress increment to the excess pore pressure is negative.Therefore, the generation of negative excess pore pressurein the unloading condition is due to that these parts canincompletely cancel each other;(b) Under isotropic conditions, excess pore pressure initiallypresents the negative and then becomes positive. Thehigher the consolidation pressure is, the greater themaximum negative pore pressure and corresponding axialstrain. Meanwhile, modified Cambridge model can efficiently predict this rule.
S.-W. Yan et al.: Pore Pressure in Clay under Unloading ConditionsThis study has realized the development of excess porepressure in isotropic condition and has validated the use of theMCC constitutive model. The research results provide theoretical basis for the development of excess pore pressure insaturated soft clay to analyze uplift of foundation and excavation of foundation pit. Further work is in progress bothnumerically and experimentally (i) to develop a more realisticconsolidation (k0 1) to investigate the effect to excess porepressure, and (ii) to thoroughly explore the development ofexcess pore pressure with various influencing factors underunloading condition.ACKNOWLEDGMENTSThis project is supported by the National Natural ScienceFoundation of China (Project number: 41272323) and the KeyProjects of Science and Technology Support Plan in Tianjin(Project number: 11JCZDJC23900).REFERENCESChen, R., C. Gaudin and M. J. Cassidy (2012). Investigation of the verticaluplift capacity ofdeep water mudmats in clay. Can. Geotech. J. 49(7),853-65.Guan, Y., F. Gao, W. Zhao and J. Yu (2010). Secondary development ofmodified Cambridge model in ANSYS software. Rock and soil mechanics 31(3), 976-981. (in Chinese)Gourvenec, S., H. E. Acosta-Martinez and M. F. Randolph (2009). Experimental study of uplift resistance of shallow skirted foundations in clayunder transient and sustained concentric loading. Géotechnique 59(6),525-537.Henkel, D. J. and G. H. Wade (1966). Plane strain tests on a saturated re-25mouldedclay. Proc. ASCE 92 (sm6).Li, X., C. Gaudin, Y. Tian and M. J. Cassidy (2014a). Effect of perforations onuplift capacity of skirted foundations on clay. Can. Geotech. J. 51(3),322-331.Li, X., C. Gaudin, Y. Tian and M. J. Cassidy (2014b). Rate effects on the upliftcapacity of skirted foundations on clay. Proceedings of 8th InternationalConference on Physical Modelling in Geotechnics, Perth, Austrilia,473-479.Li, X., Y. Tian, M. J. Cassidy and C. Gaudin (2014c). Sustained uplift ofskirted foundation in clay. Proceedings of the ASME 2014 33rd International Conference on Offshore Mechanics and Arctic EngineeringOMAE, Sanfracisco, US., V003T10A006-V003T10A.Li, X., Y. Tian, C. Gaudin and M. J. Cassidy (2015). Comparative study of thecompression and uplift of shallow foundations. Computers and Geotechnics 69, 38-45.Liu, Z., C. Y. Zhou and Y. Q. Lu (2015). Dynamic evolution model and criticalfailure criterion of the instability evolution for submarine tunnel system.Journal of Coastal Research Special Issue No 73, 776-780.Ministry of Water Resources of the People's Republic of China (1999).SL237-1999 Specification of soil test. China Water&Power Press, Beijing,China. (in Chinese)Purawana, O. A., C. F. Leung, Y. K. Chow and K. S. Foo (2006). Influence ofbase suction on extraction of jack-up spudcans. Géotechnique 55(10),741-753.Roscoe, K. H. and J. B. Burland (1968). On the generalized stress-strainbehaviour of wet clay. Engineering Plasticity, edited by CambridgeUniversity Press, Ville de Cambridge, England, 535-609.Skempton, A. W (1954). The Pore-Pressure Coefficients A and B. Geotechnique 4(4), 143-147.Zhang, X. and S. Yan (2004). Fundamentals of geotechnicsplasticity. Editedby Tianjin university Press, Tianjin, China. (in Chinese)Zhou, J., H. Wang, H. Cai and M. Huang (2002). Pore pressure characteristicanalysis of soft clay during unloading based on lab data and numericalcalculation. Chinese Journal of Geotechnical Engineering 24(5), 556-559.(in Chinese)
Key words: saturated soft clay, upl ift, negative excess pore pressure, modified Cambridge model, triaxial extension test. ABSTRACT When foundations, such as caissons, spudcans, and mud-mats, are pulled out from the saturated soft clay foundation, negative excess pore pressure wil
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