Journal of Marine Science and Technology, Vol. 24, No. 1, pp. 19-25 (2016) 19 DOI: 10.6119/JMST-016-0125-3
PORE PRESSURE CHARACTERISTICS IN ISOTROPIC CONSOLIDATED SATURATED CLAY UNDER UNLOADING CONDITIONS
Shu-Wang Yan1, Jing-Jing Zhang1, Ying-Hui Tian1, 2, and Li-Qiang Sun1
Key words: saturated soft clay, uplift, negative excess pore pressure, must be decommissioned and removed from the seabed to modified Cambridge model, triaxial extension test. comply with environmental regulations. In the removal pro- cedure, suction develops at the interface between the founda- tion base and the underlying clay soil. In the extraction test of ABSTRACT spudcans, the increase in base suction is established to be the When foundations, such as caissons, spudcans, and mud- key contributor for the larger breakout force (Purawana et al., mats, are pulled out from the saturated soft clay foundation, 2005). On soft soil, removing mudmats during maintenance negative excess pore pressure will develop in the interface or decommissioning is difficult and costly because of the between the base and the soil. This phenomenon will sig- significant suction that develops at the mudmat–soil interface nificantly increase the uplift force. Therefore, estimating the (Chen et al., 2012; Li et al., 2014). Suction is an important developed negative excess pore pressure in the interface part of uplift capacity. Therefore, the suction generation under unloading conditions is important. The development mechanism and the calculation method for the uplift analysis of excess pore pressure was investigated based on the triaxial of bottom-supported foundation in saturated soft clay are extension test under isotropic consolidation condition. The significant for offshore design guidelines. method of using the modified Cambridge model to predict The change of pore water pressure is determined by the the excess pore pressure was programmed and has been external load. Skempton (1954) proposed the relationship proven to be feasible. By associating Henkel’s theory in p-q between excess pore pressure and total pressure in the axi- space, the generation mechanism of negative pore pressure symmetric stress situation, and this theory is widely used in was revealed. The research indicates that excess pore pres- the engineering calculation. Pore pressure coefficient can be sure is initially negative and then becomes positive in triaxial easily determined through triaxial test. However, on the one extension test under isotropic consolidation. The generated hand, pore pressure coefficient A is constantly changing as soil excess pore pressure can be divided into two parts. The first stress state varies, which is inconvenience in practical appli- part generated from the change in the mean total stress is cation. On the other hand, this theory disregarded the influ- negative, whereas the second part generated from the change ence of the intermediate principal stress. Henkel (1966) in deviatoric stress is positive. However, these two parts are proposed a pore pressure calculation method generalized to unbalanced. Research results provide theoretical basis for general three-dimensional stress state. This method has a few the development of excess pore pressure in soft clay to advantages, such as considering the shear dilatancy and defi- analyze the pull-out of structure and the excavation of nite physical meaning. Zhou (2002) presented a method to foundation pit. predict excess pore pressure in triaxial extension test using modified Cambridge model, but the negative pore pressure is ignored when analyzing pore pressure characteristics. Triaxial I. INTRODUCTION compression and tension tests were first modeled by Li et al. After completing construction, certain offshore foundations (2015) to develop a rigorous understanding of the pore pres- sure responses, but lack test evidence. In the present study, the development of excess pore pres- sure was investigated based on the triaxial extension test in Paper submitted 09/29/15; revised 10/26/15; accepted 01/25/16. Author for saturated clay under isotropic consolidation condition. The correspondence: Li-Qiang Sun (e-mail: [email protected]). modified Cambridge model was used to simulate triaxial ex- 1 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. tension test to find a method to predict pore pressure. The 2 Center for offshore foundation systems, The University of Western Australia, generation mechanism of negative excess pore pressure was Perth 6009, Australia. then analyzed based on Henkel’s theory.
20 Journal of Marine Science and Technology, Vol. 24, No. 1 (2016)
Displacement sensor Table 1. Parameters of Tianjin soft clay. Parameter Value Pressure sensor plastic index, Ip 23.7
Liquid limit, wL% 46.5 Cell pressure controller Specific gravity, Gs Rubber Triaxial 2.73 2 piston specimen Coefficient of consolidation cv/(m /year) 42.5 Coefficient of permeability, k/(m/s) 3.0 10-8
Void ratio at p0 = 1 kPa on critical state line, e0 1.22 Back pressure controller Elasticity modulus E/MPa 11 Poisson's ratio, 0.3 Volumetric apparatus Slope of normally consolidated line in e – ln p space, λ 0.15 Base 0 Slope of swelling and recompression line in e – ln p0 Fig. 1. Stress path triaxial apparatus. 0.03 space, κ Slope of critical state line in p-q space, M 0.658 II. TRIAXIAL EXTENSION TEST
According to the unloading path, triaxial extension test is of 7 cm in diameter and 14 cm in height is determined. Un- divided into relief triaxial extension (RTE), common triaxial disturbed soil sample is cut into specified size, and the weight extension, and average stress p for constant triaxial extension quality of triaxial specimen is used to measure the density. (Zhang and Yan, 2004). When foundation is extracted, the bottom soil of foundation is in the unloading state in which 2) Soil Sample Saturation cell pressure is constant and the vertical stress is reduced. The Saturation process is divided into two steps. The first step question of foundation extraction can be approximately is vacuum saturation conducted in airtight container. Quality equivalent to RTE. can be repeatedly weighed after this step to evaluate the uni- formity of soil sample. Triaxial specimen is then installed in 1. Test Apparatus triaxial test chamber, and the method of back pressure satura- Fig. 1. shows the sketch of the stress path triaxial apparatus, tion is adopted to fully saturate and detect saturability simul- which is composed of a cell pressure controller, a back pres- taneously. A 95% saturation is used as back pressure saturated sure controller, and a triaxial test chamber. The back pressure termination condition. controller is connected to a volumetric apparatus that is used to measure volume deformation. The triaxial specimen is in- 3) Isotropic Consolidation stalled in the triaxial test chamber. The top of the triaxial Cell pressure and back pressure are slowly applied on the specimen is fixed through the rubber piston connecting load- triaxial specimen. These pressures are made equal to the ing cap and loading rod, whereas the bottom can be activated consolidation pressure, also called the effective cell pressure. by adjusting the rigidity base. In addition, the apparatus is Under current stress state, saturated soil samples will be isot- equipped with the displacement sensor and pressure sensor on ropically consolidated, while excess pore pressure dissipates the upper portion of the chamber, which are used to measure over time. The degree of consolidation reaches 97%, which the axial deformation and axial deviatoric stress. denotes the end of consolidation.
2. Sample Properties 4) RTE The soft clay used in this study was constituted from clay in RTE is applied using strain control, and unloading shear Tianjin Binhai New Area. Undisturbed soil sample was strain rate is 0.05%/min. The test records are shown in Table 2. coated by iron bucket and was then sealed with wax to prevent moisture loss. The properties of the soft clay have been de- III. THEORETICAL PREDICTION METHOD termined by geo-technical testing, and are listed in Table 1. Cambridge model is based on a large number of experi- 3. Test Procedure ments in the normal consolidation of clay and weak Isotropic consolidation pressures are 100, 200, and 300 kPa, over-consolidated clay, including isotropic consolidation and and the test is subject to SL237-1999 Specification of Soil Test expansion test and the triaxial drained and undrained tests of (China, 1999). The test steps are as follows: different consolidation pressures. Roscoe and Burland (1968) have modified Cambridge model and is referred to as the 1) Soil Sample Preparation modified Cam clay (denoted as MCC hereafter) constitutive According to the Specification of Soil Test and the require- model, in which yield surface is modified to oval. In the pre- ments of stress path triaxial apparatus, triaxial specimen size sent study, MCC constitutive model was used to simulate RTE
S.-W. Yan et al.: Pore Pressure in Clay under Unloading Conditions 21
Table 2. Test records. Consolidation Density Saturation Consolidation Degree of Unloading rate Test number -3 pressure P0 /kpa /(kg m ) Sr /% time T/h consolidation Ut /% v/(%/min） 1 100 18.7 99 24.7 97.9 0.05 2 200 18.6 98 26.0 99.1 0.05 3 300 18.8 100 25.1 98.6 0.05
and predict excess pore pressure. This task is conducted to volumetric strain increment and plastic shear strain increment solve the effective stress path such that pore pressure can be can be calculated. calculated according to the principle of effective stress. Elastic deformation can be determined by the Hooke’s law. Completely undrained situation is assumed, 2 = 3; and the The constitutive relation is expressed as strain of each computing step in the direction of 1 is known. p dp K() d vv d 1. Theoretical Arithmetic (6) p dq3( G d s d s ) The equation of Modified Cambridge model yield surface is
22 where K = bulk modulus; G = shear modulus; s = shearing pqp strain. fpqp,, 0 (1) c Eq. (1) is formulated using total differentiation and is taken pMppccc into Eq. (4). Therefore, d can be calculated as where p = effective mean principal stress; q = generalized shear stress; p = hardening parameter; M = slope of critical ff c dp dq state line, ( = 6sin/(3sin), where = effective internal 1 pq d (7) friction angle, the denominator of triaxial compression taking 22 H p ff minus sign, take plus triaxial extension). pq For brevity, p and q are expressed as
where pp oc qp (2) oc 1 ep0 c 11 H p 2 oo ; k 22m where η = shear compression ratio, η = q/p; o = 1/2[1 + 2 (η/M) ]. 24 1122 Hardening rule is m oo . 2 M
1 eo p pcv exp (3) Take Eq. (7) into Eq. (4) and Eq. (5). Plastic body strain in- crement and the plastic shear strain increment can be ex- pressed as p where v = plastic volumetric strain; eo = initial void ratio; = slope of normally consolidated line, and k = slope of swelling 1 and recompression line. ddpndqnn p () vpqpH If the associated flow rule is adopted, then the plastic po- P (8) tential function is equal to the yield surface function. The 1 ddpndqnn p () plastic potential flow theory is expressed as s pqq H P f ddp (4) where v p f p f p 11 dds (5) q npo ; 22m 2 ff p pq where s = plastic shear strain. If d is known, then plastic
22 Journal of Marine Science and Technology, Vol. 24, No. 1 (2016)
f p’/ kPa 2 0 60 120 180 240 300 360 q 11 -20 nqo . 22mM ff -80 pq
/ kPa -140 Critical state line
q M = 0.658 -200 p0 = 100 kPa Test Take Eq. (8) into constitutive equation Eq. (6). Thus, p0 = 200 kPa Test -260 p = 300 kPa Test 0
3Gnqs d Fig. 2. Critical state of triaxial extension test. dp () Knp 22 HKnGnpp3 q (9) 3Gnqs d dq3( G d n ) f s 22q f HKnGnpp3 q p p 22 f f According to the principle of effective stress, pore pressure pq increment is expressed as (12) f f du dp dp (10) q q 22 ff where p = total mean stress and du = excess pore pressure pq increment.
2. Realization Process where p = modified variable effective mean stress and Under completely undrained conditions, the total volume q = modified variable deviatoric stress. strain is zero. The shear strain increment is expressed as (5) Considering the correction formula of stress, calculate pore pressure increment du, cumulative excess pore pressure u, deviatoric stress q, effective mean stress p, 2 221 2 2 and total mean stress p; ddddddds []12 23 31 3 (6) In every calculation step, conduct cycle steps (3) to (5) until n = N. ddd1230 (11) IV. COMPARISON OF TEST AND THEORY
If 2 = 3, then d 2 = d 3. Therefore, d s = d 1, which According to triaxial extension test, the development of means the generalized shear strain increment is equal to the excess pore pressure under unloading condition was obtained. principal strain increment. The modified Cambridge model was used to simulate triaxial According to 2.1, excess pore pressure increment can be tests and to confirm the feasibility of pore pressure prediction calculated, if each calculation step strain increment d s is method. To easily distinguish the extension test and the com- known. The specific steps are as follows: pression test in the coordinate system, the generalized shear stress q in the compression test is represented in positive half (1) Determine the Cambridge model parameters M, , k, and shaft, whereas in negative half shaft in the extension test. soil property parameters e , K, G; o 1. Stress Path (2) Assume an initial condition q = 0, p = p0 (the consolidation pressure noted by p0), dε = 0, total strain s, total steps N; Three triaxial extension tests were consolidated in pres- (3) In every calculating step, the strain increment ds per step sures 100, 200, and 300 kPa. Effective stress paths were plot equals to s /N. Then, dq, dp can be calculated using Eq. (9); in p-q space, in which the critical state line can be determined, (4) Isotropic consolidation soil is in the initial yield surface at as shown in Fig. 2. The critical state line slope is the Cam- first, and then the stress state under unloading is con- bridge parameter M, which is 0.658. stantly changing along with yield surface affected by Effective stress path of the test and theory are compared, as hardening rule. To ensure stress points on the yield sur- shown in Fig. 3. This figure shows that the values of both test face in the entire calculation process, stress has been and theory are very close. In other words, the two curves of amended along the yield surface normal direction (Gao et effective stress path coincide basically. Shear stress predicted al., 2010). Correction formula is as follows: by modified Cambridge model is slightly lower than that of the
S.-W. Yan et al.: Pore Pressure in Clay under Unloading Conditions 23
p’/ kPa p0 = 100 kPa Theory p0 = 100 kPa Test 0 20 40 60 80 100 120 0 p0 = 200 kPa Theory p0 = 200 kPa Test
p0 = 300 kPa Theory p0 = 300 kPa Test -20 30 /% 0 p 25 / u
-40 Inicial yeild surface Δ / kPa 20 q Critical state line -60 15 p = 100 kPa 10 p = 100 kPa Test 0 -80 0 Theory 5 (a) Consolidation pressure at p = 100 kPa 0 0 p’/ kPa -5 -5 -4 -3 -2 -1 0 0 40 80 120 160 200 240 Axial strain ε /% Nomalisted pore pressure 0 s Fig. 4. Development of excess pore pressure. -40
-80 Inicial yeild surface negative in the early unloading and increases with the devel- / kPa
q opment of the strain. The negative pore pressure increases to a -120 Critical state line maximum, and then decreases gradually and develops positive value after zero. Finally, the pore pressure achieves the posi- p0 = 200 kPa -160 p0 = 200 kPa Test tive maximum number and stops. Theory As shown in Fig. 4, under consolidation pressures of 100, (b) Consolidation pressure at p = 200 kPa 0 200, and 300 kPa, the maximum values of negative pore p’/ kPa pressure are 2, 5, and 7.5 kPa in the test results, respectively. The maximum negative value increases with varying con- 0 60 120 180 240 300 360 0 solidation pressure. Meanwhile, its corresponding strain value also increases. Notably, the theoretical prediction method -60 proposed in this study can also predict this rule. The comparison of the test and theoretical calculation on -120 Inicial yeild surface stress path and the development of the pore pressure indicate / kPa
q that this prediction method is feasible in uplift question of Critical state line -180 foundation.
p = 300 kPa p = 300 kPa Test 0 -240 0 Theory V. GENERATION MECHANISM OF PORE (c) Consolidation pressure at p = 300 kPa PRESSURE IN TENSION 0 Fig. 3. Effective stress path test of triaxial extension test. Both test and theory results demonstrate that excess pore pressure is negative in the early unloading state, and then gradually becomes positive with the development of axial test, but the error is within 4%. In theoretical prediction strain. Combining with the modified Cambridge model method, the excess pore pressure equals to the difference (Roscoe and Burland, 1968) and Henkel pore pressure theory between total stress and effective stress. Hence, the closer the (Henkel and Wade, 1966), this change rule and the generation theoretical stress path compared with experimental, the more mechanism of excess pore pressure in unloading state can be accurate the predicted excess pore pressure. explained. In p-q space, p and q can be noted by principal stress 1, 2, 3: 2. Development of Excess Pore Pressure
To facilitate the analysis of the development of pore pres- p 123 /3 sure under different consolidation pressures, excess pore (13) 1 2 221/2 pressure was normally processed. The comparison of excess q []12--- 23 31 pore pressure between triaxial extension test and theoretical 2 prediction with axial strain is shown in Fig. 4. The develop- ment of pore pressure is consistent and close in test and theory, When 2 = 3, the generalized shear stress is given by q = and the predicted error is within 6.3%. Excess pore pressure is 1 – 3. When isotropic consolidation has been completed,
24 Journal of Marine Science and Technology, Vol. 24, No. 1 (2016)
0.6 Final yeild surface Total stress the critical state line, that is, the damage state points. In p-q Effective stress space, total stress and effective stress value difference is ex- 0.4 cess pore pressure, noted by u. The excess pore pressures
Critical state line Inicial yeild surface generated from the change in the mean total stress (up) can be 0.2 6 sin ϕ′ Compression M = 3 - sin ϕ′ determined by Eq. (17), whereas that generated from the 0
p 0.0 change in deviatoric (or shear) stress (uq) can be calculated
/ A q Critical state line by Eq. (18). In tension, u is negative, whereas Δu is posi- 6 sin ϕ′ p q -0.2 M = 3 + sin ϕ′ tive. Hence, these parts partially cancel each other. This B Δu Δuq cancellation results in the generation of negative excess pore -0.4 C Δup Tension pressures in section AB of tension (up > uq), but positive excess pore pressures in section BC of tension (up < uq). -0.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 This observation suggests the generation mechanism of nega- tive pore pressure and why excess pore pressure changes from pʹ/p0 or p/p0 negative to positive in this study. Fig. 5. Generation mechanism of pore pressure in tension state.
VI. LIMITATIONS OF THE STUDY
qpp3(0 ) (14) Many Centrifuge model tests only obtain negative pore pressure under unloading state (Purawana et al., 2005; Chen et which means that q = 0 and p = p0, axial unloading test is al., 2012; Li et al., 2014a; Liu et al., 2015). In this paper, the conducted in undrained conditions along with constant cell process of pore pressure existed from negative to positive. pressure. The total stress path can be expressed as The present study focuses on the isotropic consolidation state, According to Henkel and Wade (1968), the generated ex- whereas the stress state of natural foundation is for K0 con- cess pore pressures can be divided into two parts: the first part solidation. This phenomenon maybe influenced the difference is generated from the change in the mean total stress, and the of these tests. Several parameters including uplift velocity, second part is generated from the change in deviatoric (or loading history, and soil degree of consolidation influence the shear) stress. Henkel’s theory is as follows: excess pore pressure variation (Gourvenec et al., 2009; Li et al., 2014b; Li et al., 2014c). However, a more advanced re-
1 a 2 search is necessary to realistically simulate the stress state and u 0 [ 33123 12 to explore the influencing parameters of excess pore pressure.
221/2 VII. CONCLUSIONS 23 31] (15) This paper presents the results from triaxial extension test at Taking formula (13) into the formula (15) obtains the initial isotropic conditions and focuses on the development of excess pore pressure with strain. Furthermore, modified
upaqu p uq (16) Cambridge model was used to simulate RTE and to predict excess pore pressure. Hence, the feasibility of this prediction where p = excess pore pressure generated from the change in method has been confirmed through comparing theory pre- diction results and test results. Based on Henkel’s theory, the the mean total stress, noted by up ; aq = excess pore pressure generation mechanism of negative pore pressure was deter- generated from deviatoric stress, noted by uq. Considering mined and the change of pore pressure from negative to posi- tive was revealed. The following conclusions are drawn: upp (17) p 0 (a) In unloading condition, the shear stress generates positive pore pressure, whereas the contribution of the total mean According to the principle of effective stress u = p – p, stress increment to the excess pore pressure is negative. Therefore, the generation of negative excess pore pressure uppq 0 (18) in the unloading condition is due to that these parts can incompletely cancel each other; Fig. 5 presents the total and effective stress paths for triaxial (b) Under isotropic conditions, excess pore pressure initially compression and tension from the initial isotropic conditions. presents the negative and then becomes positive. The Point A denotes the stress state after the completion of iso- higher the consolidation pressure is, the greater the tropic consolidation, wherein the shear stress is zero. Point B maximum negative pore pressure and corresponding axial is the intersection of effective stress path and total stress path, strain. Meanwhile, modified Cambridge model can effi- whereas point C is the intersection of effective stress path and ciently predict this rule.
S.-W. Yan et al.: Pore Pressure in Clay under Unloading Conditions 25
This study has realized the development of excess pore mouldedclay. Proc. ASCE 92 (sm6). pressure in isotropic condition and has validated the use of the Li, X., C. Gaudin, Y. Tian and M. J. Cassidy (2014a). Effect of perforations on uplift capacity of skirted foundations on clay. Can. Geotech. J. 51(3), MCC constitutive model. The research results provide theo- 322-331. retical basis for the development of excess pore pressure in Li, X., C. Gaudin, Y. Tian and M. J. Cassidy (2014b). Rate effects on the uplift saturated soft clay to analyze uplift of foundation and exca- capacity of skirted foundations on clay. Proceedings of 8th International vation of foundation pit. Further work is in progress both Conference on Physical Modelling in Geotechnics, Perth, Austrilia, numerically and experimentally (i) to develop a more realistic 473-479. Li, X., Y. Tian, M. J. Cassidy and C. Gaudin (2014c). Sustained uplift of consolidation (k0 1) to investigate the effect to excess pore skirted foundation in clay. Proceedings of the ASME 2014 33rd Interna- pressure, and (ii) to thoroughly explore the development of tional Conference on Offshore Mechanics and Arctic Engineering- excess pore pressure with various influencing factors under OMAE, Sanfracisco, US., V003T10A006-V003T10A. unloading condition. Li, X., Y. Tian, C. Gaudin and M. J. Cassidy (2015). Comparative study of the compression and uplift of shallow foundations. Computers and Geo- technics 69, 38-45. ACKNOWLEDGMENTS Liu, Z., C. Y. Zhou and Y. Q. Lu (2015). Dynamic evolution model and critical failure criterion of the instability evolution for submarine tunnel system. This project is supported by the National Natural Science Journal of Coastal Research Special Issue No 73, 776-780. Foundation of China (Project number: 41272323) and the Key Ministry of Water Resources of the People's Republic of China (1999). Projects of Science and Technology Support Plan in Tianjin SL237-1999 Specification of soil test. China Water&Power Press, Beijing, China. (in Chinese) (Project number: 11JCZDJC23900). Purawana, O. A., C. F. Leung, Y. K. Chow and K. S. Foo (2006). Influence of base suction on extraction of jack-up spudcans. Géotechnique 55(10), 741-753. REFERENCES Roscoe, K. H. and J. B. Burland (1968). On the generalized stress-strain Chen, R., C. Gaudin and M. J. Cassidy (2012). Investigation of the vertical behaviour of wet clay. Engineering Plasticity, edited by Cambridge uplift capacity ofdeep water mudmats in clay. Can. Geotech. J. 49(7), University Press, Ville de Cambridge, England, 535-609. 853-65. Skempton, A. W (1954). The Pore-Pressure Coefficients A and B. Geotech- Guan, Y., F. Gao, W. Zhao and J. Yu (2010). Secondary development of nique 4(4), 143-147. modified Cambridge model in ANSYS software. Rock and soil mechan- Zhang, X. and S. Yan (2004). Fundamentals of geotechnicsplasticity. Edited ics 31(3), 976-981. (in Chinese) by Tianjin university Press, Tianjin, China. (in Chinese) Gourvenec, S., H. E. Acosta-Martinez and M. F. Randolph (2009). Experi- Zhou, J., H. Wang, H. Cai and M. Huang (2002). Pore pressure characteristic mental study of uplift resistance of shallow skirted foundations in clay analysis of soft clay during unloading based on lab data and numerical under transient and sustained concentric loading. Géotechnique 59(6), calculation. Chinese Journal of Geotechnical Engineering 24(5), 556-559. 525-537. (in Chinese) Henkel, D. J. and G. H. Wade (1966). Plane strain tests on a saturated re-