A MORE FUNDAMENTAL APPROACH TO PREDICT PORE PRESSURE FOR SOFT CLAY

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1 LOWLAND TECHNOLOGY INTERNATIONAL Vol. 9, No. 1, 11-17, June 27 International Association of Lowland Technology (IALT), ISSN A MORE FUNDAMENTAL APPROACH TO PREDICT PORE PRESSURE FOR SOFT CLAY A. S. Balasubramaniam 1, E. Y. N. Oh 2, C. J. Lee, S. Handali 4 and T. H. Seah 5 ABSTRACT: Skemton s (1954) ore ressure coefficient A rovides a ragmatic attemt at determining ore ressures during undrained shear, and to use these in settlement comutations and stability analysis of embankments in soft clays. Also, the Critical state concet offers a means of acquiring the undrained stress ath in normally consolidated clays through using a volumetric yield locus derived from a simle energy balance equation. However, to date there is no novel method by which the undrained stress aths of lightly over-consolidated and heavily overconsolidated clays can be redicted by using fundamental concets. Based on the work of Handali (1986), Balasubramaniam et al. (1989) resented an alternative ore ressure coefficient that was more generalised than the Skemton s coefficient. However, roosed a set of arabolas to describe the undrained stress aths of overconsolidated clays, and Lee (1995) considered ellitic aths to be more in agreement with the exerimental observations. In this aer, observed and redicted undrained stress aths both under comression and extension, and also from isotroic and K re-shear consolidation states will be resented. Such exressions can then be readily used in comuter softwares for stability analysis and settlement comutations. Keywords: Soft clay, undrained stress ath, ore ressure coefficient INTRODUCTION The classical work of Skemton (1954) and Henkel (1959) on the ore ressure coefficient is still widely used in settlement comutations by the Skemton (1964) and Bjerrum (1972) method, and in the simle stability analysis of embankments by effective stress analysis. There are of great ractical significance, as excess ore ressure in saturated clays can be derived from a single arameter A (in the axi-symmetric case) relating to the deviator stress increment. However, the arameter A is heavily deendent on the stress history of the clay (whether normally or overconsolidated) and also at the level of the deviator stress. Lo (1976) observed a unique relationshi between ore ressure and shear strain at different stages of loading and unloading and emhasised that roer estimation of ore ressure in an undrained loading cannot be carried out without taking shear strain into consideration. The resentation of test data and analysis in this aer will follow the work of Lee (1995). PROPERTIES OF CLAY SAMPLES The subsoil in the Bangkok Plain consists of quaternary deosits that originated from sedimentation at the delta of the ancient Chao Phraya River. The Chao Phraya Plain consists of a broad basin filled with sedimentary soil deosits that form alternate layers of clay, sand and gravel. The thickness of the soft to medium stiff clay in the uer layer varies from 12 to 2 m, while the total clay layer (including the first stiff clay layer) is about 15 to m. The engineering roerties of the soft clay and other layers were studied in great detail at AIT, and the triaxial behaviour of the undisturbed samles of weathered clay and the soft clay were resented in Balasubramaniam and Uddin (1977), and Balasubramaniam and Chaudhry (1978). The clay samles used in this study were from Nong Ngoo Hao site at a deth between 5.m to 6. m. The samles were taken using 25 mm thin walled tubes with.5 m long. These tubes were sufficiently large to reduce samle disturbance. The samles fall into category of very soft clay. The soil was fairly homogeneous but did 1 Professor, School of Engineering, Griffith University Gold Coast Camus, QLD 9726, AUSTRALIA 2 Geotechnical Engineer, Queensland Deartment of Main Roads, Brisbane, QLD 46, AUSTRALIA Assistant Professor, Deartment of Civil Engineering, Kangwon National University, Chun Cheon, 2-71, KOREA 4 Professor, Engineering Deartment, Immanuel Christian University, Yogyakarta, INDONESIA 5 Geotechnical Engineer, MAA Geotechnics Co., Ltd., Bangkok, THAILAND Note: Discussion on this aer is oen until December 1, 27.

2 Balasubramaniam, et al. include very thin horizontal silt layers. Table 1 summarizes the basic roerties of the tested clay samle. Table 2 resents the summary of triaxial tests. The samles under strain controlled and static loading tests are marked with symbols "ST". Samles IS-1 and IS-2 were isotroically consolidated. Tyical consolidation rocess of the samle is given in Fig. 1. Table 1 Physical roerties of base clay Proerty Values Liquid limit (%) 116 Plastic limit (%) 46 Plasticity Index (%) 7 Water content (%) 124 Secific Gravity 2.75 Organic Matter (%) -4 H 8 Grain Size Distribution Clay (%) 64 Silt (%) 27-2 Sand (%) 4-9 No. Table 2 Summary of tests Consolidation Stress q a (kn/m 2 ) i (kn/m 2 ) Consolidation Ratio, a ST ST ST ST ST ST ST ST ST IS IS UNDRAINED STRESS PATHS A simle equation for the undrained stress ath of normally consolidated samles can be derived based on the linear relationshi between ore ressure and the stress ratio. This formulation was started with the linear Void Ratio (kn/m 2 ) Fig. 1 Consolidation rocess of clay samle ore ressure-stress ratio relationshi for normally consolidated clays and the bi-linear relations noted for over consolidated clays as interreted by Handali (1986). Figure 2a shows the variation of normalised ore u/ with stress ratio ( ) for the isotroically normally consolidated samles, where is the re-shear consolidation stress. The variation is linear and the average gradient ( 1/ )( du /d ) for Bangkok clay is.5. Fig. 2b shows the ( u /, ) relationshi for the anisotroically consolidated samles, which is bi-linear. The gradients ( 1/ )( du /d ) for the initial art are.4,.1 and.25 when the anisotroic consolidation ratio a are.25,.49 and.75, resectively. The second linear art is arallel to that of the isotroically normally consolidated samles having a gradient ( 1/ )( du /d ) of.52. In Fig., an interretation is given wherein the ( u/, ) lots are shifted uwards in the direction of ( u/ ) by the values ( Δ n /). An illustration to describe Δ n is given in Fig. 4, where Δ n d i, where i is the re-shear mean consolidation stress of the anisotroically consolidated samle; and d is the value on the drained ath of the isotroically consolidated to and drawn at the same level of q a, the initial re-shear q value of the anisotroically consolidated samle. Additionally, is the re-shear consolidation stress of the samle sheared under undrained condition of the isotroic consolidated samle, having the same re-shear voids ratio of the anisotroically consolidated samle. Thus, ressure ( ) a n i 1 (1)

3 A more fundamental aroach to redict ore ressure for soft clay u/ o IS-1 IS-2 o (kpa) Fig. 2a ( ) u/, lot for normally consolidated samles under monotonic loading.8.6 ST-1 ST-4 ST-9 a samle. In Fig. 6, the bi-linear relationshis of the overconsolidated samles are shifted in the direction of ( u/) by the corresonding value ( Δ n /), where Δ n is defined as the difference between the re shear consolidation stress of the normally consolidated samle and the corresonding overconsolidated samle. The adjustment made and shown in Fig. 7 is identical to the thinking that the oint of reference for measuring ore ressure of the over-consolidated samle is the same as that of the normally consolidated samle. Such a shift results in the merging of the second linear ath of the over-consolidated samles to the ath of the normally consolidated samle as shown in Fig. 6. For normally consolidated clays the relationshi between q, and u can be given by: 1 u + q (2) u/ o.4 Also, u C () Fig. 2b ( ) consolidated samles u/, relationshi for anisotroically Combining (2) and (), it can be shown that ( 1 C ) 1 (4) Also, for the eak stress ratio condition coinciding with the critical state.8.6 ST-1 ST-4 ST-9 a C M 2 M (5) u/ o Fig. Shifted ( ) consolidated samles u/, aths for anisotroically Figure 5 shows the ( u/, ) lot for overconsolidated samles. Here again, the ( u/, ) relationshis are bi-linear. The measured gradients ( 1/ )( du /d ) of the first linear section for samles having values of 1.2, 1.6 and 2. (all the samles have the same void ratio of 2.55) are.5,.22 and.18 resectively. The gradient of the second linear section (.52) is the same as that of the normally consolidated Fig. 4 Method of Shifting the ( u/, ) ath for anisotroically consolidated samles Therefore the undrained stress ath for normally consolidated samles can be exressed as

4 Balasubramaniam, et al. 1 1 M 2 M 1 (6) u/ o ST-1 ST-6 ST Kim (1991) also extended this relationshi to overconsolidated clays following the work of Handali (1986) by introducing two arameters C 1 and C 2 for the normally consolidated and overconsolidated regions. These arameters indicate the sloes of the first and second linear sections of the ( ) u/, relationshis. The stress ratio at the intersection of these segments was defined as t. The ore ressure develoed in these two segments is determined as, Fig. 6 Shifted ( u/, ) lots for over-consolidated samles u and C1 for ( t ) (7a) u ( C C ) + C for ( > ) 1 2 t 2 t (7b) where, is re-shear mean normal stress. These equations are used for the generation of undrained stress aths 1 C and for ( > t ) for ( t ) ( ) 1+ C2 C1 t C2 1 ST-1 ST-6 ST (8a) (8b) Fig. 7 Shifting of ( u/, ) lot for overconsolidated samles C 1 or t t.6 C C 1 t C 2.75 C1 t Fig. 8 C1 relationshi from CID samles u/ o Fig. 5 ( u/, ) lots for over-consolidated samles under monotonic loading.22 The ore ressure arameter C 1 decreased as values increased, while the corresonding value of t increased. These relationshis for CIU tests are simlified and resented in Fig. 8. Thus, C 1 and t values are determined directly from this figure if the is known. The C 2 value is constant and can be determined by running an undrained test on normally consolidated clay.

5 A more fundamental aroach to redict ore ressure for soft clay PARABOLIC UNDRAINED STRESS PATHS By carefully studying the undrained stress aths, Lee (1995) concluded ellitical shaes were found to be closer to the actual shaes rather than the arabolic shaes adoted by. Thus the undrained stress aths are modelled as, 2 2 cs oc q + M cs oc oc cs oc ] oc cs 1 (9) The meaning of M oc and [ are shown in Fig. 9. Eq. (8) can be written as, Modified Theory are ellitical in nature, while the Model assumes arabolic shae. For the over-consolidated clays, the Modified Theory redicts that the undrained stress aths will rise vertically, while the Pender Model assumes Critical State seeking arabolic aths. However, the model roosed in this aer shows the undrained stress aths are of ellitical shae for the normally consolidated region and wet side of the critical state, while the undrained stress aths on the dry side are ellitic but terminate in the Hvorslev (196) tye failure enveloe. Moc cs q oc ( )( + 2 cs oc ) (1) cs oc To extend the model to a more general exression, the effect of the rotation of the direction of rincial stress can be included as q + ( AM ) oc cs oc cs oc ( )( + 2 ) cs oc (11) Fig. 1 Exected undrained stress aths (Modified Cam Clay) It is noted that Eq. (1) gives the same stress ath in normalised (, q) lot for normally consolidated clays sheared from isotroic re-shear conditions as the yield locus in the modified theory when 2 cs. Fig. 11 Parabolic undrained stress ath (Pender, 1978) Fig. 9 Definition of clay roerties used in Lee (1995) Figure 1 and Fig. 11 showed the undrained stress aths as modelled by the Modified Theory and the Pender Model resectively. For normally consolidated clay, the undrained stress aths redicted by the The undrained stress aths of normally consolidated and over-consolidated clays redicted by Pender s model and the authors are suerimosed with the exerimental data for CIU tests on normally and over-consolidated clay from Wroth and Loudon (1967) in (Fig. 12). The corresonding data for Bangkok clay are resented in Fig. 1 and Fig. 14. The CK U test data are resented in Fig. 15 together with the redictions. Similar data for extension tests on Bangkok clay are resented in Fig. 16 for normally and overconsolidated Bangkok clay. The extension data under K conditions are resented in Fig.

6 Balasubramaniam, et al. 17. It is found that the models develoed by Handali (1986) and Lee (1995) give excellent rediction of undrained stress aths in triaxial comression and extension for both normally and over-consolidated states and under isotroic and K consolidation states. Normalised Deviator Stress CIU Worth and Loudon (1967) CKU Kim (1991) Mean Normal Stress, (kpa) Fig. 15 Undrained stress aths comared with the model redictions (CK U test) Normalised Mean Normal Stress -2 Fig. 12 Normalised (q, ) lot comared with the model redictions (CIU test) CIU Gurung (1992) kpa) Deviator Stress, q ( CIUE Anwar (1992) Mean Normal Stress, (kpa) Fig. 16 Undrained stress aths comared with the model redictions (CIUE test) Mean Normal Stress, (kpa) Fig. 1 Undrained stress aths comared with the model redictions (CIU test) 4 2 CKUE Kim (1991) CIU Kim (1991) Mean Normal Stress, (kpa) Fig. 14 Undrained stress aths comared with the model redictions (CIU test) Mean Normal Stress, (kpa) Fig. 17 Undrained stress aths comared with the model redictions (CK UE test)

7 A more fundamental aroach to redict ore ressure for soft clay CONCLUSIONS In this aer alternate exressions have been derived for a ore ressure coefficient for normally and overconsolidated clays (deendent on the stress ratio) and valid for all re-shear consolidation conditions. Also, arabolic exressions are found to model the undrained stress aths of normally and over-consolidated clays more effectively than Pender s ellitic formulations. The rediction of the ore ressure coefficients is imortant in settlement and stability analysis of embankments and excavations in soft clays. These coefficients have been found to be suerior to those of Skemton and Henkel, as they are indeendent of the stress history and the level of deviator stress during shear. ACKNOWLEDGEMENTS The authors wish to thank Prof. D. T. Bergado and Dr. N. Phienwej for their valuable hel in the research work resented in this aer. REFERENCES Anwar, M. S. (1992). Extension Behaviour of Bangkok Soft Clay below State Boundary Surface. MEng Thesis, Asian Institute of Technology, Thailand. Balasubramaniam A. S. and Chaudhry A. R. (1978). Deformation and strength characteristics of soft Bangkok clay. J. Geotech Eng. Div., ASCE., 16(GT6): Balasubramaniam, A.S., Handali, S., Phien-wej, N., and Kuwano, J. (1989). Pore ressure stress ratio relationshi. Proceedings of 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, Brazil, 1: Balasubramaniam A. S. and Uddin W. (1977). Deformation characteristics of weathered Bangkok clay in extension. Geotechnique, 27(1) : Bjerrum, L. (1972). Embankment on soft ground. Proceedings of the ASCE Secialty Conference on Performance of Earth and Earth-Suorted Structures. Predue University, USA, 2: Gurung, S. B. (1992). Yielding of Soft Bangkok Clay below the State Boundary Surface under Comression Conditions. MEng Thesis, Asian Institute of Technology, Thailand. Handali, S. (1986). Cyclic Behaviour of Clays for Offshore Tye of Loading. PhD Thesis, Asian Institute of Technology, Thailand. Henkel, D. J. (1959). The relationshis between the strength ore water ressure and volume change characteristics of saturated clays. Geotechnique, 9: Hvorslev, M. J. (196). Physical comonents of the shear strength of saturated clays. Proceedings of the ASCE Research Conference on the Shear Strength of Cohesive Soils. Boulder, USA: Kim, S. R. (1991). Stress Strain Behaviour and Strength Characteristics of Lightly Overconsolidated Clays. PhD Thesis, Asian Institute of Technology, Thailand. Lee, C. J. (1995). Modelling of Stress-Strain Behaviour Below The State Boundary Surface. MEng Thesis, Asian Institute of Technology, Thailand. Lo, W. B. (1976). Reeated Load on Bangkok Subsoils. MEng Thesis, Asian Institute of Technology, Thailand. Pender, M. J. (1978). A Unified Model for Soil Stress- Strain Behaviours. Proc. 1 th ICSMFE : Skemton, A. W. (1954). The Pore Pressure Coefficients A and B. Geotechnique, 4: Skemton, A. W. (1964). Long term stability of clay sloes. Geotechnique, 14: Wroth, C. P. and Loudon, P. A. (1967). The Correlation of Strains within a Family of Triaxial s on Overconsolidated Samles of Kaolin. Proc. of the Geotech. Conf., Oslo, 1: