Behavior of Cemented Soft Clays in Undrained Situations. Abstract

Transcription

1 Behavior of Cemented Soft Clays in Undrained Situations Suksun Horiulsuk 1, Jirayut Suesuk 2, and Martin D. Liu 3 1. Corresonding Author, Associate Professor, Construction Technology Research Unit, and School of Civil Engineering, Suranaree University of Technology, Thailand. suksun@g.sut.ac.th 2. Ph.D. Scholar, School of Civil Engineering, Suranaree University of Technology, Thailand. 3. Senior Lecturer, Faculty of Engineering, The University of Wollongong, Australia. Astract In this aer, a constitutive model for cemented clay is introduced. This model is designated as Modified Structured Cam Clay (MSCC) model. In the model, the influence of cementation structure is incororated into effective stress concet, yield function, hardening rule and lastic otential function to descrie the mechanical ehavior of cemented clay during strain-hardening and softening. The methodology of modeling the shear ehavior of structured clay is simle, which is the same way as that of the other models of the Cam Clay family. The caaility of the MSCC model is verified y comaring the simulated undrained shear resonse of cemented Ariake clay under various effective confining stresses and degrees of cementation with exerimental data. Keywords: cementation, clay, constitutive relation, structure, undrained situation.

2 1. INTRODUCTION Soft clay that ossesses low strength and high comressiility is widely found in coastal and lowland regions. These mechanical roerties of the soil constitute a great challenge to geotechnical engineers, articularly in metroolitan areas. Ground imrovement techniques are increasingly emloyed to reare sites underlain y these soils for construction. Because of its relatively low cost and high efficiency, the use of cement to imrove the soft ground is now widely adoted in geotechnical engineering. The influence of the secial structure of the soil, the cementation, has a dominant effect on the mechanical roerties of the soil and is difficult for theoretical modelling (Horiulsuk et al, 24). Understanding and simulating the ore ressure develoment of the cemented clay and the influence of cementation on the undrained shear resonse ecome an imortant research toic for the rediction of the erformance of geotechnical structures during various undrained loading situations including earthquake loading. To form a model suitale for cemented clay ased on the critical state framework, the influence of cementation structure and destructuring on the effective stress, yield function, hardening rule, and lastic otential function (flow rule) must e incororated. Recently, Horiulsuk et al. (29) have summarized the main features of the cemented clay ehavior and introduced the SCC model for cemented clay. In the model, the effective stress concet, yield function, hardening rule, and lastic otential function have een develoed taking the effect of structure into account. For simlicity, the model has not considered the degradation of structure during virgin yielding. Their model can well simulate shear ehavior for oth normally and over consolidated states. Some modifications are however needed for simly and ractically imlementing into a finite element rogram and for etter caturing the main features of the cemented clay with the model arameters simly otained from the conventional laoratory. In this resent aer, attemts are made to develo a general and ractical constitutive model ased on the critical state framework for cemented clay. The roosed model, designated as the Modified Structured Cam Clay (MSCC) model, is formulated ased on the SCC model for cemented clay (Horiulsuk et al, 29). 2. MODIFIED EFFECTIVE STRESS CONCEPT AND DESTRUCTURING LAW With the resence of structure, the influence of structure is regarded akin to the effect of an increase in the effective stress and yield stress, hence yield surface (Gens and Nova, 1993; Horiulsuk, 21; Kasama et al., 2; Kavvadas and Amorosi, 2; Rouainai and Muir Wood, 2; Baudet and Stallerass, 24; Lee et al, 24; and Horiulsuk et al., 29). For cemented clay, the increase in the yield stress with cement content is clearly understood from the comression and shear test results (Horiulsuk et al., 24a and, and Miura et al., 21, etc.). The modified mean effective stress concet for cemented clay is resented in the form (Horiulsuk et al., 29): = ( + ) u (1) = + (2) where is the modified mean effective stress of cemented clay or exlicit mean effective stress, is the mean effective stress, and ' is the mean effective stress

3 increasing due to cementation structure (structure strength). It shows that when no cementation revails, the ' would e null and the =. Thus, the modified stress ratio can e exressed as follows, η = q (3) + Due to the ' caused y cementation structure, the cemented clay samles can stand without alied confining stress. Considering that the strength enveloe moves towards the right giving zero cohesion intercet, the relationshi etween deviator stress and mean effective stress can e roosed as follows, q= M( + ), (4) where Μ is the gradient of failure enveloe in the q- lane. Due to the destructuring, the decreases when the stress state is on the yield surface. Destructuring consists of two rocesses during shearing: degradation of structure and crushing of soil-cementation structure. The degradation of structure occurs when the stress state is on the yield surface whereas the crushing of the soil-cementation structure haens at ost-failure during strain softening (Horiulsuk et al., 29). For the MSCC model, the effect of destructuring on the comressiility is descried y the comression equation y Liu and Carter (2). The decrease in due to destructuring is directly related to the magnitude of lastic shear strain, ε s. The is assumed to e constant u to the virgin yielding. During virgin yielding (lastic shear strain occurs), the gradually decreases due to degradation of structure until the failure state. Beyond this state, sudden decrease in the occurs due to the crushing of soil-cementation structure and diminishes at the critical state. Figure 1 exlains the reduction in due to destructuring as lastic shear strain increases. The reduction in due to the degradation of structure (re-failure) and the crushing of soil-cementation structure (ost-failure) is roosed in terms of lastic shear strain as follows, ex = ( ε s ) for re-failure (hardening) (5) =, f ex ξ( εs εs, f ) for ost-failure (softening) (6) where is the initial structure strength,, fis the structure strength at failure (eak strength), ε s, f is the lastic shear strain at failure, and ξ is the destructuring index. The higher the ξ, the greater the reduction in at ost failure, hence the faster the reduction in deviator stress. From Eqs.(5) and (6), it is noted that change in is deendent uon the lastic shear strain, which is governed y the effective stress ath and the lastic otential function. 3. MATERIAL IDEALIZATION In the MSCC model, cemented clay is idealized as an isotroic material with elastic and virgin yielding ehavior. The yield surface varies isotroically with lastic volumetric deformation. Soil ehavior is assumed to e elastic for any stress excursion inside the current structural yield surface. Virgin yielding occurs for a stress variation originating

4 on the structural yield surface and causing it to change. During virgin yielding, the current stress of a soil stays on the structural yield surface. yi, e* IC e e* Δe Δe i e= e* +Δe ln ( ) ex = ε s q M M ( ) = ex ξ ε ε, f s s, f ε s, f ε s Fig 1 Schematic diagram of reduction in due to destructuring. d Fig 2 Material idealization for MSCC model. The idealization of the mechanical ehavior of cemented clays is illustrated in Fig. 2. In this figure e reresents the void ratio for a cemented clay, e* is the void ratio for the soil with the same mineralogy in a uncemented state at same stress state, y,i is the mean effective stress at which virgin yielding of the cemented soil egins, and Δe, the additional void ratio, is the difference in void ratio etween a cemented soil and the corresonding ideal state of the soil at the same stress state. Hence, the virgin comression ehavior of a cemented soil can e exressed y the following equation, e = e * + Δe (7) It is found that the additional void ratio for cemented clays can e descried y the following equation, * yi, = +Δ i e e e where is soil arameter, descriing the additional void ratio sustained y cementation. Δe i is the value of the additional void ratio at the start of virgin yielding (Fig. 2a). By consideration of the effect of cementation structure in the yield surface, the roosed yield function, f, of the MSCC model in q - lane is given y (Fig. 2), (8)

5 ( )( ) 2 2 f q = M + = (9) where is the yield stress in the isotroic comression condition. 3.1 Stress States on Yield Surface For models of the Cam Clay family, the direction of lastic strain increment can e determined from the lastic otential function. Even though the MSCC model emloys the yield surface similar in shae to that of the MCC model, the original lastic otential function (flow rule) is not used in the roosed model. This is ecause the lastic otential function of MCC model generally roduces too much shear strain and therefore leads to overrediction of the earth ressure at rest (McDowell and Hau, 23). It was also shown that the lastic shear strain redicted y the original lastic otential function is not suitale for cemented clay (Horiulsuk et al., 29). The lastic otential function roosed y McDowell and Hau (23) is emloyed with the consideration of cementation structure for cemented clay. The lastic otential function, g, in the MSCC model is thus introduced as follows, 2 2 ψ 2 M g = q + ( ) ( ) 1 ψ + + = (1) + where is the arameter for descriing size of lastic otential function, ψ is the arameter descriing the shae of the lastic otential function. The shae of lastic otential is shown in Fig. 3 for various ψ-values. This figure is for =.2 and M = 1.2. When ψ = 2 and =, this lastic otential function ecomes that of the Modified Cam Clay model. The lower the ψ, the lower the lastic shear strain at failure, ε s, f, associated with higher strength and stiffness ψ = 2, MCC ψ =.99 ψ =.5 M ' =.2 ' M = q/' '/' Fig 3 Shae of the lastic otential for the MSCC model.

6 For stress states on the yield surface and with η < M ( d > ), oth volumetric hardening and destructuring occur. The lastic volumetric strain increment, ε v, for the MSCC model is derived from the assumtion that the lastic volumetric strain is deendent uon the change in the and the magnitude of current shear stress. The lastic volumetric strain increment during hardening is thus derived from Eq. (8) as follows, * Μ d dεv = ( λ κ) + Δe M η (11) ( 1+ e) During the softening rocess ( η > M and d < ), it is found that the effect of current shear stress ratio is not very significant. The lastic volumetric strain increment during softening is thus roosed as follows, d dε ( * ) v = λ κ + Δe (12) 1+ e { } ( ) 4. VERIFICATION OF MSCC MODEL Few model arameters are considered for the develoment of MSCC model for the sake of ractical work. Most of the model arameters are the same as those of Modified Cam Clay model. There are only five additional arameters defining the structure effect. They are, Δe i, ', ξ and ψ and simly determined from the conventional laoratory tests. Tale 1 MSCC model arameters for the cemented Ariake clay. Model arameters λ* κ e* IC Δe i M ' (kpa) ' y,i (kpa) G' ξ ψ Cement content A w = 6% A w = 18% ,8 6, 4, Cemented Ariake clay for low and high cement contents (6% and 18%) are taken for the verification of the MSCC model. Values of model arameters identified are listed in Tale 1. Parameters e * IC, λ *, κ, y,i, and Δe i were determined from the results of isotroic comression test and G was otained from triaxial shear test. The values of strength arameters M and ' were otained y lotting the eak strength in the q - lane. Value for arameter ψ was estimated from the simulation of the stress-strain

7 relationshi. It is found that the ψ value decreases with the degree of cementation. Since the ξ is arameter reflecting the rate of strain softening, it is estimated from the stress-strain relationshi at ost-failure. The caacity of the MSCC model for descriing the influence of cementation is verified y simulating undrained shear ehavior of cemented Ariake clay under different effective confining stresses and cement contents. Comarisons etween the test data and model simulations are shown in Fig. 4. Overall seaking, the general atterns of the ehavior of cemented clays i.e., the increment in stiffness and eak strength with cementation and the raidness of the reduction in deviator stress during softening, have een catured. The model simulations cover low to high cement contents (from 6 to 18% y weight) and over a wide range of stress level (2 kpa to 3, kpa). The simulations are made with the values of model arameters essentially determined via their hysical meanings. It is a useful tool for descriing the ehavior of cemented clays. The assessment of some model arameters for different cement contents y emirical equations can e referred to the work y Horiulsuk et al. (29). Deviator stress, q (kpa) CIU A w = 6% σ' c = 4 kpa Exerimental MSCC 2 kpa Deviator stress, q (kpa) Exerimental MSCC 1 kpa σ' c = 3 kpa CIU A w = 18% 2 kpa Excess ore ressure, Δu (kpa) σ' c = 4 kpa 2 kpa Shear strain, ε s (%) Excess ore ressure, Δu (kpa) kpa σ' c = 3 kpa 2 kpa Shear strain, ε s (%) Fig 4 Comarison of exerimental and simulated CIU test results of 6% and 18% cement Ariake clay. 5. CONCLUSION In this aer, a rational and ractical model, Modified Structured Cam Clay (MSCC) model, is develoed y the extension of a simle redictive, Structured Cam clay (SCC) model for cemented clay. In the MSCC model, the influence of cementation structure is incororated into effective stress concet, yield function, hardening rule and lastic

8 otential function to descrie the mechanical ehavior of cemented clay during strainhardening and softening. Simulations are made y using the MSCC model for cemented Ariake clay with different cement contents under different effective confining stresses and these simulations are comared with exerimental data. Overall seaking, a reasonaly well descrition of the influence of soil-cementation structure on the soil ehavior has een achieved. 6. ACKNOWLEDGMENTS The financial suort rovided from the Commission on Higher Education and the Thailand Research Fund (TRF) under contract DIG5188 is areciated. The second author is grateful to the Commission on Higher Education (CHE) for financial suort under the Strategic Scholarshis Program for Frontier Research Network during his Ph.D. Study. 7. NOTATION Parameter descriing the rate of destructuring in comression CSL Critical state line dε v Volumetric strain increment dε e v Elastic volumetric strain increment dε v Plastic volumetric strain increment dε s Shear strain increment dε e s Elastic shear strain increment dε s Plastic shear strain increment Δe Additional void ratio sustained y soil structure Δe i Additional void ratio sustained y soil structure at the start of virgin yielding e Void ratio e* IC Void ratio at = 1 kpa of the intrinsic comression line (ICL) G Shear modulus ICL Intrinsic comression line (destructured) K Bulk modulus ξ Destructuring index κ Gradient of unloading or swelling line of structured clay * λ Gradient of isotroic comression line of destructured clay M Gradient of critical state line on q-' sace η Stress ratio ( q/ ) q + ) η Modified stress ratio ( ( ) / ν Poisson ratio Mean effective stress Modified mean effective stress Mean effective stress increasing due to structure or structure strength The yield stress in the isotroic comression condition

9 ' ' yi Initial structure strength in q-' lane Initial yield stress in the isotroic comression condition q Deviator stress ψ Parameter defining shae of the lastic otential function σ c Effective confining ressure 8. REFERENCES Baudet, B., and Stallerass, S. (24) A constitutive model for structured clays, Geotechnique, Vol 54, No 4, Gens, A., and Nova, R. (1993) Concetual ases for constitutive model for onded soil and weak rocks, Geotechnical Engineering of Hard Soil-Soft Rocks, Balkema. Kavvadas M., and Amorosi A. (2) A constitutive model for structured soils, Géotechnique, Vol 5, No 3, Lee, K., Chan D., and Lam K. (24) Constitutive model for cement treated clay in a critical state framework, Soils and Foundations, Vol 44, No 3, Horiulsuk, S. (21) Analysis and Assessment of Engineering Behaviour of Cement Stailized Clays, Ph.D. dissertation, Saga University, Saga, Jaan. Horiulsuk, S., Bergado, D.T., and Lorenzo, G.A. (24a) Comressiility of cement admixed clays at high water content, Geotechnique, Vol 54, No 2, Horiulsuk, S., Miura, N., and Bergado, D.T. (24) Undrained shear ehaviour of cement admixed clay at high water content, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol 13, No 1, Horiulsuk, S., Liu, M.D., Liyanaathirana, D.S., and Suesuk, J. (29) Behavior of cemented clay simulated via the theoretical framework of the SCC model, Comuters and Geotechnics (in ress). Kasama, K., Ochiai, H., and Yasufuku, N. (2) On the stress-strain ehaviour of lightly cemented clay ased on an extended critical state concet, Soils and Foundations, Vol 4, No 5, Kavvadas M., and Amorosi A. (2) A constitutive model for structured soils, Géotechnique, Vol 5, No 3, Miura, N., Horiulsuk, S., and Nagaraj, T.S. (21) Engineering ehavior of Cement stailized clays, Soils and Foundations, Vol 41, No 5, Liu, M. D., and Carter, J. P. (2) Modelling the destructuring of soils during virgin comression, Géotechnique, Vol 5, No 4, Liu, M.D. and Carter, J.P. (22) Structured cam clay model, Canadian Geotechnical Journal, Vol 39, No 6, McDowell, G.R., and Hau, K.W. (23) A simle non-associated three surface kinematic hardening model, Geotechnique, Vol 53, No 4, Rouainia M., and Muir Wood D. (2) A kinematic hardening model for natural clays with loss of structure, Géotechnique, Vol 5, No 2,