Assessment of swelling deformation of unsaturated kaolinite clay

Transcription

1 Assessment of swelling deformation of unsaturated kaolinite clay M. Dobrowolsky & C. Vrettos Division of Soil Mechanics and Foundation Engineering, Technical University of Kaiserslautern, Kaiserslautern, Germany Abstract. The swelling behaviour of kaolinite clay is systematically investigated by means of two types of oedometer devices suitably modified to measure the variation of swelling pressure in dependence of the vertical and volumetric strain. A wide range of values for initial void ratio as well as initial and final degree of saturation has been covered. Based on the experimental results approximate equations for the swelling deformation are derived that are implemented in a FEM-Code. The application to a typical situation in practice is demonstrated by the numerical solution of the respective boundary value problem. 1 ntroduction Swelling of unsaturated cohesive soils may lead to high pressures and deformations of geotechnical structures. So far, publications on swelling of geomaterials refer to rocks (Wittke 2003) or to mudstone (Wolffersdorff & Heidkamp 2005), (Heidkamp & Katz 2004). The aim of the investigation presented herein is the measurement of the volume and pressure changes of swelling cohesive soils in dependence of the moisture content and the void ratio. The influence of the constraints on geotechnical structures due to swelling caused by the non-stationary moisture diffusion in the ground is then analysed by the Finite-Element- Method using an appropriate soil model. n the following, the constitutive relation proposed for modelling the volume change is formulated, the developed oedometer apparatus are

2 2 M. Dobrowolsky & C. Vrettos described and representative test results are given. Numerical simulations of element tests and of a boundary value problem are also presented. 2 Constitutive relation for volume change The volume change behaviour due to swelling is described here in terms of the first stress and strain invariants by the following relationship: ε σ,max 0 r,0 r, = (e,s,s ) f( σ), σ,0 σ σ,max (2.1) 0 ε =, σ > σ,max (2.2) where σ,max is the maximum swelling pressure under constant volume conditions, ε is the swelling strain, σ is the actual stress, e 0 is the initial void ratio, S r,0 is the degree of saturation at the begin of the swelling phase, and S r, the accordingly value at the stress level σ,max. 3 Test Material, Equipment, and Procedure The material chosen for the tests is kaolinite clay of medium to high plasticity and is described in detail by Dobrowolsky & Becker (2002) and Dobrowolsky & Vrettos (2005). The swelling potential of this material is classified as low to medium. The test material has been investigated in the past and allows also the accurate measurement of the soil water suction at relatively low levels using standard techniques. Two new modified oedometer devices have been developed to determine the parameters in the constitutive equation (2.1). With the first oedometer, called oedometer A, it is possible to determine separately the axial and radial pressure. This apparatus as well as test results are described elsewhere, (Dobrowolsky & Vrettos 2005). The second oedometer device, called oedometer B, is designed for 100 mm diameter specimens with a thickness of 50 mm. A rubber membrane is mounted on the inner side of the oedometer allowing the control and the measurement of radial pressure and deformation. The space between membrane and ring is filled with glycerin. The axial pressure is recorded by a load cell. Thus, this apparatus works similar to conventional triaxial equipment.

3 Assessment of swelling deformation of unsaturated kaolinite clay 3 Results are reported here only for tests carried out in oedometer B. The preparation technique of the soil sample and its optimization is described in detail by Dobrowolsky (2003). Tests have been carried out for selected values of the initial and the final degree of saturation, and of the initial void ratio. The correlation between ε and σ is investigated. Through watering from S r,0 to S r, under constant volume the maximum swell stress σ,max is imposed to the sample. An isotropic deformation ε is then stepwise allowed through control of vertical and radial strain. During this process the actual swelling pressure σ is measured. This leads to swell pressure-strain relationships as exemplarily shown in Figures 4.1 and 5.1. Additional tests have been carried out in different devices to determine the characteristics of the water transport through the soil sample. The soil water suction ψ is determined by the pf value, where pf = log [ψ / (1 cm water column)]. Up to a value of pf = 3 measurement is performed by using a miniature tensiometer placed in the middle of the specimen in the oedometer. The hydraulic relations for values pf > 3 are determined by means of i) the axis translation method in a pressure plate cell (3 pf 4) and ii) the vacuum desiccator method (pf > 4). n the pressure plate cell tests are performed by dewatering and subsequent watering allowing the identification of hysteretic behaviour in the soil water characteristic - curve CC. The vacuum desiccator method allows only dewatering and is used here only for the sake of completeness since pf > 4 lies outside the range of the degree of saturation investigated (S r,0 0.7). n addition to the CC the unsaturated hydraulic conductivity K u is needed to determine the water transport characteristics of this particular soil type. The variation of K u with degree of saturation, void ratio, and temperature is taken from Wendling (2004). 4 Test results t can be shown that the swell pressure at a constant volume is of isotropic nature, cf. Dobrowolsky & Vrettos (2005). The results presented in that paper lead to the following approximation for σ :,max ( ) ( ) ( 0.95 S ) r, 0.54 r, 0 σ,max 3.29 pa exp 3.65 S 4.7 e Sr, Sr,0 = (4.1)

4 4 M. Dobrowolsky & C. Vrettos where p a is the atmospheric pressure. The above equation is valid for 0.68 e ; 0.6 S r,0 1.0 and 0.78 S r, 1.0. Fig. 4.1 Swelling strain ε vs. normalized swelling stress σ / σ,max for various values of void ratio e 0 and S r,0 = 0.7, S r, =1.0, T=20 C. The experimentally determined variation of swelling strain with normalized swelling pressure is approximated by equation (4.2) that is depicted in Figure 4.1 for the range of values investigated: a log σ ε =, Ι σ,0 σ σ,max b σ,max (4.2) σ σ,max σ,max whereby a and b are functions of e 0, and of normalized to the imposed isotropic initial pressure σ,0 =27 kpa: σ,max a = ( e ) (4.3) σ,0 σ,max b= ( e ) (4.4) A significant increase of the swell strain ε occurs with decreasing stress σ. t can be seen that the increase of swell strain is stronger for lower values of void ratio. Results from other tests not reported herein show that the swelling potential of the soil sample increases with decreasing initial degree of saturation. σ,0

5 Assessment of swelling deformation of unsaturated kaolinite clay 5 5 Numerical simulations General considerations We assume that material used in the study is homogeneous and isotropic. A nonlinear elastic ideal plastic stress-strain-relationship is assumed for the mechanical loading. Swell deformations are superimposed after completion of initial loading. nvestigations presented by the authors Dobrowolsky & Vrettos (2005) show that the swell shrinkage behaviour of the test material at a specific swell pressure level is approximately linear elastic. n the following, the plastic deformations are left-out for the sake of simplicity. Thus, the total strain is: el d d d ε = ε + ε (5.1) The elastic relationship between the stress increment and the strain increment is given by dσ = D dε + D dε (5.2) el el,m el el, where [D el,m ] is the stiffness matrix for the mechanical elastic behaviour and [D el, ] is the matrix for the elastic swelling behaviour. The FEM-code ABAQUS Version 6-4 is used for the analysis. The following general relationship between maximum volumetric swelling strain and degree of saturation is already built in: 1 jj,max = v 3 ε ε ε j= 1,2,3 (5.3) whereby S and S are the actual and initial degree of saturation, respectively. The above relation describes unhindered swelling. During our tests the strain is controlled and stress is measured. Thus, by setting σ = σ,0 and for small values of σ,0 equations (4.1) - (4.2) approximately correspond to the relationship given by equation (5.3). The value σ,0 = 27 kpa used in the tests is the lowest practicable stress level. The stiffness matrix [D el,m ] is obtained in terms of the modulus of elasticity E and the Poisson s ratio ν. For the modulus of elasticity we selected a stress dependent relationship derived from the equation for the small strain shear modulus used in dynamic analysis, Hardin (1978): ( S) v ( S )

6 6 M. Dobrowolsky & C. Vrettos 0.5 a 1 E= C f ( e) σ pa 3p 2 1+ν ( ) (5.4) For Poisson s ratio we set ν = 0.3. For small strains the constant C = 625. A value C = 156 yields a good fitting of the test results and corresponds to a reasonable approximation of the secant modulus at the strain levels under consideration. The swell-stress dependent swell modulus Q (bulk modulus) to be used in [D el, ] is obtained from the test results, as exemplarily given in Figure 4.1. Simulation of laboratory tests First, the appropriateness of the relationships given above is checked by simulation of representative laboratory tests carried out in oedometer A and B. The simulation starts with initial conditions given by S r,0 = 0.7 and e 0 = At first, an equilibrium step is computed during which suction as well as self-weight are imposed. n the next step the model is watered from the bottom at constant volume to S r, = 1.0. After that, a prescribed deformation is imposed stepwise: axial deformation in odoemeter A and volumetric deformation in oedometer B, respectively. Figure 5.1 compares the results of the tests and of the numerical simulation. The variation of the swell modulus Q (bulk modulus) yields a good fitting of the curve. Fig. 5.1 Volumetric swell strains ε vs. actual stress σ normalized to σ,max for e 0 =0.78, S r,0 =0.7, S r, =1.0, T=20 C. The solid lines describe equation (4.2), the data points are for the numerical simulation.

7 Assessment of swelling deformation of unsaturated kaolinite clay 7 Simulation of a footing on expansive soil The application to a typical situation in engineering practice is demonstrated by the numerical solution of the boundary value problem of an axisymmetric footing on an expansive soil. The footing with radius of 1.0 m and thickness of 0.4 m is placed on the surface of a homogeneous soil with initial conditions e 0 = 0.68 and S r,0 = 0.7. The size of the model is 5 m in half-width by 4 m in depth. Underneath the base of the model a porous water-bearing layer is assumed. The footing is loaded by force of 200 kpa after the equilibrium step is completed and the self-weight of footing and soil is applied. n the next step the groundwater rises within in the water-bearing stratum up to the bottom of the expansive soil. This is simulated by setting suction equal to 0 at the interface between soil and water-bearing stratum. The suction-free front propagates upwards through the soil and leads to its saturation and consequently to swelling. The time the water from the water-bearing stratum is allowed to penetrate the soil is assumed to last 150 days. Figure 5.2 displays two snapshots of the vertical heave before and after saturation, respectively. The vertical heave of the foundation amounts to 17 cm while the vertical heave of the ground at the side of the mesh is 30 cm. The differential heave of 13 cm due to swelling is noteworthy. Fig. 5.2 Vertical heave before and after watering from the bottom. 6 Conclusions A wide range of tests have been performed to determine the water transport characteristics in the soil and the associated swell pressure vs.

8 8 M. Dobrowolsky & C. Vrettos swell strain relationship of the cohesive material. The numerical simulations show the capability of the proposed analytical expressions to describing the swell behaviour. 7 Acknowledgement The investigation presented herein has been carried out within the frame of a project funded by the German Science Foundation dealing with mechanics of unsaturated soils. This support is greatly appreciated. 8 References Dobrowolsky M, Becker A (2002) Adsorptions- und Desorptionsverhalten durchströmter bindiger Böden. 4. Workshop Teilgesättigte Böden, Schriftenreihe Geotechnik, Bauhaus-Universität Weimar, Heft 8: pp Dobrowolsky M (2003) Volume change behavior of cohesive soils. Proc. nt. Conf. From Experimental Evidence towards Numerical Modeling of Unsaturated Soils, Weimar, Vol., pp Dobrowolsky M, Vrettos C (2005) Swell and shrink tests in modified oedometer apparatuses, Advanced Experimental Unsaturated Soil Mechanics, Trento, taly, pp Von Wolffersdorff P-A, Heidkamp H (2005) Quellverhalten diagenetisch verfestigter Tonsteine in den Einschnitten der Neubaustrecke Nürnberg ngolstadt der Deutschen Bahn AG, Universität Kassel, Festschrift zum 60. Geburtstag Prof. Kempfert, Schriftenreihe Geotechnik, Heft 18, pp Hardin, BO (1978) The nature of stress-strain behavior of soils, Proc. ASCE Spec. Conf. on Earthq. Eng. Soil Dyn., Pasadena, Vol., pp Heidkamp H, Katz C (2004) The swelling phenomenon of soils Proposal of an efficient continuum modelling approach, Proc. SRM Regional Symposium EUROCK & 53 rd Geomechanics Colloquium, Verlag Glückauf, pp Hibbit, Karlson & Sorensen, nc. (2002): ABAQUS / Standard User s Manual, Version 6-4, Pawtucket, R, USA Wittke M (2003) Begrenzung der Quelldrücke durch Selbstabdichtung beim Tunnelbau im anhydritführenden Gebirge, Dissertation, Fakultät für Bauingenieurwesen, TH Aachen Wendling S. (2004) Untersuchungen zur Entstehung von Austrockungsrissen in mineralischen Deponieabdichtungen, Dissertation, Heft 10, Fachgebiet Bodenmechanik und Grundbau, TU Kaiserslautern