Simulation of Direct Shear Box tests
The non-associated Mohr Coulomb plasticity constitutive model is selected for this study. The model requires the following constitutive parameters: Young’s modulus (E), Poisson’s ratio (n), friction angle (f), cohesion (c) and dilation angle (y). The hardening/softening behaviour of dense and loose sand are expressed in terms of cohesion and friction angle as functions of the “plastic strain magnitude”, g, which can be expressed as (Hibbitt et al., 1998):
where epl is the plastic strain tensor.
Finite Element Analyses
2D plane strain finite element analyses of DSB tests are performed with ABAQUS/Standard. The eight-node biquadratic element with reduced integration is used to model the soil material. The mesh size is selected in accordance with the expected shear band width (i.e. 6 to 7 mm, see section 4.1). The soil in a vertical cross-section is discretized into seventy elements as shown in Figure 2. Drained behaviour is assumed for the soil. The interface between soil and box walls is modeled using the contact surface capability implemented in ABAQUS/Standard. The lateral walls are simulated by rigid surfaces, and Coulomb friction is assumed at the interface. The steel cap of the shear box is assumed rigid and its rotation is prevented.
To express the dependency of friction angle and cohesion on g, a correspondence is sought here between shear box displacements, d, and plastic strain magnitude, g.
It is known that during strain localization, shear is concentrated in a narrow band. The width of shear band was found to be depended on the grain size, confining stress and void ratio (e.g. Tejchman et al. 1999). Most authors defined a ratio between shear band width, h, and mean grain size diameter, D50, e.g. Muhlhaus and Vardoulakis (1987). According to studies by Muhlhaus and Vardoulakis (1987) and Tejchman et al. (1999), a shear band width of about 6 to 7 mm has been postulated for the sand used here, with D50=0.7mm, and for the range of confining stresses considered in this study (20 to 80 kPa).
Due to highly non-uniform shear strain distribution in DSB test (Figure 2), finding a correspondence between box displacement and shear strain magnitude is not straightforward. To obtain a relation between