ABSTRACT
With respect to the constitutive modelling of both saturated and unsaturated soils, especially hydromechanical interaction and the smooth transition between saturated and unsaturated states, the authors (Sheng, 2011; Zhou et al., 2012b; Zhou et al., 2012c) have shown that the stress-saturation approach may be more convenient and effective than the widely used stress-suction approach. Following Zhou et al. (2012b; 2012c), the effective degree of saturation (Se) and Bishop’s effective stress ( ′σ ij ) are chosen as the basic constitutive variables here. The effective degree of saturation can be written as
S S S S Se
(1)
where Sr is the degree of saturation and Sr res is the
residual degree of saturation. Sr 0 is the degree of
saturation at zero suction. Sr 0 is usually equal to 1,
but in some special cases, it can be less than one. For example, the degree of saturation of compacted Pearl clay (Sun et al. 2007b) at zero suction
1 INTRODUCTION
Based on the sub-loading surface plasticity (Hashiguchi, 1989), Yao et al. (2009) proposed a simple but robust constitutive model for both overconsolidated and normally consolidated soils, which is referred to as the UH model. This model can reproduce the typical mechanical behaviour of saturated soils as it relates to the variation in initial density (or overconsolidated ratio) without any additional parameters beyond those required by the modified Cam-clay model. This model will be extended from the saturated state to unsaturated states using the stress-saturation approach to simulate the hydro-mechanical responses of compacted soils with different initial densities. The yield surface, sub-loading surface and corresponding hardening laws are first generated in the space of Bishop’s effective mean stress, the deviator stress and the effective degree of saturation ( )p q S′ − . The new constitutive model requires 13 parameters (6 for mechanical responses, 5 for water retention behaviour and 2 for hydro-mechanical interaction) to describe the fully coupled hydro-mechanical behaviour of unsaturated soils at various densities. Specifically, the proposed model can be used to interpret and reproduce the following behaviours of compacted soils at various suction, saturation and density levels: (i) non-linear compressibility, (ii) non-linear volume collapse, (iii) hardening and post-peak softening, (iv) peak strength
can only reach approximately 0.85. Bishop’s effective stress ( ′σ ij ) is defined as
σ σ δ′ij ij ijS s= + e (2)
where σ ij is the net stress, equal to σ ij u total
is the total stress; ua is the pore air pressure, s is the matric suction, equal to u ua w ; uw is the pore water pressure; and δ ij is the Kronecker delta. Terzaghi’s effective stress ( ′σ ij ) is a special case of Bishop’s effective stress ( ′σ ij ) when a soil is fully saturated (i.e., Se = 1).
