Implicit integration of a constitutive model for partly saturated structured porous materials

The paper concerns the integration of a rate equations system for partially saturated soils that have developed intergranular structure due to their geological history or chemical treatment. The constitutive equation adopts an effective stress concept and the hardening depends on the degree of saturation S _r. the bonding exerted by the structure is modelled accounting for the dependency of the hardening law on the cementing material mass. The implicit integration is performed adopting a backward Euler scheme and splitting the problem into two stages: An elastic predictor stage and a plastic corrector updating. In the elastic predictor stage the dimension of the elastic domain can vary accounting for the dependency of the preconsolidation pressure on S _r and debonding. This mathematical feature is a remarkable difference with respect to the original scheme for the saturated unbonded material in which the preconsolidation remains unchanged in the elastic stage. The plastic corrector stage updates the effective stress using the consistency condition. In the plastic corrector stage the non-linear system is integrated solving simultaneously for the stress invariants, the plastic multiplier and the internal variable. The paper reports the validation of the proposed algorithm by some simulations of data in literature; the numerical tests include destructuration upon loading, collapse due to water content change and the effect of the structure.