This paper deeply couples the exponential-type nonlinear strain softening with the anisotropic method of microstructure tensor combined stress invariants, proposing an effective strength formula that reflects the anisotropy evolution of soil. Furthermore, an expression for the anisotropy ratio k of strength as an equivalent plastic strain-related variable is derived. For natural clay, this evolution of strength anisotropy is incorporated into the Mohr-Coulomb-matched Drucker-Prager (MC-matched DP) yield criterion within the Cosserat continuum framework, resulting in a more refined soil constitutive model. The main strength parameters required for this model can be conveniently obtained based on conventional soil tests, and the model functionality can be degraded through parameter adjustments. The detailed procedure of stress updating algorithm and the elastoplastic tangent modulus matrix are provided for the constitutive integration. Through the finite element implementation, the superiority of the model is demonstrated compared with existing literature. Also, a biaxial compression example is systematically analyzed to prove that the model can effectively reflect the sensitivity of soil to loading direction. Moreover, the evolution of the shear band morphology, particle rotation in the shear band, and the anisotropy degree presented by the model are consistent with previous experimental studies and discrete element method (DEM)-related literature results. Furthermore, the proposed model effectively addresses numerical convergence issues and mesh size dependence usually encountered in classical models during the simulation of strain localization occurred in the soil.

The strength anisotropy and strain softening of natural soil can significantly impact the bearing capacity of shallow foundations on clay. In this article, we present a nonlocal numerical method to study the coupled rotation of the maximum normal stress axis and strain softening on the bearing capacity of shallow foundations on clay through a Cosserat strain softening constitutive model. The strength anisotropy and strain softening characteristics were numerically implemented into a finite-element (FE) program by dynamically updating the anisotropic cohesion in global Newton-Raphson iterations. Due to its nonlocal feature, the proposed nonlocal numerical method can overcome the mesh dependence in simulating the progressive failure of clay through the classical FE method. We first validated the efficacy of this method against the results of the plane strain test and numerical results in the literature. We then study the bearing capacity of a strip footing over anisotropic and strain-softening clay through the implemented numerical method. The results indicated that the deposition angle has an important effect on the bearing capacity and failure mode. The effects of the degree of anisotropy and strain softening on the ultimate bearing capacity are quantified through the numerical method. It is found that (1) the proposed method can effectively reflect the characteristics of the maximum normal stress axis rotation on the failure surface of the footing; (2) the ultimate bearing capacity of a footing (Pu) on anisotropic clay could increase linearly with an increase in the anisotropy ratio k (i.e., k is the ratio between C1 and C2) and decreases with an increase in the softening modulus; and (3) the strength anisotropy and strain softening are strongly coupling factors impacting the bearing capacity of anisotropic clay.