Numerical simulation of bearing capacity of a strip footing on strain-softening soil ground

To overcome the mesh sensitivity induced by strain softening, an implicit gradient plasticity model is put forward to simulate the bearing capacity of a rigid strip foundation on strain-softening soil. A micro-variable is introduced to serve as the additional kinematic variable, and a micro-force balance containing higher-order generalized stresses together and the classical balance of momentum equation are derived. Based on the second law of thermodynamics, the additional micro-force balance is converted into a Helmholtz equation that couples the effective plastic strain and micro-strain. Furthermore, a finite element procedure coupling both displacements and micro-strain is implemented. The applicability of the proposed methodology to capture strain localization is verified by the plane strain compression tests. Finally, the established methodology is used to simulate the bearing capacity of a rigid strip foundation on strain-softening soil, and compared to the calculations from perfectly plasticity model. The simulations show that the strain softening induces a decreasing bearing capacity. The resulted failure mode shows a smaller instability range and a larger maximum deformation magnitude.