Soil is a multi-phase and multi-scale geomaterial that exhibits dramatically inhomogeneous and discontinuous physical nature. Conventional finite element method

which is conceptualized at a single macroscale and ignores the control mechanism of soil at the micro and meso scales

cannot reproduce and predict the multi-scale and hierarchical failure of soil. In order to investigate the influence of the physical details and kinematic characteristics of soil at the microscale associated with the global mechanical responses

a multi-scale particle micro-rotation theory is established according to the concept of the soil cell element model. The method is implemented into a multi-scale finite element code

and is used to reproduce and predict the depth of foundation plastic zone. The numerical simulation results show that the multi-scale coupling finite element model can relate the motion feature of soil particles at the microscale to the mechanical response of soil at the macroscale; the rotation displacements of soil particles concentrate upon the plastic zone and has an average value of 4°; the depth of foundation plastic zone increases as the size of soil particle and elasticity modulus of soil increases respectively. The concentration and development of plastic deformation

which is caused by the particle rotation leading to a degradation of the ability of strain transmission

are the micro-mesoscale physical mechanism of the trans-scale evolution of foundation plastic zone.