Numerical Simulation of Flexural Deformation Through an Integrated Cosserat Expanded Constitutive Model and the Drucker–Prager Criterion

In this article, we propose a new numerical approach, abbreviated as Cos-SDA, for analyzing flexural deformation problems of geomaterials. The Cos-SDA is achieved by implanting the strong discontinuity approach (SDA) into the computational framework of the Cosserat continuum finite element approach (Cos-FEA). Most of the Cos-FEA is based on the Mohr–Coulomb (M-C) criterion at present. However, the M-C yield surface is not smooth because of hexagonal corners, which can cause numerical difficulties in the Cos-FEA. The Drucker–Prager (D-P) criterion can be viewed as a smooth approximation to the M-C criterion. Meanwhile, the M-C criterion does not take into account the influence of the intermediate principal stress on strength, but D-P criterion is able to reflect the combined effect of the three principal stresses. Therefore, based on the MATLAB system, an improved three-dimensional (3D) Cos-FEA is proposed by using the D-P criterion. Through a numerical example of three-dimensional flexural deformation analysis of an excavation in layered rock, it is demonstrated that the improved Cos-FEA can effectively simulate flexural deformation and the entire progressive failure process. The improved Cos-FEA inherits the advantages of both the Cos-FEA and D-P criterion and neutralizes their mechanical responses, so it is more reasonable in simulating the progressive failure process occurring in an alternating rock mass. Most importantly, the D-P criterion-based Cos-FEA is observed to have a higher convergence speed and stability.