Nonlocal peridynamic method for porous media seepage simulation

Based on the establishment of peridynamic nonlocal porous media seepage model, several kernel functions reflecting the degree of nonlocal effect are introduced to improve the calculation accuracy, and the peridynamic permeability coefficients corresponding to different kernel functions are derived. In the two-dimensional seepage model, the Weibull-distributed permeability coefficient model and the fracture network seepage model are established to realize the heterogeneous seepage in porous media matrix and fracture, respectively, which make up for the shortage of classical peridynamic model that cannot well simulate the heterogeneous seepage in porous media such as rock and soil. Different kernel function models are tested in simulating one-dimensional seepage problem, and the influence of kernel functions on simulation result is analyzed. The results show that the improved model can well converge to the theoretical solution, and the polynomial kernel function has the highest convergence accuracy relative to other kernel functions. Then, the polynomial kernel function is introduced into the two-dimensional model, and the corresponding two-dimensional permeability coefficient is derived. The proposed heterogeneous seepage model is employed in the simulation of two-dimensional seepage in porous media with and without fracture, and the results show that the proposed model can well simulate the heterogeneous seepage process in rock materials. Therefore, the proposed heterogeneous seepage model has wide application prospect in porous media seepage simulation.