Improved PINNs and Their Application in Nonlinear Consolidation Problems

The nonlinear consolidation models of saturated soft soils,generally difficult to resolve analytically,are mainly solved based on traditional numerical methods.Considering a one-dimensional nonlinear consolidation problem with continuous drainage boundary conditions,we introduce a new nontraditional numerical method,i.e.,physics-informed neural networks (PINNs),take the hard constraints into for modification,and obtain its high-precision PINNs-H solutions (PINNs-H denotes the PINNs with the hard constraints).The nonlinear factor (N_σ) in the consolidation model is correctly estimated via the PINNs-H method.It is found that when the ratio of compressibility index C_c to permeability index C_k is equal to 1,PINNs-H solutions agree well with the corresponding analytical solutions,while the PINNs solutions fail.When C_c/C_k≠1,the PINNs-H solutions are revealed to be continuous compared with the discretization solutions of the finite difference,via the PINNs-H the same average degree of consolidation can be obtained based on fewer training sample points,which correspond to the grid points of the finite difference.In addition,we find that N_σ reflected by the PINNs-H is more accurate than that via the PINNs.PINNs-H provides a new strategy for studying soft soil consolidation problems.