## 1 Introduction  
Saturated soft soil will produce excess pore water pressure under loading, and the dissipation of excess pore water pressure causes internal pore shrinkage to produce soil settlement, i.e., consolidation of the soil body. In 1925, [PERSON] [1] established a 1D consolidation theory based on a series of idealized assumptions, such as coefficients of permeability and compression remaining unchanged in the consolidation process, etc. Subsequently, researchers continuously revised its basic assumptions to develop and improve the 1D consolidation theory so that it is closer to the natural properties. [PERSON] et al. [2] derived the governing equation of 1D large deformation consolidation of soils and obtained the theory of 1D large deformation consolidation, but due to the highly nonlinear nature of the governing equation, the analytical solution could not be obtained directly. [PERSON] et al. [3] obtained the analytical solution of 1D large deformation consolidation of saturated soil by assuming that the compression coefficient is a constant and the permeability coefficient and the square of the void ratio are proportional to each other. [PERSON] and [PERSON] [4] obtained a 1D nonlinear consolidation theory for soils based on a linear \(e-\lg\sigma^{\prime}\) relationship by assuming that the coefficient of permeability \(k_{\rm v}\) varies synchronously with the coefficient of volume compressibility \(m_{\rm v}\) during consolidation and that the self-gravitational stress remains constant along depth. [PERSON] et al. [5] established a 1D nonlinear consolidation equation of soil based on a hyperbolic compression model and obtained the analytical solutions. [PERSON] et al. [6] derived an analytical solutions of 1D nonlinear consolidation of single-layer and two-layer soils under the conditions of unipolar loading on the basis of assumptions made by [PERSON] and [PERSON]. [PERSON] [7] utilized the ingress method to solve the problem of nonlinear consolidation of soil when the consolidation coefficient \(C_{\rm v}\) is a variable. [PERSON] et al. [8] obtained a semi-analytical solution to 1D nonlinear consolidation for layered soils under time-varying loading with \(C_{\rm v}\) by using the method of discretization of soil thickness. It is worth noting that it is difficult to obtain an analytical solution in nonlinear consolidation theory unless the consolidation coefficient \(C_{\rm v}\) is constant. Therefore, in most cases, nonlinear consolidation was usually solved by numerical methods such as the finite element method (FEM), finite difference method (FDM), finite volume method (FVM), etc., in order to obtain a nonlinear consolidated high-accuracy numerical solution. With the increase in available computational resources, traditional numerical methods can effectively solve such highly nonlinear problems. However, for these traditional numerical methods, careful spatio-temporal discretization is essential. In recent years, PINNs have become increasingly popular in solving partial differential equations (PDEs), which, instead of solving PDEs directly, identify the nonlinear mapping between inputs and outputs through agent modeling [9]. Although ordinary deep neural networks (DNNs) can approximate any continuous function under certain conditions, they usually require a large amount of labeled data to maintain their accuracy [10]. To overcome this drawback, [PERSON] et al. [11] introduced the concept of PINN and used PINN to solve benchmark PDEs such as the Navier-Stokes equations. PINN is the process of embedding PDEs and known physical knowledge such as initial and boundary conditions in a DNN and evaluating the model on a set of dispersed spatio-temporal points called residual points. The development of PINN has benefited from the progress of deep learning, such as libraries like Pytorch [12] and tensorflow [13], and many code libraries based on PINN have been developed, such as DeepXDE [14] and SciANN [15].