###### Abstract  
Adopting the non-Darcy flow presented by [PERSON] and considering the nonlinear compression and permeability characteristics of soils, the one-dimensional nonlinear consolidation problem of soft clays is investigated by means of a continuous drainage boundary. The numerical solutions of average consolidation degrees defined by settlement and excess pore water pressure are derived by using the finite difference method, and the correctness of these solutions is verified by comparing them with existing analytical and numerical solutions. Based on the proposed solutions, a parametric study is conducted to study the influence of interface parameter, non-Darcy flow parameter and soil nonlinearity on the consolidation behavior of soft clays. The results show that the solutions based on the continuous drainage boundary can be degenerated into the solutions based on the Terzaghi drainage boundary if the interface parameter is taken as a reasonable value. The soil consolidation behavior considering both non-Darcy seepage and nonlinear characteristics of soil is very complex. one-dimensional consolidation; continuous drainage boundary; non-Darcy flow; nonlinear consolidation; average consolidation degree 25 February 202312 March 202313 March  
consolidation of soil should also be paid more attention [3; 5]. In view of this, assuming that the permeability coefficient and the compression coefficient change synchronously during the consolidation process and the self-weight stress remains unchanged along the depth, [PERSON] and [PERSON] first derived an analytical for the 1D nonlinear consolidation of saturated soil under instantaneous loading [17]. Based on the currently recognized \(e\)-lg\(\sigma^{\prime}\) and \(e\)-lg\(\kappa\) relations, [PERSON] and [PERSON] obtained a solution for the 1D nonlinear consolidation of saturated soil by using the finite difference method [18]. Soon after, many scholars investigated the nonlinear consolidation problems of soil by considering variable load [19; 20] and layered characteristics of soils [21; 22]. In order to consider the influence of both soil nonlinear characteristics and non-Darcy seepage on the soil consolidation process, [PERSON] et al. solved the 1D nonlinear consolidation problem of saturated clay under non-Darcy seepage [23]. [PERSON] et al. investigated the influence of variable load on the 1D nonlinear consolidation of soil with non-Darcy flow [24]. Soon after, [PERSON] et al. further investigated the 1D nonlinear consolidation of soil with non-Darcy flow by considering the influence of variable load, large deformation and so on [25; 26]. Due to the complexity of the soil consolidation problem considering both soil nonlinearity and non-Darcy seepage, the drainage boundary especially may change with time, and further in-depth study on this topic is still needed. The classic Terzaghi consolidation theory assumes that the drainage boundary conditions are fully pervious and impervious, but in engineering practice, the drainage capacity of a soil boundary always changes between fully permeable and fully impermeable. To simulate the soil drainage boundary more realistically, [PERSON] [27] originally proposed the impeded drainage boundary, which was introduced by [PERSON] and [PERSON] [28] to investigate the 1D consolidation problem of layered saturated soil with variable coefficients of permeability and compressibility. Subsequently, many scholars have introduced [PERSON]'s impeded drainage boundary to study the 1D problems of single-layered [29; 30; 31; 32], bilayered [33; 34; 35] and multilayered soils [15; 36]. Nevertheless, owing to the complexity of the impeded drainage boundary, it is not easy to obtain explicit solutions for most consolidation problems. Further, the above two models do not consider the relationship between drainage boundary and time, so they cannot reflect the fact that the drainage capacity of a boundary changes with the consolidation process [37]. In order to consider the time effect of a drainage boundary, [PERSON] et al.