Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.
Geometrical nonlinearity of the soft soil and the deviation of water flow in the soft clay from Darcy's law have been well recognized in practice. However, the theory of consolidation, which can account for both the geometrical nonlinearity and the non-Darcian flow, has not been reported so far. In this contribution, a model for the consolidation of soft clay which can allow for these two factors simultaneously is proposed. Utilizing the finite difference method, the numerical model for this problem is developed. With the numerical model, the effects of the geometrical nonlinearity and the non-Darcian flow on the consolidation of the soft soil are investigated. The results show that when the self-weight stress is calculated by the same method, the rate of the non-Darcian consolidation for the large-strain case is larger than that for the small-strain case, but the difference between them is limited. However, the difference between the consolidation rates caused by the non-Darcian and Darcian flows is significant. Therefore, when the geometrical nonlinearity of the soft clay is considered in calculating the consolidation settlement, due to the complexity of the large-strain assumption, the small-strain assumption can be used to replace it if the self-weight stress for the small-strain assumption is calculated by considering its sedimentation. However, due to the aforementioned large difference between the consolidation rates with consideration of the non-Darcian flow in soft clay or not, it is better to consider the non-Darcian flow law for both the small and large stain assumptions.
