Analysis of one-dimensional rheological consolidation with flow described by non-Newtonian index and fractional-order Merchant's model

To further investigate the theological consolidation mechanism of saturated clay, the Koeller spring-pot element based on Caputo's fractional derivative is introduced to replace the Newton dashpot element of the classical Merchant model. The flow model with the non-Newtonian index is employed to describe the non-Darcian flow in the process of rheological consolidation. Accordingly, a one-dimensional theological consolidation equation is obtained, and its numerical analysis is conducted by the implicit finite difference method. In order to verify its validity, the numerical solutions by the present method for some simplified cases are compared with the results in the related literature. Then, the effects of the parameters of non-Darcian flow and fractional-order Merchant's model on the rheological consolidation are investigated. Numerical results indicate that the fractional order and the viscosity coefficient more greatly affect the ground settlement than the dissipation of pore water pressure. The rate of ground settlement lowers as the fractional order decreases or the viscosity coefficient increases. The flow described by non-Newtonian index delays the dissipation of pore water pressure and reduces the rate of ground settlement compared with the Darcy flow. Moreover, the development of ground settlement is always slower than the dissipation of pore water pressure considering the rheological effect.