Simplified solution to one-dimensional consolidation with threshold gradient

In this paper, a simplified solution of the soil consolidation problem with a threshold gradient is presented, which can be expressed by elementary functions. The analytical solution satisfies the boundary condition but does not satisfy the one-dimensional consolidation equation by Terzaghi (1923). The analytical solution is compared with the analytical and numerical solutions by Pascal et al (1981). It is concluded that the pore water pressure at the moving boundary from the analytical solution in this paper is closer to the numerical solution and can precisely satisfy the boundary conditions. The degree of dissipation of pore water pressure deviates from Pascal's analytical solution by less than 4%. The results show that the degree of dissipation of pore water pressure considering the threshold gradient is related to the dimensionless threshold gradient parameter R. When 0 R <= 1, the final degree of dissipation of pore water pressure tends to 1-R/2; When R 1, the final degree of dissipation of pore water pressure tends to 1/2R.