The Analysis For Consolidation Of Soft Clay With Threshold Hydraulic Gradient By Considering Complex Boundary Conditions

In the classical Terzaghi consolidation theory,the drainage boundary is considered as completely permeable or completely impermeable.However,many tests show that the excess pore water pressure at the drainage boundary of soft clay layer isn’t equal to0,and its value will decrease with time,and finally tends to zero infinitely.In many non Darcian seepage models,the seepage model with threshold hydraulic gradient is the most simple.It should be noted that the consolidation theory of soft clay considering both the complexity of drainage boundary(partial permeable boundary,continuous drainage boundary)and the threshold hydraulic gradient is still rarely reported.From the point of view of convenient engineering application,this paper studies the consolidation theory of soft clay considering complex boundary and threshold hydraulic gradient,and gives the one-dimionsion approximate analytical solution of the corresponding consolidation model.The innovations of the paper include:1.According to the actual condition of incompressible layer on the top of natural soft clay foundation to enhance drainage efficiency,a one-dimensional consolidation model of soft clay considering threshold hydraulic gradient under instantaneous loading is established.The governing equation of the model is established and the definite solution conditions of the model are given,and the approximate analytical solution of the consolidation model is obtained by eigenvalue method.At the same time,the numerical solution of the consolidation model is obtained by using the finite difference method.To verify their reliability,the calculation results of analytical solution are compared with numerical solution.Based on the analytical solution,the influence of threshold gradient and partial permeable boundary on consolidation behavior is analyzed.The downward movement law of moving boundary is analyzed,and the distribution of excess pore water pressure in incompressible layer and clay layer is discussed.2.In view of the fact that the load is applied slowly with time in practical engineering,a consolidation model considering the threshold hydraulic gradient of partial permeable boundary under single-stage loading is established.By using eigenvalue method and Laplace transform,the approximate analytical solution of consolidation considering partial permeable boundary and threshold hydraulic gradient is obtained.The change law of the moving boundary position and the variation law of excess pore water pressure in clay layer during consolidation are discussed.The analytical solution of the consolidation model is degenerated,and the reliability of the solution is verified by comparing with the solution in the literature.Finally,the influences of partial permeable boundary,threshold hydraulic gradient and loading rate on consolidation behavior are analyzed.3.In view of the fact that the pore water pressure at the drainage boundary of natural soft clay foundation is not completely permeable and the seepage of water in soft clay conforms to non-Darcy seepage considering threshold hydraulic gradient,a consolidation model considering continuous drainage boundary and threshold hydraulic gradient under instantaneous loading is established.The governing differential equation of consolidation and the condition of definite solution are given.The approximate analytical solution of the model is obtained by Fourier transform,and the difference solution of the consolidation model is obtained by finite difference method.The reliability of the solution is verified by comparing the analytical solution with the result of the difference solution.The influence of continuous drainage boundary and threshold hydraulic gradient parameters on consolidation behavior is discussed.4.In view of the fact that the load is applied slowly step by step in the engineering,the motion law of the moving boundary considering the continuous drainage boundary and the threshold hydraulic gradient and the distribution of excess pore water pressure under variable load are discussed.The consolidation model of soft clay considering threshold hydraulic gradient under variable load is established.The approximate analytical solution of one-dimensional consolidation considering continuous drainage boundary and threshold hydraulic gradient under single-stage loading is obtained by using Fourier transform and Laplace transform.At the same time,the analytical solution is degenerated and compared with the existing solutions to verify the correctness of the solution.Taking the single-stage loading as an example,the influence of continuous drainage boundary,threshold hydraulic gradient parameters and loading rate on consolidation behavior is analyzed.