One dimensional analytical solution of consolidation for general time-varying load cases
The existing analytical solutions for one-dimensional seepage consolidation are only applicable to specific load types,such as rectangular and triangular distributed loads.However,in practical engineering scenarios,more general load distribution forms are common,and loads often vary with time.To facilitate engineer-ing applications better,building upon previous research,this paper,under certain assumptions,employs theoreti-cal analysis to delineate the fundamental differential equations and corresponding boundary conditions for the one-dimensional seepage consolidation problem.Subsequently,utilizing the method of characteristic functions,a more general analytical solution for one-dimensional consolidation under time-varying load distributions is derived,fol-lowed by programming to solve the analytical solution.Finally,the new analytical solution is compared with exist-ing solutions for specific load types.The results demonstrate that employing the new analytical solution enables rapid and accurate determination of the one-dimensional consolidation analytical solution under general time-varying load conditions,thereby warranting its wider application in engineering contexts.
one dimensional consolidationanalytical solutiongeneral time-varying loadeigenfunction method