适用于一般时变荷载情况的一维固结解析解

One dimensional analytical solution of consolidation for general time-varying load cases

现有的一维渗流固结解析解只适用于特定的荷载类型,如矩形分布荷载和三角形分布荷载,而工程实际中常见的是更为一般的荷载分布形式,而且荷载往往是随时间而变化的。为更好地便于工程应用,结合前人研究工作,本文在一定的假设基础上,采用理论分析方法明确了一维渗流固结问题对应的基本微分方程和相应的边界条件,然后采用特征函数法,推导出更为一般的随时间变化的荷载分布形式下一维固结解析解,并且对解析解进行编程求解。最后将新解析解与已有的特定荷载类型下的解析解进行对比,结果表明采用新解析解能够快速准确地得出一般时变荷载作用下的一维固结解析解,值得在工程应用中加以推广。

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 engineering applications better,building upon previous research,this paper,under certain assumptions,employs theoretical analysis to delineate the fundamental differential equations and corresponding boundary conditions for the onedimensional 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,followed by programming to solve the analytical solution.Finally,the new analytical solution is compared with existing 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 timevarying load conditions,thereby warranting its wider application in engineering contexts.