长江科学院院报2024，Vol.41Issue(12)：126-132,7.DOI:10.11988/ckyyb.20230752
Richards方程Laplace变换解中几个遗留问题的讨论
Discussion on Several Remaining Problems in the Laplace Transform Solution of Richards Equation
摘要
Abstract
In this paper we addressed and elaborated on three critical issues concerning the Laplace transform solu-tion of the Richards equation:the convergence of the original function,the steps for inverse transform,and the ap-plicability of the equation.By presenting theoretical counterexamples,employing integral transformations and substi-tution schemes as well as real engineering cases,we demonstrated that assuming the convergence of the original function can lead to significant errors.Therefore,it is necessary to assess the convergence of the infiltration function before applying the Laplace transform.We also elucidated the steps for solving the Laplace inverse transform,theo-retically addressing a gap in geotechnical literature.Furthermore,we reveal an anomaly where,in certain applica-tions,the Laplace solution may show higher moisture content in lower soil layers than in upper layers.We analyzed this phenomenon from both physical and mathematical perspectives,highlighting inherent limitations in this solu-tion.The findings of this study may help to theoretically strengthen the framework of unsaturated soil theory.关键词
土力学/Richards方程/Laplace逆变换/非饱和入渗/微分方程求解Key words
soil mechanics/Richards Equation/inverse Laplace transform/unsaturated infiltration/solution of dif-ferential equation分类
建筑与水利引用本文复制引用
朱悦璐,李光灿,吴帅兵..Richards方程Laplace变换解中几个遗留问题的讨论[J].长江科学院院报,2024,41(12):126-132,7.基金项目
国家自然科学基金项目(52069014) （52069014）
