基坑二维稳态渗流场的解析解及简化解  

Analytical Solution and Simplified Solution of Two-Dimensional Steady Seepage Field in Foundation Pit

作　　者：余俊[1] 郑靖凡 张志中 李东凯 YU Jun;ZHENG Jingfan;ZHANG Zhizhong;LI Dongkai(School of Civil Engineering,Central South University,Changsha 410075,Hunan,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075

出　　处：《华南理工大学学报（自然科学版）》2024年第5期84-91,共8页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(52078496)。

摘　　要：在基坑工程中,地下水渗流对基坑稳定性的影响不可忽视,但现有的一维渗流理论无法完全满足渗流计算的安全性要求。针对现有理论的不足,对悬挂式不考虑厚度挡墙支护下的各向同性土层中基坑的二维稳态渗流场进行了解析。依据对称性取基坑半截面,将周围土层分成4个规则区域,利用叠加原理和分离变量法分别将4个区域内的水头表示为级数解的形式,结合区域间连续条件及级数解的正交性得出渗流场的显式解。对比解析解与PLAXIS 2D软件的水头计算结果,发现级数项取20的解收敛且取1时的解仍具有一定的精度,可分别视为精确解和简化解。提出的简化解计算方便,借助计算器即可快速完成对基坑任意一点水头的求解。对比一维静水压力、一维考虑渗流的水压力、流网法、简化解、精确解及数值解水压力计算结果,发现精确解与数值解吻合较好且较流网法精度更高,简化解较一维静水压力、一维考虑渗流的水压力精度更高。参数分析表明:精确解和简化解计算的水压力合力相对误差主要受基坑内侧水位和挡墙至不透水层距离的影响;简化解适用于基坑尺寸不大,尤其内侧水位线到挡墙底部距离大于7 m、底部不透水层到挡墙距离小于30 m的基坑,计算挡墙水压力合力作用点则适用于任意尺寸的基坑;与精确解相比,简化解误差主要出现在挡墙底部,其余位置在基坑尺寸不大时,水头误差小于5%。In foundation pit engineering,groundwater seepage significantly impacts pit stability,yet current one-dimensional seepage theory doesn’t fully meet safety standards for seepage calculation.This study addresses these gaps by analyzing two-dimensional seepage in isotropic soil layers under suspended support,disregarding retaining wall thickness.The water head in each of the four regions was expressed in the form of a series solution by using the superposition principle and the separation of variables method,and the analytical solution of the seepage field was obtained by combining the continuity conditions between the regions and the orthogonality of the series solu⁃tion.Comparing this analytical solution with PLAXIS 2D software results,it finds that a series term of 20 provides convergence,while a single term still maintains accuracy,representing exact and simplified solutions respectively.The simplified solution offers easy calculation,providing quick determination of water head at any point in the pit.Comparing the calculation results of one-dimensional water pressure,one-dimensional water pressure considering seepage,flow network method,simplified solution,exact solution and numerical solution,it is found that the exact solution is in better agreement with the numerical solution and has higher accuracy than the flow network method,and the simplified solution has higher accuracy than one-dimensional hydrostatic pressure and one-dimensional wa⁃ter pressure considering seepage.Parameter analysis reveals that relative error between accurate and simplified so⁃lutions for resultant water pressure is influenced by inner water level and distance from retaining wall to imperme⁃able layer.The simplified solution is suitable for foundation pits of small dimensions,especially when the distance from the inner water level to the bottom of the retaining wall is greater than 7 meters and the distance from the bot⁃tom impermeable layer to the retaining wall is less than 30 meters.The calculation of the point of appl

关 键 词：基坑 水压力 稳态渗流 解析解 简化解 

分 类 号：TU43[建筑科学—岩土工程]