带有两端防渗墙坝基的各向异性渗流解析解  

Analytical solution of anisotropic seepage in dam foundation with anti-seepage walls at both ends

作　　者：余俊[1] 李东凯 和振 张志中 YU Jun;LI Dong-kai;HE Zhen;ZHANG Zhi-zhong(School of Civil Engineering,Central South University,Changsha,Hunan 410075,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075

出　　处：《岩土力学》2023年第8期2381-2388,共8页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.52078496)。

摘　　要：由于目前在坝基设计中通常需要设置两个或两个以上防渗墙,对带有两端防渗墙的坝基各向异性稳态渗流进行了解析研究,将土体分为4个规则的区域,采用坐标变换将各向异性土层转换成等效各向同性土层,利用分离变量法将4个区域内的水头分布表示为级数解的形式,结合区域间的连续条件得出带有两端防渗墙的坝基各向异性渗流场显式解析解。将解析解退化到各向同性情况下的渗流量、坝底扬压力与保角变换解析解和数值计算结果进行对比,各向异性情况下的水头值与有限元软件计算结果进行对比,结果均吻合较好,验证了解析解的正确性,且相比于保角变换解析解具有更高精度。最后对坝基渗流场进行了参数分析,发现土体各向异性对坝基渗流有着不可忽略的影响,其他条件相同的情况下,竖直渗透系数与水平渗透系数比值较大土体的渗流量和出口梯度会小于竖直渗透系数与水平渗透系数比值较小的土体,竖直渗透系数与水平渗透系数比值较大的土体的最大扬压力会大于竖直渗透系数与水平渗透系数比值较小的土体。Since two or more anti-seepage walls are usually required in the present design of dam foundation,the anisotropic steady-state seepage of dam foundation with anti-seepage walls at both ends is analytically studied in this paper.The soil is divided into four regular regions,the anisotropic soil layer is converted into the equivalent isotropic soil layer by coordinate transformation,and the water head distribution in the four regions is expressed as a series solution by using the separation variable method.The explicit analytical solution of the anisotropic seepage field of the dam foundation with anti-seepage walls at both ends is obtained by combining the continuity conditions between regions.The analytical solution in this paper is reduced to the seepage flow under isotropic conditions,the uplift pressure at the dam bottom,the analytical solution and numerical results of conformal transformation are compared.The head value under anisotropic conditions is compared with the calculation results of the finite element software.The results are in good agreement,which verifies the correctness of the analytical solution in this paper,and the analytic solution has a higher accuracy than the analytical solution of conformal transformation.Finally,a parametric analysis of the seepage field at the base of the dam shows that soil anisotropy has a non-negligible effect on seepage at the base of the dam,and that,all other things being equal,the seepage volume and outlet hydraulic gradient of a soil with a larger ratio of vertical to horizontal permeability coefficient will be smaller than those of a soil with a smaller ratio of vertical to horizontal permeability coefficient;the maximum lift pressure of a soil with a larger ratio of vertical to horizontal permeability coefficient will be larger than that of a soil with a smaller ratio of vertical to horizontal permeability coefficient.

关 键 词：坝基 防渗墙 二维稳态渗流 渗透各向异性 显式解析解 扬压力 渗流量 出口梯度 

分 类 号：TV223[水利工程—水工结构工程]