渗透各向异性圆形围堰稳态渗流场解析解  

Analytical solution for steady seepage around circular cofferdam in soil layer with anisotropic permeability

作　　者：黄娟[1] 和振 余俊[1] 杨鑫歆 HUANG Juan;HE Zhen;YU Jun;YANG Xin-xin(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4期1035-1043,1088,共10页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.52078496)。

摘　　要：对渗透各向异性土层中的圆形围堰渗流场进行解析研究。将圆形围堰周围渗流场分为3个区域,通过坐标变换以及将边界条件齐次化后,用分离变量法分别得到柱坐标系下3个区域的水头分布级数解形式,结合区域间的连续条件,并利用贝塞尔函数正交性得到渗透各向异性土层中圆形围堰稳态渗流场的显式解析解,与Plaxis2D软件的计算结果进行对比,验证了解析解的正确性。基于解析解,进一步推导出了涌水量、出逸比降公式,并与不同方法的计算结果作了对比,最后对稳态渗流情况下的水压力进行了计算分析。结果表明:相比于其他近似法,解析解求取的流量、出逸比降以及渗流情况下水压力与数值计算结果高度吻合;渗流水压力会随着围堰半径、纵横向渗透系数比值的增大而减小,而后逐渐趋近于一个稳定值。The seepage field of circular cofferdam in permeable anisotropic soil layer is analyzed in present study. First, the seepage region around circular cofferdam is divided into three regular parts. The series solutions of water head distribution in three regions in cylindrical coordinate system are obtained by using method of separation of variables after coordinate transformation and homogenization of boundary conditions. And then an analytical solution of steady seepage field of circular cofferdam in permeable anisotropic soil is obtained by utilizing the orthogonality of Bessel function. The solution is verified through the comparison with the results obtained from the finite element software Plaxis2D. Based on the analytical solution, the expressions for seepage quantity and exit gradient are deduced and compared with the results obtained by different methods. Finally, the water pressure under steady seepage is calculated and analyzed. The results show that the seepage quantity, exit gradient and the water pressure obtained by analytical solution are in good agreement with numerical results as compared with results obtained by other methods;the seepage water pressure decreases with the increase of the ratio of cofferdam radius and vertical and horizontal permeability coefficients, and then gradually approaches a stable value.

关 键 词：圆形围堰渗流 解析解 渗透各向异性 出逸比降 涌水量 水压力 

分 类 号：TU43[建筑科学—岩土工程]