岩土力学 ›› 2023, Vol. 44 ›› Issue (11): 3109-3116.doi: 10.16285/j.rsm.2022.2019

• 基础理论与实验研究 • 上一篇    下一篇

考虑潜水面的基坑二维稳态渗流场解析解

余俊,张扬,郑靖凡,张志中   

  1. 中南大学 土木工程学院,湖南 长沙 410075
  • 收稿日期:2022-12-30 接受日期:2023-03-09 出版日期:2023-11-28 发布日期:2023-11-28
  • 作者简介:余俊,男,1978年生,博士,副教授,主要从事隧道与地下工程方面的教学和研究工作。
  • 基金资助:
    国家自然科学基金(No. 52078496)。

Analytical solution of two-dimensional steady-state seepage field in a pit considering a phreatic surface

YU Jun, ZHANG Yang, ZHENG Jing-fan, ZHANG Zhi-zhong   

  1. School of Civil Engineering, Central South University, Changsha, Hunan 410075, China
  • Received:2022-12-30 Accepted:2023-03-09 Online:2023-11-28 Published:2023-11-28
  • Supported by:
    This work was supported by the National Natural Science of China (52078496).

摘要: 对考虑潜水面悬挂式止水帷幕支护下的基坑二维稳态渗流场进行了解析研究,并给出一种求解潜水面的解析方法。根据对称性取基坑半截面,并根据边界的连续条件将其分为3个规则区域,使用分离变量法分别将3个区域的水头分布表示为级数解的形式,结合区域之间的连续性条件及级数正交条件得到各区域渗流场的显式解,根据潜水面所满足的总水头等于位置水头的条件确定潜水面。将解析解方法计算结果与室内试验、有限元分析结果进行比对分析,结果验证了解析解的正确性,解析方法相较于有限元数值方法具有更高效的计算效率。对潜水面位置进行参数分析,发现止水帷幕插入深度、基坑宽度及深度对潜水面位置有不可忽视的影响。随着过水断面厚度的增加,潜水面位置逐渐降低,不考虑极端状态的情况下可认为帷幕底部至不透水层顶面的距离与潜水面在止水帷幕上的位置呈线性关系;随着基坑尺寸的增加,潜水面位置呈下降趋势,基坑内侧半宽度对潜水面的影响明显小于帷幕底部至不透水层顶面的距离,且随着基坑内侧半宽度的增加影响越来越小;潜水面位置随着基坑深度的增大而降低,基坑深度对潜水面位置的影响相对较大。

关键词: 基坑, 止水帷幕, 潜水面, 二维稳态渗流, 解析解, 渗流

Abstract: The two-dimensional steady-state seepage field of the foundation pit under suspended waterproof curtains support considering the phreatic surface is studied analytically, and an analytical method for solving the phreatic surface is given. According to the symmetry, the half section of the foundation pit is taken, and it is divided into three regular regions based on the continuity conditions of the boundary. The variable separation method is used to express the water head distribution in the three regions as a series solution. The explicit solution of the seepage field in each region is obtained by combining the continuity conditions between regions and the orthogonality conditions of the series. The water table is determined based on the condition that the total water head satisfied by the water table is equal to the position water head. The analytical solution in this paper is compared with the results of laboratory tests and finite element analysis, the results verify the correctness of the analytical solution, which has higher efficient computational efficiency than that of the finite element numerical method. Performing a parametric analysis of the phreatic surface location, it was found that the insertion depth of waterproof curtain, the width and depth of foundation pit have a non-negligible effect on the phreatic surface location. As the thickness of the cross section increases, the position of the phreatic surface gradually decreases, and the distance from the bottom of the curtain to the top surface of the confining stratum has a linear relationship with the position of the phreatic surface on the waterproof curtain, without considering the extreme conditions. As the size of the foundation pit increases, the location of the phreatic surface shows a downward trend. The influence of the inner half width of the foundation pit on the phreatic surface is significantly smaller than that of the distance from the bottom of the curtain to the top surface of the confining stratum, this influence decreases with increasing the inner half width. The location of the phreatic surface decreases as the depth of the foundation pit increases, and the depth of the foundation pit has a relatively large influence on the location of the phreatic surface.

Key words: foundation pit, waterproof curtain, phreatic surface, two-dimensional steady-state seepage, analytical solution, seepage

中图分类号: 

  • TU 46+3
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