止水帷幕渗漏时基坑稳态渗流场解析解

doi:10.12068/j.issn.1005-3026.2024.12.013

摘要/Abstract

摘要：

为了研究止水帷幕渗漏时的各向同性土层中基坑的二维稳态渗流场，根据基坑的对称性取基坑的一半截面进行计算，将止水帷幕周围土层划分为5个规则的区域，利用叠加法和分离变量法求出这5个区域内的水头分布级数解，结合区域间的连续条件得出基坑周围渗流场的显式解析解.将得到的水头、水压力和止水帷幕渗漏处渗流量计算结果与有限元软件计算结果以及文献中的结果进行对比，验证了解析解的正确性，相较于有限元解，解析解具有更高的计算效率.通过参数分析发现，竖向渗漏裂缝位置和宽度对基坑水头分布和止水帷幕上的水压力的影响较小，对渗漏位置处的渗流量的影响较大.

关键词: 二维稳态渗流, 显式解析解, 水压力, 渗流量, 止水帷幕渗漏

Abstract:

To study the two‑dimensional steady‑state seepage in a pit with isotropic soil during water stop curtain leakage， half the pit’s cross‑section is analyzed due to symmetry. The soil around the water curtain is divided into five regions， and the head distribution is solved using superposition and separation of variables， leading to an explicit analytical solution for the seepage field， considering continuity between regions. Results for head， water pressure， and seepage flow volume at leakage are compared with that of finite element software and references， confirming the analytical solution’s accuracy and efficiency. Parameter analysis shows that vertical leakage crack location and width have minimal impact on head and pressure but significantly affect seepage flow volume.

Key words: two?dimensional steady?state seepage, explicit analytical solution, water pressure, seepage volume, water stop curtain leakage

中图分类号:

TU 43

余俊, 张伟杰, 李东凯. 止水帷幕渗漏时基坑稳态渗流场解析解[J]. 东北大学学报（自然科学版）, 2024, 45(12): 1778-1786.

Jun YU, Wei-jie ZHANG, Dong-kai LI. Analytical Solution for Steady-State Seepage in Pits During Water Stop Curtain Leakage[J]. Journal of Northeastern University(Natural Science), 2024, 45(12): 1778-1786.

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链接本文: https://xuebao.neu.edu.cn/natural/CN/10.12068/j.issn.1005-3026.2024.12.013

https://xuebao.neu.edu.cn/natural/CN/Y2024/V45/I12/1778

图/表 12

图1 止水帷幕渗漏时基坑二维渗流模型

Fig.1 Two‑dimensional seepage modeling of foundation pit during leakage of water curtains

表1 基坑模型的参数

Table 1 Parameters of the pit model

b/m	c/m	h₁/m	h₂/m	a/m	h₃ /m	d₂/mm	k/（m·s^-1）
10	3	16.8	11.2	5	13.45	60	1×10^-9

图2 有限元模型网格划分示意图

Fig.2 Finite element model meshing diagram

图3 本文与有限元软件水头计算结果对比

Fig.3 Comparison of this paper and finite element software head calculation results

图4 水压力计算结果对比验证

Fig.4 Comparison and verification of water pressure calculation results

图5 文献[17]渗流量计算结果与本文解对比

Fig.5 Comparison of the seepage volume calculation results from literature[17] with the solution in this paper

图6 d2对基坑周围水头的影响

Fig.6 Effect of d2 on head around the pit

图7 h3对基坑周围水头的影响

Fig.7 Effect of h3 on head around the pit

图8 本文解与止水帷幕无渗漏水头计算结果对比

Fig.8 Comparison of this paper’s solution with the results of the non‑leakage head calculation of the water stop curtains

图9 d2对基坑达到稳态渗流后水压力的影响

Fig.9 Effect of d2 on the surrounding water pressure after the pit reaches steady‑state seepage

图10 h3对基坑达到稳态渗流后周围水压力的影响

Fig.10 Effect of h3 on the surrounding water pressure after the pit reaches steady‑state seepage

图11 d2和h3对止水帷幕渗漏处渗流量的影响

Fig.11 Influence of d2 and h3 on the amount of seepage flow at the water stop curtain leakage

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