强降雨条件下单层土质覆盖层的入渗解析解及斜坡稳定性分析

李光耀; 刘兆龙; 冯嵩; 詹良通; 杜修力

doi:10.11779/CJGE20240158

强降雨条件下单层土质覆盖层的入渗解析解及斜坡稳定性分析 English Version

李光耀^{1, 2,},
刘兆龙¹,
冯嵩^3, ,,
詹良通⁴,
杜修力¹

1.
北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124
2.
北京工业大学重庆研究院, 重庆 401151
3.
福州大学土木工程学院, 福建福州 350108
4.
浙江大学软弱土与环境土工教育部重点实验室, 浙江杭州 310058

基金项目:

国家自然科学基金项目 42107186

北京市自然科学基金项目 8242001

重庆市自然科学基金项目 CSTB2023NSCQ-MSX0279

详细信息

作者简介:
李光耀(1991—)，男，博士，主要从事环境岩土工程方面的教学和研究工作。E-mail: geoguangyao@bjut.edu.cn

通讯作者:
冯嵩, E-mail: sfengaa@connect.ust.hk

中图分类号: TU43
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出版历程
- 收稿日期: 2024-02-19
- 网络出版日期: 2024-07-23
- 刊出日期: 2025-05-31

Analytical solution for infiltration into single-layer cover under heavy rainfall events and its application for slope stability analysis

1.
Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China
2.
Chongqing Research Institute, Beijing University of Technology, Chongqing 401151, China
3.
School of Civil Engineering, Fuzhou University, Fuzhou 350108, China
4.
MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China

摘要

摘要: 近年来中国极端降雨事件频发，研究强降雨条件下单层土质覆盖层的入渗规律及斜坡稳定性具有重要意义。基于二维非饱和土渗流控制方程，采用指数函数模型描述土体的土水特征曲线和渗透系数曲线，针对强降雨过程中表层土体达到饱和状态前后分别采用恒定流量和恒定压力水头作为覆盖层表面边界条件，推导了强降雨条件下单层土质覆盖层的入渗解析解。通过与有限元软件Geostudio-Seep/W的计算结果进行对比，证明了该解析解的有效性。在解析解的基础上，根据非饱和土抗剪强度理论，分析了单层土质覆盖层的斜坡稳定安全系数在强降雨条件下的发展情况，结果表明潜在滑动面的埋深越大，覆盖层稳定安全系数对降雨的响应速度越慢。强降雨期间以覆盖层底面作为滑动面的稳定安全系数始终保持最小，说明覆盖层最易沿着该滑动面发生失稳。得到的解析解为单层土质覆盖层的防渗性能评价及斜坡稳定性分析提供了简单实用的工具。
- 解析解 /
- 强降雨条件 /
- 单层土质覆盖层 /
- 雨水入渗 /
- 斜坡稳定性
Abstract: In recent years, the extreme rainfall events have occurred frequently in China, and so investigating the infiltration law and slope stability of single-layer soil covers under heavy rainfall events is of great significance. An analytical solution for rainwater infiltration into single-layer soil covers is derived based on the two-dimensional governing equation for unsaturated flows. This analytical solution is obtained by employing the constant flow rate and constant pore water pressure head as the top boundary conditions of the cover before and after the surface soil reaches saturation during a heavy rainfall event. The analytical solution is validated by comparing with the results of the finite element software Geostudio-Seep/W. Based on the analytical solution and the theory of shear strength of unsaturated soils, the variation of the factor of safety of a single-layer soil cover under a heavy rainfall event is analyzed. The results indicate that the greater depth the potential sliding surface, the slower the response of the factor of safety to rainfall. During the whole rainfall period, the factor of safety with the bottom surface of the cover as the sliding surface remains the smallest, indicating that the cover is most prone to sliding along this sliding surface. The analytical solution obtained in this study provides a simple and practical tool for evaluating the anti-seepage performance and stability analysis of single-layer soil covers.
- analytical solution /
- heavy rainfall condition /
- single-layer soil cover /
- rainwater infiltration /
- slope stability

HTML全文

图 1 倾斜单层土质覆盖层示意图

Figure 1. Schematic diagram of an inclined single-layer soil cover

下载: 全尺寸图片幻灯片

图 2 覆盖层土体的水力特性

Figure 2. Hydraulic properties of the cover soil

下载: 全尺寸图片幻灯片

图 3 覆盖层的水力响应（曲线为解析解，符号为数值解）

Figure 3. Hydraulic response of the cover (splines represent analytical results and symbols represent numerical results)

下载: 全尺寸图片幻灯片

图 4 不同解析解下覆盖层孔隙水压力水头剖面随降雨时间的变化（曲线为本文解析解结果，符号为文献[11]解析解结果）

Figure 4. Changes of pore water pressure head profile over rainfall duration for different analytical solutions (splines present results of analytical solutions in this study and symbols present results of analytical solutions in reference [11])

下载: 全尺寸图片幻灯片

图 5 覆盖层表面入渗速率和累积入渗量随时间的变化（曲线为解析解，符号为数值解）

Figure 5. Changes of infiltration rate and cumulative infiltration at top surface of cover over rainfall duration (splines present analytical results and symbols present numerical results)

下载: 全尺寸图片幻灯片

图 6 覆盖层底面渗漏速率和累积渗漏量随时间的变化（曲线为解析解，符号为数值解）

Figure 6. Changes of percolation rate and cumulative percolation at the bottom surface of cover over rainfall duration (splines present analytical results and symbols present numerical results)

下载: 全尺寸图片幻灯片

图 7 覆盖层稳定安全系数剖面随时间的变化

Figure 7. Changes of factor of safety profile of inclined cover over rainfall duration

下载: 全尺寸图片幻灯片

图 8 不同潜在滑动面稳定安全系数随降雨时间的变化

Figure 8. Changes of factor of safety of different potential slip surfaces over rainfall duration

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表 1 解析法和数值法中使用的参数

Table 1 Parameters used in analytical and numerical methods

饱和体积含水量 ${\theta _{\text{s}}}$ /%	残余体积含水量 ${\theta _{\text{r}}}$ /%	减饱和系数 $\alpha$ /m^-1	饱和渗透系数 ${k_{\text{s}}}$ /(m·s^-1)	初始体积含水量 ${\theta _0}$ /%	降雨强度 $q$ /(m·s^-1)	降雨历时/h
47.13	10.44	0.05	1.29×10^-7	34.0	2.85×10^-6	24

覆盖层厚度/m	坡度 $\delta$ /(°)	干土重度 ${\gamma _{\text{d}}}$ /(kN·m^-3)	水重度 ${\gamma _{\text{w}}}$ /(kN·m^-3)	有效黏聚力 $c'$ /kPa	有效内摩擦角 $\varphi '$ /(°)	基质吸力角 ${\varphi ^{\text{b}}}$ /(°)
1.0	arctan(1/3)	14.2	9.81	5.74	26.6	14.1

下载: 导出CSV

参考文献(26)

[1]	浦烨枫. 垃圾填埋场渗滤液对地下水的污染规律及防渗策略分析[J]. 工程建设与设计, 2022(14): 90-92. PU Yefeng. Analysis of the pollution law of landfill leachate to groundwater and the seepage prevention strategy[J]. Construction & Design for Engineering, 2022(14): 90-92. (in Chinese)
[2]	舒实, 施建勇. 气压和温度变化共同作用下垃圾填埋场边坡稳定性研究[J]. 岩土工程学报, 2022, 44(1): 82-89. doi: 10.11779/CJGE202201007 SHU Shi, SHI Jianyong. Slope stability of municipal solid waste landfills under combined effects of gas pressure and temperature changes[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(1): 82-89. (in Chinese) doi: 10.11779/CJGE202201007
[3]	何雪莲, 梁凌, 韦超前. 城镇生活垃圾填埋场环境问题分析及污染防控措施[J]. 广东化工, 2024, 51(2): 99-101, 129. HE Xuelian, LIANG Ling, WEI Chaoqian. Analysis of environmental problems and pollution prevention and control measures for urban domestic waste landfill sites[J]. Guangdong Chemical Industry, 2024, 51(2): 99-101, 129. (in Chinese)
[4]	詹良通, 冯嵩, 李光耀, 等. 生态型土质覆盖层工作原理及其在垃圾填埋场封场治理中的应用[J]. 环境卫生工程, 2022, 30(4): 1-20. ZHAN Liangtong, FENG Song, LI Guangyao, et al. Working principle of ecological soil covers and its application in landfill sealing treatment[J]. Environmental Sanitation Engineering, 2022, 30(4): 1-20. (in Chinese)
[5]	张文杰, 邱战洪, 朱成仁, 等. 长三角地区填埋场ET封顶系统的性能评价[J]. 岩土工程学报, 2009, 31(3): 384-389. https://cge.nhri.cn/article/id/13179 ZHANG Wenjie, QIU Zhanhong, ZHU Chengren, et al. Evalllation of evapotranspiration covers of landfills in Yangtze River Delta Region[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(3): 384-389. (in Chinese) https://cge.nhri.cn/article/id/13179
[6]	焦卫国, 詹良通, 季永新, 等. 植被对土质覆盖层水分运移和存储影响试验研究[J]. 岩土工程学报, 2020, 42(7): 1268-1275. doi: 10.11779/CJGE202007010 JIAO Weiguo, ZHAN Liangtong, JI Yongxin, et al. Experimental study on effects of vegetation on water transport and storage in soil cover[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(7): 1268-1275. (in Chinese) doi: 10.11779/CJGE202007010
[7]	王宜轩. 城市生活垃圾填埋场失稳破坏模式研究[D]. 杭州: 浙江理工大学, 2020. WANG Yixuan. Study on Instability and Failure Mode of Municipal Solid Waste Landfill[D]. Hangzhou: Zhejiang Sci-Tech University, 2020. (in Chinese)
[8]	HAYEK M. Analytical solution to transient Richards' equation with realistic water profiles for vertical infiltration and parameter estimation[J]. Water Resources Research, 2016, 52(6): 4438-4457. doi: 10.1002/2015WR018533
[9]	FENG S, HUANG R H, ZHAN L T, et al. Semi-analytical solution of pore-water pressure in unsaturated ground and infinite slope considering highly nonlinear soil hydraulic properties[J]. Computers and Geotechnics, 2023, 164: 105795. doi: 10.1016/j.compgeo.2023.105795
[10]	ZHAN T L T, QIU Q W, XU W J. Analytical solution for infiltration and deep percolation of rainwater into a monolithic cover subjected to different patterns of rainfall[J]. Computers and Geotechnics, 2016, 77: 1-10. doi: 10.1016/j.compgeo.2016.03.008
[11]	邱清文, 詹良通, 黄依艺. 考虑任意初始条件的均质土质覆盖层降雨入渗解析解[J]. 岩土工程学报, 2017, 39(2): 359-365. doi: 10.11779/CJGE201702021 QIU Qingwen, ZHAN Liangtong, HUANG Yiyi. Analytical solutions for rainfall infiltration into monolithic covers considering arbitrary initial conditions[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(2): 359-365. (in Chinese) doi: 10.11779/CJGE201702021
[12]	TRACY F T, VAHEDIFARD F. Analytical solution for coupled hydro-mechanical modeling of infiltration in unsaturated soils[J]. Journal of Hydrology, 2022, 612: 128198. doi: 10.1016/j.jhydrol.2022.128198
[13]	WU L Z, ZHANG L M. Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(6): 773-790. doi: 10.1002/nag.742
[14]	PU H F, WEN X J, MIN M, et al. Analytical solution for coupled water–gas transport in landfill cover[J]. Acta Geotechnica, 2023, 18(8): 4219-4231. doi: 10.1007/s11440-023-01802-x
[15]	ZHAN T L T, JIA G W, CHEN Y M, et al. An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(12): 1737-1760. doi: 10.1002/nag.2106
[16]	WU L Z, ZHANG L M, HUANG R Q. Analytical solution to 1D coupled water infiltration and deformation in two-layer unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 36(6): 798-816. doi: 10.1002/nag.1044
[17]	FREDLUND D G, MORGENSTERN N R, WIDGER R A. The shear strength of unsaturated soils[J]. Canadian Geotechnical Journal, 1978, 15(3): 313-321. doi: 10.1139/t78-029
[18]	李宁, 许建聪. 无限长均质斜坡降雨入渗解析解[J]. 岩土工程学报, 2012, 34(12): 2325-2330. https://cge.nhri.cn/article/id/14957 LI Ning, XU Jiancong. Analytical solutions for rainfall infiltration into homogenous infinite slopes[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(12): 2325-2330. (in Chinese) https://cge.nhri.cn/article/id/14957
[19]	RICHARDS L A. Capillary conduction of liquids through porous mediums[J]. Physics, 1931, 1(5): 318-333. doi: 10.1063/1.1745010
[20]	GARGNER W R. Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table[J]. Soil Sci, 1958, 85(4): 228-232. doi: 10.1097/00010694-195804000-00006
[21]	刘小川. 降雨诱发非饱和土边坡浅层失稳离心模型试验及分析方法[D]. 杭州: 浙江大学, 2017. LIU Xiaochuan. Centrifugal Model Test and Analysis Method of Shallow Instability of Unsaturated Soil Slope Induced by Rainfall[D]. Hangzhou: Zhejiang University, 2017. (in Chinese)
[22]	城镇雨水系统规划设计暴雨径流计算标准: DB11/T 969—2016[S]. 北京: 中国建筑工业出版社, 2016. Standard of Rainstorm Runoff Calculation for Urban Storm Drainage System Planning and Design: DB11/T 969—2016[S]. Beijing: China Architecture Publishing, 2016. (in Chinese)
[23]	陈学东. 浅层非饱和带降雨入渗规律的试验与数值研究[D]. 南京: 河海大学, 2005. CHEN Xuedong. Experimental and Numerical Study on Rainfall Infiltration Law in Shallow Unsaturated Zone[D]. Nanjing: Hohai University, 2005. (in Chinese)
[24]	朱伟, 程南军, 陈学东, 等. 浅谈非饱和渗流的几个基本问题[J]. 岩土工程学报, 2006, 28(2): 235-240. https://cge.nhri.cn/article/id/11960 ZHU Wei, CHENG Nanjun, CHEN Xuedong, et al. Some fundamental problems of unsaturated seepage[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(2): 235-240. (in Chinese) https://cge.nhri.cn/article/id/11960
[25]	WANG R C, WEN S J, SUN Z L. Analytical solution of rainfall infiltration in unsaturated soil slopes considering initial water content distribution[J]. KSCE Journal of Civil Engineering, 2022, 26(11): 4419-4431. doi: 10.1007/s12205-022-1750-5
[26]	邱清文. 黄土/碎石覆盖层水气耦合运移规律及填埋气减排性能[D]. 杭州: 浙江大学, 2016. QIU Qingwen. Water-Gas Coupling Migration Law and Landfill Gas Emission Reduction Performance of Loess/Gravel Overburden[D]. Hangzhou: Zhejiang University, 2016. (in Chinese)

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