边坡的渗流–应力耦合数学模型与稳定性分析
Mathematical Model of Seepage-Stress Coupling and Stability Analysis of Slope
DOI: 10.12677/pm.2025.1511279, PDF,   
作者: 王琮煜：成都理工大学，数学地质四川省重点实验室，四川 成都；成都理工大学，数学科学学院，四川 成都
关键词: 协同放大；边坡；耦合；稳定性；数值模拟；Synergistic Amplification； Slope； Coupling； Stability； Numerical Simulation
摘要: 针对松散堆积体边坡在降雨与开挖耦合作用下的稳定性问题，本文建立了饱和–非饱和渗流与应力耦合的偏微分方程模型。基于虚功原理与有效应力原理，推导了渗流–应力耦合控制方程，采用FLAC3D平台进行三维数值模拟，并结合强度折减法构建稳定性判据。通过对比单一开挖、单一降雨及耦合工况下的数值试验，揭示了耦合效应对塑性区扩展与安全系数的协同放大效应。结果表明，耦合作用下边坡安全系数显著降低至1.18，揭示了渗流–应力反馈机制在边坡灾变过程中的数学本质。
Abstract: To investigate the stability of loose accumulation slopes under the coupled effects of rainfall and excavation, this study establishes a set of partial differential equations describing the coupled saturated-unsaturated seepage and stress fields. Based on the principles of virtual work and effective stress, the governing equations for seepage-stress coupling are derived. Three-dimensional numerical simulations are performed using the FLAC3D platform, and a stability criterion is developed through the strength-reduction method. By comparing numerical experiments under excavation only, rainfall only, and coupled conditions, the study reveals a synergistic amplification effect of the coupling process on the expansion of the plastic zone and the reduction of the safety factor. The results indicate that the slope safety factor decreases significantly to 1.18 under coupled conditions, highlighting the mathematical essence of the seepage-stress feedback mechanism in slope failure evolution.
文章引用：王琮煜. 边坡的渗流–应力耦合数学模型与稳定性分析[J]. 理论数学, 2025, 15(11): 169-177. https://doi.org/10.12677/pm.2025.1511279

参考文献

[1] 叶龙珍, 柳侃, 黄瑛瑛, 等. 福建省公路铁路建设的重大工程地质问题[C]//中国地质学会工程地质专委会, 中国地质环境监测院(国土资源部地质灾害应急技术指导中心), 山西省国土资源厅. 2014年全国工程地质学术大会论文集. 福建省地质灾害重点实验室, 国土资源部丘陵山地地质灾害防治重点实验室, 福建省地质工程勘察院, 2014: 204-210.
[2] Wen, H., Li, H., Pang, T. and Wu, J. (2025) Numerical Study on Redbed Slope Stability under Multi-Factor Conditions. Applied Sciences, 15, 2502. [Google Scholar] [CrossRef] 
[3] 魏燃. Ⅴ级围岩大断面隧道开挖步序及对边坡稳定性影响研究[J]. 公路工程, 2019, 44(3): 222-227.
[4] 邓东平, 石柱, 彭文耀, 等. 卸荷损伤效应下开挖边坡稳定性极限平衡分析[J]. 工程地质学报, 2025, 33(1): 327-340.
[5] 穆成林, 裴向军, 裴钻, 等. 基于岩体结构特征和未确知测度评价模型的岩质开挖边坡稳定性研究[J]. 水文地质工程地质, 2019, 46(4): 150-158.
[6] 葛虎胜, 刘峰, 苏怀斌, 等. 高陡边坡开挖卸荷位移演变规律及边坡稳定性研究[J]. 矿业研究与开发, 2023, 43(6): 83-88.
[7] 骆文进, 郑晓蕾, 王丽英, 等. 考虑降雨入渗效应的高边坡开挖数值模拟研究[J]. 水力发电, 2020, 46(12): 31-35.
[8] 姚茂宏, 陈铁林, 樊容, 等. 强降雨条件下考虑气压和渗流作用的边坡稳定性[J]. 上海交通大学学报, 2022, 56(6): 739-745.
[9] 顾玉明, 袁云星, 李希琨, 等. 降雨条件下土体各向异性渗透对边坡稳定性的影响[J]. 中国安全生产科学技术, 2023, 19(S1): 43-49.
[10] 任东兴, 薛鹏, 叶飞, 等. 降雨入渗条件下黏性土基坑浅层边坡稳定性分析[J]. 成都理工大学学报(自然科学版), 2022, 49(2): 204-212.
[11] 陈景松, 周春梅, 吝曼卿, 等. 不同降雨类型下混合花岗岩路堑边坡稳定性分析[J]. 安全与环境工程, 2024, 31(1): 150-162.
[12] 张治国, 张洋彬, 张孟喜, 等. 考虑降雨因素影响的隧道施工扰动地层响应分析[J]. 岩土工程学报, 2021, 43(6): 1097-1108.
[13] 熊齐欢, 袁青, 于锦, 等. 强降雨作用下软土隧道仰坡稳定性分析[J]. 人民长江, 2022, 53(12): 151-156.
[14] 陈亚烽, 陈国庆, 严明, 等. 基于一阶线性应变软化理论的边坡稳定性研究[J]. 地质科技通报, 2022, 41(6): 180-188.
[15] Yang, Y., Yang, Z., Xu, W., A, F., Guo, Y. and Zheng, J. (2024) Research on the Failure Mechanism and Treatment Technology of Landslides in Typical Accumulation Bodies along Highways in Qinghai Province. Water, 17, Article 34. [Google Scholar] [CrossRef] 
[16] Cheng, Q., Hou, K., Sun, H. and Niu, X. (2024) Numerical Simulation of Rainfall-Induced Erosion on Infiltration and Slope Stability. Water, 16, Article 1517. [Google Scholar] [CrossRef] 
[17] Zienkiewicz, O.C., Humpheson, C. and Lewis, R.W. (1975) Associated and Non-Associated Visco-Plasticity and Plasticity in Soil Mechanics. Géotechnique, 25, 671-689. [Google Scholar] [CrossRef] 
[18] Wang, S., Xu, W., Yan, L., Feng, X., Xie, W. and Chen, H. (2020) Experimental Investigation and Failure Mechanism Analysis for Dacite under True Triaxial Unloading Conditions. Engineering Geology, 264, Article ID: 105407. [Google Scholar] [CrossRef] 
[19] 张鲁渝, 郑颖人, 赵尚毅, 等. 有限元强度折减系数法计算土坡稳定安全系数的精度研究[J]. 水利学报, 2003, 34(1): 21-25.

为你推荐