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Characterization model for internal erosion evolution of accumulations based on coupled seepage-erosion-stress effects
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摘要:目的
堆积体广泛分布于我国山地丘陵区，属于土石混杂的宽级配松散土体，降雨渗流作用下极易出现细颗粒迁移、流失的内侵蚀问题。内侵蚀会同时劣化土体骨架力学性能、改变渗透特性，是诱发堆积体滑坡的核心诱因，因此精准预测细颗粒侵蚀演化量，对地质灾害防控与岩土工程安全运营具有重要现实意义。
方法针对现有侵蚀量预测模型普遍忽略土体应力状态影响的缺陷，本研究以饱和堆积体五相混合介质为基础，结合质量守恒、动量平衡、有效应力原理等理论，建立渗流−侵蚀−应力多场耦合控制方程，并依托 COMSOL 平台完成数值模型开发；采用不同偏应力工况下的三轴侵蚀剪切试验数据，验证该数值方法的精度与可靠性。基于大量耦合模拟结果，将体积应变、含石率、平均渗流流速与时间作为输入参数，通过最小二乘法回归分析，构建适配复杂应力条件的堆积体内侵蚀演化表征模型，实现了内侵蚀过程的定量表征，并系统剖析了含石率、体积应变影响内侵蚀特性的内在作用机理。
结果试验与模拟结果表明，在土骨架未发生侵蚀失稳破坏的前提下，本研究建立的表征模型可精准预测不同应力水平、不同含石率堆积体的细颗粒侵蚀演化规律。含石率提升会延长孔隙水渗流路径、降低平均渗流速度，进而有效抑制土体内部侵蚀；而偏应力作用下堆积体产生剪胀变形，体积应变随之增大，是导致内侵蚀程度加剧的核心内在诱因。
结论本研究所构建的内侵蚀演化表征模型，可定量刻画渗流、侵蚀与应力耦合作用下堆积体的渗透性动态演化特征，弥补了传统侵蚀模型无法适配复杂应力场的不足，拓展了侵蚀方程的应用场景。研究成果可为山地丘陵区堆积体边坡、地基的稳定性评价以及降雨型滑坡灾害防控提供理论支撑与技术参考。
Abstract:ObjectiveSoil-rock accumulations are widely distributed in hilly and mountainous regions across China. As loose geomaterials with widely graded particles and mixed soil-rock components, they are highly prone to internal erosion induced by rainfall infiltration and subsurface seepage. During internal erosion, fine soil particles detach and migrate through intergranular pores, which simultaneously deteriorates the bearing capacity of the soil skeleton and alters the internal permeability of the accumulations. This coupled deterioration is the dominant triggering mechanism for rainfall-induced landslides, posing major threats to geotechnical facilities and geological disaster prevention. Therefore, developing an accurate method to predict the evolution and magnitude of fine particle erosion is of great theoretical significance and practical value for ensuring the safe operation of geotechnical projects and mitigating landslide risks.
MethodsTraditional internal erosion prediction models fail to consider the influence of complex in-situ stress states, limiting their application in practical engineering. To address this research gap, this study first regarded saturated soil-rock accumulations as a five-phase mixed medium and established a set of coupled governing equations for seepage, erosion, and stress fields based on mass conservation, momentum balance, and the effective stress principle. The finite element numerical model was compiled and solved on the COMSOL Multiphysics platform, and Voronoi diagrams were adopted to reconstruct geometric models of accumulations with different rock contents. A series of triaxial erosion-shear tests under three deviatoric stress conditions with a constant confining pressure of 50 kPa were carried out to verify the reliability and calculation accuracy of the proposed numerical method. On the basis of massive numerical simulation results, this study took volumetric strain, rock content, average seepage velocity, and erosion time as four input parameters, and adopted the least squares method for regression fitting. A novel evolution characterization model for internal erosion was further established, realizing the full quantitative characterization of internal erosion under complex stress conditions. Additionally, the intrinsic mechanisms of how rock content and volumetric strain affect internal erosion behaviors were systematically explored.
ResultsThe combined results of physical tests and numerical simulations demonstrated that the proposed characterization model could accurately predict the evolution of eroded fine particles in soil-rock accumulations with different stress levels and rock contents, provided that no erosion-induced instability failure occurs in the soil skeleton. The increase of rock content could extend the seepage path of pore water and reduce the average seepage velocity inside the medium, thereby effectively restraining the development of internal erosion. In contrast, when the accumulation was subjected to deviatoric stress, shear dilatancy occurred, leading to a continuous rise in volumetric strain. The enlarged volumetric strain further increased porosity and permeability, which was the essential internal factor aggravating the degree of internal erosion.
ConclusionThis newly developed internal erosion evolution model can quantitatively describe the dynamic evolution of permeability in soil-rock accumulations under the combined action of seepage, internal erosion, and complex stress fields. The major innovations of this study lie in two aspects. First, it introduces volumetric strain to quantitatively characterize the stress effect on internal erosion, compensating for the inherent limitations of traditional models that neglect stress influence. Second, it integrates multiple key parameters to establish a multi-factor coupling model, which greatly expands the applicability of classical erosion equations. This study not only enriches the theoretical system of coupled seepage-erosion-stress effects for wide-graded soils, but also provides reliable theoretical support and technical references for stability evaluation of accumulation slopes and foundations, as well as the prevention and control of rainfall-triggered landslides in mountainous areas.
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Key words:
- accumulation /
- internal erosion /
- volumetric strain /
- rock content /
- numerical simulation
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图 2 内侵蚀条件下堆积体数值模型构建流程图
Figure 2. Flowchart of construction of numerical model of accumulation under internal erosion conditions
图 3 内侵蚀条件下堆积体数值模型
A，B，C，D为模型端点编号；w，h分别为模型宽度和长度
Figure 3. Numerical model of accumulation under internal erosion conditions
图 5 3组工况下模拟与试验累计侵蚀细颗粒质量对比图(a)和回归图(b)
Figure 5. Comparison (a) and regression (b) of cumulative mass of eroded fine particles from simulation and tests under three working conditions
图 6 不同含石率下堆积体有限元计算模型
Figure 6. Finite element calculation models of accumulations with different rock contents
图 7 不同含石率下经验系数a与体积应变εv的关系（R2为决定系数）
Figure 7. Relationship between empirical coefficient a and volumetric strain εv under different rock contents
图 8 偏移量y0(a)，振幅A1(b)，时间常数t1(c)与含石率RC的关系
Figure 8. Relationship of rock content RC with offset y0 (a), amplitude A1 (b), and time constant t1 (c)
图 9 不同含石率下堆积体侵蚀细颗粒质量分数增长曲线(a)和流线分布(b～e)
Figure 9. Growth curves of mass fraction of eroded fine particles (a) and streamline distribution (b-e) of accumulations with different rock contents
图 10 含石率对侵蚀细颗粒质量百分比、平均水力梯度和平均渗流速度的影响
Figure 10. Effects of rock content on mass fraction of eroded fine particles, average hydraulic gradient, and average seepage velocity
图 11 不同体积应变下堆积体侵蚀细颗粒质量分数增长曲线(a)和轴向应变对堆积体变形、体积应变的影响(b～e)
Figure 11. Growth curves of mass fraction of eroded fine particles under different volumetric strains (a) and effects of axial strain on deformation and volumetric strain of accumulation (b-e)
图 12 体积应变对侵蚀细颗粒质量分数、渗透系数和平均渗流速度的影响
Figure 12. Effects of volumetric strain on mass fraction of eroded fine particles, permeability coefficient, and average seepage velocity
表 1 土体力学参数[41]
Table 1. Soil mechanical parameters
计算参数 工况1 工况2 工况3 初始孔隙率n0 0.524 0.522 0.532 土颗粒密度ρs/(kg·m−3) 1895 1895 1895 初始水力传导率k0/(×10−5 m·s−1) 7.5 7.3 6.8 土体弹性模量E/MPa 6 6 6 土体泊松比υ 0.23 0.23 0.23 土体黏聚力cs/kPa 25 25 25 土体内摩擦角φs/(°) 32.6 32.6 32.6 注：工况1～3偏应力q分别为 0，100，150 kPa，下同 
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表 2 块石力学参数
Table 2. Rock mechanical parameters
计算参数 值 块石骨架密度ρrk/(kg·m−3) 2700 块石弹性模量Er/MPa 6000 块石泊松比υr 0.25 块石黏聚力cr/kPa 1500 块石内摩擦角φr/° 40
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