Critical physical and hydraulic condition for fine grains migration, deposition and self-dredging in seepage erosion of gravel soil
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摘要:
细粒迁移机制是理解砂砾土渗流侵蚀过程的基础与关键，对研究砂砾土斜坡雨水侵蚀过程的细观致灾机制具有重要意义。目前其运移模式及运移状态发生转变的临界条件并不清晰，不同物理水力条件下的细粒运动类型有所不同。为掌握砂砾土侵蚀过程中细粒的整体运动类型及其发生改变的临界条件，采用可视圆柱入渗试验和离散元数值模拟，分析了细粒迁移的影响因素和内部机理。结果表明：（1）细粒迁移受级配和水力梯度影响显著，而受初始孔隙率影响不显著，且级配的影响大于水力梯度；（2）水力作用下细粒整体运动状态可分为沉积和滤通2种模式，内部结构不稳定的砂砾土细粒运动处于滤通状态，内部结构稳定和稳定性过渡型砂砾土随水力梯度升高细粒的运动状态从整体沉积转变为整体滤通；（3）细粒运动状态在粒径比和水力梯度共同作用下存在明显界限，最终得到细粒沉积-滤通转变的临界条件为$ i = 3.4 - $$ 0.12{{\text{e}}^{\left( {{D_{15}}/{d_{85}}} \right)/1.5}} $。研究可为砂砾土斜坡渗蚀失稳防护提供理论指导。
Abstract:The mechanism of fine grains migration is the basis and key to understand the seepage erosion process of gravel soil, which is significance to study the disaster-caused mesomechanism of rain erosion process on sandy gravel slopes. However, the migration mode and critical condition for the transition of migration state are unclear. The migration types of fine grains differ from different physical and hydraulic conditions. To reveal the overall movement characteristics of fine grains and the critical conditions for the change of their motion state during the process of gravel soil erosion, this study adopted the visual cylindrical infiltration test and discrete element numerical simulation to analyze the influencing factors and mechanism of the fine grains migration, deposition, and self-dredging. The results show that: 1) the migration of fine grains is significantly affected by the gradation and hydraulic gradient but not by the initial porosity. The gradation has a greater effect than the hydraulic gradient. 2) The overall motion of fine grains under hydraulic forces can be divided into two states: deposition and self-dredging. The fine grains of gravel soil with unstable internal structure are in the self-dredging state, and that with stable and transitional internal structure will change from deposition to self-dredging with the increase of hydraulic gradient. 3) The motion state of fine grains has an obvious boundary under the combined effects of grain size ratio and hydraulic gradient, and the critical condition for fine grains transition from deposition to self-dredging is obtained to be $ i = 3.4 - 0.12{{\text{e}}^{\left( {{D_{15}}/{d_{85}}} \right)/1.5}} $.
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Key words:
- gravel soil /
- seepage erosion /
- fine grains migration /
- migration mode /
- critical condition
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表 1 数值模型相关参数
Table 1. Related parameters of numerical model
固体 流体 密度/ ${\text{(kg}} \cdot {{\text{m}}^{ - 3}}{\text{)}}$ 弹性模量
/$ {\text{(N}} \cdot {{\text{m}}^{ - 2}}{\text{)}} $ 刚度比 摩擦
系数密度/ ${\text{(kg}} \cdot {{\text{m}}^{ - 3}}{\text{)}}$ 黏滞系数/
（Pa·s）2500 5×108 1.5 0.8 1000 1×10−3 
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表 2 三种应力水平下峰值应力误差平均值与内摩擦角误差
Table 2. Average value of peak stress error and internal friction angle error under three stress levels
参数 计算公式 B1数值模拟与A1
试验结果比对/%B6数值模拟与A6
试验比对结果/%应力误差
平均值$ \dfrac{{\dfrac{{\Delta {\sigma _{100}}}}{{{\sigma _{100}}}} + \dfrac{{\Delta {\sigma _{200}}}}{{{\sigma _{200}}}} + \dfrac{{\Delta {\sigma _{300}}}}{{{\sigma _{300}}}}}}{3} $ 5.6 −9.6 内摩擦角
误差$ \dfrac{\Delta \varphi }{{\varphi }_{试验}} $ 8.6 −1.3
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表 3 渗透试验与数值模拟得到的渗透系数
Table 3. Comparison of hydraulic conductivity measured by test and simulation
试验和
模拟类型试验次数 常水头试验结果/（cm·s−1） 数值模拟
结果/（cm·s−1）试验值 平均值 A6与B6 第1次 0.0557 0.0562 0.0529 第2次 0.0627 第3次 0.0501 A1与B1 第1次 0.0112 0.0107 0.0083 第2次 0.0100 第3次 0.0110
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表 4 数值模型粒径组成
Table 4. Particle size composition in the numerical model
级配编号 级配数量/种 d50/mm Cu $\dfrac{{{D_{15}}}}{{{d_{85}}}}$ 颗粒图像 级配编号 级配数量/种 d50/mm Cu $\dfrac{{{D_{15}}}}{{{d_{85}}}}$ 颗粒图像 B1 2 1.28 3.09 2.33 
B4 4 7.20 8.57 6.01 
B2 4 2.20 4.39 3.39 
B5 4 9.99 11.66 8.71 
B3 4 4.80 7.38 4.03 
B6 2 10.42 19.96 16.23 
注：D15表示粗粒组中颗粒的累计粒度分布百分数达到15%时所对应的粒径；d85表示细粒组中颗粒的累计粒度分布百分数达到85%时所对应的粒径。
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表 5 土体内部稳定性判定准则及其判定结果和数值模拟结果
Table 5. Results of soil internal stability criterion and numerical simulation
判定准则 结构稳定判定指标 Cu=3.09 Cu=4.39 Cu=7.38 Cu=8.57 Cu=11.66，19.96 Istonima准则 Cu≤10 S S S S T Burenkova法 0.76lgh″+1<h′<1.86lgh″+1 S S U S U Wan & Fell法 30/lg（d90/d60）<80
或15/lg（d20/d15）>22S S S S S Beriram准则 D15/d85≤6且D15/d15≤9 S S S U U Kenndy & Lau法 $ {f}_{4d}\geqslant 2.3{f}_{d}，{f}_{d}\leqslant \left\{\begin{array}{l}0.3，C{\mathrm{u}}\leqslant 3\\ 0.2，C{\mathrm{u}} < 3\end{array} \right.$ S S T U U 数值模拟结果 kki<0 S S T U U 注：S代表稳定；U代表不稳定；T代表稳定性过渡；fd和f4d分别为粒径小于d和小于4d的颗粒质量百分比；h′为d90/d60；h″为d90/d15；d15表示细粒组中颗粒的累计粒度分布百分数达到15%时所对应的粒径。
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