Numerical investigation of the diversion length for the capillary barrier system

Shijun Wang; Yunfei Tian; Jing Yang; Huihui Xu; Hailong Zhang; Xianting Yi; Qian Zhai; Shijun Wang; Yunfei Tian; Jing Yang; Huihui Xu; Hailong Zhang; Xianting Yi; Qian Zhai

doi:10.3934/geosci.2025037

AIMS Geosciences

2025, Volume 11, Issue 4: 867-884. doi: 10.3934/geosci.2025037

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Research article

Numerical investigation of the diversion length for the capillary barrier system

1.
Gansu Electric Power Corporation, State Grid Corporation of China, Lanzhou, 730050, China
2.
School of Civil Engineering, Southeast University, Jiangsu Nanjing 211189, China
3.
Advanced Ocean institute of Southeast University, Southeast University, Jiangsu Nantong 226010, China

Received: 26 March 2025 Revised: 15 May 2025 Accepted: 04 June 2025 Published: 22 October 2025

The capillary barrier system (CBS) is commonly used to control rainwater infiltration into the slope soil and enhance slope stability under rainfall conditions. In the CBS, a fine-grained layer is commonly overlayered on top of the coarse-grained layer. Because the hydraulic conductivity of unsaturated coarse-grained soil is much lower than that of fine-grained soil, the infiltrated rainwater flows only in the fine-grained layer. With the accumulation of the rainwater, rainwater in the fine-grained layer can finally penetrate the coarse-grained layer, and "breakthrough" occurs. The horizontal length from the initial point to the breakthrough point is commonly defined as the diversion length (L). Various empirical models have been proposed for the estimation of L, but the results from those empirical equations differ from each other. In this paper, the limitations associated with different empirical models for the estimation of L were discussed. Subsequently, both diversion lengths and the time corresponding to the breakthrough obtained from numerical analyses were presented and compared with those from empirical equations. When the rainfall intensity is higher than 10% of k_s of fine-grained soil, the empirical models showed that L increases with the increase in slope angle, while the numerical results showed the opposite. Empirical models were based on steady-state infiltration analysis, while the numerical models were based on transient infiltration analysis. The results in this paper indicate that the numerical results are more reliable than those from empirical equations.
- capillary barrier system (CBS),
- diversion length (L),
- numerical analysis,
- steady-state infiltration,
- transient infiltration
Citation: Shijun Wang, Yunfei Tian, Jing Yang, Huihui Xu, Hailong Zhang, Xianting Yi, Qian Zhai. Numerical investigation of the diversion length for the capillary barrier system[J]. AIMS Geosciences, 2025, 11(4): 867-884. doi: 10.3934/geosci.2025037

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Abstract

The capillary barrier system (CBS) is commonly used to control rainwater infiltration into the slope soil and enhance slope stability under rainfall conditions. In the CBS, a fine-grained layer is commonly overlayered on top of the coarse-grained layer. Because the hydraulic conductivity of unsaturated coarse-grained soil is much lower than that of fine-grained soil, the infiltrated rainwater flows only in the fine-grained layer. With the accumulation of the rainwater, rainwater in the fine-grained layer can finally penetrate the coarse-grained layer, and "breakthrough" occurs. The horizontal length from the initial point to the breakthrough point is commonly defined as the diversion length (L). Various empirical models have been proposed for the estimation of L, but the results from those empirical equations differ from each other. In this paper, the limitations associated with different empirical models for the estimation of L were discussed. Subsequently, both diversion lengths and the time corresponding to the breakthrough obtained from numerical analyses were presented and compared with those from empirical equations. When the rainfall intensity is higher than 10% of k_s of fine-grained soil, the empirical models showed that L increases with the increase in slope angle, while the numerical results showed the opposite. Empirical models were based on steady-state infiltration analysis, while the numerical models were based on transient infiltration analysis. The results in this paper indicate that the numerical results are more reliable than those from empirical equations.

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