Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study

Abstract

Groundwater is an important factor of slope stability, and 90% of slope failures are related to the influence of groundwater. In the past, free surface calculations and the prediction of water inflow were based on Darcy's law. However, Darcy's law for steady fluid flow is a special case of non-Darcy flow, and many types of non-Darcy flows occur in practical engineering applications. In this paper, based on the experimental results of laboratory water seepage tests, the seepage state of each soil layer in the open-pit slope of the Yanshan Iron Mine, China, were determined, and the seepage parameters were obtained. The seepage behaviour in the silt layer, fine sand layer, silty clay layer and gravelly clay layer followed the traditional Darcy law, while the gravel layers showed clear nonlinear characteristics. The permeability increases exponentially and the non-Darcy coefficient decreases exponentially with an increase in porosity, and the relation among the permeability, the porosity and the non-Darcy coefficient is investigated. A coupled mathematical model is established for two flow fields, on the basis of Darcy flow in the low-permeability layers and Forchheimer flow in the high-permeability layers. In addition, the effect of the seepage in the slope on the transition from Darcy flow to Forchheimer flow was considered. Then, a numerical simulation was conducted by using finite-element software (FELAC 2.2). The results indicate that the free surface calculated by the Darcy–Forchheimer model is in good agreement with the in situ measurements; however, there is an evident deviation of the simulation results from the measured data when the Darcy model is used. Through a parameter sensitivity analysis of the gravel layers, it can be found that the height of the overflow point and the water inflow calculated by the Darcy–Forchheimer model are consistently less than those of the Darcy model, and the discrepancy between these two models increases as the permeability increases. The necessity of adopting the Darcy–Forchheimer model was explained. The Darcy–Forchheimer model would be applicable in slope engineering applications with highly permeable rock.

A state-of-the-art review on rock seepage mechanism of water inrush disaster in coal mines

“…To understand the mining disturbance-induced water inrush, some researchers (Shi et al 2016;Yang et al 2018aYang et al , 2008 Scientists (Huang et al 2018a;Kundu et al 2016;Zhang et al 2021b) also studied the seepage state transformation in the broken rock media from the perspective of parameter variation. Kundu et al (2016) regarded broken rocks as a kind of isotropic media with different porosity, and discussed the transform point of seepage state based on the parameter evolution.…”

Assessment of Slope Stability by the Fellenius Slice Method: Analytical and numerical approach

“…These methods are based on mathematical equations derived from soil mechanics and are particularly suitable for the analysis of simple, homogeneous slopes. However, other sources emphasize the importance of numerical methods for dealing with more complex situations, such as the effects of runoff and erosion on slope stability (13), (14).…”