Design and Optimisation of Drainage Systems for Fractured Slopes Using the XFEM and FEM

Abstract

The reliable and optimised design of a drainage system for saturated slopes is often a challenging geotechnical task. Such a task becomes even more challenging when a slope contains pre-existing joints and discontinuities. In saturated and semi-saturated conditions, the existence of joints may lead to a complex distribution of pore water pressure within the slope, affecting the effective stress distribution and the stability of the slope. This paper aims to study the effect of horizontal borehole drainage systems with different arrangements on pore water pressure distributions within a saturated fractured slope. In this study, several coupled pore fluid diffusion and stress-strain analyses were conducted using the e-Xtended Finite Element Method (XFEM) in conjunction with the Finite Element Method (FEM) to simulate the efficiency of a drainage system of a deep slope at the second largest open-cut mine in Australia. As one of the objectives of this study, the effect of water flow inside a joint and normal to the joint surface (normal flow) is considered as an essential simulation component. The results show that the pore water pressure distribution at the vicinity of the joint is considerably influenced by the magnitude of normal flow. Such influence should be taken into account when designing a drainage system, as the magnitude of normal flow and the performance of the drainage system may affect each other directly.

Introduction

It is widely accepted in geotechnical engineering practice that groundwater may have impose a considerable influence on the stability and deformation of geotechnical structures. The existence of groundwater can reduce the magnitude of effective stresses indirectly resulting in a decrease in shear strengths of geomaterial subjected to shear forces and finally an increase in the possibility of slope failure [1], [2], [3], [4].

Reducing the groundwater pressure by employing a drainage or depressurisation system is one of the approaches to improve the strength of a slope efficiently [5, 6]. By installing a borehole beneath the water table, water begins to flow from the porous medium material surrounding the opening. This water loss in the porous medium causes a reduction in the pore water pressure distribution [7]. Simultaneously, the medium undergoes consolidation due to the increase in effective stresses [8]. This process surrounding the borehole creates a depressurised zone leading to initiation of flows from the material further away, towards the depressurised zone. Furthermore, the expansion of the depressurised zone is related to the permeability of the porous medium [8, 9].

In the process of depressurisation of a slope by the use of a drainage system, the magnitude of permeability plays an essential role. This is when the significance of permeability becomes detrimental when studying discontinuous soft rock masses [4, 10]. Generally, the permeability of a discontinuous rock mass can be significantly larger than the intact ones due to naturally occurring cracks and joints [11, 12]. This phenomenon may become crucial when the non-uniform distribution of discontinuities could lead to a considerable fluctuation of the groundwater table and pore water distribution in rock mass slopes [13]. In fractured rock slopes, the process of stress relief and pore water re-distribution can result in the opening of pre-existing joints or even the initiation of new joints and discontinuities [14]. Such a process affects the distribution of pore pressures within the rock mass and makes the rock mass even more permeable. In addition, the occurrence of normal flow inside the joint can affect the pore water distribution within the rock slope. The design and optimisation of drainage systems for a jointed slope is more challenging than for continuous slopes. Overall, the performance of a horizontal borehole drainage system for a jointed rock slope can be considered as a function of the rock mass permeability, the normal flow inside the joint, the location of the joint, the length of the drains, and the space between drains.

One of the common discontinuity modelling techniques classified in continuum numerical techniques is the e-Xtended Finite Element Method (XFEM). In this method, some of the Finite Element Method (FEM) limitations associated with localised discontinuities and the features which are not efficiently resolved by mesh refinement are removed [15]. The XFEM employs the local partition of the unity concept and enriches degrees of freedom of the cracked elements with special displacement functions. The application of the XFEM has been recently extended to numerous fields of study including two-phase flow [16], fluid-structure interaction [17], biomechanics [18], multi-field problems [19] and simulation of initiation and propagation of complex geotechnical substances like coal [20, 21].

The XFEM has been broadly applied to coupled mechanical and fluid flow modelling in saturated or partially saturated fractured porous media [22], [23], [24], [25], [26]. Faivre et al. [27] employed the XFEM approach in conjunction with a cohesive zone model to conduct a fully coupled hydromechanical analysis of groundwater flow throughout a fractured saturated poroelastic media. Salimzadeh et al. [28] employed two flow models consisting of a two-dimensional Darcy flow through a porous media, and a one-dimensional laminar flow inside the fracture, to perform a fully coupled hydromechanical analysis of fractured porous media in the XFEM framework. Roth et al. [29] performed a coupled hydromechanical crack modelling in concrete by using the XFEM, where the model can create a link between the permeability of the porous medium and the damage coefficient. Furthermore, one of the most popular current applications of the XFEM is to carry out a coupled hydromechanical analysis in fractured porous media to simulate the hydraulic fracturing or fluid-driven fractures in rock masses for oil and gas extraction from reservoirs [27, [30], [31], [32], [33], [34]].

This paper, aims to model the pore water distribution in a saturated fractured soft rock slope by conducting several coupled pore fluid diffusion and stress analyses using the XFEM in conjunction with the FEM. The model is then used to optimise a drainage system design to minimise the excess pore water pressure behind a fractured slope.