2D and 3D numerical modelling of flow through composite liners involving partially saturated GCLs

Abstract

A numerical study was performed in order to investigate the influence on the flow rate of the presence of defects in the geomembrane of a composite liner involving GCLs. In the approach presented in this paper, porous media in the composite liner, i.e. the interface, the GCL and the underlying soil liner, which is a CCL, are partially saturated in the numerical modelling performed. The first aim of the paper is to evaluate the impact of this partial saturation on the flow rates and the lateral extension of the wetted area for circular defects and defects of infinite length in the geomembrane through 2D numerical modelling. Results from existing analytical solutions are used as a reference. Results obtained in terms of flow rates and wetted areas reveal that: (i) a good agreement is obtained as regards flow rates between numerical modelling and analytical solutions; and (ii) larger differences between numerical and analytical results were observed for the wetted area, attributed to the difference in saturation state in both cases. The second aim of the paper is to check the impact of the shape of the ends of defects of finite length – circle or square – and to test the impact of 2D and 3D modelling of this end on the resulting flow rates. Results obtained show that the impact on the flow rate of the shape of the ends is negligible. However, 2D and 3D modelling can lead to significantly different results depending on the defect length, especially as regards the evolution of the flow rate with the hydraulic head.

Numerical modelling of advective flow through composite liners in case of two interacting adjacent square defects in the geomembrane

“…This is consistent with previous works performed by Foose et al (2001), Cartaud et al (2005a) and Saidi et al (2006). The interface was represented by quadrilateral elements that shared nodes with the upper layer of elements of the GCL mesh.…”

“…For the sake of consistency with previous papers dealing with experimental (Barroso et al, 2006a, b) and numerical investigation of flow rates through partially saturated composite liners incorporating a GCL (Saidi et al, 2006), the following ranges of parameters were adopted: square defects width varying from 3 Â 10 À3 to 3 Â 10 À2 m; hydraulic heads ranging from 0.3 to 3 m; A CCL thickness equal to 1 m; A GCL thickness equal to 9 Â 10 À3 m which is consistent with the saturated hydraulic conductivity presented in the following section.…”

“…The reason for this is that in the 3D modelling performed the mesh is made of square or rectangular elements. This assumption is justified as Saidi et al (2006) have shown in a previous numerical study that flow rates due to a circular hole of diameter 2b or a square of width 2b are close to each other for CCL-GCL-geomembrane composite liners.…”

“…The numerical code used, Metis, previously proved to be suitable for modelling flow rates through composite liners in case of interfaces of uniform or variable thickness (Cartaud et al, 2005a, b;Saidi et al, 2006). Flow through the unsaturated medium is modelled using Richards' equation (Richards, 1931).…”

“…Various analytical solutions (Rowe, 1998;Touze-Foltz et al, 1999), empirical equations (Touze-Foltz and Giroud, 2003;Giroud and Touze-Foltz, 2005; Barroso et al, 2006a), experimental works (Estornell and Daniel, 1992;Harpur et al, 1993;Koerner and Koerner, 2002;Barroso et al, 2006a;Touze-Foltz et al, 2006) and numerical works (Foose et al, 2001;Saidi et al, 2006) were performed in the past to quantify advective flow rates through composite liners incorporating GCLs. They assume the existence of a single defect in the geomembrane or of multiple defects that are not hydraulically interacting.…”