Geomechanical modelling of sinkhole development using Distinct Elements: Model verification for a single void space and application to the Dead Sea area

Abstract

Abstract. Mechanical and/or chemical removal of material from the subsurface may generate large sub-surface cavities, the destabilisation of which can lead to hazardous ground collapse and the formation of enclosed depressions termed sinkholes. Numerical simulation of the interaction of cavity growth, host material deformation and overburden collapse is desirable to better understand the sinkhole hazard, but is a challenging task due to the involved high strains and material discontinuities. Here we present a 2D Distinct Element Method numerical simulations of cavity growth and sinkhole development. Firstly, we simulate cavity formation by quasi-static, step-wise removal of material in a single growing zone of an arbitrary geometry and depth. We benchmark this approach against analytical and Boundary Element Method models of a deep void space in a linear elastic material. Secondly, we explore the effects of material properties on cavity stability and sinkhole development. We perform simulated biaxial tests to calibrate macroscopic geomechanical parameters of three model materials that reflect literature and field-based estimates for three materials in which sinkholes develop at the Dead Sea shoreline: mud, alluvium and salt. We show that weak materials do not support large cavities, leading to gradual sagging or suffusion style subsidence. Strong materials support quasi-stable to stable cavities, the overburdens of which may fail suddenly in a caprock or bedrock collapse style. Thirdly we examine the consequences of layered arrangements of weak and strong materials. We find that these are more susceptible to sinkhole collapse than uniform materials not only due to a lower integrated strength of the overburden, but also due to an inhibition of stabilising stress arching. Fourthly we compare our model sinkhole geometries to observations at the Ghor al-Haditha sinkhole site on the eastern shore of the Dead Sea in Jordan. Sinkhole depth to diameter ratios of 0.15 in mud, 0.37 in alluvium and 0.33 in salt are reproduced successfully in the calibrated model materials. The model results suggest that the observed distribution of sinkhole depth/diameter values in each material type may partly reflect sinkhole growth trends.

Distinct Element geomechanical modelling of the formation of sinkhole cluster within large-scale karstic depressions

“…The mechanical interaction of a single void space with its surrounding rock mass hereby has been thoroughly investigated by analytical methods (Tharp, 1999) and numerical modelling studies (Al-Halbouni et al, 2018;Baryakh et al, 2009;Fazio et al, 2017;Hatzor et al, 2010;Parise and Lollino, 2011). Little is known, however, about the mechanical relationships between multiple actively evolving void spaces in the sub-surface and how these may lead to the development of sinkhole clusters and large-scale depressions.…”

“…The particles follow the Newton-Euler laws of motion and the linear force-displacement law as they interact elastically at each contact point. The assembly is generated via a gravitation settling scheme (Al-Halbouni et al, 2018), after which particles can be bonded with their neighbours (Potyondy and Cundall, 2004). In this study, we used the parallel-bond model (PBM) in the commercially available software PFC2D (Potyondy, 2014), which sets a second pair of elastic springs that incorporate moments and can fail either in shear or tension, allowing for complex deformation patterns to build.…”

“…Each model requires multiple realisations as the outcomes generally depend on the randomised particle packing. For more mathematical details on the calculations and modelling scheme refer to (Al-Halbouni et al, 2018;Itasca Cooperation Group, 2014;Jing and Stephansson, 2007;Potyondy, 2014;Wang et al, 2018).…”

“…model height H x width W = 400 x 400 m; a mean particle radius of ̅ = 0.32 m; initial porosity of the unsettled assembly of n = 0.2; no-slip boundary conditions; and a fixed wall elastic modulus of = 5 GPa. Instead of simulating material removal in a single void as in Al-Halbouni et al, 2018, however, we here implemented the quasi-static, incremental growth of an array of multiple cavities of arbitrary shape (Figure 3, cf. Appendix A.1).…”

“…The bonded particle assembly's bulk material properties, which emerge from the properties defined on the particle scale, were constrained by simulated rock tests on material samples (Schöpfer et al, 2007;Al-Halbouni et al, 2018 For (1) a bond healing procedure has been implemented to account for a more realistic recombination behaviour of naturally wet muddy material.…”