Investigating the Deformation Characteristics of Dry Mohr-Coulomb Material During Radial Fluid Injection
Authors: Kumar J. S. , Kandasami R. K. , Chaudhuri A. , Detournay E. 
Published: August 2024

ABSTRACT:
Understanding of the deformation behaviour of porous geomaterials during fluid injection has direct relevance in several field applications. Studies exploring the resulting deformation field and instability growth within porous media during fluid injection remains limited. Prior research has focused on utilising steady-state/asymptotic cavity expansion models to study the deformation characteristics, with only a few transient models predicting the time-dependent cavity growth. Increased fluid pressure relative to porous material stiffness enhances fluid-solid coupling, inducing plastic deformations beyond linear poroelasticity. Hence, in this study, a transient cavity expansion model proposed by Kumar et al. (2024a) for dry porous media is used to investigate the poroelastic-plastic deformation characteristics during fluid injection. By introducing a new time dependent parameter known as the permeation coefficient, the model adeptly captures the fluid-induced transient behavior of dry porous media. It employs Mohr-Coulomb theory to represent the constitutive behavior under assumptions of small deformation and zero-far field stress. Further, the sensitivity of solid parameters such as porosity and yield strength are investigated for better understanding. During small deformation conditions, crucial dimensionless model parameters such as n and Y exerted significant control over interface growth. It's noteworthy that the expansion of the cavity radius and the elastic-plastic boundary were governed by the dimensionless constant Y.

1 INTRODUCTION
The flow of fluid through porous media is critical in many geomechanics related applications such as grouting (Kandasami and Kumar, 2022; Christodoulou et al., 2021; Kumar and Kandasami, 2024; Kumar et al., 2024b), hydraulic fracturing (Peirce and Detournay, 2022; Konstantinou et al., 2023; de Borst, 2017; Kumar and Kandasami, 2021; Atefi Monfared and Rothenburg, 2016), energy extraction (Wang et al., 2018; Mujeebu et al., 2009; Kandasami et al., 2023), and tunneling (Lukose and Thiyyakkandi, 2022). The complexity of these problems lies in precisely coupling and modeling the fluid-solid interactions using appropriate constitutive models and boundary conditions. Further, the material and geometric non-linearity also influences the kinematic response of porous medium under both steady state and transient conditions. When fluid is injected into the medium, the pressure gradient across the boundaries results in permeation which induces an effective stress causing both elastic and plastic deformations. In addition to the permeation front, there exists an elastic-plastic deformation boundary which are a function of time (Huynen and Detournay, 2017). At larger time scales, the plastic deformation accumulates leading to the formation of instabilities (Konstantinou et al., 2021; Huang et al., 2012; MacMinn et al., 2015). Previous poroelastic-plastic models focused only on understanding the steady-state deformation characteristics of the saturated porous medium. However, the emphasis on the coupled time-dependent response of dry porous medium during fluid injection is not properly investigated. The existing time-dependent models (MacMinn et al., 2015, 2016; Auton and MacMinn, 2018) which are capable of predicting the fluid-induced poroelastic deformation, generally consider the fluid as a means of applying pressure (without considering the flux) on the saturated medium, while the coupled elastic-plastic responses are ignored. Recently, Kumar et al. (2024a) proposed a time-dependent poroelastic plastic model on a Mohr-Coulomb porous dry medium with a point source of injection. In this research, a parametric study on this model is carried out to understand the formation and evolution of permeation zone, plastic zone and the deformation characteristics along with the sensitivity analysis of the fluid and solid parameters on the interface growth.