Numerical Modelling of Noordbergum Effect Using Coupled Poromechanics Approach

The soil-water constitutive relationship was first introduced by Terzaghi for pore fluid pressure driven one-dimensional consolidation [1]. M. A. Biot later established a three-dimensional constitutive relationship for pore-saturated soil system [2]. The interaction between porous media and fluid is a complex coupled phenomenon governed by the intricate relationship between the soil matrix and the pore-occupying fluid. Closed form solutions of this poroelastic model can only be obtained for highly simplified cases. Numerical modelling is widely accepted method for simulating the poromechanical scenarios. An Open-Source based model, satBiotFoam, is developed over the Finite-Volume (FV) based framework of OpenFOAM^® for solving coupled poromechanical problems. The proposed model employs an iterative approach based on mathematical operator splitting to eliminate non-physical oscillations. The presented model is capable of accurately capturing coupled interaction validated against widely accepted benchmark solutions. This coupled constitutive relationship is characterized by a non-monotonic pressure variation in deforming porous media or pumped aquifer systems. This phenomenon was first reported from the well fields of Noordbergum village in the Netherlands by Verruijt [3].  Noordbergum and Reverse Noordbergum Effects are such poromechanical phenomena which can be captured using the proposed model. The present works aims to characterize these phenomena under various homogeneous and heterogeneous domains, demonstrating the applicability of the model for poromechanical applications near pumping and recharging wells. A variety of two- and three-dimensional problems are presented related to soil deformation and pumping in aquifer-aquitard systems with physically consistent solutions. Findings of the proposed work aims to understand the critical physical relationship among pore fluid and heterogenous/homogeneous soil systems under aquifer pumping or recharging scenarios.

References:

[1] Terzaghi, C., 1925. Principles of soil mechanics: V-physical differences between sand and clay. Eng. News Rec. 96, 912–915.

[2] Biot, M. A. (1941). General Theory of Three‐Dimensional Consolidation. Journal of applied physics, 12(2), 155-164.

[3] Verruijt, A., 1969. Elastic storage of aquifers. In: Flow Through Porous Media, vol. 1. San Diego, California, pp. 331–376.