Qinghui Jiang

Approximate analytical solution to the Boussinesq equation with a sloping water‐land boundary

An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.

Modelling of hydro-mechanical coupling and transport in densely fractured rock mass

A numerical model is presented to study hydro-mechanical coupling process based on the rigid body spring method and the discrete fracture network model. In order to realistically simulate the constitutive behaviours of fractures, a non-linear constitutive model is employed, in which non-linear normal stress deformation relationship, tangential slipping failure and dilation effects are considered. To investigate coupling effects on transport, a particle tracking procedure is also incorporated to account for solute movement. Stress effects on flow field and transport are studied on a typical fracture network provided by the DECOVALEX project. Results show that it is the non-linear normal deformation that mainly influences flow and transport when the confining stress is relatively low and the stress difference is not large. When the stress increases and stress difference becomes larger, dilation effect gradually becomes the governing mechanism. These results are compared with other researcher’s work and reasonable agreements are obtained.

The Parabolic Variational Inequalities for Variably Saturated Water Flow in Heterogeneous Fracture Networks

Fractures are ubiquitous in geological formations and have a substantial influence on water seepage flow in unsaturated fractured rocks. While the matrix permeability is small enough to be ignored during the partially saturated flow process, water seepage in heterogeneous fracture systems may occur in a non-volume-average manner as distinguished from a macroscale continuum model. This paper presents a systematic numerical method which aims to provide a better understanding of the effect of fracture distribution on the water seepage behavior in such media. Based on the partial differential equation (PDE) formulations with a Signorini-type complementary condition on the variably saturated water flow in heterogeneous fracture networks, the equivalent parabolic variational inequality (PVI) formulations are proposed and the related numerical algorithm in the context of the finite element scheme is established. With the application to the continuum porous media, the results of the numerical simulation for one-dimensional infiltration fracture are compared to the analytical solutions and good agreements are obtained. From the application to intricate fracture systems, it is found that water seepage flow can move rapidly along preferential pathways in a nonuniform fashion and the variably saturated seepage behavior is intimately related to the geometrical characteristics orientation of fractures.

Numerical simulation of rock failure process using improved rigid body spring method

Rock failure process is simulated using an improved rigid body spring model (RBSM). A procedure based on point saturation theory is proposed to generate uniformly distributed random Voronoi cell, which is employed as the basic mesh for the improved RBSM. The midpoint contact model of original RBSM is modified into distributed interface contact model. A simple failure criterion combining Mohr-Coulomb criterion with tension strength is employed to account for fracture evolution. It is found from a series of numerical tests that mesh size and mesh arrangement have little effects on the relationship between macro-and meso-elastic parameters. A fitting formula is developed for determination of relationship between macro and micro elastic parameters. Numerical studies against Vienne rock tests under various confining pressures show that a good agreement is obtained between experiments and numerical results from the proposed model.