Alexander H.-D. Cheng

Fundamentals of poroelasticity

Publisher Summary This chapter focuses on fundamentals of poroelasticity. The presence of a freely moving fluid in a porous rock modifies its mechanical response. Two mechanisms play a key role in the interaction between the interstitial fluid and the porous rock: (i) an increase of pore pressure induces a dilation of the rock; and (ii) compression of the rock causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. These coupled mechanisms bestow an apparent time-dependent character to the mechanical properties of the rock. If excess pore pressure, induced by compression of the rock, is allowed to dissipate through diffusive fluid mass transport, further deformation of the rock progressively takes place. The rock is more compliant under drained conditions than undrained ones. The chapter discusses the formulation and analysis of coupled deformation–diffusion processes, within the framework of the Biot theory of poroelasticity. The Biot model of a fluid-filled porous material is constructed on the conceptual model of a coherent solid skeleton and a freely moving pore fluid.

Seawater Intrusion in Coastal Aquifers — Concepts, Methods and Practices

Preface. List of Contributors. 1. Introduction J. Bear, A.H.-D. Cheng. 2. Geophysical Investigations M.T. Stewart. 3. Geochemical Investigations B.F. Jones, et al. 4. Exploitation, Restoration and Management J.C. van Dam. 5. Conceptual and Mathematical Modeling J. Bear. 6. Analytical Solutions A.H.-D. Cheng, D. Ouazar. 7. Steady Interface in Stratified Aquifers of Random Permeability Distribution G. Dagan, D.G. Zeitoun. 8. USGS SHARP Model H.I. Essaid. 9. USGS SUTRA Code - History, Practical Use, and Application in Hawaii C.I. Voss. 10. Three-Dimensional Model of Coupled Density-Dependent Flow and Miscible Salt Transport G. Gambolati, et al. 11. Modified Eulerian Lagrangian Method for Density Dependent Miscible Transport S. Sorek, et al. 12. Survey of Computer Codes and Case Histories S. Sorek, G.F. Pinder. 13. Seawater Intrusion in the United States L.F. Konikow, T.E. Reilly. 14. Impact of Sea Level Rise in the Netherlands G.H.P. Oude Essink. 15. Movement of Brackish Groundwater Near a Deep-Well Infiltration System in the Netherlands A. Stakelbeek. 16. A Semi-Empirical Approach to Intrusion Monitoring in Israeli Coastal Aquifer A.J. Melloul, D.G. Zeitoun. 17. Nile Delta Aquifer in Egypt M. Sherif. Bibliography. Index.

Material coefficients of anisotropic poroelasticity

The material coefficients of Biots anisotropic poroelasticity are interpreted following micromechanical considerations. The adoption of the micro-homogeneity and micro-isotropy assumptions leads to a most practical model for laboratory measurement: the material is defined within 21 drained elastic constants M ijkl , a solid grain bulk modulus K s , and a Biot modulus M. To facilitate engineering applications, relations among Hookean, engineering and micromechanical constitutive constants are explicitly and extensively listed. These relations are used to convert a set of anisotropic data measured in traditional engineering tests under undrained condition to various continuum mechanical constants.

Pumping optimization in saltwater-intruded coastal aquifers.

This paper investigates the hydraulic issues of pumping well optimization in saltwater-intruded coastal aquifers. The well field includes freshwater outflow, pumping wells, and a recharge canal. The objective is to maximize the total pumping rate subject to the constraint of no intrusion of the saltwater front into the wells. Analytical solutions are presented for one-well, two-well, and one-well-with-recharge-canal problems. For problems involving multiple pumping wells, a structured messy genetic algorithm is used to search for the optimal solution.

Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions

Particular solutions of higher order radial basis functions of conical and spline types are obtained for the Laplacian, Helmholtz-type, and polyharmonic operators. These particular solutions are needed in the implementation of the Dual Reciprocity Boundary Element Method.

Transient wave propagation in a one-dimensional poroelastic column

SummaryBiots theory of porous media governs the wave propagation in a porous, elastic solid infiltrated with fluid. In this theory, a second compressional wave, known as the slow wave, has been identified. In this paper, Biots theory is applied to a one-dimensional continuum. Despite the simplicity of the geometry, an exact solution of the full model, and a detailed analysis of the phenomenon, so far have not been achieved. In the present approach, an analytical solution in the Laplace transform domain is obtained showing clearly two compressional waves. For the special case of an inviscid fluid, a closed form exact solution in time domain is obtained using an analytical inverse Laplace transform. For the general case of a viscous fluid, solution in time domain is evaluated using the Convolution Quadrature Method of Lubich. Of all the inverse methods previously investigated, it seems that only the method of Lubich is efficies and stable enough to handle the highly transient cases such as impact and step loadings. Using properties of three widely different real materials, the wave propagating behavior, in terms of stress, pore pressure, displacement, and flux, are examined. Of most interest is the identification of second compressional wave and its sensitivity of material parameters.

A comparison of efficiency and error convergence of multiquadric collocation method and finite element method

In this paper, we demonstrate the efficiency and accuracy of the multiquadric collocation method as compared to the finite element method. When used as interpolants, the multiquadric (MQ) radial basis function has the property of exponential convergence with respect to a shape parameter, according to a proof by Madych and Nelson. Although the optimal choice of shape parameter is still an unsettled issue, we demonstrate by three examples that the accuracy achieved by the MQ solution cannot be rivaled by the FEM.

SEEPAGE FORCE ON A PIPELINE BURIED IN A POROELASTIC SEABED UNDER WAVE LOADINGS

The water wave induced seepage force on a pipeline buried in the seabed is investigated. The seabedis modeled as a porous and elastic medium containing a nearly saturated pore water, which is generally known as the Biot model. The pipeline is assumed to be rigid. It is not supported by any anchoring force. The governing equations describing soil stresses as well as pore water pressure under periodic wave loadings are solved numerically using a Boundary Integral Equation Method. Numerical results of pore water pressure amplitude around the pipeline are compared with laboratory data. Agreement is fairly good. Sensitivities of pore water pressure response to different soil and fluid parameter are also examined. It is found that with realistic parameters the uplift seepage force on the pipeline can be as much as 60% of the displaced water weight if the pipeline is located in the pore water pressure boundary layer.

A nonlinear compaction model for fibrous preforms

Abstract Based on the mechanics of porous media and physical insight gained from experimental observation, a model for predicting the nonlinear compaction of fibrous preforms in the resin transfer molding process is developed. A key physical constant — namely, preform bulk compressibility — is proposed to establish the relationship between the applied pressure and the preform bulk volume. The preform bulk compressibility is a function of fiber volume fraction and five parameters — the initial fiber volume fraction, the final (maximum attainable) fiber volume fraction, the initial pore volume compressibility, the fiber compressibility, and an empirical index. Results of compaction experiments on plain-woven fabric preforms and unidirectional non-woven materials support the validity of the model. Excellent agreement between theory and experiments has been obtained. The present model provides for fibrous preforms a nonlinear constitutive law whose coefficients can be physically interpreted.

Plane strain analysis of a stationary hydraulic fracture in a poroelastic medium

Abstract This paper presents a plane strain analysis of a constant length hydraulic fracture embedded in an infinite poroelastic domain. The fracture is uniformly loaded by fluid pressurisation. For clarity of physical interpretation, this loading is decomposed into two modes, consisting respectively of a unit step for the normal stress and a unit step for the pore pressure along the fracture. For each loading mode, the transient fracture profile, the fracture volume, the leak-off volume, and the stress intensity factor are analyzed. First, short- and long-term asymptotic expressions are derived in closed form based on analytical arguments. The full transient behaviors are then formulated as a pair of coupled singular integral equations. The solutions are found via Laplace transform, and numerical discretization of the integral equations.