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The Analytical Method in Geomechanics

[+] Author and Article Information
A. P. Selvadurai

Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 2K6 Canadapatrick.selvadurai@mcgill.ca

Appl. Mech. Rev 60(3), 87-106 (May 01, 2007) (20 pages) doi:10.1115/1.2730845 History:

This article presents an overview of the application of analytical methods in the theories of elasticity, poroelasticity, flow, and transport in porous media and plasticity to the solution of boundary value problems and initial boundary value problems of interest to geomechanics. The paper demonstrates the role of the analytical method in geomechanics in providing useful results that have practical importance, pedagogic value, and serve as benchmarking tools for calibrating computational methodologies that are ultimately used for solving more complex practical problems in geomechanics. There are 315 references cited in this article.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Boussinesq’s and Kelvin’s problems

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Figure 2

Indentation of a nonhomogeneous elastic halfspace

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Figure 3

Settlement of a rigid circular footing on a nonhomogeneous isotropic elastic halfspace. (P¯ is the nondimensional load defined by Eq. 18; ζ¯ defines the variation in the inhomogeneity; the modular ratio Gs∕G∞ is defined by Eq. 16.)

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Figure 4

Indentation of a halfspace with a harmonic elastic nonhomogeneity

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Figure 5

Consolidation characteristics of a rigid foundation on a poroelastic layer

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Figure 6

Interacting rigid foundations on a poroelastic halfspace

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Figure 7

Consolidation behavior of interacting identical foundations of radius a: (a) influence of surface drainage conditions; (b) interaction of symmetrically loaded foundations (a) (Δ(t) is the displacement at the point of application of the load; Δ0e=(1−ν)Pz∕4Ga; εf=f∕a; c=2Gk(1−ν)∕(1−2ν)γw)

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Figure 8

Advective transport of a contaminant from a penny-shaped cavity in a porous medium with attenuation coefficient ξ=0.005∕day

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Figure 9

The column experiment

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Figure 10

The concentration profiles for the advective–diffusive transport of a plug of chemical in a porous column due to a velocity field that decays exponentially with time

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Figure 11

A comparison of results for the time-dependent movement of a plug of chemical dye in a fluid-saturated porous column: (a) experimental results; (b) analytical results; and (c) numerical results derived from the MLS method

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