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REVIEW ARTICLES

# Constitutive Models for Wave Propagation in Soils

[+] Author and Article Information
Frederick Bloom

Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115

Appl. Mech. Rev 59(3), 146-175 (May 01, 2006) (30 pages) doi:10.1115/1.2177685 History:

## Abstract

A survey is provided of the various constitutive models that have been used to study the phenomena of wave propagation in soils. While different material models have been proposed for the response of soils, it is now generally understood that no single model may be used over the entire range of pressures which are typically studied. The constitutive models reviewed in this paper include a number of effective stress and multiphase models, the volume distribution function model, and various versions of the $P−α$ model. Also discussed are classical elastic-plastic models, models possessing different elastic constants in loading and unloading, variable modulus models, and capped elastic-plastic models.

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## Figures

Figure 1

Geometry for one-dimensional consolidation of a half-space. (Adopted from Ref. 13-14.)

Figure 2

Dependence of capillary pressure Pc′, permeability ksℓ, and coefficient of consolidation c on liquid saturation sℓ. (Adopted from Ref. 13.)

Figure 3

Fluid-pressure profiles for consolidation of a saturated and a partially saturated half-space. (Adopted from Ref. 13-14.)

Figure 4

Frequency dependence of phase velocity for several values of the ratio (V2∕V1)2. The value of (λ0∕V12ωr2)=0.19. (Adopted from Ref. 22.)

Figure 5

Particle velocity versus time profiles for a small-amplitude shock wave shown at five different locations in the material corresponding to (ω,X∕V1)=0,1,2,3,4. The ratio (V2∕V1)2=0.55 and (λ0∕V12ωr2)=0.19. (Adopted from Ref. 22.)

Figure 6

Volume distribution function versus time profiles for a small-amplitude shock wave shown at five different locations in the material corresponding to (ω,X∕V1)=0,1,2,3,4. The ratio (V2∕V1)2=0.55 and (λ0∕V12ωr2)=0.19. (Adopted from Ref. 22.)

Figure 7

Particle velocity versus time profiles for three small-amplitude shock waves corresponding to values of (V2∕V1)2=0.55,0.25,0.05. For each wave, (ωrX∕V1)=4 and (λ0∕V12ω42)=0.19. (Adopted from Ref. 22.)

Figure 8

Shock wave profiles ϵ(X) in a uniformly distributed granular material with E−>G−>0 at a specific time t. The wave is propagating into unstrained material at rest and the slope immediately behind the shock jump is [ϵX]. (Adopted from Ref. 28.)

Figure 9

Solid curves are α−P curves for spheres of initial pore radius a0=20μ and initial porosities α0=1.1, 1.3, 1.8, and 2.5, with applied external pressure rates Ṗ=0.025, 0.05, 0.1, and 0.2kbar∕ns. The dashed curve is the initial yield locus for static collapse, and the dotted curve is the total yield locus or static plastic collapse curve. (Adopted from Ref. 27.)

Figure 10

Solid curves are α−P curves for spheres of initial pore radius a0=20μ and initial porosities α0=1.1, 1.3, 1.8, and 2.5, with applied external pressure rates Ṗ=0.025, 0.05, 0.1, and 0.2kbar∕ns. The dashed curve is the initial yield locus for static collapse, and the dotted curve is the total yield locus or static plastic collapse curve. (Adopted from Ref. 27.)

Figure 11

Solid curves show pore collapse of hollow spheres of initial pore radius a0=20μ and initial porosities 1.1, 1.3, 1.8, and 2.5, with applied external pressure rates Ṗ=0.025, 0.05, 0.1, and 0.2kbar∕ns. The dashed curves give the pore collapse predicted by the approximate pore-collapse relation Eq. 2226 for the same initial porosities and pressures. The initial discrepancy is accounted for by the approximate initial conditions of Eq. 2226. Note that both sets of calculations predict a great slowing down of the collapse process near α=1 for the slowest rate, Ṗ=0.025kbar∕ns. (Adopted from Ref. 27.)

Figure 12

Typical experimental results for soils. (Adopted from Ref. 1.)

Figure 13

Uniaxial strain, von Mises, and Drucker-Prager models. (Adopted from Ref. 35)

Figure 14

Transition between yield conditions. (Adopted from Ref. 35.)

Figure 15

Uniaxial strain, elimination of net dilation. (Adopted from Ref. 2.)

Figure 16

Pressure-volumetric strain, permissible states with and without dilatancy. (Adopted from Ref. 2.)

Figure 17

Stress path in uniaxial strain, elastic ideally-plastic model. (Adopted from Ref. 2.)

Figure 18

Yield condition for soil-cap model. (Adopted from Ref. 2.)

Figure 19

Soil-cap model. (Adopted from Ref. 2.)

Figure 20

Movement of soil cap. (Adopted from Ref. 2.)

Figure 21

Details of soil cap. (Adopted from Ref. 2.)

Figure 22

Stress paths in uniaxial strain, triaxial compression and proportional loading tests, soil-cap model. (Adopted from Ref. 2.)

Figure 23

Uniaxial strain test for McCormick Ranch sand, soil-cap model. (Adopted from Ref. 2.)

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