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Effects of body force on transient poroelastic consolidation due to groundwater pumping

  • Original Article
  • Published:
Environmental Geology

Abstract

By applying linear poro-elasticity theory, the body force effect on steady soil consolidation, i.e., settlement, caused by constant water table depression due to groundwater pumping was investigated. The result shows that when the soil is soft or thick, or both, neglecting the body force effect can lead to severe underestimation of soil displacement and incremental effective stress. However, the transient response of soil consolidation was not analyzed. In addition, the water table depression due to groundwater pumping in fact varies with time. In this study, the body force effect on transient consolidation of soil subjected to variable water table depression is further examined. A poroelastic consolidation numerical model is developed herein to conduct this examination.

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Abbreviations

B :

thickness of clay

C d :

the average degree of consolidation

f :

body force

f 0 :

initial steady value of body force

f e :

consolidation-producing incremental value of body force

g :

gravitational acceleration

G :

Lame constant

h :

water table depression

h**:

effective water table depression

K :

hydraulic conductivity

M :

body force number

n :

porosity

n 0 :

initial steady value of porosity

n e :

consolidation-producing incremental value of porosity

P :

pore water pressure

P 0 :

initial steady value of pore water pressure

P e :

consolidation-producing incremental value of pore water pressure

P e* :

nondimensionalized pore water pressure

q r :

Darcy’s velocity

q 0 r :

initial steady value of Darcy’s velocity

q e r :

consolidation-producing incremental value of Darcy’s velocity

S 1 :

the integration of transient pore water pressure with respect to z* at time t*

S 2 :

the integration of pore water pressure difference between the steady state and time t*

t :

time

t * :

nondimensionalized time

u :

displacement of solid

u z :

soil displacement in z direction

u * z :

nondimensionalized soil displacement

z :

co-ordinate

z * :

nondimensionalized coordinate

ρ w :

density of fluid

ρs :

density of solid

Δρ:

difference in density between solid and fluid

\(\sigma_{i,j}^{\prime}\) :

effective stress tensor

\({\sigma_{i,j}^{\prime}}^{0}\) :

initial steady value of effective stress tensor

\({\sigma_{i,j}^{\prime}}^{\rm e}\) :

consolidation-producing incremental value of effective stress tensor

λ:

Lame constant

Δt :

time step

Δt*:

nondimensionalized time step

Δz :

grid space

Δz*:

nondimensionalized grid space

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Authors and Affiliations

  1. Department of Civil Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC

    Chung-Min Tseng & Liang-Hsiung Huang

  2. Department of Civil and Water Resources Engineering, National Chiayi University, 300 Sefu Road, Chiayi City, 60004, Taiwan, ROC

    Tung-Lin Tsai

Authors
  1. Chung-Min Tseng
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  2. Tung-Lin Tsai
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  3. Liang-Hsiung Huang
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Correspondence to Tung-Lin Tsai.

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Tseng, CM., Tsai, TL. & Huang, LH. Effects of body force on transient poroelastic consolidation due to groundwater pumping. Environ Geol 54, 1507–1516 (2008). https://doi.org/10.1007/s00254-007-0932-2

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  • DOI: https://doi.org/10.1007/s00254-007-0932-2

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