Environmental Geology

, 54:1507

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

  • Chung-Min Tseng
  • Tung-Lin Tsai
  • Liang-Hsiung Huang
Original Article

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.

Keywords

Poroelastic media Transient consolidation Body force Groundwater pumping 

List of symbols

B

thickness of clay

Cd

the average degree of consolidation

f

body force

f0

initial steady value of body force

fe

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

n0

initial steady value of porosity

ne

consolidation-producing incremental value of porosity

P

pore water pressure

P0

initial steady value of pore water pressure

Pe

consolidation-producing incremental value of pore water pressure

Pe*

nondimensionalized pore water pressure

qr

Darcy’s velocity

qr0

initial steady value of Darcy’s velocity

qre

consolidation-producing incremental value of Darcy’s velocity

S1

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

S2

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

t

time

t*

nondimensionalized time

u

displacement of solid

uz

soil displacement in z direction

uz*

nondimensionalized soil displacement

z

co-ordinate

z*

nondimensionalized coordinate

Greek symbols

ρw

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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Chung-Min Tseng
    • 1
  • Tung-Lin Tsai
    • 2
  • Liang-Hsiung Huang
    • 1
  1. 1.Department of Civil EngineeringNational Taiwan UniversityTaipeiTaiwan, ROC
  2. 2.Department of Civil and Water Resources EngineeringNational Chiayi UniversityChiayi CityTaiwan, ROC

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