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

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## 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

*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*_{r}^{0}initial steady value of Darcy’s velocity

*q*_{r}^{e}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

### Greek symbols

- ρ
_{w} density of fluid

- ρ
_{s} 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

- Δ
*t* time step

- Δ
*t** nondimensionalized time step

- Δ
*z* grid space

- Δ
*z** nondimensionalized grid space

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