Abstract
Abstract. There are many factors causing land subsidence, and groundwater extraction is one of the most important causes of subsidence. A set of coupled partial differential equations are derived in this study by using the poro-elasticity theory and linear stress-strain constitutive relation to describe the one-dimensional consolidation in a saturated porous medium subjected to pore water pressure change due to groundwater table depression. Simultaneously, the closed-form analytical solutions for excess pore water pressure and total settlement are obtained. To illustrate the consolidation behavior of the poroelastic medium, the saturated layer of clay sandwiched between two sand layers is simulated, and the dimensionless pore water pressure changes with depths and the dimensionless total settlement as function of time in the clay layer are examined. The results show that the greater the water level change in the upper and lower sand layers, the greater the pore water pressure change and the total settlement of the clay layer, and the more time it takes to reach the steady state. If the amount of groundwater replenishment is increased, the soil layer will rebound.
Highlights
The consolidation of soil induced by excessive withdrawal of groundwater is a worldwide problem and usually known as land subsidence which has occurred in many cities, for example, Bangkok, Venice, Mexico, Shanghai and so on
The change of pore water pressure in the clay layer is directly related to pressures at the upper and lower boundaries resulting from pumping, and the change of pore water pressure is from the boundary to the medium of the layer
A set of coupled partial differential equations are presented in this study by using the poro-elasticity theory and linear stress-strain constitutive relation to describe the onedimensional consolidation in a saturated porous medium subjected to pore water pressure change due to groundwater table depression
Summary
The consolidation of soil induced by excessive withdrawal of groundwater is a worldwide problem and usually known as land subsidence which has occurred in many cities, for example, Bangkok, Venice, Mexico, Shanghai and so on. Despite the significant advance of this theory in capturing the essence of consolidation process, the coupling between fluid flow and deformation in a fully-saturated porous medium is not truly laid on a firm theoretical base. This conceptual breakthrough was achieved later by Biot (1941), who brought the role of the solid and fluid constituents on equal footing to formulate a pair of coupled equilibrium equations of motion using the displacement vector of solid and fluid pore pressure as dependent variables, known as poroelasticity. After the closed-form analytical solutions for excess pore water pressure together with total settlement are obtained, numerical studies are undertaken for highly permeability porous sand (aquifers) surrounding an impervious clay (aquitard)
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