The Transient Ground Surface Displacements due to a Point Sink/Heat Source in an Elastic Half-Space

Abstract

Thermoelastic deformation due to a point heat source is the analog of poroelastic response caused by a point sink. In this paper, Biot's three-dimensional consolidation theory is introduced to derive the analytical solutions of the transient consolidation deformation with a point sink in saturated isotropic porous elastic half-space. The transient ground surface displacement produced by a point heat source is described through analog quantities between poroelasticity and thermoelasticity. Closed-form solutions of the horizontal and vertical displacements are obtained by using Laplace and Hankel integral transforms. Attention is focused on the maximum surface horizontal displacement compared to the maximum surface settlement. Results show that the horizontal displacement is about 30% of the maximum ground surface settlement. The study concludes that horizontal displacement is significant and should be considered in prediction of the transient settlement induced by groundwater withdrawal.

Land Subsidence Analysis in Urban Areas

“…Wilson and Gorelick (1996) found that pulsed pumping may cause a greater amount of subsidence as compared with constant pumping rate. Lu and Lin (2005 displayed transient displacements of the pervious half space due to steady pumping rate. Lu and Lin (2005 displayed transient displacements of the pervious half space due to steady pumping rate.…”

Golden Ratio in the Point Sink Induced Consolidation Settlement of a Poroelastic Half Space

“…Assuming the model is decoupled, i.e., the flow field is independent from the displacement field. Considering a point sink of constant strength Q located at point   0, h , the basic governing equations of the elastic saturated aquifer for linear axially symmetric deformation can be expressed in terms of displacements i u and excess pore water pressure p in the cylindrical coordinates   , , r z  as follows (Lu & Lin, 2006: …”

“…Chen (2002Chen ( , 2005 presented analytical solutions for the steady-state response of displacements and stresses in a half space subjected to a point sink. Lu and Lin (2006) displayed transient ground surface displacement produced by a point heat source/sink through analog quantities between poroelasticity and thermoelasticity. Hou et al (2005) found that pumping induced ground horizontal velocities range from 31 to 54 mm/yr towards azimuths 247° to 273° in the Pingtung Plain of Taiwan.…”

Closed-Form Solutions of the Cross-Anisotropic Stratum Due to a Point Heat Source

“…However, it was found that the anisotropic property in the permeability of the soils has significant effects on the excess pore 13 www.intechopen.com water pressure generated by a heat source (Savvidou and Booker, 1989). Lu and Lin (2006) displayed transient ground surface displacement produced by a point heat source/sink through analog quantities between poroelasticity and thermoelasticity. Based on Biot's three-dimensional consolidation theory of porous media, analytical solutions of the transient thermo-consolidation deformation due to a point heat source buried in a saturated isotropic porous elastic half space were presented by Lu and Lin (2007), Lin and Lu (2009).…”