Displacement Distribution Caused by Pumping from the Aquifer in Soil

Abstract

A new phenomenon that the accumulative multi-layered settlement is not equal to the land subsidence was discovered during the engineering dewatering. Displacement distribution induced by pumping from the confined aquifer was investigated using axisymmetric consolidation of multi-layered soils based on the theory of Biot’s consolidation. The variations of the displacement showed tensile and shear deformations that appeared in the overlying aquitard when pumping from the confined aquifer. The tensile deformation decreased with the increasing distance away from the pumping well. The shear deformation first increased and then decreased with the growing distance away from the pumping well.

Appendix

$$ \hat{p}_{0} = A_{1} e^{ - \xi z} + A_{2} e^{\xi z} + A_{3} e^{ - qz} + A_{4} e^{qz} - Q_{1} (\xi ,\Delta H,s) $$

$$ \begin{aligned} \hat{u}_{r1} = & \frac{1 - (M - G)\varphi }{2G}ze^{ - \xi z} A_{1} - \frac{1 - (M - G)\varphi }{2G}ze^{\xi z} A_{2} \\ & \quad + \frac{{\xi e^{ - qz} }}{{M( - q^{2} + \xi^{2} )}}A_{3} + \frac{{\xi e^{qz} }}{{M( - q^{2} + \xi^{2} )}}A_{4} \\ & \quad + e^{ - \xi z} A_{5} + e^{\xi z} A_{6} - Q_{2} (\xi ,\Delta H,s) \\ \end{aligned} $$

$$ \begin{aligned} \hat{u}_{z0} = & \frac{1 - G\varphi - M\varphi + z\xi (1 + G\varphi - M\varphi )}{2G\xi }e^{ - \xi z} A_{1} \\ & \quad + \frac{G\varphi + M\varphi - 1 + z\xi (1 + G\varphi - M\varphi )}{2G\xi }e^{\xi z} A_{2} \\ & \quad - \frac{{qe^{ - qz} }}{{M(q^{2} - \xi^{2} )}}A_{3} + \frac{{qe^{qz} }}{{M(q^{2} - \xi^{2} )}}A_{4} + e^{ - \xi z} A_{5} - e^{\xi z} A_{6} \\ \end{aligned} $$

$$ \hat{V}_{0} = - \xi k_{z} e^{ - \xi z} + \xi k_{z} e^{\xi z} - qk_{z} e^{ - qz} + qk_{z} A_{4} e^{qz} $$

$$ \begin{aligned} \hat{\sigma }_{rz1} & = (G\varphi - z\xi (1 + G\varphi - M\varphi ))e^{ - \xi z} A_{1} \\ & \quad - (G\varphi - z\xi (1 + G\varphi - M\varphi ))e^{\xi z} A_{2} + \frac{{2q\xi Ge^{ - qz} }}{{M(q^{2} - \xi^{2} )}}A_{3} \\ & \quad - \frac{{2q\xi Ge^{qz} }}{{M(q^{2} - \xi^{2} )}}A_{4} - 2e^{ - \xi z} G\xi A_{5} + 2e^{\xi z} G\xi A_{6} \\ \end{aligned} $$

$$ \begin{aligned} \hat{\sigma }_{z0} = & ( - 1 + M\varphi - z\xi (1 + G\varphi - M\varphi ))e^{ - \xi z} A_{1} \\ & \quad - (1 - M\varphi - z\xi (1 + G\varphi - M\varphi ))e^{\xi z} A_{2} \\ & \quad + \frac{{2\xi^{2} Ge^{ - qz} }}{{M(q^{2} - \xi^{2} )}}A_{3} + \frac{{2\xi^{2} Ge^{qz} }}{{M(q^{2} - \xi^{2} )}}A_{4} - 2e^{ - \xi z} G\xi A_{5} \\ & \quad - 2e^{\xi z} G\xi A_{6} + Q_{3} (\xi ,\Delta H,s) \\ \end{aligned} $$

where, G is the shear modulus; $M = 2\eta G$; $q^{2} = \alpha \xi^{2} + \frac{{\gamma_{w} s}}{{Mk_{z} }}$