Estimation of Land Subsidence Based on Groundwater Flow Model

Abstract

This article presents an approach for estimating land subsidence due to withdrawal of groundwater. The proposed method calculates the groundwater seepage in 3-D-condition and calculates the land subsidence one-dimensionally. The governing equation on groundwater seepage is based on the three-dimensional mass conservation law and the principle of effective stress. The land subsidence calculation method is derived based on the following assumptions: (1) displacements occur only in the vertical direction, and (2) in vertical direction the total stresses do not change. The governing equation is solved by numerical method, i.e., finite element method (FEM) in spatial discretization and finite difference method (FDM) in time series discretization. In FEM Galerkin method is adopted and in FDM, lumped matrix method is employed. The proposed method is calibrated via analyzing 1-D consolidation problem and the results are compared with those from Terzaghi's one-dimensional consolidation theory and oedometer test. The proposed method is employed to analyze the consolidation of a soft layer due to withdrawal of groundwater from an aquifer under it. Moreover, this method is also applied to a field case of land subsidence due to groundwater pumping in a gas production field in Japan. The analytical results are compared with the field observed data. The results show that this approach simulates the field case well.

Keywords:

• Galerkin method
• groundwater flow model
• land subsidence
• lumped matrix method
• subsidence model
• withdrawal of groundwater

This work is financially supported by the Open Research Foundation of Nanjing Hydraulic Research Institute (NHRI) (Contract No. YK90505). The first author is grateful to M. Nishigaki, I. Tohno, and K. Imai for their collaboration and instructions in the numerical analyses during the first author's stay in Japan.

Notes

Note: For aquitard, k _x  = k _y  = 1.5k _z ; for aquifer, k _x  = k _y  = 10k _z .