Amin Keshavarz

Phenomena in nature can be modeled with linear or non-linear differential equations. To solve these equations, various numerical methods can be used, and in this thesis, in order to model the amount of soil surface settlement and pore water pressure due to the withdrawal of groundwater from Biot's equation, the differential quadrature method is used to solve it. The aim of this thesis is to develop the DQ method to analyze Biot's equation and predict surface settlement and pore water pressure. Quadrature differential method is a numerical method with high capability and potential because it approximates the differential equations governing the problem as a linear and weighted sum of function values at specific points and is a high-order method that is often used for problems It is used with regular geometry. After the discretization of the governing equations by the differential quadrature method, the differential balance equations are converted into algebraic equations. This method has been converted into a computer code by MATLAB software, and various types of surface settlement and pore water pressure diagrams have been investigated by examining various parameters, including the effects of the water pumping radius in relation to the water withdrawal depth (a/h), which has a direct relationship with the settlement. Poisson's ratio, which has an inverse relationship with the amount of settlement, water output flow, which has a direct relationship with pore water pressure, and shear modulus, which has an inverse relationship with ground settlement, have been obtained. In order to compare the results obtained with the finite element method, the studies of previous researchers have been used, and the results indicate the high accuracy and consistency of the differential quadrature method in solving the Biot equation.