Abstract:  A recently proposed model coupled with the solid-fluid of the saturated sand is utilized by introducing the Newton-PCG algorithm.A Newton-PCG composite algorithm is established,with a Newtonian step and p steps of preconditioned conjugate gradient,which is coded by FORTRAN program.Based on the critical state plasticity model,a model coupled with the solid-fluid of the saturated sand is derived by considering the function of the fluid flow.FEM numerical simulation of a saturated sand slope is performed to study the onset and development of the liquefaction,and the mechanism of the pore pressure and the liquefaction are discussed at last.The results show that the Newton-PCG algorithm can solve the multidimensional nonlinear problems efficiently.The proposed constitutive model works well,and can reflect the mechanical behaviors of the coupling of the sand-fluid.It is also found that the pore pressure will affect the development of the shear band greatly.What is more,the pore pressure increases around the shear band region obviously with the direction toward the outer side of the normal of the shear band.The slip surface of the slope liquefaction is obtained according to the criteria for the onset of liquefaction,which will be important to predict the onset of the liquefaction.