The Effective Forces Form Of Spencer And Morgenstern-price Method For Soil Slope Stability Analysis

Seepage plays an important role in slope stability,so the influence of seepage on slope stability analysis must be considered correctly.The seepage force is transformed from the surface water pressure on the boundary.In this paper,it is proved strictly that the equilibrium between the floating weight and seepage force of the soil is used instead of the equilibrium between the saturated weight of soil and the water pressure at the boundary.The two methods are equivalent,and the analysis by seepage force not only simplifies the problem,but also simplifies the programming calculation.Spencer and Morgenstern-Price method are widely used for soil slope stability analysis.While in the original paper,total stress method is applied for mathematic derivation.So that effective stress of soil body is calculated indirectly from water pressure which related to pore-pressure ratio.The resultant of weight of water with same volume of soil under the phreatic line and pore-water pressure act on sides of soil is seepage force.Forces act on soil body under phreatic line can be separate into effective forces from soil skeleton and buoyancy from pore water.The forces acting upon soil slice were reanalyzed.The expression of force equilibrium and moment equilibrium in effective stress form is established based on Spencer's original derivation method,which can solve the expression of force resultant between strips in effective stress form,and then obtain the minimum safety factor,forming the effective stress form of Spencer method for slope stability analysis.Two equations of equilibrium in respect of effective forces and effective moments were founded.The safety factor and scaling factor of the effective forces form can be obtained and the effective forces form of Morgenstern-Price method for slope stability analysis can be formed.According to the streamline distribution in the seepage field of homogeneous isotropic soil slope is simplified in the form of approximate multi-section broken line at the top,the surface and the bottom of the slope,the effective stress form of the newly established Spencer and Morgenstern-Price method is validated by classic examples.The new result is similar to that of the original total stress form and is validated by Geo-Studio.The slope stability analysis module SLOPE / W is used to establish an example model,and SLOPE / W is used to verify the calculation results.The results show that the calculation results are close to the total stress form,whichproves the method is correct.The effective stress of soil mass is of decisive significance to its strength and deformation.In this paper,an effective stress form of Spencer method and Morgenstern-Price method for slope stability analysis are established,which has theoretical significance and application value,and can be used as a calculation method for slope stability analysis and evaluation.