Study On Lateral Earth Pressure Of Layered Soils On Rigid Retaining Walls Using Variational Method

The earth pressure on retaining wall is an important problem in engineering practice.In particular,reasonable calculation of the earth pressure on the wall under the actual multi-layer filling has always been one of the focuses of relevant practices.In this thesis,in light of the pseudo-static approach and using the variational method based on limit equilibrium conditions,an analytical slolution to the active and passive earth pressure and the corresponding slip surfaces is provided for the two-layered and three-layered filling retained by a general rigid wall under random local surcharge and seismic forces.Further,main factors which influence the earth pressure and slip surface are discussed.The main research work and results are as follows:(1)Based on the limit equilibrium principle of sliding body behind a rigid retaining wall,the active or passive earth pressure problem can be transformed into a functional extreme value problem with two unknown curves,which are the normal stress on the sliding surface and the sliding surface respectively.Using the variational method,in a given range of active and passive earth pressure under point position,through mechanics equilibrium equation,the initial boundary conditions,the euler equation and the movable boundary problem of transversality condition equations containing six independent unknowns,reuse of fsolve function in MATLAB can solve equations only convergence of the solution,The possible range of earth pressure,sliding crack surface and earth pressure operating point coefficient on rigid retaining wall is obtained.(2)As the position of earth pressure gradually increases,the value of active earth pressure gradually increases,and the overall variation range is less than 10%.For the passive state,the passive earth pressure increases gradually with the increasing position of the earth pressure operation point in the case of homogeneous fill,while the passive earth pressure changes more complicated in the case of two-layer and three-layer fill and gradually decreases in general,with a maximum reduction of 50%.When the total soil thickness behind the wall is fixed,the active and passive earth pressures are mainly affected by the proportion of the thickness of hard soil in the total soil thickness.The higher the value is,the smaller and larger the active and passive earth pressures are respectively.With the increase of the coefficient of earth pressure,the active and passive sliding surfaces move slightly to the outside and inside of the fill,respectively,and gradually change from plane to curved surface and always present curved state.(3)An example shows that the earth pressure calculated by this method is in good agreement with the results of the existing methods,and the errors of active and passive earth pressure are within 15% and 12%,respectively.The active and passive earth pressure values calculated by this method are slightly larger and smaller than those calculated by the existing methods,and the results of this method are relatively conservative.(4)The active earth pressure and fill weight,fill top load,vertical seismic coefficient and retaining wall height,dip Angle of each soil layer,dip Angle of fill surface and horizontal seismic coefficient show linear and nonlinear positive correlation,and the internal friction Angle and cohesion show nonlinear and linear negative correlation.The passive earth pressure has a positive correlation with these factors,and has a nonlinear correlation with the height of retaining wall,the dip Angle of each soil layer interface,the dip Angle of fill surface,the horizontal seismic force coefficient and the friction Angle of fill.The effective variation range of active and passive earth pressure increases with the increase of horizontal seismic coefficient,but the vertical seismic coefficient has little effect on it.In this thesis,the research results of active and passive earth pressure variation decomposition of multi-layered rigid retaining wall can provide theoretical guidance and reference for engineering design,and have important theoretical significance and engineering application value.