| The calculation of earth pressure is a classic problems in soil mechanics.Predecessors deduced various calculation methods for earth pressure of retaining walls on the premise of homogeneous soil behind the wall.For the calculation of Multi-layered soil,except for Rankine's earth pressure theory,other approximate calculation methods such as equivalent method and multi-layered calculation method are used.These methods have great limitations in application.Starting from the limit equilibrium variational method,this paper proposes an accurate model and calculation method for the calculation of stratified earth pressure,and applies it to the design and calculation of actual supporting engineering.The details are as follows:(1)Using the simplified broken line model of the strength envelope considering the actual tensile strength of the soil,the calculation formula for determining the cracking depth of the soil behind the wall is deduced,and the variational calculation model of the earth pressure considering the tensile strength is proposed.The accuracy of the improved variational model is verified through method discussion and comparison of calculation examples.Under Coulomb or Rankine conditions,the resultant earth pressure of the Coulomb solution or Rankine's solution is within the range of the solution in this paper,but the position of the resultant earth pressure of the Coulomb solution or Rankine's solution is different from the solution in this paper.(2)Based on the variational theory,it is proved that when the independent variable function has a sharp point,the extreme value of the functional exists,and both ends of the independent variable function's sharp point satisfy Euler's differential equation,and the isoperimetric constants of each segment of the curve with the sharp point are the same.It is possible to use the theory of limit equilibrium variational method to solve the problem of stratified earth pressure,and based on this,the variational calculation model of stratified earth pressure behind the wall is deduced.(3)Propose a calculation method to solve the multi-layered soil pressure,consider the continuity of the slip surface and its upper normal stress function,and consider the constraint conditions of the upper and lower endpoints of each section of the slip surface,and obtain the shape and shape of the slip surface in each layer of soil.The distribution of the normal stress on it solves the limitation of the traditional multi-layered earth pressure on the hypothesis of the slip surface.The earth pressure obtained by FLAC3 D simulation in the translational mode is close to the result calculated by the variational method model,which fully proves the accuracy of the earth pressure variational method calculation model derived in this paper.(4)The factors affecting the calculation of multi-layer soil variation are studied: 1)The influence of groundwater action on the variational model of earth pressure is analyzed,and the results show that whether it is water-soil separate calculation or the principle of water-soil combined calculation,only the value parameters are different,which has no effect on the variational model;2)The existence of the transition zone between layers is analyzed.The influence of the slip surface is discussed,and the two situations of the slip surface passing through the transition zone are theoretically discussed;3)Considering the influence of the soil layer properties of the layered soil on the calculation results of the earth pressure variation,reveal the calculation of the earth pressure variation The main influencing factor of the result.(5)Combined with MATLAB,a calculation program for earth pressure is developed.The program considers the effect of groundwater and can calculate the main and covered earth pressures.The method in this paper is applied to the earth pressure calculation of an anti-slide pile engineering example,which provides a reference for the application of the method in this paper to engineering design. |
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