Study On The Calculation Method Of Stress And Deformation Of Geosynthetic-Encased Stone Columns Based On Symplectic System

In recent years,China has been actively engaged in the construction of expressways and high-speed railways.Limited by the geological conditions,many highway and railway subgrades need to be built on the soft foundation,which brings the vigorous development of soft foundation treatment technology.As a new treatment method of soft foundation,the method of geosynthetic-encased stone columns has been widely used in engineering because of its high economic benefit and good treatment effect.However,Because of the h oop effect of geogrid,the mechanism of stress and deformation of geosynthetic-encased stone columns is complex,and its theoretical research is still in the initial stage.Therefore,on the basis of the existing research,combined with the basic principle and method of symplectic system,this paper will make a further study on the stress and deformation mechanism of geosynthetic-encased stone columns,which is in order to provide an effective reference for the practical engineering application of the metho d of geosynthetic-encased stone columns.In this paper,firstly,the definition and classification of composite foundation are briefly described,and the development history and research status of geosynthetic-encased stone columns composite foundation and symplectic system are summarized.On this basis,the load transfer mechanism of geosynthetic-encased stone columns composite foundation is analyzed,the failure mode is summarized,and then the bearing mechanism and the deformation law under the load are analyzed.At the same time,the basic concepts of symplectic space,symplectic matrix,adjoint symplectic orthonormality and so on in symplectic system are briefly introduced.Euclidean space and symplectic space are compared,and then Legendre transformation,Hamiltonian canonical equation and variational principle of symplectic system in elasticity are briefly summarized.Based on the theory of geosynthetic-encased stone columns composite foundation and symplectic system,this paper studies the stress and deformation of ordinary stone columns and geosynthetic-encased stone columns.In the analysis,the stress and deformation of a single stone column is regarded as a space axisymmetric problem.Based on the symplectic system theory,a symplectic dual equati on considering the shear stress of the cross section of the column is constructed,and the variables of the equation are separated,then the distribution functions of settlement and radial deformation of stone columns are finally obtained according to the boundary conditions.On this basis,the influence of reinforcement constraint on the side condition and the special solution of non-homogeneous differential equation is analyzed,and then the symplectic system solution of settlement and radial displacement of geosynthetic-encased stone columns is obtained.Then,the specific method of parameter selection in this paper is clarified.The rationality of this method is verified by the analysis of the practical example,and the further parameter analysis shows that the settlement and bulging of geosynthetic-encased stone columns are related to the rigidity of the reinforcement,the depth of reinforcement and the stress ratio of pile and soil.The larger the rigidity of the reinforcement,the smaller the settlement and bulging of geosynthetic-encased stone columns.When the reinforcement depth is larger than the optimal reinforcement depth,the settlement and bulging of geosynthetic-encased stone columns will not change.Meanwhile,the optimal reinforcement depth increases with the increase of load,pile spacing and the decrease of lateral pressure coefficient.With the increase of the stress ratio of pile and soil,the growth rate of the settlement and bulging of geosynthetic-encased stone columns will gradually decrease.At last,the engineering examples of ordinary stone columns composite foundation and geosynthetic-encased stone columns composite foundation are selected,and the results calculated by this method are compared with the existing research results to verify the rationality and feasibility of the stress and deformation calculation method of geosynthetic-encased stone columns based on symplectic system.