Buckling Analysis Of Piles Based On The Cusp Catastrophe Theory

The pile foundation has been widely used in thick soft soil layer due to its high bearing capacity and small settlement.In recent years,super-long pile and tapered pile are becoming more and more extensive with the rapid development of large infrastructure construction in thick soft soil layer of high-rise buildings,large span bridges and port projects.The biggest difference between the super-long pile and the ordinary pile in soft layer is that its buckling stability problem is gradually concerned.Some research has shown that lateral resistance of soil,frictional resistance between pile and soil and self-weight of pile all have an important influence on the buckling load.However,the calculation of buckling load for super-long pile with considering all these factors is rarely reported.The tapered pile has been paid more and more attention due to its bearing capacity which is much higher than that of uniform pile with the same volume and it makes designers have more options in the selection of the pile foundation.One of the reasons why the tapered pile is not widely used in the engineering is that the existing calculation theory of tapered pile which can't fully reflect its own characteristics is based on the uniform pile.However,the buckling analysis for tapered pile is rarely reported.In this paper,the influences of the self-weight of pile,lateral frictional resistance of soil and elastic resistance of lateral soil are considered.By determining the potential function and the equations of bifurcation sets of pile and soil system,the model of cusp catastrophe theory is established and the instability condition of pile-soil system is derived based on cusp catastrophe theory and principles of energy method.At the same time,the buckling load of pile is determined by the method of Rayleigh-Ritz and the reliability of the calculated result by cusp catastrophe theory is verified.The studies of this paper consist of the following parts:1.The model of elastic resistance of lateral soil is an important factor affecting the buckling analysis of pile.In view of the limitation of classical m method and constant method in buckling analysis of pile such as super-long pile and tapered pile,the most general exponential distribution of subgrade reaction modulus was assumed.The total potential energy equation of pile-soil system is established by Winkle elastic foundation beam theory.Based on the principle of minimum potential energy,the buckling load and the analytical solution of the stable length of pile are derived.On this basis,the influence of the model of elastic resistance of lateral soil on buckling load of pile is analyzed emphatically.2.Based on the theory of cusp catastrophe,the influences of the self-weight of pile,lateral frictional resistance of soil and elastic resistance of lateral soil are considered.According to the end condition of pile,the flexural deformation function of pile is selected.By determining the potential function and the equations of bifurcation sets of pile and soil system,the model of cusp catastrophe theory is established and the instability condition of pile and soil system is derived based on cusp catastrophe theory and principles of energy method.At the same time,the buckling load of pile is determined by the method of Rayleigh-Ritz and the reliability of the calculated result by cusp catastrophe theory is verified.Finally,the influences of the self-weight of super-pile,lateral frictional resistance of soil and elastic resistance of lateral soil on the buckling load are analyzed.3.The influences of the self-weight of pile and elastic resistance of lateral soil are considered.The buckling analysis of tapered pile is analyzed by cusp catastrophe theory and the calculation method of buckling load of tapered pile is given.The buckling load of tapered pile is determined by the method of Rayleigh-Ritz and the reliability of the calculated result by cusp catastrophe theory is verified.Finally,the influences of the self-weight of tapered pile and the variation ratio of pile diameter on the buckling load are analyzed.