Initial post-buckling analysis for super-long rock-socketed piles

To investigate the initial-post buckling behaviors of super-long rock-socketed piles,a mechanical model simplifying the pile as partially supported Winkler foundation beam is adopted,and a combination model of soil resistance of the pile-soil system is applied to establish the potential energy equation.The expression of buckling critical load is derived by using the variational method.And then by using the perturbation method and the variational method,the general expression of the critical load change relative to different pile-soil system parameters in the initial-post buckling process is deducted,and effects of these parameters on the initial-post buckling behaviors of the piles are discussed.The results show that the initial-post buckling has balance path of the piles with symmetry branching points,and the balance of the pile-soil system relates to the soil resistance patterns,soil-pile stiffness ratio,the embedded proportion of pile shaft and other parameters of the system.The m method can not exactly reflect the real model of pile side soil resistance and a larger pile critical buckling load will be derived.So the combination model of soil resistance is more reasonable than the m method of soil-pile side resistance mode.