弹性地基上HDAJ接头桩的非线性稳定性分析

本文采用弧坐标首先建立了弹性地基中受轴向载荷作用的高柔性抗震拼接头桩(High Ductility Aseis-matic Joint Spliced Pile)的非线性数学模型，并假定土(基础)对桩基的反作用力服从Winkler模型；在此基础上对该模型进行了线性化，并得到HDAJ接头桩的临界载荷。最后根据分叉理论的观点和方法，讨论了HDAJ接头桩在临界载荷处的稳定性问题。研究结果表明HDAJ接头桩在临界载荷附近必发生分叉，且分叉解是唯一的，稳定的，并且给出了分叉解的渐近表达式。物理上，这表示HDAJ接头桩的平衡构形在临界载荷处必然发生改变，并且从一个稳定的平衡构形变化到另一个稳定的平衡构形。同时考察了土的液化对临界载荷的影响，说明液化的影响是非常明显的。当考虑土的液化时，桩基的临界载荷低于不考虑土的液化时桩基的临界载荷。

Non-Linear Stability Analysis for HDAJ Spliced Piles in Elastic Ground

In this paper, we first impose arc-coordinate to give a nonlinear mathematical model of a HDAJ (High Ductility Aseismatic Joint) spliced pile subjected to an axial load in an elastic soil, in which, one assumes that the reaction of the elastic ground obeys the Winkler model. Then, the nonlinear mathematical model is linearized at the trivial solution and critical loads are obtained. Finally, following the viewpoint and method of bifurcation theory, the stability of piles is discussed near the critical loads. Results show that it is necessary that the HDAJ spliced pile will lose its stability near the critical load, namely, there exists the bifurcation solution. And the bifurcation solution is unique and stable and its asymptotic expression is also obtained. Physically, this means that the equilibrium configuration of HDAJ spliced pile must occur branches at a critical load and it changes from a stable equilibrium state to other stable equilibrium state. At the same time, the effects of liquefaction on the critical loads of pile foundations are considered. The results show that the effect of liquefaction is very in evidence and it would reduce the critical loads of piles.