考虑桩身自重影响的楔型桩屈曲稳定性分析

摘要

To study the effect of pile shape on the buckling behaviour of a tapered pile,the first-type stability of the tapered pile was analyzed based on the cusp catastrophe model of the pile-soil system with considering the self-weight of the pile.By determining the potential function and the equations of the bifurcation sets of the pile-soil system,the cusp catastrophe model was established,and the instability condition of the pile-soil system was derived based on the cusp catastrophe theory and the principles of the energy method.Meanwhile,the buckling load of the tapered pile was determined by the Rayleigh-Ritz method,and the reliability of the results from the cusp catastrophe theory was verified.Finally,the influences of the self-weight of the tapered pile and the variation ratio of pile diameters on the buckling load were analyzed.The result shows that when h/L increases from 0 to 0.4,the ratio of the buckling load reduction of the tapered pile with considering the self-weight of the pile to the buckling load without considering the self-weight of the pile decreases to 42.82％,and the ratio of the buckling load reduction for an equal-diameter pile with considering the self-weight to the buckling load without considering the self-weight decreases to 75.27％.Under the identical conditions,the greater the tapering angle of the tapered pile,the better the stability.When the dimensionless length of the pile tends to be zero,the calculation length of a tapered pile with a free end and a fixed end tend to be zero and that of a tapered pile with a free end and a hinged end tend to be infinite.%为了研究桩身特性对楔形桩稳定屈曲性状的影响,基于考虑桩身自重的桩-土体系尖点突变模型,对楔形桩的第一类稳定问题进行了分析;通过确定桩-土体系的势函数和分岔集方程,建立桩-土体系的尖点突变模型并导出桩-土体系失稳条件,得到了楔形桩的屈曲临界荷载;应用能量法原理及瑞利-里兹法计算楔形桩的屈曲临界荷载,验证突变理论计算结果的可靠性;通过算例分析了楔形桩的桩身自重和楔形桩桩径变化对屈曲临界荷载的影响.研究结果表明:当桩身埋置率从0增加到0.4时,考虑桩身自重后楔形桩和等截面桩的临界荷载减小值与不考虑桩身自重下临界荷载的比值分别减小了42.82％和75.27％;其他条件相同时,楔形桩的楔形锥角越大,稳定性越好;当无量纲桩长趋于0时,桩顶自由、桩端嵌固和桩端铰接条件下楔形桩稳定计算长度分别趋于0和无穷大.