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应用突变理论建立了超长桩在竖向静荷载作用下的尖点突变模型,推导得到了超长桩的竖向极限承载力预测公式。在静荷载分析的基础上,引入动荷载,建立了超长桩在动静组合荷载作用下的双尖点突变模型,并对其动力稳定性进行了分析。动力分析表明:动静组合荷载作用下超长桩的振幅H、频率关系q与结构非线性系数α三者之间符合双尖点突变模型;超长桩失稳时动载频率的变化值与桩顶预变形值及系统非线性系数有一定的关系;动载作用“路径”对超长桩的响应特征有很大的影响。工程算例表明:应用尖点突变理论对超长桩的竖向极限承载力进行预测具有较好的适用性。
The catastrophic catastrophe model of overlength piles under vertical static load is established by using catastrophe theory. The prediction formula of ultimate bearing capacity of overlength piles is deduced. Based on the static load analysis, the dynamic load is introduced to establish the double-cusp catastrophe model of ultra-long piles under the combined action of static and dynamic loads. The dynamic stability of the piles is analyzed. The dynamic analysis shows that the amplitude of H, the frequency relationship q and the structural nonlinear coefficient α of the super-long pile under the combined action of static and dynamic loads conform to the double point mutation model. The top pre-deformation value and the system nonlinear coefficient have a certain relationship; the dynamic load effect “path” has a great influence on the response characteristics of the super-long pile. The engineering example shows that the cusp catastrophe theory is applied to predict the ultimate bearing capacity of the super-long pile.