基于尖点突变理论的桩基屈曲稳定分析

发布时间：2018-05-12 13:17

  本文选题：屈曲分析 + 超长桩　； 参考：《江苏大学》2017年硕士论文

【摘要】：桩基础因其承载力高、沉降量小等优点在深厚软土地区广泛应用。近年来,随着我国大型基础设施建设的迅猛发展,在我国东部沿海深厚软土地区超高层建筑、大跨度桥梁以及港口工程中超长桩、楔形桩等桩基础的应用日益广泛。软土地区超长桩与普通桩的最大不同之处在于其屈曲稳定问题更值得关注。已有研究表明影响桩屈曲荷载的重要因素不仅有桩侧土弹性抗力,还有桩侧摩阻力和桩身自重,能够同时考虑这些因素影响的超长桩屈曲荷载计算目前还很少报道。楔形桩因其承载力大大高于同体积等截面桩而受到越来越多的关注,从而使设计者在桩基础选型时有更多选择。但现有的楔形桩计算理论大多基于等截面桩展开,其并不能完全体现楔形桩自身特性,这也是楔形桩不能在工程中被广泛应用的原因之一。目前针对楔形桩自身特性的屈曲稳定分析理论研究也相对较少。基于此,本文应用尖点突变理论对超长桩和楔形桩屈曲稳定性进行研究。同时考虑桩身自重、桩侧摩阻力和桩侧土弹性抗力,通过确定桩-土体系的势函数和分岔集方程,基于尖点突变理论建立桩-土体系的尖点突变模型并导出桩-土体系失稳条件,进而得到桩基的屈曲临界荷载。同时基于能量法原理并应用瑞利-里兹法得到桩基的屈曲临界荷载,从而验证突变理论计算结果的可靠性。主要研究内容包括以下几个方面:1.桩侧土弹性抗力模式是影响桩基屈曲稳定的重要因素。鉴于经典m法和常数法在超长桩、楔形桩等桩基础屈曲分析中的局限性,考虑桩侧土弹性抗力系数为更为复杂的幂数分布模式,通过Winkle弹性地基梁理论建立桩-土体系总势能方程,基于能量法和最小势能原理,导出桩身屈曲临界荷载和桩身稳定计算长度的计算公式,并据此着重分析了桩侧土弹性抗力分布模式对桩身屈曲稳定的影响规律。2.引入非线性科学中的尖点突变理论,同时考虑桩侧土抗力、桩侧摩阻力和桩身自重的影响,根据桩端约束条件选取桩身挠曲变形函数,通过确定桩-土体系的势函数和分岔集方程,基于尖点突变理论建立桩-土体系的尖点突变模型并导出桩-土体系失稳条件,进而得到超长桩的屈曲临界荷载。同时基于能量法原理并应用瑞利-里兹法计算超长桩的屈曲临界荷载,从而验证突变理论计算结果的可靠性。最后着重分析了桩侧土抗力、桩侧摩阻力和桩身自重对超长桩屈曲稳定的影响。3.在考虑楔形桩桩侧土弹性抗力的基础上,计入桩身自重,首先应用尖点突变理论对楔形桩屈曲稳定性进行分析,给出楔形桩屈曲失稳临界荷载的计算方法。同时应用能量法进一步验证突变理论计算的屈曲临界荷载的可靠性。最后着重分析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。
[Abstract]:Pile foundation is widely used in deep soft soil area because of its high bearing capacity and small settlement. In recent years, with the rapid development of large-scale infrastructure construction in China, the application of super-tall buildings, long-span bridges, super-long piles, wedge-shaped piles and other pile foundations in deep soft soil areas along the eastern coast of China has become increasingly widespread. The biggest difference between super-long pile and ordinary pile in soft soil area is that the buckling stability of pile is more worthy of attention. It has been shown that the important factors affecting pile buckling load are not only the elastic resistance of pile side soil, but also pile friction and pile body weight. The calculation of buckling load of super-long pile which can take account of these factors at the same time is seldom reported at present. Because the bearing capacity of wedge pile is much higher than that of the same volume and equal section pile, more and more attention is paid to it, which makes the designer have more choice in pile foundation selection. However, most of the existing theories of wedge pile are based on the equal section pile, which can not fully reflect the characteristics of the wedge pile itself, which is one of the reasons why the wedge pile can not be widely used in engineering. At present, there are few researches on buckling stability analysis of wedge pile. Based on this, the buckling stability of super-long pile and wedge-shaped pile is studied by using the cusp catastrophe theory. At the same time, considering the weight of the pile body, the friction of the pile side and the elastic resistance of the soil around the pile, the potential function and bifurcation set equation of the pile-soil system are determined. Based on the cusp catastrophe theory, the cusp catastrophe model of pile-soil system is established and the instability condition of pile-soil system is derived, and the critical buckling load of pile foundation is obtained. At the same time, based on the principle of energy method and using Rayleigh-Ritz method, the buckling critical load of pile foundation is obtained, which verifies the reliability of the calculation results of catastrophe theory. The main research contents include the following aspects: 1. The elastic resistance model of pile side soil is an important factor affecting the buckling stability of pile foundation. In view of the limitations of the classical m method and the constant method in the buckling analysis of super-long pile, wedge-shaped pile and other pile foundations, the elastic resistance coefficient of the soil around the pile is considered as a more complex power distribution model. Based on the Winkle elastic foundation beam theory, the total potential energy equation of pile-soil system is established. Based on the energy method and the principle of minimum potential energy, the formulas for calculating the critical buckling load of pile body and the calculating length of pile body stability are derived. Based on this, the influence of elastic resistance distribution mode of pile side soil on the buckling stability of pile body is analyzed emphatically. In this paper, the cusp catastrophe theory of nonlinear science is introduced. Considering the influence of soil resistance, frictional resistance and weight of pile body, the deflection deformation function of pile body is selected according to the constraint condition of pile end. By determining the potential function and bifurcation set equation of pile-soil system, the cusp catastrophe model of pile-soil system is established based on the cusp catastrophe theory, and the instability condition of pile-soil system is derived, and the buckling critical load of super-long pile is obtained. At the same time, based on the principle of energy method and using Rayleigh-Ritz method, the buckling critical load of super-long pile is calculated, which verifies the reliability of the calculation results of catastrophe theory. Finally, the effects of soil resistance, friction and weight on the buckling stability of super-long pile are analyzed. On the basis of considering the elastic resistance of soil on the side of wedge-shaped pile and taking into account the weight of pile body, the buckling stability of wedge-shaped pile is analyzed by using the cusp-point catastrophe theory, and the calculation method of critical buckling load of wedge-shaped pile is given. At the same time, the reliability of the buckling critical load calculated by the catastrophe theory is further verified by the energy method. Finally, the influence of pile weight and diameter variation on buckling critical load of wedge pile is analyzed.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU473.1

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