考虑侧阻与端阻影响的基桩水平承载力传递矩阵解

Transfer matrix solutions for lateral behavior of pile foundation considering the skin and end resistance effect

  • 摘要: 为研究桩侧竖向摩阻力、桩端竖向阻力及水平剪应力对基桩水平承载特性的影响,该文首先根据桩侧摩阻力三折线τ-s曲线推导得出了附加弯矩-转角本构模型线性解析表达式。随后在四弹簧模型基础上结合该文所提出的桩侧、桩端附加弯矩以及桩端水平剪力本构关系进而建立桩身受力微分方程,并采用Laplace变换解得桩身弹性、塑性段的传递矩阵系数解析解。最后在给出的迭代求解方法基础上进而求得考虑侧阻与端阻影响的基桩水平承载力响应解。通过两组案例对比分析不但验证了该文推导的正确性,也证明了该文所提出的桩侧、桩端附加弯矩以及桩端水平剪力本构模型的合理性;同时结果也表明当地基土体较好、桩径较大时桩侧附加弯矩Ms、桩端附加弯矩Mb和剪力Fb对水平承载特性影响不可忽略。

     

    Abstract: To investigate the contributions of vertical skin friction, vertical end resistance and horizontal shear stress of pile tip to the lateral bearing capacity of a pile foundation, this work firstly deduces analytical expression of a linear constitutive model characterizing the relationship between additional moment and slope based on the trilinear τ-s curve model of pile shafts. Furthermore, combining the four-type spring model with the presented constitutive relations for additional moment of pile shafts and pile ends, as well as the shear force of pile tip, the differential equations for a pile section is established and the corresponding transfer matrix coefficients for piles in elastic and plastic stage are derived analytically by means of Laplace transformation. Finally, transfer matrix solutions for the lateral behavior of a pile foundation is obtained on the basis of a proposed iterative methodology. The agreement between test data and the calculated results by the proposed method is quite good, which verifies the correctness of the derivation and confirms the rationality of the produced constitutive relations for additional moment of pile shafts, as well as additional moment and shear force of pile tip. Moreover, the comparison also implies that the values of additional moment Ms of pile shafts, additional moment Mb and shear force Fb of pile ends have a significant influence on the lateral load-bearing capacity of piles when large-diameter piles are embedded in stiff materials.

     

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