水平受荷桩桩身响应的线性方程解及应用分析

李炀; 吴曙光; 张四平; 高倩德; 黄磊

doi:10.11779/CJGE2020S1014

水平受荷桩桩身响应的线性方程解及应用分析 English Version

重庆大学土木工程学院,重庆　400045

详细信息

作者简介:
李炀（1993— ）,男,硕士,主要从事岩土工程方面的研究工作。E-mail：906075057@qq.com

通讯作者:
吴曙光, E-mail：wushuguang@cqu.edu.cn

中图分类号: TU473.1
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出版历程
- 收稿日期: 2020-06-03
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-10-31

Linear equation solution of horizontally loaded piles and its application

College of Civil Engineering, Chongqing University, Chongqing 400045, China

摘要

摘要: 根据Winkler地基梁理论,将地基系数沿着深度方向的任意函数以积分中值定理为原则进行微段常数化,引入四阶微分方程的张氏解析解,通过结点内力与位移连续的条件对全桩全结点构建线性方程组,避免矩阵多次传递即可一次性解得所有结点的内力与位移,相比幂级数法与有限元法更加简单,将此过程用matlab编制程序进行实现,通过两个算例验证了线性方程解法在单层地基与多层地基情况下水平受荷桩桩身响应计算的正确性。最后分别在算例基础上更改多组参数,表明在桩顶水平荷载的作用下,桩身弯矩最大值、弯矩零点值与位移零点值出现的位置分别受桩顶附近土层抗力、桩中部土层的抗力与整个桩周土层抗力大小控制,且对于同一种情况下的桩身水平响应而言,其弯矩零点所出现的位置将比位移零点所出现的位置滞后（2～3）d。
- 水平受荷桩 /
- Winkler地基梁 /
- m法 /
- 矩阵传递法 /
- 线性方程
Abstract: According to the Winkler foundation beam theory, the foundation function is constantized by the integral median theorem, and a linear equation system is constructed for the entire pile and all nodes through the condition that the internal forces and displacements of the nodes are continuous. This process is implemented by matlab programming, and two examples are used to verify the correctness of the calculation of the response of the horizontally loaded pile body in the case of single-layer foundation and multi-layer foundation. In the calculation example, multiple sets of parameters are changed, which shows that the location of the maximum value of the bending moment of the pile body, the zero point value of the bending moment and the zero point value of displacement are affected by the resistance of the soil layer near the pile top and the soil layer in the middle of the pile under the horizontal load of the pile top. The resistance is controlled by the resistance of the entire soil layer around the pile, and for the horizontal response of the pile body under the same situation, the position where the bending moment zero appears will lag behind the position where the displacement zero appears by about (2~3)d.
- pile foundation /
- Winkler foundation beam /
- m method /
- matrix transfer method /
- linear equation

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图 1 线性方程力学模型

Figure 1. Linear equation mechanics model

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图 2 不同分段数桩身弯矩

Figure 2. Moments of pile body with different numbers of sections

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图 3 不同桩端约束的桩身弯矩

Figure 3. Moments of pile body restrained by different pile ends

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图 4 不同桩端约束的桩身位移

Figure 4. Displacements of pile body with different pile end constraints

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图 5 不同地层情况桩身弯矩

Figure 5. Moments of pile body in different strata

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图 6 不同地层情况桩身位移

Figure 6. Pile displacements in different strata

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表 1 不同计算方法结果对比

Table 1 Results of different calculation methods

计算方法	桩顶位移/mm	最大弯矩/(kN·m)	最大弯矩位置/m
精确解^[18]	4.3735	336.81	3
规范解^[6]	3.0156	238.95	3
挠度加权换算^[9]	4.2093	343.83	3
有限差分法^[11]	4.2989	337.60	3
杆系有限元法^[11]	4.2520	336.07	3
矩阵传递法^[12]	4.2990	337.60	3
本文法	4.2703	335.85	3

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参考文献(18)

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