﻿ 梁-桩-土竖向耦合振动特性分析
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 力学学报  2015, Vol. 47 Issue (1): 169-173  DOI: 10.6052/0459-1879-14-082 0

引用本文 [复制中英文]

[复制中文]
Lü Shuhui, Wang Kuihua, Zhang Peng. VERTICAL COUPLING VIBRATION OF BEAM-PILE-SOIL SYSTEM[J]. Chinese Journal of Ship Research, 2015, 47(1): 169-173. DOI: 10.6052/0459-1879-14-082.
[复制英文]

文章历史

2014-09-22收稿
2014-11-05录用
2014-12-03网络版发表

1 数学模型及求解 1.1 梁－桩－土动力系统几何模型

 图 1 梁-桩-土动力系统几何模型 Fig.1 Geometry for beam-pile-soil system

1.2 梁－桩－土竖向振动控制方程及求解

 ${K_k} = 2\pi {r_{{\text{p}}k}}G_{{\text{s}}k}^*{{\text{K}}_1}\left( {{\zeta _k}{r_{{\text{p}}k}}} \right)/{{\text{K}}_0}\left( {{\zeta _k}{r_{{\text{p}}k}}} \right)$ (1)

 $\chi _k \dfrac{\partial ^2W_k }{\partial z^2} - \left( {\rho _{{\rm p}k}A_{{\rm p}k} s^2 + K_k } \right)W_k = 0$ (2)

 $\left[{\begin{array}{*{20}{c}} \begin{gathered} {W_k} \hfill \\ N_{\text{p}}^k \hfill \\ \end{gathered} \end{array}} \right] = \left[\begin{gathered} \hfill \\ G_{11}^kG_{12}^k \hfill \\ G_{21}^kG_{22}^k \hfill \\ \end{gathered} \right]\left[{\begin{array}{*{20}{c}} \begin{gathered} m_1^k \hfill \\ m_2^k \hfill \\ \end{gathered} \end{array}} \right]$ (3)

 ${m_2^k } /{m_1^k } = {\left( {G_{21}^k - Z_{k - 1}G_{11}^k } \right)}/{\left( {Z_{k - 1} G_{12}^k - G_{22}^k }\right)}$ (4)

 ${Z_{\text{b}}} = {G_0}{A_{{\text{p1}}}}\left( {4/{r_{{\text{p1}}}} + 3.2s/{v_{{\text{s}}0}}} \right)/{\text{ }}\left[ {\pi \left( {1 - {\mu _0}} \right)} \right]$

 $\left. {\begin{array}{*{20}{l}} \begin{gathered} {A_{{\text{b}}j}}{G_{{\text{b}}j}}{\mu _{{\text{b}}j}}\left( {\frac{{\partial {Y_j}}}{{\partial x}} - {\Theta _j}} \right) = - {E_{{\text{b}}j}}{I_{{\text{b}}j}}\frac{{{\partial ^2}{\Theta _j}}}{{\partial {x^2}}} + {\rho _{{\text{b}}j}}{I_{{\text{b}}j}}{s^2}{\Theta _j} \hfill \\ {A_{{\text{b}}j}}{G_{{\text{b}}j}}{\mu _{{\text{b}}j}}\left( {\frac{{{\partial ^2}{Y_j}}}{{\partial {x^2}}} - \frac{{\partial {\Theta _j}}}{{\partial x}}} \right) = {\rho _{{\text{b}}j}}{A_{{\text{b}}j}}{s^2}{Y_j} \hfill \\ \end{gathered} \end{array}} \right\}$ (5)

 $\left[{\begin{array}{*{20}{c}} \begin{gathered} {Y_j} \hfill \\ {\Theta _j} \hfill \\ Q_{\text{b}}^j \hfill \\ M_{\text{b}}^j \hfill \\ \end{gathered} \end{array}} \right] = \left[\begin{gathered} M_{11}^jM_{12}^jM_{13}^jM_{14}^j \hfill \\ M_{21}^jM_{22}^jM_{23}^jM_{24}^j \hfill \\ M_{31}^jM_{32}^jM_{33}^jM_{34}^j \hfill \\ M_{41}^jM_{42}^jM_{43}^jM_{44}^j \hfill \\ \end{gathered} \right]\left[{\begin{array}{*{20}{c}} \begin{gathered} {A_j} \hfill \\ {B_j} \hfill \\ {C_j} \hfill \\ {D_j} \hfill \\ \end{gathered} \end{array}} \right]$ (6)

 $\left[{\begin{array}{*{20}{c}} \begin{gathered} {Y_j} \hfill \\ {\Theta _j} \hfill \\ \end{gathered} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} \begin{gathered} {Y_{j - 1}} \hfill \\ {\Theta _{j - 1}} \hfill \\ \end{gathered} \end{array}} \right],\;\left[{\begin{array}{*{20}{c}} \begin{gathered} Q_{\text{b}}^j \hfill \\ M_{\text{b}}^j \hfill \\ \end{gathered} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} \begin{gathered} Q_{\text{b}}^{j - 1} + Q_{\text{w}}^j \hfill \\ M_{\text{b}}^{j - 1} + M_{\text{w}}^j \hfill \\ \end{gathered} \end{array}} \right]$ (7)

 ${v_{\text{b}}}\left( t \right) \approx \frac{1}{{2\pi }}\sum\limits_{\eta = 1}^{{\eta ^*}} {{\text{i}}{\omega _\eta }{Y_j}\left( {{\omega _\eta }} \right){{\text{e}}^{{\text{i}}{\omega _\eta }t}}\Delta \omega }$ (8)

2 半解析方法与有限元模拟对比

 图 4 桩身缺陷对梁和桩竖向动力响应的影响 Fig.4 Effects of pile defect on vertical dynamic responses of beam and pile
4 结论

 [1] Gassman SL, Finno RJ. Cutoff frequencies for impulse response tests of existing foundation. Journal of Performance of Constructed Facilities, 2000, 14: 11-21 [2] 柴华友, 刘明贵, 李祺等. 应力波在平台-桩系统中传播的试验研究. 岩土力学, 2002, 23(4): 459-464 (Chai Huayou, Liu Minggui, Li Qi, et al. Propagation of stress waves in a plate-pile system: experimental studies. Rock and Soil Mechanics, 2002, 23(4): 459-464 (in Chinese)) [3] 柴华友, 刘明贵, 白世伟等. 应力波在承台-桩系统中传播数值分析. 岩土工程学报, 2003, 25(5): 624-628 (Chai Huayou, Liu Minggui, Bai Shiwei, et al. Numerical analysis of wave propagation in platform-pile system. Chinese Journal of Geotechnical Engineering, 2003, 25(5): 624-628 (in Chinese)) [4] Baxter SC, Islam MO, Gassman SL. Impulse response evaluation of drilled shafts with pile caps: modeling and experiment. Canadian Journal of Civil Engineering, 2004, 31(2): 169-176 [5] Shahmohamadi M, Khojasteh A, Rahimian M, et al. Seismic response of an embedded pile in a transversely isotropic half-space under incident P-wave excitations. Soil Dynamics and Earthquake Engineering, 2011, 31(3): 361-371 [6] Wu WB, Wang KH, Zhang ZQ, et al. Soil-pile interaction in the pile vertical vibration considering true three-dimensional wave effect of soil. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37: 2860-2876 [7] Novak M, Mitwally H. Random response of offshore towers with pile-soil-pile interaction. Journal of Offshore Mechanics and Arctic Engineering, 1990, 112: 35-41 [8] 任青, 黄茂松, 钟锐等. 部分埋入群桩的竖向振动特性. 岩土工程学报, 2009, 31(9): 1384-1390 (Ren Qing, Huang Maosong, Zhong Rui, et al. Vertical vibration of partially embedded pile groups. Chinese Journal of Geotechnical Engineering, 2009, 31(9): 1384-1390 (in Chinese)) [9] Randolph MF, Deeks AJ. Dynamic and static soil models for axial pile response. In: Proceedings of 4th International Conference on the Application of Stress Wave Theory to Piles, The Hague, 1992. 3-14 [10] Su YC, Ma CC. Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods. International Journal of Solids and Structures, 2012, 49: 1158-1176
VERTICAL COUPLING VIBRATION OF BEAM-PILE-SOIL SYSTEM
Lü Shuhui, Wang Kuihua, Zhang Peng
Research center of coastal and urban geotechnical engineering, Zhejiang University, Hangzhou 310058, China
Fund: The project was supported by the National Natural Science Foundation of China (51378464).
Abstract: The vertical coupling vibration of beam-pile-soil system is investigated. First, the piles are assumed to be viscoelastic rods, and the plane strain model is employed to simulate the dynamic interactions between piles and surrounding soil layers. The dynamic beam-pile interactions are simplified as vertical point loads. On this basis, the matrix equation for solving the governing equations of motions for beam and piles is constructed in the frequency domain. The quasi-analytical solution in the time domain is then obtained by the discrete inverse Fourier transform. A comparison with numerical simulation is conducted to verify the rationality of the present solution. Finally, the effects of the geometric parameters of beam and pile defect on the dynamic response of beam-pile-soil system are discussed.
Key words: beam    pile group    layered soil    vertical coupling vibration    pile defect