竖向地震作用下饱和土-桩体系的耦合动力响应研究

张石平; 陈曦菲; 姚绍伟; 邓晨

doi:10.6052/j.issn.1000-4750.2022.01.0024

竖向地震作用下饱和土-桩体系的耦合动力响应研究

doi: 10.6052/j.issn.1000-4750.2022.01.0024

张石平^{1, 2, 3},
陈曦菲^{1, 2, 3},
姚绍伟⁴,
邓晨^1, ,

1.
长沙理工大学交通运输工程学院，湖南，长沙 410114
2.
公路养护技术国家工程研究中心，湖南，长沙 410114
3.
湖南省公路先进建养技术国际创新合作基地，湖南，长沙 410114
4.
中交中南工程局有限公司，湖南，长沙 410114

基金项目: 国家重点研发计划项目(2021YFB2600900)；国家自然科学基金项目(52278434，51908070)；湖南省科技创新计划资助项目(2022RC1180)；湖南省自然科学基金项目(2020JJ5596)；公路养护技术国家工程研究中心开放基金项目(kfj190103)；湖南省大学生创新创业训练计划项目(S202113635007)；长沙理工大学研究生建设项目(CLSJCX22012)

详细信息

作者简介:
张石平(1988−)，男，云南红河人，副教授，博士，主要从事土-结构相互作用方面的研究(E-mail: zhangshipingwy@126.com)

陈曦菲(1998−)，女，湖北宜昌人，硕士生，主要从事桩基动力学方面的研究(E-mail: 602794436@qq.com)

姚绍伟(1987−)，男，湖南邵阳人，本科生，主要从事桩基动力学方面的研究(E-mail: 549731766@qq.com)

通讯作者:
邓　晨(1999−)，男，湖南长沙人，硕士生，主要从事桩基动力学方面的研究(E-mail: zjhseu@126.com)

中图分类号: TU43
计量
- 文章访问数: 229
- HTML全文浏览量: 68
- PDF下载量: 56
- 被引次数: 0
出版历程
- 收稿日期: 2022-01-06
- 修回日期: 2022-05-07
- 网络出版日期: 2022-05-12
- 刊出日期: 2023-09-06

COUPLED DYNAMIC RESPONSES BETWEEN SATURATED SOIL AND PILE SYSTEMS UNDER VERTICAL EARTHQUAKES

ZHANG Shi-ping^{1, 2, 3},
CHEN Xi-fei^{1, 2, 3},
YAO Shao-wei⁴,
DENG Chen^{1
, ,}

1.
School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Changsha, Hu’nan 410114, China
2.
National Engineering Research Center of Highway Maintenance Technology, Changsha, Hu’nan 410114, China
3.
International Innovation Cooperation Base of Advanced Highway Construction and Maintenance Technology in Hu’nan Province, Changsha, Hu’nan 410114, China
4.
CCCC Central-South Engineering Company, LTD, Changsha, Hu’nan 410114, China

摘要

摘要: 为揭示竖向地震荷载作用下桩土系统的耦合动力特性，首先将基桩视为具有径向和竖向变形的三维轴对称杆件，采用Hamilton变分原理建立其运动方程，而桩周土体视为充满流体的三维多孔连续介质，采用Boer多孔弹性介质模型描述其动力学行为。在不引入势函数的情况下，先将土骨架的体积应变和孔隙流体压力作为中间变量处理土体运动方程，然后采用分离变量法求解土体和基桩的运动方程，进而结合桩-土系统的边界和连续条件，推导得到桩顶的运动放大系数和运动响应因子解析解。通过与相应有限元模型数值计算结果及已有解的比较，验证所提出解的正确性。最后分析桩土主要参数对桩土耦合系统动力特性的影响，得到了一些有意义的结论，可为相关工程实践提供参考。研究结果表明：当桩长径比较小时，基桩的径向变形对饱和土-桩系统的动力响应存在显著影响，忽略基桩的径向变形，将高估桩土系统的共振行为；对于单相土而言，在低频阶段，桩顶响应相对于自由场表面响应偏小，在高频阶段，其随着桩长径比的增大而偏大。桩土系统的共振行为发生于激振频率接近于土体自由场的自振频率。随着桩长径比的增大，桩土系统对基岩运动的放大效应呈增大趋势；对于饱和土而言，饱和土层表面的响应与基岩运动基本上一致。随着桩长径比的增大，桩土系统对基岩运动的放大效应呈减小趋势。
- 桩土相互作用 /
- 饱和土 /
- 三维轴对称杆 /
- 径向变形 /
- Boer多孔介质模型
Abstract: To reveal the coupling dynamic characteristics of pile-soil systems under vertical seismic loads, the pile foundation was firstly regarded as a three-dimensional axisymmetric bar with radial and vertical deformation, and its motion equation was established by using a Hamiltonan variational principle. The soil around the pile was treated as a three-dimensional fluid-filled porous continuous medium, and its dynamic behavior was described by using Boer’s poroelastic media model. Without the introduction of potential functions, the volumetric strain of soil skeleton and pore fluid pressure were taken as intermediate variables to deal with the soil motion equation, and then the motion equations of soil and pile were solved by the method of variable separation. Combined with the boundary and continuity conditions of the pile-soil system, the analytical solutions of the kinematic amplification factor and kinematic response factor of the pile top were derived. The correctness of the proposed solution was verified by comparing the numerical results of the corresponding finite element model with the existing solutions. Finally, the influence of the main pile-soil parameters on the dynamic characteristics of the pile-soil coupling system was analyzed, and some meaningful conclusions were obtained, which can provide a reference for related engineering practice. The results show that: when the pile length-radius ratio is small, the radial deformation of pile foundation has a significant effect on the dynamic response of saturated soil-pile system. If the radial deformation of the pile foundation could be ignored, the resonance behavior of the pile-soil system might be overestimated. For single-phase soil, in the low frequency range, the response of a pile top is smaller than that of a free field surface and, in the high frequency range, it is larger with the increase of pile length-radius ratio. The resonance behavior of a pile-soil system occurs when the excitation frequency is close to the natural frequency of a soil free field. As the length-radius ratio of piles increases, the magnifying effect of a pile-soil system on bedrock movement tends to increase. For saturated soil, the response of saturated soil surface is basically the same as the movement of bedrock. With the increase of pile length-radius ratio, the magnifying effect of a pile-soil system on bedrock movement tends to decrease.
- pile-soil interaction /
- saturated soil /
- three-dimensional axisymmetric bar /
- radial deformation /
- Boer’s poroelastic media model

HTML全文

图 1 基岩竖向稳态运动作用下饱和土-桩体系相互作用模型

Figure 1. Interaction model of a saturated soil-pile system under the vertical steady-state movement of bedrock

下载: 全尺寸图片幻灯片

图 2 轴对称荷载作用下二维实体桩的力学模型

Figure 2. Mechanical model of a two-dimensional solid pile under axisymmetric loads

下载: 全尺寸图片幻灯片

图 3 本文退化一维桩解与已有解^[28]的比较

Figure 3. Comparison between the degenerated one-dimensional pile solution in this paper and the existing solution^[28]

下载: 全尺寸图片幻灯片

图 4 桩土系统轴对称ADINA有限元模型

Figure 4. Axisymmetric ADINA finite element model of the pile-soil system

下载: 全尺寸图片幻灯片

图 5 本文解与ADINA有限元计算结果的比较

Figure 5. Comparison between the proposed solution and ADINA finite element calculation results

下载: 全尺寸图片幻灯片

图 6 本文解场变量沿桩身的分布

Figure 6. Distribution of the field variables in the present solution along the pile shaft

下载: 全尺寸图片幻灯片

图 7 二维桩、一维桩-饱和土系统的运动放大系数

Figure 7. Kinematic amplification coefficient of two-dimensional pile and one-dimensional pile-saturated soil system

下载: 全尺寸图片幻灯片

图 8 二维桩-单相土系统的运动响应因子

Figure 8. Kinematic response factor of two-dimensional pile and single-phase soil system

下载: 全尺寸图片幻灯片

图 9 二维桩-单相土系统的运动放大系数

Figure 9. Kinematic amplification coefficient of two-dimensional pile and single-phase soil system

下载: 全尺寸图片幻灯片

图 10 二维桩-饱和土系统的运动放大系数和运动响应因子

Figure 10. Kinematic amplification coefficient and kinematic response factor of two-dimensional pile and saturated soil system

下载: 全尺寸图片幻灯片

表 1 桩土参数

Table 1. Pile and soil parameters

类别	参数	取值
基桩	桩长L/m	10.00
	桩半径r₀/m	0.25
	桩弹性模量E_p/GPa	20.00
	桩密度ρ _p/(kg/m³)	2500.00
	桩泊松比υ_p	0.10
饱和土	土弹性模量E_s/MPa	20.00
	土泊松比υ^s	0.20
	土阻尼比η^s	0.05
	土骨架实际密度ρ^sR/(kg/m³)	1800.00
	孔隙流体实际密度ρ^fR/(kg/m³)	1000.00
	孔隙流体体积分数n^f	0.40
	Darcy渗透系数k^f/(mm/s)	0.10

下载: 导出CSV

参考文献(43)

[1]	ZHANG Y P, JIANG G S, WU W B, et al. Analytical solution for distributed torsional low strain integrity test for pipe pile [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2022, 46(1): 47 − 67. doi: 10.1002/nag.3290
[2]	WU W B, YANG Z J, LIU X, et al. Horizontal dynamic response of pile in unsaturated soil considering its construction disturbance effect [J]. Ocean Engineering, 2022, 245: 110483. doi: 10.1016/j.oceaneng.2021.110483
[3]	ZHANG Y P, YANG X Y, WU W B, et al. Torsional complex impedance of pipe pile considering pile installation and soil plug effect [J]. Soil Dynamics and Earthquake Engineering, 2020, 131: 106010. doi: 10.1016/j.soildyn.2019.106010
[4]	陈志雄, 李康银, 王成龙, 等. 液化侧向扩展场地刚性排水管桩群桩振动台试验研究[J]. 工程力学, 2022, 39(9): 141 − 152. doi: 10.6052/j.issn.1000-4750.2021.05.0374 CHEN Zhixiong, LI Kangyin, WANG Chenglong, et al. Shaking table tests on rigid-drainage pipe pile groups at liquefied laterally spreading site [J]. Engineering Mechanics, 2022, 39(9): 141 − 152. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.05.0374
[5]	徐丹, 杜春波, 王涛, 等. 可液化场地高桩桥梁振动台模型试验研究[J]. 工程力学, 2020, 37(增刊 1): 168 − 171. doi: 10.6052/j.issn.1000-4750.2019.05.S031 XU Dan, DU Chunbo, WANG Tao, et al. Shaking table test on elevated pile bridges in liquefiable ground [J]. Engineering Mechanics, 2020, 37(Suppl 1): 168 − 171. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.05.S031
[6]	邹佑学, 王睿, 张建民. 碎石桩加固可液化场地数值模拟与分析[J]. 工程力学, 2019, 36(10): 152 − 163. doi: 10.6052/j.issn.1000-4750.2018.10.0559 ZOU Youxue, WANG Rui, ZHANG Jianmin. Numerical investigation on liquefaction mitigation of liquefiable soil improved by stone columns [J]. Engineering Mechanics, 2019, 36(10): 152 − 163. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.10.0559
[7]	孙苗苗. 任意排列的空心管桩屏障对SH波的多重散射[J]. 岩土力学, 2014, 35(4): 943 − 950, 958. SUN Miaomiao. Multiple scattering of SH waves by rows of arbitrarily arranged tubular piles [J]. Rock and Soil Mechanics, 2014, 35(4): 943 − 950, 958. (in Chinese)
[8]	巴振宁, 刘世朋, 吴孟桃, 等. 饱和土中周期排列管桩对平面SV波隔振的解析求解[J]. 岩土力学, 2021, 42(3): 1 − 12. BA Zhenning, LIU Shipeng, WU Mengtao, et al. Analytical solution for isolation effect of plane SV waves by pipe piles with periodic arrangement in saturated soil [J]. Rock and Soil Mechanics, 2021, 42(3): 1 − 12. (in Chinese)
[9]	杨骁, 方晓雯, 汪德江. SH波作用下液化土中桩-土-上部结构的动力相互作用[J]. 工程力学, 2017, 34(1): 101 − 108. doi: 10.6052/j.issn.1000-4750.2015.04.0310 YANG Xiao, FANG Xiaowen, WANG Dejiang. Dynamic interaction of pile-soil-superstructure in liquefied soil under SH wave [J]. Engineering Mechanics, 2017, 34(1): 101 − 108. (in Chinese) doi: 10.6052/j.issn.1000-4750.2015.04.0310
[10]	刘林超, 杨骁. 地震作用下饱和土-桩-上部结构动力相互作用研究[J]. 岩土力学, 2012, 33(1): 120 − 128. doi: 10.3969/j.issn.1000-7598.2012.01.020 LIU Linchao, YANG Xiao. Dynamic interaction of saturated soil-pile-structure system under seismic loading [J]. Rock and Soil Mechanics, 2012, 33(1): 120 − 128. (in Chinese) doi: 10.3969/j.issn.1000-7598.2012.01.020
[11]	闫启方, 刘林超. 考虑波动效应的SH简谐地震波作用下单桩水平振动研究[J]. 岩土工程学报, 2012, 34(8): 1483 − 1487. YAN Qifang, LIU Linchao. Lateral vibration of a single pile under SH harmonic seismic waves considering three-dimensional wave effect [J]. Chinese Journal of Geotechnical Engineering, 2012, 34(8): 1483 − 1487. (in Chinese)
[12]	邵艳丽, 方晓雯, 杨骁. SH波作用下桩-液化土-结构体系的水平振动特性[J]. 振动与冲击, 2017, 36(20): 210 − 217. SHAO Yanli, FANG Xiaowen, YANG Xiao. Horizontal vibration characteristics of a pile-liquefied soil-superstructure under SH wave [J]. Journal of Vibration and Shock, 2017, 36(20): 210 − 217. (in Chinese)
[13]	付毳, 黄福云, 陈宝春, 等. 沿海软土地区PHC管桩-土-结构模型振动台试验[J]. 中国公路学报, 2017, 30(10): 81 − 92. doi: 10.3969/j.issn.1001-7372.2017.10.011 FU Cui, HUANG Fuyun, CHEN Baochun, et al. Shaking table test on structure-soil-pile of PHC in coastal soft-soil area [J]. China Journal of Highway and Transport, 2017, 30(10): 81 − 92. (in Chinese) doi: 10.3969/j.issn.1001-7372.2017.10.011
[14]	王安辉, 章定文, 丁选明, 等. 桩筏连接形式对劲芯复合桩地震响应影响试验研究[J]. 中国公路学报, 2021, 34(5): 24 − 36. doi: 10.3969/j.issn.1001-7372.2020.01.001 WANG Anhui, ZHANG Dingwen, DING Xuanming, et al. Experimental study on effect of connection type of pile-raft on seismic response of piles improved with cement-treated soil [J]. China Journal of Highway and Transport, 2021, 34(5): 24 − 36. (in Chinese) doi: 10.3969/j.issn.1001-7372.2020.01.001
[15]	吴鹏, 任伟新. 竖向激励场下考虑桩土滑移的单桩动力性态[J]. 土木工程学报, 2009, 42(6): 92 − 96. doi: 10.3321/j.issn:1000-131X.2009.06.015 WU Peng, REN Weixin. Response of single piles to vertical excitation with pile-soil slip [J]. China Civil Engineering Journal, 2009, 42(6): 92 − 96. (in Chinese) doi: 10.3321/j.issn:1000-131X.2009.06.015
[16]	MAMOON S M, AHMAD S. Seismic response of piles to obliquely incident SH, SV, and P waves [J]. Journal of Geotechnical Engineering, 1990, 116(2): 186 − 204. doi: 10.1061/(ASCE)0733-9410(1990)116:2(186)
[17]	JI F, PAK Y S R. Scattering of vertically-incident P-waves by an embedded pile [J]. Soil Dynamics and Earthquake Engineering, 1996, 15: 211 − 222. doi: 10.1016/0267-7261(94)00055-7
[18]	MYLONAKIS G, GAZETAS G. Kinematic pile response to vertical P-wave seismic excitation [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(10): 860 − 867. doi: 10.1061/(ASCE)1090-0241(2002)128:10(860)
[19]	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 [J]. Soil Dynamics and Earthquake Engineering, 2011, 31: 361 − 371. doi: 10.1016/j.soildyn.2010.09.005
[20]	ANOYATIS G, LAORA D R, MYLONAKIS G. Axial kinematic response of end-bearing piles to P waves [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37: 2877 − 2896. doi: 10.1002/nag.2166
[21]	LIU Q J, DENG F J, HE Y B. Kinematic response of single piles to vertically incident P-waves [J]. Earthquake Engineering & Structural Dynamics, 2014, 43(6): 871 − 887.
[22]	KE W H, ZHANG C, DENG P. Kinematic response of single piles to vertical P-waves in multilayered soil [J]. Journal of Earthquake and Tsunami, 2015, 9(2): 1550004. doi: 10.1142/S1793431115500049
[23]	BARROS L D A P, LABAKI J, MESQUITA E. IBEM-FEM model of a piled plate within a transversely isotropic half-space [J]. Engineering Analysis with Boundary Elements, 2019, 101: 281 − 296. doi: 10.1016/j.enganabound.2018.12.013
[24]	DAI D H, NAGGAR E H M, ZHANG N, et al. Kinematic response of an end-bearing pile subjected to vertical P-wave considering the three-dimensional wave scattering [J]. Computers and Geotechnics, 2020, 120: 103368. doi: 10.1016/j.compgeo.2019.103368
[25]	ZHENG C J, KOURETZIS G, LUAN L B, et al. Kinematic response of pipe piles subjected to vertically propagating seismic P-waves [J]. Acta Geotechnica, 2021, 16(3): 895 − 909. doi: 10.1007/s11440-020-01050-3
[26]	徐平, 夏唐代, 吴明. 刚性空心管桩屏障对P波和SH波的隔离效果研究[J]. 工程力学, 2008, 25(5): 210 − 217. XU Ping, XIA Tangdai, WU Ming. Study on the effect of barrier of a row of rigid hollow pipe piles for the isolation of P and SH waves [J]. Engineering Mechanics, 2008, 25(5): 210 − 217. (in Chinese)
[27]	孙苗苗, 夏唐代. 多排任意排列的弹性桩屏障对平面P波或SV波多重散射[J]. 振动与冲击, 2014, 33(6): 148 − 155. SUN Miaomiao, XIA Tangdai. Multiple scattering of P and SV waves by muti-row arbitrarily arranged elastic piles barrier [J]. Journal of Vibration and Shock, 2014, 33(6): 148 − 155. (in Chinese)
[28]	ZHANG S P, CUI C Y, YANG G. Coupled vibration of an interaction system including saturated soils, pile group and superstructure under the vertical motion of bedr ocks [J]. Soil Dynamics and Earthquake Engineering, 2019, 123: 425 − 434. doi: 10.1016/j.soildyn.2019.03.033
[29]	巴振宁, 刘世朋, 吴孟桃, 等. 周期分布群桩屏障对平面弹性波隔振效应的解析求解[J]. 岩石力学与工程学报, 2020, 39(7): 1468 − 1482. BA Zhenning, LIU Shipeng, WU Mengtao, et al. Analytical solution for isolation effect of periodically distributed pile-group barriers against plane elastic wave [J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(7): 1468 − 1482. (in Chinese)
[30]	PAK Y S R, GOBERT A T. Axisymmetric problems of a partially embedded rod with radial deformation [J]. International Journal of Solids and Structures, 1993, 30(13): 1745 − 1759. doi: 10.1016/0020-7683(93)90231-U
[31]	MASOUMI H R, DEGRANDE G, LOMBAERT G. Prediction of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation [J]. Soil Dynamics and Earthquake Engineering, 2007, 27: 126 − 143. doi: 10.1016/j.soildyn.2006.05.005
[32]	MASOUMI H R, DEGRANDE G. Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation [J]. Journal of Computational and Applied Mathematics, 2008, 215: 503 − 511. doi: 10.1016/j.cam.2006.03.051
[33]	张玲, 张旭波, 徐泽宇, 等. 基于辛体系的筋箍碎石桩受力变形分析[J]. 岩土工程学报, 2020, 42(11): 2040 − 2049. ZHANG Ling, ZHANG Xubo, XU Zeyu, et al. Stress and deformation analysis of geosynthetic-encased stone columns based on Symplectic system [J]. Chinese Journal of Geotechnical Engineering, 2020, 42(11): 2040 − 2049. (in Chinese)
[34]	MINDLIN R D, HERRMANN G. A one-dimensional theory of compressional waves in an elastic rod [C]// Proc. 1st Nat. Congr. Appl. Mech. Chicago: 1951: 187− 191.
[35]	MORSE P M, FESHBACH H. Methods of theoretical physics [M]. New York: McGraw-Hill, 1953.
[36]	ACHENBACH J D. Wave propagation in elastic solids [M]. London: North-Holland, Amsterdam, 1973.
[37]	BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range [J]. Journal of the Acoustic Society of America, 1956, 28(2): 168 − 178. doi: 10.1121/1.1908239
[38]	BOER D R, LIU Z F. Plane waves in a semi-infinite fluid saturated porous medium [J]. Transport in Porous Media, 1994, 16: 147 − 173. doi: 10.1007/BF00617549
[39]	WILMANSKI K. A few remarks on Biot’s model and linear acoustics of poroelastic saturated materials [J]. Soil Dynamic and Earthquake Engineering, 2006, 26: 509 − 536. doi: 10.1016/j.soildyn.2006.01.006
[40]	BOER D R. Theory of porous media: Highlights in the historical development and current state [M]. Berlin: Springer, 2000.
[41]	ZHANG S P, PAK Y S R, ZHANG J H. Three-dimensional frequency-domain Green's functions of a finite fluid-saturated soil layer underlain by rigid bedrock to interior loadings [J]. International Journal of Geomechanics, 2022, 22(1): 04021267. doi: 10.1061/(ASCE)GM.1943-5622.0002235
[42]	WANG L H, AI Z Y. Vertical vibration analysis of a pile group in multilayered poroelastic soils with compressible constituents [J]. International Journal of Geomechanics, 2021, 21(1): 04020232. doi: 10.1061/(ASCE)GM.1943-5622.0001881
[43]	HUSSIEN N M, TOBITA T, IAI S, et al. Soil-pile-structure kinematic and inertial interaction observed in geotechnical centrifuge experiments [J]. Soil Dynamics and Earthquake Engineering, 2016, 89: 75 − 84. doi: 10.1016/j.soildyn.2016.08.002