热效应作用下S波入射弹性地基自由场地地震地面运动研究

PDF(1945 KB)

振动与冲击 ›› 2024, Vol. 43 ›› Issue (10) : 114-122.

论文

杨奕琪1，马强1,2

作者信息 +

Seismic response of a S-wave incident elastic foundation free field under the effect of heat

YANG Yiqi1，MA Qiang1,2

Author information +

文章历史 +

摘要

基于热弹性介质中波的传播理论，建立了平面S波入射下弹性地基自由场地模型，采用亥姆霍兹矢量分解原理，对热效应作用下弹性地基自由场地中的波场进行分析，获得了热效应作用下平面S波入射弹性地基自由场地地震地面运动的解析解答。通过数值计算，分析了热传导系数、介质温度、热膨胀系数等热物性参数对弹性地基自由场地地震地面运动所产生的影响规律。研究结果表明：考虑热效应和不考虑热效应的两种理论模型下所得到的水平和竖向位移放大系数有着明显差异；地表水平和竖向位移放大系数以及相应的加速度随着热膨胀系数和介质温度的增大而增大；热传导系数和热通量相位延迟对地表位移放大系数和加速度的影响较小；随着入射波频率的增大，地表位移放大系数和加速度均逐渐增大。

Abstract

Based on the theory of wave propagation in thermoelastic media, this paper establishes a model of an elastic foundation free-field under plane S-wave incidence, uses the Helmholtz vector decomposition principle to analyze the wave field in the elastic foundation-free field under thermal effects, and obtains the analytical solution of seismic ground motion in elastic foundation free field under plane S-wave incidence under thermal effects. The influence law of thermal conductivity, medium temperature, thermal expansion coefficient, and other thermal physical parameters on the seismic ground motion of elastic foundation free field is analyzed through numerical calculations. The results show that there are significant differences between the horizontal and vertical displacement amplification coefficients obtained under the two theoretical models with and without thermal effects; the amplification coefficients of surface level and vertical displacement and the corresponding acceleration increase with the increase of thermal expansion coefficient and medium temperature; the effects of thermal conduction coefficient and heat flux phase delay on the amplification coefficients of surface displacement and acceleration are smaller; the amplification coefficients of surface displacement and acceleration increase gradually with the increase of incident wave frequency.

导出引用

杨奕琪1，马强1,2. 热效应作用下S波入射弹性地基自由场地地震地面运动研究[J]. 振动与冲击, 2024, 43(10): 114-122

YANG Yiqi1，MA Qiang1,2. Seismic response of a S-wave incident elastic foundation free field under the effect of heat[J]. Journal of Vibration and Shock, 2024, 43(10): 114-122

参考文献

[1] 何卫平, 李小军, 杜修力等. P波入射分界面叠加区质点运动形成机制与峰值规律[J]. 振动与冲击, 2023, 42(18): 81-87+163. HE Weiping, LI Xiaojun, Du Xiuli, et al. Formation mechanism and peak law of plasmonic motion in the superposition region of P-wave incident manifold[J]. Journal of Vibration and Shock, 2023, 42(18): 81-87+163. [2] 张懂懂, 刘洋, 熊峰等. P波与SV波斜入射下岩体隧道洞口段地震响应分析[J]. 振动与冲击, 2022, 41(24):278-286. ZHANG Dongdong, LIU Yang, XIONG Feng, et al. Seismic response analysis of rock tunnel portal section under oblique incidence of P-wave and SV-wave[J]. Journal of Vibration and Shock, 2022, 41(24): 278-286. [3] 周凤玺, 梁玉旺, 刘佳. 多空沟对弹性波的散射及隔振性能分析: SH波入射[J]. 振动与冲击, 2021, 40(24): 263-268. ZHOU Fengxi, LIANG Yuwang, Liu J. Analysis of scattering and vibration isolation performance of elastic waves by multiple hollow grooves: SH wave incidence[J]. Journal of Vibration and Shock, 2021, 40(24): 263-268. [4] BA Z N, SANG Q Z, LIANG J W. Seismic analysis of a lined tunnel in a multi-layered TI saturated half-space due to qP1-and qSV-waves[J]. Tunnelling and Underground Space Technology, 2022, 119: 104248. [5] 巴振宁, 张家玮, 梁建文, 等. 地震波斜入射下层状TI饱和场地地震反应分析[J]. 工程力学, 2020, 37(05):166-177. BA Zhengning, ZHANG Jiawei, LIANG Jianwen, et al. Analysis of seismic response of stratified TI saturated site under oblique incidence of seismic waves[J]. Engineering Mechanics, 2020, 37(05):166-177. [6] 张季, 梁建文, 巴振宁. 水平层状饱和场地地震响应分析的等效线性化方法[J]. 工程力学, 2016, 33(10):52-61. ZHANG Ji, LIANG Jianwen, BA Zhengning. Equivalent linearization method for seismic response analysis of horizontally stratified saturated sites[J]. Engineering Mechanics, 2016, 33(10): 52-61. [7] 何颖, 丁晓凡, 刘中宪, 等. 考虑沉积河谷非线性放大效应的空间相关多点地震动模拟[J]. 工程力学, 2022:1-13. HE Ying, DING Xiaofan, LIU Zhongxian, et al. Simulation ofspatially correlated multipoi-nt ground shaking considering nonlinear amplification effects in sedimentary valleys[J]. Engineering Mechanics, 2022:1-13. [8] LIU Z X, WANG Z K, CHENG A H D, et al. The method of fundamental solutions for the elastic wave scattering in a double-porosity dual-permeability medium[J]. Applied Mathematical Modelling, 2021, 97: 721-740. [9] HUANG L, LIU Z X, WU C Q, et al. A three-dimensional indirect boundary integral equation method for the scattering of seismic waves in a poroelastic layered half-space[J]. Engineering Analysis with Boundary Elements, 2022, 135: 167-181. [10] DUHAMEL. Some memoire sur les phenomenes thermo-mechanique[J]. Journal de l’ Ecole Polytechnique 15 (1885). [11] NEUMANN F, Vorlesungen U¨ ber die Theorie der Elasticita¨t, Brestau, Meyer, 1885. [12] BIOT M A. Thermoelasticity and irreversible thermo-dynamics[J]. Journal of applied physics, 1956, 27, 249–253. [13] LORD H, SHULMAN Y. A Generalized Dynamical Theory of Thermoelasticity[J]. Journal of the mechanics and physics of solids, 1967, vol, 15, pp. 299-309. [14] GREEN A E, LINDSAY K A, Thermoelasticity[J]. Journal of Elasticity, 1972, vol. 2, no. I, pp. 1-7. [15] GREEN A E, NAGHDI P M. A Re-Examination of the Basic Postulates of Thermomechanics[J]. Proceedings: Mathematical and Physical Sciences, 1991, 432(1885). [16] GREEN A E, NAGHDI P M. Thermoelasticity without energy dissipation[J]. Journal of Elasticity, 1993, 31(3). [17] TZOU D Y. A Unified Field Approach for Heat Conduction from Macro-to Micro-Scales[J]. Journal of Heat Transfer-transactions of The Asme, 1995, 117(1): 8-16. [18] TZOU D Y. Experimental support for the lagging behavior in heat propagation[J]. Journal of Thermophysics and Heat Transfer, 1995, 9(4): 686-693. [19] HETNARSKI R B, IGNACZAK J. Generalized Thermo-elasticity. Journal of Thermal Stresses, 1999, 22, 451–476. [20] ABOUELREGAL A E. Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model[J]. International Journal of Engineering Science, 2011, 49(8). [21] SINHA A N, SINHA S B. Reflection of thermoelastic waves at a solid half-space with thermal relaxation[J]. Journal of Physics of the Earth, 1974, 22, 237–244. [22] SINHA S B, ELSIBAI K A. Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times[J]. Journal of Thermal Stresses, 1996, 19, 763–777. [23] SINHA S B, ELSIBAI K A. Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times[J]. Journal of Thermal Stresses, 1997, 20, 129–146. [24] ABD-ALLA A N, AL-DAWY A A S. The reflection phen-omena of SV waves in a generalized thermoelastic medium[J]. International Journal of Mathematics and Mathematical Sciences,2000, 23, 529–546. [25] SHARMA J N, KUMAR V, DAYAL C. Reflection of generalized thermoelastic waves from the boundary of a half-space[J]. Journal of Thermal Stresses, 2003, 26(10). [26] SINGH B. Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion[J]. Journal of Sound and Vibration, 2005, 291(3). [27] SINGH B. Reflection of P and SV waves from free surface of an elastic solid with generalized thermos diffusion[J]. Journal of earth system science, 2005, 114(2). [28] KUMAR R, SHARMA J N. Reflection of plane waves from the boundaries of a micropolar thermoelastic half-space without energy dissipation[J]. International journal of applied mechanics and engineering, 2005, 10(4). [29] CHAKRABORTY N, Singh C M. Reflection and refraction of a plane thermoelastic wave at a solid–solid interface under perfect boundary condition, in presence of normal initial stress[J]. Applied Mathematical Modelling, 2011, 35(11). [30] HOU W T, FU L Y, CARCIONE J M, et al. Reflection and Transmission of Inhomogeneous Plane Waves in Thermoelastic Media[J]. Frontiers in Earth Science, 2022, 10. [31] 王相宝, 赵凡. 单相土体与饱和土体地下结构地震反应对比研究[J]. 四川水泥, 2022, (03):22-23+26. WANG Xiangbao, ZHAO Fan. Comparative study of seismic response of subsurface structures in single-phase soils and saturated soils[J], Sichuan cement. 2022, (03): 22-23+26. [32] 杨猛. 地震SV波全反射作用下的场地反应[D].西安理工大学, 2022. YANG Meng. Site response under the effect of total reflection of seismic SV waves[D]. Xi'an University of Technology, 2022. [33] 王进廷, 金峰, 张楚汉. 位于弹性半空间上的理想流体层动力反应—平面P波入射[J]. 工程力学, 2003(06): 12-17. WANG Jinting, JIN Feng, ZHANG Chuhan. Dynamic response of an ideal fluid layer located on an elastic half-space-planar P-wave incidence[J]. Engineering Mechanics, 2003(06): 12-17. [34] ZHAO W S, CHEN W Z, YANG D S, et al. Analytical solution for seismic response of tunnels with composite linings in elastic ground subjected to Rayleigh waves[J]. Soil Dynamics and Earthquake Engineering, 2022, 153. [35] LIU H B, DAI G L, ZHOU F X, et al. Propagation behavior of homogeneous plane-P1-wave at the interface between a thermoelastic solid medium and an unsaturated porothermoelastic medium[J]. The European Physical Journal Plus, 2021, 136(11).