|
|
- 2017
P波在饱和粗颗粒夹层界面上的反射和透射
|
Abstract:
为研究应力波在埋入式桩板路基饱和粗颗粒夹层结构界面的反射和透射效应，以平面P波为例，结合埋入式桩板路基的结构特点，基于Biot饱和多孔介质波动理论和弹性波动理论，建立了考虑饱和粗颗粒夹层反射波叠加影响的弹性介质-饱和粗颗粒夹层-弹性介质界面效应模型；采用引入势函数的方法推导了应力波在饱和粗颗粒夹层交界面上的反射和透射系数；通过数值算例研究了不同因素对反射和透射系数的影响规律。研究结果表明：夹层厚度、孔隙率、剪切模量改变了能量在交界面上的分配关系，且表现出周期性谐振特性，孔隙率由0.2变化到0.4时，反射系数增大了约25%；剪切波的传播引起反射系数在剪切波谐振频率处震荡且受阻尼作用，渗透率及透水条件对粗颗粒夹层的反射系数影响明显。
： In order to study the reflection and transmission of stress wave at interfaces of the sandwiched coarse granular structure in embedded pile-board subgrade, an interface effect model for the coupled elastic solid-saturated coarse granular layer-elastic solid sandwich structure is established according to the structure characteristic of embedded pile-board subgrade, taking into consideration the superimposed effect of plane P waves reflected from the coarse granular interlayer. Based on the Biot theory and the elastic wave theory, reflection and transmission coefficients at the upper and lower interfaces in the model are derived theoretically by introducing scalar and vector potential functions. Using the derived theoretical formulas, influences of various factors on the reflection and transmission coefficients are discussed through numerical examples. The results show that thickness, porosity and shear modulus of the sandwiched coarse granular structure will change the energy distribution on interfaces, and make it present a periodic resonance characteristic. As the porosity varies from 0.2 to 0.4, the reflection coefficient increases by about 25%. In addition, the propagation of shear wave causes the reflection coefficient to oscillate with damping at the resonant frequencies of the shear wave, and the permeability and flow conditions also have significant effect on the wave reflection
| [1] | 苏谦,白皓,黄俊杰. 埋入式连续桩板结构温度效应计算方法[J]. 西南交通大学学报,2012,47(2): 181-186. SU Qian, BAI Hao, HUANG Junjie. Method for embedded continuous pile-boardstructure under thermal stresses[J]. Journal of Southwest Jiaotong University, 2012, 47(2): 181-186. |
| [2] | ZHAN Y, YAO H, JIANG G. Design method of pile-slab structure roadbed of ballastless track on soil subgrade[J]. Journal of Central South University, 2013, 20: 2072-2082. |
| [3] | CHEN R, CHEN J, WANG H. Recent research on the track-subgrade of high-speed railways[J]. Journal of Zhejiang University Science A, 2014, 15(12): 1034-1038. |
| [4] | 李尧,崔志文,张玉君,等. 弹性波在流体与饱和孔隙固体界面上的反射[J]. 岩土力学,2007,28(8): 1595-1599. LI Yao, CUI Zhiwen, ZHANG Yujun, et al. Reflection of elastic waves at fliud/fliud saturated poroelastic solid interface[J]. Rock and Soil Mechanics, 2007, 28(8): 1595-1599. |
| [5] | HAJRA S, MUKHOPADHYAY A. Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid[J]. Bulletin of the Seismological Society of America, 1982, 72(5): 1509-1533. |
| [6] | BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid: Ⅰ low-frequency range[J]. Journal of the Acoustical Society of America, 1956, 28(2): 168-178. |
| [7] | BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid: Ⅱ higher frequency range[J]. Journal of the Acoustical Society of America, 1956, 28(2): 179-191. |
| [8] | 刘志军,夏唐代,黄睿,等. Biot 理论与修正的 Biot 理论比较及讨论[J]. 振动与冲击,2015,34(4): 148-152. LIU Zhijun, XIA Tangdai, HUANG Rui, et al. Comparison and discussion on Biot theory and modified Biot theory[J]. 2015, 34(4): 148-152. |
| [9] | STOLL R D, KAN T K. Reflection of acoustic waves at a water-sediment interface[J]. The Journal of the Acoustical Society of America, 1981, 70(1): 149-156. |
| [10] | MAGHLAOUI N, DJELOUAH H, OURAK M, et al. Numerical simulation of the transient ultrasonic wave reflection at a liquid-solid interface[J]. Journal of Mechanical Science and Technology, 2015, 29(1): 165-172. |
| [11] | BONOMO A L, CHOTIROS N P, ISAKSON M J. On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer[J]. The Journal of the Acoustical Society of America, 2015, 138(2): 748-757. |
| [12] | 杨峻,吴世明. 地震波在饱和土层界面的反射与透射[J]. 地震学报,1997,19(1): 29-35. YANG Jun, WU Shiming. Reflection and transmission of seismic wave at the interfaces of saturated soils[J]. Acta Seismologica Sinica, 1997, 10(1): 29-35. |
| [13] | VASHISTH A K, SHARMA M D, GOGNA M L. Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solid[J]. Geophysical journal international, 1991, 105(3): 601-617. |
| [14] | 魏征,汪越胜,章梓茂. 波由单相弹性介质向横观各向同性液体饱和多孔介质传播时的反射与透射[J]. 固体力学学报,2002,23(2): 183-189. WEI Zheng, WANG Yuesheng, ZHANG Zimao. Reflection and transmission of elastic waves propagating from a single phase elastic medium to a transversely isotropic liquid saturated porous medium[J]. Acta Mechanica Solid Sinica, 2002, 23(2): 183-189. |
| [15] | SHEKHAR S, PARVEZ I A. Wave propagation across the imperfectly bonded interface between cracked elastic solid and porous solid saturated with two immiscible viscous fluids[J]. International Journal of Solids and Structures, 2015, 75: 299-308. |
