饱和土中夹水混凝土复合式隔振屏障的隔振分析
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摘要
构建了饱和土中夹水混凝土复合隔振屏障计算模型,通过引入势函数及利用饱和土与混凝土及混凝土与水交界面的连续性边界条件,求解了P波穿过隔振屏障后位移振幅衰减系数的解析解。研究结果表明,屏障的隔振效果与入射波的入射角有关,入射角在14°左右时,屏障的隔振效果最差,之后随入射角的增大,隔振效果总体越来越好;垂直入射时,屏障隔振效果随混凝土层厚及水层宽度增加先减弱后增强,随混凝土弹性模量及泊松比的增加而减弱;入射角为30°时,隔振效果随混凝土厚及水层宽度增加先增强后减弱,当混凝土厚和水层宽为入射波波长的1倍和0. 3倍时,位移振幅基本衰减为0,随混凝土弹性模量及泊松比的增加,隔振效果增强,且弹性模量对隔振效果影响更为明显,泊松比影响不大;随入射波频率增加屏障的隔振效果总体越来越好。
A dynamic model for a concrete-water-concrete composite vibration isolation barrier in saturated soil was established. The analytical solution to the delay coefficient of displacement amplitude of P wave passing through the barrier was obtained by introducing the potential function and using continuous boundary conditions on interfaces of saturated soilconcrete and concrete-water. The results showed that the vibration isolation effect of the barrier is related to incident wave's incident angle,the barrier's isolation effect is the minimum at incident angle of 14°,and then the barrier's isolation effect gets better with increase in incident angle; at vertical incidence,the barrier's isolation effect decreases at first and then increases with increase in concrete layer thickness and water layer width,it decreases with increase in concrete elastic modulus and Poisson's ratio; when incident angle is 30°,the barrier's isolation effect increases at first and then decreases with increase in concrete layer thickness and water layer width,when concrete layer thickness and water layer width are 1 time and 0. 3 time of incident wave length,respectively,displacement amplitude decay basically is0,the barrier's vibration isolation effect increases with increase in concrete elastic modulus and Poisson's ratio,and concrete elastic modulus affects the barrier's vibration isolation effect more obviously than Poisson's ratio does; the barrier's isolation effect gets better with increase in incident wave frequency.
A dynamic model for a concrete-water-concrete composite vibration isolation barrier in saturated soil was established. The analytical solution to the delay coefficient of displacement amplitude of P wave passing through the barrier was obtained by introducing the potential function and using continuous boundary conditions on interfaces of saturated soilconcrete and concrete-water. The results showed that the vibration isolation effect of the barrier is related to incident wave's incident angle,the barrier's isolation effect is the minimum at incident angle of 14°,and then the barrier's isolation effect gets better with increase in incident angle; at vertical incidence,the barrier's isolation effect decreases at first and then increases with increase in concrete layer thickness and water layer width,it decreases with increase in concrete elastic modulus and Poisson's ratio; when incident angle is 30°,the barrier's isolation effect increases at first and then decreases with increase in concrete layer thickness and water layer width,when concrete layer thickness and water layer width are 1 time and 0. 3 time of incident wave length,respectively,displacement amplitude decay basically is0,the barrier's vibration isolation effect increases with increase in concrete elastic modulus and Poisson's ratio,and concrete elastic modulus affects the barrier's vibration isolation effect more obviously than Poisson's ratio does; the barrier's isolation effect gets better with increase in incident wave frequency.
引文
[1]STOLL R D,KAN T.Reflection of acoustic waves at a water sediment interface[J].Journal of the Acoustical Society of America,1981,69(1):149-156.
[2]WANG Jinting,ZHANG Chuhan,JIN Feng.Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence[J].Earthquake Engineering and Engineering Vibration,2004,3(2):263-271.
[3]WANG J T,ZHANG C H,JIN F.Analytical solutions for dynamic pressures of coupling fluid-porous medium-solid due to SV wave incidence[J].International Journal for Numerical&Analytical Methods in Geomechanics,2010,33(12):1467-1484.
[4]JUN Yang.Influence of water saturation on horizontal and vertical motion at porous soil interface induced by incident Pwave[J].Soil Dynamics and Earthquake Engineering,2000,19(81):575-581.
[5]陈炜昀,夏唐代,王宁,等.不同饱和度土层分界面上剪切波的反射与透射[J].岩土力学,2013,34(3):894-900.CHEN Weiyun,XIA Tangdai,WANG Ning,et al.Reflection and transmission of shear wave at interdace between soil layers with different saturation degrees[J].Rock and Soil Mechanics,2013,34(3):894-900.
[6]徐平,夏唐代.弹性波在准饱和土和弹性土界面的反射与透射[J].力学与实践,2006,28(6):58-63.XU Ping,XIA Tangdai.Reflection and transmission of elastic wave at the interface of nearly saturated soil and elastic soil[J].Mechanics in Engineering,2006,28(6):58-63.
[7]叶陈江,史焱永,蔡袁强.S波由饱和土入射于弹性土时在界面上的反射与透射[J].振动与冲击,2005,24(2):41-45.YE Chenjiang,SHI Yanyong,CAN Yuanqiang.The reflection and transmission of S wave on the interface when the saturated soil is in the elastic soil[J].Journal of Vibration and Shock,2005,24(2):41-45.
[8]俞缙,钱七虎,宋博学,等.不同应力波穿过多条非线性变形节理时的透射特性[J].工程力学,2012,29(4):1-6.YU Jin,QIAN Qihu,SONG Boxue,et al.Transmission of various stress waves across multi-fracture with nonlinear deformation behavior[J].Engineering Mechanics,2012,29(4):1-6.
[9]WOODS R D.Screening of surface waves in soils[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(4):951-979.
[10]HAUPT W A.Model tests on screening of surface waves[C]∥Proceedings of the 10th International Conference in Soil Mechanics and Foundation Engineering.Stockholm,1981.
[11]朱兵见,熊浩.二维饱和地基中空沟主动隔振分析[J].岩土力学,2013,34(2):462-467.ZHU Bingjian,XIONG Hao.Analysis of active vibration isolation by open trench in two-dimensional saturated ground[J].Rock and Soil Mechanics,2013,34(2):462-467.
[12]时刚,郭院成,高广运.饱和地基中二维填充沟远场被动隔振研究[J].岩土工程学报,2011(1):104-111.SHI Gang,GUO Yuancheng,GAO Guangyun.Twodimensional analysis of in-filled trenches as passive as passive barriers in saturated soil[J].Chinese Journal of Geotechnical Engineering,2011(1):104-111.
[13]袁万.基于2.5维有限元饱和土地基中隔振沟屏障性能研究[D].杭州:浙江大学,2013.
[14]徐平,邓亚虹,吴明.饱和土体中多排桩屏障对压缩快波的隔离[J].工程力学,2014,31(5):120-127.XU Ping,DENG Yahong,WU Ming.Isolation of fast compressive waves by barriers composed of several rows of piles in saturated soils[J].Engineering Mechanics,2014,31(5):120-127.
[15]PAO Y H,MOW C C,ACHENBACH J D.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane and Russak.1973.
[16]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498.
[17]ACHENBACH J D.弹性固体中波的传播[M].徐植信,洪锦如,译.上海:同济大学出版社,1992.
[18]宫全美.轨道交通线路动力学[M].北京:人民交通出版社股份有限公司,2015.
[2]WANG Jinting,ZHANG Chuhan,JIN Feng.Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence[J].Earthquake Engineering and Engineering Vibration,2004,3(2):263-271.
[3]WANG J T,ZHANG C H,JIN F.Analytical solutions for dynamic pressures of coupling fluid-porous medium-solid due to SV wave incidence[J].International Journal for Numerical&Analytical Methods in Geomechanics,2010,33(12):1467-1484.
[4]JUN Yang.Influence of water saturation on horizontal and vertical motion at porous soil interface induced by incident Pwave[J].Soil Dynamics and Earthquake Engineering,2000,19(81):575-581.
[5]陈炜昀,夏唐代,王宁,等.不同饱和度土层分界面上剪切波的反射与透射[J].岩土力学,2013,34(3):894-900.CHEN Weiyun,XIA Tangdai,WANG Ning,et al.Reflection and transmission of shear wave at interdace between soil layers with different saturation degrees[J].Rock and Soil Mechanics,2013,34(3):894-900.
[6]徐平,夏唐代.弹性波在准饱和土和弹性土界面的反射与透射[J].力学与实践,2006,28(6):58-63.XU Ping,XIA Tangdai.Reflection and transmission of elastic wave at the interface of nearly saturated soil and elastic soil[J].Mechanics in Engineering,2006,28(6):58-63.
[7]叶陈江,史焱永,蔡袁强.S波由饱和土入射于弹性土时在界面上的反射与透射[J].振动与冲击,2005,24(2):41-45.YE Chenjiang,SHI Yanyong,CAN Yuanqiang.The reflection and transmission of S wave on the interface when the saturated soil is in the elastic soil[J].Journal of Vibration and Shock,2005,24(2):41-45.
[8]俞缙,钱七虎,宋博学,等.不同应力波穿过多条非线性变形节理时的透射特性[J].工程力学,2012,29(4):1-6.YU Jin,QIAN Qihu,SONG Boxue,et al.Transmission of various stress waves across multi-fracture with nonlinear deformation behavior[J].Engineering Mechanics,2012,29(4):1-6.
[9]WOODS R D.Screening of surface waves in soils[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(4):951-979.
[10]HAUPT W A.Model tests on screening of surface waves[C]∥Proceedings of the 10th International Conference in Soil Mechanics and Foundation Engineering.Stockholm,1981.
[11]朱兵见,熊浩.二维饱和地基中空沟主动隔振分析[J].岩土力学,2013,34(2):462-467.ZHU Bingjian,XIONG Hao.Analysis of active vibration isolation by open trench in two-dimensional saturated ground[J].Rock and Soil Mechanics,2013,34(2):462-467.
[12]时刚,郭院成,高广运.饱和地基中二维填充沟远场被动隔振研究[J].岩土工程学报,2011(1):104-111.SHI Gang,GUO Yuancheng,GAO Guangyun.Twodimensional analysis of in-filled trenches as passive as passive barriers in saturated soil[J].Chinese Journal of Geotechnical Engineering,2011(1):104-111.
[13]袁万.基于2.5维有限元饱和土地基中隔振沟屏障性能研究[D].杭州:浙江大学,2013.
[14]徐平,邓亚虹,吴明.饱和土体中多排桩屏障对压缩快波的隔离[J].工程力学,2014,31(5):120-127.XU Ping,DENG Yahong,WU Ming.Isolation of fast compressive waves by barriers composed of several rows of piles in saturated soils[J].Engineering Mechanics,2014,31(5):120-127.
[15]PAO Y H,MOW C C,ACHENBACH J D.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane and Russak.1973.
[16]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498.
[17]ACHENBACH J D.弹性固体中波的传播[M].徐植信,洪锦如,译.上海:同济大学出版社,1992.
[18]宫全美.轨道交通线路动力学[M].北京:人民交通出版社股份有限公司,2015.