饱和地基中地下结构地震反应若干问题研究
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摘要
简要综述笔者所在课题组近十年在饱和地基中地下结构抗震研究方面的主要成果,包括:(1)饱和两相介质中波动方程及波动特性的探究;(2)动力有限元计算的传输边界研发;(3)饱和地基中地下结构地震反应离心机模型试验研究;(4)饱和地基中地下结构地震响应的有限元分析;(5)饱和砂土地基中地下结构上浮机理研究等。这些成果以较为深入地研究饱和两相介质波动理论为基础,通过模型试验、数值仿真、机理探究等方法认知饱和地基中地下结构地震反应机理,对于完善饱和地基中地下结构抗震设计方法及提高抗震安全措施等均具有参考价值。
The main achievements of 10 years of research on the seismic response of underground structures in a saturated foundation are presented in this paper.Systematic clarification and investigation are conducted on the dynamic basic formulations and wave propagation characteristics of saturated soils.In the dynamic analysis of saturated soils,the interaction between the soil skeleton and pore water consists of two parts:seepage force and inertial coupling force.It is also revealed that due to the existence of the inertial coupling force,the speeds of two dilatational waves are not equal to those in single-phased solid skeleton and pore water even if the permeability approaches infinity.Moreover,several transmitting boundaries for dynamic analysis of saturated porous media are developed,including the viscous-spring transmitting boundaries derived from both the u-p formulation and u-Uformulation in addition to the high-order time-domain transmitting boundary derived from the cylindrical elastic wave radiation problem based on the u-pformulation.Despite the zero permeability assumption made in the derivation of the undrained boundary,results show that it can provide sufficiently accurate results for earthquake engineering problems.The drained boundary performs well for all permeabilities.In addition,four dynamic centrifuge tests at 1:50scale are performed to study the earthquake response of a subway tunnel in liquefiable soils.The response characteristics of the subway tunnel in horizontal or oblique liquefiable soils including floatation,lateral displacement of the tunnel,and internal force increments in tunnel segments due to earthquake-induced liquefaction are investigated in addition to the effectiveness of cut-off walls in resisting tunnel flotation.Further,finite element simulation is conducted to analyze the earthquake response of underground structures in saturated soils.We adopt the finite element program DIANA SWANDYNE II,which is a two dimensional(2D),effective stress-based program compiled from the fully coupled u-pformulation.The liquefiable sandy soil is modeled by using the generalized plasticity constitutive model Pastor-Zienkiewicz III,which is capable of simulating cyclic liquefaction,contraction of loose sand,and dilatation of dense sand.The contact characteristics between soil and the structure are also considered.Finally,the mechanism of underground structure flotation in liquefiable soils during earthquakes is studied.Due to the smaller apparent density of the tunnel structure compared with the saturated liquefiable sand,the soils at both sides beneath the tunnel structure tend to intrude into the space underneath the tunnel structure,leading to the structure flotation.The mechanisms of various remedial treatment methods for liquefiable soils such as increasing the tunnel buried depth,retrofitting the soil under the tunnel structure,and setting cut-off walls are studied by finite element simulation.The effectiveness of these methods is evaluated,and references for parameter design are proposed.These new achievements,which allow insight into the mechanism of the seismic response of underground structures in saturated foundations,are obtained from theoretical research on the wave propagation characteristics and are based on model tests,numerical simulations,and mechanism analysis.The study outcome will be beneficial for further research on the improvement of seismic design methods and seismic safety measures for underground structures in saturated foundations.
The main achievements of 10 years of research on the seismic response of underground structures in a saturated foundation are presented in this paper.Systematic clarification and investigation are conducted on the dynamic basic formulations and wave propagation characteristics of saturated soils.In the dynamic analysis of saturated soils,the interaction between the soil skeleton and pore water consists of two parts:seepage force and inertial coupling force.It is also revealed that due to the existence of the inertial coupling force,the speeds of two dilatational waves are not equal to those in single-phased solid skeleton and pore water even if the permeability approaches infinity.Moreover,several transmitting boundaries for dynamic analysis of saturated porous media are developed,including the viscous-spring transmitting boundaries derived from both the u-p formulation and u-Uformulation in addition to the high-order time-domain transmitting boundary derived from the cylindrical elastic wave radiation problem based on the u-pformulation.Despite the zero permeability assumption made in the derivation of the undrained boundary,results show that it can provide sufficiently accurate results for earthquake engineering problems.The drained boundary performs well for all permeabilities.In addition,four dynamic centrifuge tests at 1:50scale are performed to study the earthquake response of a subway tunnel in liquefiable soils.The response characteristics of the subway tunnel in horizontal or oblique liquefiable soils including floatation,lateral displacement of the tunnel,and internal force increments in tunnel segments due to earthquake-induced liquefaction are investigated in addition to the effectiveness of cut-off walls in resisting tunnel flotation.Further,finite element simulation is conducted to analyze the earthquake response of underground structures in saturated soils.We adopt the finite element program DIANA SWANDYNE II,which is a two dimensional(2D),effective stress-based program compiled from the fully coupled u-pformulation.The liquefiable sandy soil is modeled by using the generalized plasticity constitutive model Pastor-Zienkiewicz III,which is capable of simulating cyclic liquefaction,contraction of loose sand,and dilatation of dense sand.The contact characteristics between soil and the structure are also considered.Finally,the mechanism of underground structure flotation in liquefiable soils during earthquakes is studied.Due to the smaller apparent density of the tunnel structure compared with the saturated liquefiable sand,the soils at both sides beneath the tunnel structure tend to intrude into the space underneath the tunnel structure,leading to the structure flotation.The mechanisms of various remedial treatment methods for liquefiable soils such as increasing the tunnel buried depth,retrofitting the soil under the tunnel structure,and setting cut-off walls are studied by finite element simulation.The effectiveness of these methods is evaluated,and references for parameter design are proposed.These new achievements,which allow insight into the mechanism of the seismic response of underground structures in saturated foundations,are obtained from theoretical research on the wave propagation characteristics and are based on model tests,numerical simulations,and mechanism analysis.The study outcome will be beneficial for further research on the improvement of seismic design methods and seismic safety measures for underground structures in saturated foundations.
引文
[1]Hwang J H,Yang C W,Chen C H.Investigations on Soil Liquefaction During the Chi-Chi Earthquake[J].Soils and Foundations,2003,43(6):107-123.
[2]Elnashai AS.Analysis of the Damage Potential of the Kocaeli(Turkey)Earthquake of 17 August 1999[J].Engineering Structures,2000,22(7):746-754.
[3]Samata S,Ohuchi H,Matsuda T.A Study of the Damage of Subway Structures During the 1995 Hanshin-Awaji Earthquake[J].Cement and Concrete Composites,1997,19(3):223-239.
[4]Biot MA.Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid:I.Low-frequency Range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[5]门福录.波在饱含流体的孔隙介质中的传播问题[J].地球物理学报,1981,24(1):65-75.Men F L.Problems of Wave Propagation in Porous Fluid-saturated Media[J].Acta Geophysica Sinica,1981,24(1):65-75.(in Chinese)
[6]吴世明.土介质中的波[M].北京:科学出版社,1997.WU Shi-ming.Waves in Soil Medium[M].Beijing:Science Press,1997.(in Chinese)
[7]Zienkiewicz O C,Shiomi T.Dynamic Behavior of Saturated Porous Media;The Generalized Biot Formulation and Its Numerical Solution[J].International Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1):71-96.
[8]李鹏,宋二祥.渗透系数极端情况下饱和土中压缩波波速及其物理本质[J].岩土力学,2012,33(7):1979-1985.Li P,Song EX.Compressional Wave Velocity and Its Physical Nature in Saturated Soils with Extreme Permeability Values[J].Rock and Soil Mechanics,2012,33(7):1979-1985.(in Chinese)
[9]刘光磊,宋二祥.饱和无限地基数值模拟的粘弹性传输边界[J].岩土工程学报,2006,28(12):2128-2133.Liu G L,Song E X.Visco-elastic Transmitting Boundary for Numerical Analysis of Infinite Saturated Soil Foundation[J].Chinese journal of Geotechnical Engineering,2006,28(12):2128-2133.(in Chinese)
[10]Li P,Song E X.A Viscous-spring Transmitting Boundary for Cylindrical Wave Propagation in Saturated Poroelastic Media[J].Soil Dynamics and Earthquake Engineering,2014,65:269-283.
[11]王子辉,赵成刚,董亮.流体饱和多孔介质黏弹性动力人工边界[J].力学学报,2006,38(5):605-611.Wang Z H,Zhao C G,Dong L.A Viscous-spring Dynamical Artificial Boundary for Saturated Porous Media[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(5):605-611.(in Chinese)
[12]Li P,Song E X.A High-order Time-domain Transmitting Boundary for Cylindrical Wave Propagation Problems in Unbounded Saturated Poroelastic Media[J].Soil Dynamics and Earthquake Engineering,2013,48:48-62.
[13]Zienkiewicz OC,Chan AHC,Pastor M,et al.Computational Geomechanics with Special Reference to Earthquake Engineering[J].New York:John Wiley&Sons,1998.
[14]刘光磊,宋二祥,刘华北,等.饱和砂土地层中隧道结构动力离心模型试验[J].岩土力学,2008,29(8):2070-2076.Liu G L,Song E X,Liu H B,et al.Dynamic Centrifuge Tests on Seismic Response of Tunnel in Saturated Sandy Foundation[J].Rock and Soil Mechanics,2008,29(8):2070-2076.(in Chinese)
[15]刘光磊,宋二祥,刘华北.可液化地层中地铁隧道地震响应数值模拟及其试验验证[J].岩土工程学报,2007,29(12):1815-1822.Liu G L,Song E X,Liu H B.Numerical Modeling of Subway Tunnels in Liquefiable Soil Under Earthquakes and Verification by Centrifuge Tests[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1815-1822.(in Chinese)
[2]Elnashai AS.Analysis of the Damage Potential of the Kocaeli(Turkey)Earthquake of 17 August 1999[J].Engineering Structures,2000,22(7):746-754.
[3]Samata S,Ohuchi H,Matsuda T.A Study of the Damage of Subway Structures During the 1995 Hanshin-Awaji Earthquake[J].Cement and Concrete Composites,1997,19(3):223-239.
[4]Biot MA.Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid:I.Low-frequency Range[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[5]门福录.波在饱含流体的孔隙介质中的传播问题[J].地球物理学报,1981,24(1):65-75.Men F L.Problems of Wave Propagation in Porous Fluid-saturated Media[J].Acta Geophysica Sinica,1981,24(1):65-75.(in Chinese)
[6]吴世明.土介质中的波[M].北京:科学出版社,1997.WU Shi-ming.Waves in Soil Medium[M].Beijing:Science Press,1997.(in Chinese)
[7]Zienkiewicz O C,Shiomi T.Dynamic Behavior of Saturated Porous Media;The Generalized Biot Formulation and Its Numerical Solution[J].International Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1):71-96.
[8]李鹏,宋二祥.渗透系数极端情况下饱和土中压缩波波速及其物理本质[J].岩土力学,2012,33(7):1979-1985.Li P,Song EX.Compressional Wave Velocity and Its Physical Nature in Saturated Soils with Extreme Permeability Values[J].Rock and Soil Mechanics,2012,33(7):1979-1985.(in Chinese)
[9]刘光磊,宋二祥.饱和无限地基数值模拟的粘弹性传输边界[J].岩土工程学报,2006,28(12):2128-2133.Liu G L,Song E X.Visco-elastic Transmitting Boundary for Numerical Analysis of Infinite Saturated Soil Foundation[J].Chinese journal of Geotechnical Engineering,2006,28(12):2128-2133.(in Chinese)
[10]Li P,Song E X.A Viscous-spring Transmitting Boundary for Cylindrical Wave Propagation in Saturated Poroelastic Media[J].Soil Dynamics and Earthquake Engineering,2014,65:269-283.
[11]王子辉,赵成刚,董亮.流体饱和多孔介质黏弹性动力人工边界[J].力学学报,2006,38(5):605-611.Wang Z H,Zhao C G,Dong L.A Viscous-spring Dynamical Artificial Boundary for Saturated Porous Media[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(5):605-611.(in Chinese)
[12]Li P,Song E X.A High-order Time-domain Transmitting Boundary for Cylindrical Wave Propagation Problems in Unbounded Saturated Poroelastic Media[J].Soil Dynamics and Earthquake Engineering,2013,48:48-62.
[13]Zienkiewicz OC,Chan AHC,Pastor M,et al.Computational Geomechanics with Special Reference to Earthquake Engineering[J].New York:John Wiley&Sons,1998.
[14]刘光磊,宋二祥,刘华北,等.饱和砂土地层中隧道结构动力离心模型试验[J].岩土力学,2008,29(8):2070-2076.Liu G L,Song E X,Liu H B,et al.Dynamic Centrifuge Tests on Seismic Response of Tunnel in Saturated Sandy Foundation[J].Rock and Soil Mechanics,2008,29(8):2070-2076.(in Chinese)
[15]刘光磊,宋二祥,刘华北.可液化地层中地铁隧道地震响应数值模拟及其试验验证[J].岩土工程学报,2007,29(12):1815-1822.Liu G L,Song E X,Liu H B.Numerical Modeling of Subway Tunnels in Liquefiable Soil Under Earthquakes and Verification by Centrifuge Tests[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1815-1822.(in Chinese)
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