A new boundary element solution to evaluate the geometric effects of the canyon site on the displacement response spectrum
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摘要
This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.
This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.
This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.
引文
Ahmad S and Banerjee PK(1988),“Multi-Domain BEMfor Two Dimensional Problems of Elastodynamics,”International Journal for Numerical Methods in Engineering,26:891?911.
Beskos DE(1997),“Boundary Element Methods in Dynamic Analysis:Part II(1986-1996),”Applied Mechanics Review ASME,50:149-197.
Brandow HP and Lee V(2017),“Scattering and Diffraction of Plane P-Waves in a 2-D Elastic Half-Space II:Shallow Arbitrary Shaped Canyon,”Earthquake Engineering and Engineering Vibration,16(3):459-485.
Brebbia CA and Dominguez J(1989),“Boundary Elements:An Introductory Course.Mcgraw-Hill,USA.
Demirel V and Wang S(1987),“An Efficient Boundary Element Method for Two-Dimensional Transient Wave Propagating Problems,”Applied Mathematical Modeling,11(6):411-416.
Dominguez J(1993),“Boundary Elements in Dynamics,”U.K.Computational Mechanics publications.
Eurocode 8(1996),Design Provisions for Earthquake Resistance of Structures-Part 5.Foundations,Retaining
Structures and Geotechnical Aspects.
Eshraghi H and Dravinski M(1989),“Scattering of Plane Harmonic SH,SV,P and Rayleigh Waves by NonAxisymmetric Three Dimensional Canyons:a Wave Function Expansion Approach,”Earthquake Engineering and Structural Dynamics,18(7):983-998.
Gatmiri B,Arson C and Nguyen KV(2008),“Seismic Site Effects by an Optimized 2D BE/FE Method I.Theory,Numerical Optimization and Application to Topographical Irregularities,”Soil Dynamics and Earthquake Engineering,28:632-645.
Gatmiri B and Arson C(2008),“Seismic Site Effects by an Optimized 2D BE/FE Method II.Quantification of Site Effects in Two-Dimensional Sedimentary Valleys,”Soil Dynamics and Earthquake Engineering,28:646-661.
Gatmiri B,Maghoul P and Arson C(2009),“SiteSpecific Spectral Response of Seismic Movement due to Geometrical and Geotechnical Characteristics of Sites,”Soil Dynamics and Earthquake Engineering,29:51-70.
Geli L,Bard PY and Jullien B(1988),“The Effect of Topography on Earthquake Ground Motion:A Review and New Results,”Bulletin of Seismological Society of America,78(1):42-63.
Hesami S,Ahmadi S and Taghavi Ghalesari A(2016),“Numerical Modeling of Train-Induced Vibration of Nearby Multi-Story Building:A Case Study,”KSCEJournal of Civil Engineering,20(5):1701-1713.
Huang HC and Chiu HC(1995),“The Effect of Canyon Topography on Strong Ground Motion at Feitsui Damsite:Quantitive Results,”Earthquake Engineering and Structural Dynamics,24(7):977-990.
Kamalian M,Jafari MK,Sohrabi Bidar A,Razmkhah Aand Gatmiri B(2006),“Time-Domain Two-Dimensional Site Response Analysis of Non-Homogeneous Topographic Structures by a Hybrid FE/BE Method,”Soil Dynamics and Earthquake Engineering,26(8):753-765.
Kamalian M,Gatmiri B,Sohrabi-Bidar A and Khalaj A(2007),“Amplification Pattern of 2D Semi-Sine-Shaped Valleys Subjected to Vertically Propagating Incident Waves,”Communications in Numerical Methods in Engineering,23:871-887.
Lachat JC(1975),“A Further Development of the Boundary Integral Technique for Elastostatics,”Ph.D.Thesis,University of Southampton,U.K.,.
Luco JE and Wong HL(1990),“De Barros FCP,Three Dimensional Response of a Cylindrical Canyon in a Layered Half-Space,”Earthquake Engineering and Structural Dynamics,19:799-817.
Manolis GD and Beskos DE(1988),“Boundary Element Methods in Elastodynamics,”Unwin Hyman Ltd,U.K..
Mansur WJ(1983),“A Time-Stepping Technique to Solve Wave Propagating Problems Using the Boundary Element Method,”Ph.D.Dissertation,University of Southamppton,U.K.
Mossessian TK and Dravinski M(1990),“Amplification of Elastic Waves by a Three Dimensional Valley,part1:Steady-State Response,”Earthquake Engineering and Structural Dynamics,19(5):667-680.
Mossessian TK and Dravinski M(1990),“Amplification of Elastic Waves by a Three Dimensional Valley,Part2:Transient Response,”Earthquake Engineering and Structural Dynamics,19(5):681-691.
Paolucci R(2002),“Amplification of Earthquake Ground Motion by Steep Topographic Irregularities,”Earthquake Engineering and Structural Dynamics,31(10):1831-1853.
Sanchez-Sesma FJ and Campillo M(1991),“Diffraction of P,SV,and Rayleigh Waves by Topographic Features:A Boundary Integral Formulation,”Bulletin of the Seismological Society of America,81(6):2234-2253.
Shyu WS,Teng TJ and Chou CS(2016),“Anti-Plane Response Induced by an Irregular Alluvial Valley Using a Hybrid Method with Modified Transfinite Interpolation,”Soil Dynamics and Earthquake Engineering,90:250-264.
Soares JD and Mansur WJ(2009),“An Efficient TimeTruncated Boundary Element Formulation Applied to the Solution of the Two-Dimentional Scalar Wave Equation,”Engineering Analysis with Boundary Element,33(1):43-53.
Taghavi Ghalesari A,Barari A,Fardad Amini P and Ibsen LB(2015),“Development of Optimum Design from Static Response of Pile-Raft Interaction,”Journal of Marine Science and Technology,20(2):331-343.
Taghavi Ghalesari A,Isari M,Tarinejad R,Sohrabi-Bidar A(2019),“Development of a Procedure to Predict the Precise Seismic Response of Arch Dams in Time Domain Using Boundary Element Formulation,”Journal of Rock Mechanics and Geotechnical Engineering,in Press.
Tarinejad R(2008),“Seismic Loading for Canyon Site Structures,”Ph.D.Dissertation,Tarbiat Modares University,Tehran,Iran.
Tarinejad R,Ahmadi MT and Khaji N(2007),“Analysis of Topographic Amplification Effects on Canyon Sites Using 3D Boundary Element Method,”Journal of Seismology and Earthquake Engineering(JSEE),9(1):63-72.
Tarinejad R,Fatehi R and Harichandran RS(2013),
Response of an Arch Dam to Non-Uniform Excitation Generated by a Seismic Wave Scattering Model,”Soil Dynamics and Earthquake Engineering,52:40-54.
Tarinejad R,Isari M and Sohrabi-Bidar A(2019),“A New Solution to Estimate the Time Delay on the Topographic Site Using Time Domain 3D Boundary Element Method,”Earthquake Engineering and Engineering Vibration,in Press.
Yu G,Mansur WJ,Carrer JAM and Gron L(2000),“Stability of Galerkin and Collocation Time the Scalar Wave Equation,”Computers and Structures,74(4):495-506.
Zhang L and Chopra AK(1991),“Three-Dimensional Analysis of Spatially Varying Ground Motions Around a Uniform Canyon in a Homogeneous Half-Space,”Earthquake Engineering and Structural Dynamics,20:911-926.
Zhao C,Valliappan S and Wang YC(1992),“A Numerical Model for Wave Scattering Problems in Infinite Media due to P-and SV-Wave Incidences,”International journal for Numerical methods in Engineering,33(8):1661-1682.
Beskos DE(1997),“Boundary Element Methods in Dynamic Analysis:Part II(1986-1996),”Applied Mechanics Review ASME,50:149-197.
Brandow HP and Lee V(2017),“Scattering and Diffraction of Plane P-Waves in a 2-D Elastic Half-Space II:Shallow Arbitrary Shaped Canyon,”Earthquake Engineering and Engineering Vibration,16(3):459-485.
Brebbia CA and Dominguez J(1989),“Boundary Elements:An Introductory Course.Mcgraw-Hill,USA.
Demirel V and Wang S(1987),“An Efficient Boundary Element Method for Two-Dimensional Transient Wave Propagating Problems,”Applied Mathematical Modeling,11(6):411-416.
Dominguez J(1993),“Boundary Elements in Dynamics,”U.K.Computational Mechanics publications.
Eurocode 8(1996),Design Provisions for Earthquake Resistance of Structures-Part 5.Foundations,Retaining
Structures and Geotechnical Aspects.
Eshraghi H and Dravinski M(1989),“Scattering of Plane Harmonic SH,SV,P and Rayleigh Waves by NonAxisymmetric Three Dimensional Canyons:a Wave Function Expansion Approach,”Earthquake Engineering and Structural Dynamics,18(7):983-998.
Gatmiri B,Arson C and Nguyen KV(2008),“Seismic Site Effects by an Optimized 2D BE/FE Method I.Theory,Numerical Optimization and Application to Topographical Irregularities,”Soil Dynamics and Earthquake Engineering,28:632-645.
Gatmiri B and Arson C(2008),“Seismic Site Effects by an Optimized 2D BE/FE Method II.Quantification of Site Effects in Two-Dimensional Sedimentary Valleys,”Soil Dynamics and Earthquake Engineering,28:646-661.
Gatmiri B,Maghoul P and Arson C(2009),“SiteSpecific Spectral Response of Seismic Movement due to Geometrical and Geotechnical Characteristics of Sites,”Soil Dynamics and Earthquake Engineering,29:51-70.
Geli L,Bard PY and Jullien B(1988),“The Effect of Topography on Earthquake Ground Motion:A Review and New Results,”Bulletin of Seismological Society of America,78(1):42-63.
Hesami S,Ahmadi S and Taghavi Ghalesari A(2016),“Numerical Modeling of Train-Induced Vibration of Nearby Multi-Story Building:A Case Study,”KSCEJournal of Civil Engineering,20(5):1701-1713.
Huang HC and Chiu HC(1995),“The Effect of Canyon Topography on Strong Ground Motion at Feitsui Damsite:Quantitive Results,”Earthquake Engineering and Structural Dynamics,24(7):977-990.
Kamalian M,Jafari MK,Sohrabi Bidar A,Razmkhah Aand Gatmiri B(2006),“Time-Domain Two-Dimensional Site Response Analysis of Non-Homogeneous Topographic Structures by a Hybrid FE/BE Method,”Soil Dynamics and Earthquake Engineering,26(8):753-765.
Kamalian M,Gatmiri B,Sohrabi-Bidar A and Khalaj A(2007),“Amplification Pattern of 2D Semi-Sine-Shaped Valleys Subjected to Vertically Propagating Incident Waves,”Communications in Numerical Methods in Engineering,23:871-887.
Lachat JC(1975),“A Further Development of the Boundary Integral Technique for Elastostatics,”Ph.D.Thesis,University of Southampton,U.K.,.
Luco JE and Wong HL(1990),“De Barros FCP,Three Dimensional Response of a Cylindrical Canyon in a Layered Half-Space,”Earthquake Engineering and Structural Dynamics,19:799-817.
Manolis GD and Beskos DE(1988),“Boundary Element Methods in Elastodynamics,”Unwin Hyman Ltd,U.K..
Mansur WJ(1983),“A Time-Stepping Technique to Solve Wave Propagating Problems Using the Boundary Element Method,”Ph.D.Dissertation,University of Southamppton,U.K.
Mossessian TK and Dravinski M(1990),“Amplification of Elastic Waves by a Three Dimensional Valley,part1:Steady-State Response,”Earthquake Engineering and Structural Dynamics,19(5):667-680.
Mossessian TK and Dravinski M(1990),“Amplification of Elastic Waves by a Three Dimensional Valley,Part2:Transient Response,”Earthquake Engineering and Structural Dynamics,19(5):681-691.
Paolucci R(2002),“Amplification of Earthquake Ground Motion by Steep Topographic Irregularities,”Earthquake Engineering and Structural Dynamics,31(10):1831-1853.
Sanchez-Sesma FJ and Campillo M(1991),“Diffraction of P,SV,and Rayleigh Waves by Topographic Features:A Boundary Integral Formulation,”Bulletin of the Seismological Society of America,81(6):2234-2253.
Shyu WS,Teng TJ and Chou CS(2016),“Anti-Plane Response Induced by an Irregular Alluvial Valley Using a Hybrid Method with Modified Transfinite Interpolation,”Soil Dynamics and Earthquake Engineering,90:250-264.
Soares JD and Mansur WJ(2009),“An Efficient TimeTruncated Boundary Element Formulation Applied to the Solution of the Two-Dimentional Scalar Wave Equation,”Engineering Analysis with Boundary Element,33(1):43-53.
Taghavi Ghalesari A,Barari A,Fardad Amini P and Ibsen LB(2015),“Development of Optimum Design from Static Response of Pile-Raft Interaction,”Journal of Marine Science and Technology,20(2):331-343.
Taghavi Ghalesari A,Isari M,Tarinejad R,Sohrabi-Bidar A(2019),“Development of a Procedure to Predict the Precise Seismic Response of Arch Dams in Time Domain Using Boundary Element Formulation,”Journal of Rock Mechanics and Geotechnical Engineering,in Press.
Tarinejad R(2008),“Seismic Loading for Canyon Site Structures,”Ph.D.Dissertation,Tarbiat Modares University,Tehran,Iran.
Tarinejad R,Ahmadi MT and Khaji N(2007),“Analysis of Topographic Amplification Effects on Canyon Sites Using 3D Boundary Element Method,”Journal of Seismology and Earthquake Engineering(JSEE),9(1):63-72.
Tarinejad R,Fatehi R and Harichandran RS(2013),
Response of an Arch Dam to Non-Uniform Excitation Generated by a Seismic Wave Scattering Model,”Soil Dynamics and Earthquake Engineering,52:40-54.
Tarinejad R,Isari M and Sohrabi-Bidar A(2019),“A New Solution to Estimate the Time Delay on the Topographic Site Using Time Domain 3D Boundary Element Method,”Earthquake Engineering and Engineering Vibration,in Press.
Yu G,Mansur WJ,Carrer JAM and Gron L(2000),“Stability of Galerkin and Collocation Time the Scalar Wave Equation,”Computers and Structures,74(4):495-506.
Zhang L and Chopra AK(1991),“Three-Dimensional Analysis of Spatially Varying Ground Motions Around a Uniform Canyon in a Homogeneous Half-Space,”Earthquake Engineering and Structural Dynamics,20:911-926.
Zhao C,Valliappan S and Wang YC(1992),“A Numerical Model for Wave Scattering Problems in Infinite Media due to P-and SV-Wave Incidences,”International journal for Numerical methods in Engineering,33(8):1661-1682.