To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the ...To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the initial disturbance of the wave field induced by geological heterogeneity.The method transforms equivalent twodimensional free-field responses into equivalent nodal forces applied at the boundaries of a 3D numerical model.A longitudinally heterogeneous“hard-soft-hard”site and tunnel system is established,in which the surrounding rock is modeled using the Mohr-Coulomb constitutive law,while the concrete lining is described by the concrete damaged plasticity model.The deformation patterns and failure mechanisms of the site-tunnel system under SV-wave excitation are systematically investigated.The results indicate that seismic damage under SV-wave loading is mainly concentrated in the soft-rock region.Failure of the soft surrounding rock induces pronounced sliding of the overlying hard rock,and the tunnel suffers severe damage due to the combined effects of soft-rock failure and strong ground shaking.Parametric analyses further show that smaller impedance ratios,larger soft-rock widths,and larger incidence angles significantly intensify the seismic response of the tunnel.The findings of this study provide valuable insights for the seismic design of tunnels crossing longitudinally heterogeneous geological formations.展开更多
The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of sea...The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).展开更多
This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green's functions of compressive and shear wave sources are de...This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green's functions of compressive and shear wave sources are derived based on Biot's theory.The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity,and their magnitudes are determined by the boundary conditions.Verification of the accuracy is performed by:(1)checking the satisfaction extent of the boundary conditions,(2)comparing the degenerated solutions of a single-phased case with well-known solutions,and(3)examining the numerical stability of the solutions.The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.展开更多
An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the sol...An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.展开更多
An analytical solution for scattering of incident plane SV waves by a circular-arc canyon with a covering layer was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the ef...An analytical solution for scattering of incident plane SV waves by a circular-arc canyon with a covering layer was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of the covering layer on incident plane SV waves. It was shown that the covering layer in a canyon, even if it is very thin, amplifies incident plane SV waves tremendously, and the amplification can be two and half times more than that for a simple canyon; the stiffness and thickness of the covering layer also have great effects on incident plane SV waves.展开更多
Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper...Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.展开更多
A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion metho...A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.展开更多
This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the d...This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.展开更多
Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction....Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.展开更多
We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the...We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.展开更多
Based on the theory of wave dynamics,this study systematically derives the steady-state analytical solution for the scattering of plane SV-waves by composite lined tunnels in an infinite space using the wave function ...Based on the theory of wave dynamics,this study systematically derives the steady-state analytical solution for the scattering of plane SV-waves by composite lined tunnels in an infinite space using the wave function expansion method.On this basis,a theoretical calculation model for circular composite linings under blast loading is established.Based on the steady-state analytical solution,theδ(x)-function and the Heaviside step function are introduced to construct the Duhamel integral,transforming the transient wave problem into an integral form.By further incorporating the Fourier integral transform,an analytical solution for the transient response around a composite lining tunnel subjected to a plane blast SV wave is ultimately derived.The computational results of this study are subsequently validated against those reported in existing literature.On this basis,a systematic investigation was conducted into the influence of parameters such as blast loading duration,lining thickness,and elastic modulus on the transient dynamic stress concentration factor(DSCF)of the tunnel,incorporating engineering data from theHongshan South Road tunnel group.The results indicate that the DSCF values in the secondary lining of the composite tunnel are greater than those in the surrounding rock.The elastic moduli of both the surrounding rock and the secondary lining have a significant influence on the DSCF of the lining.Therefore,under the premise of ensuring adequate stability of the surrounding rock,materials with lower stiffness should be preferentially selected for the secondary lining.Increasing the thickness of both the surrounding rock and the secondary lining can markedly reduce the DSCF within the lining.The analytical results can provide a theoretical basis for the anti-blast design of tunnels.展开更多
基金supported by the National Key Research and Development Program(Grant No.2024YFF0508203)the National Natural Science Foundation of China(Grant No.52378475)the Science and Technology Innovation Special Project of Xiongan New Area,National Key R&D Program(Grant No.2025XAGG0056)。
文摘To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the initial disturbance of the wave field induced by geological heterogeneity.The method transforms equivalent twodimensional free-field responses into equivalent nodal forces applied at the boundaries of a 3D numerical model.A longitudinally heterogeneous“hard-soft-hard”site and tunnel system is established,in which the surrounding rock is modeled using the Mohr-Coulomb constitutive law,while the concrete lining is described by the concrete damaged plasticity model.The deformation patterns and failure mechanisms of the site-tunnel system under SV-wave excitation are systematically investigated.The results indicate that seismic damage under SV-wave loading is mainly concentrated in the soft-rock region.Failure of the soft surrounding rock induces pronounced sliding of the overlying hard rock,and the tunnel suffers severe damage due to the combined effects of soft-rock failure and strong ground shaking.Parametric analyses further show that smaller impedance ratios,larger soft-rock widths,and larger incidence angles significantly intensify the seismic response of the tunnel.The findings of this study provide valuable insights for the seismic design of tunnels crossing longitudinally heterogeneous geological formations.
基金the 973 Program under Grant No.2011CB013601Basic Science Research Foundation of IEM,CEA under Grant No.2011B02+1 种基金National Natural Science Foundation of China under Grant No.51238012,9121530113,50938006International Science&Technology Cooperation Program of China under Grant No.2012DFA70810
文摘The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).
基金Program for New Century Excellent Talents in University Under Grant No.NCET-05-0248the Key Program for Applied Basic Research of Tianjin Municipality Under Grant No.07JCZDJC10100
文摘This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green's functions of compressive and shear wave sources are derived based on Biot's theory.The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity,and their magnitudes are determined by the boundary conditions.Verification of the accuracy is performed by:(1)checking the satisfaction extent of the boundary conditions,(2)comparing the degenerated solutions of a single-phased case with well-known solutions,and(3)examining the numerical stability of the solutions.The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.
基金National Natural Science Foundation of China (50378063) and Program for New Century Excellent Talents in University.
文摘An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.
基金State Natural Science Foundation of China (No.59878032).
文摘An analytical solution for scattering of incident plane SV waves by a circular-arc canyon with a covering layer was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of the covering layer on incident plane SV waves. It was shown that the covering layer in a canyon, even if it is very thin, amplifies incident plane SV waves tremendously, and the amplification can be two and half times more than that for a simple canyon; the stiffness and thickness of the covering layer also have great effects on incident plane SV waves.
基金sponsored by the National Natural Science Foundation of China (50608066)the National Science and Technology Pillar Program of China(2006BAC13B02)
文摘Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.
基金National Natural Science Foundation of China(50378063)EYTP of MOESRF for ROCS,MOE
文摘A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method.The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion.It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.
基金National Natural Science Foundation of China Under Grant No.50908156 and 50978183Tianjin Natural Science Foundation Under Grant No. 07JCZDJC10100
文摘This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.
基金National Basic Research Program of China under Grant No.2015CB057902Beijing Municipal Natural Science Foundation under Grant No.8164049Young Foundation of the National Science of China under Grant No.51608015
文摘Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774377 and 11574343)。
文摘We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.
基金supported by the Research Project on Micro-Vibration Blasting Technology for Tunnels in High-Altitude Cold Regions(2024HX01)the Jiangxi“Ganpo Jun Cai”Program for Young Sci-Tech Talents(2024QT04)the Natural Science Foundation of Jiangxi Province(20242BAB204095).
文摘Based on the theory of wave dynamics,this study systematically derives the steady-state analytical solution for the scattering of plane SV-waves by composite lined tunnels in an infinite space using the wave function expansion method.On this basis,a theoretical calculation model for circular composite linings under blast loading is established.Based on the steady-state analytical solution,theδ(x)-function and the Heaviside step function are introduced to construct the Duhamel integral,transforming the transient wave problem into an integral form.By further incorporating the Fourier integral transform,an analytical solution for the transient response around a composite lining tunnel subjected to a plane blast SV wave is ultimately derived.The computational results of this study are subsequently validated against those reported in existing literature.On this basis,a systematic investigation was conducted into the influence of parameters such as blast loading duration,lining thickness,and elastic modulus on the transient dynamic stress concentration factor(DSCF)of the tunnel,incorporating engineering data from theHongshan South Road tunnel group.The results indicate that the DSCF values in the secondary lining of the composite tunnel are greater than those in the surrounding rock.The elastic moduli of both the surrounding rock and the secondary lining have a significant influence on the DSCF of the lining.Therefore,under the premise of ensuring adequate stability of the surrounding rock,materials with lower stiffness should be preferentially selected for the secondary lining.Increasing the thickness of both the surrounding rock and the secondary lining can markedly reduce the DSCF within the lining.The analytical results can provide a theoretical basis for the anti-blast design of tunnels.
