This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetr...This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.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National Natural Science Foundation of China Under Grant No.51278382
文摘This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
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.
