Incident SV Waves Research Articles

Implementation of PMDL and DRM in OpenSees for Soil-Structure Interaction Analysis

It is widely acknowledged that the effects of soil-structure interaction (SSI) can have substantial implications during periods of intense seismic activity; therefore, accurate quantification of these effects is of paramount importance in the design of earthquake-resistant structures. The analysis of SSI is typically conducted using either direct or substructure methods. Both of these approaches involve the use of numerical models with truncated or reduced-order computational domains. To ensure effective truncation, it is crucial to employ boundary representations that are capable of perfectly absorbing outgoing waves and allowing for the consistent application of input motions. At present, such capabilities are not widely available to researchers and practicing engineers. In order to address this issue, this study implemented the Domain Reduction Method (DRM) and Perfectly Matched Discrete Layers (PMDLs) in OpenSees. The accuracy and stability of these implementations were verified through the use of vertical and inclined incident SV waves in a two-dimensional problem. In terms of computational efficiency, PMDLs require a shorter analysis time (e.g., with PMDLs, the analysis concluded in 35 min as compared to 250 min with extended domain method) and less computational power (one processor for PMDLs against 20 processors for the extended domain method) thus offering a balance between accuracy and efficiency. Furthermore, illustrative examples of the aforementioned implemented features are presented, namely the response analysis of single-cell and double-cell tunnels exposed to plane waves inclined at an angle.

Nonlinear Seismic Response of Tunnel Structures under Traveling Wave Excitation

Tunnels traditionally regarded as resilient to seismic events have recently garnered significant attention from engineers owing to a rise in incidents of seismic damage. In this paper, the reflection characteristics of the elastic plane wave incident on the free surface are analyzed, and the matrix analysis method SWIM (Seismic Wave Input Method) for the calculation of equivalent nodal loads with artificial truncated boundary conditions for seismic wave oblique incidence is established by using coordinate transformation technology, according to the displacement velocity and stress characteristics of a plane wave. The results show that the oblique incidence method is more effective in reflecting the traveling wave effect, and the “rotational effect” induced by oblique incidence must be considered for P wave and SV wave incidence, including the associated stress and deformation. This effect exhibits markedly distinct rotational phenomenon. In particular, the P wave incidence should be focused on the vault and the inverted arch due to the expansion wave. With the increase of the oblique incidence angle, the structural stress and deformation are rotated to a certain extent, and the values are significantly increased. Simultaneously, the shear action of the SV wave may result in “ovaling” of the tunnel structure, thereby facilitating damage to the arch shoulder and the sidewall components. As the oblique incidence angle, the potentially damaging effects of the “rotational effect” to the vault and the inverted arch, but the numerical value does not change significantly. In addition, in comparison to a circular cross-section, the low-frequency amplification of seismic waves in the surrounding rock and the difference of frequency response function in different parts of the lining are more pronounced. In particular, the dominant frequency characteristics are significant at P wave incidence and the seismic wave signal attenuation tends to be obvious with increasing incidence angle. In contrast, SV waves exhibit more uniform characteristics.

Plane SV-waves scattering by seawater convex surface topography and underlying lined tunnel in a saturated half-space

Analytical solutions of boundary-valued problems for aboveground topography and underground buried structures, especially for sites with overlying seawater, have always been challenging. Based on the region decomposition technique (RDT) and Hankel integral transform method (HITM), SV-waves scattering by the convex circular topography with seawater and underlying tunnel in a saturated half-space is solved. The primary problem is tackling additional scattered waves introduced by the water–soil interface and convex topography, while ensuring boundary conditions are all met. To this end, scattering wave potential functions in cylindrical coordinates are first transformed into the Hankel integral form in Cartesian coordinates. This greatly facilitates the straightforward application of free boundary conditions at the soil–seawater flat interface, rather than making a large circular arc approximate assumption, which, in turn, avoids the resultant accumulating errors. Secondly, scattering problem to be solved is mathematically and analytically formulated as solving a 5 × 5 linear equation system comprised of wave functions inside the convex topography and lining tunnel while satisfying all physical continuous boundary conditions. This is the main innovation and resulting consequence from the theoretical derivation process. Finally, validation of numerical examples between this paper, existing studies and theoretical analysis further demonstrates the reliability and general adaptability of solutions. Parametric studies of the incident SV waves are conducted to investigate the spatially varying seismic response. The effects of SV-waves incident angles and frequencies, tunnel burial depth, tunnel lining thickness, saturated soil porosity, and seawater depth are investigated and analyzed in detail. This study provides a feasible scheme of investigating the dynamic response of complex submarine sites, which is of great significance for both theoretical value and engineering purposes.

Study on the Seismic Response of a Water-Conveyance Tunnel Considering Non-Uniform Longitudinal Subsurface Geometry and Obliquely Incident SV-Waves

The longitudinal seismic response characteristics of a shallow-buried water-conveyance tunnel under non-uniform longitudinal subsurface geometry and obliquely incident SV-waves was studied using the numerical method, where the effect of the non-uniform longitudinal subsurface geometry due to the existence of a local one-sided rock mountain on the seismic response of the tunnel was focused on. Correspondingly, a large-scale three-dimensional (3D) finite-element model was established, where different incidence angles and incidence directions of the SV-wave were taken into consideration. Also, the non-linearity of soil and rock and the damage plastic of the concrete lining were incorporated. In addition, the wave field of the site and the acceleration response as well as damage of the tunnel were observed. The results revealed the following: (i) a local inclined subsurface geometry may focus an obliquely incident wave due to refraction or total reflection; (ii) a tunnel in a site adjacent to a rock mountain may exhibit a higher acceleration response than a tunnel in a homogeneous plain site; and (iii) damage in the tunnel in the site adjacent to a rock mountain may appear in multiple positions, and the effect of the incidence angle on the mode of compressive deformation and damage of the lining is of significance.

Seismic response analysis of subway station under obliquely incident SV waves

This paper aims to investigate the dynamic response characteristics of subway station under earthquakes. To this end, seismic waves are transformed into equivalent nodal loads on viscoelastic artificial boundaries using theories and methods of wave motion. The calculation formulas for equivalent nodal loads of SV waves incident at any angle are established, and ANSYS' APDL program compiles to automatically generate the viscoelastic artificial boundary and input the seismic loads. A finite element model of soil-subway station interaction was established, and the seismic response characteristics of a two-story three-span subway station under different incidence angles of SV waves were investigated using the above seismic input method. The results indicate that the incidence angle of seismic waves has a significant impact on the seismic response of subway station. Inclined incidence of seismic waves causes non-uniform loading and deformation of the subway station. Specifically, a small angle leads to predominantly transverse shear deformation, while a large angle causes mainly vertical shear deformation. The inclined incidence of seismic waves significantly increases the vertical acceleration of the subway station, with the effect becoming more pronounced as the angle increases. Additionally, special attention should be given to the joints between the structural slab and the side wall, slab and center column, as well as the two ends of the center column as they are vulnerable areas during earthquakes and require careful consideration in seismic design.

Reflection of Elastic Waves in Dipolar Gradient Half-Space under the Control of External Magnetic Field

This paper investigated the reflection of plane waves at the interface of dipolar gradient elastic solids under the control of an external magnetic field. This study focused on the increasing influence of the microstructural effect as the incident wavelength approaches the characteristic length of the microstructure or at higher frequencies. Initially, the dispersion equation for the propagation of elastic waves was derived from the dipole strain gradient theory and Maxwell’s electromagnetic theory. Subsequently, the amplitude ratios of various reflected waves to incident P-waves and incident SV-waves were calculated based on the interface conditions. Finally, the numerical results were used to discuss the impact of the external magnetic field and microstructural characteristic length on the propagation of the reflected wave. It was observed that the microstructural effect generated new wave modes and introduced dispersion characteristics into the elastic waves. Conversely, the external magnetic field primarily influences the amplitude of the elastic wave propagation via the Lorentz force without creating new wave modes or affecting the dispersion properties of the elastic wave in the dipolar gradient elastic solid.

Topographic Effects on the Seismic Response of Trapezoidal Canyons Subjected to Obliquely Incident SV Waves

Topographic Effects on the Seismic Response of Trapezoidal Canyons Subjected to Obliquely Incident SV Waves

Seismic performance assessment of hydraulic tunnels considering oblique incoming nonstationary stochastic SV waves based on the generalized PDEM

An important aspect of a seismic performance assessment framework is to adequately consider the stochastic nature of SGMs. This requires an appropriate method for synthesizing random SGMs, a crucial step in conducting structural response analysis. Additionally, affected by topographic and geological conditions, the incident angle of SGMs is also uncertain and random, which may induce unexpected damage to structures. To date, a framework is presented to assess the seismic performance of hydraulic tunnels under stochastic obliquely incident SV waves. The framework incorporates the spectral representation method of SGMs and obliquely incident SV waves into stochastic dynamic analysis. To create the appropriate PDFs and CDFs for numerous performance indices, the generalized PDEM and equivalent extreme-value event are introduced. Subsequently, stochastic dynamic analysis and seismic performance assessment of the hydraulic tunnel are performed. Finally, the disparity between the hydraulic tunnel fragility curves generated using conventional linear regression and generalized PDEM is examined. The difference between vertically incident and obliquely incident SV waves is discussed. The results indicated that (1) different performance indices exhibit great differences in the stochastic dynamic response of structures and the failure probability of seismic performance evaluation; (2) compared with the traditional linear regression method, the probability of damage of hydraulic tunnels under strong SGMs may be overestimated; and (3) nonstationary stochastic obliquely incident SV waves can cause more seismic demand than nonstationary stochastic vertically incident SV waves under low/medium earthquake intensity levels for hydraulic tunnel.

An analytical solution for the dynamic response of a seawater‐sloping seabed‐bedrock system under an oblique incident SV wave

AbstractThe characteristics of seabed ground motion are the theoretical basis for the study of seawater‐soil‐structure interactions and seismic‐induced geological hazards. There are numerous offshore marine structures located on sloping seabeds. Therefore, the sloping seabed's seismic response requires to be investigated. Engineers and scholars are more interested in the SV waves because they carry more energy than the P waves in earthquakes. An analytical solution for the steady‐state response of the inclined seafloor under an oblique incident SV wave is offered. The impacts of the seafloor angle on the fluid pressure and displacement of the saturated sediment layer are investigated under different incident wave frequencies, incident angles, and thicknesses of the seawater layer and sediment layer. By observing along the seabed surface, we discovered that the slope angle might cause considerable variances between different positions even at a small site. While examining the seabed at varying depths, we discovered that the incline angle has distinct impacts on different areas of the seabed. It has an amplifying effect at some depths and a reducing effect at other depths. Generally, as the slope angle increases, the distinction between the responses of the inclined and horizontal seabed becomes more prominent. Especially when the incidence angle of the SV waves is near the critical angle, the impacts of the slope angle become more significant. Even if the horizontal seabed model is employed with the same seawater depth, it is not suitable for analyzing the seismic response of a sloping seabed. Otherwise, significant errors would arise.

Numerical investigations on the dynamic responses of metro tunnel-soil-ground building under oblique incidence of seismic wave

With the development of urban rail transits, the metro tunnels frequently underpass the above-ground buildings, and understanding the dynamic responses of metro tunnel-soil-ground buildings experiencing oblique incidence of seismic waves is of crucial importance. Considering that the seismic waves in the near-field seismic area are mostly obliquely incident to the ground at a certain angle, a two-dimensional numerical model for tunnel-soil interaction system and tunnel-soil-above ground structure was established by Abaqus software, in which the viscoelastic boundary and equivalent nodal forces were adopted to simulate the ground motion. The effects of tunnel burial depth, tunnel spacing, and tunnel frame spacing on the seismic responses of metro tunnel-soil and metro tunnel-soil-above ground building were analyzed under oblique incidence of SV wave with different incident angles. It was found that the tunnel depth has a significant effect on the lining dynamic bending moment and axial force peak, and its influence is closely related to the site category. The tunnel spacing has a minor impact on the dynamic response of the lining structure. The incident angle has a significant effect on the peak value of the dynamic shaft force of the lining. The application of the frame on the ground has a significant impact on the tunnel. The influence of above-ground buildings and tunnel burial depth should be considered when tunnel design is carried out.

Dynamic response of a shallow lined circular tunnel by incident P1 and SV waves in an unsaturated half-plane

The dynamic response of a shallow lined circular tunnel in the unsaturated half-plane during earthquakes is investigated in this paper using the complex function method. The wave fields of the unsaturated medium with unknown coefficients are solved by Fredlund’s theory and Helmholtz’s decomposition based on the momentum and mass balance equations. General expressions for the displacements and total stresses of the solid skeleton, pore pressures, and seepage are derived using the complex function method and conformal mapping technique. The half-plane surface and the tunnel in the physical domain are mapped onto two bonded ring regions in the image plane using two conformal mapping functions. The boundary value problem yields a series of algebraic equations by the boundary conditions and the continuity conditions along the liner-medium interface. The unknown coefficients in the infinite series of algebraic equations can be solved numerically by truncating the series number. A parametric study is performed to investigate the dynamic responses of the medium and the liner by the incident P1 waves. Numerical results reveal that the embedded depth of the tunnel, the saturation degree of the medium, the liner-medium rigidity ratio, the frequency and angle of the incident P1 waves significantly affect the dynamic responses of the medium and the liner. The shielding effect on the tunnel to the incident P1 waves is obvious. The response of the liner-medium system to the incident waves is independent of the saturation degree of the unsaturated medium when its value is high. The effect of the liner-medium rigidity ratio is great on the dynamic stress concentrations of the liner-medium system and weak on the displacements along the half surface. The frequency of the incident excitation has a great influence on the displacements of the half surface.

Dynamic Response Analysis of Intake Tower-Hydrodynamic Coupling Boundary Based on SV Wave Spatial Incidence

In view of the insufficient analysis of the coupled joint seismic response of the intake tower–reservoir water–foundation boundary under the oblique incidence of SV wave space, a three-dimensional dynamic equation of the oblique incidence of SV wave space is established in this paper. The external wave input method of viscoelastic artificial boundary combined with equivalent load and the acoustic medium theory are used to simulate the action of reservoir water, and the angle change in the SV wave incidence is realized by controlling the incident vector. The dynamic response of the structure is analyzed and the dynamic response characteristics of the structure at different incidence angles are discussed. The results show that the dynamic response and damage degree of the intake tower decreases first and then increases with the change in angle. When the vertical incidence is 0°, the maximum displacement drop is 82.05%, and the displacement response of the intake tower is more sensitive to the change in SV wave incidence angle. When SV wave is vertically incident at 0° and 35° (near the maximum critical angle of incident), the dynamic response, dynamic water pressure, damage diffusion velocity, damage area, and damage degree of the intake tower are relatively large, which seriously affects the safety and stability of the intake tower. Therefore, the influence of the oblique incidence should be considered comprehensively in the aseismic stability design of the water intake tower to provide a new idea for the safety evaluation of the same type of engineering.

The influences of external magnetic field on the reflection and transmission waves at the interface of two dipolar gradient elastic solids

The elastic wave propagation and the reflection and transmission at interface with consideration of the microstructure effects and the Lorentz force simultaneously are investigated in the present work. The microstructure effects are modelled by the dipolar gradient elasticity and the Lorentz force due to the external magnetic field is derived by the electromagnetic induction law and Maxwell equation. The numerical results are provided for incident P wave, incident SV wave and incident SH wave, respectively. It is found that the microstructure effects induce the dispersive feature of elastic waves but the external magnetic field do not contribute to the dispersion with only influence on the amplitude of speed. The surface waves are more sensitive to the external magnetic field and the microstructure effects compared with the bulk waves.

Effect of Oblique SV Wave on the Seismic Response of Mountain Tunnel

In order to study the dynamic response of parallel mountain tunnels under the oblique incidence of seismic waves, based on the display finite element method and using viscoelastic artificial boundary, the oblique incidence of three-way seismic waves was realized by angular incident mode. The displacement and stress distribution characteristics of the tunnel lining under different propagation angles and vibration angles of SV waves were studied. The results show that the oblique incidence of SV wave has a certain effect on the displacement of the double tunnel, the forces in the tunnel are symmetrical and the axis displacement increases with the increase of incident angle, and the vertical displacement changes greatly. The stress of the tunnel lining under the oblique incidence of the SV wave is elliptical. The peak value of the maximum principal stress appears at the maximum span on both sides, and the maximum principal stress decreases with the increase of the vibration angle. The maximum principal stress of the right tunnel is flat. The minimum principal stress of the left and right holes decreases with the increase of vibration angle, and the minimum principal stress of the left hole is 90°∼270°. The distribution of the minimum principal stress in the range is large. Mises stress increases with the increase of the incidence angle of seismic waves.

Effect of Randomness of Parameters on Amplification of Ground Motion in Saturated Sedimentary Valley

Based on Biot’s theory and the indirect boundary element method (IBEM), the Monte Carlo method is utilized to generate random samples to calculate the displacement response of a saturated sedimentary valley under SV wave incidence. The purpose of this paper is to explore the effects of randomness of porosity, permeability coefficient, and geometric shape on the seismic amplification effect of saturated complex sites. It is shown that the change of media porosity in the saturated site with defined boundary has relatively little influence on the ground motion, and the influence of the permeability coefficient is slightly larger. While in the site with a random boundary, the influence of both the porosity and permeability coefficient are significant, which cannot be ignored. The conclusion plays an important guiding role in earthquake disaster prevention and mitigation, such as seismic risk analysis and earthquake microzonation in saturated sedimentary valleys.

Seismic Response of Immersed Tunnel Subject to Oblique Incidence of SV Wave

In view of the near-field seismic action, considering that oblique incidence of seismic waves is more realistic than vertical incidence, the seismic response of the Hong Kong–Zhuhai–Macao immersed tunnel subjected to an obliquely incident SV wave is investigated. Using the finite element method and time-domain wave method, the seismic input is transformed into an equivalent node load with a viscous–spring artificial boundary, and a three-dimensional simulation technology for SV waves of oblique incidence is presented. A half-space numerical example is given to demonstrate the accuracy of the proposed simulation technology. Taking the stress field formed by the self-weight stress and hydrostatic pressure as the initial state of the dynamic response analysis, the static–dynamic coupling numerical simulation of the seismic response of a soil-immersed tunnel system is realized. The results show that the amplification in the vertical and longitudinal response of the tunnel, due to the oblique incidence, reaches maximum when the incident angle is close to the critical angle. Furthermore, the horizontal response and incident angle show the inverse relation and tend to be stable. In addition, the oblique incidence also causes asymmetric shearing in symmetric parts of the tunnel. The root of the shear key easily produces tensile cracks, while the end angle of the shear key is prone to stress concentration and local damage. Thus, the impact of oblique incidence should be considered in the seismic design, and attention should be paid to the optimization of the end angle of the shear key and the configuration of anti-crack reinforcement at the root of shear key to meet the seismic requirements.

Seismic Dynamic Response Analysis of Mountain Tunnels with Seismic Reduction and Isolation Measures

In this paper, the multi-domain indirect boundary element method (IBEM) is developed for the seismic response analysis of double-line mountain tunnels with seismic reduction and isolation measures. The dynamic response of the tunnel with seismic reduction and isolation measures under incident SV waves is analyzed, and the effect of the mountain topography on the tunnel is also investigated. Further, the effects of the isolation layer and the grouting reinforcement with different thicknesses on the seismic response of the tunnel are discussed in detail. The results show that the scattering of seismic waves by mountain topography significantly increases tunnel stress. In general, with the increase of incident frequency, the isolation layer will increase the peak displacement of the tunnel by about 12.7% at most, and the isolation ratio of the isolation layer on the tunnel stress exceeds 40%. The seismic reduction performance of the grouting reinforcement also depends on the incident frequency, and the amplitude decreases by approximately 20% at most frequencies. However, it is possible that the lining displacement under high-frequency waves becomes larger. This method can provide valuable insights and assessments for damage prediction.

Nonlinear Seismic Response of SV Wave Incident Angle and Direction to Concrete Gravity Dam

Nonlinear Seismic Response of SV Wave Incident Angle and Direction to Concrete Gravity Dam

Analytical solutions for circular composite-lined tunnels under obliquely incident seismic SV and P waves

An analytical solution can easily and quickly give the internal forces in tunnels due to seismic waves, by which, the relationship between the key parameters could also be clarified. These methods are widely used in preliminary seismic design of tunnels. This paper presents new analytical solutions for thrust and moment of circular composite-lined tunnels with arbitrary layer linings under obliquely incident SV waves and P waves. Wherein, the lining is regarded as a thick-wall cylinder. Moreover, the proposed analytical solutions can consider different contact conditions of the ground-tunnel and lining-lining interface. The new analytical solutions are verified by comparing with the dynamic finite element analysis results. The results show the accuracy and applicability of the proposed analytical solutions. Parametric analyses are performed to explore the effects of the flexibility coefficient δ, incident angle and steel lining on the seismic response of tunnels.

Scattering of harmonic P1 and SV waves by a shallow lined circular tunnel in a poroelastic half-plane

An analytical solution for the scattering of harmonic P1 and SV waves in a poroelastic half-plane with a shallow lined tunnel is obtained using the plane complex theory in elastodynamics. In light of the wave function expansions, the wave fields of the poroelastic medium and the liner with unknown coefficients are obtained based on Biot's theory and Helmholtz decomposition. Complex-valued expressions of the effective stresses, the fluid stress, and the displacements of the poroelastic medium and the liner are expressed by the complex variable function method and the conformal transformation technique. With the boundary conditions and the continuity of the medium-liner interface, the boundary value problem results in a series of algebraic equations. The unknown coefficients in the infinite set of algebraic equations can be solved numerically by truncating the series number. A parametric study for the incident SV waves is performed to investigate dynamic stress concentrations and fluid stress of the medium and the liner. Numerical results show that the embedment depth of the tunnel, the incident angle of the excitations, and the porosity of the medium have considerable influence on the dynamic responses of the medium and the liner. The shielding effect of the tunnel on the incident SV waves is obvious. For the big embedment depth of the tunnel, the scattered waves contribute little to the displacements and dynamic stress concentration of the medium and the liner. For a high porosity close to the critical value, the response of the medium-liner system to the incident waves is great.