Homogeneous Elastic Half-space Research Articles

Rayleigh wave propagation in an initially stressed orthotropic elastic solid half-space lying under inviscid liquid and viscous liquid layers

PurposeThe purpose of this article is the propagation of Rayleigh waves in a homogeneous, isotropic, initially stressed orthotropic elastic solid half-space lying under a homogeneous, viscous, inviscid liquid layer of finite thickness.Design/methodology/approachIn the presence of both viscous and inviscid liquids, it derives the phase velocity, initial stress, and wave number-dependent frequency equation for an orthotropic elastic solid. With the help of the MATLAB program, the thickness effects of liquid layers, initial stress, and viscosity on the phase velocity and attenuation coefficient of the Rayleigh wave are explained for a particular model.FindingsThe phase velocity-dependent dispersion relation of Rayleigh waves at the interface of viscous liquid and solid half-space is a function of initial stress and wave number. Rayleigh waves along the free surface of an orthotropic elastic half-space are also derived as a particular case. The classical results of an inviscid liquid are achieved when the thickness of a viscous liquid approaches zero. Well-known classical results for initially stressed orthotropic elastic solids were also derived.Originality/valueSo far, many researchers have looked into the propagation of surface waves at the interfaces of solid–inviscid liquid, solid–solid, and multilayer interfaces. But in this article, the dispersion behavior of Rayleigh wave propagation in an initially stressed homogeneous orthotropic elastic solid half-space under a double layer of viscous liquid and inviscid liquid is studied.

High-Speed Train-Induced Vibration of Bridge–Soft Soil Systems: Observation and MTF-Based ANSYS Simulation

In this paper, a multi-transmitting formula (MTF) was integrated into ANSYS software through secondary development, enabling dynamic finite element simulation of wave propagation in infinite domains. The numerical reliability and accuracy of the MTF were verified through a plane wave problem involving a homogeneous elastic half-space, as well as 3D scattering and source problems in a three-layered soil site. Additionally, a comparative analysis of various artificial boundaries was conducted to highlight the advantages of the MTF. Field observations of environmental vibrations caused by high-speed railway operations revealed localized amplification of vibrations along the depth direction at the Kunshan segment of the Beijing–Shanghai high-speed railway. Based on these observations, a series of numerical analyses were conducted using the customized ANSYS integrated with the MTF to investigate the underlying causes and mechanisms of this phenomenon, as well as the spatial variation characteristics of foundation vibrations induced by bridge vibrations during high-speed train operations. This study reveals the mechanism by which the combined effect of bridge piles and soft soil layers influences the depth variation in peak ground accelerations during site vibrations. It also demonstrates that the presence of bridge piers and pile foundations effectively reduces vibration intensity in the vicinity of the railway, playing a crucial role in mitigating vibrations induced by high-speed train operations.

Reconstruction of Co-Seismic and Post-Seismic Processes for the February 6, 2023 Earthquake in Turkey from Data of Satellite SAR Interferometry

Using different methods for processing SAR images from the Sentinel-1A satellite, the displacement fields were determined in the region of the East Anatolian Fault Zone (EAFZ) and the Sürgü-Çardak faults, as well as a small fault on the continuation of the East Hatay fault zone, which rupture initiated a series of catastrophic earthquakes in Turkey on February 6, 2023. DInSAR and offset methods were applied. The most detailed data on the displacements were obtained by the offset method using images from the descending orbit. When constructing the model from the available SAR data, the data with the maximum signal-to-noise ratio were selected. For the northern part of the region, above 37.4° N, the range displacements obtained by the offset method from a descending orbit were used. South of parallel 37.0° N, we used azimuth displacements from the same descending orbit. The model of the seismic rupture was constructed on the basis of solution of (Pollitz, 1996) of the problem of deformations at the surface of a layered spherical Earth caused by along dip and strike displacements on a rectangular fault located inside the planet. Pollitz (1996) demonstrated that ignoring the radial layering of the planet leads to errors up to 20%, with the largest errors occurring in the presence of a large strike-slip component. Ignoring sphericity also introduces an error when using the solution in the framework of the idealization of an elastic homogeneous half-space with a flat free surface (Okada, 1985) which was used when constructing USGS and (Barbot et al., 2023) models. In our model the surfaces of seismic rupture are approximated by 19 rectangular elements along the strike, divided into three levels along the dip. Another element approximated a rupture along the extension of the East Hatay Fault Zone. As in the models of other authors (USGS; Barbot et al., 2023), in our model in the southern part of the EAFZ, the displacements increase from south to north, and are mainly concentrated in the upper part of the Earth’s crust to a depth of 10 km. At the southern end of this rupture, displacements in our model with an amplitude of up to 2 m are obtained at the lower levels of the model, and at its upper level, the displacements were only 0.11 m, and in this area on February 20, 2023 an earthquake of magnitude 6.3 occurred with a hypocenter depth of 11.5 km. The main displacements on the EAFZ are determined on its central segment. Here, the displacements go to a greater depth, their value reaches 10.2 m. On the Sürgü-Çardak fault, significant displacements occurred down to a depth of 20 km; displacements exceeded 10.2 m. In our model, at the northeast end of the seismic rupture along the EAFZ, a displacement area of 6.8 m overlaps with the southwest end of the seismic rupture model of the Doğanyol-Sivrice earthquake of January 24, 2020 with Mw 6.7, published on the USGS website. Therefore, our model does not confirm the hypothesis of the presence of a seismic gap here, which, according to (Barbot et al., 2023), is a zone of a possible nearest earthquake.

Reconstruction of Co-Seismic and Post-Seismic Processes for the February 6, 2023 Earthquake in Turkey from Data of Satellite SAR Interferometry

Abstract—Using different methods for processing SAR images from the Sentinel-1A satellite, the displacement fields were determined in the region of the East Anatolian Fault Zone (EAFZ) and the Sürgü-Çardak faults, as well as a small fault on the continuation of the East Hatay fault zone, which rupture initiated a series of catastrophic earthquakes in Turkey on February 06, 2023. DInSAR and offset methods were applied. The most detailed data on the displacements were obtained by the offset method using images from the descending orbit. When constructing the model from the available SAR data, the data with the maximum signal-to-noise ratio were selected. For the northern part of the region, above 37.4° N, the range displacements obtained by the offset method from a descending orbit were used. South of parallel 37.0° N, we used azimuth displacements from the same descending orbit. The model of the seismic rupture was constructed on the basis of solution of (Pollitz, 1996) of the problem of deformations at the surface of a layered spherical Earth caused by along dip and strike displacements on a rectangular cut located inside the planet. Pollitz (1996) demonstrated that ignoring the spherical layering of the planet leads to errors up to 20%, with the largest errors occurring in the presence of a large strike-slip component. Ignoring sphericity also introduces an error when using the solution in the framework of the idealization of an elastic homogeneous half-space with a flat free boundary (Okada, 1985) which was used when constructing USGS and (Barbot et al., 2023) models. In our model the surfaces of seismic rupture are approximated by 19 rectangular elements along the strike, divided into three levels along the dip. Another element approximated a rupture along the extension of the East Hatay Fault Zone. As in the models of other authors (USGS; Barbot et al., 2023), in our model in the southern part of the EAFZ, the displacements increase from south to north, and are mainly concentrated in the upper part of the Earth’s crust to a depth of 10 km. At the southern end of this rupture, displacements in our model with an amplitude of up to 2 m are obtained at the lower levels of the model, and at its upper level, the displacements were only 0.11 m, and in this area on February 20, 2023 an earthquake of magnitude 6.3 occurred with a hypocentre depth of 11.5 km. The main displacements on the EAFZ are determined on its central segment. Here, the displacements go to a greater depth, their value reaches 10.2 m. On the Sürgü-Çardak fault, significant displacements occurred down to a depth of 20 km; displacements exceeded 9.8 m. In our model, at the northeast end of the seismic rupture along the EAFZ, a displacement area of 6.8 m overlaps with the southwest end of the seismic rupture model of the Doğanyol-Sivrice earthquake of January 24, 2020 with Mw 6.7, published on the USGS website. Therefore, our model does not confirm the hypothesis of the presence of a seismic gap here, which, according to (Barbot et al., 2023), is a zone of a possible nearest earthquake.

Transient scattering of a Rayleigh wave by a cluster of subwavelength resonators—Towards asymptotic modeling of seismic surface metabarriers

A seismic metabarrier (intended for surface waves mitigation effect) is modeled as a cluster of single-degree-of-freedom resonator units deposited on the surface of an isotropic homogeneous elastic half-space. It is assumed that each resonator has a frictionless flat rigid base of diameter much smaller than the wavelength of an incoming surface wave. The slow-motions asymptotic method is applied for constructing the first-order asymptotic model of multiple time-dependent scattering of a pulsed Rayleigh wave with respect to the vertical displacements of the resonators (including their rigid bases and inertial elements) and the normal contact forces (time-dependent integral characteristics of the contact reactions beneath the resonator bases). Both the stationary and transient multiple scattering scenarios are considered. The variation of the amplitude reduction factor due to the model parameters variation is studied in detail.

Optimization of a punch shape with a doubly connected contact domain

The objective is to optimize the distribution of the normal pressure under a rigid punch (indenter) having a doubly connected contact domain close to a circular ring and interacting with a homogeneous isotropic elastic half-space. In the problem considered here, the required design variable is the punch shape. The functional to be minimized is the root-mean-square deviation of the present pressure distribution from some given distribution. An analytical technique is developed for solving the problem for the punches with doubly connected shape, by reducing to a sequence of similar problems for the circular ring punches using expansions of the simple layer potential. The method of expansion in terms of a small parameter is used. The simple layer potential expansion is proposed when mapping a doubly connected integration domain onto a circular ring by transforming the integration variables and transforming the coordinates of the pole of the kernel. As a result, a set of similar problems was obtained for a circular ring to determine the functions characterizing the normal pressure distribution over a non-circular ring contact domain under the punch, as well as the normal displacements, from where the optimal punch shape is determined.

Effect of Non-Linear Properties of Intermediate Layer on Sliding Contact of Homogeneous and Coated Elastic Solids

Lubrication in the contact area can be considered as a viscoelastic layer, especially in the presence of particles in it, or under conditions of low temperatures. The properties of this layer are often non-linear, in particular, they depend on local pressure. The paper presents a formulation and numerical-analytical method for solving the contact problem in the presence of viscoelastic layers, the compliance of which depends on the applied pressure and is included in the formulation as the corresponding operator. The layer is homogeneous or coated elastic half-space. For the selected type of operator, the influence of parameters, which characterize the nonlinearity of the model, on the distribution of contact pressure and the coefficient of friction due to hysteresis losses was analyzed. It is shown that for the nonlinear model, the maximum contact pressures are higher, and the friction coefficient is lower than for the linear model with constant compliance. The effect of non-linearity for a wide range of sliding velocities is considered. An analysis of principal shear and tensile-compressive stresses for a homogeneous elastic half-space and for a coating, in particular, for a coating-substrate interface, was also carried out.

The February 6, 2023, Earthquakes in Turkey: A Model of the Rupture Surface Based on Satellite Radar Interferometry

Two strike–slip faults, displacements along which caused the catastrophic earthquakes in Turkey on February 6, 2023, were mapped from satellite radar interferometry data. According to the satellite data, the relative displacements of the sides of the East Anatolian Fault Zone (EAFZ), with which the first event of Mw 7.8 was associated, exceeded 5 m in the central segment. The rupture surface extends from the area of the Doğanyol-Sivris earthquake Mw 6.7 of January 24, 2020, in the north to the Mediterranean coast in the south, where the earthquake Mw 6.3 occurred on February 20, 2023. The second event Mw 7.5 is associated with the Surgü-Çardak fault; the relative displacements of its sides, according to satellite data, exceeded 7 m. The obtained displacement fields of the Earth’s surface were used to construct a model of the seismic rupture. This model was worked out on the basis of the Pollitz, 1996 solution, which defines displacements on the surface of the spherically stratified planet as a result of along dip and strike displacements on a rectangular rupture located inside the sphere. Ignoring the spherical stratification of the planet leads to errors of up to 20%, especially in the presence of a large strike–slip component [5]. Ignoring sphericity also causes an error, when using the solution obtained for an elastic homogeneous half-space, as the US Geological Survey (USGS) has done, in modeling the seismic rupture for earthquakes in Turkey in 2023. Our model differs in the detailed consideration of the fault geometry. For this purpose, the faults were approximated by 19 planes along the strike, divided into two levels along the dip. In our rupture model strike–slip displacements in the central segment of the EAFZ reached 12.7 m. In the southern segment of this rupture, the displacements are much smaller. It should be emphasized that we registered the displacements for the period from January 29, 2023, to February 10, 2023; therefore, together with co-seismic ones, they also include post-seismic displacements for four days after the main seismic events. The displacements on the rupture surface along the Surgü-Çardak Fault, where the Mw 7.5 earthquake occurred, were up to 10 m. The results demonstrate, in particular, the efficiency of application of the satellite radar interferometry in the operative study of catastrophic geodynamic phenomena and processes.

A numerical study of 3D topographic site effects considering wavefield incident direction and geomorphometric parameters

The topographic site effect plays a vital role in controlling the characteristics of earthquake ground motions. Due to its complexity, the factors affecting topographic amplification have not been fully identified. In this study, 100 ground motion simulations generated by double-couple point sources in the homogeneous linear elastic half-space are performed based on the 3D (three-dimensional) Spectral Element Method, taking the Menyuan area of Qinghai Province, China as a local testbed site. A relationship between incident direction and the strength of topographic amplification has been observed. The horizontal ground motion is affected by the back-azimuth, which is typically chosen to be the direction from seismic station to seismic source measured clockwise from north. Specifically, the east-west PGA (Peak Ground-motion Acceleration) is significantly amplified when back-azimuth is about 90° or 270°, and the north-south PGA is significantly amplified when back-azimuth is around 0° or 180°. The vertical ground motion is affected by the dipping angle, which is the angle from vertical at which an incoming seismic wave arrives. The vertical PGA is strongly amplified when the seismic wave is almost horizontally incident (e.g., dipping angle = 78°). A correlation study between geomorphometric parameters and frequency-dependent topographic amplification indicates that relative elevation and smoothed curvature contain similar information, both of which are closely related to the topographic amplification of horizontal components, but not the vertical component. Our study reveals the influence of source and propagation path on topographic amplification and provides a reference for considering the topographic site effect in real engineering sites.

ЗАМЕЧАНИЕ О ВЫЧИСЛЕНИИ СКОРОСТИ ВОЛНЫ РЭЛЕЯ И ПРОИЗВОДНОЙ ОПРЕДЕЛИТЕЛЯ РЭЛЕЯ В УПРУГИХ СРЕДАХ

There are many approximate and exact formulae to calculate surface wave velocity in an elastic medium. An analytical expression for Rayleigh wave velocity in volume wave velocity values has been obtained. A formula which determines the remainder in the excitation and diffraction of surface acoustic waves in a homogeneous isotropic elastic half-space involving solutions for the strain and stress fields in the form of quadratures is worked out. The values of the Rayleigh wave velocity and the derivative of the Rayleigh determinant for different media according to the reference data were obtained. The results can help in obtaining analytic expressions and reducing the calculation time of numerical solutions of the diffraction and excitation of acoustic waves.

Modeling Locations with Enhanced Earth’s Crust Deformation during Earthquake Preparation near the Kamchatka Peninsula

In seismically active regions of the Earth, to which the Kamchatka peninsula refers, pre-seismic anomalies are recorded in different geophysical fields. One of such fields is the acoustic emission of rocks, the anomalies of which are recorded 1–3 days before earthquakes at the distance of the first hundreds of kilometers from their epicenters. Results of joint acoustic-deformation measurements showed that growth of geoacoustic radiation intensity occurs during the increase in the level of deformations in rock masses by more than one order compared to the background values. Simulation studies of the areas with increased deformation are realized to understand the causes of anomalous acoustic-deformation disturbance occurrences before strong earthquakes. The model is based on the assumption that the Earth’s crust in the first approximation can be considered as a homogeneous isotropic elastic half-space, and an earthquake source can be considered as a displacements along a rectangular fault plane. Based on these assumptions, deformation regions of Earth’s crust were modeled during the preparations of two earthquakes with local magnitudes ML≈5 occurred on the Kamchatka Peninsula in 2007 and 2009. The simulation results were compared for the first time with the data of a laser strainmeter-interferometer installed at the Karymshina observation site (52.83∘ N, 158.13∘ E). It was shown that, during the preparation of the both earthquakes, the Karymshina observation site was within the region of shear deformations ≈10−7, which exceeded the tidal ones by an order. On the whole, simulation results corresponded to the results of the natural observations. Construction of an adequate model for the generation of acoustic-deformation disturbances before strong earthquakes is topical for the development of an early notification system on the threat of catastrophic natural events.

Dispersive staggered grid finite difference modelling of Rayleigh waves

Non-destructive surface wave-based ground exploration techniques such as multichannel analysis of surface wave (MASW) require a rigorous numerical model to predict the soil properties accurately. The staggered grid finite difference (SGFD) method is widely used to simulate elastic wave propagation due to its stability and ease of implementation. However, in the presence of low-velocity layers, the SGFD method requires computationally expensive high spatial grid resolution to accurately model the surface waves. On the other hand, velocity dependent grid approaches become unstable for the highly irregular soil profile. In order to overcome these challenges, a vertically non-uniform dispersive staggered grid scheme is proposed that significantly reduces the computing time without sacrificing accuracy. The proposed non-uniform discretization strategy is based on the Rayleigh wave dispersion relation, where the penetration depth of each frequency is assumed to be roughly one and half of the wavelength. Based on the above assumption, an exponential relationship between grid size and grid number is developed. The proposed method calculates continuously increasing grid length while ensuring grid points at the exact layer interface. Five different soil profiles: a homogenous elastic half-space, an irregularly dispersive crustal level profile, a low velocity layer at a deeper depth model, a real-world model, and a lateral heterogeneous model are used to demonstrate the efficacy of the proposed approach. For all the cases, the results of the proposed dispersive grid match those of the uniform grid with a correlation coefficient value (R) > 0.99. Compared to the uniform and velocity dependent grid approaches, the proposed dispersive grid scheme requires ½ to 1/4th of elements and CPU time. Furthermore, unlike the velocity dependent grid scheme, the proposed method does not become unstable for a highly irregular profile. Results indicate that the proposed method is superior to the traditional uniform and velocity dependent grid approaches for modelling elastic waves in layered media.

Dynamic soil impedance functions for cylindrical structures buried in elastic half-space

Spatially-distributed buried structures are highly susceptible to seismic ground motions. The macroscopic soil reactions to soil–structure relative displacements, aka. soil impedance functions (SIFs) and represented by a set of springs and dashpots, are thus very important for the assessment and design of those systems. Previous models to investigate the interaction problems between soil and horizontally buried structures (such as pipelines, tunnels) have been using spring stiffness chosen as static or frequency-independent constants, ignoring the nature of seismic loading and the energy reflected from the ground free surface. This paper presents analytical solutions for computing the frequency-domain SIFs for an infinitely-long cylindrical structure buried horizontally in homogeneous elastic half-space. The main challenge lies in mixed-boundary-value condition, where displacements are prescribed at the circular soil–structure interface and traction-free condition is satisfied along the straight-line ground surface. We used Hankel–Fourier series expansion, image technique, and Graf’s addition theorem to derive solution for axial SIFs. For a more complex in-plane SIFs problem, meanwhile, we used Hankel- and Bessel–Fourier series expansion. The in-plane solution requires numerical evaluation of contour integrals on the physical Riemann sheet, thus nested Gauss–Kronrod quadrature rule as well as Cauchy’s residue theorem are employed. We then verified our analytical solutions using results obtained from finite element simulations, in which a perfect agreement is shown between two approaches. The half-space SIFs are shown to also converge to their full-space counterparts in case of large burial depth. Additionally, parametric study was conducted to examine the variation of frequency-dependent SIFs, normalized with soil shear modulus, in response to the changes in soil Poisson’s ratio and the structure burial depth.

Explanation and Application of the Evolving Contact Traction Fields in Shallow Foundation Systems

The present paper provides a qualitative discussion of the evolution of contact traction fields beneath rigid shallow foundations resting on granular materials. A phenomenological similarity is recognized in the measured contact traction fields of rigid footings and at the bases of sandpiles. This observation leads to the hypothesis that the stress distributions are brought about by the same physical phenomena, namely the development of arching effects through force chains and mobilized intergranular friction. A set of semi-empirical equations are suggested for the normal and tangential components of this contact traction based on past experimental measurements and phenomenological assumptions of frictional behaviors at the foundation system scale. These equations are then applied to the prescribed boundary conditions for the analysis of the settlement, resistance, and stress fields in supporting granular materials beneath the footing. A parametric sensitivity study is performed on the proposed modelling method, highlighting solutions to the boundary-value problems in an isotropic, homogeneous elastic half-space.

Dynamic behavior of soil-foundation-structure systems subjected to scour

Earthquake and scouring are the leading causes of bridge failure worldwide, resulting not only in casualties and fatalities but also in enormous societal and economic losses. A great number of bridges in earthquake-prone countries cross rivers and have shallow foundations, which renders them highly vulnerable to the combined effects of earthquake and flood-induced scour. Thus, the research on the dynamic response of bridges with shallow foundations under scour and earthquake hazards is timely and imperative. This study investigates the problem through the development of a numerical model for evaluating the effect of scour on the impedance functions of a massless rigid strip foundation resting on a homogenous elastic half-space. The developed impedance functions are then used in an extensive parametric study analyzing the changes of the fundamental frequency of bridge piers for different combinations of the geometrical and mechanical properties of the soil-structure-foundation system. The study results shed light on the effects of scour on the dynamic properties and fundamental frequency of vibration of bridges with shallow foundations and have important implications on the development of inverse techniques for scour identification based on the evaluation of the changes in the bridge modal properties.

Coupling the first and second attenuation zones in seismic metasurface

Semi-infinite elastic metamaterials and metasurfaces on homogeneous elastic half-spaces have attracted significant attention in the past two decades as efficient artificial structures to control and mitigate surface waves. In this research, the first two attenuation zones of an elastic metasurface composed of different arrangements of pillars on a substrate are investigated. First, the lowest frequency attenuation zone (LFAZ) is numerically investigated. Then, the rainbow trapping effect of the second attenuation zone (SAZ) is demonstrated by numerical simulations and experiments. The different characteristics of these two attenuation zones are brought together to connect the lower bound of the SAZ and the upper bound of the LFAZ, allowing to design a seismic metasurface that only uses one kind of artificial structure on a half-space to attenuate Rayleigh waves in the frequency range extending from 5 to 22 Hz.

Axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure

This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered halfspace. The analysis uses the axisymmetric boundary element method (BEM) associated with the fundamental solution of a multilayered elastic fullspace subject to the concentrated ring-body force. The BEM is further verified for its high efficiency and accuracy by comparing its result with the analytical and FEM solutions for the problem of a homogeneous elastic halfspace whose spherical cavity is under internal pressure. The BEM is used to examine the effect of the volcano-shaped mantle, the cavity shape, the layered material properties and the internal pressure on the elastic behavior of the halfspace under the internal pressure loading within the cavity. The displacements and stresses at the external and internal boundaries and within the layered halfspace are presented and analyzed in detail. The presence of the volcano-shaped mantle can reduce significantly the swelling ground movement induced by the expansive pressure in the cavity in the layered halfspace. The cavity shape can have significant effect to the location and magnitude of the maximum tensile principal hoop stress on the cavity surface induced by its internal pressure.

2-D Analysis of Generalized Thermoelastic Porous Medium under the Effect of Laser Pulse and Microtemperature

The paper presents the analytical solutions for a generalized thermoelastic medium consisting of microtemperatures and voids subjected to a laser pulse loading the medium thermally. The 0.02 ps pulse duration of the non-Gaussian laser beam is apt for heating a homogenous isotropic elastic half-space. A method called the normal mode analysis is employed to evaluate numerically the effects of various variables such as the micro-temperature vector, variation in the fraction field of the volume, first heat flux moment tensor, temperature distribution on the stresses and displacement components of the medium. In addition, the graphical illustration of the physical response of the medium has been presented in the presence and absence of void parameters, as well as in the presence of laser pulse with two different acting periods.

Effect of longitudinal joint on train-induced vibrations from subway shield-driven tunnels in a homogeneous half-space

With the rapid increase of urban rail transit networks, the environmental problems induced by vibrations from subway traffic become more and more prominent. Most subway tunnels are constructed by the shield machine, which are assembled by tunnel linings connected by joints. This study investigates the effect of the tunnel longitudinal joints on the train-induced vibrations from a subway shield-driven tunnel in a homogeneous half-space. The shield-driven tunnel is considered as an elastic lining ring connected by longitudinal joints, while the ground is simplified as a homogeneous elastic half-space. The general solution for the tunnel and the ground are derived by using the thin-shell theory and the elastic continuum theory, respectively. By satisfying the boundary conditions on the tunnel-ground interface, the tunnel is coupled to the ground in a half-space domain. The responses during the running of a metro train are calculated by coupling the tunnel-ground model with the vehicle-track model. The longitudinal joint has a significant impact on ground vibrations, which increases the running RMS values of the vertical velocity by 20% ∼ 70% and of the horizontal verticity by 10% ∼ 20%. As the stiffness of the longitudinal joint decreases, the ground vibrations increase.

Seismic evaluation of steel plate shear wall systems considering soil-structure interaction

This study investigates the various effects of Soil-Structure Interaction (SSI) on the seismic behavior of steel frames with Steel Plate Shear Wall (SPSW) lateral resisting systems. Nine steel frames with various aspect ratios are studied under multiple seismic hazard levels. The SPSWs are modeled based on the strip model concept, and the Soil-Structure Systems are simulated using the substructure method. The soil beneath the structure is considered as a homogeneous elastic half-space. The Endurance Time method is exploited for nonlinear dynamic analysis of the fixed-base structures and soil-structure systems. Results indicate that use of fixed-base models leads to the significant overestimation of the damage of SPSWs in the lower stories of the structure. Neglecting SSI in squat structures is undoubtedly a conservative choice, while in slender structures, it may lead to the underestimation of structural responses, especially in the upper stories. In the design procedure of the structures with SPSW lateral load resisting system located on soft soils, ignoring SSI effects results in very heavy and cost-intensive code-based designs.