Analytical solution for longitudinal seismic response of long tunnels subjected to Rayleigh waves

Yang, Yuxuan; Yu, Haitao; Yuan, Yong; Zhao, Mi

doi:10.1002/nag.3066

Cited by 29 publications

(3 citation statements)

References 32 publications

(37 reference statements)

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“…Wave propagating through the medium is considered to propagate along x − axis with temporal time t. The amplitude of the wave varies exponentially along the z − axis with field variables converging to zero as z → ∞ . The solution of the Rayleigh wave can be represented as [41]:…”

Section: Solution Of the Problemmentioning

confidence: 99%

Rayleigh wave through half space semiconductor solid with temperature dependent properties

Saeed,

Ali Khan,

Alzahrani

et al. 2024

Phys. Scr.

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he article focuses on Rayleigh wave propagation in a homogeneous isotropic semi conductor thermoelastic medium rotating with fixed angular frequency with temperature de pendent properties. The elastic constants depends upon the temperature function. The effectsof temperature dependency parameter and time derivative, fractional order are illustrated. Bythe theory of thermo-elasticity, waves results in generation of thermal signals that propagatethrough the medium. A heat conduction model of three phase lag (3PL) along with frac tional order time derivative is used to analyzed the thermal signals. The secular equations ofRayleigh waves are derived mathematically at the stress-free, carrier density and thermally in sulated boundaries. Some specific properties like velocity, attenuation coefficient, specific heatloss and penetration depth for Rayleigh waves have been evaluated and presented graphically.The secular equations are computed numerically depicted graphically using Matlab.

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Section: Solution Of the Problemmentioning

confidence: 99%

Rayleigh wave through half space semiconductor solid with temperature dependent properties

Saeed,

Ali Khan,

Alzahrani

et al. 2024

Phys. Scr.

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“…When the yield limit is exceeded, the material will undergo an irrecoverable plastic deformation, and it reaches the maximum when the material is almost destroyed, which means that the accumulated plastic strain energy reached the maximum [43,44]. With seismic excitation, the structure elements alternatively exhibit tension and compression; they will experience the cycle of loading, compaction, elasticity, plasticity, and unloading, which induces cyclic impact on the material and brings about crack expansion, crack penetration, and even damage of the structure [45].…”

Section: Strength Failure Criterion Based On the Dissipatedmentioning

confidence: 99%

The Stability Analysis of Tunnel Lining Structure with Seismic Excitation Based on the Energy Evaluation Principle

Wen

Xin

Zhang

et al. 2021

Shock and Vibration

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Earthquakes are vibrations induced by the rapid releases of large quantities of energy from the crustal movements. During seismic excitation, there are kinetic energy, damping energy, and strain energy acting on the tunnel structure. Based on the indexes of the total energy, releasable elastic strain energy, and dissipated energy, this paper proposes three energy evaluation criteria for the tunnel structure, which are applied to the optimization of the aseismic design of the cross-sectional shape and material property of the tunnel structure. It can be concluded that the peak values and accumulated values of elastic strain energy at the spandrel and arch springing are significantly larger than other positions, which indicates that the strengths of the spandrel and arch springing are the most influential factor for the seismic damage of the tunnel structure. Considering this factor, the width-to-height ratio of 1.33 and Poisson’s ratio of 0.3 are determined as the most optimal cross-sectional shape and material property, respectively. Furthermore, by analyzing the relationship between the internal energy and the input energy of the tunnel structure with seismic excitation and proposing an equation for the evaluation of the dynamic stability of tunnel structure, the stabilities of the tunnel structure with different PGAs are analyzed; it can be concluded that the larger the peak value of seismic wave acceleration, the longer the instable period and the greater the degree of dynamic instability. The derived equations can be used as references for the seismic analysis of the tunnel structure, and the conclusions of this paper can contribute to the aseismic design of tunnel lining.

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“…In recent years, surface waves have been the subject of many analytical and numerical seismic studies in civil engineering. These researches are mostly limited to realizing the subjects like diffraction of Rayleigh waves by surface topographic features [42][43][44][45][46][47], cavity detection [48][49][50][51], evaluating bending deformation of tunnel and lining response [36,37,[52][53][54][55][56], the response of high-rise structure, and soil-structure interaction [32,57,58]. Therefore, seldom studies are related to investigating the seismic interaction of surface waves with underground structures on the free surface ground motion.…”

Section: Introductionmentioning

confidence: 99%

A numerical study on effect of underground cavities on seismic ground response due to Rayleigh wave propagation

2023

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Recent studies found that some structural damage can be attributed to the effect of surface waves. A shallow underground structure may be heavily influenced by surface waves, which makes to lose energy over distance more slowly than body waves. This study deals with evaluating the effect of Rayleigh waves (R-waves) interaction with underground cavities on the seismic ground response and amplification pattern using the Finite Element Method (FEM). First, the FEM model was verified to ensure its accuracy. Then, the influences of the effective parameters, such as cavity burial depth, distance from the cavity axis, and dimensionless incident frequency were investigated. Parametric studies revealed that the amplitude of ground motion is greater in the presence of a cavity with respect to that in the free-field condition. It was indicated that shallow cavities cause more amplification than cases with a larger depth ratio. By moving away from the wave source, the response of receiver points has a declining trend. Due to the complex interaction of R-waves with a cavity, the right side of the cavity has less amplitude than the left side. Finally, by increasing the dimensionless incident frequency, the distribution of the surface displacements and wave diffraction patterns gradually becomes more complicated while the peak displacement components decrease. Consequently, in light of the importance of the R-wave interaction with subsurface spaces, the findings of this study can help improve seismic design procedures and seismic microzonation guidelines.

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Analytical solution for longitudinal seismic response of long tunnels subjected to Rayleigh waves

Cited by 29 publications

References 32 publications

Rayleigh wave through half space semiconductor solid with temperature dependent properties

Rayleigh wave through half space semiconductor solid with temperature dependent properties

The Stability Analysis of Tunnel Lining Structure with Seismic Excitation Based on the Energy Evaluation Principle

A numerical study on effect of underground cavities on seismic ground response due to Rayleigh wave propagation

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