Viscous-spring Artificial Boundary Research Articles

Seismic Vulnerability Assessment of the Cliff-Attached Buildings Equipped with Energy Dissipation Devices Under Obliquely Incident Seismic Waves

Cliff-attached structures are structures attached to slopes and connected tightly, which is particularly complex to analyze due to the foundations’ unequal grounding and the lateral stiffness’ irregularity. In rare earthquakes, seismic waves are usually obliquely incident on the foundation at a certain angle. Therefore, it is not appropriate to consider only seismic waves’ vertical incidence, and it is necessary to consider multi-angle oblique incidence. In this paper, based on the theory of viscous-spring artificial boundary and the principle of equivalent nodes at the interface of oblique incidence of ground shaking P-waves, and combined with the dynamic properties related to Buckling-Restrained Brace, the numerical models of slopes and two kinds of cliff-attached structures considering the slope amplification effect and soil-structure interaction are established. The dynamic response of the obliquely incident seismic waves under the action of the cliff-attached vibration reduction structure is studied in depth, and the additional effective damping ratios of the nonlinear energy-dissipated units based on the deformation energy are compared and analyzed. It is shown that under the four oblique incidence angles of incidence (compression waves in the vertical plane) studied in this paper, the seismic dynamic response and damage degree peaked at an angle of incidence of 60°, with a tendency to increase and then decrease with increasing angles of incidence. The ability of an energy-dissipating vibration reduction device to change structural vibration characteristics decreases with an increase in incidence angle. The difference between the total strain energy of the structure in the X-direction (Transverse slope direction) and Y-direction (Down-slope direction) and the total energy dissipation of the dissipative components is obvious, with the X-direction being about 10 times that of the Y-direction.

Study of the dynamic interactions between helix-stiffened cement mixing piles and soft soil under oblique incidence of SV waves in arbitrary space

Helix stiffened cement mixing (HSCM) piles are extensively utilized in soft soil sites due to their excellent seismic and pullout resistance. Initially, the equivalent nodal force formulas for each face under the oblique incidence of SV waves in any spatial direction are derived based on the viscous-spring artificial boundary. The method's applicability in studying pile–soil interactions is verified based on existing pile–soil tests. Subsequently, the HSCM pile–soil model is constructed using finite element software through a Python program. Various analyses of accelerations, relative displacements, soil reactions, and pile–soil dynamic p-y curves are conducted using two different directions of incidence angles (horizontal and vertical) and various types of seismic waves. Subsequently, the backbone line of the dynamic p-y curve is plotted, revealing the pile–soil interaction mechanism under spatial oblique incidence. Finally, Matlock's formula is modified to ensure its applicability to pile–soil interactions under spatially oblique incidence. The results demonstrate that loading the Kobe wave causes the peak acceleration in the x direction, the peak pile–soil relative displacement, and the peak pile-side soil reaction force to increase by 22.64 %, −18.90 % and 18.42 %, respectively, compared to those of the El Centro wave.

A new equivalent acceleration-based non-uniform response spectrum method for efficient seismic SSI analysis

A complex multiple-support response spectrum (CMSRS) method with a concise and universal expression is required to estimate the seismic responses of soil–structure interaction (SSI) systems under non-uniform seismic excitations to replace existing complex methods. This paper introduces and defines a new concept called equivalent acceleration of boundary load (EABL) that converts widely used equivalent loads into equivalent accelerations, and further develops an efficient CMSRS-EABL method for the seismic analysis of the SSI system. First, EABL offers three main benefits: it simplifies the expressions without sacrificing precision, extends the applicable scope of viscous-spring artificial boundary (VSAB) to all stress-type artificial boundaries, and presents dynamic equations in a familiar form. Subsequently, the CMSRS–EABL formula was successfully deduced based on the equivalent simplified dynamic equations. This formula significantly simplifies the traditional method by reducing the effective modal participation factors, mean-square-roots, and cross-correlation coefficients by 4, 5 and 15 items, respectively. Finally, a rectangular construction surrounded by a VSAB–soil combination was used as an example to illustrate the convenience of the developed CMSRS–EABL method and verify its precision. The results indicate that the proposed method is characterized by greater simplicity and ingenuity, and it is capable of high precision similar to that of the conventional methods. We believe this method will be of significant benefit in evaluating the anti-seismic performance of deeply buried and long-standing structures.

Seismic responses and failure mechanism of the superstructure-integrated underground structure considering the seismic aboveground-underground interaction

The superstructure-integrated underground structure (SIUS) is an innovative infrastructure in an urban city, in which the aboveground part and underground part are coupled together to be a large synthesis structure. During earthquakes, the SIUS is primarily influenced by the soil deformation and structural vibration, and the seismic aboveground-underground interaction (SAUI) would be considerable due to structural characteristics. This paper aims to investigate the seismic response and failure mechanism of the SIUS and reveal the influence mechanism of the SAUI with a quantitative method for the seismic aboveground-underground interaction coefficient (SAUIC). In this paper, a credible numerical model of the whole soil-SIUS system compiled with the viscous-spring artificial boundary is established. The modal analysis of the SIUS is carried out, and the distinctive structural characteristics are discussed. The seismic responses of the SIUS are thoroughly investigated, and the failure mechanism of vulnerable positions is further revealed. Based on the modal frequency response analysis and a novel correlation analysis, the SAUIC is quantitatively proposed to evaluate influence effects of the SAUI on seismic responses of the SIUS. The results show that the SAUI has great influence effects on seismic responses of the SIUS, even changes the seismic failure mode of the underground part to be flexural failure; the quantitative SAUIC demonstrates the SAUI increases with the increasing seismic intensity and increases from outside to inside of the SIUS, and the SAUI would be highly considerable on positions with irregularities in structural stiffness, especially on the aboveground-underground interface.

An integrated model for offshore wind turbine monopile in porous seabed under multi-directional seismic excitations

This study proposes an integrated three-dimensional time-domain finite element model for offshore wind turbine (OWT) monopile in porous seabed under multi-directional seismic excitations. Biot's u-p formulation is used to describe the dynamic interaction between the soil skeleton and pore water. Potential-based fluid elements are used for seawater to accurately model fluid–structure interaction (FSI). Moreover, FSI interface elements are applied to the interface of seawater and pile and to the interface of seawater and mud line. To analyze the response of the OWT-monopile-seabed-seawater system to multi-directional seismic excitations, a viscous-spring artificial boundary is implemented in the finite element model. The integrated model was sufficiently verified in terms of the vibration characteristics of OWTs, the displacement and the excess pore water pressure using implemented viscoelastic artificial boundary, and the FSI interaction under both horizontal and vertical excitation. The results indicated that: (1) The hydrodynamic pressure and the excess pore water pressure varied with different positions along the OWT and the pile; (2) Adding the excitation of the EW component ground motion caused the change of the distribution of transient liquefaction with respect to that under the excitation of only NS component ground motion; (3) The vertical ground motion caused a substantial fluctuation of the vertical displacement of the OWT and larger area of transient liquefaction near the surface of the seabed and near the tip of the pile; (4) resonance occurred when the frequency of input motion was approaching to the first natural frequency of OWT, leading to extremely large acceleration and displacement of OWT.

Seismic damage characteristics of high arch dams under oblique incidence of SV waves

This study investigates the seismic damage characteristics of high arch dams considering the oblique incidence of seismic waves. Based on the dynamic implicit finite element method, a viscous-spring artificial boundary is applied to consider radiation damping of the infinite foundation, the seismic wave input is converted into an equivalent nodal force of the artificial boundary, and the equivalent nodal loads of the wave input under oblique incidence of the SV wave is deduced. Taking JP Ⅰ arch dam as an example, combined with the concrete damaged plasticity (CDP) model, the nonlinear dynamic response of the dam under 25° oblique incidence of the SV wave is conducted considering the geometrical nonlinearity of contraction joints and the dynamic mechanical properties of concrete materials. Based on the incremental dynamic analysis (IDA) method, the relative displacement and transverse joint opening are selected as the damage measures for fragility analysis of the arch dam. According to the damage distribution from the analysis of a large number of seismic time-history responses, the damage levels of the arch dam are classified. Three limit states of slight damage, moderate damage and severe damage are proposed for the arch dam. The average responses of the 10 earthquakes are considered as the limit values to quantitatively describe the damage of the arch dam. By fitting the results of incremental dynamic analysis, the seismic probabilistic demand model and seismic fragility curves for the two damage measures to predict the probability of the arch dam reaching damage levels under different seismic actions have been established. The fragility curve shows that the probability of severe damage is almost zero under the maximum design earthquake (PGA = 0.1971 g) and less than 5% under the maximum credible earthquake (PGA = 0.2299 g). It is concluded that JP Ⅰ arch dam has a high degree of safety redundancy and fully satisfies the “two levels” design requirements.

Effect of oblique incidence angle and frequency content of P and SV waves on the dynamic behavior of liquid tanks

The dynamic behavior of liquid tanks is very different from those of other structures. Great effort has been put into the study of water tanks under vertical incident ground motion, but studies are still lacking regarding how different incidence angles influence the dynamic characteristics. This paper developed a model for the tank-soil-fluid system to study the variation and distribution of impulsive, convective, and total hydrodynamic pressures on the tank wall duel to water when subjective to earthquakes from different angles of incidence. The role of earthquake type (P or SV waves) and frequency contents are also considered. The tank-fluid interaction is modelled by the coupled acoustic-structural approaches. With the viscous-spring artificial boundary, the ground motions of oblique incidence can be transformed into the forces acting on the nodes of the truncated boundary of the finite-element model. It is concluded that the response of the tank-soil-fluid system is highly sensitive to incidence angles, earthquake type (P or SV waves), and earthquake record frequency contents. Therefore, in the design of tanks, not only the characteristics of the tank should be considered, but also the seismic characteristics should be considered.

Seismic Response and Damage Analysis of Shield Tunnel with Lateral Karst Cavity under Oblique SV Waves

The dynamic effects of the lateral karst cavity on the shield tunnels under different incident angles of seismic waves are investigated by numerical analysis in this paper, based on the Dalian Metro Line 5 project. The viscous-spring artificial boundary is applied and verified to guarantee the accuracy of seismic input. A simplified finite element model of shield tunnel is established based on the equivalent bending stiffness model. This paper compares the seismic response characteristics and damage states of the tunnel under different incident angles by analyzing the axial deformation, stress distribution, and damage severity, respectively. A new damage state classification criterion is proposed by introducing the relationship between cracks and tensile damage. The results show that the tunnel’s affected scope by the lateral karst cavity is twice the cavity diameter. As the incident angle increases, the tunnel’s displacement and stress increase and show the structural spatial difference, and the tunnel’s damage state is increasingly severe. The displacement and stress reach the max values when the incident angle is 30°. The cracks along the axial direction extend on the outer surface of the vault and bottom, and the crack width is greater than 0.2 mm, as that angle is 30°. The damage severity at the tunnel’s central zone is minimum along axial directions during seismic action, while the damage concentration occurs on the bottom at the end of seismic. The lateral karst cavity plays an energy dissipation and vibration reduction role to a certain extent, but it also aggravates the local damage. This paper can serve as a reference for the seismic design of tunnels in karst regions.

Nonlinear seismic response and index correlation of high arch dams under cross-stream oblique incidence of near-fault SV waves based on wavelet decomposition

This paper aims to propose an analysis framework for the response index correlation of high arch dams under cross-stream oblique incidence of near-fault pulse-like and non-pulse seismic waves. The influence of the dynamic pulse effect of near-fault seismic waves on the index correlation at different incidence angles is evaluated. Further, the seismic response through an arbitrary incident angle is quantitatively estimated. Several typical near-fault records of extracted strong velocity pulses are selected, and their decomposed non-pulse ground motions (GMs) are used to ensure the similarity and uniformity of the response spectra. Furthermore, a seismic input model of the oblique incidence of the SV wave is established based on the three-dimensional viscous-spring artificial boundary method, and its accuracy was confirmed through the numerical application. The engineering demand parameters (EDPs) of pulse-like SV waves and non-pulse SV waves, including dam damage, dynamic displacement, and joint opening, with cross-stream incident angles are discussed emphatically. Finally, the correlation between the response indices of near-fault SV waves at different incident angles is quantitatively analyzed. The numerical results indicate that pulse-like seismic waves with different input angles are more destructive than non-pulse seismic waves, and different response indices of the dam may have different most unfavorable incident angles. A prediction model of the dam response considering different input angles of seismic waves is proposed to roughly estimate the response index values of each input angle. The influence of the dynamic pulse characteristics on the correlation degree of response indices under different input angles is mainly divided into three types: no impact, increasing correlation degree, and decreasing correlation degree. In the seismic design and performance evaluation of arch dams, it should be suggested to comprehensively consider the influence of the oblique incident angle of GMs and near-fault pulse characteristics.

Influence of seismic wave type and incident direction on the dynamic response of tall concrete-faced rockfill dams

Owing to the stochastic behavior of earthquakes and complex crustal structure, wave type and incident direction are uncertain when seismic waves arrive at a structure. In addition, because of the different types of the structures and terrains, the traveling wave effects have different influences on the dynamic response of the structures. For the tall concrete-faced rockfill dam (CFRD), it is not only built in the complex terrain such as river valley, but also its height has reached 300 m level, which puts forward higher requirements for the seismic safety of the anti-seepage system mainly comprising concrete face slabs, especially the accurate location of the weak area in seism. Considering the limitations of the traditional uniform vibration analysis method, we implemented an efficient dynamic interaction analysis between a tall CFRD and its foundation using a non-uniform wave input method with a viscous-spring artificial boundary and equivalent nodal loads. This method was then applied to investigate the dynamic stress distribution on the concrete face slabs for different seismic wave types and incident directions. The results indicate that dam-foundation interactions behave differently at different wave incident angles, and that the traveling wave effect becomes more evident in valley topography. Seismic wave type and incident direction dramatically influenced stress in the face slab, and the extreme stress values and distribution law will vary under oblique wave incidence. The influence of the incident direction on slab stress was particularly apparent when SH-waves arrived from the left bank. Specifically, the extreme stress values in the face slab increased with an increasing incident angle. Interestingly, the locations of the extreme stress values changed mainly along the axis of the dam, and did not exhibit large changes in height. The seismic safety of CFRDs is therefore lower at higher incident angles from an anti-seepage perspective. Therefore, it is necessary to consider both the seismic wave type and incident direction during seismic capacity evaluations of tall CFRDs.

An Arc-Consistent Viscous-Spring Artificial Boundary for Numerical Analysis of Seismic Response of Underground Structures

A new arc-consistent viscous-spring artificial boundary (ACVAB) was proposed by changing a traditional flat artificial boundary based on the theory of viscous-spring artificial boundaries. Through examples, the concept underpinning the establishment and specific setting of the boundary in the finite element software were described. Through comparison with other commonly used artificial boundaries in an example for near-field wave analysis using the two-dimensional (2D) half-space model, the reliability of the ACVAB was verified. Furthermore, the ACVAB was used in the numerical analysis of the effects of an earthquake on underground structures. The results were compared with the shaking table test results on underground structures. On this basis, the applicability of the ACVAB to a numerical model of seismic response of underground structures was evaluated. The results show that the boundary is superior to common viscous-spring boundaries in terms of accuracy and stability, and therefore, it can be used to evaluate radiation damping effects of seismic response of underground structures and is easier to use.

Dynamic-Response Analysis of the Branch System of a Utility Tunnel Subjected to Near-Fault and Far-Field Ground Motions in Different Input Mechanisms

There are few studies on the dynamic-response mechanism of near-fault and far-field ground motions for large underground structures, especially for the branch joint of a utility tunnel (UT) and its internal pipeline. Based on the theory of a 3D viscous-spring artificial boundary, this paper deduced the equivalent nodal force when a P wave and an SV wave were vertically incident at the same time and transformed the ground motion into an equivalent nodal force using a self-developed MATLAB program, which was applied to an ABAQUS finite element model. Based on near-fault and far-field ground motions obtained from the NGA-WEST2 database, the dynamic responses of a utility tunnel and its internal pipeline in different input mechanisms of near-fault and far-field ground motions were compared according to bidirectional input and tridirectional input, respectively. Generally, the damage to the utility tunnel caused by the near-fault ground motion was stronger than that caused by the far-field ground motion, and the vertical ground motion of near-fault ground motion aggravated the damage to the utility tunnel. In addition, the joint dislocation of the upper and lower three-way joints of the pipeline in the branch system under the seismic action led to local stress concentrations. In general, the branch system of the utility tunnel had good seismic performance to resist the designed earthquake action and protect the internal pipeline from damage during the rare earthquake.

Nonlinear 3D finite element analysis of suction caisson-tower-soil system subjected to horizontal earthquake excitation

Suction caissons are widely used as a promising alternative foundation for offshore structures under variable offshore environments. In this paper, a three-dimensional finite-element model which takes into account soil inelasticity was used to study the seismic behavior of a suction caisson in clay taken from an offshore wind farm in the Hebei province of China. The results showed that the maximum acceleration of the soil increases with increasing depth. There is a distinct amplification for relatively low frequencies when seismic waves propagate to the mudline. It was assumed that the rotation center of suction caisson under seismic conditions was virtually existent. The rotation center was obtained by the proposed formula to explore the movement positions of the suction caisson. The time of the peak of lateral displacement of the lid did not synchronize with that of the changing direction of displacement of the rotation center, indicating that the displacement of the lid can not be a comprehensive assessment of the position state of suction caissons. The point mass at the top of the wind turbine tower was responsible for the increase of vibration amplitude of displacement. • In this paper, a three-dimensional finite-element model taking account of soil inelasticity was carried out to study the seismic behavior of suction caisson in soft clay. A 3D equivalent viscous-spring artificial boundary element is applied to eliminate the unnatural reflection wave generated on the boundary. • It is assumed that the rotation center of suction caisson under seismic conditions is virtually existent and it was obtained by the proposed formula to explore the movement positions of the suction caisson. • The time histories of lateral and vertical displacement were extracted for studying seismic behavior of the wind turbine tower under seismic loading.

Seismic response analysis of complicated soil-structure interaction using inelasticity-separated scaled boundary finite element method

Inelastic seismic response analysis of large infrastructure needs to consider the soil-structure dynamic interaction with a reasonable absorbing boundary condition and generally requires refined simulation, which is an extremely complicated and time-consuming process. Because these structures are generally irregular, the use of a conventional finite element mesh for refined simulation makes the process of modelling pretreatment more complicated, and the corresponding computation scale is usually large. Although the development of computer hardware has greatly improved the computational efficiency of nonlinear problems, studies related to an efficient solving algorithm and appropriate element formulation that can achieve refined simulation, flexible mesh generation, and high precision for large-scale complex structures are still the focus of civil engineers. Because the material nonlinearity of a structure generally occurs in local regions, various emerging algorithms have been developed to accelerate the computation of inelastic response analyses based on various methods such as the reanalysis method and the inelasticity-separated finite element method (IS-FEM). The scaled boundary finite element method (SBFEM), which is a semi-analytical method, is known for its flexible meshing capability and high precision. The idea of inelasticity-separated is introduced into the SBFEM, and the viscous-spring artificial boundary is combined with a novel inelasticity-separated S-element formulation to propose a dynamic solution scheme that can solve the problems associated with element meshing and the nonlinearity of models with complicated soil-structure dynamic interaction. To implement the semi-analytical S-element for use in inelasticity-separated method, the Gaussian numerical integration scheme is performed for each subelement. The proposed dynamic solution scheme for soil-structure interaction is basically the same as that of a static problem and can also be solved by the efficient Woodbury approximation approach because a more inelastic strain interpolation point layout in the S-element leads to larger inelastic degrees of freedom (IDOFs). In this paper, not only the mesh flexibility and high precision of the SBFEM is retained but also the nonlinear solving efficiency is greatly improved without decreasing precision. Numerical examples demonstrate the validity and efficiency of the proposed inelasticity-separated S-element formulation and dynamic solution scheme.

Evaluation of Ground Motion Amplification Effects in Slope Topography Induced by the Arbitrary Directions of Seismic Waves

The incident directions of seismic waves can change the ground motions of slope topography. To elaborate on the influences of the directions of seismic waves, a dynamic analysis of the slope topography was performed. Seismic waves were input using an equivalent nodal force method combined with a viscous-spring artificial boundary. The amplification of ground motions in double-faced slope topographies was discussed by varying the angles of incidence. Meanwhile, the components of seismic waves (P waves and SV waves), slope materials and slope geometries were all investigated with various incident earthquake waves. The results indicated that the pattern of the amplification of SV waves was stronger than that of P waves in the slope topography, especially in the greater incident angels of the incident waves. Soft materials intensely aggravate the acceleration amplification, and more scattered waves are produced under oblique incident earthquake waves. The variations in the acceleration amplification ratios on the slope crest were much more complicated at oblique incident waves, and the ground motions were underestimated by considering only the vertical incident waves. Therefore, in the evaluation of ground motion amplification of the slope topography, it is extremely important to consider the direction of incident waves.

Three-dimensional nonlinear seismic response analysis of subway station crossing longitudinally inhomogeneous geology under obliquely incident P waves

With the rapid development of underground space, more adverse site conditions are occurring in the construction of underground structures. For example, a subway station passes through longitudinally inhomogeneous geology. When the subway station crosses the interface of soft soil and hard soil, this may lead to the destruction of underground structures. In this paper, three-dimensional (3D) nonlinear seismic response analysis of subway stations crossing longitudinally inhomogeneous geology subjected to obliquely incident P waves is presented based on actual engineering background. The earthquake input method for the longitudinally inhomogeneous site that transforms the site seismic response into an equivalent nodal load is first developed and verified. The viscous-spring artificial boundary is used to simulate the radiation damping effect of infinite domain media. Subsequently, the topographic and geological effects on seismic response of engineering site are investigated. Finally, the failure mechanism of the subway station structure crossing longitudinally inhomogeneous geology under the obliquely incident P waves is revealed. The investigation demonstrates that the plastic zone of site usually appears along the interface between the hard and soft soil media, and appears on the side of the soft soil. The sidewall and bottom slab of the structure experience obvious tensile damage at the interface location between the hard and soft soil media. The results show that topographic and geological effects should be considered in seismic analysis and design of underground structures when the topography and geology change significantly.

Numerical Algorithm for Dynamic Impedance of Bridge Pile-Group Foundation and Its Validation

The characteristics of bridge pile-group foundation have a significant influence on the dynamic performance of the superstructure. Most of the existing analysis methods for the pile-group foundation impedance take the trait of strong specialty, which cannot be generalized in practical projects. Therefore, a project-oriented numerical solution algorithm is proposed to compute the dynamic impedance of bridge pile-group foundation. Based on the theory of viscous-spring artificial boundary, the derivation and solution of the impedance function are transferred to numerical modeling and harmonic analysis, which can be carried out through the finite element method. By taking a typical pile-group foundation as a case study, the results based on the algorithm are compared with those from existing literature. Moreover, an impact experiment of a real pile-group foundation was implemented, the results of which are also compared with those resulting from the proposed numerical algorithm. Both comparisons show that the proposed numerical algorithm satisfies engineering precision, thus showing good effectiveness in application.

Estimation of seismic wave incident angle using vibration response data and stacking ensemble algorithm

The determination of the incident angle of an earthquake is one of the critical research issues in modeling the seismic input mechanism at a dam site and it is also for geological exploration. At present, the incident angle calculation methods mostly rely on accurate geological models, complex theoretical formulations, and complicated procedures. To this end, an incident angle estimation method using dam vibration response data and a machine learning algorithm is presented in this study. First, a three-dimensional finite element gravity dam-foundation system model is constructed. A wave input method based on the viscous-spring artificial boundary is used to simulate the multi-angle incidence of P and SV waves. The vibration responses of key dam points are obtained. Nine features that have geometric interpretation are constructed by the response data and the new data are substituted into a stacking ensemble algorithm for training. Finally, the angles of obliquely incident P and SV waves are estimated using the trained stacking ensemble estimation model. The results reveal correlation between dam responses and the incident angle with the average R2 values of the estimation model of 0.996 (P waves) and 0.996 (SV waves), and the average root mean square errors of 1.765° (P waves) and 0.546° (SV waves). It is thus confirmed that the estimation model integrated multiple features from several measurement points with high accuracy and stability. In addition, the proposed method can be extended to other types of large structures because of its universality.

Simulated seismic response analysis of subway tunnels under complex geological conditions of obliquely incident seismic SV waves

To investigate the seismic performance of simulated subway tunnels under complex geological conditions of obliquely incident earthquake excitations, a new input method for oblique incidence of SV waves with arbitrary incident angles in 3D space has been proposed. The method relies on explicit finite element method (EFEM) and viscous-spring artificial boundary (VSAB) condition, which simultaneously considers soil-structure interaction, surrounding soil characteristics, and seismic wave incident characteristics. It is applied and verified based on the seismic wave theory. The overall numerical model of subway tunnel and soil foundation is then established, and the dynamic response of subway tunnel in soft and hard interbedded soils under oblique incidence of SV waves is systematically analyzed. The obtained simulated results indicate that the dynamic response of each point in subway tunnel is decreased by increasing incident SV wave angle. It is also found that the dynamic responses of the site interbedded by soft and hard soils are significantly higher than that in other points of the site at the same incident angle, indicating that the mentioned zone has weak seismic resistance. In addition, the dynamic response of each point in tunnel structure tends to become closer when the bulk moduli of soft and hard soils are getting close. The displacement and moment of the site interbedded by soft and hard soils are reduced by increasing the thickness of lining structure, therefore improving the seismic resistance of the tunnel. The results of parametric study show that these factors could have significant influences on the seismic responses of tunnel structures during earthquake and should be considered during earthquake-resistant design of subway tunnels under complex geological conditions.

Dynamic Finite Element Analysis of the Interaction of Rubber-Soil Foundation and Structure

A more reasonable method of semi-infinite foundation analysis was realized in this paper through the introduction of viscous-spring artificial boundary to simulate the radiation damping and elastic recovery performance of the foundation. The viscous-spring artificial boundary is realized by Combine14 element in ANSYS finite element software to realize the real dynamic characteristics of complex rubber-soil foundation under dynamic loading. Firstly, the reliability of the method is verified by comparing the method with the example of numerical solution. Finally, the optimal tunnel shape is obtained by combining the rubber-soil foundation with different shapes of tunnels.