Seismic Response Of Underground Structures Research Articles

Longitudinal seismic analysis for underground structures passing through soft-hard strata based on periodic stratum deformation

Poor geological conditions, e.g., soft and hard strata, have a significant impact on the seismic response of underground structures. In this study, a series of longitudinal seismic analysis for underground structures passing through soft-hard strata were conducted based on the concept of periodic stratum deformation. Firstly, the analytical expressions of stratum deformation in soft-hard strata at the oblique incidence of plan P-, and S- wave were obtained via decomposing the stratum deformation into the reflected- and transmitted wave fields. Then, the wave propagation history in soft-hard strata in the time domain was transformed into strata deformation in a period via introducing concept of the periodic stratum deformation. Base on the proposed expressions, a self-developed Python program was implemented into finite element software ABAQUS to establish seismic analysis model and to calculate the longitudinal seismic response of underground structures. Finally, example analyses were conducted to study the influence of plane P- and S- wave, wave velocity ratio of soft and hard media, as well as incident wave angle on the seismic response of underground structures located in soft- hard strata. This study may provide a reference for seismic design of underground structures located in soft- hard strata.

Response spectrum-based intensity measure for underground structures

The purpose of this study is to present a novel approach to constructing intensity measures (IMs) for underground structures using seismic response spectrums. The proposed IM takes the form of an integral of the product of the response spectrum and an arbitrary function that reflects the relative importance of each range of period to the seismic response of underground structures. To obtain the arbitrary function, an artificial neural network (ANN) technique is employed. To demonstrate the effectiveness of this method, we develop two different soil-subway station dynamic systems, referred to as Case I and Case II. Based on both cases, the probabilistic seismic demand model (PSDM) for the proposed IM and eight existing IMs are developed. The performance of the proposed IM is compared with that of the existing IMs in terms of their proficiency, practicality, and efficiency, as well as their ability to describe the probabilistic distribution of damage measure (DM). The results indicate that the proposed IM outperforms the existing IMs since it has the highest proficiency for both cases. Moreover, the fragility curves calculated using the proposed IM are more effective than those calculated using traditional IMs, with narrower uncertainty ranges, which can help reduce the uncertainty in evaluating seismic risk. Comparing the function solved by the ANN with the seismic response of subway stations under different periods of harmonic excitation, it can be found that the solved function and the seismic response reach their peak points at the same period. This finding suggests that the proposed IM can account for the interaction between the surrounding soil and underground structures, as well as the softening of soil layers during earthquakes, making it a suitable IM for underground structures.

A three-dimensional numerical simulation method for seismic nonlinear response of underground structure in liquefiable site and analysis of structural damage

Considering the effect of dynamic interaction between liquefiable soil and underground structure, simulating the nonlinear seismic response of underground structures through simple, convenient, and reliable 3D numerical model is still a great challenge at present. A three-dimensional numerical simulation method for dynamic response of underground structure in liquefiable site is proposed based on the centrifuge shaking table test designed for a subway station buried in liquefiable interlayer site carried out in the previous period. The numerical model takes into account the characteristics of sand prone to large deformation after liquefaction and the nonlinear characteristics of the contact between saturated soil and structure. The typical numerical calculation results are compared with the experimental results to verify the correctness of the numerical model, and the extended analysis of the structural damage is carried out, which visually shows the damage distribution of structure under different functional states after earthquake. The analysis of structural damage shows that the junction position of middle column and longitudinal beam is more prone to tensile damage under the horizontal earthquake action; while after considering the horizontal-vertical seismic effect, the middle column will produce additional compressive damage due to the vertical inertia force, and the end of middle column should be paid attention to in seismic design.

Effective-mode superposition response spectrum method for three dimensional seismic response analysis of underground structures

Response spectrum method (RSM) has been applied in seismic analysis of underground structures. However, the RSM is computationally low efficient for processing large soil domains. In this paper, the dynamic characteristics of underground structures are first investigated through three rectangular subway station structures. The results show that only a small number of effective frequencies and modes of soil-structure interaction (SSI) system significantly affect the seismic response of underground structure. These effective frequencies and modes are related to the natural vibration characteristics of site. An effective method is then developed to obtain the effective natural frequencies and modes of the SSI system. Subsequently, the effective modal superposition response spectrum method (ERSM) for seismic analysis of underground structure is developed by only combining the effective natural frequencies and modes of the SSI system to improve efficiency. Finally, the accuracy of ERSM is investigated through seismic response analysis of subway station structures. Numerical examples show that the ERSM can be used for seismic analysis of underground structures considering 3D SSI.

Quasi-static model test and numerical simulation of a single-story double-span underground subway station

The model test method is crucial for studying the seismic performance of underground structures. Presently, model tests for the seismic response of underground structures are primarily performed with 1-g and N-g centrifuge shaking table. The 1-g shaking table model test is limited by the stress similarity in the soil-structure interaction system and cannot reproduce the seismic damage process and extent of the underground structure. The small table size of the N-g centrifuge model test makes it difficult to reflect the spatial effects of the seismic response of large underground structures. Seeking a large-scale model test method that can directly simulate the seismic damage process is essential for investigating the seismic performance of underground structures. Herein, based on the seismic response characteristics of underground structures, a quasi-static pushover test device applicable to underground structures was designed, and the corresponding tests and numerical model calculations were executed using the Daikai subway station as a prototype. Based on the macroscopic phenomena of structural damage development of the subway station in the test, the damage mechanism of the station structure was analyzed and compared with the numerical model. The strain amplitudes, displacements, and digital scatter strain color maps were analyzed to verify the reliability of the cyclic pushover loading test simulating the seismic performance level and damage process of the underground structure. Simultaneously, the rationality of the proposed quantification system for classifying the seismic performance level of single-story underground structures was verified.

Seismic response analysis of subway station structure under random excitation based on probability density evolution method

The subway station structure mainly faces the uncertainty of ground motion and surrounding soil mass. Comprehensive analysis of the seismic response of subway station structures under random excitation is the key to ensuring the safety of urban people's lives and property. In this paper, the random shear wave velocity profile model and the random ground motion model characterizing uncertainty are established. Using a high-dimensional space optimization point selection strategy significantly reduces the number of sample points and computational costs of nonlinear time history analysis (NLTHA). Combining the probability density evolution method (PDEM) with finite element analysis, the stochastic seismic response analysis of the subway station structure under dual random excitations is realized. In addition, statistical methods are used to analyze the distribution characteristics of the most unfavorable seismic responses of the subway station structure. The research results show that when random excitation is not considered, the adverse seismic damage risk of subway station structures will be ignored. The evolution of the seismic dynamic response of subway station structures is mainly controlled by the amplitude of random ground motion acceleration. Additional random shear wave velocities can increase the lateral deformation range of the subway station structure, leading to a decrease in the dynamic reliability of the structure. PDEM can conduct stochastic seismic response analysis of the subway station structure from both time and response dimensions. The proposed method provides strong support for a comprehensive analysis of the seismic response of underground structures.

Prediction of nonlinear seismic response of underground structures in single- and multi-layered soil profiles using a deep gated recurrent network

A deep learning method consisting of the gated recurrent (GRU) neural network is proposed to predict the seismic responses of underground structures in single-layered soil and multi-layered soil. The proposed neural network employed ground motion as the input, and the acceleration time history of underground structure acquired by a finite element method (FEM) to be the output. The distribution of the normalized errors and the error of the peak value of the predicted acceleration time history are adopted to evaluate the prediction performance and extrapolating ability of the proposed GRU architecture. The GRU network showed better prediction performance in the seismic response of a tunnel in a homogeneous sand layer than in a clay layer, as sand has a higher shear modulus representing lower nonlinearity of the soil-structure system. The peak acceleration of a two-story three-span subway station in multi-layered soil exhibited similar prediction accuracy to the tunnel in single-layered clay. The proposed GRU neural network generally displayed satisfactory prediction performances on the acceleration responses of underground structures in various soil conditions.

Numerical analysis on the seismic performance of subway station in ground crack area

The site soil with ground cracks would cause strong motion and large deformation under major earthquakes, which brings a serious threat to underground structures. However, the ground crack effect on the seismic response of underground structures was unclear. This study developed a series of numerical analyses to study the seismic performance and damage mechanism of a rectangular-section subway station located in a ground crack area. After verification of the developed model, the structural responses of the subway stations in different sites subject to different earthquakes were evaluated in terms of acceleration response, inter-story drift, and damage pattern. Furthermore, a parameter analysis was performed to address the effects of structural position in the site, structural overburden depth and dynamic shear modulus of soils on the seismic performance of the subway station in the ground crack area. The results showed that the presence of ground crack exacerbated the shear deformation of the site soil and increased the internal forces of the lateral members, resulting in substantial damage to the subway station. The subway station in the ground crack area had poorer seismic performance than the station in the uncracked area, especially for station crossing the ground crack. Particularly, the ground crack effect on the seismic performance of subway stations should be carefully considered in the design of shallow-buried underground structures in soft soils.

Study on the effect of burial depth on seismic response and seismic intensity measure of underground structures

Considering the complexity of the soil-structure dynamic interaction mechanism, underground structures are restrained and influenced by the surrounding soil in earthquakes, and their seismic damage under strong earthquakes is different from that of above-ground structures. The seismic response of underground structures is influenced by several coupling factors, including structural form, ground motion parameters, and soil properties, etc. In addition, the burial depth of the underground structure is also one of the critical parameters affecting its seismic response. In this study, the computational model of soil-structure dynamic interaction at different burial depths was established by using the finite element software ABAQUS with a single-story, double-span Daikai subway station as the prototype. The influence laws of different burial depth conditions on the seismic response characteristics such as inter-story drift ratio, internal force of critical sections, and seismic damage of subway stations are systematically studied. Meanwhile, this paper compares the correlation and applicability of PGA (peak ground acceleration), PSSRD (peak site soil relative displacement), and SSSRD (structural side soil relative displacement) with the seismic response of underground structures under different burial depths by applying the principle of vulnerability analysis. The results show that PGA and SSSRD are relatively better IMs (intensity measure) in shallowly buried structures, while the relative superiority of PSSRD gradually increases with increasing burial depth, and PSSRD is a more reasonable IM in deeply buried underground structures.

Numerical Analysis on Seismic Responses of a Large Metro Station in Sandy Area

A new assessment method is proposed considering shortcomings of the current investigations for the assessment of underground structures considering seismic load. First, the dynamic elastic modulus and damping ratio of sand are studied based on the dynamic characteristic experiment of the soil. Subsequently, a series of design acceleration time history curves are obtained using the proposed methods. Finally, the seismic response of underground structures is evaluated by a three-dimensional numerical simulation. The results indicate that the dynamic elastic modulus of sand decreases with the increase of dynamic elastic strain and increases with the increase of confining pressure. The influence of confining pressure on the damping ratio of sand is slight, but it can still be seen that the damping ratio decreases with the increase of confining pressure, especially when the dynamic elastic strain is relatively low. The interlayer displacement between the top and middle plate is 2.1 mm and the interlayer displacement angle is 1/2650. The interlayer displacement between the middle and bottom plate is 1.7 mm and the interlayer displacement angle is 1/4117. Under the action of fortification earthquake, the interlayer displacement angles of Taiyuan Street station are less than 1/550, indicating that the structure meets the seismic requirements.

Seismic performance analysis of underground structures based on random field model of soil mechanical parameters

Soils with spatial variability are the product of natural history. The mechanical properties tested by soil samples from boreholes in the same soil layer may be different. Underground structure service in surrounding soils, their seismic response is controlled by the deformation of the surrounding soils. The variability of soil mechanical parameters was not considered in the current research on the seismic response of underground structures. Therefore, a random field model was established to describe the spatial variability of surrounding soils based on the random field theory. Then the seismic response of underground structures in the random field was simulated based on the time-domain explicit global FEM analysis, and the soil mechanical parameters and earthquake intensity influencing the seismic response of surrounding soils and underground structures were studied. Numerical results presented that, the randomness of soil parameters does not change the plastic deformation mode of surrounding soils significantly. The variation coefficients of inter-story deformation of structures and lateral deformation of columns are much smaller than that of mechanical parameters, and the randomness of soil parameters has no obvious effect on the structural deformation response.

Seismic Sources in Stress‐Induced Anisotropic Media

Rocks in the upper mantle are extensively subjected to initial stress. The rock exhibits elastic anisotropy under the deviatoric stress, which affects the seismic response of underground structures. This paper aims to study the effect of stress-induced anisotropy on the seismic source. The seismic moment tensor generated by a shear faulting in a homogeneous isotropic medium with initial stress is derived by using the motion description in the intermediate configuration, the constitutive relation of third-order elasticity, and the boundary condition considering the effect of initial stress. Then the seismic moment tensor is decomposed to investigate seismic source characters quantitatively. Our results show that shear faulting in a stress-induced anisotropic medium can produce significant non-double-couple (non-DC) mechanisms, including compensated linear vector dipole (CLVD) and isotropic (ISO) components. ISO and CLVD components vary linearly with the initial shear stress on faults. In addition, stress-induced anisotropy causes the double-couple (DC) to deviate from the plane defined by the fault normal and slip direction. The initial stress not only affects the source intensity but also affects the propagation of seismic waves. The radiation patterns of longitudinal waves have non-uniform lobes, which shows the characteristic of anisotropy. Stress-induced anisotropic parameters are smaller than intrinsic anisotropy at high-stress levels and a nearly linear function of the increased initial stress. These results underscore the importance of considering stress-induced anisotropy in the inversion of focal mechanisms and provide a new perspective for monitoring underground stress.

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.

Influence of vertical ground motion on the seismic response of underground structures and underground-aboveground structure systems in liquefiable ground

Vertical ground motion components are often observed during earthquakes, which could affect the seismic performance of underground structures. This study investigates the influence of vertical ground motion on the seismic response of underground structures and underground-aboveground structure systems (UASS) in liquefiable ground. Both centrifuge shaking table tests and numerical simulations are conducted. The centrifuge shaking table tests provide basic insights into the seismic response of underground structures under simultaneous horizontal and vertical shaking, and also serve to validate the numerical simulation method. Numerical simulations are conducted using solid–fluid coupled FEM with a constitutive model for soil liquefaction analysis. The analysis results show that although the influence of vertical ground motion on the shearing related motions and internal forces of underground structures is limited, its influence on the axial force of the structure is significant, especially for the center column. The inertia effect of the aboveground structure in UASS can amplify the influence of vertical ground motion via structure-soil-structure interaction. For UASS, the horizontal and vertical relative positions of the aboveground structure and the underground structure also affect the influence of vertical ground motion.

Analysis of Shaking Table Tests of Underground Structures considering the Influence of the Structure-Soil Interface

To investigate the seismic performance of underground structures under the action of the structure-soil interface, in this study, experiments were performed using plexiglass structures (two pieces) and a concrete structure (one piece) as the research objects. The surface of one plexiglass structure was prepainted with a layer of cement mortar as the contact surface between the structure and soil, and the other plexiglass structure was not treated and used for comparison. A rigid model box measuring 2.25 m × 2.25 m × 1.5 m was placed on a 3 m × 3 m shaking table, and the box was filled with the configured model soil and the underground structure prepared in advance. Input transverse uniform excitation was imparted to the whole system. A shaking table model test was performed on the underground structures to analyse the acceleration response, stress strain, and earth pressure changes in the underground structure, and the influence of the contact surface on the seismic dynamics of the underground structure was evaluated. The test results showed that under uniform excitation, the dynamic characteristics of the underground structures were greatly affected by the intensity and depth of the seismic waves. (1) When the soil-structure contact was considered, the stress and strain of the structures increased significantly, and the stress-strain value was significantly greater than the stress-strain value of the soil-structure interface in a fully bonded state. (2) There were inconsistencies between the acceleration peak curve of the plexiglass structure considering the contact effect and the acceleration peak curve of the plexiglass structure without considering the contact effect. The difference between the two lies mainly in the corresponding maximum peak acceleration and the Fourier spectrum amplitude. With respect to the value and frequency composition, regardless of whether the input acceleration intensity was 0.2 g or 0.5 g, the peak acceleration of the organic structure was greater when the contact surface effect was considered than without the contact surface effect. Therefore, the structure-soil interface needs to be considered in actual engineering. The presence of the contact surface improves the safety of the structure and is helpful for seismic design. The results of this study provide a basis for further research on the influence of soil-pipe contact on the seismic response of underground structures.

“Research on the Seismic Response and Analysis Method of Underground Structures Based on the Response Deformation Method”

In order to study the underground structure under the action of an earthquake, the relationship between the displacement and the stress between layers of different soils under the action of the earthquake was carried out through the finite element numerical analysis software. The influencing mechanism of soil layer depth on the seismic response of underground structure was discussed, and the seismic response law of the system was worked out. The research results indicated that the displacement response of the soil layer structure in three directions depicted obvious laws with the change of soil layer depth. There were evident similarities and differences in the response of soils with different properties to seismic responses. These conclusions provided a certain reference for the seismic design of underground structures.

Effect of nearby ground structures on the seismic response of underground structures in saturated sand

With the development of urbanization, underground structures unavoidably come within the vicinity of ground surface structures, and interaction between ground structure, soil, and underground structure interaction can significantly affect the seismic response of underground structures. Three-dimensional high-fidelity numerical dynamic analysis is conducted to investigate underground structures' seismic response in saturated sand with and without a ground structure. In the numerical analysis, saturated sand is simulated using a plasticity constitutive model for large post-liquefaction deformation of sand. The numerical analysis method is first validated based on a centrifuge shaking table test for a ground structure-underground structure system in liquefiable sand, and then applied to reveal the influence of ground structures on nearby underground structure seismic behavior. Results show that nearby ground structures significantly affect the underground structure's seismic response in saturated sand. A ground structure directly above an underground structure can amplify the underground structure's dynamic internal forces and restrict its uplift, whereas a ground structure to the side can amplify the underground structure's deformation and cause rotation. Factors including relative structure positions, ground structure characteristics, and ground motion properties influence the ground structure's effects on the underground structure's seismic response.

Evaluation of various seismic response analysis methods for underground structures in saturated sand

Underground structures in liquefiable saturated sand are prone to earthquake damage. Various simplified pseudo-static seismic response analysis methods for underground structures have been recommended by current design codes and guidelines, but lack adequate systematic validation in liquefiable ground. In this study, the effectiveness of four categories of simplified pseudo-static methods in saturated sand are evaluated. These methods include a displacement-based method, a force-based method, a F(flexibility ratio)-R(racking ratio) method, and a detailed equivalent static method. High-fidelity dynamic analysis of circular and rectangular cross-section underground structures in non-liquefiable and liquefiable ground under different input ground motions are conducted, using a validated plasticity constitutive model for large post-liquefaction deformation of sand, to serve as a basis for the evaluation. Although the pseudo-static methods can generally provide adequate analysis results for underground structures in non-liquefiable ground, especially the displacement-based method, their performance in saturated sand are generally poor. The deviation of pseudo-static analysis results from reality stems from their inadequacies in considering the effects of dynamic soil-structure interaction in liquefiable ground. Temporal and spatial variability of soil-structure interaction in saturated sand, caused by the accumulation of excess pore pressure and subsequent decrease in soil effective stress and constraint on underground structures, are not considered in pseudo-static analysis methods. Modifications to the pseudo-static analysis methods and high-fidelity dynamic analysis methods are suggested to be adopted for the evaluation of the seismic response of underground structures in liquefiable ground.

Shaking table tests on the seismic responses of underground structures in coral sand

To reveal the seismic response of underground structures in coral sand, a series of shaking table model tests on underground structures at four different groundwater levels were carried out. The seismic responses of the coral sand and the underground structure were obtained and analyzed. The results showed that the excess pore pressure ratio and the liquefaction degree of coral sand increased with increasing groundwater level, resulting in a more significant separation between the sidewall and the surrounding soil. However, the acceleration amplification factor of the coral sand site, the dynamic strain and bending moment of the underground structure could be reduced. Moreover, the increase in the groundwater level contributed to the settlement of the ground surface. However, due to the presence of an uplift force caused by the liquefaction of the coral sand, the settlement of the underground structure decreased as the groundwater level increased. Furthermore, the distribution of the dynamic soil pressure under the groundwater level was found to be quite different from that under dry soil condition.

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.