Seismic Design Of Underground Structures Research Articles

Response of Semicircular Canyons and Movable Cylindrical Cavities to SH Waves in Anisotropic Half-space Geology

The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. In this paper, we investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wave field in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space medium. Then, combining the free boundary conditions with a Fourier series expansion method we solve for the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency and time domain analysis, we investigate the effects of the relevant parameters on the surface motion| w1|( w), the dynamic stress concentration factor (DSCF) and the displacement amplitude| w2|. The results show that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but can also provide a basis for seismic design of underground structures.

The damage and response of some underground structures by the 2023 February 6 Great Turkish Earthquakes and some considerations

Two successive disastrous earthquakes occurred on February 6, 2023 in the province of Kahramanmaraş of Türkiye. These earthquakes resulted in loss of more than 50.000 lives and several cases of serious damage to various engineering structures. Some roadways and railway and underpass tunnels were also damaged by the earthquakes as a result of heavy shaking as well as faulting. In addition, many rockfalls occurred at the portals of railway and roadway tunnels. The faulting caused quite severe damage at the railway tunnel near Ozan village. The concrete lining of the new Erkenek tunnels ruptured at several places. The damage in the new Erkenek twin tunnels may be related to mass movements caused by heavy ground shaking as well as an inclined geological structure together with low overburden next to a valley. Sinkholes of man-made and natural cavities occurred in several locations including urbanized areas. In this study, the authors describe the damage to underground structures by the doublet Kahramanmaraş earthquakes with some detailed analyses of Erkenek tunnels. Furthermore, the causes of the damages are described and their implications on the seismic design of underground structures are discussed. The observations indicated that underground openings crossing by faults and fracture zones may be enlarged to accommodate relative slips along faults and fracture zones. Furthermore, the ductility of support should be high in such zones in order to prevent brittle failure, which may have very disastrous effects. In addition to man-made underground structures, natural underground rock structures may be damaged or sinkholes may be caused by earthquakes as observed in the 2023 Kahramanmaraş earthquakes. The computational results clearly explain why the valley-side of one of the tunnels was more damaged compared to that of the mountain-side tunnel. It is also noted that some of the sinkholes in the earthquake region can be explained using some techniques available in literature.

Estimation of soil displacement profile for seismic design of underground structures in shallow soil

Estimation of soil displacement profile for seismic design of underground structures in shallow soil

Shaking table test for subway station considering the influence of diaphragm walls

AbstractUnderground diaphragm walls are commonly used as a support system for the construction of subway stations, working together with inner side walls of subway stations to withstand the pressure from surrounding soils. However, the effect of diaphragm walls on the seismic response of subway stations is still not well understood yet, or at least not well considered during design. In this paper, a series of 1 g shaking table tests is designed to investigate the seismic response of a typical two‐story and three‐span subway station considering the influence of underground diaphragm walls. The stratum is simulated by synthetic model soil (a mixture of sand and sawdust), and the model structure and diaphragm walls are made by granular concrete with galvanized steel wires. A test case of the structure without diaphragm walls is also involved and taken as a benchmark comparison to understand the impact of diaphragm walls on the seismic response of subway station. The seismic excitations for the test include actual seismic records with the amplitude of 0.2, 0.4, and 0.8 g, respectively. Based on the test data analysis, a comprehensive discussion is conducted on the influence of diaphragm walls on the seismic design of underground structures. Current misconceptions that ignoring the role of diaphragm walls is a conservative way in seismic design of underground structures are also reviewed. Results show that the presence of underground diaphragm walls would enhance the lateral stiffness of the structure, and thus significantly reduce the lateral deformation of subway stations during earthquakes. Notably, the structure with diaphragm walls also exhibits a significant amplification in acceleration response and experiences greater dynamic earth pressures on the sidewalls, and furthermore the strains at the connection between the sidewalls and diaphragm walls are dramatically amplified during the earthquake. It is worth noting that these adverse effects of the diaphragm walls on the amplification of dynamic earth pressures on the structure as well as the increase of internal forces at the sidewalls end‐diaphragm walls connection should be carefully considered in the seismic design of underground structures.

Numerical analysis on the seismic performance of subway station reinforced by ECC-BFRP

In areas with high seismic activity, enhancing the seismic performance of subway station structures is of paramount importance. This paper presents a novel approach involving the application of an ECC-BFRP (Engineered Cementitious Composite with Basalt Fiber Reinforced Polymer) composite layer to reinforce central columns of subway stations situated in loess site. To evaluate the effectiveness of this reinforcement method, a three-dimensional finite element model of subway station structure, accounting for soil-structure interaction (SSI) effects, was meticulously developed using the finite element software Abaqus. The seismic responses of the subway stations with various reinforcement scenarios such as reinforced by the cement mortar, ECC, Mortar-BFRP and ECC-BFRP layer were respectively analyzed in comparison to the unreinforced station. Both the structural displacement response and the changing pattern of damage development for the overall and local structural members were obtained. The results indicated that the ECC-BFRP composite layer could effectively improve the stiffness of the central column and reduce the seismic response of the station. Meanwhile, the seismic damage of the central column was significantly reduced, and the seismic damage distribution of other structural members was uniformly distributed. Consequently, the seismic performance of the station was effectively improved. The research results provided valuable guidance for the seismic design of underground structures.

Seismic fragility analysis of subway station structure subjected to sequence-type ground motions

As a critical urban infrastructure, the subway station damaged in an earthquake not only leads to interruption of underground transportation, but may also result in serious casualties and economic losses. The current seismic design of underground structures only considers the mainshock effects but ignores the potential hazards of aftershocks. However, most mainshocks are often followed by aftershocks in a short period of time. In the past earthquakes, it was reported that the mainshock-damaged engineering structures suffered more serious structural damage and even complete collapse when subjected to aftershocks before restoration. This paper proposes a framework for the development of seismic fragility curves of underground structures subjected to sequence-type ground motions. Finite element models of a two-story, three-span subway station considering nonlinear dynamic soil-structure interaction (SSI) was established in this study. A comprehensive assessment of the seismic performance of the subway station structure under the sequence-type ground motions was conducted on the SSI model. Both the mainshock-aftershock fragility analysis of the intact structure and the aftershock fragility analysis of the mainshock-damaged structures were performed by combining the traditional seismic probability demand model and the back-to-back mainshock-aftershock probability demand model. The numerical results indicated that the impact of aftershocks on the seismic performance of subway station structures cannot be ignored. The aftershock fragility of the structure is highly dependent on the mainshock-damaged state. The failure probability of a severely mainshock-damaged subway station structure is much higher in the aftershocks than structures in other damage states. Besides, the probability of the mainshock-damaged structure transferring to a more severe level of damage state increases with the increase of the intensity of aftershock motions. For the subway station under sequence-type ground motions, the transition probability of one severer level of damage state is greater than 40 % for the 1.0 g peak ground acceleration of aftershocks and the transition probability of more than two severer level of damage state is less than 10 %.

Research on seismic fragility of subway station based on incremental dynamic analysis method

Seismic intensity measure is an significant parameter that affects the accuracy of structural seismic risk assessment, and plays an important role in the performance-based earthquake engineering research framework. Taking a two story, three span, and shallow buried subway station as the research object, a two-dimensional finite element analysis model of soil structure underground in a typical engineering site was established using ANSYS. Ten earthquake records were selected from PEER as input, and the structural seismic fragility analysis method based on incremental dynamic analysis (IDA) method was introduced into the subway station structure. The maximum story drift angle was used as the structural damage index, and three typical seismic intensity measures were selected, the exploration is conducted on the seismic intensity measures applicable to shallow buried subway stations and the variation pattern of seismic response of subway stations with increasing seismic amplitude. The seismic fragility curve of shallow buried subway station structures is established to obtain the failure probability of the structure at different seismic intensity levels. The analysis results indicate that for shallow buried subway stations, PGA is the most suitable seismic intensity measure, and the comparison with existing empirical fragility curves shows that the vulnerability analysis method is feasible and can quantitatively provide the failure probability of structures at different performance levels, providing reference for seismic design of underground structures.

Experimental Investigations of the Seismic Response of a Large Underground Structure at a Soft Loess Site

Based on an underground structure located at a soft loess site in Xi’an as the engineering background, this paper investigated a seismic response and damage model of subway stations at a soft loess site using a large-scale shaking table test, considering the different characteristics of ground motions. The quantitative analysis of the acceleration response and the seismic subsidence of the soft loess site were subjected to different earthquake excitations; based on the experimental results and the corresponding analysis, the development and distribution of seismic structural damage were studied, and the damage mechanism of underground structures in a soft loess area under a strong earthquake was explored. The results indicate that the peak accelerations of the site soil first remained unchanged then increased significantly along the soil height, and the amplification effect of the acceleration response was the most significant at the soil surface. The soft loess soil underwent significant subsidence, and the underground structure was raised compared to both sides of the cover soil; the collapsibility of the soft loess soil was sensitive to strong earthquakes with vertical components. The underground structures in soft loess suffered heavy damage, which rapidly entered the elastic–plastic stage. The composite effect of the collapsibility and vertical seismic excitation impaired the load-carrying capacity of the middle columns, and the strong horizontal seismic excitation enlarged the lateral force and accelerated structural damage development; the underground structure reached failure when plastic damage expended most of the middle columns and structural joints. These results are significant for the seismic design of underground structures in adverse soil conditions.

Anti-planar response due to cylindrical cavity with linear crack under semicircular canyon

Surface depressions and subsurface defects have been a trendy topic in ground shaking problems. In the case of canyon tunnels and canyon pipeline projects, surface movement and cavity edge stress concentrations have been a concern in the design, and the effects of cracks need to be considered if the underground structure contains cracks. In this paper, the wave scattering problem in an elastic half-space medium containing semicircular depression(canyon), cylindrical cavity and crack is investigated by using theoretical methods, the wave function expansion method, the complex function method and the mirror image method to solve the control equation in the form of Helmholtz equation satisfying the zero-stress boundary condition, and the corresponding displacement function is solved. The Green function method and the crack “cutting” technique are used to construct cracks. The unknown coefficients in the system of equations to be determined are solved by free boundary conditions combined with Fourier expansion. The displacement field is a superposition of appropriate wave fields. Finally, the effects of the relevant parameters on ground motion |w| (w), dynamic stress intensity factor (DSIF) of the tip of crack and the dynamic stress concentration factor (DSCF)of the cylindrical cavity were investigated by frequency and time domain analysis. This study not only provides a theoretical basis for practical unlined tunnels or pipeline projects, but also provides a basis for the seismic design of underground structures.

Determination of damage potential of seismic ground motion to underground structures at soft sites through experimental approach

The selection of a ground motion intensity measure (IM) is an essential criterion for judging the expected intensity level of ground motion in the vulnerability analysis of underground structures, and it is also part and parcel of the resilience-based seismic design of underground structures. Most of the current studies are based on a statistical analysis of numerical simulation results to obtain a specific IM measuring the damage potential of ground motions for an underground structure, and there is a lack of mechanistic studies based on experimental ways. In view of this, a series of large-scale shaking-table tests of an underground structure in soft soils were carried out in this paper to explore the appropriate IMs for measuring the damage potential of ground motions. It is found that the response characteristics of the tested soil-structure interaction (SSI) system gradually become similar to the long-period system as the ground motion intensity increases. The transient fundamental frequency of the tested SSI system moves from the acceleration-sensitive band to the velocity-sensitive band in the ground motion response spectrum. This leads to a decrease in the correlation between the response indicators (RIs) of the system and acceleration-based IMs and an increase in the correlation between RIs and velocity-based IMs as well as displacement-based IMs. Based on the test results, the site fundamental period (Tg) and the boundary periods between the sensitive bands in the bedrock response spectrum (Tc and Td) are proposed as identification indexes for selecting the appropriate IM. One of the three measures, PBA, PBV, and PBD, or a composite measure consisting of two of the three, can be adopted as an appropriate IM for an actual underground structure in soft soils in different cases.

Effect of parameters associated with soil-to-structure relative stiffness on seismic fragility curves of subway station

Seismic response and vulnerability of subway station underground structures are greatly influenced by kinematic soil-structure interaction, which is a function of soil properties and stiffness. Therefore, this paper investigates the influence of parameters associated with soil-to-structure relative stiffness (F) on the seismic fragility curves of underground structures. Incremental dynamic analysis method is conducted employing finite element analysis to establish the fragility curves of the station structure considering 44 earthquake records. The soil was simulated as a two-dimensional (2D) finite element domain and its nonlinear behavior is described employing the Davidenkov constitutive model. Appropriate plasticity models simulated the nonlinearity of concrete and reinforcing rebars. It was found that the failure probability of the structure decreases significantly as soil shear wave velocity increases, and the change of probability of structural failure was quantified for changes in shear wave velocity within the range 200 m/s to 600 m/s. It was also found that the failure probability of subway station in heterogeneous soil is significantly higher than that of a structure buried in homogeneous soil. On the other hand, the cross-section type of the structure has less influence on its seismic vulnerability. The seismic performance of the structure with higher F is relatively better, while there are special cases where some structures with high F that are more susceptible to failure under earthquake than structures with lower F. The findings can provide helpful guide for the performance-based seismic design of underground structures.

Seismic fragility analysis for subway station considering varying ground motion ensembles

The seismic fragility analysis involves employing an ensemble of ground motion records to establish the seismic performance. This paper investigates the effect of number of ground motion records in the considered ensemble on the calculated post-earthquake failure probability of subway structure. A two-dimensional (2D) finite element model was established considering the soil-subway station underground structure interaction. The cloud and incremental dynamical analysis (IDA) methods are employed to compute the seismic demand of the structure and the seismic fragility curves considering different ensembles of ground motion records. The results revealed that the number of records have a significant influence on the structure seismic fragility analysis in both cloud and IDA methods. It is suggested that the optimal ensemble size should comprise 300 ground motion records in the cloud-based seismic fragility analysis, and 24 ground motion records in the IDA method. The results also showed that the failure probability of structure predicted by the cloud method is greater than that predicted by the IDA method. These findings provide practical guidance for the performance-based seismic design of underground structures.

Influence of soil to structure stiffness on the accuracy of the pushover method for underground structures

The pushover method for underground structures is a seismic analysis method featured by high calculation accuracy and a simple implementation process. The method has been widely used in seismic design and other related scientific research; however, the influence of different soil-structure flexibility ratios on the accuracy of this method is still not well understood. In this study, we select the cross-section structures beneath the Daikai subway station as the research object and establish 12 finite element analysis models with different soil-structure flexibility ratios using ABAQUS. All models are computed by the dynamic time-history method or the pushover method. Furthermore, the dynamic time-history solution result is taken as the standard solution, and the precision and application of the pushover analysis method are discussed based on the parameters of peak interlayer displacement and peak internal force of the middle column section. The results show that the soil-structure flexibility ratio has a significant influence on the calculation accuracy of the pushover method, and the calculation accuracy of this method is the most ideal when the soil-structure flexibility is equal to 1. The research results can provide significant references for the seismic design of underground structures or the improvement of simplified seismic analysis methods.

Seismic Performance Evaluation of Two-story and Three-span Subway Station in Different Engineering Sites

ABSTRACT This study firstly investigates the seismic intensity measures (IMs) from the existing scalar ones that are suitable for the prediction of seismic response of shallowly buried rectangular underground structures. The peak acceleration and peak velocity at the ground surface are identified as the optimal IMs based on their efficiency, practicality, and proficiency. A series of seismic fragility curves are then developed for a two-story and three-span underground subway station embedded in three different typical engineering sites using nonlinear incremental dynamic analyses. In this study, the input ground motions at the level of engineering bedrock for the underground structure–soil interaction system are obtained through one-dimensional equivalent linear site response analysis according to the one-dimensional wave propagation theory. Comparison of the numerical results in this paper with the previous empirical and numerical fragility curves shows that the fragility analysis method in this paper is feasible, which can quantitatively give the failure probability of structures at different performance levels, and can provide reference for seismic design of underground structures. The numerical results indicate that both the characteristics of ground motions and the site profile have significant influence on the seismic fragility curves of underground structures. Underground subway stations are generally more vulnerable to seismic damage when embedded in engineering sites with lower average shear velocity. Moreover, seismic damage margin ratios are proposed for the underground structure in different site classes to show the confidence levels of its seismic performance when subjected to different levels of earthquake events, and can be used as a preliminary index for the earthquake risk assessment of subway station.

Stochastic Dynamic Response Analysis and Probability Evaluation of Subway Station Considering Subjected to Stochastic Earthquake Excitation

As a relatively new means of transportation, the subway has become an important tool for the sustainable development of many cities. Being buried deep in soil under the weight of vital infrastructure, subway stations can be vulnerable to seismic excitations. Considering the high randomness of ground motions, it is important to research the failure probability and seismic performance of the subway station based on stochastic dynamic analysis. In this paper, a probability density evolution method (PDEM) coupled with a spectral representation random function is used to analyze the stochastic dynamic response and seismic probability of a subway station. First, according to the improved power spectral density model and the seismic design code of urban rail transit structures in China (GB 50909-2014), a set of nonstationary ground motions consistent with the code spectrum are obtained. Then, a great deal of deterministic dynamic calculations for Daikai subway station considering soil–structure interaction based on elastic–plastic methods are performed. In addition, the nonlinear stochastic response analysis and the dynamic probability analysis are obtained for the subway station by solving the PDEM equation. Finally, the probability density function (PDF) and cumulative distribution function (CDF) of the subway station under stochastic earthquake excitations are obtained based on three performance indices, including drift angle in the middle column, relative vertical displacement between floor and roof, and damage area ratio (DAR). The results show that the stochastic dynamic analysis and the probability density evolution method can analyze seismic response and evaluate seismic performance of subway stations effectively. The proposed method will serve as an effective tool for the seismic design 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.

Improved pushover method for seismic analysis of shallow buried underground rectangular frame structure

Simplified methods are widely used in the seismic design of underground structures, but they generally ignore the influence of vertical ground motion. This can result in unreliable design because seismic earth pressure induced by vertical ground motion can have a significant adverse effect on their seismic performance. Therefore, this paper proposes an improved pushover analysis method (I-PAM) that applies distributed horizontal and vertical inertial forces to simulate the mechanical behavior of underground structures under both horizontal and vertical ground motions. The profile of load distribution and target displacement is calculated from corresponding site response analysis. A rigorous time-history dynamic analysis method (TDAM) based on the finite element numerical analysis was employed in three case studies to evaluate the performance of the developed I-PAM. The results showed that the I-PAM can accurately predict the structure's peak axial force, bending moment and displacement under the combined action of horizontal and vertical ground motions, especially for lower ground motion intensity. It was also found that the responses of the center column and middle slap were calculated with higher accuracy compared to that of the components in direct contact with soil including sidewalls and top and bottom slabs. The developed I-PAM offers a framework for further development and enhancement of simplified analysis methods for seismic design of underground structures.

Interstory drift ratio associated with performance objectives for shallow‐buried multistory and span subway stations in inhomogeneous soil profiles

AbstractThe interstory drift ratios (IDRs) associated with the performance objectives for the underground structure are not well defined. In this paper, four levels of performance objectives are defined for shallow‐buried subway station structure: operational, immediate occupancy, life safety, and collapse prevention. In order to develop IDRs corresponding to these performance objectives, 18 subway station structures were selected for this study. Pushover analyses were conducted using three‐dimensional finite‐element models considering two conditions of seismic loading: vertical and horizontal ground motions; and horizontal ground motion only. Shear‐displacement capacity curves of the 18 subway station structures were obtained, and IDR limits were defined for each structure based on the relationship between the capacity curves and performance objective. Statistical analysis of the results demonstrated that the IDR limits considering the vertical ground motion (characterized by the same frequency with horizontal component) are smaller than that without consideration of the vertical ground motion. Based on these results, the IDR limit of 0.05%, 0.21%, 0.46%, and 0.72% is assigned for the four performance levels, respectively, for rectangular frame underground structures. The performance evaluation applied to Daikai station based on the proposed limits is found to be consistent with the actual postearthquake damage observations. The proposed limits of IDR could provide some guidance to the seismic design of underground structures, and could form the basis for developing appropriate performance limits for seismic provisions in design codes relevant to underground structures.

Laboratory Tests for Subgrade Reaction Coefficient in Seismic Design of Underground Engineering Domain

Subgrade reaction coefficient is commonly considered as the primary challenge in simplified seismic design of underground structures. Carrying out test is the most reliable way to acquire this intrinsic soil property. Owing to the limitations of experimental cost, time consumption, soil deformation mode, size effect, and confined condition, the existing testing methods cannot satisfy the requirements of high-precision subgrade reaction coefficient in seismic design process of underground structures. Accordingly, the present study makes an attempt to provide new laboratory testing methods considering realistic seismic response of soil, based on shaking table test and quasistatic test. Conventional shaking table test for sandy free-field was performed, with the results indicating that the equivalent normal subgrade reaction coefficients derived from the experimental hysteretic curves are reasonable and verifying the deformation mode under seismic excitation. A novel multifunctional quasistatic pushover device was invented, which can simulate the most unfavorable deformation mode of soil during the earthquake. In addition, the first successful application of an innovative quasistatic testing method in evaluating subgrade reaction coefficient was reported. The findings of this study provide preliminary detailed insights into subgrade reaction coefficient evaluation which can benefit seismic design of underground structures.

Response spectrum method for seismic soil–structure interaction analysis of underground structure

The response spectrum method (RSM) has been incorporated into many codes for seismic design of aboveground structures since 1950s. However, no RSM is presented in details for the seismic design of underground structures due to the complexity of seismic soil–structure interaction (SSI). In this paper, the RSM is developed for the seismic analysis of the underground structures including SSI. First, the underground design response spectrum is derived using two different procedures from the ground design response spectrum that is commonly available in most seismic design codes. Second, the SSI analysis model consisting of the underground structure and its adjacent soil is established with the roller side boundaries and the bottom boundary subjected to the underground response spectrum. Third, the RSM is applied to the SSI analysis model to estimate the structural response under the underground response spectrum. Finally, the numerical examples are presented to demonstrate the feasibility of the RSM for the SSI analysis model of underground structure.