Selecting the severest seismic design ground motions for cut-and-cover underground structures

Abstract

This paper proposes an innovative method for selecting the severest design ground motions based on overall damage characterization of underground structures. The selection procedure is elaborated using 4749 ground motions, exemplifying various forms of underground structures in class III sites. Initially, an overall damage index, predicated on dual-parameters of deformation and hysteretic energy dissipation, is proposed as an engineering demand parameter to quantitatively depict the failure state of underground structures. Subsequently, given the inadequacy of a single intensity measure in evaluating the damage of underground structures, composite intensity measures with higher correlation to the index are constructed using partial least squares regression method. The composite intensity measures served as the damage potential characterization parameter for ground motions concerning underground structures. Consequently, alternative databases of severest design ground motions are derived through these composite intensity measures. The ground motions in this alternative database are employed as inputs for nonlinear dynamic analysis of underground structures. The severest design ground motions are identified by ranking the overall damage index to underground structures. Finally, a comparison with traditional selecting method demonstrates that the proposed method yields more accurate results.

Headnote

Abstract

This paper proposes an innovative method for selecting the severest design ground motions based on overall damage characterization of underground structures. The selection procedure is elaborated using 4749 ground motions, exemplifying various forms of underground structures in class III sites. Initially, an overall damage index, predicated on dual-parameters of deformation and hysteretic energy dissipation, is proposed as an engineering demand parameter to quantitatively depict the failure state of underground structures. Subsequently, given the inadequacy of a single intensity measure in evaluating the damage of underground structures, composite intensity measures with higher correlation to the index are constructed using partial least squares regression method. The composite intensity measures served as the damage potential characterization parameter for ground motions concerning underground structures. Consequently, alternative databases of severest design ground motions are derived through these composite intensity measures. The ground motions in this alternative database are employed as inputs for nonlinear dynamic analysis of underground structures. The severest design ground motions are identified by ranking the overall damage index to underground structures. Finally, a comparison with traditional selecting method demonstrates that the proposed method yields more accurate results.

Keywords: Underground structures; Severest seismic design ground motions; Overall damage index; Composite intensity measures; Damage potential; Partial least squares regression

(ProQuest: ... denotes formulae omitted.)

1 Introduction

Several major earthquakes have occurred near large cities over the past few decades, such as the Hanshin earthquake in Japan and the Chi-Chi earthquake in Taiwan, China. These earthqua kes have caused massive casualties and economic losses for human society, as well as extensive damages to underground structures (Wang et al., 2001; Hashash et al., 2001; Parra-Montesinos et al., 2006). Therefore, the seismic design of underground structures has become increa singly important. Especially for critical underground structures, it is essential to ensure that they can withstand the severest earthquakes that may occur during their design service life. However, different input ground motions, even at the same level of intensity, can induce varying seismic responses in underground structures. This requires that the ground motion which put such underground structures in the most unfavorable state should be selected as input in seismic design. The seismic responses of structures are usually expressed in terms of engineering demand parameter (EDP). Nevertheless, it is not clear how to obtain such ground motions.

Regarding this type of issue, as early as 2004, Zhai and Xie (2004) have proposed the concept of severest design ground motion (SDGM), and the comprehensive method for estimating damage potential of ground motions was used in selecting the SDGM of ground frame structures. Herein, the damage potential refers to the potential ability of ground motion to cause damage and destruction to engineering structures. The study of the SDGM can offer a valuable reference for selecting input ground motions in seismic design of related engineering structures and can also provide a nov el approach to studying the damage mechanisms of ground motions on those structures. In recent years, research on this topic has continued across various engineering disciplines, including but not limited to nuclear power stations (Li et al., 2019) and ground frame structures (Hu et al., 2021; Lai et al., 2022).

As for underground structures, the current seismic code of Standard for seismic design of underground struc tures (GB/T 51336-2018, MOHURD & SAMR, 2018) in China explicitly stipulates that supplementary computation of dynamic time-history analysis should be performed for impor tant underground structures, and the input ground motion must contain the real and artificial ground motions. However, the code does not provide any specific input real ground motions or effective selected criteria. Therefore, the input ground motions of seismic design of underground structures need to be determined through special studies, such as the research of SDGM. Nevertheless, most existing studies on the SDGM have focused on aboveground structures. Only a few literature sources have addressed underground structure (Chen et al., 2023), without considering the effects of different site conditions and underground structural forms. Due to the unique surroundings and complex soil-structure system mechanisms of underground structures, their seismic dynamic responses are different from those of aboveground frame structures. While the seismic dynamic responses of aboveground frame structures, which are strongly related to the natural vibration period of the structure itself, the seismic dynamic responses of underground structures are mainly induced by the deformation and inertial force of the surrounding soil. Therefore, the existing research findings on the SDGM of aboveground structures cannot be directly applied to underground structures.

A method for searching SDGM based on the earthquake-induced overall damage of underground structures is needed. The simplest way to identify the SDGM for underground structures is to perform nonlinear dynamic analyses for each ground motion record in a strong earthquake database and then select the SDGM according to the EDP of underground structures. However, this method is impractical because there are vast number of ground motion records collected by various seismic stations worldwide. Given that the ground motion intensity measures (IMs) are crucial parameters for characterizing the risk and damage potential of input ground motions, the number of ground motion records can be significantly reduced by using reasonable IMs. An alternative database of the SDGM can be then obtained based on these IMs. The reasonable IMs should effectively characterize the damage to underground structures, increa sing the likelihood of incorporating the true SDGM into the alternative database. However, it is unclear which IMs can effectively capture the damage to underground structures.

In recent years, many scholars have conducted studies on the correlation between the EDP of underground structures and IMs. Chen et al. (2013) pointed out that the impulse effect of gro und motions can cause the structural failure of mountain tunnels and can be de scribed by the IM of maximum incremental velocity (MIV). Zhong et al. (2020) found that peak ground acceleration (PGA) and acceleration spectral intensity (ASI) are the best IM for predicting the EDP of a single-storey double-span su bway station structure. Huang et al. (2021) argued that PGA is the optimal IM for shallow tunnels, while peak ground acceleration (PGV ) is the optimal IM for moderat ely deep and deep tunnels. Yang et al. (2023) found that PGA is more suitable for predicting seismic fragility curves of shallow-buried underground structures when the soil stiffness is high, while PGV is recommended when the soil stiffness is low. These studies have yielded valuable insights and suggested specific IMs for certain underground structures. However, due to the strong randomness of ground motions, single IMs will inevitably omit a significant amount of ground motion infor mation and fail to comprehensively capture ground motion characteristics (Ye et al., 2009), which is not conducive to the safe seismic design of engineering structures. To address this issue, T. Liu et al. (2019, 2020) and Sun et al. (2023) constructed some composite IMs for aboveground frame structures and tunnel structures using partial least square (PLS) regression method and demonstrated their effectiveness, practicality, and proficiency. This method of con structing composite IMs has been successfully applied in seismic research on above ground frame structures and tunnel structures, offering a new approach for identifying IMs that can characterize the damage pot ential of ground motions of undergrou nd structures.

In the process of constructing composite IMs for underground structures, it is imperative to select appropriate EDPs that can effectively characterize the failure state of the structure. Currently, the failure index commonly employed for underground structures include driftratio (Zhuang et al., 2019, 2021; Andreot ti & Lai, 2019; Zhong et al., 2020; Qiu et al., 20 23), section bending moment s (Argyroudis & Pitilakis, 2012; Nguyen et al., 20 19), joint displacement, and rotation angles (Qiu et al., 2023) of key components. Among these, the driftratio is extensively utilized in rectangular underground structures. However, followin g a comprehensive examination of both underground and aboveground structures, J. Liu et al. (2019) posited that the driftratio was not suitable for underground frame structures. In fact, the failure of underground structures during an earthquake is caused by the accumulated plastic deformation and damage due to the energy input from the earthquake. Despite the plastic deformation amplitude of underground structures being relatively small, irreversible plastic damage accumulates due to the sustained effect of earthquake excitation, eventually pervading the entire undergroun d structure, leading to an overall damage or even collapse. Therefore, a structural overall damage index that comprehensively considers both deformation and hysteretic energy parameters can provide a more accurate depiction of the failure state of underground structures than a single index that only considers deformation.

This paper proposes a method for selecting severest design input ground motions for rectangular frame underground structures. An overall damage index is also proposed to characterize the failure state of underground structures. The classification of site and underground structure forms follows the seismic code GB/T 51336-2018. Taking single-underground structures of one-, two-, three-, and four-stor ey in class III sites as examples, the paper presents the selecting process of the SDGM in detail. The paper also verifies the advantag e of this method by comparing it with the traditional method of selecting the SDGM for aboveground structures.

2 Proposed method for selecting severest design ground motions for underground structures

The procedure of the method for selecting SDGM in this paper is illustrated in Fig. 1, and the method mainly consists of the following steps :

(I) Group the site types and structural forms according to CiB/T 51336-2018. The sites are divided into four categories of classes 1, 11, 111, and IV. The underground structures are divided into tunnel, single-underground, and multi-underground structures.

(2) Collect strong ground motions from domestic and foreign database and select representative single I Ms and EDP. Meanwhile, establish the soil-structure numerical model corresponding to specific soil category and underground structural form, and select a part of the strong ground motions as samples to perform nonlinear dynamic analysis.

(3) Construct composite lMs by PLS and cross-validity analysis using the results of the dynamic analysis in previous step and the selected I Ms of input ground motion as data samples.

(4) Verify the validity of PLS model through regression coefficients significance test.

(5) Establish the damage potential ranking of the collected ground motion records through composite lMs.

(6) Select the top 50 ground motion records as the alternative ground motion database of SDGM. This step Is the most critical one.

(7) Perform further nonlinear dynamic analysis of the soil-structure numerical model corresponding to specific soil category and underground structural form using the ground motions in the alternative ground motion database as input, and calculate the HDP of each analysis.

(8) Establish the EDP ranking of the ground motions in alternative database, and select the top IU ground motions as the SDGM of the specific underground structure in specific soil category.

This paper takes single-underground structures of 4 types, including one-, two-, three-, and four-storey subway station structures, in class III sites as examples, and illustrates the new method of selecting the SDGM in detail.

3 Recorded strong ground motions database

The main purpose of this paper is to identify the SDGM from the strong ground motion records worldwide. After reviewing and co mparing multiple strong ground motion databases at home and abroad, the NGA-West2 ground motion database (PEER, 2013, https://peer.Berkeley.edu/ nga) was finally selected. This database can provide complete site and earthquake information, and the ground motion records in the database are widely distributed around the world and include many typical earthquakes, which make them highly valuable for research.

The selection of ground motions in this section has two main purposes: (1) to select the data to be used as input ground motions for nonlinear dynamic analysis of underground structures, so as to provide necessary data samples for the construction of composite IMs for undergrou nd structures; (2) to select the data to be used for the research of the SDGM. The candidate database of SDGM is then built from the acquired ground motions by using composite IMs.

In pursuit of enhanced outcomes for the selection of input ground motions for nonlinear dynamic analysis, it is imperative that the composition of data samples is both representative and extensive, given a fixed quantity of data sample. The ground motions employed are recommended to originate from sites of high seismicity, associated with earthquakes of moderate-to-large magnitudes. Such ground motions may exert significant structural demand, thereby rendering them meaningful for the estimation of earthquake damage potential (Liu et al., 2020). In this study, a total of 64 ground motions were procured from PEER database to sever as the input ground motion for analysis. The criteria for ground motion selection stipulated that the moment magnitude (Mw) shou ld exceed 6.0, and the PGA should surpass 0.05g. Figure 2 provides a visual representation of the intensity level of the selected 64 ground motions in the form of ASI.

In the context of the SDGM research, the basic design ground motion acceleration value in the seismic code GB/T 51336-2018 is 0.05g. Consequently, the conditions for ground motion selection specify that PGA should exceed 0.05g. Ultimately, 4749 strong ground motions were procured from the PEER database. The selected strong ground motions are geographically diverse, with origins spanning Asia, Europe, North America and Oceania. The mess age of magnitude V s30, and rupture distance are shown in Fig. 3.

4 Numerical modeling of the soil-structure system

To enhance the characterization of the damage potential of ground motion on underground structures, this paper used PLS methodology to formulate composite IMs. Prior to the construction of these composite IMs, it is necessary to conduct nonlinear dynami c analyses of underground structures, thereby generating the requisite data samples. These samples encompass the represen tative single IMs of the input ground motion and EDP.

The numerical models of underground structures established in this study are predicated on both domestic and foreign subway stations as prototypes. To mitigate randomness and enhance the representativeness of this study, the soil layer distribution varie s across the site environment where the four subway station models are situated. According to the seismic code, Code for seismic design of buildings (China Academy of Building Research, 2010), the soil sites of four numerical model are classified as class III. Given that the modeling methodology for the numerical models of all four types of underground structures is identical, only the modeling process of four-storey underground structure is delineated in this section. The soil layer parameters and standard cross-sectional dimensions of one-storey (Iida et al., 1996; Liu et al., 2017), tw o-storey (Chen & Liu, 2018), and three-storey underground structures can be seen in Appendices A and B.

The standard cross-sectional dimensions of four-storey underground structure, as depicted in Fig. 4, reveal a soil cover thickness of 3.2 m, and station width an d height of 23.6 and 29.1 m, respectively (Liu et al., 2021). The detailed information of the soil layers' stratification and their respective physical and mechanical parameters are listed in Table 1. A dynamic soil-structure system analysis model is established with the general finite element software, ABAQUS. For a detailed modeling process, readers can refer to our previous research (Liu et al., 2021). Figure 5 illustrates the soil-underground structure system.

To more accurately simulate the dynamic response of the structure during the elastic-plastic stage, an isotropic bilinear model is used for reinforcement, while a concrete damage plastic model is utilized for concret e. According to foundational theory of Lubliner et al. (1989) and Lee and Fenves (1998), the damage index, denoted as D, is used to quantify the degree of concrete damage and the degradation of its stiffness. The mathematical representation of this factor is as follows:

... (1)

where a is the effective stress; E is the initial elastic stiffness tensor; ... Ls the strain tensor; ... Ls plastic strain tensor; ... the damage factor, which can be calculated with the damage factor D. and the compression damage factor Dc. Due to different response characteristics in tension and compression, two variables are defined to present damage states respectively as Eq. (2):

... (2)

where the value of D is within the range of [0, 1] D = 0 indicates that the structure is in the elastic state; D > 0 indicates that the struc ture is in the plastic state.

5 Intensity measures of the seismic inputs

The judicious selection of IMs forms a crucial foundation for evaluating the EDP of underground structures. The chosen representative single-IM should encapsulate as much fundamental information as feasible from the original ground motion. At present, the commonly used IMs include (Zhang et al., 2023): (I) IMs related to the characteristics of ground motion itself, such as the cumulative absolute velocity (-4CT), Arias intensity (/a), PGA, and PGV, among others; (2) IMs germane to the seismic response of underground structures, such as acceleration response spectrum (5a), velocity response spectrum (5V), displacement response spectrum (Sd), etc- Given the pronounced randomness of ground motions, this study incorporates various characteristics of ground motion, including amplitude, energy, and spectral attributes, when selecting representative IMs. Based on the frequency of utilization of these IMs in seismic design or research within the engineering domain, 12 types of IMs spanning 3 categories have been selected, as delineated in Table 2.

6 Engineering demand parameters

EDPs serve as quantitative indicators of the extent of structural damage under earthquake excitation and are crucial in conducting nonlinear dynamic analyses for underground structures. Presently, the failure indices commonly employed for underground structures encompass sectional bending moment, joint displacement, rotation angle of key components (such as the central column of a subway station), and maximum storey driftratio. However, the evaluation of the seismic performance of subterranean structures based solely on the performance indices of key components lacks comprehensiveness. The dynamic behaviors of general componen ts, including increased deformation and stiffness degradation, can expedite the damage of key components, culminating in the overall destruction of the underground structure. To address this issue, this paper proposes an overall damage index for underground structures that judiciously considers the impact of the size and damage of each component of a subway station on its overall seismic performance.

The overall damage index of underground structures proposed in this study takes into account the damage of components of central columns, slabs, and sidewalls. The damage index of each component is computed as the average value of the damage values of all elements within that component. In conjunction with Eq. (2), the damage index of the jth component can be expressed as below:

... (3)

where ... are the damage index of the ith element of the jth component; ... is the cumulative hysteretic energy consumption of the jth element of they ith component; / is the number of whole elements of the jth component.

The overall damage index of the structure is obtained by adding the weighted damage indexes of the components, that is

... (4)

where ... is the comprehensive damage index of underground structures; Dj is the damage index of the jth component; ... is the weighting coefficient of the jth component; m is the number of all components.

In the computation of the overall damage index, the selection of the weighting coefficient ... is of paramount importance. Currently, methods for determining the weighting coefficient ... encompass the component hys-teretic energy consumption ratio weighted method, the component damage index ratio weighted method, and the magnitude of component vertical force weighted method. The widely adopted method for determining the value of the weighting coefficient, proposed by Park et al. (1985), utilizes the proportion of hysteretic energy consumption of components as a weighting coefficient. However, given the considerable variation in the size of each component in a subway station structure, it is possible that a component of smaller size may significantly impact the seismic performance of the overall structure. For instance, while the central column is generally considered the key component of a subway station struct lire, its hysteretic energy dissipation is smaller due to its smaller size compared to the lop and bottom slabs and sidewalls, resulting in a lower weighting coefficient. This is inconsistent with reality. To rectify this, this paper enhances the hysteretic energy consumption ratio parameter by employing the component hysteretic energy consumption density ratio ... as a weigh! evaluation standard to negate the impact of component size. The expression of ..., is shown in Eq. (5):

... (5)

where ... is the symbol of calculating the density of cumulative hysteretic energy of the target component ... is the total cumulative hysteretic energy consumption of the of the jth component, and Vj is the volume of the jth component. Therefore, the weighting coefficient ... in this paper can be expressed as

... (6)

In this study, the DUi was selected as the EDP for the underground structure. Drawing upon the descriptions of damage levels for mountain tunnels as delineated by Chen and Wei (2013), the damage slates are defined as follows: when Dm = 0, the structure has no damage; when 0 < Dus < 0.4, the structure is slightly damaged; when 0.4 < Dus < 0.7, the structure is severely damaged; when Dm > 0.7, the structure is collapsed.

Figure 6 presents the distribution cloud chart of tensile and compressive damage of the underground structure. The overall damage index D^ of the underground structure under each ground motion can be subsequently derived from the tensile and compressive damage values output by the numerical analysis model.

7 Composite intensity measures1

In the process of employing regression methods to construct composite IM, the issue of multicollinearity among different independent variables is a non-trivial concern. The detrimental effects of multicollinearity can be profound, including influencing parame ter estimation, amplifying model errors, and undermining the robustness of the regression model. Frank and Friedman (1993). conducted a comparative analysis of various regression methods from a predictive standpoint, encompassing PLS, principal component analysis (PCA), ordinary least squares regression (OLS), variable subset selection (VSS), and ridge regression (RR). The results of the analysis indicated that PLS and PCA are impervious to the effects of multicollinearity, and the regression performance of PLS surpasses those of other methods, as depicted in Table 3. Consequently, this study adopts the PLS method to construct composite IMs.

7.1 Definition proces s

In this study, the dependent variable is the overall damage index ... of the underground structure, and the independent variable is the selected representative IMs. The process of constructing composite IMs primarily encompasses the following steps (Draper & Smith, 1998; Wold et al., 2006).

Slep 1. The dependent variable and independent variable are denoted as ... where n refers to the number of data sample, and p refers to the number of independent variables. In this paper n = 64, and p = 12. The standardized matrices are further denoted as ... the first principal component of ... is the first principal component of ... are the first data projection axes of fo and £o. respectively.

In PLS, it is required that the covariance between t\ and ill is maximized, that is

... (7)

where r(tfi, H|J is the correlation matrix. Equation (7) can be transformed into solving the following optimization problem, that is

... (8)

Step 2. Use the Lagrange algorithm to solve Eq. (8). For univariate partial least squares regression, since there is only one variable in ...

... (9)

... (10)

Step 3. Find the regression of E 0 on t1 and the regression of F0 on t1, that is

... (11)

... (12)

where ... regression coefficients of principal component; ... are residual matrices. That is

... (13)

Step 4. Replace E0 and F0 with residual matrices E1 and F1, and find the second principal components ...

... (14)

where ... are the first data projection axes of F1 and E1 respectively.

By repeating steps (1)-(3), the second principal components ... can be obtained ... are residual matrices of ... and so forth.

Step 5. Repeat the previous steps to find ... is the number of principal components, and it can be determined by cross-validity analysis.

Further, find Ihe linear regression equation of F respect to ...

... (15)

where

... (16)

Step 6. Let ..., where ... is the ith component of ... and Eq. (15) can be written as

... (17)

where , ... are the regression coefficients of independent varia ble.

Restore the standardized variables in Eq. (17) to the original variables:

... (18)

where ... is the residual of the regression model.

Step 7. Given that the bootstrap resampling method can generate data samples without necessitating additional assumptions or the inclusion of new samples, and solely relies on the information provided by the given sample, this study employs the regression parameter significance test method predicated on bootstrap resampling to test the significance of regression coefficients (T. Liu et al., 2019). To ascertain that ... a hypothesis test must be conducted. The null hypothe H0 and acceptable hypothesis H1 are respectively

... (19)

... (20)

Randomly select nB samples with replacement from the sample sets and ..., to obtain Bootstrap samples. Repeat this process r times to obtain r groups of Bootstrap samples. For each group of samples, find the partial least squares model with h principal components. The partial regression coefficient for each model is then computed as

... (21)

Let ... Suppose that the hypothesis test level is a and the a quantile of ..., is taken as the critical value of the rejection region. If ..., and the independent variable has statistical significance, otherwise remove the variab le. Remove variables that have not passed the significance test from the regression equation and continue to repeat the above process until all variables pass the significance test and stop.

7.2 Cross-validity a nalysis

In Step 5 of Section 7.1, the number of principal components to be selected can be determined through the following process. First, remove the rth sample point from all sample points to form a new set of sample points (containing a total of n-1 sample points), use the new set of sample points, and use h principal components to fit a regression equation ... Then substitute the excluded the ith sample point into ..., and the fitted value is denoted as ... For ... repeat the above operation and substitute the excluded ith sample point into Eq. (18). Then the predicted error square sum of y can be defined as PRESSh, which is

... (22)

In addition, use all sample points to fit a regression equation with h principal components. At this time, the predicted value of the ith sample point is denoted a ..., and the error square sum of y an be defined as S which is

... (23)

If the disturbance error of the regression equation with h components is smaller than the fitting error of the regression equation with (h-1) components to a certain extent, it is considered that adding one component th can significantly improves the accuracy of the prediction model. Therefore, it is hoped that the ratio of PRESSh/SSh, can be as small as possible. Specify,

... (24)

When ..., the marginal contribution of the th component is significant. Besides, for ..., there is at least one k such that ...

Tlie numerical model of one-, two-, three-, and four-storey subway station structures in class III sites was established. By taking the 64 ground motions as input, the nonlinear dynamic time-history analysis was carried out, and 256 (64 x 4) groups of sample data were obtained. According to the process introduced in Section 7.1, 256 groups of data samples were substituted to obtain the expression of composite IMs. Figure 7 shows the 0~h values of 12 principal components of 4 numerical models. It can be seen from Fig. 7 that when the third partial least squares component was extracted, for PLS models of one-, two-, and three-storey structures, Qi < 0.0975. Therefore, according to cross-validity analysis, by extracting 2 principal components, the accuracy of prediction can be ensured. Similarly, the second partial least squares component was extracted, for PLS models of four-storey structure, ... Therefore, according to cross-validity analysis, by extracting I principal component, the accuracy of prediction can be ensured.

7.3 Regression coefficients signi ficance test

After the expression for the composite I Ms was obtained, a regression coefficients significance test method based on bootstrap sampling was used to test the regression coefficients. By taking nB - 50, r = 100, a total of 100 bootstrap samples were obtained. Then, the critical value of the rejection domain ... is the level of significance test, which is 0.05) is obtained through these samples. If ... rejected. That means ... is significantly not equal to 0; otherwise the null hypothesis is accepted, and the significance test is not passed at this time. Table 4 gives the bootstrap test results of one-storey, two-storey, three-storey, and four-storey PLS models. From Table 4, it can be seen that all 12 regression coefficients of all PLS models have passed the significance test.

The composite IMs sought in this paper are finally obtained, and the composite IMs corresponding to one-storey, two-storey, three-storey, and four-storey subway station structures are denoted as ..., respectively. The regression coefficients of the composite IMs are listed in Table 5.

The performance of composite IMs constructed by the PLS method have been confirmed in previous study (Chen et al., 2023). Compared with the single IMs, the composite IMs have better effectiveness, practicability and proficiency in charactering the damage degree of underground structures.

8 Selection of the severest design ground motion for underground structure

Upon constructing the composite IMs corresponding to four types of underground structures, including one-storey, two-storey, three-storey, and four-storey structures, in class III site, the rankings of damage potential of 4749 ground motions for the four types of underground structures are established respectively according to the value of composite IMs of ... The top 50 ground motions are selected into the alternative database of SDGM according to the rankings. Table 6 provides a brief overview of the ground motions in the alternative databases.

Subsequently, a nonlinear dynamic analysis of the four types underground structures is conducted using the ground motions in the alternative database as input, and the corresponding EDPs are computed. Finally, the SDGMs of single-underground structure of four types in class III site can be obtained according to the ranking of EDPs.

Table gives the top 10 recommended SDGMs of single-underground structures of four types in class III site. By combining Tables 6 and 7, it can be observed that the PGA of the ground motion "RSN5657_IWATE_JWT H25UD" is 38.40 m/s'2. However, the overall damage index D^ caused by this ground motion does not rank in the lop 10 according to dynamic analysis results. This suggests that a real ground motion with a large IM of PGA does not always characterize the severest overall damage to single-underground structures.

9 Verification of the proposed method

The primary distinction between the proposed method and the traditional method proposed by Zhai and Xie (2004) lies in the construction of IMs to characterize the damage potential of ground motion, and their utilization in building the alternative databases of the SDGM. The crux of the SDGM selection is whether the built alternative databases can encompass the potential reality SDGM to the greatest extent as anticipated in this study.

To validate the accuracy of the new method for selecting the SDGMs proposed in this study, the following steps are undertaken. (1) The collected 4749 strong ground motions were ranked using 12 single IMs as the damage potential characterization parameter respectively, and the lop 10 ground motions of each single IM were gathered to form an alternative database A of the SDGM. After removing duplicate ground motion records, 50 ground motions remained. (2) Using the composite IMs as damage potential characterization parameter, the top 50 ground motions were collected to form an alternative database B of the SDGM. (3) By merging alternative databases A and B, the alternative database C was obtained after removing duplicate earthquake motions. (4) Each ground motion in alternative database C was used as input to carry out nonlinear dynamic analysis of four types of underground structures and calculate the corresponding EDP values. Then, the ground motion records were ranked according to the EDP values and the top 10 and lop 20 ground motions were recorded as potential reality SIXiM. (5) The number of occurrences of these IU and 20 ground motions in alternative databases Aand B were counted, respectively. (61 Comparison of the number of occurrences of these 10 and 20 ground motions contained in alternative databases A and B indicated that the larger the number of ground motions the alternative database contained, the better the effectiveness of the method of selecting the SIXiM.

The final statistical results are depicted in Fig. K. From Fig. 8, it can be observed that for four types of underground structures, the number of top 10 and top 20 ground motions contained in alternative database B exceeds that in alternative database A. For example, for three-storey and four-storey underground structures, alternative database B contains all top 10 and top 20 ground motions, while alternative database A contains only 7 and 12, respectively. This indicates that the alternative database of the SDCiM selected by using the composite IM as the ground motion damage potential characterization parameter yields a more accurate effect than that of 12 single IMs. By comparing with the existing method of selecting the severest design ground motion, the method proposed in this study can more effectively identify the SDGM.

10 Conclusions

This study introduces an approach for the selection of severest design ground motions (SDGMs) specifically tailored for underground structures. Additionally, an overall damage index has been proposed to effectively characterize the failure state of underground structures. The index is weighted by the hysteretic energy consumption density of each individual component of the underground structure. The findings of this research can serve as a reference for the selection of SDGM in the seismic design of underground structures, given specific form and site cond itions. The primary conclusions drawn from this study are as follows.

(1) Based on the obtained severest design ground motion ranking results of four underground structures, it is observed that the input ground motion with a large IM of PGA of38.40 m/s! is absent. This suggests that an input ground motion with a large single-IM does not always characterize the severest damage inflicted on underground structures. When seeking a ground motion that can put underground structures in the most unfavorable state, it is not sufficient to rely solely on a single-IM, such as PGA, even though it is recommended in relevant seismic codes. Instead, specialized research for selecting such ground motions is necessary.

(2) Upon contrasting the conventional approach for selecting SDGMs with the methodology proposed in this study, it Is discerned that the alternative ground motion database of the SDGM, built by employing the methodology of this study, can encompass more potential SDGM than the conventional approach. The comparison results of underground structure with different structural forms shows that: (1) for one-storey structure, the alternative database B contains 9 and 18 ground motions of top IU and top 20 ground motions, respectively, while alternative database A contains only 6 and 12; |2| for two-storey structure, alternative database B contains 9 and IS ground motions of top IU and top 20 ground motions, respectively, while alternative database A contains only 7 and 13; |3| for three-storey and four-storey underground structures, alternative database B contains all top 10 and top 20 ground motions, while alternative database A contains only 7 and 12. Therefore, it is substantiated that the SDGM selection method proposed by this study can yields more accurate results.

(3) It is imperative to note that these SDGMs recommended in this study are derived solely from the 4749 strong ground motions amassed from the PEER ground motion database. This collection does not encapsulate all the strong ground motions globally or within a specific district. Consequently, further investigations concentrating on the strong ground motions of a particular district with a specific site class are necessitated to construct a SDGM database. This would facilitate underground structure design engineers in selecting input ground motions directly.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonabl e request.

CRediT authorship contribution statement

Wei Yu: Writing - review & editing, Writing - original draft, Visualization, Validation, Software, Methodology, Conceptualization. Zhi-Yi Chen: Writing - review & editing, Supervision, Methodology , Conceptualization. Zhi- Qian Liu: Writing - review & editing, Val idation, Software, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research was supported by the National Key Research and Development Program of China (Grant No. 2022YFE0104400), and the Key Science and Technology ProgramofYunnanProvince(Grant No.202402AC080003).

Sidebar

Received 26 December 2023; received in revised form 22 March 2024; accepted 11 May 2024 Available online 29 October 2024

References

References

Andreotti, G., & Lai, C. G. (2019). Use of fragility curves to assess the seismic vulnerability in the risk analysis of mountain tunnels. Tunnelling and Underground Space Technology, 91, 103008.

Argyroudis, S. A., & Pitilakis, K. D. (2012). Seismic fragility curves of shallow tunnels in alluvial deposits. Soil Dynamics and Earthqua ke Engineering, 35, 1-12.

Chen, Z. Y., & Liu, Z. Q. (2018). Effects of central column aspect ratio on seismic performances of subway station structures. Advances in Structural Engineering, 21 (1), 14-29.

Chen, Z. Y., & Wei, J. S. (2013). Correlation between ground motion parameters and lining damage indices for mountain tunnels. Natural Hazards, 65 (3), 1683-1702.

Chen, Z. Y., Yu, W., Zhu, H. H., & Xie, L. L. (2023). Ranking method of the severest input ground motion for underground structures based on composite ground motion intensity measures. Soil Dynamics and Earthquake Engineering, 168, 107828.

China Academy of Building Research (2010). GB 50011-2010: Code for seismic design of buildings. Beijing: China Archite cture & Building Press (in Chines e).

Draper, N., & Smith, H. (1998). Applied regression analysis. New York: John Wiley & Sons (pp. 115-131).

Frank, I. E., & Friedman, J. H. ( 1993). A statistical view of some chemometrics regression tools. Technometrics, 35 (2), 109-135.

Hashash, Y. M. A., Hook, J. J., Schmidt, B., & Yao, J. I. (2001). Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology, 16 (4), 247-293

Hu, J. J., Lai, Q. H., Li, S., & Xie, L. L. (2021). Procedur e for ranking ground motion records based on the destructive capacity parameter . KSCE Journal of Civil Engineering, 25 (1), 197-207.

Huang, Z. K., Pitilakis, K., Argyroudis, S., Tsinidis, G., & Zhang, D. M. (2021). Selection of optimal intensity measures for fragility assessment of circular tunnels in softsoil deposits. Soil Dynamics and Earthquake Engineering, 145, 106724.

Iida, H., Hiroto, T., Yoshida, N., & Iwafuji , M. (1996). Damage to Daikai subway station. Soils and Foundations, 36(Supplement), 283-300.

Lai, Q. H., Hu, J. J., Xu, L. J., Xie, L. L., & Lin, S. B. (2022). Method for ranking pulse-like ground motions according to damage potential for reinforced concrete frame structures. Buildings, 12 (6), 745.

Lee, J., & Fenves, G. (1998). Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 124 (8), 892-900.

Li, C. H., Zhai, C. H., Kunnath, S., & Fajia, D. (2019). Methodology for selection of the most damaging ground motions for nuclear power plant structures. Soil Dynamics and Earthquake Engineering, 116, 345-357.

Liu, J. B., Lan, X. H., & Tan, H. (2019). Comparative study on the seismic performances of underground vs above ground reinforced concrete structure with rectangular cross section. China Earthquake Engineerin g Journal, 41 (2), 271-277 (in Chinese).

Liu, T., Chen, Z. Y., Yuan, Y., & Shao, X. Y. (2017). Fragility analysis of a subway station structure by incremental dynamic analysis. Advances in Structural Engineering, 20 (7), 1111-1124.

Liu, T. T., Lu, D. G., & Yu, X. H. (2019). Development of a compound intensity measure using partial least-squares regression and its statistical evaluation based on probabilistic seismic demand analysis. Soil Dynamics and Earthquake Engineering, 125, 105725.

Liu, T. T., Yu, X. H., & Lu, D. G. (2020). An approach to develop compound intensity measures for prediction of damage potential of earthquake records using canonical correlation analysis. Journal of Earthquake Engineering, 24(11), 1747-1770.

Liu, Z. Q., Chen, Z. Y., & Zhao, H. (2021). Characteristics of earthquake input energy of a subway station structur e based on probabilit y density evolution method. International Journal of Computational Methods, 18, 2041014.

Lubliner, J., Oliver, J., Oller, S., & Onate, E. (1989). A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), 299-326.

Ministry of Housing and Urban-Rural Developme nt of the People's Republic of China (MOHURD) Administration, S., & for Market Regulation (SAMR) (2018). GB/T 51336-2018 : Standard for seismic design of underground structures. Beijing: China Architecture & Building Press (in Chinese).

Nguyen, D. D., Park, D., Shamshers, S., Nguyen, V. Q., & Lee, T. H. (2019). Seismic vulnerability assessment of rectangular cut-and-cove r subway tunnels. Tunnelling and Underground Space Technology, 86, 247.

Pacific Earthquake Engineering Research Center (PEER) (2013, March 27). PEER NGA-west2 strong motion databas. Peer Ground Motion Database. https://ngawest2.berkeley.edu/.

Parra-Montesinos, G. J., Bobet, A., & Ramirez, J. A. (2006). Evaluation of soil-structure interaction and structural collapse in Daikai subway station during Kobe earthquake. ACI Structural Journal, 103 (1), 113.

Prak, Y., Ang, A., & Wen, Y. (1985). Seismic damage analysis of reinforced-concrete buildings. Journal of Structural Engineering, 111(4), 740-757.

Qiu, D., Ren, W., & Chen, J. (2023). The multi-dime nsional fragility analysis of the underground large-scale frame structure based on the internal relationships of different seismic performance evaluati ng indexes. Tunnelling and Underground Space Technology, 136, 105093.

Sun, B. B., Liu, W. Y., Deng, M. J., Zhang, S. R., Wang, C., Guo, J. J., Wang, J., & Wang, J. Y. (2023). Compound intensity measures for improved seismic performance assessment in cross-fault hydraulic tunnels using partial least-squares methodo logy. Tunnelling and Underground Space Technology, 132, 104890.

Wang, W., Wang, T., Su, J., Lin, C., Seng, C., & Huang, T. (2001). Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi earthquake. Tunnelling and Underground Space Technology, 16 (3), 133-150.

Wold, S., Martens, H., & Wold, H. (2006). The multivaria te calibration problem in chemistry solved by The PLS method. Berlin: Springer (pp. 286-293). .

Yang, J., Zhuang, H., Zhang, G., Tang, B., & Xu, C. (2023). Seismic performance and fragility of two-story and three-span undergrou nd structures using a random forest model and a new damage description method. Tunnelling and Underground Space Technology, 135, 104980.

Ye, L. P., Ma, Q. L., & Miao, Z. W. (2009). Study on earthquake intensities for seismic analysis of structur es. Journal of Earthquake Engineering and Engineering Vibration, 29 (4), 9-22 (in Chinese).

Zhang, C. M., Zhao, M., Zhong, Z. L., & Du, X. L. (2023). Optimal intensity measures in probabilistic seismic demand model of subway station. Tunnelling and Underground Space Technology, 142, 105443.

Zhai, C. H., & Xie, L. L. (2004). Study on the severest design ground motions. In 13th World Conference on Earthquake Engineering Vancouver . British Columbia, Canada.

Zhong, Z. L., Shen, Y. Y., Zhao, M., Li, L., Du, X. L., & Hao, H. (2020). Seismic fragility assessment of the Daikai subway station in layered soil. Soil Dynamics and Earthquake Engineering, 132, 106044.

Zhuang, H. Y., Ren, J. W., Miao, Y., Jing, L. G., Yao, E. L., & Xu, C. J. (2019). Seismic performance levels of a large underground subway station in different soil foundations. Journal of Earthquake Engineerin g, 25(7), 1-26.

Zhuang, H. Y., Yang, J., Chen, S., Dong, Z. F., & Chen, G. X. (2021). Statistical numerical method for determin ing seismic performance and fragility of shallow-buried underground structur e. Tunnelling and Underground Space Technology, 116, 104090.

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