Open AccessArticle

Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers

Zigang Xu

^1,*,

Chunyu Li

¹,

Zongyao Xia

¹ and

Runbo Han

State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure, East China Jiaotong University, Nanchang 330013, China

School of Resources, Environment and Architectural Engineering, Chifeng University, Chifeng 024000, China

Author to whom correspondence should be addressed.

Appl. Sci. 2024, 14(15), 6608; https://doi.org/10.3390/app14156608

Submission received: 15 June 2024 / Revised: 19 July 2024 / Accepted: 25 July 2024 / Published: 28 July 2024

(This article belongs to the Special Issue Seismic Analysis and Design of Ocean and Underground Structures)

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Abstract

Challenges related to seismic performance and seismic mitigation are more pronounced in the presence of weak interlayers compared to typical layered soil conditions. This study focuses on a double-layer double-span rectangular frame subway station structure. A coupled static–dynamic finite element analysis model of the soil-structure system is established by using the finite element software ABAQUS/CAE V 6.14. The research investigates the influence of factors such as interlayer thickness, location, and strength on the seismic response of subway station structures. Furthermore, in order to evaluate the effectiveness of FPB in mitigating seismic effects in the weak interlayer ground, two different schemes are proposed in this paper. One is the structure without FPB and the other is the structure with FPB on the top of the central column. The findings reveal that weak interlayers exert a significant influence on the seismic response of subway station structures, especially when these lower-strength weak interlayers are located within the central portion of the subway station structure and exhibit considerable thickness. The FPB on the top of the central column can reduce the overall lateral stiffness of the subway station structure. This, in turn, results in a slight increase in the deformation of sidewall and inter-story displacement angles, accompanied by a marginal exacerbation of sidewall damage. However, the implementation of FPB effectively reduces the deformation of the central column and substantially mitigates the extent of damage to the central column.

Keywords:

weak interlayer; subway station structure; friction pendulum bearing; numerical simulation; seismic response

1. Introduction

With rapid global development and exponential population growth, the pursuit of more extensive living spaces has made the development and utilization of underground areas a vital direction for advancement. Currently, underground structures have broad applications across various construction domains, with subway projects being notable examples within this realm. Rock formations and soil exert constraints on the vibrational deformations of underground structures. Hence, it was commonly believed that underground structures exhibited superior seismic performance compared to their above-ground counterparts. However, until the 1990s, there was a scarcity of seismic damage data related to underground structures, which resulted in a prolonged lack of emphasis on seismic analysis theories and design methods in this field [1,2,3]. Recent seismic disasters have highlighted the vulnerability of underground structures to earthquakes, with some experiencing severe damage [4,5,6,7]. For instance, during the Great Hanshin Earthquake in Japan, Daikai station suffered extensive destruction. The Great Hanshin Earthquake’s powerful horizontal and vertical seismic forces caused the central column to fracture, resulting in the roof’s collapse and creating a distinctive “M” shaped pattern of devastation [8]. This earthquake-induced damage has acted as a wake-up call for experts and scholars worldwide.

Complex site characteristics significantly impact the safety of underground structures and weak interlayers are a common variety among these complex site types. Consequently, the study of weak interlayer’s impact on underground structures holds significant importance for seismic design. Seokwon et al. [9] employed a combination of scaled model testing and numerical analysis to investigate the influence of rock faults and weak surfaces on the stability of underground structures. Huang et al. [10] conducted model testing and numerical simulations, concluding that factors such as position, angle, thickness, and distance from the tunnel significantly affect tunnel stability. Some scholars [11,12,13,14] pointed out in their work that adverse soft soil conditions exacerbate the deformation of subway station structures. Huang et al. [15,16]. taking into account the influence of the soil-structure interaction and structural depth, conducted vulnerability assessments for circular tunnels located within soft interlayers in the Shanghai subway system.

Since the Great Hanshin Earthquake, seismic mitigation measures for underground structures have garnered significant research attention. Some engineers [17,18,19,20] have proposed the seismic mitigation scheme by installing an isolation layer between the rock and lining, resulting in the isolation layer reducing the deformation of the lining. Chen et al. [21] delved into the utilization of isolation layers for underground structures and conducted pertinent experimental studies. The results showed that isolation layers can absorb seismic energy and efficiently reduce structural bending moments. Several scholars [22,23,24,25] carried out research on Daikai stations, which suffered the most damage during the Great Hanshin Earthquake. Their results demonstrated that the central column of subway station structure is particularly susceptible to seismic forces and prone to shear failures under earthquake motion. Therefore, mitigating shear deformations of central column under seismic forces is a crucial step in enhancing the seismic performance of subways. Studies have investigated the seismic mitigation effects of various approaches, including rubber bearings on the top of the central column [26,27,28], shear plate dampers [29], sliding bearings [30,31,32], and split columns [33]. The results indicated that all these measures effectively reduce the shear deformations of the central column.

Rubber bearing is a commonly used form of seismic mitigation support. However, in comparison to rubber bearing, friction pendulum bearing (FPB) is cost-effective, highly durable, and possess self-centering capabilities. In 1987, Zayas et al. [34] introduced FPB at the University of California, Berkeley. The bearing operates on the principle of a pendulum, extending the structural natural period by the swaying motion of the upper support and slider. The swaying motion can effectively dissipate seismic energy. In practical engineering applications, FPB have become widely employed. Tesopelas et al. [35] explored the application of FPB in bridge structures and found that the bearing effectively reduces deformation and damage to bridge structures under seismic forces. Jangid et al. [36] studied the mitigation seismic performance of FPB under near-fault motion and derived the optimal range for the friction coefficient of the bearing. Mazza [37] conducted seismic analyses on reinforced concrete frames fitted with FPB and observed that a lower friction coefficient leads to greater story rotations and residual displacements. However, many studies on seismic mitigation mechanisms have been focused on above-ground structures and the research of seismic mitigation of underground structure started relatively late. Xu et al. [38] delved into the effectiveness of FPB in underground structures by drawing inspiration from the accomplishments in seismic mitigation research for above-ground structures.

Based on the research findings of several scholars, it is evident that weak interlayers have detrimental effects on subway station structure deformations and structural forces. The seismic mitigation effects of the FPB in subway station structure situated within the weak interlayer site is not clear and needs further study. This paper proposes a seismic mitigation scheme with FPB on the top of the central column for the subway station structure situated within the weak interlayer site. This study focuses on a two-storey two-span subway station structure, employing the finite element software ABAQUS to establish a two-dimensional model of the soil and subway station structure. The impact of weak interlayers on the seismic response of the subway station structure and the effectiveness of FPB in improving the seismic performance of the subway station structure within the weak interlayer site is studied by time-history analysis.

2. Seismic Response of the Subway Station in the Site with Weak Interlayers

2.1. Engineering Profile

The structural model used in this study is a double-story double-span rectangular frame structure for the station, with cross-sectional dimensions and reinforcement details shown in Figure 1. The station’s dimensions are as follows: a width of 17 m and a height of 12 m. The thickness of the top slab, middle slab, bottom slab, and side wall of the station are 0.75 m, 0.45 m, 0.8 m, and 0.8 m, respectively. The cross-sectional size of the central column is 0.7 m × 0.7 m, with a longitudinal spacing of 7 m. The site consists of 11 layers of soil, with a vertical distance of 40 m from the soil surface to the bedrock. The site has a width of 119 m and the structural depth is 7 m. Table 1 provides the relevant parameters for the soil in the normal layered site, including soil density (ρ), shear wave velocity (Vs), and Poisson’s ratio (ν).

In order to analyze the seismic response patterns of subway station structures situated within weak interlayer sites, three factors such as the thickness, location, and strength of the weak interlayer are discussed. The simplified diagram of the conditions is presented in Figure 2. By modifying the shear wave velocity of soil layer 4 (adjusted from 275 m/s to 80 m/s), a weak interlayer site is introduced at the midsection of the subway station structure. The thickness of the weak interlayer is varied (1, 1.5, 2, and 2.5 m) to study its impact on the seismic response of the subway station structure. Five different conditions are set up to discuss the effects of the interlayer’s position relative to the subway station structure. To analyze the influence of the interlayer’s strength on the seismic response of the subway station structure, assuming that the interlayer passes through the center of the structure, this paper designs five conditions with varying shear wave velocities for the weak interlayer (80, 90, 100, 110, and 120 m/s). The parameters for each condition are summarized in Table 2.

2.2. Finite Element Model

The numerical simulation method is a research method in the civil engineering field, which is verified by some studies [39,40]. In this study, a two-dimensional model of the soil and subway station structure is established by using the finite element software ABAQUS [41]. The soil model has a width of 119 m and a height of 40 m. The specific values for the soil parameters are listed in Table 1 and the elastic modulus can be calculated using Equations (1) and (2). Here, ρ represents the density of the soil layer, Vs stands for the shear wave velocity of the soil layer, and ν represents the Poisson’s ratio of the soil layer.

G = ρ {V_{s}}^{2}

(1)

E = 2 (1 + ν) G

(2)

During the modeling process, the selection of soil layer damping deserves careful consideration as it is a pivotal factor. In this study, the Rayleigh damping model was chosen. Using the frequency analysis module in the ABAQUS software, we determined the first and second natural frequencies of the soil layers. Subsequently, the Rayleigh damping coefficients of the soil layers were calculated using Equations (3) and (4).

α = \frac{2 D \times w_{1} \times w_{2}}{w_{1} + w_{2}}

(3)

β = \frac{2 D}{w_{1} + w_{2}}

(4)

In the equation, where w₁ and w₂ represent the first and second natural frequencies of the soil layers, D is the damping ratio, set as 0.1 [42].

The concrete’s constitutive model employed is the plastic damage model proposed by Jeeho Lee et al. [43], which is an improvement based on the model introduced by Lubliner et al.‘s work [44]. This model is grounded in the principles of fracture energy within concrete and introduces two key variables: tensile damage and compressive damage factors. These factors are employed to represent the stiffness degradation in concrete under tension and compression, respectively. The C40 concrete is used for the main structure of the station, with a density of 2500 kg/m³, an elastic modulus of 3.25 × 10⁴ MPa, and a Poisson’s ratio of 0.2. The other corresponding parameters are listed in Table 3, Table 4 and Table 5. The materials for the station’s column include C50 concrete. The column is uniformly spaced along the alignment, with a 7 m interval. The material properties of the column are equivalently determined following established principles [38]. As a result of this equivalency, the column has a density of 250 kg/m³, an elastic modulus of 3.45 × 10³ MPa, a Poisson’s ratio of 0.2, a peak compressive strength of 1.83 MPa, and a peak tensile strength of 0.13 MPa. Reinforcement is simulated using truss elements, employing an ideal elastic–plastic constitutive model. The initial elastic modulus is set at 200 GPa, with a Poisson’s ratio of 0.3 and a yield stress of 335 MPa.

The outer surface of the station is set to have frictional contact with the surrounding soil, in which the tangential friction coefficient is set as 0.4. A hard contact is established in the normal direction of the interface. The hard contact allows for separation after contact but prevents embedding. The soil model employs fixed constraints at the bottom; the lateral artificial boundary is implemented using a binding boundary approach. The binding boundary utilizes the MPC (Multi-Point Constraint) node degree of freedom coupling feature within ABAQUS, effectively binding the finite element model nodes of the soil to the boundary nodes at the same height, ensuring that these nodes share identical displacements throughout the analysis. Research by Kampitsis [45] has demonstrated that the equidistant displacement boundary condition model effectively simulates free-field motion. The acceleration time history curves at various elevations remain largely consistent and seismic waves do not radiate toward the soil boundaries, significantly enhancing the calculation accuracy. Mesh division is crucial for finite element models as it directly impacts the model’s calculation accuracy. Uniform mesh dimensions of 0.5 m × 0.5 m are used for the entire soil. The station is divided into elements with a mesh size of 0.25 m. Both the soil and station are simulated using four-node plane strain elements, as shown in Figure 3 in the finite element model.

The seismic input in this study considers only horizontal seismic motion. To prevent the idiosyncrasies of single-spectrum seismic waves from affecting the computational results, we have chosen to analyze three typical seismic motions: the Chi-Chi earthquake, Duzce earthquake, and Manjil earthquake. Furthermore, we have adjusted the amplitudes of these seismic waves, setting peak accelerations at 0.05 g, 0.1 g, 0.2 g, and 0.4 g. The acceleration time history curves for these seismic waves are depicted in Figure 4.

2.3. Computational Result

Under seismic loading, significant lateral displacement of the station’s sidewall is a critical factor in the structural damage of the station. Simultaneously, damage to the station’s central column often precedes that of the sidewall. The extraction of horizontal displacements for the sidewall and central column along with an evaluation of seismic damage to the station’s structure are selected as analytical indicators. This paper uses these indicators to assess the impact of the weak interlayer on the station’s seismic response. As shown in Figure 5, the absolute values of the relative horizontal displacement values at points A and B represent the horizontal displacement values for the traditional structure; the absolute values of the relative horizontal displacement values at points C, D and E, F represent the horizontal displacement values of the upper and lower central columns of the station, respectively.

(1): Influence of the position of weak interlayers

In this condition, a weak interlayer with a thickness of 2 m is assumed, positioned at various heights within the subway station structure, including the upper, top, middle, bottom, and lower sections. A layered site without an interlayer is established for comparison by analyzing these six different conditions to assess the influence of the interlayer’s position on structural seismic response. Figure 6, Figure 7 and Figure 8 present the maximum displacement values of the station’s sidewall and central column when the interlayer is located at different positions within the station. Due to the length of the article, input accelerations only consider 0.2 g and 0.4 g in this context. From Figure 6, Figure 7 and Figure 8, it becomes evident that when the weak interlayer is situated in the middle of the station, it has the most significant seismic impact. When the weak interlayer is at the top or bottom of the subway station structure, it substantially affects the subway station structure. However, when the weak interlayer is placed in the upper or lower sections of the station, its impact is similar to that of the layered site condition, or even less. The weak interlayer effectively separates the soil into upper and lower portions. When the weak interlayer is positioned in the upper or lower sections of the structure, it does not make direct contact with the subway station structure. Consequently, the forces generated by the deformation of the weak interlayer under seismic action do not directly affect the subway station structure, resulting in minimal impact. When the weak interlayer is located at the top or bottom of the station, only half of its thickness is in contact with the subway station structure. The deformation generated by the weak interlayer during seismic action is only partially transferred to the structure. Therefore, its impact on the underground structure is less pronounced compared to the condition where the interlayer is in the middle of the subway station structure.

Figure 9 and Figure 10 depict the tensile damage of the subway station structure when the weak interlayer is positioned at different locations. When DAMAGET approaches 1, it indicates that the concrete has completely cracked under tension. Given the more pronounced seismic response patterns under the Chi-Chi earthquake, this section only illustrates subway station structure tensile damage under 0.2 g and 0.4 g Chi-Chi earthquakes. It can be seen from these illustrations that, compared to the subway station structure situated on a layered soil site, the presence of a weak interlayer at the station’s midsection significantly exacerbates the tensile damage of the main subway station structure. The next most affected condition is when the weak interlayer is located at the station’s bottom, resulting in noticeable increases in tensile damage to the station’s bottom slab, lower-level central column, and middle plate. When the weak interlayer is positioned at the station’s top, the weak interlayer increases the tensile damage to the upper central column and top slab. The influence on the subway station structure is nearly negligible when the weak interlayer is situated at the top or bottom of the station. These patterns become even more conspicuous when the input acceleration is set to 0.4 g.

(2): Influence of the Influence of the thickness of weak interlayers

Figure 11, Figure 12 and Figure 13 present the maximum displacements of the structure’s side wall and central column under various thicknesses of the weak interlayer, where H represents the interlayer’s thickness. From these figures, it is evident that the maximum horizontal displacements of the station’s side wall and central column in the weak interlayer site are greater than those in the layered soil site. This indicates that the weak interlayer has an adverse effect on structural horizontal deformations. It is important to note that the maximum horizontal displacement of the station’s side wall and central column does not continuously increase with an increase in the thickness of the weak interlayer. Instead, it follows a pattern of decreasing and then increasing as the thickness reaches a certain level. When the thickness of the weak interlayer is 3 m, it has the most significant impact on the horizontal deformation of the structure.

To further analyze the impact of the thickness of the weak interlayer on the seismic response of subway station structure, Figure 14, Figure 15, Figure 16 and Figure 17 present the damaged nephograms of the station’s main structure under varying weak interlayer thicknesses. Observing these figures reveals that under different levels of seismic intensity, station structures located within the weak interlayer experience significantly more severe damage compared to those on layered soil sites. This difference becomes more pronounced as the seismic intensity increases. When the seismic input acceleration is 0.05 g, the subway station structure experiences minimal damage. As the thickness of the weak interlayer increases, only minor damage occurs to the top and bottom slabs of the station. However, the damage to the structural column, side wall, and middle slab intensifies as the thickness of the weak interlayer increases when the input acceleration is set to 0.1 g. In the case of a 3 m thick weak interlayer during the Chi-Chi earthquake, seismic tensile damage almost permeates the entire lower part of the middle column. Under strong seismic activity (with peak input accelerations of 0.2 g and 0.4 g), the influence of the weak interlayer’s thickness becomes more pronounced. In comparison to layered soil sites, structures within the weak interlayer experience severe tensile damage at the connections between the middle plates and side walls on both sides. As the thickness of the weak interlayer increases, the extent of damage to the middle column, side wall, top slab, and bottom slab intensifies. The subway station structure is nearly destroyed under seismic activity with a 0.4 g acceleration, resulting in severe damage throughout the subway station structure. Particularly noteworthy is the pronounced damage to the station’s side wall as the interlayer thickness increases. The computational results presented above underscore the adverse effect of the weak interlayer on subway station structure deformation and its exacerbation of structural seismic damage.

(3): Influence of the strength of the weak interlayer

A 2 m thick weak interlayer located in the middle of the subway station structure is assumed in this section. The aim is to investigate the impact of the interlayer’s strength on the seismic response of the subway station structure by varying the interlayer’s shear wave velocity. Figure 18 illustrates the maximum displacements of the station’s side wall and middle columns under a 0.4 g earthquake. From this figure, it is evident that as the shear wave velocity increases, the maximum displacement of the structure’s side wall and middle column decreases. In general, firmer soil layers correspond to higher shear wave velocities. Therefore, an increase in the stiffness of the weak interlayer can, to some extent, limit the deformation of the structure.

Figure 19 displays the seismic tensile damage nephograms of the subway station structure under various shear wave velocities of the weak interlayer conditions. The seismic input used here is the Chi-Chi earthquake, with a magnitude of 0.4 g. From the figure, it becomes apparent that as the shear wave velocity of the weak interlayer increases, there is a noticeable reduction in damage to the station’s side wall. However, the impact on other parts of the subway station structure remains relatively minor. This highlights the positive effect of increased stiffness in the weak interlayer on the subway station structure’s seismic resistance.

3. Seismic Mitigation Effect of FPB in Weak Interlayer Site

The research in the previous section indicates that the weak interlayer has an adverse impact on subway station structure. This section proposes a seismic mitigation measure that involves installing FPB on the top of the central column in subway station structure situated within weak interlayer site. In order to investigate the seismic damping effect of FPB in ground with a weak interlayer, the structural dynamic time-history analysis of this proposed mitigation measure is conducted.

3.1. The Mechanical Model of FPB

FPB is typically categorized into single-sliding-surface and double-sliding-surface bearings. The single-sliding-surface FPB is the most commonly used type. The FPB primarily consists of upper support, a slider, and lower support. The main structural material of the bearing is typically metal, ensuring high reliability and easy quality assurance. The friction surface is coated with low-friction materials such as polytetrafluoroethylene (PTFE). The specific structural configuration of the bearing is depicted in Figure 20.

Within the friction pendulum bearing, the slider, under the influence of seismic motion, experiences a vertical load denoted as W. The sliding friction force on the bottom surface of the slider is represented as f. The horizontal restoring force of the friction pendulum bearing is designated as F. The normal force on the sliding surface is labeled as N. The radius of the sliding surface is R and the horizontal sliding distance of the slider is D. The angular displacement of the slider relative to the axis of symmetry is represented as θ. As illustrated in Figure 21, when analyzing the forces acting on the bearing, the friction force can be expressed as follows, with μ denoting the friction coefficient of the sliding surface and the normal force being represented by N. The equilibrium of forces on the slider can be expressed as

F \cdot R \cos θ = W \cdot D + f \cdot R

(5)

When the angular displacement of the slider is small, N is almost equal to W, and Equation (5) can be simplified to

F = \frac{W \cdot D}{R} + f = \frac{W \cdot D}{R} + μ W sgn (θ)

(6)

3.2. Validation of Model Suitability

To ensure the model’s validity, it is imperative to conduct finite element simulations on the FPB. Using the finite element software ABAQUS, a three-dimensional model of the friction pendulum bearings is constructed. The cross-section and finite element model of FPB are shown in Figure 22 and Figure 23, respectively. The FPB was modeled by using an elastic constitutive model. The material of FPB is steel characterized by a density of 7850 kg/m³, an elastic modulus of 2 × 10⁵ MPa, and a Poisson’s ratio of 0.3. The friction coefficient of the FPB is 0.1. The normal direction indicates a rigid contact. The contact between the slider’s sliding surface and the lower support’s sliding surface follows the same conditions. The mesh employed consists of C3D8R (a linear reduced integration solid element with eight nodes) with a mesh size ranging from 10 to 50 mm.

Vertical concentrated forces of 100 kN and 200 kN were individually applied at the center of the upper support to obtain the hysteresis curve. The curve representing the restoring force–displacement relationship of the FPB is shown in Figure 24. The curve calculated using finite element software is compared with the curve obtained from Equation (6). The comparison reveals a close alignment between the two curves, demonstrating a consistent trend. This indicates that the finite element model of the FPB effectively simulates its mechanical characteristics.

3.3. The Seismic Mitigation Effect of FPB

The dimensions of the FPB used in this study are shown in Figure 22. The radius of the bottom plate sliding surface is 1000 mm and the friction coefficient of the FPB is assumed as 0.1. The upper support surface of the FPB is anchored to the bottom of the beam and the lower support surface of the lower support block is anchored to the top of the central column. The specific finite element model is depicted in Figure 25. The boundary condition of the soil layer and the contact between the soil and the station are consistent with the calculation model in Section 2. Here, the Chi-Chi earthquake is selected as the input earthquake, only considering the horizontal ground motion. Calculations are performed for the scenarios listed in Table 2. The seismic response of the subway station structure with and without the FPB is analyzed to assess the seismic mitigation effects of the FPB. In this section, the subway station structure without the FPB model is referred to as the original structure, while the subway station structure with the FPB is referred to as the seismic mitigation structure.

Figure 26, Figure 27 and Figure 28 present the differences in maximum displacements of the subway station structure’s side wall and central column under various conditions. A positive difference in displacement indicates that the FPB can reduce the structure’s displacement, while a negative difference suggests that the FPB may increase the structure’s displacement. In some of the figures, red boxes are used to highlight and magnify specific areas, which are also shown within the same figure. From Figure 26, Figure 27 and Figure 28, it is evident that the seismic mitigation structure has slightly increased the maximum displacement of the side wall compared to the original structure, but the increase is relatively small. On the other hand, the subway station structure with FPB has led to a reduction in the maximum displacement of the central columns. This reduction is relatively small under minor seismic forces (0.05 g, 0.1 g) but more significant under severe seismic conditions (0.2 g, 0.4 g); the maximum reduction could reach approximately 36 mm. The displacement values of the side wall of the subway station structure with FPB on the top of the central column are slightly bigger than that of the original structure, which is due to the decreased lateral stiffness of the structure with FPB on the top of the central column. The reduction in central column displacement is attributed to the change in boundary constraints on the top of the central column, transforming it from a fixed connection to an approximate hinge. This change substantially releases the horizontal displacement of the central column, resulting in the displacement of the top slab of the seismic mitigation structure not being transferred to the upper central column effectively.

In order to gain a deeper understanding of the deformation characteristics of the subway station structure, Figure 29 illustrates the inter-story displacements for various conditions. As shown in Figure 29, the inter-story displacements of the subway station’s structural layers remain well below 1/250 under seismic forces, which meets the design standard. Importantly, the implementation of FPB on the top of the central column leads to an increase in inter-story displacements. The maximum inter-story displacement angle occurs at the lower level of the subway station structure. The increase in the inter-story displacement angle of the subway station structure is attributed to the release of horizontal displacement in the central column by the FPB, resulting in an overall reduction in the station’s lateral stiffness.

Figure 30 compares tensile damage nephograms of the structure under two unfavorable conditions and in a layered soil site. From this illustration, it is evident that the central column of the original structure is nearly destroyed, while the seismic mitigation structure experiences only minor tensile damage. When the subway station structure is situated in a site with a weak interlayer, the implementation of FPB shifts the damage that occurs at the connection of the top and bottom slabs with the central column to the connection points between the top and bottom slabs with the side wall. During an earthquake, the damage to the central column typically occurs earlier than that to the side wall. The use of FPB can effectively mitigate the seismic damage to the central column, ensuring the protection of the subway station structure.

To provide a more intuitive illustration of the seismic damping effect of FPB in a site with a weak interlayer, the shear forces and bending moments on the bottom of the structural central column between the original and seismic mitigation structures are compared. In this context, the damping ratio is employed as the criterion for evaluating the damping effectiveness. The damping ratio can be defined using Equation (7) in this context.

γ = \frac{A_{0} - A_{R}}{A_{0}}

(7)

In the equation, under the same conditions, A₀ represents the internal force values within the top and bottom cross-sections of the central columns of the original structure, while A_R represents the internal force values within the top and bottom cross-sections of the central columns of the seismic mitigation structure.

Figure 31 provides the damping ratio plots for structures under different site conditions. It can be seen from Figure 31 that the damping ratio of the seismic mitigation structure in the weak interlayer site is higher compared to that in the layered soil site. This implies that the seismic mitigation effect of FPB in weak interlayer sites surpasses their seismic mitigation effect in layered soil sites. The maximum damping ratio observed in the shear force of the central column could reach 94%. The central column of the subway station structure is the component most vulnerable to seismic forces and prone to shear failure under seismic motion. The seismic mitigation scheme with FPB on the top of the central column of the subway station in a site with a weak interlayer can effectively reduce the damage to the subway station structure, demonstrating excellent seismic mitigation effects. Therefore, when the station is situated on a site with a weak interlayer, the use of FPB for seismic design is worth considering.

4. Conclusions

This study investigates the seismic response of the subway station structure with a double-layer double-span rectangular underground foundation. The influence of factors such as weak interlayer thickness, location, and strength on the seismic response of subway station structures is investigated by establishing the two-dimensional finite element model of the soil-structure interaction. This paper proposes a seismic mitigation structure that involves installing FPB on the top of the central column within the subway station. Then, the seismic mitigation effectiveness of FPB in weak interlayer conditions is discussed by the two-dimensional dynamic time history analysis method of the soil structure systems. The main conclusions are as follows:

(1) When the weak interlayer is situated in the middle of the subway station structure, the seismic effect is most pronounced. If the weak interlayer is located at the top or bottom of the subway station structure, the structural impact is less pronounced. The influence is close to that of a layered soil site condition when the weak interlayer is situated in the upper and lower sections of the station. These patterns become especially evident when the seismic acceleration reaches 0.4 g;

(2) When the weak interlayer is situated in the middle of the subway station structure, the maximum horizontal displacement of the structure follows a trend of initially decreasing and then increasing with an increase in the thickness of the weak interlayer. The greater thickness of the weak interlayer exacerbates seismic tensile damage to the structure, particularly affecting the central columns and side wall. A weak interlayer thickness of 3 m is the most detrimental to structural safety;

(3) With the increase in shear wave velocity, there is a decreasing trend in the maximum displacement of the structural side wall and central column. In other words, an increase in the hardness of the weak interlayer can restrain structural deformations and reduce tensile damage to the structural side wall;

(4) In comparison to the original structure, the installation of FPB on the top of central columns reduces the overall structural lateral stiffness of the station, resulting in a slight increase in the maximum displacement of the side wall and the inter-story displacement angle of the upper and lower levels of the subway station structure. It also increases tensile damage to the side wall;

(5) The installation of FPB effectively reduces the deformation of central columns, especially under strong seismic conditions (0.4 g), the maximum reduction could reach 36 mm. This effectively reduces tensile damage of the central column but simultaneously transfers damage at the connection points of the top and bottom slabs with the central columns to the connection points with the side wall;

(6) The seismic mitigation scheme with FPB on the top of central column of subway station structure significantly reduces the internal forces in the central column. The most pronounced seismic reduction is observed in shear forces, with a reduction rate of up to nearly 95%. In complex site conditions involving weak interlayers, the seismic reduction effect of the seismic mitigation structure is superior to that of layered ground conditions.

In general, based on the findings of this study, it is evident that a weak interlayer has an adverse impact on the seismic performance of station structures. The installation of FPB on the top of the central column of the subway station structure effectively reduces seismic damage to the structure. The proposed seismic mitigation scheme in this paper is suitable for situations where the subway station structure is located in a weak interlayer site. Additionally, the seismic mitigation effectiveness in weak interlayer sites surpasses that in layered soil sites. Particularly in the case of larger seismic events, the seismic mitigation effect becomes more pronounced. This highlights the importance of using FPB for seismic design in complex site conditions. However, it should be noted that the installation of FPB may increase damage to the connections between the structural side wall and the top and bottom slabs. Therefore, it is necessary to strengthen the seismic performance at these locations, especially when subjected to significant seismic input.

Author Contributions

Conceptualization, Z.X. (Zigang Xu) and C.L.; methodology, Z.X. (Zigang Xu) and R.H.; software, C.L.; validation, Z.X. (Zigang Xu); formal analysis, Z.X. (Zongyao Xia); data curation, Z.X. (Zigang Xu); writing—original draft preparation, C.L.; writing—review and editing, Z.X. (Zongyao Xia); visualization, Z.X. (Zongyao Xia); project administration, Z.X. (Zigang Xu); funding acquisition, Z.X. (Zigang Xu) and R.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research is jointly funded by the National Natural Science Foundation of China (No. 52108453), the Youth Talent Support Project Program of Jiangxi Province (No. 2024QT02), the Natural Science Foundation of Jiangxi Province (No. 20212BAB214014 and No. 20232BAB204084), the China Postdoctoral Science Foundation Project (No. 2023M741159), and the Natural Science Foundation of Inner Mongolia Autonomous Region (No. 2023QN05012).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are available in a publicly accessible repository.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Size and reinforcement of the subway station. (a) Size of the subway station. (b) Reinforcement diagram of the subway station.

Figure 2. Schematic diagram of the soil-underground structure working condition.

Figure 3. Finite element model.

Figure 4. Input ground motion acceleration time history curve. (a) Chi-Chi earthquake. (b) Dzuce earthquake. (c) Manjil earthquake.

Figure 5. Schematic diagram of the section node.

Figure 6. Maximum displacement of the station side wall at different positions. (a) 0.2 g. (b) 0.4 g.

Figure 7. Maximum displacement of the station upper column at different positions. (a) 0.2 g. (b) 0.4 g.

Figure 8. Maximum displacement of the station lower column at different positions. (a) 0.2 g. (b) 0.4 g.

Figure 9. Tensile damage of the station at different positions under a 0.2 g Chi-Chi earthquake. (a) Layered soil site. (b) Upper. (c) Top. (d) Middle. (e) Bottom. (f) Lower.

Figure 10. Tensile damage of the station at different positions under a 0.4 g Chi-Chi earthquake. (a) Layered soil site. (b) Upper. (c) Top. (d) Middle. (e) Bottom. (f) Lower.

Figure 11. Maximum displacement of the station side wall. (a) Chi-Chi earthquake. (b) Dzuce earthquake. (c) Manjil earthquake.

Figure 12. Maximum displacement of the station upper column. (a) Chi-Chi earthquake. (b) Dzuce earthquake. (c) Manjil earthquake.

Figure 13. Maximum displacement of the station lower column. (a) Chi-Chi earthquake. (b) Dzuce earthquake. (c) Manjil earthquake.

Figure 14. Tensile damage of the station at different positions under a 0.05 g Chi-Chi earthquake. (a) H = 0 m. (b) H = 1 m. (c) H = 1.5 m. (d) H = 2 m. (e) H = 2.5 m. (f) H = 3 m.

Figure 15. Tensile damage of the station at different positions under a 0.1 g Chi-Chi earthquake. (a) H = 0 m. (b) H = 1 m. (c) H = 1.5 m. (d) H = 2 m. (e) H = 2.5 m. (f) H = 3 m.

Figure 16. Tensile damage of the station at different positions under a 0.2 g Chi-Chi earthquake. (a) H = 0 m. (b) H = 1 m. (c) H = 1.5 m. (d) H = 2 m. (e) H = 2.5 m. (f) H = 3 m.

Figure 17. Tensile damage of the station at different positions under a 0.4 g Chi-Chi earthquake. (a) H = 0 m. (b) H = 1 m. (c) H = 1.5 m. (d) H = 2 m. (e) H = 2.5 m. (f) H = 3 m.

Figure 18. Maximum displacement of the station side wall and column. (a) Side wall. (b) Upper column. (c) Lower column.

Figure 19. Tensile damage of the station with different shear wave velocities. (a) Shear wave velocity of 80 m/s. (b) Shear wave velocity of 90 m/s. (c) Shear wave velocity of 100 m/s. (d) Shear wave velocity of 110 m/s. (e) Shear wave velocity of 120 m/s.

Figure 20. Section of the friction pendulum bearing.

Figure 21. Force analysis diagram of the slide block.

Figure 22. Cross section of the friction pendulum bearing.

Figure 23. 3D detailed finite element model of the friction pendulum bearing.

Figure 24. Verification of the finite element simulation results of the friction pendulum bearing. (a) 100 kN. (b) 200 kN.

Figure 25. Finite element model of friction pendulum bearing.

Figure 26. Difference in the maximum displacement of the side wall and column with different thicknesses. (a) Side wall. (b) Upper column. (c) Lower column.

Figure 27. Difference in the maximum displacement of the side wall and column at different positions. (a) Side wall. (b) Upper column. (c) Lower column.

Figure 28. Difference in the maximum displacement of the side wall and column with different shear wave velocities. (a) Side wall. (b) Upper column. (c) Lower column.

Figure 29. Interstorey displacement angle of the station under different conditions. (a) Thickness of the interlayer. (b) Positions. (c) Shear wave velocity.

Figure 30. Tensile damage of the station under different conditions. (a) H= 3 m at 0.4 g (original structure). (b) H = 3 m at 0.4 g (shock absorption structure). (c) Middle at 0.4 g (original structure). (d) Middle at 0.4 g (shock absorption structure). (e) Layered soil site at 0.4 g (original structure). (f) layered soil site at 0.4 g (shock absorption structure).

Figure 31. Decreasing amplitude ratio of the force of structure under the Chi-Chi earthquake. (a) Bending moment. (b) Shearing force. (c) Bending moment. (d) Shearing force.

Table 1. Site soil parameters.

Layer No.	Thickness (m)	ρ (kg/m³)	Vs (m/s)	ν
1	4	2000	170	0.3
2	4	2000	205	0.3
3	4	2000	240	0.3
4	2	2000	275	0.3
5	2	2000	275	0.3
6	4	2000	310	0.3
7	4	2000	345	0.3
8	4	2000	380	0.3
9	4	2000	415	0.3
10	4	2000	450	0.3
11	4	2000	485	0.3

Table 2. List of operating conditions.

Condition	Interlayer Position (m)	Relationship between Interlayer and Underground Structure Position	Thickness of Interlayer (m)	Shear Wave Velocity (m/s)
1	Layered soil site
2	2	Upper	2	80
3	6	Top	2	80
4	12	Middle	2	80
5	19	Bottom	2	80
6	22	Lower	2	80
7	12.5	Middle	1	80
8	12.25	Middle	1.5	80
9	11.75	Middle	2.5	80
10	11.5	Middle	3	80
11	12	Middle	2	90
12	12	Middle	2	100
13	12	Middle	2	110
14	12	Middle	2	120

Table 3. Dynamic plastic–damage model parameters of concrete.

Model Parameters	Parameter Values	Model Parameters
Initial yield compressive stress σ c/MPa	20.72	Tensile stiffness recovery coefficient/ωt	0
Ultimate compressive stressσ cu/MPa	29.6	Compression stiffness recovery coefficient/ωc	1
Initial yield tensile stressσ t0/MPa	2.95	Damage factor	dc, dt
Divergence angle ψ/(°)	38

Table 4. Compressive stress and damage factor versus plastic strain.

Plastic strain (%)	0.0	0.13	0.19	0.26	0.31	0.42	0.53	0.78	1.48
Compressive stress (MPa)	29.6	26.5	21.53	17.32	14.18	10.15	7.79	5.25	2.32
Damage factor	0.0	0.37	0.49	0.59	0.65	0.74	0.79	0.85	0.93

Table 5. Tensile stress and damage factor versus cracking displacement.

Cracking strain (%)	0.0	0.011	0.018	0.058	0.107	0.205	0.399	1.56	3.07
Tensile stress (MPa)	3.42	2.7	2.17	1.05	0.68	0.43	0.27	0.11	0.07
Damage factor	0.0	0.34	0.49	0.78	0.86	0.93	0.96	0.98	0.99

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Xu, Z.; Li, C.; Xia, Z.; Han, R. Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers. Appl. Sci. 2024, 14, 6608. https://doi.org/10.3390/app14156608

AMA Style

Xu Z, Li C, Xia Z, Han R. Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers. Applied Sciences. 2024; 14(15):6608. https://doi.org/10.3390/app14156608

Chicago/Turabian Style

Xu, Zigang, Chunyu Li, Zongyao Xia, and Runbo Han. 2024. "Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers" Applied Sciences 14, no. 15: 6608. https://doi.org/10.3390/app14156608

APA Style

Xu, Z., Li, C., Xia, Z., & Han, R. (2024). Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers. Applied Sciences, 14(15), 6608. https://doi.org/10.3390/app14156608

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