Seismic responses of an intensively constructed metro station-passageway-shaft structure system

Abstract

Intensive construction methods offer benefits for metro station development, yet they present challenges for seismic design due to the spatially asymmetric configuration of passageway-shaft structures. In this study, a detailed numerical model of a station-passageway-shaft structure system built using intensive construction methods was developed and the deformation and damage modes under seismic loadings were analyzed. The results indicate that inconsistent deformation between the shaft and the station generates interaction through the connecting passageway, leading to damage near the opening of the station structure and both ends of the connecting passageway Damage is more severe under longitudinal excitation. Compared with the opening plan that spans four segments, the opening plan that spans five segments exacerbates the overall degree of damage to the structure system. Under transverse excitation, the presence of interior structures intensifies the damage to the station and connecting passageway, while with such internal structure in place the impact is relatively minor under longitudinal excitation. Reinforcement with steel segments near the station opening can appreciably attenuate the damage. In contrast, introducing flexible joints at both ends of the connecting passageway intensifies the damage. Hence, reinforcement using steel segments emerges as an optimal seismic mitigation strategy.

Graphical abstract

Keywords

earthquake / intensive construction / metro station / numerical simulation

1 Introduction

Metro systems play an important role in urban rail transportation networks, while station is the crucial connection node. At present, the cut-and-cover method is the main method of construction of metro stations [1]. The long construction period, hindering routine traffic, as well as narrow space formed by the dense buildings and pipelines in the vicinity, present challenges for the construction [2]. Thus, developing intensive metro station construction technology could improve utilization of underground space while minimizing impact on the urban operation.

In an attempt to achieve such intensive construction, a shield-driving tunnel method could be adopted to form the linings of an underground station in soft ground [3]. This could significantly mitigate the impact of construction on surrounding facilities and buildings. To access the station hall, openings should be made in the tunnel, connecting the pedestrian passageway with the ground-through shaft, forming the structural system of station-passageway-shaft. To reach a favorable seismic performance of the complex spatial structure system, the open section of the tunnel should not be a weak point.

A complex underground system with intersection of structural axes must have spatial variability of its dynamic response, due to the asymmetry of the three-dimensional structure [4,5]. These characteristics, together with the differences in stiffness, will produce different responses between different components of the system, and can amplify damage in the junctions of structures under uniform excitations. This also suggests that seismic safety of a more complex shaft-passageway-tunnel system constructed using a shield-driven tunnel becomes a crucial issue. Investigating the seismic response of a shaft-tunnel system can provide an opportunity to reveal the dynamic characteristics of each part as well as of the entire system. On this basis, the unfavorable sections can be identified before targeted seismic mitigation measures can be proposed.

Centrifuge tests and shaking table tests are often used to qualitatively study the seismic response of underground structures, and they offer an intuitive understanding of dynamic characteristics of such structures. The intuitive observation can provide validation for numerical simulations and analytical solutions. A few studies have focused on the junctions of tunnel-shafts. Zhang et al. [6,7] conducted a series of shaking table tests to analyze the different responses of a complex structural system composed of a vertical shaft and shield tunnels. The study evaluated the influence of the shaft under different excitations. Meanwhile, proposed analytical solutions have been validated by tests results [8–10]. Ma et al. [11] conducted shaking table tests on a joint structure of subway station and tunnel. The strains, and the differences between them, affecting the tunnel and station under seismic loading, were compared. Zhuang et al. [12] conducted shaking table tests to investigate the seismic safety of subway stations in liquefiable ground. Although model tests could accurately simulate the soil-structure interaction of underground structures, the high cost and the difficulty in fully satisfying similarity law, make it impossible to carry out parametric analysis of the complex system to understand its underlying mechanism.

In view of the complex spatial variability of an underground structure, numerical simulations have been widely adopted in seismic analysis for their advantages of being able to accurately simulate the complex geometries and the nonlinear interaction between soil and structure. Duran et al. [13] analyzed the seismic response of a shield tunnel connected to a vertical shaft considering soil nonlinearities. The results indicated that the torsional effect during shaft rocking is the decisive factor in the increase of deformation of the tunnel near the shaft-tunnel junction. Yu et al. [14] used a multi-scale method to simulate the seismic response of a full-length tunnel with three vertical shafts. According to the simulation, stress concentrations can be found at the junctions of tunnel and shaft. Chen et al. [15] established validated numerical models of a metro station connected by a tunnel and investigated the inconsistent deformation between the station and tunnel. The section located at the junction between the tunnel and the end wall of the station is the most vulnerable area. Similar studies have been carried out by other researchers [16,17]. Although a number of studies have been carried out on the seismic response of shaft-tunnel systems, few studies have been reported on a more complicated but not uncommon case: a shaft and a tunnel connected by a passageway. The dynamic characteristics of the shaft, the passageway and the tunnel differ considerably, and the dynamic interaction between them and the dynamic characteristics of the formed system are yet to be investigated.

For seismic mitigation measures in shaft-tunnel systems, current research mainly focuses on flexible joints. By installing flexible joints in areas of stiffness changes, the stress concentration in local areas can be effectively reduced. The effectiveness of flexible joints has been verified by several studies [14,15]. Kawamata et al. [18] conducted a series of shaking table tests to analyze the seismic responses of a cut-and-cover tunnel with two vertical shafts and to evaluate the seismic mitigation effect of flexible joints. The study showed that a flexible joint was effective in reducing the strain of the tunnel under seismic loading. However, damage could occur due to the differential settlement between the tunnel and shaft. Although the installation of flexible joints is a potential measure to reduce the seismic response of a shaft-tunnel system, for more complex systems such as an intensively constructed shaft-passageway-tunnel system, the dynamic response mode remains unclear. In addition, it is unclear whether there are alternative seismic mitigation measures for such a complex underground structural system.

In this paper, refined numerical models of a station intensively constructed with tunnel-passageway-shaft were established in ABAQUS. In a quest to elucidate the dynamic response mechanisms and failure modes within intricate structure systems, a Ricker wavelet, characterized by its elementary waveform yet with a spectrally rich composition, was employed as the seismic input to mitigate the uncertainties introduced by the stochastic nature of seismic activity. A simplified model, consisting solely of the station, was established for comparative analysis. This investigation analyzed the influence of station opening, shaft structure, and their interaction with the station, on the model’s intrinsic dynamic response. Furthermore, the impact of varying opening configurations and the interior layout of the station on its dynamic response of the entire structure system was discussed. Building upon this, two distinctive seismic mitigation measures––the integration of localized steel segments for reinforcement, and the incorporation of flexible joints in connecting passageway––were evaluated and contrasted for their efficacy in optimizing the seismic performance of the station-passageway-shaft structure assemblage.

2 Numerical model

2.1 Finite element model

To accurately simulate the reliable dynamic response of the station-passageway-shaft structure system, it is essential to establish a credible and robust numerical model. In this study, a typical stratified site in Shanghai was selected. Considering the depth of bedrock and the boundary effects in the direction of seismic vibrations, the overall dimensions of the model were set at 120 m (in the x-direction, transverse), 100 m (in the z-direction, longitudinal), and 70 m (in the y-direction, vertical). 102778 C3D8R elements (8-node linear hexahedral solid elements with reduced integration in ABAQUS) were utilized to simulate the strata, as shown in Fig.1(a). The simulated metro station, buried at a depth of 15 m to the top of the tunnel, was constructed from segmental linings of shield-driving tunnel with a diameter of 15.2 m, assembled with staggered joints. 2-m width segments with thickness of 0.65 m were interconnected via circumferential and longitudinal bolts, as illustrated in Fig.1(d). Preliminary simulations indicated that the influence range of the shaft and passage on the shield tunnel was approximately eight shield segments on either side and the influence range of the free boundaries at the tunnel ends was approximately 10 m. Therefore, to enhance computational efficiency, a refined model was employed within a 40 m range along the longitudinal direction at the station opening, while the remainder was approximated with homogenous segments through stiffness equivalence. The station had an opening on its linings at 10 m from the lining bottom (as can be seen in Fig.1(c)), and was connected to the entry-exit building (henceforth referred to as the “shaft”) through a connecting passageway culvert, which had a width of 8 m (equivalent to the width of 4 segments), a height of 4.5 m, and a top length of 15.6 m. The dimensions of the shaft structure were 16 m (x-direction) by 32 m (z-direction) by 15 m (y-direction), with a structural thickness of 0.8 m, as depicted in Fig.1(c). In total, 210232 C3D8R elements were employed to simulate the station-passageway-shaft structure system.

2.2 Constitutive models

2.2.1 Soils

The soil presents complex nonlinearity under seismic loading. The dynamic properties of soil, such as shear modulus and damping ratio, typically decrease with increasing shear strain. The equivalent linear method, widely used in the analysis of nonlinear seismic response of horizontally layered sites [19], is based on the theory of one-dimensional shear wave propagation. The equivalent shear modulus and damping ratio are adopted to approximately calculate the nonlinear response of the soil layers. In the equivalent linear method, the shear modulus and damping ratio of soil are determined according to its equivalent shear strain. The equivalent shear strain of the soil is influenced by its shear modulus and damping ratio, so an iterative approach is adopted to calculate the equivalent shear strain step by step. The SHAKE91 program is adopted to iterate the equivalent shear modulus and damping ratio of the typical Shanghai site. The calculated shear modulus is used as the equivalent shear modulus at the required strain levels and the derived damping ratio is employed as a computational parameter for Rayleigh damping using in ABAQUS. The equivalent shear modulus and decreased damping ratio can, to some extent, reflect the nonlinear feature of soil. The material parameters of the ground are listed in Tab.1.

2.2.2 Concrete

Concrete damaged plasticity (CDP) model developed by Lubliner et al. [20] and Lee and Fenves [21] is assigned to the lining sections, interior structure, and passageway culvert. Given that the shaft structure is not the central focus of this study, its material properties have been simplified to linear elasticity. The CDP model assumes that the failure modes of concrete are tensile cracking and compressive crushing. This model can simulate both tensile cracking and compressive crushing, as well as the degradation mechanism of concrete stiffness and the mechanical properties of stiffness recovery under reverse loading. Stiffness degradation happens during unloading after the stress surpasses its peak value. If the concrete is partially damaged by tensile cracking or compressive crushing, the initial (undamaged) elastic modulus of concrete E₀ is reduced to (1 – d_c)·E₀ and (1 – d_t)·E₀, respectively. Here, d_c and d_t are the compressive and tensile damage indices of concrete, respectively, which characterize the degradation of the elastic stiffness of concrete, ranging from 0 to 1.

The material parameters of concrete are listed in Tab.2, in which the eccentricity is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote; K_c is the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian; initial stress ratio is the ratio of initial equiaxial compressive yield stress to initial uniaxial compressive yield stress.

2.3 Artificial boundary

The equal displacement boundary is widely applied and is convenient for practical use [22]. Taking the horizontal direction as the x-axis and vertical as the y-axis, the vertical direction shear wave propagation equation is:

(1)\frac{{\mathrm{\partial }}^{2}u(x,y,t)}{\mathrm{\partial }{y}^2}-\frac{1}{c_s^2}\frac{{\mathrm{\partial }}^{2}u(x,y,t)}{\mathrm{\partial }{t}^2}=0,

where u(x,y,t) represents the particle displacement, and c_s denotes the shear wave velocity. From Eq. (1), it can be seen that the motion of the medium particles is independent of x, meaning that the motion of medium particles at the same height remains consistent with time. The equal displacement boundary is employed to simulate vertical-direction shear wave propagation problems in earthquake engineering by constraining nodes at the same height on both sides of the model. This approach helps avoid the effect of reflected waves due to interference at the side boundary.

2.4 Contacts and connectors

2.4.1 Interfaces

Given the complexity of the structural system that is numerically examined in this study, numerous interfaces are significant. Contact surface pairs (master-slave surface in ABAQUS) are utilized to simulate the interfaces between segments, and between linings and soils. For the normal mechanical behavior at an interface, when the contact pressure between surfaces drops to zero or becomes negative, the two surfaces separate, and the constraint is lifted. This type of behavior exemplifies a “hard” contact. Regarding tangential mechanical behavior, an interface is characterized by Coulomb friction. The default tangential movement remains at zero until the tangential force on the surface reaches a critical shear stress value. The critical shear stress, as determined by Eq. (2) below, depends on the normal contact pressure:

(2){\tau }_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=\mu p,

where μ is the coefficient of friction; p is the contact pressure between the two contact surfaces. Equation (2) gives the critical frictional shear stress on the contact surfaces. Relative sliding between the contact surfaces does not occur until the shear stress between the contact surfaces is equal to the ultimate frictional shear stress µ p. For most situations µ is usually less than 1. The friction coefficient between the segments is set at 0.6, while the friction coefficient between the segments and the soil is established as 0.3.

2.4.2 Bolts

The bolts are characterized using a linear elastic model. The bolt density is 7850 kg/m³, with an elastic modulus of 200 GPa and a Poisson ratio of 0.3. The bolts are simulated as embedded elements in the segments. The embedded element technique is used to specify that an element or group of elements is embedded in “host” elements. If a node of an embedded element lies within a host element, the translational degrees of freedom and pore pressure degree of freedom at the node are eliminated and the node becomes an “embedded node”. The translational degrees of freedom and pore pressure degree of freedom of the embedded node are constrained to the interpolated values of the corresponding degrees of freedom of the host element. Tie-constraint is assumed at the junctions where the connecting passageway interfaces with both the station and the shaft structure.

2.5 Input motions

Both real seismic waves and synthetic waves are highly random, and as the structure system in this paper is very complex, it is necessary to simplify the input seismic waves as much as possible and clarify the response characteristics of the structure system. Ricker wavelets possess a distinct characteristic spectrum and can generate an adequate broadband energy to stimulate the response of the model. Such wavelets are extensively utilized in pertinent numerical simulations and experimental testing [23,24]. Furthermore, the time history contains a singular pulse waveform, enabling a clear observation of the structure acceleration response pattern. The Ricker wavelet is defined in the time domain as:

(3)a(t)=\left(1-2{\text{π}}^2{f}_{\mathrm{c}}^2{t}^2\right)\exp \left(-{\text{π}}^2{f}_{\mathrm{c}}^2{t}^2\right),

where f_c is the central frequency of Ricker wavelets. Fig.2 presents the Ricker wavelet with a central frequency of 1 Hz, and a peak acceleration of 0.1g. Here, the natural frequency of the site is 1 Hz.

3 Seismic response of station-passageway-shaft structure system

3.1 Dynamic response characteristics

This subsection is dedicated to the analysis of the dynamic response characteristics of the station-passageway-shaft structure system. Given that incorporating the interior structure of the station introduces a multitude of contact pairs, which consequently diminishes computational convergence, the interior structure is deliberately omitted from consideration in this subsection. The influence of the interior structure on the overall response is separately examined in Subsection 3.3. To facilitate the analysis of the impact of the shaft structure and passageway on the station, a numerical model that includes the station alone has been established for comparative purposes.

3.1.1 Deformation pattern

The characteristic deformation patterns of the station-passageway-shaft structure system under varying excitation directions are illustrated in Fig.3 and Fig.4. Fig.3 reveals that under transverse excitation, the rectangular shaft structure exhibits a racking-rocking deformation similar to that of the rectangular station [25], while the circular station structure displays a typical ovaling deformation [26]. The two structures of distinct shapes are interconnected via a connecting passageway, which exerts a certain influence on the deformation in both cases, inducing some twisting at the junctures of the passageway with the shaft structure and the station structure. Further analysis of Fig.3(c) reveals that, compared to the deformation of a single station at the same moment in time, the station within the station-passageway-shaft structure system is subject to compression from the connecting passageway.

Fig.4 demonstrates that under longitudinal excitation, the shaft structure likewise shows a racking-rocking deformation similar to that of the rectangular station, while longitudinal deformation of the station structure is not pronounced. The presence of the connecting passageway causes inconsistent motion of the shaft structure and the station, inducing a torsional effect from the shaft structure on the station. Further insights from Fig.4(c) indicate that the station not only experiences torsional effects along the axial direction, but, due to the racking deformation of the connecting passageway, the opening of the station also concurrently manifests racking deformation with the connecting passageway.

Under transverse excitation, the maximum principal stress of the connecting bolts in the station peaks at the longitudinal bolts located at the opening corner, with a value of 380.7 MPa. Under longitudinal excitation, this value rises to 403.9 MPa at the same location. For comparison, for the singular station model without an opening, the bolt’s maximum principal stresses are 363.9 MPa (located at the circumferential bolts in the shoulder) and 0.3 MPa (also at the circumferential bolts in the shoulder).

3.1.2 Damage pattern

The results of the simulation for tensile damage of the structure system for different excitation directions are depicted in Fig.5. As the shaft building is considered an auxiliary structure of the station, its damage is not accounted for. Instead, the study focuses exclusively on the destruction of the connecting passageway and station lining. As can be seen from the figure, under transverse excitation, the area of damage in the connecting passageway is primarily located at the junction with the vertical shaft. The damage direction extends at a 45° angle, a pattern caused by the racking-rocking deformation of the shaft structure. The damage to the station lining is mainly situated in the opening lining and the adjacent lining, with the level of damage being less than that of the connecting passageway. This damage is primarily due to the compression of the opening by the connecting passageway. For the single station structure without the opening and interior deck, as shown in Fig.6, the primary damage is oriented at a 45° angle to the lining, with the upper part more damaged than the bottom. Furthermore, damage is concentrated around the key segment, a phenomenon consistent with the observations made in the study by Liu et al. [27]. Compared to the damage of structural system, the level of damage is minor.

Under longitudinal excitation, the main areas of damage in the connecting passageway are located at the top and bottom corners, with the damage at the top being more severe, as shown in Fig.7. This is caused by the passageway’s own racking deformation and the torsional movement induced by the inconsistent motion between the shaft structure and the station. The primary damage area of the station lining is located at the bottom corners of the opening, as a result of the racking deformation of the passageway and the torsional effect exerted by the shaft structure. Compared with damage due to transverse excitation, the damage scope and severity under longitudinal excitation are greater. Since there is no damage in the single station structure under longitudinal excitation, a comparison was not made with that.

To further analyze the distribution pattern of damage within the structure system, the levels of tensile damage in the concrete of the station and connecting passageway have been extracted separately. In accordance with the research by Zhong et al. [28], based on the concrete tensile damage factor, the degree of concrete damage has been categorized into four grades, as presented in Tab.3, where the damage level is determined by the crack width of the concrete, and the relationship between crack width and d_t (tensile damage indices) is derived from previous study [29].

Fig.8 presents a bar chart illustrating the distribution of the degree of concrete damage in the station and passageway under different excitation directions. The total volume of the station is 1159 m³ and the total volume of the passageway is 175 m³. It can be observed that overall, the level of damage in the structure system is relatively low, with negligible damage being dominant. Under transverse excitation, the station features mostly negligible damage, with only a small amount of moderate damage, while the connecting passageway shows varying degrees of damage. Under longitudinal excitation, although the total volume of station damage has decreased compared to that in the case of transverse excitation, the severity of the damage is more pronounced. Conversely, the volume of damage of all degrees in the connecting passageway has increased compared to that under transverse excitation.

3.2 Comparison between different opening plans

In view of the potentially different station lining opening plans, it is necessary to compare the seismic response differences between these plans. The original plan involves opening at four segments of the lining, while another feasible plan, denoted as Plan B, opens at five segments. In Plan B, the lining segments on both sides of the opening are each cut to half of the segment width, as shown in Fig.9. All other model settings are kept constant.

Fig.10 presents the contour of concrete tensile damage in the structure system under transverse excitation for Plan B. Compared to the original plan, it can be seen that the range of damage in the connecting passageway is reduced with Plan B, but the degree of damage at the connection point with the shaft structure increased. No significant difference can be observed in the area of damage within the station structure. Under transverse excitation, the peak value of the maximum principal stress of the connecting bolts in the station segments is 380.4 MPa, at the longitudinal bolts of the opening corner.

Fig.11 depicts the concrete tensile damage contour in the structure system under longitudinal excitation for Plan B. It can be seen that the range of damage in the connecting passageway is significantly reduced with Plan B, compared to the original plan. However, the degree of damage at the connection point with the station is increased, while the area of damage within the station structure remains largely the same. Under longitudinal excitation, the peak value of the maximum principal stress of the connecting bolts in the station segments is 430.9 MPa, at the longitudinal bolts of the opening corner.

Fig.12 is a bar chart illustrating the distribution of the degree of concrete damage in the station and passageway under different excitation directions with Plan B. It can be observed that under different excitation directions, although the volume of negligible damage in the connecting passageway is reduced with Plan B, the volumes of damage of other degrees in both the station and the connecting passageway are increased. Particularly under longitudinal excitation, Plan B significantly increases the volume of severe damage in the station. Therefore, compared to the original plan, Plan B exacerbates the overall degree of damage to the structure system and is not a desirable choice.

3.3 Effects of interior structure

The interior structure has a significant impact on the dynamic performance of the station. Some studies have shown that the presence of interior structures has a constraining effect on the extension/closure of longitudinal joints in the lower half of the segmental lining, while it induces adverse effects on the extension/closure of the longitudinal joints in the upper half of the segmental lining [30]. To investigate the influence of interior structures on the seismic performance of station-passageway-shaft structure system, a model considering the interior structures was established. Fig.13 presents the diagram of interior models.

Fig.14 represents the concrete tensile damage in the structure system under transverse excitation when taking account of the interior structure. Compared to when the interior structure is not considered, there is no difference in the distribution of damage on the side of the connecting passageway connected to the shaft structure, whereas the range of damage on the side connected to the station increases. Upon introducing the interior structure, the damage severity within the station significantly increases. In addition to the increased range of damage around the opening, varying degrees of damage appear in the area connected to the bottom slab of the interior structure. It is worth noting that no damage occurs to the key segments in this area, as the joint deformation of the key segments absorbs the deformation from the interior structure, resulting no damage to occur to the concrete of the segments. Additionally, the damage to the interior structure itself is quite severe, mainly concentrated at the connection between the concourse level and the station lining, as well as at the tops and bottoms of the columns. The maximum principal stress of the connecting bolts in the station segments is greatest at the circumferential bolts appearing in the area connected to the bottom slab of the interior structure, measuring 344.7 MPa.

Fig.15 illustrates the contour of concrete tensile damage in the structure system under longitudinal excitation when considering the interior structure. Compared to when the interior structure is not considered, there is no difference in the distribution of damage on the side connecting the passageway to the shaft structure, while the range of damage on the side connected to the station increases. Adding the interior structure also slightly increases the damage severity within the station. However, no damage occurs within the interior structure itself. The peak value of the maximum principal stress of the connecting bolts in the station segments is 397.2 MPa, at the longitudinal bolts of the opening corner.

Fig.16 is a bar chart showing the distribution of the degree of concrete damage in the station and passageway under different excitation directions when taking account of the interior structure. Under transverse excitation, the volumes of damage of different degrees in both the station and the connecting passageway significantly increase, with the damage to the interior structure itself being the most severe. Under longitudinal excitation, the damage to the interior structure itself is rather slight. While the volume of negligible damage in the station and the connecting passageway is increased, the volume of severe damage is decreased. In conclusion, under transverse excitation, the interior structure has severe detrimental effects on the structure system, while under longitudinal excitation, it can reduce the severity of significant damage to the structure system to some extent.

4 Potential seismic mitigation methods

4.1 Steel shield segment reinforcement

In light of the previous analysis of the deformation and damage patterns of the structure system, reinforcing weak areas of the system with steel segments to reduce concrete damage emerges as a viable approach to enhancing the seismic resistance of the system. Therefore, the segments at the station opening and its adjacent segments are replaced with steel segment, and the connection between the connecting passageway and the station is replaced with steel joints, as shown in Fig.17. The material parameters of the steel segments are detailed in Tab.4. To simulate the lattice-like steel segments used in actual engineering projects with a homogenous steel segment, and to ensure consistent bending stiffness between the two, numerical simulations determine that the elastic modulus of the homogenous steel segment should be 80 GPa.

Fig.18 depicts the contour of concrete tensile damage in the structure system under transverse excitation after reinforcement with steel segments. It can be seen that since the station opening and the connecting passageway linked to it have been replaced with steel segments, damage is confined to the connection between the connecting passageway and the shaft structure, and the distribution pattern has not undergone any changes. The peak value of the maximum principal stress of the connecting bolts in the station segments is 381.2 MPa, at the longitudinal bolts of the opening corner.

Fig.19 displays the contour of concrete tensile damage in the structure system under longitudinal excitation after reinforcement with steel segments. As for transverse excitation, as the station opening and part of the connecting passageway linked to it are replaced with steel segments, damage is confined to the connection between the connecting passageway and the shaft structure, and the distribution pattern remains unchanged. The peak value of the maximum principal stress of the connecting bolts in the station segments is 437.4 MPa at the longitudinal bolts of the opening corner.

Fig.20 is a bar chart demonstrating the distribution of the degree of concrete damage in the station and the passageway under different excitation directions after reinforcement with steel segments. It is discernible that regardless of the excitation direction, reinforcement with steel segments effectively reduces the degree of damage to the structure system. This effect is especially significant for the station, whereas some level of damage still exists in the connecting passageway due to the lack of reinforcement at the connection with the shaft structure. In summary, reinforcing with steel segments is a commendable seismic mitigation measure that can effectively lessen the degree of concrete damage in the structure system.

4.2 Flexible joint

Given the previous analyses, the root cause of damage to the structure system is the inconsistent movement between the station and the shaft structure. This inconsistency, mediated by the presence of the connecting passageway, leads to an interaction between these elements, resulting in damage at the opening of the station and the connecting passageway. Hence, the use of flexible joints, placed at the junctions of the connecting passageway with the station and the shaft structure, could potentially reduce the damage to the structure system by lowering the axial rigidity and shear resistance of the connecting passageway. Fig.21 provides a schematic illustration of the flexible joints. The material parameters of the flexible joints are detailed in Tab.5.

Fig.22 shows the contour of concrete tensile damage in the structure system under transverse excitation after the application of flexible joints. It is noticeable that the incorporation of flexible joints has altered the damage distribution pattern in the connecting passageway, with concrete damage concentrated on both sides of the joint and an apparent increase in the damage level. However, the damage distribution pattern in the station remains unchanged. The peak value of the maximum principal stress of the connecting bolts in the station segments is 272.0 MPa, at the longitudinal bolts of the opening corner.

Fig.23 presents the contour of concrete tensile damage in the structure system under longitudinal excitation after the application of flexible joints. The application of flexible joints has not altered the damage distribution pattern in the connecting passageway but has significantly increased the damage level at the junction of the connecting passageway and the station. However, the damage extent within the station has diminished. The peak value of the maximum principal stress of the connecting bolts in the station segments is 434.2 MPa, at the longitudinal bolts of the opening corner.

Fig.24 is a bar chart showing the distribution of concrete damage levels in the station and the passageway under different excitation directions after the application of flexible joints. It can be observed that under transverse excitation, the application of flexible joints not only fails to decrease the damage to the structure system but, conversely, intensifies the damage in both the station and the connecting passageway. Under longitudinal excitation, while the application of flexible joints increases the volume of slight to severe damage in the connecting passageway, it reduces the degree of damage to the station.

Flexible joints, while capable of mitigating deformation in the connecting passageway by undergoing deformation themselves, encounter a limitation due to their intrinsic pliability. This characteristic leads to significant deformation of the joints, which, in turn, induces commensurate deformation in the surrounding concrete, culminating in structural damage. However, by attenuating the interaction forces generated from the disparate deformations between shaft and station, the flexible joint imparts a slight reduction in the extent of damage to the station structure. Thus, the application of flexible joints may not be an optimal seismic mitigation measure.

5 Conclusions

In this paper, refined numerical models of intensively constructed station-passageway-shaft were established. A simplified model, consisting solely of the station, was constructed and juxtaposed with a more complex structure arrangement for comparative analysis. This investigation scrutinized the influence of station apertures and shaft structures and their interaction with the station on the station’s intrinsic dynamic response. Furthermore, the impact of varying station opening configurations and the interior layout on the dynamic response of the entire structure system was discussed. Building upon this, two distinctive seismic mitigation measures––the integration of localized steel segments for reinforcement, and the incorporation of flexible joints in the connecting passageway––were evaluated and contrasted for their efficacy in optimizing the seismic performance of the station-passageway-shaft structure system.

Under transverse excitation, the rectangular shaft structure exhibits a racking-rocking deformation, while the circular station structure displays a typical ovaling deformation. Both structures of distinct shapes are interconnected via a connecting passageway, inducing some twisting at the junctures of the shaft structure with the connecting passageway and station with the connecting passageway, and making the station subject to compression from the passageway. Under longitudinal excitation, owing to the inconsistent motion between the shaft structure and the station, a torsional effect from the shaft structure on the station can be observed. Due to the racking deformation of the connecting passageway, the opening of the station also concurrently manifests racking deformation with the connecting passageway.

The following conclusions can be drawn.

1) The area of damage in the connecting passageway is primarily located at the junction with the vertical shaft, while the damage of the station is mainly situated in the opening lining. The degree of damage to the station is lighter than that of the connecting passageway. The areas of damage in the connecting passageway are located at the top and bottom corners, while the damage of the station is located at the bottom corners of the opening. In general, the damage to the structure system is more severe under longitudinal excitation than that under transverse excitation.

2) Compared with the opening plan that opens 4 segments, the opening plan that opens 5 segments exacerbates the overall degree of damage to the structure system and is not a desirable choice.

3) The presence of interior structures considerably exacerbates the extent of damage to the structure system under transverse excitation with the interior structures themselves sustaining significant damage under seismic actions. Conversely, under longitudinal excitation, the interior structures do not considerably contribute to the overall damage of the system.

4) The reinforcement around station openings with steel segments can appreciably attenuate the damage attributed to the inconsistent movements within the complex structure system, thus representing a commendable seismic mitigation measure. The installation of flexible joints at both ends of connecting passageway alters the damage patterns of the structure system, localizing the damage in the vicinity of the joints. However, this configuration tends to increase the overall extent of damage of the passageway, thus rendering it a suboptimal seismic mitigation measure.

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