Effect of strata restraint on seismic performance of prefabricated sidewall joints in fabricated subway stations

Abstract

A disadvantage of the conventional quasi-static test method is that it does not consider the soil restraint effect. A new method to test the seismic performance of prefabricated specimens for underground assembled structures is proposed, which can realistically reflect the strata restraint effect on the underground structure. Laboratory work combined with finite element (FE) analysis is performed in this study. Three full-scale sidewall specimens with different joint forms are designed and fabricated. Indices related to the seismic performance and damage modes are analyzed comprehensively to reveal the mechanism of the strata restraint effect on the prefabricated sidewall components. Test results show that the strata restraint effect effectively improves the energy dissipation capacity, load-bearing capacity, and the recoverability of the internal deformation of the precast sidewall components. However, the strata restraint effect reduces the ductility of the precast sidewall components and aggravates the shear and bending deformations in the core region of the connection joints. Additionally, the strata restraint effect significantly affects the seismic performance and damage mode of the prefabricated sidewall components. An FE model that can be used to conduct a seismic performance study of prefabricated specimens for underground assembled structures is proposed, and its feasibility is verified via comparison with test data.

Graphical abstract

Keywords

underground structures / precast sidewall specimen / seismic test method / bearing capacity / energy dissipation capacity / plastic deformation

1 Introduction

In the “safe, fast, and green” construction method, assembled structures are widely used for aboveground assembled buildings, and shield tunnels for underground structure construction [1,2], but are adopted less frequently in subway stations. Currently, subway stations are constructed using cast-in-place concrete. However, during the cold season or in cold regions, this construction method is primarily constrained by weather conditions and temperature, which affect the concrete strength after casting [3–5]. Therefore, the construction of assembled subway stations has garnered the attention of researchers and construction enterprises.

Underground prefabrication technology began in the 19th century, where it was used for subway construction in Japan, the Netherlands, and the former Soviet Union [6]. However, its application did not expand owing to the development of tunneling shield technology. The demand for metro transportation is increasing owing to urbanization and the increase in population density. In recent years, assembled subway station technology has received more attention from construction enterprises and research institutes. The Yuanjiadian Station in Changchun [7,8], as shown in Fig.1, is the first single-arch large-span prefabricated assembly subway station in China. The standard ring of the prefabricated subway station measures 2 m wide and comprises seven prefabricated blocks connected via mortise-tenon joints. Owing to the successful construction of five assembled subway stations along Changchun Metro Line 2, other cities have begun to adopt assembled structures in open-cut subway construction. Beijing Jin’anqiao Station [9], as shown in Fig.2, is the first assembled monolithic underground structure in China. Its transverse section features a double-layered, three-span box structure, with prefabricated components connected by grout sleeves. Since its construction, other cities in China such as Shenzhen, Guangzhou, and Qingdao have begun to consider or have applied prefabricated assembly subway construction methods. Assembly subway construction technology is likely to become the preferred method for future subway construction.

As a fundamental component of urban transportation, the seismic performance of underground structures is particularly important. He and Li [8] analyzed the effect of the joint distribution form on the seismic performance of assembled station structures based on Yuanjiadian Station in Changchun, China. They discovered that the sidewall joints were the critical joints of the overall structure and that they were damaged the most severely. Ding et al. [9] and Tao et al. [10,11] conducted numerical simulations and shaking table tests on assembled subway stations with mortise-tenon joints to qualitatively reproduce macroscopic phenomena under actual seismic conditions. They investigated the seismic response of the overall structure of metro stations. However, the seismic performance of connection joints in prefabricated components should be prioritized instead of the dynamic response characteristics of the assembled metro station structure. Liu et al. [12–14] conducted a quasi-static test on structural connection joints with grout sleeves based on an assembled monolithic subway station similar to Beijing Jin’anqiao Station. The seismic performance of the connection joints at different locations of the station structure was obtained; however, the strata restraint effect was not considered.

Based on existing studies pertaining to underground structures [15–17], underground structures primarily depend on the constrained deformation of the surrounding soil and, to a lesser extent, the mechanical properties of the surrounding soil; this is different from the dynamic response of aboveground structures, which is characterized by vibration caused by the inertial forces of the structures. Wang et al. [18], Zhuang et al. [19,20], and Sayed et al. [21] investigated the effect of the mechanical properties of a soil–structure contact surface on the dynamic response of large subway stations. The results indicated that the dynamic response of subway stations decreased when the dynamic contact effect was considered. Sun et al. [22], Deng et al. [23], and Chen et al. [24] conducted a dynamic analysis on an interval tunnel at the junction of soft and hard strata. The presence of soft soil layers increased the deformation and the internal forces of the tunnel. Qiu et al. [25,26] compared the vibration effects of large underground structures and small frame structures and discovered that the seismic response of the former was more significant, whereas the deformation and internal forces of the latter were greater. Chian and Madabhushi [27], Li and Chen [28] discovered that the burial depth significantly affected the seismic response of subway stations. The aforementioned studies show that the strata restraint effect is vital to the dynamic response of subway stations and thus cannot be disregarded. However, the effect of soil restraint on the seismic performance of prefabricated sidewall components of underground assembly structures has not been reported.

Under seismic conditions, the stress characteristics of underground and aboveground structures differ significantly. Seismic test methods of aboveground assembled structural prefabricated components must not be applied directly to underground assembled structural prefabricated components. Based on existing studies and assembled subway station projects, a strata restraint quasi-static method is proposed herein for underground precast components, which can realistically reflect the strata restraint effect on underground structures. Tests are conducted on three full-scale sidewall specimens with different joint forms using the proposed method to reveal the effect of strata restraint on the dynamic performance and failure mode of prefabricated sidewall components. Additionally, a finite element (FE) model that can be used to conduct seismic performance studies of prefabricated specimens for underground assembled structures is proposed. This study serves as a reference for the seismic design of assembled subway-station structures.

1.1 Seismic test method for prefabricated sidewall specimens

1.1.1 Underground structure force state

Fig.3 shows the relationship between the surrounding soil and underground structures.

(1) The underground structure is primarily affected by the earth-water pressure and the all-encompassing restraining effect from the surrounding strata, which serve as both a load and carrier.

(2) The subway station is “enveloped” in soil under synchronous vibration and shared deformation with the ground. Deformation from the surrounding soil imposes a significant effect.

1.2 Mechanical model and parameter determination

1.2.1 Mechanical model

Existing seismic test methods primarily include quasi-static, quasi-dynamic, and shaking table tests. Among them, quasi-dynamic and shaking table tests are time dependent and can only reflect the seismic demand of a structure or component. Quasi-static tests are widely performed owing to their simple test conditions and their ability to reveal the seismic capacity of a structure.

According to the Chinese Standard JGJ/T101-2015, “Building Seismic Test Procedure,” a cyclic reciprocal horizontal force or displacement must be applied to the structure or component under investigation in the quasi-static test. The mechanical model for the test is presented in Fig.4, which shows that the conventional quasi-static method is primarily applied to aboveground structures or components, and thus only considers the deformation of the structure due to inertial forces during an earthquake. Underground structures are not only deformed together with the soil during an earthquake, but are also subjected to the restraint effect of the soil. Therefore, the conventional quasi-static test method cannot be used for the seismic analysis of underground structures.

Based on the conventional quasi-static method, a strata restraint quasi-static method is proposed by considering the constrained deformation of the soil during an earthquake. The mechanical model of this method is shown in Fig.5. The distribution of the earth load on the sidewall is assumed to exhibit an inverted triangular shape [10,11]. Because the height of the sidewall of the specimens is significantly smaller than that of the actual structure, the model is simplified by considering the soil restraint load as a uniform load. Compared with the test method for prefabricated specimens of aboveground assembled structures, the model provides a better visualization of the forces on the prefabricated sidewalls of underground assembled structures, such as those at Yuanjiadian Station, during an earthquake.

1.2.2 Key parameter determination

The seismic test method proposed herein, which considers the strata restraint effect, requires the value of spring stiffness in the horizontal direction of the prefabricated sidewall components.

According to the Chinese standard GB50909-2014, “Code for Seismic Design of Urban Rail Transit Structures” [29] and the Japanese standard “Underground Structures” [30], the reaction displacement method introduces foundation springs to reflect the strata restraint effect of on underground structures, whereas the mutual effect between the soil and structure can be quantitatively expressed. Therefore, the foundation spring stiffness can be considered in the reaction displacement method, i.e., the static FE method [29]. The calculation model is shown in Fig.6.

A uniform load q in the horizontal direction is applied to the soil on the sidewall. The deformation under load is calculated to obtain the foundation bed coefficient, K=q/\delta. For simplification, the size of the prefabricated sidewall specimens used in the test is set to significantly smaller than the actual size of the station sidewalls, and the spring stiffness on the same surface of the underground structure is assumed to be the same. After determining the foundation bed coefficient, the foundation spring stiffness is calculated using Eq. (1).

(1)k=KLd,

where k is the compressed foundation spring stiffness (N/m), K is the foundation bed coefficient (MPa/m), L is the concentrated spring space of the foundation (m), and d is the calculated length of the strata along the longitudinal direction of the underground structure (m).

2 Experimental details

The production process, test equipment, and scheme of the specimens are described comprehensively in this section.

2.1 Specimen design

Precast sidewall full-scale specimens with parallel threaded sleeves (PTCWJ specimens), precast sidewall full-scale specimens with mortise-tenon joints (MTWJ specimens), and cast-in-place sidewall full-scale specimens (CWJ specimens) were designed and fabricated. The specimens were cast in C50 concrete and reinforced with HRB400 ribbed steel via a 25 mm longitudinal reinforcement and a 12 mm hoop reinforcement. The parallel-threaded sleeves were composed of #45 steel with a length of 72 mm. The mortise and tenon of the MTWJ specimens were reinforced with steel measuring 25 mm in diameter, and two precast pieces were poured simultaneously and then assembled on site. The PTCWJ specimens were first prepared by pouring two prefabricated components, followed by connecting the two prefabricated components through parallel threaded sleeves after maintenance was completed, and finally pouring the components onto the connection area. Fig.7–Fig.9 show the geometric dimensions of the specimens.

In addition, the ground anchor bolt holes around the base were locally reinforced with spiral reinforcement. Tests were performed on the reinforced concrete specimens to determine the mechanical properties of the reinforcement and concrete. The concrete compressive and tensile strengths were 55.1 and 2.9 MPa, respectively. The yield strength and ultimate strength of the reinforcement were 447 and 645 MPa, respectively. The yield strength and ultimate strength of the reinforcement with parallel threaded sleeves were 443 and 621 MPa, respectively.

2.2 Loading equipment and loading scheme

2.2.1 Loading equipment

Ding et al. [31] simulated the effect of soil load on a segmental joint using vertical jacks and distribution beams. Zhou et al. [32] used two points of simultaneous loading on both sides of a segmental joint to simulate the loading impact from surrounding soil. Additionally, the damage mechanism of the single-loop structure of a shield tunnel under a strata restraint load was investigated via multipoint concentrated force simultaneous loading [33]. The studies above show that loading using a jack and distribution beam and loading via the multipoint simultaneous approach can simulate the effect of strata restraint loads on underground structures. However, the loading method for precast components primarily uses jacks and distribution beams [34–36]. Based on previous studies and experience, and considering the necessity to apply horizontal reciprocating loads on the top of precast specimens, we applied loading to precast sidewalls using a horizontal jack and a distribution beam to simulate the restraint effect of lateral soil loads.

To determine the axial pressure ratio, the depth of the underground structure, seismic wave strength, and test equipment conditions must be considered comprehensively. Researchers [37,38] discovered the axial compression ratio of precast sidewalls was 0.1–0.3 under the action of a design earthquake. Based on a reference value of 0.15 for the axial pressure ratio used in the seismic test [14] of precast sidewalls and the loading limit, we set the axial pressure ratio to 0.15 in this study.

The following loading method was adopted in this study. The bases of the specimens were fixed using ground anchor bolts. Horizontal jacks were applied to the outside of the specimens. Vertical jacks were installed on the reaction frame, which was used to exert axial forces on the specimens. During the test, horizontal jacks were used to apply uniform soil loads via the distribution beam to simulate the strata restraint effect on the precast sidewall components. The horizontal jack connector was hinged to ensure the uniformity of the soil load. Steel beams and cables were used to ensure that the jacks were positioned stably. The test loading equipment is shown in Fig.10.

2.2.2 Loading scheme

The test method is a quasi-static test that considers the strata restraint effect under a constant axial force. It comprises the following two main components: (i) a quasi-static test under the action of a constant axial force (the relevant loading methods are available in the literature [39,40]); (ii) a load applied using a horizontal jack to simulate the strata restraint effect. The actuator first applies a pushing force during the test as positive loading, followed by a pulling force as negative loading.

A horizontal jack was applied at one-half the height of the specimen from the base, and a uniform soil load was applied to the specimen outside through the distribution beam. The soil restraint load was calculated using Eq. (2).

(2)F=K\times S\times \mathrm{\Delta }/2,

where F is the earth pressure load of the precast sidewall components (kN), K is the spring stiffness coefficient (MPa/m), S is the contact surface area between the soil and prefabricated sidewall components (m²), and ∆ is the horizontal deformation of the precast components (m). Using the calculation method described in Subsubsection 1.2.2, the foundation bed coefficient of the soil was set to 8 MPa/m. The displacement of the specimen and the loading schedule are shown in Fig.11.

3 Experimental results and discussion

3.1 Crack development and damage mode

Fig.12–Fig.14 show the damage state and crack distribution of the CWJ, PTCWJ, and MTWJ specimens. The surface cracks of the CWJ specimen were uniformly distributed along the specimen height. By contrast, the PTCWJ specimen shows dense cracks in the core area and sparse cracks in the upper and lower regions of the joint. The crack development of both coincided at the middle of the specimen; eventually, the concrete at the base of the specimens was crushed and destroyed. The damage pattern of the MTWJ specimen differed significantly from those of the CWJ and PTCWJ specimens. The crack distribution of the MTWJ specimen was concentrated in the core region of the mortise-tenon joint, which included the variable section and tenon shoulder position; finally, the concrete of the tenon shoulder was crushed and destroyed.

3.2 Hysteresis curve, skeleton curve, and ductility

The load–displacement curves of the specimens are shown in Fig.15. The yield point, peak point, ultimate point, and corresponding displacements of the specimens are listed in Tab.1. The initial stiffness of the specimen was increased by connecting the reinforcement through a parallel threaded sleeve; consequently, the forward load capacity of the PTCWJ specimen was 4.6% higher than that of the CWJ specimen. Compared with the positive load capacity of the CWJ specimen, that of the MTWJ specimen reduced by 51.5% owing to the absence of longitudinal connection at the intersection in the core area.

The weaker bond between the sleeve and concrete resulted in a larger slip at the connection joint, which was consistent with the longitudinal cracking in the joint region of the PTCWJ specimen. Therefore, the ductility coefficient of the CWJ specimen was slightly lower than that of the PTCWJ specimen, with an increase of 10.8% in the positive loading direction. The inherent characteristics of the mortise-tenon joints significantly affected the ductility and caused the MTWJ specimen to undergo plastic deformation earlier. Compared with the ductility coefficient of the CWJ specimen, that of the MTWJ specimen in the positive loading direction increased by 72.3%. Meanwhile, the strata restraint effect reduced the ductility coefficients of the outside of the CWJ, PTCWJ, and MTWJ specimens by 6.7%, 11.4%, and 32.2%, respectively. The results above show that the strata restraint effect significantly reduced the ductility coefficient of the sidewall of the specimens; furthermore, it affected the MTWJ and CWJ specimens the most and least significantly, respectively.

The load–displacement curves began to harden at the yield point, and the hardening section spanned from the yield point to the peak point. The concrete compression cracks expanded and the reinforcement exhibited tensile yielding during loading in the CWJ and PTCWJ specimens. The steel indicated a relatively long plastic deformation phase after reaching the tensile yield; however, its stress did not change during this phase. Therefore, the hardening was primarily due to the tensile hardening characteristics of the steel. Meanwhile, a different hardening phenomenon was observed in the MTWJ specimen. At the beginning of loading, the tenon of the MTWJ specimen appeared to be cracked, at which time the concrete at the tenon position was cracked, and the reinforcement was in the elastic stage. As the loading continued, the intersection of the precast components of the MTWJ specimen was not reinforced longitudinally and primarily relied on the extrusion of the concrete at the mortise shoulder to resist the external force. The extrusion stress of the concrete at the mortise shoulder edge increased continuously, during which the internal cracks of the concrete expanded stably, but the growth rate of the concrete stress was lower than that of the strain. At this instance, the load–displacement curve of the MTWJ specimen was in the hardening stage.

3.3 Energy dissipation capacity

The energy dissipation coefficient (EDC) h_e and cumulative energy dissipation (CED), E, were used to evaluate the energy dissipation performance of the specimens. The energy-dissipation capacities of the three full-scale sidewall specimens are shown in Fig.16 and Fig.17, and the hysteresis loops and areas at the peak points are shown in Fig.18.

Based on Fig.16 and Fig.17, the EDC and CED of the PTCWJ specimens were similar to those of the CWJ specimen; this is attributable to the reinforcement in the PTCWJ specimen, which was connected by parallel threaded sleeves. The strength of the reinforcement with parallel-threaded sleeves was the same as that of the uninterrupted reinforcement, which can be determined via the materiality test. Cracks in the CWJ specimen developed more intensely along the height of the specimen. By contrast, the crack development of the MTWJ specimen was concentrated in the core region of the mortise-tenon joint, and energy was not dissipated from the concrete at other locations. The CED of the MTWJ specimen was slightly lower than that of the CWJ specimen, whereas the EDC was significantly larger than that of the CWJ specimen.

As shown in Fig.18, the hysteresis loops of the negatively loaded specimens are fuller than those of the positively loaded specimens, which is due to the strata restraint effect. Compared with the CED during the positive loading of the specimen at the peak point, the CED was increased by the stratum restraint effect during the negative loading of the CWJ, PTCWJ, and MTWJ specimens by 31%, 28.4%, and 35.5%, respectively. The result above shows that the strata restraint effect significantly affects the CED of the specimens, which is more evident in the MTWJ specimen. The noncontinuous longitudinal reinforcement at the intersection of the mortise and tenon joints of the MTWJ specimen increased the plastic deformation in the joint region. This finding is consistent with the test results of the prefabricated specimens.

3.4 Reinforcement strain analysis

The connection area of the joint is the weak region of the prefabricated specimens; therefore, strain was applied to the steel inside and outside the joint area to analyze the deformation mechanism. Fig.19 shows the strain–horizontal displacement relationship curve of the reinforcement 50 mm from the upper end of the joint. The arrangement of the measurement points is shown in Fig.7–Fig.9, where points 1 and 2 indicate the inside and outside strain gauges of the specimens, respectively.

The variations in the reinforcement strains on the inside and outside of the sidewall specimens were discrepant owing to the strata restraint effect. The strata restraint effect did not affect the CWJ specimen significantly owing to the higher integrity of the specimen. The strata restraint effect renders the steel strain on the outside of the sidewall specimens significantly lower than that on the inside, primarily because of the concentration of stress in the joint connection area of the precast specimens. Meanwhile, the strata restraint effect weakens the stress concentration in the joint region. This indicates that the strata restraint effect can effectively reduce the stress concentration in the joint area. Notably, a higher stress concentration imposes a more significant effect.

3.5 Stiffness degradation curve

Stiffness degradation is a specific indication of the degree of damage to reinforced concrete components during test loading. The loop stiffness and secant stiffness of the hysteresis curve of the specimens can be used to evaluate their stiffness degradation.

1) Secant stiffness

The secant stiffness is calculated using Eq. (3).

(3)K_i=\frac{\left|+P_i\right|+\left|-P_i\right|}{\left|+{\mathrm{\Delta }}_i\right|+\left|-{\mathrm{\Delta }}_i\right|},

where K_i is the secant stiffness of the ith loading cycle (kN/mm); +P_i and -P_i are the peak loads of the ith positive- and negative-direction loading cycles, respectively (kN); +{\mathrm{\Delta }}_i and -{\mathrm{\Delta }}_i are the displacements corresponding to the peak load of the ith positive- and negative-direction loading cycles, respectively (mm).

Fig.20 shows that the secant stiffness of the reinforced concrete components decreased as the load cycle number and displacement angle increased. The secant stiffness of the PTCWJ specimen was consistent with that of the CWJ specimen. The secant stiffness of the MTWJ specimen decreased from 31.7% to 45.2% compared with that of the CWJ specimen. The performance of the reinforcement in the PTCWJ specimen was the same as that of the uninterrupted reinforcement connected by parallel thread sleeves. However, the MTWJ specimen did not exhibit any longitudinal reinforcement connections, which resulted in a significantly smaller load capacity compared with those of the CWJ and PTCWJ specimens.

2) Loop stiffness

The loop stiffness is calculated using Eq. (4).

(4)K_i=P_i/{\mathrm{\Delta }}_i,

where K_i denotes the loop stiffness for the ith semi-loading cycle (kN/mm), P_i is the peak load of the ith half-loading cycle (kN), and {\mathrm{\Delta }}_i is the displacement corresponding to the peak load of the ith half-loading cycle (mm).

Fig.21 shows that the loop stiffness in the positive direction differed from that in the negative direction owing to the strata restraint effect. Compared with the loop stiffness during the positive loading of the specimens, the loop stiffness during the negative loading of the CWJ, PTCWJ, and MTWJ specimens increased by 16.5%, 17.1%, and 53.9%, respectively, owing to the strata restraint effect. This shows that the strata restraint effect decelerates the stiffness degradation, particularly in the MTWJ specimen. This occurred primarily because the strata restraint effect increases the height of the compression zone in the cross-section of the full-scale sidewall specimens during negative loading.

3.6 Strength degradation curve

The strength of the specimens increased initially and then decreased during loading. The strength degradation coefficient was specified as the ratio of the peak load of the ith cyclic loading to the maximum load of the specimens (see Eq. (5)), which reflects the strength degradation characteristics of the components during the entire loading process. In the test, each component was loaded for two cycles per stage; the strength degradation coefficient relationship curve obtained is shown in Fig.22.

(5){\lambda }_i=P_i/P_{max},

where {\lambda }_i is the strength degradation coefficient corresponding to the ith cyclic loading, P_i is the peak strength of the specimens in the ith cycle, and P_{max} is the peak strength of the specimens during the entire loading cycle.

Fig.22 shows that the strength of the specimens degraded gradually as the loading displacement increased. The strength degradation laws of the three sidewall specimens differed significantly at the initial stage in the positive loading direction. As the plastic deformation of concrete developed further, the stiffness degradation coefficients of the specimens gradually approached each other. The strata restraint effect decelerated the strength degradation of the prefabricated sidewall specimens in the early stage of deformation but imposed less effect on the final deformation displacement of the damage.

3.7 Plastic zone deformation

The reinforced concrete specimen evolved from the elastic stage to the plastic stage during the continuous loading process. The bending deformation consumes seismic energy and reduces structural damage during the plastic deformation process. However, shear and slip deformations cause the hysteresis loop to become pinched, thereby reducing energy dissipation. A schematic illustration of the plastic deformation in the joint region is shown in Fig.23, and the shear deformation can be calculated using Eq. (6).

(6)y=\frac{\sqrt{h^2+b^2}}{hb}\cdot \frac{\left|{\mathrm{\Delta }}_3+{\mathrm{\Delta }}_4\right|+\left|{\mathrm{\Delta }}_3^{\prime }+{\mathrm{\Delta }}_4^{\prime }\right|}{2}.

The plastic deformation of the joint position was primarily composed of bending, shear, and slip deformations during the entire loading process. The bending deformation was measured using displacement meters 1, 2, and 3, and the shear deformation was measured using displacement meters 4 and 5.

3.7.1 Shear deformation

The shear deformation of the specimens is shown in Fig.24.

The shear angle of the specimens increased with their displacement. The shear angle of the PTCWJ specimen was the same as that of the CWJ specimen, and both were greater than that of the MTWJ specimen. The changes in the shear angle of the PTCWJ and CWJ specimens under the strata restraint effect were ambiguous, whereas the shear angle of the MTWJ specimen increased significantly. When the MTWJ specimen were loaded, the strata restraint effect increased the shear force at the intersection interface of the joint. Owing to the absence of longitudinal reinforcement connections, the specimen could not effectively resist shear deformation, which consequently resulted in a significant shear deformation.

3.7.2 Bending deformation

Fig.25 shows that the bending deformation increased gradually with the loading displacement. The bending deformation of the PTCWJ specimen was the same as that of the CWJ specimen in the positive loading direction, and both were greater than that of the MTWJ specimen. However, the bending deformation of the PTCWJ and CWJ specimens in the negative loading direction under the strata restraint effect was less variable and significantly smaller than that of the MTWJ specimen. This indicates that the strata restraint effect changes the plastic deformation characteristics of the specimens and significantly affects the MTWJ specimen. Hence, one can infer that for prefabricated sidewall joints of underground assembly structures, the strata restraint effect is not negligible during the loading process in seismic tests.

3.7.3 Residual deformation

Studies regarding the hazards of earthquakes indicate that the residual deformation of building structures is critical for evaluating post-earthquake recovery performance. Fig.26 shows the residual deformation of the prefabricated components compared with that of the CWJ specimen under cyclic loading.

The residual deformation of the CWJ and PTCWJ specimens was symmetrical during the positive and negative loadings. Owing to the strata restraint effect, the residual deformation of the MTWJ specimen fluctuated in the vicinity of zero in the positive loading direction. Furthermore, the residual deformation of the MTWJ specimen in the negative loading direction was significantly larger than that in the positive loading direction, and was more significant than that of the CWJ specimen. This finding is consistent with the shear and bending deformations of the MTWJ specimen.

Because the negative loading of the specimens accounts for the soil load, the shear action results in a large residual deformation in the negative direction. Nevertheless, the soil outside the structure can effectively avoid the overturning effect of the underground structure. In the forward loading direction, the residual deformation of the PTCWJ specimen was significantly smaller than that of the CWJ specimen. Considering that the residual deformation of the structure is the most important feature of a recoverable structure, the residual deformation degree is defined as the ratio of the residual deformation in each loading cycle to the maximum loading displacement of the stage, as shown in Eq. (7).

(7)\alpha \text{=}\frac{{\mathrm{\Delta }}_{\text{R}}}{{\mathrm{\Delta }}_{max}},

where \alpha =0 implies that the structure exhibits complete self-restoring ability, and \alpha =1 indicates otherwise; meanwhile, implies that the structure offers some degree of self-restoring ability.

The change in the residual deformation degree with the interstory displacement angle is shown in Fig.27. The residual deformation degree of the CWJ and PTCWJ specimens decreased slightly under the strata restraint effect, which indicates that the strata restraint effect improved the recoverable capacity of the sidewall specimens. The residual deformation degree of the MTWJ specimens was approximately zero in the positive direction, which implies that the MTWJ specimens were completely self-restoring. The residual deformation degree of the MTWJ specimens was slightly higher than those of the CWJ and PTCWJ specimens in the negative loading direction; nonetheless, the safety of the structure was ensured owing to the strata restraint effect. Therefore, the strata restraint effect can effectively improve the recoverability of precast sidewall structures, as shown the most clearly in the MTWJ specimen. Moreover, the inside of the MTWJ specimen demonstrate complete self-recovery ability, whereas the outside relied on strata restraint deformation to ensure safety. Thus, compared with the CWJ and PTCWJ specimens, the MTWJ specimen resisted the earthquake load more effectively and demonstrated better recovery after the earthquake.

4 Numerical analysis

An FE model that can predict the seismic performance of prefabricated sidewall components was established, and the feasibility of the FE model was verified. The proposed FE model serves as a basis for subsequent studies pertaining to the effects of the soil restraint load, axial compression ratio, and others.

4.1 Establishment of numerical models

The ABAQUS software was used to conduct a nonlinear analysis of the precast sidewall specimens. The Poisson’s ratio and elastic modulus of steel were set as 0.3 and 210 GPa, respectively, whereas those of concrete were set as 0.2 and 34.5 GPa, respectively. The specific parameters of the concrete and steel reinforcements are presented in Subsection 2.1. Element C3D8R and the concrete plastic damage model were used to model the concrete, as shown in Fig.28. The concrete damage plastic (CDP) is a material in ABAQUS material library, which is used to describe the deformation behavior and strength characteristics of concrete. The CDP model is typical and widely used, and its stress−strain curve can be described by damage factor and plastic strain.

The tensile and compressive constitutive relationships as well as the damage factors were calculated based on to the Chinese standard GB50010-2010, “Code for Design of Concrete Structures” [41], and the results are shown in Tab.2. Element T3D2 was used for the steel reinforcement, and the ideal elastic–plastic model of steel was adopted, which included linear elastic and linear strain hardening zones for compressive and tensile behaviors [42], as shown in Fig.29. Because of the complexity of the parallel-threaded sleeve, element C3D4 was used.

The reinforcement was embedded into the concrete via the “embedded” function, and the bond slip effect between them was not considered. The contact surfaces of the precast concrete components were modeled based on “general contact,” i.e., penalty friction contact in the tangential direction, and hard contact in the normal direction. The friction coefficient was set to 0.2. To consider the strata restraint effect on the precast sidewall specimens of a subway station structure, nonlinear spring elements were applied to the nodes of the FE model, which were subjected to compression only (i.e., no tension). The spring stiffness applied to the unit nodes in the FE model was calculated using Eq. (1), and the specific spring application method is available in Ref. [43]. The established FE models are illustrated in Fig.30. The FE model of the CWJ specimen is shown in Fig.30(a); notably, the PTCWJ and MTWJ specimens differed from the CWJ specimen only in terms of the joint position. The connection joints of the PTCWJ and MTWJ specimens are shown in Fig.30(b) and Fig.30(c). The constraint relationships and boundary conditions of the FE models are shown in Fig.31.

4.2 Mesh sensitivity analyses and validation of the numerical model

4.2.1 Mesh sensitivity analyses

To ensure the convergence of the FE models and to determine the optimum grid size, we conducted mesh sensitivity analyses [44,45].

The grid sizes of the CWJ specimen were simulated and analyzed based on spacings of 50 and 100 mm, and the calculated curves are shown in Fig.32(a). Fig.32(a) shows that changing the grid size spacing from 50 to 100 mm did not significantly affect the simulation results, and that the error of the two calculation results was less than 6%. To account for time constraints, a grid size of 100 mm is recommended for follow-up studies. The difference between the prefabricated specimens and CWJ specimens is the presence of the joints. The joints of the PTCWJ and MTWJ specimens were calculated with grid size spacings of 20 and 50 mm, and the results are shown in Fig.32(b) and Fig.32(c). Based on these figures, changing the grid size spacing from 20 to 50 mm in the joint region did not significantly affect the calculation results. The difference between the two calculation results was less than 5%. Considering the calculation efficiency and calculation results, the grid size of the joint area was set to 20 mm, and the mesh size on both sides of the joint area was set to 50–100 mm.

4.2.2 Validation of the numerical model

Fig.33 shows the hysteretic curves obtained from the FE analysis of the CWJ, PTCWJ, and MTWJ specimens.

Based on Fig.33, the loading and boundary conditions specified for the modeling were not ideal; therefore, the out-of-plane tilt of the wall and the microslip of the ground anchor bolts could not be simulated accurately. The slip between the reinforcement and concrete was not considered, which resulted in fuller hysteresis curves for the simulation results of the CWJ and PTCWJ specimens. The “pinching” of the MTWJ specimen was more evident as compared with the numerical simulation results owing to the small gap in the mortise-tenon joint area during the production. Slight differences were observed between the hysteresis curves of the experiment and simulation; however, the skeleton curves of the three specimens agreed well. In general, the FE results were consistent with the test data, and the feasibility of the FE model was verified.

5 Conclusions

Based on the basic principles and calculation models of the quasi-static test method for prefabricated components of aboveground assembled structures, a seismic test method was proposed herein for prefabricated sidewalls while considering the strata restraint effect. Subsequently, seismic tests were conducted on full-scale sidewall specimens of three different joint forms to analyze the effect of strata restraint on the damage mode and seismic performance. This study serves as a reference for the seismic performance testing and design of precast sidewall components used in assembled subway station structures. The main conclusions obtained were as follows.

(1) Unlike the conventional quasi-static method, the strata constraint quasi-static method considers the strata restraint effect, which can reflect the soil–structure interaction during an earthquake as well as reveal the seismic performance of prefabricated sidewall components more realistically.

(2) The strata restraint effect changed the seismic performance of the prefabricated sidewall components, particularly the energy dissipation and bearing capacities. Compared with the seismic performances of the prefabricated sidewall specimens, the strata restraint effect increased the bearing capacity on the outside of the CWJ, PTCWJ, and MTWJ specimens by 17.6%, 22.7%, and 59.1%, respectively; increased the cumulative energy dissipation by 31%, 28.4%, and 35.5%, respectively; and reduced the ductility coefficient by 6.7%, 11.4%, and 32.2%, respectively. Additionally, the stress concentration and the degradation rate of the strength and stiffness in the core area of the joints decreased.

(3) The strata restraint effect caused more significant damage to the concrete on the outside of the specimens and aggravated bending and shear deformations on the outside of the precast sidewall components, as compared with its effect on the inside of the precast sidewall specimen. The strata restraint effect caused the residual deformation on the outside of the precast sidewall components to increase significantly, but also improved the recoverability of the deformation on the inside.

(4) The effect of strata restraint on the damage and seismic performance of the prefabricated sidewall components of assembled subway station structures was not negligible, particularly in dry joints without longitudinal reinforcement connections, such as mortise-tenon joints; hence, it should be considered in actual studies.

Only the seismic performance of a prefabricated sidewall structure under the effects of a single axial pressure ratio and soil load was considered in the experimental study presented herein. The mortise-tenon joint is a typical variable-stiffness joint, and the effect of the axial pressure ratio on the bearing capacity was significant. Meanwhile, the effects of different uniform soil loads or non-uniform soil loads (upper soft and lower hard) on the seismic performance of the prefabricated sidewall specimens have not been investigated. The two deficiencies above will be addressed in future studies.

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