Seismic damage analysis of shallow buried subway station in clayey sand soil under mainshock-aftershock earthquakes

During earthquake events, a mainshock may trigger a number of following aftershock earthquakes in a short time. Usually, structures will be damaged to a certain extent by the mainshock, and aftershocks can further exacerbate the damage to structures, making post-disaster rescue and rehabilitation extremely challenging. Yet, most of research on seismic performance of underground structures only considered the single mainshock, ignoring the effect of aftershocks. In this study, a nonlinear numerical model of the shallow buried shallow subway station in clayey sand soil under mainshock-aftershock sequences was constructed to replicate the damage evolution process of underground structures. A limited numerical sensitivity analysis was performed considering the influences of the magnitude of mainshock and aftershock intensity. The results indicate that the damage of subway station is closely related to the magnitude of mainshock intensity. The aftershocks might cause more serious incremental damage to underground structures and secondary displacement of the site, potentially lead to collapse of the subway station, when the mainshock magnitude is greater. With the superposition of the mainshock and aftershock, the relative horizontal displacement of the subway station could reach the inter-story drift limit value. Therefore, the aftershock should be taken into account for seismic safety design of shallow underground structures.


Introduction
Historical seismic records show that approximately 89% of strong earthquakes will have a number of following aftershocks within a short time after the end of the earthquake.Among them, there are many aftershocks of the same magnitude as the main earthquake [1].For example, The Wenchuan strong earthquake in China (Ms 8.0, May 12, 2008) had five strong aftershocks with a magnitude greater than Ms 6.0 in the following 20 days.Nepal's tremendous earthquake (Ms 8.1, April 25, 2015) was followed by a powerful aftershock (Ms 7.0) just 34 minutes later.In addition, Turkey suffered two significant earthquakes (Ms 7.8) on February 6, 2023, and another strong aftershock (Ms 7.0) occurred only 11 minutes afterwards.In general, when structures have been damaged to some certain degree under powerful mainshocks, strong aftershocks within a short period can produce additional damage to the structures, thereby increasing the risk of damage or collapse [2].Therefore, it is of great significance to study the structural response under the mainshock-aftershock sequence.
Compared with ordinary above-ground structures, underground structures have a longer service life.Once damaged in seismic event, the direct and indirect losses caused are substantially more than those of general above-ground structures, in addition to the concealment of damage and the difficulty of repair 1334 (2024) 012050 IOP Publishing doi:10.1088/1755-1315/1334/1/012050 2 [3,4].Initially, it was believed that the seismic response of underground structures would be weaker than that of above-ground structures because they were surrounded by soil layers.Since the Hanshin Earthquake in Japan caused the collapse and destruction of Daikai station, scholars around the world have begun to pay more attention to the seismic resistance of underground structures [5][6][7].The model tests and numerical simulations were carried out to investigate the seismic response of underground subway stations, exploring the influence laws of soil parameters, artificial boundaries, structural depth, and complexity types [8][9][10].By applying different soil constitutive models, the seismic vulnerability laws of underground structures were obtained [11][12][13].In addition, some scholars [14][15][16][17] have studied the seismic response law of the interaction system between underground structures and above-ground structures.However, in current earthquake engineering, most seismic analyses of underground structures assume strong earthquakes to consist of single events without taking aftershocks for consideration.
In summary, there is limited research on damage exacerbation effect of underground structures due to the occurrence of natural aftershocks.Consequently, the damage and destruction law of the actual site structure is still unclear.It is essential to study the damage mechanism of the mainshock-aftershock sequence to the underground structure for seismic design and post-earthquake rescue efforts.Therefore, in this study, a three-dimensional numerical model of the shallow buried shallow subway station in clayey sand soil under mainshock-aftershock sequences was constructed.The effects of different mainshock peak intensities and mainshock-aftershock peak intensity ratios on the damage of the subway station structure are investigated by constructing different mainshock-aftershock sequences.This study aims to guide the seismic design procedure and post-earthquake rescue work of urban underground structures in soft ground areas in the future.

Model Size and Parameters
A single layer of soil with a shallow buried subway station structure is considered with the finite element simulation software Abaqus.In order to eliminate the dimensional effect in the Y direction, the size of the site soil in the model should be greater than seven times the structural size [18].The length, width and height of the soil model in the model are 119 m, 11 m, and 35 m, respectively.Daikai station, which is the only collapsed underground structure during an earthquake, is taken as an example to explore the damage evolution of underground structures under mainshock-aftershock earthquakes.The subway station structure has an outer dimension of 17 m length and 7.17 m height, respectively.The burial depth is 4.8 m and 3 pillars with a center distance of 3.5 m are featured in the structure model.Considering the deformation mode and the calculation cost, the C3D8R element is used for the site soil and the subway station model, and the T3D2 element is utilized for the steel bar as illustrated in Figure 1.The reinforced structure and the subway station are bound together by embedded constraints in the finite element numerical simulation model.The frictional contact is applied to the surfaces between the subway station structure and the site soil model.The friction coefficient is set as 0.4.There is no displacement in the X-direction on the front and back faces and the seismic acceleration is added in the Y-direction at the bottom of the model.To replicate the free field boundary conditions, the multi-point constraints (MPC) are used on the left and right sides of the model.
In order to analyze the damage mechanism of subway station structures subjected to mainshockaftershock earthquake in saturated soft sites, the site soil is assumed to be clayey sand.An improved SANISAND04 constitutive model [19] is employed in this work.The parameters of the soil model are provided in Table 1.It should be mentioned that a shift value of effective mean principal stress is introduced to the yield surface of the model.The shift parameter can produce an intercept of the critical stress state line in the stress space, which is used to define the soil cohesion.The structural material of the subway station is selected as C30 concrete.The concrete plastic damage constitutive model is adopted to reflect the structural damage process of the subway station.The steel bars and stirrups are selected as HRB400 steel bars, and the ideal elastic-plastic constitutive model is applied.The parameters of the plastic damage model and ideal elastic-plastic model for the subway station structure are shown in Table 2

Mainshock-Aftershock Earthquake Sequences
To study the dynamic response of underground structures under the mainshock-aftershock earthquakes, reasonable seismic inputs are the basis for analyzing the problem.Although the current record of seismic waves is very rich, regrettably, it is limited to collect usable mainshock-aftershock recordings which are also difficult to use for the mainshock-aftershock analysis of sites and structures.Therefore, it is important to construct a suitable mainshock-aftershock sequence for the seismic design of structures.
Considering that the prototype of the subway station structure model in this study is Daikai subway station, the seismic dynamic load was also selected from the seismic acceleration of Kobe earthquake (Ms 7.2, January 17, 1995) in Japan.The Kobe seismic acceleration record with peak ground acceleration (PGA) of 0.834 g measured by the Kobe Marine Meteorological Station was selected [20] for the seismic analysis.By adjusting the amplitude of Kobe seismic acceleration waves, the mainshock earthquake acceleration with PGA = 0.65 g, 0.5 g and 0.35 g are designed for the numerical simulations in this study.
It is generally accepted that aftershocks are relatively weak in magnitude and therefore cause little structural damage.However, it is not difficult to find from the seismic data that the intensity of aftershocks is not as little as it is perceived to be.On the contrary, in most circumstances, the relative intensity of aftershocks is as great as that of the mainshock.In this study, the repetitive method of the mainshock-aftershock sequence construction is utilized.It is to construct one or more aftershock sequences by reducing the mainshock by a certain ratio.Then, the complete mainshock-aftershock sequences are used as the acceleration for the dynamic simulation analysis, regardless of the influence of the time intervals.This method presupposes that the dynamic characteristics of the main earthquake and the aftershock are the same.Although this assumption is more idealistic, it is still extensively utilized in the study of the mainshock-aftershock sequence.In this work, the reduction ratio is selected as 0.5, 0.75 and 1.0.Although the assumption that the dynamic characteristics of the mainshock and aftershock are the same is idealized, it is still widely used in the research of mainshock-aftershock sequences.Here, the reduction ratio, which is also termed the mainshock-aftershock peak intensity ratio as given in Equation (1), is selected as 0.5, 0.75 and 1.0.The seismic accelerations time history, 5%-damped response spectrum and the Arias intensity of the mainshock-aftershock acceleration constructed by repetition method based on the Kobe wave seismic record with PGA = 0.65 g are displaced in Figure 2.
where  is the mainshock-aftershock peak intensity ratios, PGAAS is the peak ground acceleration of aftershock and PGAMS is the peak ground acceleration of mainshock earthquake.

Vertical Displacement
The vertical displacements of the clayey sand soil site including the subway station structure with the mainshock earthquake PGAMS = 0.65 g and aftershock intensity ratio  = 1.0, 0.75 and 0.5, respectively, are shown in Figure 3.It can be observed that there is no collapse of the subway station structure under the mainshock PGAMS = 0.65 g, and when the aftershock with  = 1.0 and 0.75 occurred, the pillars of the subway station structure undergo bending deformation.However, the pillar of the subway station structure under aftershock with  = 0.5 was not bent.This clearly illustrates the incremental damage effect of aftershock loadings on the underground structure, where the structure may be damaged but not collapsed during the mainshock, while the damage is aggravated during the aftershock, especially when the aftershock intensity is considerable.Comparing the vertical displacements of the soil and structure of the site subjected to different mainshock and aftershock earthquakes, the occurrence of aftershocks leads to secondary displacement of both the soil and the structure.When the intensity of the aftershock is larger, the value of the secondary displacement is larger.In addition, the vertical displacement distribution of the soil around the subway station structure is not uniform in level compared to the surrounding soil far away from the structure.Except for the ground collapse caused by the bending of subway station pillars, the soil around the structure has risen to a certain extent due to the uplift of the underground structure.The growth curves of vertical displacements of the surface soil above the subway station under the mainshock-aftershock with different intensities are presented in Figure 4.It can be seen that the vertical displacement of the surface soil is phased with the application of the mainshock-aftershock loadings.When the mainshock earthquake is applied, within the first 3.5 s, the vertical displacement of the surface soil is extremely small.Then between 3.5~10 s, the vertical displacement suddenly increases and develops rapidly.In the last 10~20 s, the vertical displacement slows down until the mainshock is complete.When the PGA of the mainshock is 0.65 g, 0.5 g and 0.35 g, the values of surface vertical displacement under the mainshock earthquake are 0.7 m, 0.6 m and 0.4 m, respectively.In the aftershock stage, the vertical displacement also exhibits phases comparable to that of the mainshock earthquake.With the increasing intensity of the aftershock, the final vertical displacement increases.For example, when PGAMS = 0.65 g, the final vertical displacement of the surface soil is 1.9 m, 1.58 m and 0.93 m for the aftershock intensity  = 1.0, 0.75 and 0.5, respectively.In particular, the vertical displacements increased by about 1.7 and 1.2 times, respectively when the aftershock intensity ratio  is 1.0 and 0.75, comparing to the vertical displacements under the mainshock loading.It is mainly due to the bending deformation of pillars of the subway station and the collapse of the ground surface under the aftershock intensity ratios  = 1.0 and 0.75, respectively.

Excess Pore Water Pressure
Under the mainshock-aftershock sequence loading (PGAMS = 0.65 g), the distribution of the excess pore water pressure in the clayey sand soil site is shown in Figure 5.It can be discovered that the subway station structure has a large impact on the excess pore water pressure of the surrounding soils, while the distribution of the excess pore water pressure of the soils is more uniform beyond about 10 m far away from the subway station structure.The excess pore water pressure of the soil on both the upper and lower sides of the subway station structure is larger than that of the soil at the same horizontal position.This is due to the larger stiffness of the station structure, which may extrude the surrounding soil under the horizontal seismic action, resulting in deformation of the soil to generate excess pore water pressure, confirming that the subway station structure has a great impact on the excess pore water pressure of soils.In addition, when the bending deformation of pillars of the subway station has occurred ( = 1.0 and 0.75), the values of excess pore water pressure of the soil at the surface above the station are relatively lowered due to collapse.The development curves of the excess pore water pressure of the soil under the subgrade of the subway station are illustrated in Figure 6.It can be found that under the loading of the mainshockaftershock accelerations, the development of development of excess pore water pressure is showing an increasing trend.Within 3.5 s of the mainshock loading, the excess pore water pressure does not change substantially, after which the excess pore water pressure starts to increase rapidly, though the growth rate gradually decreases.After the mainshock, the excess pore water pressure at PGAMS = 0.65 g and 0.5 g were both about 30 kPa, which was about three times of the excess pore water pressure at PGAMS = 0.35 g.Under the aftershock, the growth of excess pore water pressure was slow at PGAMS = 0.65 g and 0.5 g, but when PGAMS = 0.35 g, the excess pore water pressure under aftershock with intensity  = 1.0 showed rapid growth after 30 s.At the end of the aftershock, the excess pore water pressure reached about 34 kPa, indicating that although the mainshock earthquake PGAMS is small, but the superposition of the mainshock and aftershock can cause greater disturbances to the soil.

Surface Acceleration of Site
The development curves of horizontal acceleration for the surface soil above the subway station under different intensities of mainshock-aftershocks are given in Figure 7.The acceleration values with PGAMS = 0.65 g and 0.5 g are obviously larger than those with PGAMS = 0.35 g under the mainshock-aftershock loads, showing that the surface soil is subjected to less disturbance and the structure will not produce large collapse deformation when the mainshock is weak.Comparing the horizontal acceleration when the PGAMS = 0.65 g and 0.5 g, it can be seen that within 5~10 s of the mainshock earthquake, the acceleration at PGAMS = 0.65 g is greater than the acceleration at PGAMS = 0.5 g.However, after roughly 10s, the acceleration at PGAMS = 0.5 g shows a significant increase, which may be owing to the amplification effect of the soil and the underground structure on the seismic waves.Comparing the horizontal acceleration at the surface and at the bottom of the model, the amplitude of the maximum horizontal acceleration at the surface is magnified by about 2.5 times.In addition, when PGAMS = 0.35 g, the acceleration under the aftershock with intensity ratio  = 1.0 shows abrupt and violent fluctuations, while under the aftershock with intensity ratio  = 0.75 and 0.5, the acceleration development is small.

Damage Deformation of Subway Station Structure
From the analysis of the results of the seismic response of the site soil and structure under mainshockaftershock loadings, it can be seen that the site model produces certain vertical displacement and excess pore water pressure under mainshock seismic loadings.Figure 8 demonstrates the compression damage deformation diagram of the subway station structure under different mainshock-aftershock loads.It can be noticed that none of the subway station structures collapsed under the mainshock earthquake.However, the damage deformation of the top and bottom slabs as well as the side walls and pillars of the subway station structures at PGAMS = 0.65 g and 0.5 g is obviously larger than that at PGAMS = 0.35 g.When the aftershock intensity ratio  = 1.0, the pillars of the subway station structure were damaged by bending deformation and the top slab fell as well as the bottom slab bulged.In contrast, with PGAMS = 0.35 g, the structure only showed large compression damage, which indicates that the superposition of the mainshock and aftershock could also cause damage to the structure even with small PGA.Under aftershocks with intensity ratios  = 0.75 and 0.5, only the pillar of the subway station structure was damaged at PGAMS = 0.65 g, whereas the structure did not collapse at PGAMS = 0.5 g and 0.35 g.It reveals that the collapse damage of the subway station structure is mainly related to the mainshock intensity.When the mainshock intensity is large, the structure will be seriously damaged and be likely to collapse under aftershocks.

Inter-Story Drift of Subway Station Structure
To evaluate the seismic performance of the underground structure, the relative horizontal displacements of the top and bottom slabs of the subway station under the mainshock-aftershock loading are displayed in Figure 9.It can be seen that the horizontal displacements of the subway station structure under the mainshock-aftershock loads exhibit a big difference.Under the mainshock earthquake, the relative horizontal displacement of the top and bottom slabs of the subway station has reached the limit value 1/250 of the inter-story drift when the PGAMS = 0.65 g and 0.5 g.During the aftershock, the relative horizontal displacement shows an increasing trend.In particular, the maximum relative horizontal displacement reaches 0.07 m at PGAMS = 0.65 g.The residual values of the relative horizontal displacement of the subway station structure exceed the limit value of the inter-story drift 1/100 under aftershocks with intensity ratios  = 1.0 and 0.75.At PGAMS = 0.35 g, the subway station structure is less affected by the mainshock-aftershock.Only at the aftershock intensity ratio  = 1.0 the maximum relative horizontal displacement approaches the limit value of the inter-story drift 1/250, indicating that the mainshock plays a dominant role in the destruction of the structure.

Mainshock Aftershock
Inter-story drift limit: 1/250 Inter-story drift limit: 1/100 In order to further reveal the damage evolution law of the subway station structure under mainshockaftershock loading, the relative horizontal displacements of the structure are normalized here according to the concept of the inter-story drift as stated in Equation ( 2).According to the distribution of the maximum inter-story drift of the subway station structure with the mainshock PGAMS and aftershock intensity ratio , a four-parameters model as shown in Equation ( 3) is employed here to fit the distribution as shown in Figure 10.The fitting parameters are summarized in Table 3.The maximum inter-story drift of the structure increases gradually with the mainshock PGA and aftershock intensity ratio .However, it does not simply increase linearly.The deformation capacity, stiffness, and loadbearing ability are weakened accordingly because it has entered the stage of plastic damage.At this time, the occurrence of aftershocks is not a simple accumulation to the structure, but more of a multiplication of the danger of the underground structure.Therefore, it is necessary to consider the damage development of the structure under the mainshock-aftershock sequence.
where U2 is the relative horizontal displacements of the subway station structure and H is the height of the subway station structure.

Conclusions
In this study, the numerical simulation model of the shallow buried shallow subway station in clayey sand soil under mainshock-aftershock sequences was constructed and the effects of different mainshock and aftershock peak intensity on the damage of the subway station structure were analyzed.The main conclusions are as follows.
(1) Under the mainshock, structure may be damaged but not collapsed.The occurrence of aftershocks can lead to incremental damage to the underground structure and secondary displacement of the site.When the intensity of the aftershock is larger, the value of the secondary displacement is larger.
(2) The subway station structure has a considerable impact on the surrounding soil.The soil around the structure has risen to a certain extent due to the uplift of the underground structure.The excess pore water pressure of the soil around the subway station structure is larger than that of the soil far away from the structure.(3) The mainshock plays a dominant role in the damage of the structure.when the mainshock is weak, the horizontal acceleration at the surface is smaller.The amplitude of the maximum horizontal acceleration at the surface is magnified by about 2.5 times of that at the bottom of the model.
(4) Under the superposition of the mainshock and aftershock earthquake, the relative horizontal displacement of the subway station could surpass the inter-story drift limit value.The proposed fourparameters model could well describe the distribution of the maximum inter-story drift with respect to the mainshock and aftershock intensity.

5 Figure 3 .
Figure 3. Vertical displacement of the clayey sand site and shallow buried subway station structure under mainshock-aftershock earthquake with PGAMS = 0.65 g and  = 1.0, 0.75 and 0.5.

Figure 6 .
(a) PGAMS = 0.65 g (b) PGAMS = 0. 5 g (c) PGAMS = 0.35 g Excess Pore water pressure time history of the soil around the bottom of the subway station structure under mainshock-aftershock earthquake with different PGAMS and .

5 Figure 8 .
Figure 8. Compressive damage of subway station structure under mainshock-aftershock earthquake with different PGAMS and .

3 .Figure 10 .
Figure 10.The maximum inter-story drift of the subway station structure under mainshock-aftershock earthquake with different PGAMS and .

Table 2 .
Parameters of concrete damage plasticity model and steel model.