# Effects of Burial Depth on the Seismic Response of Subway Station Structure Embedded in Saturated Soft Soil

Authors: Xuelei Cheng; Zongguang Sun
Journal: Advances in Civil Engineering
 (2018)

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## Abstract

For the aim to study the effects of burial depth on seismic response in the subway station’s structure embedded in saturated soft soil, on the basis of the OpenSEES program, numerical models with four cases of burial depth for the nonlinear interaction system including subway station’s structure and saturated soft soil are developed with theu-p formulations of Biot’s theory as it seeks to describe the saturated two-phase media. The effects of burial depth on the seismic response and the failure pattern of the subway station structure are investigated. The numerical results show that (1) the burial depth has a significant effect on the nonuniform uplift of station’s structure due to the movement of soil from far field towards baseplate; (2) with the increase of burial depth, the inertial effect of overlaying soil of the subway station structure becomes more obvious, and the peak zone of the pore pressure ratio contracts from the outer area to the baseplate bottom with decreasing amplitude; (3) the dynamic index R decreases with the increasing burial depth of the station’s structure; and (4) in terms of the middle column, the burial depth of the station’s structure has the most crucial effect on the additional dynamic shear force and bending moment at the top end.


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## Body

## 1. Introduction

The current antiseismic code design of the subway station structure system in the soft soil site is rougher than that of liquefiable sandy soil foundation. There are only a number of qualitative and general provisions, and there is still a lack of more in-depth and systematic research [1–4]. In this way, the consideration of the influence of the soft site on seismic response of the subway station structure dynamic system has an important theoretical value and practical significance to deepen the antiseismic understanding of the subway station structure and promotes the development of geotechnical earthquake engineering. As we all know, burial depth is one of the important factors that affect the seismic response of subway station structures [5, 6]. All previous earthquake disasters show that the subway station structure with a different thickness of a soft overlying soil layer has different site effects; that is, the dynamic damage degree and model of the subway station structure in the saturated soft soil site under different burial depth conditions has a significant difference [7, 8]. On the one hand, the shear effect and the soil dynamic pressure of the overlaying soil layer on the subway station structure are increased with the increase of the burial depth, which is unfavorable to the seismic response of the subway station structure. On the other hand, the constraint effect of the site on the subway station structure is strengthened with the increase of the burial depth, restricting the deformation reaction of the subway station structure, which is beneficial to the seismic response of the subway station structure. Therefore, it is significantly necessary and urgent to study the seismic response characteristics of subway stations under different burial depth conditions in the soft site.Many scholars have conducted many researches on the seismic response of the subway station structure under different burial depth conditions. Liu et al. [9, 10] applied the nonlinear liquid-solid two-phase body dynamic finite element method to study the response of the burial depth of the subway station structure in the saturated liquefiable sand site under the horizontal and vertical seismic actions. Bilotta et al. [11] based on the total stress finite element method studied the dynamic response of a circular tunnel of 6 m diameter, with the axis at a depth of 15 m in a 30 m thick layer of medium dense gravel, sand, or soft clay, overlying a relatively stiff bedrock. Chen et al. [12] studied the response of the burial depth to the seismic displacement of the subway station structure based on the dynamic total stress finite element method and compared and analyzed the internal forces of the subway station structure under the seismic action. Zhuang et al. [13] made numerical simulation analysis of the seismic response of the subway station structure in 5 soft sites of the two-storey three-span island subway station with soft soil layers of different burial depth conditions in the side and bottom foundations and 1 general site based on the dynamic total stress finite element method. Amorosi et al. [14] adopted two different approaches, both accessible in the engineering practice to evaluate the increments of seismic-induced loads in the transverse direction of the tunnel lining in terms of hoop force and bending moment to study the seismic transversal response of a shallow tunnel built in two ideal clayey deposits of different consistencies. Chen et al. [15] based on the dynamic total stress finite element method carried out the numerical analysis of rock mass and tunnel lining and modeled the incident waves as harmonic S and P waves to investigate the influence of the depth of a tunnel on its seismic damage. Wang et al. [16] used the ultimate shear stress as the failure criterion based on the dynamic total stress finite element method, simulated the seismic damage process of the subway station structure by the birth-death element method, and considered the impact of the initial ground stress on the antiseismic property of the subway station structure by the burial depth of the structure. Li et al. [17] established two analysis models of subway station structure’ burial depth based on the dynamic total stress finite element method to study the influence of the distribution of different soil layers of layered foundation on the seismic response of the structure. Tsinidis [18] conducted a numerical parametric study on diverse soil-rectangular tunnel systems, aiming at shedding light on critical response characteristics of rectangular tunnels subjected to transversal ground shaking based on the dynamic total stress finite element method. Cui et al. [19] adopted the orthogonal design scheme of the “four factors and three levels” numerical test and two-phase medium dynamic analysis method to analyze the dynamic response characteristics and the catastrophic mechanism of the subway station structure in the soft site and combined with the multiindex comprehensive balance method to carry out the sensitivity analysis of material parameters in view of the changes of the indexes such as the dynamic pore pressure ratio at the soil typical point and the dynamic response indexes including the internal force at the characteristic positions of the subway station structure caused by the change of soft foundation soil parameter factors.Due to the complexity of the research problem of the antiseismic subway station structure in the saturated soft soil site and the limitation of calculation theory and hardware calculation, most of the existing research results in the subject of the seismic response of the subway station structure under the conditions of different burial depth conditions in the soft soil site are based on the total stress dynamic analysis method without considering the influence of pore pressure, in which the influence of dynamic pore pressure distribution change cannot be considered [20]. However, the decoupled effective stress dynamic analysis method based on the pore pressure model has some limitations in the complex stress state deformation characteristics of saturated soil [21, 22]. It is rare in the existing research results to comprehensively consider the complex factors such as the multiphase medium property of saturated soft soil, the dynamic nonlinearity of the foundation-structure system, and so on to conduct the related research on the effect of burial depth on the underground structure.On this base and based on the characteristics and limitations of the existing domestic and foreign research results, the dynamic Biot’ two-phase medium coupling theory is adopted to describe the dynamic constitutive nonlinearity of saturated soft soil with the elastoplastic multiyield surface plastic kinematic model, and the nonlinearity dynamic performance of the station structure is described with the fiber section element and the modified Kent–Park concrete model. On this basis, the effective stress coupling nonlinear dynamic numerical solving model is established to analyze the effect of burial depth on the seismic response of the subway station structure dynamic system in the saturated soft soil layer, so as to provide guidance and reference for the antiseismic design and analysis of the subway station structure in the soft soil site.


## 2. Numerical Calculation Model

The numerical example is based on the typical single-storey double-span subway station in the saturated soft clay site, as shown in Figure1, in which the cross section size of the subway station structure is 17 m (width), 7.17 m (height), and 3.5 m (center column spacing). Figure 2 shows the 2-dimensional plane strain finite element model mesh of the established dynamic system of the subway station structure in saturated soft soil foundation, the size of which is 170 m × 30 m. The more unfavorable cases between soil and structure of complete bond and coordinated deformation are considered without considering the separation and sliding between them. Four different burial depth working conditions (2 m, 5 m, 8 m, and 11 m, resp.) are established to make a related analysis of the coupled effective stress numerical model for the saturated soft soil site-subway station structure dynamic interaction system.Figure 1
The cross section of the subway station structure (unit: m).Figure 2
Finite element model of calculation.In the analyses, the boundary between the soil deposit and the bedrock was assumed fixed in both horizontal and vertical directions and serving as the bottom boundary of the analyzed domain. The ground surface was assumed flat and free of loadings. The test simulated the free-field boundary conditions using laminar boxes. In the OpenSEES program, the behavior of the laminar box can be modeled by adopting the tied node feature. This feature allows the horizontal and vertical displacements at the two boundaries with the identical value. The stress-strain behavior of the material model for saturated soil could simulate the hysteresis damping to a certain extent. The bottom and both sides of the site are set as undrained boundaries, the surface is set as a drainage boundary, and both sides of the model are set as the tied boundary [23]. The more unfavorable cases are considered without considering the separation and sliding between soil and structure, that is, complete bond and coordinated deformation between them [24, 25]. Energy dissipation effect is stimulated by the Rayleigh damping adopted in the numerical model, and the specific damping ratio is selected as 5% [26]. The HHT step-wise time integration method is used in the dynamic calculation, which can consider the energy dissipation and the second-order accuracy.The numerical formula of the saturated two-phase medium matrix used in the present paper is as follows [27]:(1)Mu¨+Cu˙+∫ΩBTσ′dΩ−Qp=fu,QTu˙−Sp˙−Hp˙=fp,where M is the total mass matrix; u is the displacement vector; B is the strain-displacement matrix, B≡LNu, which is related to the strain and displacement increment dε=Bdu¯; σ′ is the effective stress tensor; Q is the discrete gradient operator for soil-water coupling; p is the pore pressure vector; S is the compression coefficient matrix; H is the permeability coefficient matrix; and vectors fu and fp, respectively, indicate the given boundary conditions of the volume force in the soil-water mixture and the liquid phase.Theu-p form plastic constitutive relation of the elastic-plastic multiyield surface motion based on Biot’s theory as shown in Figure 3 is adopted for clay. The yield surface formula of the clay multiyield surface model is(2)fm=32τ−αm:τ−αm1/2−Km=0m=1,2,…,n,where τ is the partial stress tensor; m is the number of the mth yield surface, m∈1,2,…,n; n is the total quantity of the yield surface; the parameters αmand K, respectively, indicate the center and radius of the mth yield surface; and Km is equal to 3/2times of the radius of the yield surface. The double dot product of tensors A and B is A:B=Aij:Bij.Figure 3
Shear stress-strain curve of soft soil.The plastic constitution of the clay multiyield surface adopts the law of partial kinematic hardening, and the movement direction tensor of the yield surface is defined as(3)μ=sT−αm−MmMm+1sT−αm+1,where sT is the second-order deviatoric stress tensor, which represents the deviatoric stress tensor of the intersection point of the yield surfaces fm+1 and fm, and αmand p′+p′0αm+1are the center of the yield surfaces fm and fm+1, respectively.Figure4 shows a representation of the nonlinear soil behavior in terms of normalized shear modulus and damping curves vs shear strain amplitude and a comparison with standard literature behaviors [28]. It can be seen that the nonlinear soil behavior in terms of normalized shear modulus and damping curves vs shear strain amplitude is in line with standard literature behaviors. Therefore, the numerical model in the present paper can be used to simulate the dynamic properties of clay.Figure 4
Comparison of the (G)/(G)max vs γ and λ vs γ curves.The site soil is simulated by the quadUP element. The soft soil constitutive calculation parameters are obtained by referring to the recommended values of OpenSEES clay constitution, specifically as listed in Table1 [29]. The designed strength of the concrete with established embedded depth is C40 and the density is 2500 kg/m3 [30, 31]. The adoption of the fiber section unit of the underground structure considers its nonlinear dynamic performance. The schematic diagram of the fiber section is shown in Figure 5 [32]. Specifically, the Concrete02 constitutive model (modified Kent–Park concrete model) is used in the structural concrete, and the stress-strain relationship is shown in Figure 6(a). The steel bar uses Steel02 dynamic isotropic hardening bilinear material model, and the stress-strain relation is shown in Figure 6(b), in which the elastic modulus of the steel bar is 200 GPa and the yield strength is 400 MPa.Table 1
Model parameters of soft clay.
Soil parameter
ρ (kg/m3)
G
ref (MPa)
B
ref (MPa)
c (kPa)
γ
max
φ
n
p
Parameter value
1700
17
79
18
0.1
0
0
Note:ρ is the saturated soil mass density; Gref is the reference low-strain shear modulus; Bref is the reference bulk modulus; c is the apparent cohesion at zero effective confinement; γmax is an octahedral shear strain at which the maximum shear strength is reached; φ is the friction angle at peak shear strength in degrees; np is an optional nonnegative constant defining variations of G and B as a function of initial effective confinement.Figure 5
Schematics of fiber cross section.Figure 6
Constitutive model of reinforced concrete: (a) stress-strain curve of concrete; (b) stress-strain curve of the steel bar.
(a)
(b)The north-south component of the 1995 Kobe earthquake is scaled 0.2 g and used as the horizontal excitation in the analyses. The magnitude is 6.9. North-south component was recorded at the Kobe Japanese Meteorological Agency (JMA) station during the Hyogo-ken Nanbu (Kobe) earthquake (Rjb (km): 0.94, Rrup (km): 0.96, and VS30 (m/s): 312). The Kobe seismic wave with duration of 30 s is selected and input horizontally from the base rigid boundary, and the acceleration input of the seismic ground motion and corresponding Fourier spectrum are shown as Figure7. Initial ground stress balance (the elastic + plastic stage) is first carried out, and then the seismic action is applied. The numerical calculation is completed by a 64-bit 32-core CPU-64G memory DELLT7600 high-performance desktop workstation, and all the numerical results are extracted and visualized by the self-compiled MATLAB interface program.Figure 7
Ground motion acceleration input: (a) ground motion time history; (b) Fourier spectrum.
(a)
(b)


## 3. Analysis of Seismic Response of Burial Depth to the Subway Station Structure in Saturated Soft Foundation

### 3.1. Influence of Burial Depth on Displacement of the Subway Station Structure

Figure8 shows the residual displacement of the soft site after the earthquake under different burial depth conditions. It can be seen from Figure 8 that, with the increase of burial depth, the uneven uplift effect of the subway station structure caused by the movement and extrusion of soil from the far field to the bottom of the floor is weakened gradually. The displacement time history curve of the middle point of the floor of the subway station structure in the soft soil site under different burial depth conditions is shown in Figure 9. It can be seen from Figure 9 that the peak of the horizontal and vertical displacements time history curve of the subway station structure gradually decreases with the increase of the burial depth, and the uplift amount of the typical point of the structure of 11 m (burial depth) is reduced by 50% than that of 5 m (with burial depth). It can be seen that the burial depth of the subway station structure in the saturated soft soil site has a significant influence on the uneven uplift effect.Figure 8
Contours of postearthquake residual displacement of soft soil ground with different burial depths (unit: (m): (a) 2 m; (b) 5 m; (c) 8 m; (d) 11 m.
(a)
(b)
(c)
(d)Figure 9
Time history of displacement of subway station structures with different burial depths: (a) horizontal displacement; (b) vertical displacement.
(a)
(b)


### 3.2. Influence of Burial Depth on the Peak of Soil Dynamic Pore Pressure Ratio

According to the principle of effective stress, the dynamic pore pressure ratio (representative symbol: DPPR) is computed as the ratio of excess pore pressure to initial effective vertical stress. Figure10 shows the peak envelope diagram of the dynamic pore pressure ratio of the soft soil site under different burial depth conditions. It can be seen from the diagram that the predominance area of the dynamic pore pressure ratio peak of the soft soil around the shallow-buried subway station shows a typical ring-shaped distribution characteristic, and the maximum dynamic pore pressure ratio (0.5) appears near the floor of the subway station and the shear wall. With the increase of the burial depth of the station structure, the vertical effective stress level of the deep soil near the structure becomes higher, and the inertial dynamic extrusion effect of the overlaying soil in the station structure is increased accordingly. Therefore, the range of the dynamic pore pressure ratio peak area of soft soil around the subway station structure is gradually close to the structure from outside, and the peak also decreases.Figure 10
Contours of peak response of the dynamic pore pressure ratio of soft soil ground with different burial depths: (a) 2 m; (b) 5 m; (c) 8 m; (d) 11 m.
(a)
(b)
(c)
(d)Figure11 shows the time-history curves of the dynamic pore pressure ratio at the locations of characteristics points of soft soil sites under different burial depth conditions. It can be seen from Figure 11 that, with the increase of the burial depth of the station structure, the dynamic pore pressure ratio peak of the soil typical points F1 and F2 around the structure gradually decreases, which is in accordance with the variation of the peak range and peak level of the dynamic pore pressure ratio of the soft soil around the subway station structure in Figure 9.Figure 11
Time-history curves of the dynamic pore pressure ratio of typical points with different burial depths in soft soil ground: (a)F1; (b) F2.
(a)
(b)


### 3.3. Influence of Burial Depth on Internal Force Response of the Subway Station Structure

The position of the structural column-slab joint as shown in Figure12 is selected as the typical section of the structure for analysis. For example, Tables 2–4 show the peak of the internal force response at the typical section of the subway station structure under different burial depth conditions, and the figure in the brackets in the tables is the peak increase percentage of the dynamic internal force with the burial depth of 11 m compared with that of 2 m. It can be seen from the tables that, with the increase of burial depth, the peak position of the maximum internal force in the whole structure will also be adjusted under the seismic action. Specifically, the maximum axis force peak of the whole structure appears at the left end of the floor (position of P1) when the burial depth is 2 m, while the maximum axial peak position of the whole structure appears at the lower end of the middle column (position of P7) when the burial depth is 11 m; the maximum shear peak of the structure appears at the lower end of the left wall (position of P5) when the burial depth is 2 m, and when the burial depth is 11 m, the maximum shear peak position of the whole structure appears at the lower end of the right wall (position of P9); and the maximum bending moment peak of the whole structure under the condition that the burial depth is 2 m appears at the left end of the floor (position of P1), while the maximum bending moment peak position of the overall structure appears at the middle end of the roof (position of P12) when the burial depth is 11 m. In addition, with the increase of burial depth, the peak of internal forces at typical sections of structural members also increases in varying degrees. In particular, for the typical section of the same structure, the maximum bending moment peak of the middle end (position of P2 and P3) of the structure floor when the burial depth is 11 m has an increase rate of about 750% compared with that of 2 m (burial depth), which is far greater than the increase rate of the maximum internal force peak of the other typical sections in the whole structure.Figure 12
Schematic diagram of key parts of dynamic force of the subway station structure.Table 2
The maximum axial forces at typical sections of the structure with different burial depths (unit: kN).
Burial depth (m)
P11
P12
P13
P14
P6
P8
P10
2 m
550
544
526
598
768
2201
783
5 m
1331
1342
1317
1382
1636
3778
1648
8 m
2028
2045
2009
2095
2454
5427
2484
11 m
2686 (↑388%)
2661(↑389%)
2606 (↑395%)
2761 (↑362%)
3239 (↑322%)
7080(↑222%)
3281 (↑319%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
2335
2200
2196
2332
1512
2269
1499
5 m
2880
2709
2709
2869
2362
3848
2320
8 m
3348
3116
3144
3314
3216
5495
3114
11 m
3844 (↑65%)
3568 (↑62%)
3583 (↑63%)
3843 (↑65%)
4174 (↑176%)
7150(↑215%)
3889 (↑159%)Table 3
The maximum shear forces of typical sections of the structure with different burial depths (unit: kN).
Burial depth (m)
Position of P11
Position of P12
Position of P13
Position of P14
Position of P6
Position of P8
Position of P10
2 m
467
1043
1032
466
580
39
618
5 m
1135
1701
1681
1168
1239
69
1289
8 m
1837
2416
2341
1875
1882
102
1966
11 m
2459 (↑427%)
3131 (↑200%)
2994 (↑190%)
2488(↑434%)
2501 (↑331%)
131(↑236%)
2597 (↑320%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
1482
834
846
1474
1795
53
1780
5 m
2053
1502
1539
2043
2349
77
2270
8 m
2524
2219
2257
2569
2762
116
2740
11 m
3015 (↑103%)
2940 (↑253%)
2947 (↑248%)
3071 (↑108%)
3157 (↑76%)
144(↑172%)
3200 (↑80%)Table 4
The maximum bending moments at typical sections of the structure with different burial depths (unit: kN·m).
Burial depth (m)
P11
P12
P13
P14
P6
P8
P10
2 m
608
2710
2709
631
608
143
631
5 m
1839
3739
3737
2034
1839
248
2034
8 m
3138
4935
4836
3441
3137
367
3441
11 m
4286 (↑605%)
6019 (↑122%)
5852 (↑116%)
4590 (↑627%)
4284 (↑605%)
472(↑230%)
4589 (↑627%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
3228
443
445
3169
3225
156
3165
5 m
4232
1493
1496
4118
4230
256
4106
8 m
5066
2608
2645
4913
4993
385
4895
11 m
5741 (↑78%)
3754 (↑747%)
3823(↑759%)
5747 (↑81%)
5699 (↑77%)
482(↑209%)
5701 (↑80%)The above analysis is aimed at the maximum internal force peak of the key point of the structure and the increase with the change of the burial depth. In order to further understand the effect of different burial depth conditions on the dynamic internal force response of the structure under the seismic action, the nondimensional dynamic response evaluation indexR is defined, which is the ratio of additional dynamic internal force to total internal force (seismic action + gravity action) caused by seismic action.Figure13 shows the R distribution of the dynamic evaluation index at the typical section of the structure when the burial depth is 2 m. According to the order of the value of R in each dynamic internal force evaluation index in the figure, the positions of the first 2 typical sections are selected as the most unfavorable antiseismic component position in the subsequent analysis. Specifically, the dynamic axial force and dynamic bending moment of P14, the dynamic shear and dynamic bending moment of P10, the dynamic axial force of P11, and the dynamic shear force of P6 are selected as the most unfavorable antiseismic component positions and indexes, and the change of corresponding dynamic evaluation indexes with burial depth is analyzed.Figure 13
Comparison of the dynamic index at typical sections of the structure with 2 m burial depth.
(a)
(b)
(c)Figure14 shows that the dynamic evaluation index of the most unfavorable typical section above varies with the burial depth of the structure. It can be seen from Figure 14 that, with the increase of the structural burial depth, the value of the dynamic response evaluation index R for each corresponding position has a decreasing trend, which illustrates from the other perspective that the dynamic failure of the shallow-buried subway station in the saturated soft soil site may be more serious. In fact, the internal force increase of the underground structure caused by the gravity of the system is larger than that of the additional internal force, that is, the R ratio decreases. The dynamic evaluation index of the dynamic bending moment at the upper end of the right wall (position of P10) and the right end of the roof (position of P14) is the highest, and the changes with the burial depth of the structure are also the most significant.Figure 14
Variations of the dynamic index with burial depths at typical sections.In particular, the shear and bending moment of the middle column are close to zero only under the gravity, there isR ⟶1 at each burial depth condition for the middle column, and the nondimensional dynamic response evaluation index R is not applicable. In particular, the increase of the shear and bending moment of the middle column is close to zero only under the system gravity; that is, for the middle column, there is R ⟶1 at each burial depth condition, and the nondimensional dynamic response evaluation index R is not applicable. As we know, the roof collapse caused by dynamic failure of the middle column is one of the important forms of seismic damage of the subway station structure. On this basis, in addition to the analysis of the most unfavorable seismic position according to the R value increase, the middle column is further selected as the most unfavorable seismic component position, and the change of additional dynamic internal force which increases with the burial depth is adopted for evaluation and analysis. Figure 14 shows that the additional internal forces of the upper and the lower ends of the middle column vary with the burial depth. As shown in Figure 15, the additional dynamic shear and dynamic bending moment at the upper end of the middle column (position of P8) are most significantly influenced by the burial depth (the variation coefficients are 0.468 and 0.464, resp.), second to which is the additional dynamic shear and the dynamic bending moment at the lower end of the middle column (position of P7) (the variation coefficients are 0.445 and 0.448, resp.), and the additional dynamic axial force of the upper and lower ends of the middle column are most slightly influenced by the burial depth (the variation coefficient is 0.199). In addition, Tables 2–4 also show that the maximum internal force peak and the change and increase of the middle column are lower than those of the other key characteristic positions under all burial depth conditions.Figure 15
Variations of dynamic internal forces with burial depths at typical sections.


## 3.1. Influence of Burial Depth on Displacement of the Subway Station Structure

Figure8 shows the residual displacement of the soft site after the earthquake under different burial depth conditions. It can be seen from Figure 8 that, with the increase of burial depth, the uneven uplift effect of the subway station structure caused by the movement and extrusion of soil from the far field to the bottom of the floor is weakened gradually. The displacement time history curve of the middle point of the floor of the subway station structure in the soft soil site under different burial depth conditions is shown in Figure 9. It can be seen from Figure 9 that the peak of the horizontal and vertical displacements time history curve of the subway station structure gradually decreases with the increase of the burial depth, and the uplift amount of the typical point of the structure of 11 m (burial depth) is reduced by 50% than that of 5 m (with burial depth). It can be seen that the burial depth of the subway station structure in the saturated soft soil site has a significant influence on the uneven uplift effect.Figure 8
Contours of postearthquake residual displacement of soft soil ground with different burial depths (unit: (m): (a) 2 m; (b) 5 m; (c) 8 m; (d) 11 m.
(a)
(b)
(c)
(d)Figure 9
Time history of displacement of subway station structures with different burial depths: (a) horizontal displacement; (b) vertical displacement.
(a)
(b)


## 3.2. Influence of Burial Depth on the Peak of Soil Dynamic Pore Pressure Ratio

According to the principle of effective stress, the dynamic pore pressure ratio (representative symbol: DPPR) is computed as the ratio of excess pore pressure to initial effective vertical stress. Figure10 shows the peak envelope diagram of the dynamic pore pressure ratio of the soft soil site under different burial depth conditions. It can be seen from the diagram that the predominance area of the dynamic pore pressure ratio peak of the soft soil around the shallow-buried subway station shows a typical ring-shaped distribution characteristic, and the maximum dynamic pore pressure ratio (0.5) appears near the floor of the subway station and the shear wall. With the increase of the burial depth of the station structure, the vertical effective stress level of the deep soil near the structure becomes higher, and the inertial dynamic extrusion effect of the overlaying soil in the station structure is increased accordingly. Therefore, the range of the dynamic pore pressure ratio peak area of soft soil around the subway station structure is gradually close to the structure from outside, and the peak also decreases.Figure 10
Contours of peak response of the dynamic pore pressure ratio of soft soil ground with different burial depths: (a) 2 m; (b) 5 m; (c) 8 m; (d) 11 m.
(a)
(b)
(c)
(d)Figure11 shows the time-history curves of the dynamic pore pressure ratio at the locations of characteristics points of soft soil sites under different burial depth conditions. It can be seen from Figure 11 that, with the increase of the burial depth of the station structure, the dynamic pore pressure ratio peak of the soil typical points F1 and F2 around the structure gradually decreases, which is in accordance with the variation of the peak range and peak level of the dynamic pore pressure ratio of the soft soil around the subway station structure in Figure 9.Figure 11
Time-history curves of the dynamic pore pressure ratio of typical points with different burial depths in soft soil ground: (a)F1; (b) F2.
(a)
(b)


## 3.3. Influence of Burial Depth on Internal Force Response of the Subway Station Structure

The position of the structural column-slab joint as shown in Figure12 is selected as the typical section of the structure for analysis. For example, Tables 2–4 show the peak of the internal force response at the typical section of the subway station structure under different burial depth conditions, and the figure in the brackets in the tables is the peak increase percentage of the dynamic internal force with the burial depth of 11 m compared with that of 2 m. It can be seen from the tables that, with the increase of burial depth, the peak position of the maximum internal force in the whole structure will also be adjusted under the seismic action. Specifically, the maximum axis force peak of the whole structure appears at the left end of the floor (position of P1) when the burial depth is 2 m, while the maximum axial peak position of the whole structure appears at the lower end of the middle column (position of P7) when the burial depth is 11 m; the maximum shear peak of the structure appears at the lower end of the left wall (position of P5) when the burial depth is 2 m, and when the burial depth is 11 m, the maximum shear peak position of the whole structure appears at the lower end of the right wall (position of P9); and the maximum bending moment peak of the whole structure under the condition that the burial depth is 2 m appears at the left end of the floor (position of P1), while the maximum bending moment peak position of the overall structure appears at the middle end of the roof (position of P12) when the burial depth is 11 m. In addition, with the increase of burial depth, the peak of internal forces at typical sections of structural members also increases in varying degrees. In particular, for the typical section of the same structure, the maximum bending moment peak of the middle end (position of P2 and P3) of the structure floor when the burial depth is 11 m has an increase rate of about 750% compared with that of 2 m (burial depth), which is far greater than the increase rate of the maximum internal force peak of the other typical sections in the whole structure.Figure 12
Schematic diagram of key parts of dynamic force of the subway station structure.Table 2
The maximum axial forces at typical sections of the structure with different burial depths (unit: kN).
Burial depth (m)
P11
P12
P13
P14
P6
P8
P10
2 m
550
544
526
598
768
2201
783
5 m
1331
1342
1317
1382
1636
3778
1648
8 m
2028
2045
2009
2095
2454
5427
2484
11 m
2686 (↑388%)
2661(↑389%)
2606 (↑395%)
2761 (↑362%)
3239 (↑322%)
7080(↑222%)
3281 (↑319%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
2335
2200
2196
2332
1512
2269
1499
5 m
2880
2709
2709
2869
2362
3848
2320
8 m
3348
3116
3144
3314
3216
5495
3114
11 m
3844 (↑65%)
3568 (↑62%)
3583 (↑63%)
3843 (↑65%)
4174 (↑176%)
7150(↑215%)
3889 (↑159%)Table 3
The maximum shear forces of typical sections of the structure with different burial depths (unit: kN).
Burial depth (m)
Position of P11
Position of P12
Position of P13
Position of P14
Position of P6
Position of P8
Position of P10
2 m
467
1043
1032
466
580
39
618
5 m
1135
1701
1681
1168
1239
69
1289
8 m
1837
2416
2341
1875
1882
102
1966
11 m
2459 (↑427%)
3131 (↑200%)
2994 (↑190%)
2488(↑434%)
2501 (↑331%)
131(↑236%)
2597 (↑320%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
1482
834
846
1474
1795
53
1780
5 m
2053
1502
1539
2043
2349
77
2270
8 m
2524
2219
2257
2569
2762
116
2740
11 m
3015 (↑103%)
2940 (↑253%)
2947 (↑248%)
3071 (↑108%)
3157 (↑76%)
144(↑172%)
3200 (↑80%)Table 4
The maximum bending moments at typical sections of the structure with different burial depths (unit: kN·m).
Burial depth (m)
P11
P12
P13
P14
P6
P8
P10
2 m
608
2710
2709
631
608
143
631
5 m
1839
3739
3737
2034
1839
248
2034
8 m
3138
4935
4836
3441
3137
367
3441
11 m
4286 (↑605%)
6019 (↑122%)
5852 (↑116%)
4590 (↑627%)
4284 (↑605%)
472(↑230%)
4589 (↑627%)
Burial depth (m)
P
1
P
2
P
3
P
4
P
5
P
7
P
9
2 m
3228
443
445
3169
3225
156
3165
5 m
4232
1493
1496
4118
4230
256
4106
8 m
5066
2608
2645
4913
4993
385
4895
11 m
5741 (↑78%)
3754 (↑747%)
3823(↑759%)
5747 (↑81%)
5699 (↑77%)
482(↑209%)
5701 (↑80%)The above analysis is aimed at the maximum internal force peak of the key point of the structure and the increase with the change of the burial depth. In order to further understand the effect of different burial depth conditions on the dynamic internal force response of the structure under the seismic action, the nondimensional dynamic response evaluation indexR is defined, which is the ratio of additional dynamic internal force to total internal force (seismic action + gravity action) caused by seismic action.Figure13 shows the R distribution of the dynamic evaluation index at the typical section of the structure when the burial depth is 2 m. According to the order of the value of R in each dynamic internal force evaluation index in the figure, the positions of the first 2 typical sections are selected as the most unfavorable antiseismic component position in the subsequent analysis. Specifically, the dynamic axial force and dynamic bending moment of P14, the dynamic shear and dynamic bending moment of P10, the dynamic axial force of P11, and the dynamic shear force of P6 are selected as the most unfavorable antiseismic component positions and indexes, and the change of corresponding dynamic evaluation indexes with burial depth is analyzed.Figure 13
Comparison of the dynamic index at typical sections of the structure with 2 m burial depth.
(a)
(b)
(c)Figure14 shows that the dynamic evaluation index of the most unfavorable typical section above varies with the burial depth of the structure. It can be seen from Figure 14 that, with the increase of the structural burial depth, the value of the dynamic response evaluation index R for each corresponding position has a decreasing trend, which illustrates from the other perspective that the dynamic failure of the shallow-buried subway station in the saturated soft soil site may be more serious. In fact, the internal force increase of the underground structure caused by the gravity of the system is larger than that of the additional internal force, that is, the R ratio decreases. The dynamic evaluation index of the dynamic bending moment at the upper end of the right wall (position of P10) and the right end of the roof (position of P14) is the highest, and the changes with the burial depth of the structure are also the most significant.Figure 14
Variations of the dynamic index with burial depths at typical sections.In particular, the shear and bending moment of the middle column are close to zero only under the gravity, there isR ⟶1 at each burial depth condition for the middle column, and the nondimensional dynamic response evaluation index R is not applicable. In particular, the increase of the shear and bending moment of the middle column is close to zero only under the system gravity; that is, for the middle column, there is R ⟶1 at each burial depth condition, and the nondimensional dynamic response evaluation index R is not applicable. As we know, the roof collapse caused by dynamic failure of the middle column is one of the important forms of seismic damage of the subway station structure. On this basis, in addition to the analysis of the most unfavorable seismic position according to the R value increase, the middle column is further selected as the most unfavorable seismic component position, and the change of additional dynamic internal force which increases with the burial depth is adopted for evaluation and analysis. Figure 14 shows that the additional internal forces of the upper and the lower ends of the middle column vary with the burial depth. As shown in Figure 15, the additional dynamic shear and dynamic bending moment at the upper end of the middle column (position of P8) are most significantly influenced by the burial depth (the variation coefficients are 0.468 and 0.464, resp.), second to which is the additional dynamic shear and the dynamic bending moment at the lower end of the middle column (position of P7) (the variation coefficients are 0.445 and 0.448, resp.), and the additional dynamic axial force of the upper and lower ends of the middle column are most slightly influenced by the burial depth (the variation coefficient is 0.199). In addition, Tables 2–4 also show that the maximum internal force peak and the change and increase of the middle column are lower than those of the other key characteristic positions under all burial depth conditions.Figure 15
Variations of dynamic internal forces with burial depths at typical sections.


## 4. Conclusions

Based on theu-p form of Biot’s dynamic consolidation equation and the effective stress dynamic solution method of saturated two-phase medium, a numerical model of effective stress coupled dynamic analysis for the saturated soft soil site-subway station structure interaction system is established in the present paper, and the seismic dynamic response law of the saturated soft soil site-subway station structure interaction system under different burial depth conditions is analyzed. The calculation and analysis results show the following:(1)
With the increase of burial depth of the station, the uneven uplift effect of the subway station structure caused by the movement and extrusion of soil from the far field to the bottom of the floor is weakened gradually, and the burial depth in the saturated soft soil site has a significant influence on the uneven uplift effect.(2)
With the increase of the burial depth of the station structure, the soil's vertical effective stress level at the depth of the structure becomes higher, and the inertial dynamic extrusion effect of the overlying soil layer is enhanced simultaneously. The range of the dynamic pore pressure ratio peak of the soft soil around the station structure is gradually close to the structure from the outside, and the peak level also decreases.(3)
With the increase of the burial depth of the station structure, the value of nondimensional dynamic response evaluation indexR for all positions shows a decreasing trend, in which the dynamic moment evaluation index of the upper end of the right wall and the right end of the roof is the largest, and the change with the structural burial depth is the most significant.(4)
For the internal force index of the middle column, the additional dynamic shear and dynamic bending moment at the upper end of the middle column are most significantly affected by the burial depth of the structure, followed by the lower end of the middle column. Compared with the corresponding value of the other key characteristic positions of the structure, the maximum internal force peak of the middle column and the increase with the burial depth are lower.



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*Source: 8978467-2018-09-05.xml*