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Shaking table test on the seismic response of large-scale subway station in a loess site: A case study
Soil Dynamics and Earthquake Engineering 123 (2019) 173–184
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Shaking table test on the seismic response of large-scale subway station in a loess site: A case study
T
Su Chena, Haiyang Zhuangb, Dengzhou Quanc, Jie Yuand, Kai Zhaob, Bin Ruanb,∗ a
Institute of Geophysics, China Earthquake Administration, Beijing, 100081, China Institute of Geotechnical Engineering, Nanjing Tech University, Nanjing, 210009, China c Chang'an University, Xi'an, 710061, China d State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Underground structure Seismic response Shaking-table test Loess site Dynamic interaction
More and more underground infrastructures have been built in special soil in recent years, especially in the loess area of western China. The loess, as a special soft soil, can have particular influence on the seismic characteristics of underground structures. Therefore, the seismic performance and safety evaluation of underground structures in loess area should be concerned. A series of large-scale shaking table tests were performed to investigate the damage mechanisms of a frame-type subway station structure in a loess site. The test results showed that the model soil softening and the stiffness degradation of the soil-structure system were more serious under stronger input motions. The acceleration response of the soil-structure interaction system in a loess site was more like that of a free-field when input PGA is lower. However, the soil-structure interaction phenomenon was more remarkable both in horizontal and vertical direction when higher PGA was input. The dominant frequency of the input motion had an inverse effect on the lateral soil deformation. The direct-force action mode of the dynamic earth pressure acting on underground structures presents a trumpet-type distribution. Meanwhile, the soilstructure interaction exhibited complex mechanical behavior, and slipping or gapping in test cases with higher PGA may occur. The strain measured in the center pillar and middle slab of the subway station was larger than that in other components. The results provide an insight into how strong ground motion might induce the influence and a possible way to describe quantitatively the damage of subway structure in loess ground.
1. Introduction With rapid development and urbanization in China, exploitation and utilization of underground space has become a major issue in China. Till the end of 2017, subways projects have been built or approved in 34 Chinese cities with a total operating mileage of 5021 km. Especially, some lines have been built in the cities of western China, such as Lanzhou, Xi'an, Taiyuan and so on, and some subway stations are located in loess area. The seismic research of underground structures has gone through three stages. Stage 1: before the 1995 Kobe earthquake in Japan, underground structures were assumed to be earthquake resistant. However, the Kobe earthquake showed that underground structures are also vulnerable to seismic motions, as a large number of central reinforced concrete pillars of the underground subway stations were damaged, which has induced the collapse of the whole subway station. There are several possible reasons for this damage, such as strong ground motions and permanent ground movement
∗
[1–3]. Stage 2: a large number of tests and numerical analyses have given qualitative and semi-quantitative understanding [4–17]. Stage 3: the seismic problem of underground structures has developed from the response research to the performance-based research. The research work of seismic response of underground structure can be divided into experimental, theoretical and numerical simulation. However, little attention was paid to the underground structural damage characteristics in special soil, for example loess ground. For loess soil, in terms of sedimentary characteristics, loess is typical quaternary unconsolidated sediments, and unique generating environment and material source make it form special macroporous, unconsolidated and unsaturated porous weakly cemented aerial structure. This structural form of loess makes its dynamic characteristics significantly difference from other soils, which is mainly reflected in the water sensitivity of loess. Then, the original structural of the loess site is more likely to collapse under the earthquake motions. With the pore gas compressed and expelled, the site showed the characteristics of seismic
Corresponding author. E-mail address: [email protected] (B. Ruan).
https://doi.org/10.1016/j.soildyn.2019.04.023 Received 19 November 2018; Received in revised form 10 April 2019; Accepted 23 April 2019 Available online 08 May 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
Soil Dynamics and Earthquake Engineering 123 (2019) 173–184
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Table 1 The similitude ratio of the soil-structure system. Types
Physical quantity
Similitude relation
Similitude ratio Model structure
Model soil
1/30 1/30 1.2 × 10−6
1/4.5 1/4.5 /
Geometry properties
Length l Linear displacement r Inertia moment I
Material properties
Equivalent density ρ
SI = Sl 4 Sρ = SE / Sl Sa
3.0
1
Elastic modulus E Shear wave velocity of soil vs Shear modulus of soil Gravity acceleration g
SE Sv SG Sg
1/5 / / 1
/ 1/3 1/9 1
Dynamic properties
Sl Sr = Sl
Mass m
Sm = Sρ⋅Sl3
1.11 × 10-4
/
Force F
SF = Sρ⋅Sl3⋅Sa
2.22 × 10-4
/
Frequency ω Acceleration a Duration t
Sω = 1/ St Sa
7.75 2.0 0.13
3.0 2.0 0.33
St =
Sl/ Sa
2. Shaking table test
subsidence with sudden subsidence and subsequent slow subsidence. In addition, compared with other sites, the loess site with thick overburden has more significant seismic amplification effect [18]. Due to the special structure and water sensitivity of the loess, the earthquake damage in the loess site is more serious. Previous studies showed that, the loess site was prone to seismic collapse, landslide, liquefaction and significant seismic amplification effect under strong earthquake motions, which induced and aggravated the earthquake disaster of the engineering structure [19]. In addition, historical data show that earthquake disasters in loess areas are relatively serious. For example, the 1556 Huaxian earthquake in Shanxi province, China (Mw 8.0) struck a large number of loess areas; Weinan area, located in the extreme earthquake area, is full of earth surface cracks. In the 1718 Tongwei earthquake in Gansu province, China (Mw 7.5), a large number of landslides formed in the malan loess layer of Longxi region. In 1920 Haiyuan earthquake in Gansu province, China (Mw 8.5), the earthquake damage is more serious due to the formation of serious landslide concentration area of more than 4000 square kilometers. In the 1970 Xiji earthquake in Ningxia, the intensity of the epicenter was only 7.0 degrees, but many landslides and cracks also occurred. What's more, according to the analysis of seismic activity, the Fenwei and Longmen mountain seismic belt (seismic belts have greater impact on the Xi ‘an area) would be slightly active in the next 50–100 years. However, with the increasing number of metro projects in the loess area of western China, the seismic performance and safety evaluation of underground structures in the loess area should be studied. Xi ‘an subway is the first subway project built in loess region in China. Historical seismic data show that there is strong seismic activity around Xi ‘an. There have been 3 earthquakes with Mw 7.0 or above and 11 earthquakes with Mw 6.0 or above. To above view, in this paper, we choose Feitianlu station, Xi'an Metro Line 4, as prototype subway station, and the model soil comes from the construction site, and then an experimental study was carried out on the seismic performance of an underground structure in loess ground. Based on the Xi'an subway project, this study experimentally investigated the dynamic interaction between loess and an underground subway station. The ground motion and loading scheme were confirmed according to the earthquake environment in the Xi'an area. By the test result, some new findings and conclusions were made in this study, which can provide reliable reference and guidance for the seismic design and earthquake safety evaluation of loess-area subway stations, tunnels, and underground commercial streets.
2.1. Test apparatus and similitude ratio design The dimensions of the shaking table are 3.36 m × 4.86 m in a plane. The maximum acceleration of the shaking table is 1 g, with a maximum bearing capacity of 25 tons. The frequency of the input motion ranges from 0.1 to 50 Hz. The laminar shear model soil container is 3.5 m × 2.0 m × 1.7 m. This container can effectively eliminate the reflection and scattering of a seismic wave at the boundary of the container [11]. The testing data from the model structure and the soil were collected in real time by an independently developed dynamic signal-acquisition system [20]. This study employed the scaling laws recommended by Buckingham π theorem [21]. Based on the characteristics of the model structure and the soil, various basic physical quantities are selected, including the length, elastic modulus, and acceleration of the model structure, as well as the shear wave velocity, density, and acceleration of the model soil. In the soil-structure shaking table test, that all parameters meet the similitude law is unprocurable. The principles of the similarity ratio design of this test are presented as follows: (1). the inertial force of underground structure should be concerned; (2). the input ground motion's frequency band must be controlled; (3) the material property should be selected properly. The similarity ratios are given in Table 1. The relative stiffness plays a key role in soil-structure interaction effects under strong earthquake motions. Some researchers have made many meaningful studies for this issue [22–25]. For the shaking table test, [26] gave the formula for calculating the stiffness ratio of the tunnel and the soil. For this test, the similitude ratio for the relative stiffness SF is:
SF =
Gm △m ⋅ Gp △p
Where Gm and Gp are the dynamic shearing modulus of the model soil and the field soil, respectively, and Δm and Δp are the displacements for the numerical model of the test and the practical tunnel, respectively. Before shaking table test, the average shear wave velocity of the model soil were 90.0 m/s which equals to the one third of the average shear wave velocity of the prototype site (270.0 m/s). For structure, we carried out a simple numerical simulation (software ABAQUS), the result showed that the deformation ratio between model and prototype equals to 5.0. Hence, the SF in this test equals to 1/1.8. 2.2. Model soil and structure The model soil consists of a 1200-mm-thick loess layer. During the 174
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For the model structure, the designed strength and stiffness of the model structure were calculated according to the similitude ratio. Galvanized steel wire and micro-concrete were used to simulate the steel rebar and prototype concrete, respectively. The concrete mix ratio was determined based on a strength test of the micro-concrete, and the scale material shows different dynamic response [31]. Hence, based on the desired strength of the micro-concrete, the mixture ratio of the model concrete was determined as water: cement: lime: coarse sand = 1.4: 1.0: 0.5: 6.5, and the compressive strength of the microconcrete was approximately 8.11 MPa and the elasticity modulus was approximately 6.60 GPa. The diameter of the galvanized steel wire ranged from 0.9 mm to 2.0 mm: 2.0 mm for beam and column, 0.9 mm for plate and side wall. (The similarity ratio of length is 1/30). Tensile yield strength and elastic modulus of galvanized steel wire were 1190 MPa and 200 GPa, respectively. The construction process of model structure can be seen in Fig. 2. 2 mm-thick plexiglas was used to seal the model structure, the structure reinforcement design can be seen in Fig. 3.
Table 2 Material properties of model soil. Dry density (g/cm3)
Unit weight (kN/m3)
Soil moisture content (%)
Liquid limit (LL)
Plastic limit (PL)
Void ratio
1.41
16.7
22.7
20.3
34.2
0.973
preparation, the soil was placed in the model soil container layer by layer. Each layer was composed of tamped backfill, approximately 200 mm thick; meanwhile, when preparing the model foundation, number of hammers is basically the same for each soil layer, and, before each layer of loess was filled, the surface of the lower soil was subjected to brushing. After the preparation, the model soil was allowed to stand in the laboratory for 10 days in its natural state. The soil properties can be seen in Table 2. Before the test, the triaxial test was carried to obtain the dynamic parameters of the soil and the curve was fitted by the classical Hardin model, which can describe the variation of soil dynamic parameters over a wide strain range [27,28]. Fig. 1 show G/Gmax and γ for loess used in this study and range of data for cohesionless sand and clay. As shown in Fig. 1a, G/Gmax ∼γ of loess are distributed at the lower bound of γ for clay and close to the upper bound of cohessionless sand, compared with the non-viscous soil, the G/Gmax of loess shows more obvious nonlinearity with the increase of shear strain, This means that the loess presents a more rapid stiffness attenuation with the increase of shear strain. Meanwhile, λ ∼γ of loess are distributed at the upper bound of clay, the growth rate of λ for loess is greater than that of clay, This means that the loess presents a stronger ability to dissipate energy compared to clay. In addition, when λ ∼γ of loess falls between the upper bound and the lower bound of cohesionless sand. In conclusion, the dynamic characteristics of the loess are obvious different from those of conventional clay, and shown between the dynamic characteristics of non-viscous soil and clay [29,30]. In addition, considering soil moisture content would influence on the dynamic characteristics of loess, we performed some soil dynamic tests with different soil moisture. The testing result can be seen in Table 3. It is found that soil moisture content and initial consolidation pressure have significant effects on the dynamic characteristic of the remolded loess. With the same moisture content, the higher the initial consolidation pressure at the same dynamic strain, the higher the shearing modulus of the soil. Meanwhile, under the same initial consolidation pressure, the higher the moisture content, the lower the shearing modulus of the soil, and this is related to the weakening of the connection strength and the gradual destruction of the loess due to the increase of water content. Meanwhile, when the moisture content is less than the plastic limit, the dynamic shear modulus of the loess decreases greatly with the increase of the moisture content; when the moisture content is greater than the plastic limit, the dynamic shear modulus changes little with the increase of the moisture content.
2.3. Input motion and loading conditions A lot of underground structures damaged in Hyogoken-Nanbu Earthquake, Chi-Chi earthquake, and Wenchuan Earthquake. The seismic behavior and mechanism of underground structure are related with intensity of ground motion, fault and site condition; meanwhile, the input motions selected in this paper should be in the range from the lower level (63% probability of exceedance in 50 years) to the upper level (2% probability of exceedance in 50 years) of the target spectrum of the engineering site. The existence of the underground structure has little influence on the selection of the predominant period of the motions [32,33]. Hence, when estimating the predominant period (Tp) of the input motions, the most important period is decided by the period of the site (Ts). The purpose of the series of shaking table tests is to study the seismic behavior of the frame-type underground subway station structure in loess ground; therefore, the input motions should have different frequency-spectrum characteristics and durations. The ground motions from the Songpan and Taft earthquakes and a Xi'an artificial wave were selected as input motions, and the intensity of the input motion was set to 0.1 g, 0.2 g, 0.6 g, 0.8 g, and 1.2 g by adjusting the peak acceleration of the original ground motion. The acceleration time histories and corresponding response spectra are shown in Fig. 4. The Songpan ground motions were recorded at 51SPT seismologic recording stations during the Ms8.0 Wenchuan earthquake on May 12, 2008 in Sichuan Province, China. The original peak acceleration, fault distance, and duration of the Songpan records were 0.041 g, 122 km, and 213 s, respectively. The Taft ground motion was recorded at the Taft seismological recording station during the Ms7.7 Kern County earthquake on July 21, 1952 in California, USA, with an original peak acceleration, fault distance, and duration of 0.176 g, 43.5 km, and 54 s,
Fig. 1. The G/ Gmax ∼ γ and λ ∼ γ curve of loess used in the shaking table test. 175
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Table 3 The testing results of loess dynamic parameters. Soil moisture content (%)
18.1
21.1
24.1
Initial consolidation confining pressure(kPa)
50
100
150
50
100
150
50
100
150
G,max(MPa) γr(10−3)
27.10 1.67
32.70 1.94
42.70 2.25
6.80 4.38
8.10 4.10
12.10 7.50
5.30 4.08
6.30 5.68
10.40 6.53
Remarks: G,max means maximum dynamic shear modulus, γr means reference shear strain.
Fig. 2. The construction process of the model structure.
Fig. 3. Typical section and structure reinforcement (unit: mm).
0.200 g, while the duration is 80 s. The loading cases can be seen in Table 4. In order to obtain the seismic response characteristics of the structure from elastic to damage stage to the maximize utilization, the input motions follow the principle of stepwise loading. The durations of
respectively. The Xi'an bedrock artificial wave was synthesized based on the site condition characteristics of referenced subway station engineering. According to the synthetic probability of the seismic wave, the return period of this wave is 475 years, and the peak acceleration is 176
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Fig. 4. Original ground motions time histories and spectrum. Table 4 Loading cases for the shaking table test. No
Loading
PGAa (g)
No
Loading
PGA (g)
No
Loading
PGA (g)
B1 S1 T1 X1 B2 S2 T2 X2 B3
White noise Songpan record Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave White noise
0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.05
S3 T3 X3 B4 S4 T5 X6 B5 S4
Songpan record Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave White noise Sonpan record
0.2 0.2 0.2 0.05 0.4 0.4 0.4 0.05 0.6
T4 X4 B6 S5 T5 X5 X6 B7 –
Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave Xi'an artificial wave White noise –
0.6 0.6 0.05 0.8 0.8 0.8 1.2 0.05 –
a
Peak ground acceleration, the unit is g.
3. Results and interpretation
scaled Songpan wave, Taft wave and the Xi'an artificial wave were 26.00s, 7.02s, and 10.4s, respectively.
3.1. Dynamic characteristics of the soil-structure system We used the acceleration obtained in the shaking table as input motion, and the acceleration measured in the ground surface as output motion, and then the transfer function can be calculated. The mode of the transfer function expresses the response amplitude-frequency characteristics of the target system. The frequency-response schematic diagram can be seen in Fig. 7. The modal damping ratio can be obtained F −F as the formula ζ= b2F a . n The natural frequencies of the model soil-structure system were experimentally obtained from the transfer function of accelerations at the surface (A19) with respect to base (A25). The first-order mode of natural frequencies and the modal damping ratio of the model soilstructure system measured by the flat-noise test can be seen in Fig. 8. The natural frequencies of the model soil-structure system decreased from 8.39 Hz to 7.76, 7.41, and 6.57 Hz, and the modal damping ratio increased from 2.57% to 3.77%, 4.08%, and 4.92% from test case B1 to that measured in the test cases B3,B4,B5, respectively. The test results showed that with the increase of peak acceleration, the first-order natural vibration frequency of the model system decreased, which indicated that the model soil-structure interaction system exhibited nonlinear characteristics and certain plastic damage. In our view, this phenomenon is resulted from the coupling of soil and underground structure. The results suggest: i) the softening and non-linear appearance of soil; ii) the comprehensive effect of structural damage. However, when we choose accelerations at the surface (A14) with respect to base (A25), some different phenomenon appears: the natural frequencies of the model soil increased from 8.37 Hz to 9.21, 10.42, and
2.4. Test instrumentation and sensor layout Many sensors were deployed to record various parameters throughout the series of shaking table tests, e.g., acceleration, earthquake-induced ground settlement, structural strain, and dynamic soil pressure. The middle cross section of the model box in the shaking direction was selected as the observation section. The sensor layout is shown in Fig. 5, which includes 25 accelerometers, 2 displacement transducers, 7 soil-pressure transducers, 5 dynamic displacement targets, and 28 strain gauges, denoted as A, D, P, Plt, and S, respectively. Based on the calibration for the accelerometers and soil-pressure transducers, the measurement accuracy of the sensors was better than 0.5% full-scale (F.S.), and the resistance value of the strain gauges was 120 Ω ± 0.2 Ω. The sensors we used in the test can be seen in Fig. 6. The operating frequency, working current, and voltage sensitivity of the accelerometer are 0.1–2000 Hz, 2 mA, and 100mV/m−2, respectively. The dimensions of soil pressure are 28 mm in diameter and 10 mm in height, and the working range was 0–100 kPa. We filtered to suppress or remove measurement noise of acceleration at both low and high frequencies using Butterworth filter (Filter configuration: Bandpass, Fpass = 0.1 Hz, Fstop = 50 Hz). Then, time histories of soil pressure were decompounded by five-point moving average method which can remove the burr on the curve. The lateral displacement of soil was processed by vision-based displacement method [34].
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Fig. 5. Sensor layout in the cross sections of the model soil-structure (unit: mm). (a) coordinate system (b) sensor inside soil, (c) accelerometer in structure, (d) strain gauge layout, (e) displacement target.
damped) of the filtered (Butterworth low-pass filter with a prototype scale-corner frequency of 30 Hz for noise reduction, as well as a highpass filter with a prototype scale-corner frequency of 0.1 Hz) records within the model soil during the tests are shown in Fig. 10. This figure shows that basically the same spectral distribution was shown in different positions at the same level; however, at different soil depth, the acceleration spectrum shows different characteristics. In addition, as the PGA of the input motions increased, the amplification effect of the acceleration β spectra exhibited obvious selectivity for different frequency components of the input motions. The high-frequency filtering phenomenon of the model soil appeared because the soil was softened, and the peak of the β spectra certainly moved toward longer periods, which means that the model-soil spectra were concentrated and amplified for the low-frequency components. Meanwhile, the period band of the response acceleration of the soil was clearly widened; in other words, the increased seismic intensity should increase the seismic risk of a subway station with respect to its natural vibration period.
11.14 Hz, from test case B1 to that measured in the test cases B3,B4,B5, respectively, which illustrates that the soil indeed was compacted and hardened. 3.2. Acceleration response of the interaction system We adopted the measured acceleration data and the Kriging interpolation method (Surfer version 8.0) to chart the acceleration response distribution, which can be seen in Fig. 9. It shows the distribution of the model soil-structure acceleration response for different test cases. It is quite clear that the acceleration peak value of the shallower soil layer is greater than that of the deeper soil layer, which reflects the soil amplification effect. Meanwhile, the acceleration response of the soilstructure system was more like a free-field response, which also prove that the underground structure has few effect on the acceleration responses of the soil foundation in testing cases with lower PGA. This may be caused by the lower nonlinearity of soil under lower PGA earthquakes. The seismic response of the soil-structure system is similar to the seismic response of the free field (without the underground structure). The opposite phenomenon was observed for test cases with higher PGA (e.g., 0.4 and 0.8 g), which means the amplification effects on the acceleration response are more evident as the PGA of input motion increases. Moreover, the acceleration peak value at the position above the model structure was the greatest with higher PGA, which illustrates that the presence of the structure would affect the acceleration distribution in case of higher PGA. The soil above the structure was controlled by the surrounding soil, and this constraint condition would be weakened when suffering strong motions. Thus, the acceleration response becomes larger. The dynamic amplitude factors β (5%
3.3. The lateral deformations of the model soil The horizontal shear deformation of the laminar shear box can approximately reflect the shear deformation of the soil foundation, and its test method is a knotty problem in the shaking table test involving soilstructure interaction. In this test, we used a vision-based displacement test method to solve the problem [34]. The basic principle of the method can be expressed as: we use the least squares method (LSM) circle detection and video processing technology. Firstly, dynamic video is captured by a camera, and then preprocessed into continuous static images. These preprocessing included image noise reduction, gray
Fig. 6. The Sensors for experiment. (a) structural accelerometer (b) soil pressure sensor, (c) accelerometer in soil, (d) laser displacement meter. 178
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Fig. 7. The sensor used for calculation and frequency-response schematic diagram.
distribution can be seen in Figs. 11 and 12. The maximum lateral displacement data of the soil at different measuring points showed that the degree of leftward swinging of soil was different from that of the rightward swinging, due to the asymmetry of the input motions for the positive and negative peak displacements. In addition, the effects of several parameters on the lateral soil displacement were addressed. First, as the PGA of the input motions increased, the lateral soil displacement also increased. Secondly, the dominant frequency of the input motion had an inverse effect on the lateral soil deformation. Furthermore, the maximum lateral displacement of the upper soil was greater than that of the lower soil. Fig. 8. Dynamic characteristics of the soil-structure system.
3.4. Dynamic soil-structure interaction scale processing, and adjusting the RGB (red, green, blue) color proportion. Secondly, image binarization algorithm and image edge detection for edge detection were used. After the preprocessing, center coordinates and radii of target circles can be obtained by the optimal circle fitting program. Then, the center coordinates are stored successively according to the continuous static image sequence; therefore, the horizontal and vertical displacements of the target circle center in the image space were obtained. By calibrating the relationships between the image pixels and coordinates of the actual objects, the actual displacement can be achieved. The time history and the deformation
To test the dynamic soil pressure around the underground structure, soil-pressure cells nos. P1-P5 is affixed to the sidewall at the top and bottom of the subway station. Fig. 13 shows the dynamic soil pressure measured in the sidewall. In the seismic design, dynamic soil pressure is estimated according to the calculation method of retaining wall. For embedded underground structures, the precise magnitude and distribution of dynamic soil pressure are poorly understood. The earth pressure estimated by referring to semi-embedded structures (such as retaining walls) may be too high or too low. Meanwhile, some previous literature gave the dynamic soil pressure distribution pattern [35,36].
Fig. 9. Contour plot of the acceleration response distribution for different test cases. 179
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Fig. 10. Dynamic amplification factors of the model soil in the observation section for different input motions.
Fig. 11. Time histories of horizontal displacement in loess ground.
Fig. 12. Horizontal-displacement amplitudes of the ground under different loading conditions.
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Fig. 13. Dynamic soil pressure. (a) Xi'an test cases, (b) Songpan test cases (c) Taft test cases.
should be concerned, and its intuitive performance can be expressed by two parameters: i) the soil pressure difference between top and bottom of model structure; ii) and the uplift of structure in vertical direction. The relationship between these two parameters can be seen in Fig. 14. Based on this phenomenon, the relationship between these two parameters was fitted, and the expression is △F = a × πr 2 × e|b△y|, where △F means the soil pressure difference between the top and bottom of the model structure, △y denotes the uplift amount of the model structure, r is the soil pressure sensor radius, and a, b means fit coefficient. The relationship between two parameters can be seen in Fig. 15, and the correlation coefficient is greater than 0.95. Meanwhile, it can be found that the fitting formula of power exponent can better simulate the relationship between the two parameters. The soil pressure difference between the top and bottom of the structure reflects the mechanical properties of the soil-structure interaction, and the seismic subsidence is the deformation behavior of the soil-structure interaction. The relationship between the two reveals the characteristics of soilstructure interaction, and can also provide reference for the estimation of seismic subsidence of soil-structure systems in soft soil areas. We define a parameter Ky to refer to the vertical dynamic soil∂ |△F| structure interaction, and it can be calculated by K y= ∂ |△y| . This parameter shows the vertical stiffness ratio between soil and structure. When Ky goes to infinitesimal, sufficient slip between underground structure and soil may occur; when Ky goes to infinity, the structure sticks completely to the soil. Ky reflects the mechanical behavior of the soil and the structure cooperative characteristics in vertical direction. In this test, The Ky-
However, the distribution pattern has significant relationship with the soil, different distribution patterns were shown in different test cases, and this is due to the different interaction mode between soil and underground structure. The soil-structure interaction mode presents a trumpet-type distribution in horizontal direction. The peak dynamic soil pressure appears at the top of the structure sidewall, while the secondary peak appears at the bottom of the structure. A relatively significantly weak zone shows up in the central part of the sidewall. The distribution characteristics of dynamic soil pressure on the structure sidewall are more evident as the PGA of input motion increases. In addition, this distribution pattern makes it necessary to pay more attention to the additional dynamic soil pressure at the top and bottom of the structure when designing underground structures in such sites. The elevating of the underground structure causes certain uplift on the adjacent ground surface, which equals to the settlement value at point G1 minus the settlement value at point G2. The settlements of model system under different loading conditions are shown in Table 5. Small settlement occurred when the input PGA was lower, and the value of uplift of model structure increased with the increase of PGA, which was caused by the vertical inertial force of the model structure differing from the soil. This was caused by the difference of vertical inertial force between soil and structure in different cases, relative movement between the model structure and the soil would occur. An interesting phenomenon was observed in this test: a significant uplift of the ground surface occurred when the PGA increases to 0.4 g, and the uplift of model structure decreased with increasing PGA when PGA exceeded 0.4 g. Hence, the vertical dynamic soil-structure interaction Table 5 Settlements of model system under different loading conditions (unit: mm). PGA(g)
0.05 0.1 0.2 0.4 0.6 0.8
Settlements at point G1
Settlements at point G2
Uplift of model structure (G1-G2)
Songpan record
Taft record
Xi'an artificial wave
Songpan record
Taft record
Xi'an artificial wave
Songpan record
Taft record
Xi'an artificial wave
0.002 0.005 0.165 1.219 1.322 1.983
0.009 0.077 0.627 4.144 1.426 4.790
0.001 0.130 1.059 11.020 12.823 11.086
0.001 0.003 0.065 0.760 1.000 1.756
0.005 −0.008 0.044 2.158 1.155 4.405
−0.003 0.075 0.968 6.770 12.047 10.860
0.001 0.002 0.099 0.458 0.322 0.228
0.004 0.085 0.583 1.986 0.271 0.385
0.004 0.055 0.091 4.250 0.776 0.225
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Fig. 14. The relationship between two parameters soil pressure and uplift of structure.
acceleration (in this test, equals to 0.4 g), the vertical inertial forces would be increase; meanwhile, the uplift of structure would reduce.
3.5. Strain distribution of station structure The maximum strain of the model structure under different ground motions can be seen in Table 6. Different grayscale means different damage degree. It indicates that the strain amplitude of the subway station gradually increases with the increase of the PGA. The strain responses at the top of the upper center pillar S4 is greatest in the center pillar. When it comes to side wall, the top of the upper side wall S16 and the bottom of the lower side wall S13 of the station structure are greater than those at other positions of the side wall. The strain measured in the top slab and bottom slab are smaller than that in pillar and sidewall. However, in this test, the middle slab was subjected to more serious damage, and the strain possessed the maximum value when input PGA was higher. The above rules mainly relate to the distribution characteristics of the dynamic soil pressure both in horizontal and vertical direction. In addition, the strain values measured in this study are larger than that measured in the previous experiments in liquefiable site [36]. This is because that the s-wave component of the ground motion is filtered in the liquefied ground, and the strain in this test is significantly smaller than that in the same position measured in liquefied ground. The structural failure phenomenon is shown in Fig. 18. It is obvious that, the damage position was consistent with strain distribution; combining the analyses of section 3.4 and 3.5, the additional forces acting on the model structure were the vertical pressure in combination with the horizontal bending. Hence, we speculate that the structure damage process may be as follows: i) the earthquake force on the pillar lost its shear strength; ii) then, the vertical pressure and horizontal bending would act on the slab and sidewall, because the sidewall had a large longitudinal stiffness and uneven stress distribution in the model structure appeared. Therefore, we conclude that the damage degree of underground subway station may be caused by following parameters: axial pressure ratio of center pillar, stiffness ratio between slab and sidewall, dynamic soil pressure distribution, and the site conditions, etc.
Fig. 15. Relationship between differential soil pressure and model-structure uplift.
value decreased with the increase of the PGA and is shown in Fig. 16. It is clear that the vertical dynamic soil-structure interaction mainly experiences three stages. During the initial stage, soil and structure tended to move synergistically and Ky maintained in a stable value (e.g. 0.05 g and 0.1 g). During the second stage, non-harmonious movement and vertical dynamic soil-structure interaction appeared due to the cumulative seismic effect, and the value of Ky decreased and the soil above the structure exhibited arch characteristic when PGA equals to 0.2 g. In the third stage, Ky tended to be the smallest and close to zero, which indicated that slipping or gapping phenomenon in vertical direction occurred and the upper soil above the structure formed an independent part and became dead weight; the value of △F would tend to zero and the Ky also shows the same tendency. This also can be seen in the macroscopic phenomena after the test which is shown in Fig. 17. When PGA is greater than 0.4 g, the soil-structure system loses its vertical constraints, and the dynamic soil pressure near the top of underground structure unloaded. Hence, when input PGA exceeded the critical
Fig. 16. Different vertical stiffness between soil and structure. 182
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Fig. 17. Macroscopic phenomena after test. Table 6 Strain amplitudes of the station in the primary observation section under different ground motions.
PGA-cases, and the period band of the main response acceleration of the soil is clearly widened. In other words, the increased seismic intensity should increase the seismic risk of a subway station with respect to its natural vibration period. (2) The dominant frequency of the input motion had an inverse effect on the lateral soil deformation. The soil-structure interaction mode presents a trumpet-type distribution in horizontal direction and the distribution characteristics of dynamic soil pressure on the structural sidewall are more evident as the PGA of input motion increases. In this test, the vertical dynamic soil-structure interaction has been concerned, and we defined a parameter Ky to refer to the vertical dynamic soil-structure interaction and analyzed its variation tendency with changing of PGA. (3) The strain measured in the center pillar and middle slab were larger than that in other positions. Comparing with the previous experiments, the underground structure failure mode is related with the soil dynamic characteristics. Hence, different ground conditions may cause different results on the underground seismic response.
Fig. 18. Structural failure phenomenon after the test.
4. Concluding remarks Acknowledgments
The seismic behavior of subway structure under strong ground motions in loess ground was investigated in the paper through shaking table test on a scaled structure model. From the results of the test, the following conclusions can be obtained:
The authors gratefully acknowledge the financial support of this study by the National Key R&D Program of China (2017YFC1500400) and Natural Science Foundation of China (No.51878626, U1839202, 51778290). The authors also sincerely thank the anonymous reviewers for their insightful comments and suggestions. Especially, the authors thank Dr. Yao Erlei for its linguistic assistance during the preparation of this manuscript.
(1) The underground structure has smaller effect on the acceleration responses of the soil foundation in lower PGA cases. However, the presence of the structure would affect the acceleration in higher183
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Shaking table test on the seismic response of large-scale subway station in a loess site: A case study
T
Su Chena, Haiyang Zhuangb, Dengzhou Quanc, Jie Yuand, Kai Zhaob, Bin Ruanb,∗ a
Institute of Geophysics, China Earthquake Administration, Beijing, 100081, China Institute of Geotechnical Engineering, Nanjing Tech University, Nanjing, 210009, China c Chang'an University, Xi'an, 710061, China d State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Underground structure Seismic response Shaking-table test Loess site Dynamic interaction
More and more underground infrastructures have been built in special soil in recent years, especially in the loess area of western China. The loess, as a special soft soil, can have particular influence on the seismic characteristics of underground structures. Therefore, the seismic performance and safety evaluation of underground structures in loess area should be concerned. A series of large-scale shaking table tests were performed to investigate the damage mechanisms of a frame-type subway station structure in a loess site. The test results showed that the model soil softening and the stiffness degradation of the soil-structure system were more serious under stronger input motions. The acceleration response of the soil-structure interaction system in a loess site was more like that of a free-field when input PGA is lower. However, the soil-structure interaction phenomenon was more remarkable both in horizontal and vertical direction when higher PGA was input. The dominant frequency of the input motion had an inverse effect on the lateral soil deformation. The direct-force action mode of the dynamic earth pressure acting on underground structures presents a trumpet-type distribution. Meanwhile, the soilstructure interaction exhibited complex mechanical behavior, and slipping or gapping in test cases with higher PGA may occur. The strain measured in the center pillar and middle slab of the subway station was larger than that in other components. The results provide an insight into how strong ground motion might induce the influence and a possible way to describe quantitatively the damage of subway structure in loess ground.
1. Introduction With rapid development and urbanization in China, exploitation and utilization of underground space has become a major issue in China. Till the end of 2017, subways projects have been built or approved in 34 Chinese cities with a total operating mileage of 5021 km. Especially, some lines have been built in the cities of western China, such as Lanzhou, Xi'an, Taiyuan and so on, and some subway stations are located in loess area. The seismic research of underground structures has gone through three stages. Stage 1: before the 1995 Kobe earthquake in Japan, underground structures were assumed to be earthquake resistant. However, the Kobe earthquake showed that underground structures are also vulnerable to seismic motions, as a large number of central reinforced concrete pillars of the underground subway stations were damaged, which has induced the collapse of the whole subway station. There are several possible reasons for this damage, such as strong ground motions and permanent ground movement
∗
[1–3]. Stage 2: a large number of tests and numerical analyses have given qualitative and semi-quantitative understanding [4–17]. Stage 3: the seismic problem of underground structures has developed from the response research to the performance-based research. The research work of seismic response of underground structure can be divided into experimental, theoretical and numerical simulation. However, little attention was paid to the underground structural damage characteristics in special soil, for example loess ground. For loess soil, in terms of sedimentary characteristics, loess is typical quaternary unconsolidated sediments, and unique generating environment and material source make it form special macroporous, unconsolidated and unsaturated porous weakly cemented aerial structure. This structural form of loess makes its dynamic characteristics significantly difference from other soils, which is mainly reflected in the water sensitivity of loess. Then, the original structural of the loess site is more likely to collapse under the earthquake motions. With the pore gas compressed and expelled, the site showed the characteristics of seismic
Corresponding author. E-mail address: [email protected] (B. Ruan).
https://doi.org/10.1016/j.soildyn.2019.04.023 Received 19 November 2018; Received in revised form 10 April 2019; Accepted 23 April 2019 Available online 08 May 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 The similitude ratio of the soil-structure system. Types
Physical quantity
Similitude relation
Similitude ratio Model structure
Model soil
1/30 1/30 1.2 × 10−6
1/4.5 1/4.5 /
Geometry properties
Length l Linear displacement r Inertia moment I
Material properties
Equivalent density ρ
SI = Sl 4 Sρ = SE / Sl Sa
3.0
1
Elastic modulus E Shear wave velocity of soil vs Shear modulus of soil Gravity acceleration g
SE Sv SG Sg
1/5 / / 1
/ 1/3 1/9 1
Dynamic properties
Sl Sr = Sl
Mass m
Sm = Sρ⋅Sl3
1.11 × 10-4
/
Force F
SF = Sρ⋅Sl3⋅Sa
2.22 × 10-4
/
Frequency ω Acceleration a Duration t
Sω = 1/ St Sa
7.75 2.0 0.13
3.0 2.0 0.33
St =
Sl/ Sa
2. Shaking table test
subsidence with sudden subsidence and subsequent slow subsidence. In addition, compared with other sites, the loess site with thick overburden has more significant seismic amplification effect [18]. Due to the special structure and water sensitivity of the loess, the earthquake damage in the loess site is more serious. Previous studies showed that, the loess site was prone to seismic collapse, landslide, liquefaction and significant seismic amplification effect under strong earthquake motions, which induced and aggravated the earthquake disaster of the engineering structure [19]. In addition, historical data show that earthquake disasters in loess areas are relatively serious. For example, the 1556 Huaxian earthquake in Shanxi province, China (Mw 8.0) struck a large number of loess areas; Weinan area, located in the extreme earthquake area, is full of earth surface cracks. In the 1718 Tongwei earthquake in Gansu province, China (Mw 7.5), a large number of landslides formed in the malan loess layer of Longxi region. In 1920 Haiyuan earthquake in Gansu province, China (Mw 8.5), the earthquake damage is more serious due to the formation of serious landslide concentration area of more than 4000 square kilometers. In the 1970 Xiji earthquake in Ningxia, the intensity of the epicenter was only 7.0 degrees, but many landslides and cracks also occurred. What's more, according to the analysis of seismic activity, the Fenwei and Longmen mountain seismic belt (seismic belts have greater impact on the Xi ‘an area) would be slightly active in the next 50–100 years. However, with the increasing number of metro projects in the loess area of western China, the seismic performance and safety evaluation of underground structures in the loess area should be studied. Xi ‘an subway is the first subway project built in loess region in China. Historical seismic data show that there is strong seismic activity around Xi ‘an. There have been 3 earthquakes with Mw 7.0 or above and 11 earthquakes with Mw 6.0 or above. To above view, in this paper, we choose Feitianlu station, Xi'an Metro Line 4, as prototype subway station, and the model soil comes from the construction site, and then an experimental study was carried out on the seismic performance of an underground structure in loess ground. Based on the Xi'an subway project, this study experimentally investigated the dynamic interaction between loess and an underground subway station. The ground motion and loading scheme were confirmed according to the earthquake environment in the Xi'an area. By the test result, some new findings and conclusions were made in this study, which can provide reliable reference and guidance for the seismic design and earthquake safety evaluation of loess-area subway stations, tunnels, and underground commercial streets.
2.1. Test apparatus and similitude ratio design The dimensions of the shaking table are 3.36 m × 4.86 m in a plane. The maximum acceleration of the shaking table is 1 g, with a maximum bearing capacity of 25 tons. The frequency of the input motion ranges from 0.1 to 50 Hz. The laminar shear model soil container is 3.5 m × 2.0 m × 1.7 m. This container can effectively eliminate the reflection and scattering of a seismic wave at the boundary of the container [11]. The testing data from the model structure and the soil were collected in real time by an independently developed dynamic signal-acquisition system [20]. This study employed the scaling laws recommended by Buckingham π theorem [21]. Based on the characteristics of the model structure and the soil, various basic physical quantities are selected, including the length, elastic modulus, and acceleration of the model structure, as well as the shear wave velocity, density, and acceleration of the model soil. In the soil-structure shaking table test, that all parameters meet the similitude law is unprocurable. The principles of the similarity ratio design of this test are presented as follows: (1). the inertial force of underground structure should be concerned; (2). the input ground motion's frequency band must be controlled; (3) the material property should be selected properly. The similarity ratios are given in Table 1. The relative stiffness plays a key role in soil-structure interaction effects under strong earthquake motions. Some researchers have made many meaningful studies for this issue [22–25]. For the shaking table test, [26] gave the formula for calculating the stiffness ratio of the tunnel and the soil. For this test, the similitude ratio for the relative stiffness SF is:
SF =
Gm △m ⋅ Gp △p
Where Gm and Gp are the dynamic shearing modulus of the model soil and the field soil, respectively, and Δm and Δp are the displacements for the numerical model of the test and the practical tunnel, respectively. Before shaking table test, the average shear wave velocity of the model soil were 90.0 m/s which equals to the one third of the average shear wave velocity of the prototype site (270.0 m/s). For structure, we carried out a simple numerical simulation (software ABAQUS), the result showed that the deformation ratio between model and prototype equals to 5.0. Hence, the SF in this test equals to 1/1.8. 2.2. Model soil and structure The model soil consists of a 1200-mm-thick loess layer. During the 174
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For the model structure, the designed strength and stiffness of the model structure were calculated according to the similitude ratio. Galvanized steel wire and micro-concrete were used to simulate the steel rebar and prototype concrete, respectively. The concrete mix ratio was determined based on a strength test of the micro-concrete, and the scale material shows different dynamic response [31]. Hence, based on the desired strength of the micro-concrete, the mixture ratio of the model concrete was determined as water: cement: lime: coarse sand = 1.4: 1.0: 0.5: 6.5, and the compressive strength of the microconcrete was approximately 8.11 MPa and the elasticity modulus was approximately 6.60 GPa. The diameter of the galvanized steel wire ranged from 0.9 mm to 2.0 mm: 2.0 mm for beam and column, 0.9 mm for plate and side wall. (The similarity ratio of length is 1/30). Tensile yield strength and elastic modulus of galvanized steel wire were 1190 MPa and 200 GPa, respectively. The construction process of model structure can be seen in Fig. 2. 2 mm-thick plexiglas was used to seal the model structure, the structure reinforcement design can be seen in Fig. 3.
Table 2 Material properties of model soil. Dry density (g/cm3)
Unit weight (kN/m3)
Soil moisture content (%)
Liquid limit (LL)
Plastic limit (PL)
Void ratio
1.41
16.7
22.7
20.3
34.2
0.973
preparation, the soil was placed in the model soil container layer by layer. Each layer was composed of tamped backfill, approximately 200 mm thick; meanwhile, when preparing the model foundation, number of hammers is basically the same for each soil layer, and, before each layer of loess was filled, the surface of the lower soil was subjected to brushing. After the preparation, the model soil was allowed to stand in the laboratory for 10 days in its natural state. The soil properties can be seen in Table 2. Before the test, the triaxial test was carried to obtain the dynamic parameters of the soil and the curve was fitted by the classical Hardin model, which can describe the variation of soil dynamic parameters over a wide strain range [27,28]. Fig. 1 show G/Gmax and γ for loess used in this study and range of data for cohesionless sand and clay. As shown in Fig. 1a, G/Gmax ∼γ of loess are distributed at the lower bound of γ for clay and close to the upper bound of cohessionless sand, compared with the non-viscous soil, the G/Gmax of loess shows more obvious nonlinearity with the increase of shear strain, This means that the loess presents a more rapid stiffness attenuation with the increase of shear strain. Meanwhile, λ ∼γ of loess are distributed at the upper bound of clay, the growth rate of λ for loess is greater than that of clay, This means that the loess presents a stronger ability to dissipate energy compared to clay. In addition, when λ ∼γ of loess falls between the upper bound and the lower bound of cohesionless sand. In conclusion, the dynamic characteristics of the loess are obvious different from those of conventional clay, and shown between the dynamic characteristics of non-viscous soil and clay [29,30]. In addition, considering soil moisture content would influence on the dynamic characteristics of loess, we performed some soil dynamic tests with different soil moisture. The testing result can be seen in Table 3. It is found that soil moisture content and initial consolidation pressure have significant effects on the dynamic characteristic of the remolded loess. With the same moisture content, the higher the initial consolidation pressure at the same dynamic strain, the higher the shearing modulus of the soil. Meanwhile, under the same initial consolidation pressure, the higher the moisture content, the lower the shearing modulus of the soil, and this is related to the weakening of the connection strength and the gradual destruction of the loess due to the increase of water content. Meanwhile, when the moisture content is less than the plastic limit, the dynamic shear modulus of the loess decreases greatly with the increase of the moisture content; when the moisture content is greater than the plastic limit, the dynamic shear modulus changes little with the increase of the moisture content.
2.3. Input motion and loading conditions A lot of underground structures damaged in Hyogoken-Nanbu Earthquake, Chi-Chi earthquake, and Wenchuan Earthquake. The seismic behavior and mechanism of underground structure are related with intensity of ground motion, fault and site condition; meanwhile, the input motions selected in this paper should be in the range from the lower level (63% probability of exceedance in 50 years) to the upper level (2% probability of exceedance in 50 years) of the target spectrum of the engineering site. The existence of the underground structure has little influence on the selection of the predominant period of the motions [32,33]. Hence, when estimating the predominant period (Tp) of the input motions, the most important period is decided by the period of the site (Ts). The purpose of the series of shaking table tests is to study the seismic behavior of the frame-type underground subway station structure in loess ground; therefore, the input motions should have different frequency-spectrum characteristics and durations. The ground motions from the Songpan and Taft earthquakes and a Xi'an artificial wave were selected as input motions, and the intensity of the input motion was set to 0.1 g, 0.2 g, 0.6 g, 0.8 g, and 1.2 g by adjusting the peak acceleration of the original ground motion. The acceleration time histories and corresponding response spectra are shown in Fig. 4. The Songpan ground motions were recorded at 51SPT seismologic recording stations during the Ms8.0 Wenchuan earthquake on May 12, 2008 in Sichuan Province, China. The original peak acceleration, fault distance, and duration of the Songpan records were 0.041 g, 122 km, and 213 s, respectively. The Taft ground motion was recorded at the Taft seismological recording station during the Ms7.7 Kern County earthquake on July 21, 1952 in California, USA, with an original peak acceleration, fault distance, and duration of 0.176 g, 43.5 km, and 54 s,
Fig. 1. The G/ Gmax ∼ γ and λ ∼ γ curve of loess used in the shaking table test. 175
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Table 3 The testing results of loess dynamic parameters. Soil moisture content (%)
18.1
21.1
24.1
Initial consolidation confining pressure(kPa)
50
100
150
50
100
150
50
100
150
G,max(MPa) γr(10−3)
27.10 1.67
32.70 1.94
42.70 2.25
6.80 4.38
8.10 4.10
12.10 7.50
5.30 4.08
6.30 5.68
10.40 6.53
Remarks: G,max means maximum dynamic shear modulus, γr means reference shear strain.
Fig. 2. The construction process of the model structure.
Fig. 3. Typical section and structure reinforcement (unit: mm).
0.200 g, while the duration is 80 s. The loading cases can be seen in Table 4. In order to obtain the seismic response characteristics of the structure from elastic to damage stage to the maximize utilization, the input motions follow the principle of stepwise loading. The durations of
respectively. The Xi'an bedrock artificial wave was synthesized based on the site condition characteristics of referenced subway station engineering. According to the synthetic probability of the seismic wave, the return period of this wave is 475 years, and the peak acceleration is 176
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Fig. 4. Original ground motions time histories and spectrum. Table 4 Loading cases for the shaking table test. No
Loading
PGAa (g)
No
Loading
PGA (g)
No
Loading
PGA (g)
B1 S1 T1 X1 B2 S2 T2 X2 B3
White noise Songpan record Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave White noise
0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.05
S3 T3 X3 B4 S4 T5 X6 B5 S4
Songpan record Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave White noise Sonpan record
0.2 0.2 0.2 0.05 0.4 0.4 0.4 0.05 0.6
T4 X4 B6 S5 T5 X5 X6 B7 –
Taft record Xi'an artificial wave White noise Songpan record Taft record Xi'an artificial wave Xi'an artificial wave White noise –
0.6 0.6 0.05 0.8 0.8 0.8 1.2 0.05 –
a
Peak ground acceleration, the unit is g.
3. Results and interpretation
scaled Songpan wave, Taft wave and the Xi'an artificial wave were 26.00s, 7.02s, and 10.4s, respectively.
3.1. Dynamic characteristics of the soil-structure system We used the acceleration obtained in the shaking table as input motion, and the acceleration measured in the ground surface as output motion, and then the transfer function can be calculated. The mode of the transfer function expresses the response amplitude-frequency characteristics of the target system. The frequency-response schematic diagram can be seen in Fig. 7. The modal damping ratio can be obtained F −F as the formula ζ= b2F a . n The natural frequencies of the model soil-structure system were experimentally obtained from the transfer function of accelerations at the surface (A19) with respect to base (A25). The first-order mode of natural frequencies and the modal damping ratio of the model soilstructure system measured by the flat-noise test can be seen in Fig. 8. The natural frequencies of the model soil-structure system decreased from 8.39 Hz to 7.76, 7.41, and 6.57 Hz, and the modal damping ratio increased from 2.57% to 3.77%, 4.08%, and 4.92% from test case B1 to that measured in the test cases B3,B4,B5, respectively. The test results showed that with the increase of peak acceleration, the first-order natural vibration frequency of the model system decreased, which indicated that the model soil-structure interaction system exhibited nonlinear characteristics and certain plastic damage. In our view, this phenomenon is resulted from the coupling of soil and underground structure. The results suggest: i) the softening and non-linear appearance of soil; ii) the comprehensive effect of structural damage. However, when we choose accelerations at the surface (A14) with respect to base (A25), some different phenomenon appears: the natural frequencies of the model soil increased from 8.37 Hz to 9.21, 10.42, and
2.4. Test instrumentation and sensor layout Many sensors were deployed to record various parameters throughout the series of shaking table tests, e.g., acceleration, earthquake-induced ground settlement, structural strain, and dynamic soil pressure. The middle cross section of the model box in the shaking direction was selected as the observation section. The sensor layout is shown in Fig. 5, which includes 25 accelerometers, 2 displacement transducers, 7 soil-pressure transducers, 5 dynamic displacement targets, and 28 strain gauges, denoted as A, D, P, Plt, and S, respectively. Based on the calibration for the accelerometers and soil-pressure transducers, the measurement accuracy of the sensors was better than 0.5% full-scale (F.S.), and the resistance value of the strain gauges was 120 Ω ± 0.2 Ω. The sensors we used in the test can be seen in Fig. 6. The operating frequency, working current, and voltage sensitivity of the accelerometer are 0.1–2000 Hz, 2 mA, and 100mV/m−2, respectively. The dimensions of soil pressure are 28 mm in diameter and 10 mm in height, and the working range was 0–100 kPa. We filtered to suppress or remove measurement noise of acceleration at both low and high frequencies using Butterworth filter (Filter configuration: Bandpass, Fpass = 0.1 Hz, Fstop = 50 Hz). Then, time histories of soil pressure were decompounded by five-point moving average method which can remove the burr on the curve. The lateral displacement of soil was processed by vision-based displacement method [34].
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Fig. 5. Sensor layout in the cross sections of the model soil-structure (unit: mm). (a) coordinate system (b) sensor inside soil, (c) accelerometer in structure, (d) strain gauge layout, (e) displacement target.
damped) of the filtered (Butterworth low-pass filter with a prototype scale-corner frequency of 30 Hz for noise reduction, as well as a highpass filter with a prototype scale-corner frequency of 0.1 Hz) records within the model soil during the tests are shown in Fig. 10. This figure shows that basically the same spectral distribution was shown in different positions at the same level; however, at different soil depth, the acceleration spectrum shows different characteristics. In addition, as the PGA of the input motions increased, the amplification effect of the acceleration β spectra exhibited obvious selectivity for different frequency components of the input motions. The high-frequency filtering phenomenon of the model soil appeared because the soil was softened, and the peak of the β spectra certainly moved toward longer periods, which means that the model-soil spectra were concentrated and amplified for the low-frequency components. Meanwhile, the period band of the response acceleration of the soil was clearly widened; in other words, the increased seismic intensity should increase the seismic risk of a subway station with respect to its natural vibration period.
11.14 Hz, from test case B1 to that measured in the test cases B3,B4,B5, respectively, which illustrates that the soil indeed was compacted and hardened. 3.2. Acceleration response of the interaction system We adopted the measured acceleration data and the Kriging interpolation method (Surfer version 8.0) to chart the acceleration response distribution, which can be seen in Fig. 9. It shows the distribution of the model soil-structure acceleration response for different test cases. It is quite clear that the acceleration peak value of the shallower soil layer is greater than that of the deeper soil layer, which reflects the soil amplification effect. Meanwhile, the acceleration response of the soilstructure system was more like a free-field response, which also prove that the underground structure has few effect on the acceleration responses of the soil foundation in testing cases with lower PGA. This may be caused by the lower nonlinearity of soil under lower PGA earthquakes. The seismic response of the soil-structure system is similar to the seismic response of the free field (without the underground structure). The opposite phenomenon was observed for test cases with higher PGA (e.g., 0.4 and 0.8 g), which means the amplification effects on the acceleration response are more evident as the PGA of input motion increases. Moreover, the acceleration peak value at the position above the model structure was the greatest with higher PGA, which illustrates that the presence of the structure would affect the acceleration distribution in case of higher PGA. The soil above the structure was controlled by the surrounding soil, and this constraint condition would be weakened when suffering strong motions. Thus, the acceleration response becomes larger. The dynamic amplitude factors β (5%
3.3. The lateral deformations of the model soil The horizontal shear deformation of the laminar shear box can approximately reflect the shear deformation of the soil foundation, and its test method is a knotty problem in the shaking table test involving soilstructure interaction. In this test, we used a vision-based displacement test method to solve the problem [34]. The basic principle of the method can be expressed as: we use the least squares method (LSM) circle detection and video processing technology. Firstly, dynamic video is captured by a camera, and then preprocessed into continuous static images. These preprocessing included image noise reduction, gray
Fig. 6. The Sensors for experiment. (a) structural accelerometer (b) soil pressure sensor, (c) accelerometer in soil, (d) laser displacement meter. 178
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Fig. 7. The sensor used for calculation and frequency-response schematic diagram.
distribution can be seen in Figs. 11 and 12. The maximum lateral displacement data of the soil at different measuring points showed that the degree of leftward swinging of soil was different from that of the rightward swinging, due to the asymmetry of the input motions for the positive and negative peak displacements. In addition, the effects of several parameters on the lateral soil displacement were addressed. First, as the PGA of the input motions increased, the lateral soil displacement also increased. Secondly, the dominant frequency of the input motion had an inverse effect on the lateral soil deformation. Furthermore, the maximum lateral displacement of the upper soil was greater than that of the lower soil. Fig. 8. Dynamic characteristics of the soil-structure system.
3.4. Dynamic soil-structure interaction scale processing, and adjusting the RGB (red, green, blue) color proportion. Secondly, image binarization algorithm and image edge detection for edge detection were used. After the preprocessing, center coordinates and radii of target circles can be obtained by the optimal circle fitting program. Then, the center coordinates are stored successively according to the continuous static image sequence; therefore, the horizontal and vertical displacements of the target circle center in the image space were obtained. By calibrating the relationships between the image pixels and coordinates of the actual objects, the actual displacement can be achieved. The time history and the deformation
To test the dynamic soil pressure around the underground structure, soil-pressure cells nos. P1-P5 is affixed to the sidewall at the top and bottom of the subway station. Fig. 13 shows the dynamic soil pressure measured in the sidewall. In the seismic design, dynamic soil pressure is estimated according to the calculation method of retaining wall. For embedded underground structures, the precise magnitude and distribution of dynamic soil pressure are poorly understood. The earth pressure estimated by referring to semi-embedded structures (such as retaining walls) may be too high or too low. Meanwhile, some previous literature gave the dynamic soil pressure distribution pattern [35,36].
Fig. 9. Contour plot of the acceleration response distribution for different test cases. 179
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Fig. 10. Dynamic amplification factors of the model soil in the observation section for different input motions.
Fig. 11. Time histories of horizontal displacement in loess ground.
Fig. 12. Horizontal-displacement amplitudes of the ground under different loading conditions.
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Fig. 13. Dynamic soil pressure. (a) Xi'an test cases, (b) Songpan test cases (c) Taft test cases.
should be concerned, and its intuitive performance can be expressed by two parameters: i) the soil pressure difference between top and bottom of model structure; ii) and the uplift of structure in vertical direction. The relationship between these two parameters can be seen in Fig. 14. Based on this phenomenon, the relationship between these two parameters was fitted, and the expression is △F = a × πr 2 × e|b△y|, where △F means the soil pressure difference between the top and bottom of the model structure, △y denotes the uplift amount of the model structure, r is the soil pressure sensor radius, and a, b means fit coefficient. The relationship between two parameters can be seen in Fig. 15, and the correlation coefficient is greater than 0.95. Meanwhile, it can be found that the fitting formula of power exponent can better simulate the relationship between the two parameters. The soil pressure difference between the top and bottom of the structure reflects the mechanical properties of the soil-structure interaction, and the seismic subsidence is the deformation behavior of the soil-structure interaction. The relationship between the two reveals the characteristics of soilstructure interaction, and can also provide reference for the estimation of seismic subsidence of soil-structure systems in soft soil areas. We define a parameter Ky to refer to the vertical dynamic soil∂ |△F| structure interaction, and it can be calculated by K y= ∂ |△y| . This parameter shows the vertical stiffness ratio between soil and structure. When Ky goes to infinitesimal, sufficient slip between underground structure and soil may occur; when Ky goes to infinity, the structure sticks completely to the soil. Ky reflects the mechanical behavior of the soil and the structure cooperative characteristics in vertical direction. In this test, The Ky-
However, the distribution pattern has significant relationship with the soil, different distribution patterns were shown in different test cases, and this is due to the different interaction mode between soil and underground structure. The soil-structure interaction mode presents a trumpet-type distribution in horizontal direction. The peak dynamic soil pressure appears at the top of the structure sidewall, while the secondary peak appears at the bottom of the structure. A relatively significantly weak zone shows up in the central part of the sidewall. The distribution characteristics of dynamic soil pressure on the structure sidewall are more evident as the PGA of input motion increases. In addition, this distribution pattern makes it necessary to pay more attention to the additional dynamic soil pressure at the top and bottom of the structure when designing underground structures in such sites. The elevating of the underground structure causes certain uplift on the adjacent ground surface, which equals to the settlement value at point G1 minus the settlement value at point G2. The settlements of model system under different loading conditions are shown in Table 5. Small settlement occurred when the input PGA was lower, and the value of uplift of model structure increased with the increase of PGA, which was caused by the vertical inertial force of the model structure differing from the soil. This was caused by the difference of vertical inertial force between soil and structure in different cases, relative movement between the model structure and the soil would occur. An interesting phenomenon was observed in this test: a significant uplift of the ground surface occurred when the PGA increases to 0.4 g, and the uplift of model structure decreased with increasing PGA when PGA exceeded 0.4 g. Hence, the vertical dynamic soil-structure interaction Table 5 Settlements of model system under different loading conditions (unit: mm). PGA(g)
0.05 0.1 0.2 0.4 0.6 0.8
Settlements at point G1
Settlements at point G2
Uplift of model structure (G1-G2)
Songpan record
Taft record
Xi'an artificial wave
Songpan record
Taft record
Xi'an artificial wave
Songpan record
Taft record
Xi'an artificial wave
0.002 0.005 0.165 1.219 1.322 1.983
0.009 0.077 0.627 4.144 1.426 4.790
0.001 0.130 1.059 11.020 12.823 11.086
0.001 0.003 0.065 0.760 1.000 1.756
0.005 −0.008 0.044 2.158 1.155 4.405
−0.003 0.075 0.968 6.770 12.047 10.860
0.001 0.002 0.099 0.458 0.322 0.228
0.004 0.085 0.583 1.986 0.271 0.385
0.004 0.055 0.091 4.250 0.776 0.225
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Fig. 14. The relationship between two parameters soil pressure and uplift of structure.
acceleration (in this test, equals to 0.4 g), the vertical inertial forces would be increase; meanwhile, the uplift of structure would reduce.
3.5. Strain distribution of station structure The maximum strain of the model structure under different ground motions can be seen in Table 6. Different grayscale means different damage degree. It indicates that the strain amplitude of the subway station gradually increases with the increase of the PGA. The strain responses at the top of the upper center pillar S4 is greatest in the center pillar. When it comes to side wall, the top of the upper side wall S16 and the bottom of the lower side wall S13 of the station structure are greater than those at other positions of the side wall. The strain measured in the top slab and bottom slab are smaller than that in pillar and sidewall. However, in this test, the middle slab was subjected to more serious damage, and the strain possessed the maximum value when input PGA was higher. The above rules mainly relate to the distribution characteristics of the dynamic soil pressure both in horizontal and vertical direction. In addition, the strain values measured in this study are larger than that measured in the previous experiments in liquefiable site [36]. This is because that the s-wave component of the ground motion is filtered in the liquefied ground, and the strain in this test is significantly smaller than that in the same position measured in liquefied ground. The structural failure phenomenon is shown in Fig. 18. It is obvious that, the damage position was consistent with strain distribution; combining the analyses of section 3.4 and 3.5, the additional forces acting on the model structure were the vertical pressure in combination with the horizontal bending. Hence, we speculate that the structure damage process may be as follows: i) the earthquake force on the pillar lost its shear strength; ii) then, the vertical pressure and horizontal bending would act on the slab and sidewall, because the sidewall had a large longitudinal stiffness and uneven stress distribution in the model structure appeared. Therefore, we conclude that the damage degree of underground subway station may be caused by following parameters: axial pressure ratio of center pillar, stiffness ratio between slab and sidewall, dynamic soil pressure distribution, and the site conditions, etc.
Fig. 15. Relationship between differential soil pressure and model-structure uplift.
value decreased with the increase of the PGA and is shown in Fig. 16. It is clear that the vertical dynamic soil-structure interaction mainly experiences three stages. During the initial stage, soil and structure tended to move synergistically and Ky maintained in a stable value (e.g. 0.05 g and 0.1 g). During the second stage, non-harmonious movement and vertical dynamic soil-structure interaction appeared due to the cumulative seismic effect, and the value of Ky decreased and the soil above the structure exhibited arch characteristic when PGA equals to 0.2 g. In the third stage, Ky tended to be the smallest and close to zero, which indicated that slipping or gapping phenomenon in vertical direction occurred and the upper soil above the structure formed an independent part and became dead weight; the value of △F would tend to zero and the Ky also shows the same tendency. This also can be seen in the macroscopic phenomena after the test which is shown in Fig. 17. When PGA is greater than 0.4 g, the soil-structure system loses its vertical constraints, and the dynamic soil pressure near the top of underground structure unloaded. Hence, when input PGA exceeded the critical
Fig. 16. Different vertical stiffness between soil and structure. 182
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Fig. 17. Macroscopic phenomena after test. Table 6 Strain amplitudes of the station in the primary observation section under different ground motions.
PGA-cases, and the period band of the main response acceleration of the soil is clearly widened. In other words, the increased seismic intensity should increase the seismic risk of a subway station with respect to its natural vibration period. (2) The dominant frequency of the input motion had an inverse effect on the lateral soil deformation. The soil-structure interaction mode presents a trumpet-type distribution in horizontal direction and the distribution characteristics of dynamic soil pressure on the structural sidewall are more evident as the PGA of input motion increases. In this test, the vertical dynamic soil-structure interaction has been concerned, and we defined a parameter Ky to refer to the vertical dynamic soil-structure interaction and analyzed its variation tendency with changing of PGA. (3) The strain measured in the center pillar and middle slab were larger than that in other positions. Comparing with the previous experiments, the underground structure failure mode is related with the soil dynamic characteristics. Hence, different ground conditions may cause different results on the underground seismic response.
Fig. 18. Structural failure phenomenon after the test.
4. Concluding remarks Acknowledgments
The seismic behavior of subway structure under strong ground motions in loess ground was investigated in the paper through shaking table test on a scaled structure model. From the results of the test, the following conclusions can be obtained:
The authors gratefully acknowledge the financial support of this study by the National Key R&D Program of China (2017YFC1500400) and Natural Science Foundation of China (No.51878626, U1839202, 51778290). The authors also sincerely thank the anonymous reviewers for their insightful comments and suggestions. Especially, the authors thank Dr. Yao Erlei for its linguistic assistance during the preparation of this manuscript.
(1) The underground structure has smaller effect on the acceleration responses of the soil foundation in lower PGA cases. However, the presence of the structure would affect the acceleration in higher183
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