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Response characteristics of an atrium subway station subjected to bidirectional ground shaking
Soil Dynamics and Earthquake Engineering 125 (2019) 105737
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Response characteristics of an atrium subway station subjected to bidirectional ground shaking
T
Huiling Zhaoa, Yong Yuanb,∗, Zhiming Yea, Haitao Yuc,d,∗∗, Zhiming Zhange a
Department of Civil Engineering, Shanghai University, Shanghai, 200444, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China c Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China d Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai, 200092, China e Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Shaking table test Atrium subway station Rocking Bending vibration Earthquake
The stiffness distribution of an atrium subway station with zero buried depth spatially varies when columns in the first level underground are removed and lateral beams replace the middle part of the floor slabs. It is pertinent to the mechanism and effects of multidirectional ground shaking on such structures. In this paper, the response characteristics of an atrium subway station subjected to bidirectional ground motions in a shaking table test were presented. Under horizontal seismic shaking, the structure, without a soil cover, showed a non-negligible rocking mode coupled with the well-known racking of the structure. Under vertical seismic shaking, the lateral beams, without supporting columns, demonstrated an obvious bending vibration associated with an overall up and downward movement. Overall, the horizontal component contributed more to dynamic response of the structure than the vertical component.
1. Introduction Recently, underground structures in seismic active areas have undergone extensive damage [1–3]. Recent studies have focused on the effects of seismic excitation and earthquake-induced ground failures on the response of embedded rectangular structures, including tunnel [4–8] and subway station [9–12], which are inferior to circular structures. It also has been noted that shallow embedded structures in soft soil are more vulnerable to seismic shaking [13–15]. Shallow burial depth (low depth ratio) is often associated with large amplification of seismic ground motions as they travel from bedrock to the ground surface and also with the low confining pressure from the surrounding soil, hence increasing dynamic responses and leading to considerable racking and rocking [16]. In this paper, a typical two-story atrium station with zero burial depth in soft soil is presented. The first level underground is considered a beam-wall system, where the side walls are connected by large-span lateral beams. To maximize daylight and the view, the top floor slabs are replaced by lateral beams and the columns beneath are removed. The second level underground is beam-column-wall system with two rows of columns. Compared with traditional underground subway
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stations, the atrium station system has zero buried depth, removed top slabs and columns, large-span lateral beams, and strip bottom columns. However, these particularities have indefinite vulnerability to earthquakes due to irregularity of the structural stiffness, variation of the load transfer mechanism, and even uncertainty in the interaction between soil and structure. Therefore, it is necessary to acquire knowledge of the seismic soil-structure response to enhance the safety and resiliency of such underground structures. Experimental investigations, such as centrifuge tests and shaking table tests, provide an actual and comprehensive estimation of the dynamic responses of underground structures. In geotechnical engineering, centrifuge tests are a powerful approach to determine real stress conditions in the test ground and have been conducted to study soil-pile interaction and tunnels response [17–19]. However, a low scale factor often limits the expression of structural details, and instruments attached to the model may produce unwarranted dynamic effects. One common method to analyze structural response of complicated underground structures is a1g shaking table test [20]. For instance, Chen et al. [10,11] performed a series of shaking table tests for typical subway stations, which mainly focused on the dynamic soiltunnel interaction in liquefiable soil. Chen et al. [12] carried out a
Corresponding author. Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China. Corresponding author. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China. E-mail addresses: [email protected] (Y. Yuan), [email protected] (H. Yu).
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https://doi.org/10.1016/j.soildyn.2019.105737 Received 11 December 2018; Received in revised form 25 May 2019; Accepted 22 June 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
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shaking table test on a six-story subway station under pulse-like seismic excitations. Results from both studies revealed that the columns are the most vulnerable structural component. Yet, atrium stations without top columns have attracted increasing interest as to which part of the station acquires the most severe damage. Some researches have shown that earthquake motion characteristics display significant effects on seismic responses of soil and structures [21–23], considering the frequency content, duration, intensity and spatial difference. Although the multidirectional nature of earthquakes is generally neglected, it is important for the structure with three-dimensional spatial variability. Several recent experimental and numerical results have shown the detrimental effects of multidirectional shaking, yet it is still unclear how these effects should be properly addressed in practice. Consequently, attention also needs to direct on how to consider and quantify the influence of intensity, frequency spectrum, and multi-direction of seismic excitations on the dynamic behaviors of such underground structures. This study presents a shaking table test performed on an atrium subway station model embedded in dry model soil. In the design of similitude ratio, consistency of the flexibility ratio (structure to soil between the prototype and model) was guaranteed to simulate interactions between the soil and structure. The system response was recorded with an extensive instrumentation array comprised of miniature accelerometers and strain gauges. The quantitative relation of the dynamic amplification was tested in free field model soil with depth and frequency and verified based on the analytic solution in the frequency domain. Structural dynamic responses reveal some unusual characteristics, including rocking when subjected to horizontal ground motions with sensitivity to frequency and intensity of motions, bending vibration of beams when subjected to vertical ground motions, and distinctive weak regions indicated by dynamic strain distribution when subjected to real bidirectional recorded earthquake motions.
Fig. 2. Illustration of the prototype structure and its dimensions (Unit: mm).
effects. Linear bearings were placed between the top steel plate and bottom of the rubber bucket, and universal joints were set between the top steel plate and the top laminar of the bucket to allow lateral displacement of the bucket. A gravel layer was set at the bottom of the container to make it rough, thereby reducing the relative slip at the interface between the soil and container. The boundary effect and attenuation of this container were previously investigated by Lu et al. [24]. Recorded responses of the structure are impervious to the container's lateral boundaries when the ratio of the diameter of soil to the width of structure in soil is no less than 5. 2.2. Model development
2. Shaking table test
2.2.1. Similitude ratio design The prototype structure in this study is a two-story atrium subway station with zero burial depth. As shown in Fig. 2, the cross section of the structure is 21.54 m wide and 15.89 m high. The first level underground is a beam-wall system, and the floor system is set up with oblique braces and beams. The second level underground is a beamcolumn-wall system with two rows of narrow columns. The columns are designed with a stripe cross section, 300 mm × 3040 mm, with a large height to width ratio for space efficiency. The floor system is composed of two side slabs and beams. The spacing of crossbeams, with a cross section 1500 mm × 1000 mm each, at the first level underground is 8900 mm. The crossbeams at the second level underground have the large spacing 22800 mm and with the cross section of 3040 mm × 800 mm. There are no slabs between crossbeams in order to bring natural light to the two levels. The geometric dimension of the model was 1/30 of the prototypical structure based on the size and bearing capacity of the shaking table and considering the boundary effect. Dimensional analysis, Buckingham-π theorem, and the method of governing equations are used for similitude design in geotechnical engineering [25]. Buckingham-π theorem [26] was adopted to define the similitude ratio. Geometry, density, acceleration, and elastic modulus were chosen as the fundamental factors governed by the similitude equation:
2.1. Shaking table and soil container The test was carried out in the State Key Laboratory on Disaster Reduction in Civil Engineering, located in Tongji University, Shanghai, China. The shaking table is three dimensional with six degrees of freedom, i.e., two horizontal and one vertical translational as well as three rotational degrees of freedom. The table is a 4 × 4 m2 square and is capable of applying motions with frequency between 0.1 and 50 Hz. The flexible laminar soil container is made from a cylindrical rubber bucket with a diameter of 3000 mm, height of 1800 mm, and thickness of 5 mm, as shown in Fig. 1. The container was reinforced with 34 4 mm-diameter steel rings with a spacing of 60 mm, which provided two dimensional horizontal motions without considerable boundary
Sa = SE /(Sl⋅Sρ)
(1)
where Sa , SE , Sl , and Sρ denote acceleration, elastic modulus, geometry, and density factor, respectively. The acceleration factor, Sa , was determined to be 1.0. The elastic modulus and density factor are material properties that guide the selection of the materials for model structure and soil. Previous studies [27]; Hashash 2010 [28], revealed that site response depends on the dynamic characteristics of the site soil, indicating the
Fig. 1. Schematic diagram of the soil container (Unit: mm). 2
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Table 1 Similitude scale factors of the soil-structural system model. Type
Physical quantity
Geometry properties Material properties Dynamic properties
Length Displacement Modulus Density Acceleration Duration time Frequency Strain
Similitude ratios Structure
Soil
1/30 1/30 0.14 0.75 1 0.18 5.48 1
1/30 1/30 0.12 0.40 1 0.18 5.48 1
Fig. 3. Variations of dynamic modulus and damping ratio with shear strain for model soil.
necessity to consider the similarity between the model soil and site soil. Model soil preparation was guided by Yan [29], and the model soil was made of sawdust and sand with a ratio of 1:2.5. Dynamic shear modulus and density of the model soil were determined to be 2.84 GPa and 700 kg/m3, respectively. The curves of the model soil and site soil in Fig. 3, Gd/ Gdmax -γd curves and ξ -γd curves, represent the variations in their dynamic shear modulus ratio and damping ratio as shear strain. It can be seen from the comparison that the dynamic properties of the model soil are similar to the prototype soil. Sand was poured in layers, while the model structure and instruments were properly positioned. The target material properties of the model need to be designed based on the previous scaling law. However, the 1 g-test facility and material tend to limit the specimen from achieving a fully-scaled down model of the prototype. It is also difficult to satisfy the similitude ratio derived from the scaling law for the elastic modulus and density. Since the seismic response and interaction effects are mainly affected by the relative flexibility between the soil and structure [2], the main target stiffness property of the model is determined by the relative flexibility ratio of the structure to soil. The flexibility ratio of the structure, denoted F, can be calculated as:
F=
GW SH
Fig. 4. Model structure for the atrium station.
2.2.2. Model structure As shown in Fig. 4, the structure of the model atrium subway station with two levels was manufactured using micro-concrete and galvanized steel wire nets. The structure has a longitudinal length of 1.25 m, width of 0.71 m, and height of 0.57 m. The amount of steel wire in the model was determined according to the same reinforcement ratio as the prototype, and diameters of the steel wire ranged 0.7–1.2 mm. The structure was placed in the center of the model box, and the outer wall of the model was 1.15 m away from the bucket wall.
(2)
where G denotes the shear modulus of soil; W , and H denote the width and height of the structure, respectively; and S is the unit racking stiffness, the reciprocal of the lateral racking deflection caused by a unit concentrated force. The relation between the shear modulus of the model soil and elastic modulus of the model structure is controlled by the flexibility ratio similitude governing equation:
SF = (SG SL)/(SS SL) = SG / SE = 1
2.3. Sensors layout A dense instrumentation array was implemented to monitor the soilstructure dynamic response. Miniature piezoelectric accelerometers were used to record the acceleration in the soil, structure, and shaking table. Strain gauges were attached to the sidewall, beams, columns, and joints to record strains and obtain data of the strain distributions at important locations. The model structure with zero buried depth was set at the center of the soil container, as shown in Fig. 5. Three cross sections, A-A, B–B, and C–C at mid-length, mid-beam of the first level, and mid-beam of the second level, respectively, were monitored to investigate the seismic response of the structure in horizontal and vertical directions, i.e. X and Z directions in the coordinate system in Fig. 5. According to Yang's research [31] when the distance of the cross section to the longitudinal end is larger than 0.38 times the structure width, the variation of internal force at the section, arising from the end effect, reaches 7% on average. In the test, the distance of sections A-A, B–B, and C–C to the longitudinal end were 0.87, 0.62 and 0.39 times the structure's width, respectively. In addition, the longitudinal end boundary effect can be neglected. The layout of the sensors is shown in Fig. 6, where the
(3)
According to the properties of the model soil and site soil, SG is 0.12. In order to satisfy eq. (3), a scaling factor for the elastic modulus of the model structure's material needs to be close to that of the model soil. In this work, the material was composed of micro-concrete, which contains water, cement, lime, and medium sand in volume ratio of 1.16:1:0.8:5. The elastic modulus and density of the micro-concrete were tested at 4.2 GPa and 1864 kg/m3, respectively. The density scale factor of the model structure does not conform to the scaling law. Since the atrium station structure has an incomplete and uneven floor slab, adding mass to the local plate confuses the relative dynamic characteristics between the members. Given that the structural dynamic response is weakly affected by its own inertial force [30], no additional mass was added to the structure. The detailed similitude ratios of the model structure and soil are listed in Table 1. 3
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denoted as the Z-axis. Table 2 shows a list of motions applied to the model. Two different kinds of acceleration time histories were selected as input motions: 1) a stepped sine motion and 2) record earthquake motions from the PEER Strong Motion Database [32]. According to Fourier amplitude spectra for 100 record ground motions from sites close to the prototype site, the average of the first dominant frequency was determined to be 1.2 Hz. The threshold was estimated as 0.2 Hz and 3.4 Hz in terms of the 5th and 95th percentiles, which are scaled to 1.1 Hz and 18.6 Hz based on the frequency similitude, respectively. Frequencies of the sine motions were selected as 1, 5, 10, 15, and 20 Hz, and the amplitude was 0.1 g. The horizontal component of Loma Prieta 1989 earthquake motion was recorded at the site where the shear velocity (Vs) was close to the prototype site with the distance of 24.6 km to the rupture surface (Rup). The modulated Loma Prieta motions with PGA 0.1 g, 0.3 g, and 0.5 g were selected to obtain the effect of ground motion intensity. The horizontal component of Kobe 1995 Earthquake motion (modulated PGA 0.1 g), recorded at the harder sites with Vs of 312 m/s and with a distance to a rupture surface of 0.9 km, was also selected as one of the input motions. Based on the Fourier amplitude spectra in Fig. 7, the Kobe (1995) motion has a greater energy, especially for frequency ranging from 6 to 8 Hz than the Loma Prieta motion. In order to consider the combined X and Z direction motions, the Northridge x, z (1994) motions were introduced as a relatively large vertical component, which promotes a high-frequency band distribution due to a small attenuation with a Vs of 550 m/s. The time history accelerations of the Northridge motion in the X and Z directions were applied synchronously to obtain the effect of bidirectional motion on the dynamic responses of the model.
Fig. 5. The soil-structure model on shaking table.
accelerometer and strain gauge are denoted A and S, respectively. Acceleration and strain measurements of the surrounding soil and structure were collected by a set of sensors during the shaking table tests. These sensors are: (1) Accelerometers A1s to A13s were set on the structure to collect accelerations in the horizontal direction. At some locations, two accelerometers were installed together to collect bidirectional accelerations simultaneously. For example, A7s, and Az7s denote the No.7 accelerometer recording acceleration in the horizontal and vertical directions, respectively. (2) Accelerometers A1 to A16 collect accelerations of the surrounding soil in the horizontal direction. A6, A8, A9, A11, and A12 were set at the same heights and close to A2s, A3s, A5s, A6s, and A9s on the sidewall of the structure to investigate the motion differences between the soil and structure. A1, A2, A4, A3, A5, A7, A10, and A14 were set to record the wave propagation from the base to surface. A13, A14, A15, and A16 were set to inspect the boundary effect. (3) Strain gauges S1 to S32 record strains of the structure. S1 to S16 were set to record stains at the sidewall and bottom slab. S17 to S24 record strains at the end of the columns. S25 to S32 record the strains at the end of the beams. S1 to S24, S25 to S28, and S29 to S32 strain gauges are located at the A-A, B–B, and C–C cross sections, respectively.
3. Free field verification 3.1. Surface amplification variation with frequency A series of analytical solutions to different kinds of site soil responses was obtained from the site response analyses in the frequency domain developed by Kramer (1996). The latter responses have been widely used to estimate or validate site dynamic effects. For uniform, damped soil on a rigid base, an amplification function (eq. (4)) was used to describe the ratio of the free surface motion amplitude to the base motion amplitude.
2.4. Input motions
F (z) =
Acceleration time history motions were input into the shaking table base to act on the model soil-structure system, with emphasis on the transversal cross section of the model structure. As shown in Fig. 5, the critical input motion direction is parallel to the cross section of the station, and denoted as the X-axis, while the vertical direction is
1 cos 2 (2 πωZ/ vs ) + [ξ(2 πωZ/ vs )]2
(4)
where ω denotes the frequency of base shaking; Z and vs represent depth and shear velocity of the soil, respectively; and ξ is the damping ratio assumed to be 0.05. The fundamental frequency is given as vs /4Z .
Fig. 6. Layout of sensors for the soil and structure. 4
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Table 2 Characteristics of the input motions. Name
Freq.
PGAx
PGAz
Name
Earthquake
PGAx
PGAz
1SIN-x0.1 5SIN-x0.1 10SIN-x0.1 15SIN-x0.1 20SIN-x0.1 5SIN-z0.2 10SIN-z0.2 20SIN-z0.2
1 Hz 5 Hz 10 Hz 15 Hz 20 Hz 5 Hz 10 Hz 20 Hz
0.1 g 0.1 g 0.1 g 0.1 g 0.1 g 0 0 0
0 0 0 0 0 0.2 g 0.2 g 0.2 g
K-x0.1 LP-x0.1 LP-x0.3 LP-x0.5 N-x0.2-z0.17 N-x0.3-z0.28 N-x0.4-z0.34
Kobe,1995 Loma Prieta,1989 Loma Prieta,1989 Loma Prieta,1989 Northridge,1994 Northridge,1994 Northridge,1994
0.1 g 0.1 g 0.3 g 0.5 g 0.2 g 0.3 g 0.4 g
0 0 0 0 0.17 g 0.28 g 0.34 g
Sine Sine Sine Sine
Fig. 7. Input record earthquake motions.
factors are 11.7 and 10.8, respectively. However, differences between the two results during the high-frequency domain may result from nonuniform shear velocity in the soil after vibrations. 3.2. Boundary effect of the soil container The soil-structure model on the shaking table appeared to be affected by the boundary condition of the soil container. Accelerations at the surface of the free field soil monitored by an array of points with different distances to the centerline were obtained to analyze the boundary effect of the soil container. The peak acceleration of these points in soil under 0.1 g sine motions with different frequencies are demonstrated in Fig. 9. It can be seen that the peak accelerations of the points in the soil were almost the same when their distance from the soil container wall exceeded 0.5 m with standard deviations of 0.007, 0.006, and 0.008 under sine motions with frequencies 5, 10, and 15 Hz, respectively. This result indicates the negligible boundary effect for these points.
Fig. 8. The variation of surface soil amplification with frequency by test and analytical solution.
In the free field test, white noise motion in the X direction was input to check the amplification variation in the soil with different frequencies. The amplification factor (AF in figures) at the surface was obtained using the ratio of the free surface motion amplitude to the shaking table motion amplitude. The influences of frequency on the soil response via test and analytical solutions are depicted in Fig. 8. The two curves are in good agreement with the low-frequency domain of the free field. The first natural frequency from the test and analytical solutions are as 6.8 Hz and 7.0 Hz, and the corresponding amplification
4. Dynamic response of the structure 4.1. Horizontal acceleration When the soil-structure model was subjected to horizontal 0.1 g sine motions, the acceleration peak of points in the structure were almost the same as that of points in the closest soil, as displayed in Fig. 10(a). In these low PGA cases, the structure and soil at the interface moved consistently, which was hardly affected by the frequency. When the 5
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was under bidirectional Northridge motion, the acceleration peak of points on the slab were larger than those of the side wall, implying the vibration difference between the different structural members at the same height. The large differences between responses of the structure and soil at the surface was mainly caused by the sensor at the soil surface. No enough constraints to the sensor at the soil surface resulting in the error of the data by this sensor. 4.2. Rocking effect Dynamical acceleration characteristics of the structure under horizontal motion were further analyzed. Although the horizontal acceleration is presented in Fig. 10, only the vertical acceleration was studied herein. The rocking mode of vibration was found when the structure was subjected to horizontal motion. Fig. 11 compares vertical acceleration distribution in the structure under horizontal 0.1 g sine motion with different frequencies, which were obtained by sensors Az1s, Az4s, Az7s, and Az8s. Accelerations by Az7s and Az8s located at the corners of the structure were the largest with opposite direction. Acceleration by Az1s located at the center of slab was the lowest and close to zero. Antisymmetric distribution of the vertical acceleration with respect to the centerline of the structure indicates the rocking vibration of the structure. It can be seen from Fig. 11(a) that rocking is more obvious under high-frequency motions than low-frequency. The vertical accelerations were too large to be compared with the input horizontal acceleration of 0.1 g. Fig. 11(b) shows that rocking increased with the PGA of the record earthquake motion. The acceleration at the centerline deviated from zero when PGA of the motion was 0.5 g, indicating that a slight overall up and down movement occurred in the structure. The rocking effect was also found to vary with the record
Fig. 9. The acceleration of the surface points with different distances to the centerline.
model was under horizontal 0.3 g and 0.5 g Loma motions, a significant difference between the structure and soil at interface occurred, as demonstrated in Fig. 10(b). Consequently, under the horizontal low-PGA motions, the movement of the structure was constrained by the lateral surrounding soil, even when the acceleration response was large (e.g. under 5 Hz motion), and the structure and soil moved consistently. The constraint effect of the soil on structural movement is mainly influenced by the PGA of input ground motions, rather than the frequency content. When under PGA 0.1 g motions, the soil around the structure amplified the motions, and the amplification effect became more obvious when the Fourier dominant frequency was closer to the soil fundamental frequency 6.8 Hz. As shown in Fig. 10(b), when PGA of the input motion was 0.5 g, the maximum accelerations of the soil was 0.35 g, indicating that the soil attenuated accelerations of the motion propagated from the base. The attenuation effect increased as PGA because the soil damping increased by the high PGA ground motion. When the model
Fig. 10. X-direction acceleration distribution of the structure points, side wall and closest soil. 6
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Fig. 11. Z-directional (vertical) acceleration distribution of the structure under horizontal motions.
Fig. 6(b) are depicted in Fig. 13. The axial strain at the ends of the beams, columns, and sidewall was approximately antisymmetrically distributed about the centerline of the structure under different horizontal motions, which indicates the lateral shear effect. Positive (tensile) strains at the left ends of beams were less than the negative (compressive) strains at the right ends of beams in both levels because the constrain from the surrounding soil provides reaction to the structural movement. Strains at the ends of the beam in the first level underground were the largest, followed by strains of the beam in second level. Strains at the ends of the column were also significant. It can be inferred that the weak parts of the structure were the ends of the top beams, middle beams, columns, and junction of the side wall and the bottom plate. As shown in Fig. 13(a), the strain response increased nonlinearly with the PGA. The strains under Loma motion with PGA 0.5 g were quite close to those with PGA 0.3 g. Strong nonlinearity and damping of the soil under the high-PGA motions decreased the movement of the model and suppressed the dynamic strain response. No obvious difference in strain response was found between Kobe and Loma earthquake motions with the same PGA 0.1 g. The strains under Kobe motion were slightly larger than the other two motions, which corresponds with the acceleration response in Fig. 11(b). As shown in Fig. 13(b), the strain response under 5 Hz sine motion was obviously larger than that of the other frequencies. 5 Hz is the closest to the fundamental frequency in the horizontal direction, resulting in amplification of the soil prominently. As demonstrated in Fig. 13(c), the axial strains of the structural members under Z directional (vertical) motions were less than those under X directional (horizontal) motions. The frequency of 10 Hz was closest to the fundamental frequency in the vertical direction; hence, a strain response under 10 Hz sine motion is obviously larger than the response of the other frequencies. The axial strains at the beam ends in the second level underground and the top ends of columns were
earthquake motions of different contents. For instance, the high-frequency content in Kobe motion caused more serious rocking than other earthquake motions. For the atrium subway station, no covered soil above the structure is also attributed to the rocking effect. This finding is in good agreement with the recent studies of Cilingir and Madabhushi [8] and Tsinidis et al. [15]. 4.3. Vertical bending vibration Dynamical vertical acceleration of the structure under the z-direction (vertical) sine motions with PGA of 0.2 g and bidirectional Northridge motions are represented in Fig. 12. It can be seen from Fig. 12(a) that the AF of the structure under 10 Hz sine motion is about 4, much larger than those under 5 and 20 Hz. This response is in accordance with the frequency domain analytic solution. The fundamental frequency of the soil under z-direction motion input was calculated to be 11.6 Hz by means of replacing the shear velocity with compress velocity in eq. (4). Because 10 Hz is the closest to the fundamental frequency, amplification of the ground motion in the test was significantly enlarged. The monitoring points of the slab and beam at the same height had the different accelerations, such as the group containing Az7s, Az10s, and Az8s and the group of Az4s, Az12s, and Az13s. Differences between accelerations (Az7s, Az10s, Az8s) at different locations of the large-span beam in first level underground are relatively large. It indicates the bending vibration of the large-span beam. When the bidirectional record Northridge earthquake motion acted on the model, the rocking contributed much more than the bending vibration to the vertical accelerations, as shown in Fig. 12(b). 4.4. Dynamic strain distribution Dynamic strain responses of the model obtained by sensors in
Fig. 12. Vertical accelerations of the structure under Z directional and bidirectional motions. 7
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Fig. 13. Dynamic strain distribution of the structure under horizontal motions.
similar to those under the X-0.4 g-Z-0.34 g motion, which was induced by the decreased amplification effect in the soil under high PGA motions.
approximately symmetrically distributed about the centerline of the structure, which may be induced by the bending vibration effect of beams and plates under Z directional motions. The axial strains at the beam ends in the first level underground showed approximate antisymmetric distribution, which may be attributed to the sensors that were set only on one sidewall. Unequal friction on both side walls resulted in an additional bending moment to the structure. Motions from the base propagated upwards, and the top beam was seriously affected by the additional bending. As demonstrated in Fig. 13(d), the axial strain distribution on the structure under bidirectional Northridge motions is neither antisymmetric distribution nor symmetric distribution. It is clear that the horizontal component contributed more to the dynamic strains than the vertical component. The strains under the X-0.3 g-Z0.28 g motion were
5. Conclusion This paper presents an experimental investigation on the seismic responses of an atrium subway station using a shaking table test of the soil-structure system. The unique features, including zero buried depth, removal of columns, and replacement of floor plates by lateral beams, of the system present challenges associated with capturing interactions between the soil and structure, with revealing dynamic response mechanism and weak parts of the structure under earthquake excitations, and also with quantifying correlation of these characteristics with input 8
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ground motions. These have been the focus of this study. Subsequently, the frequency content, intensity, and bidirectional were considered when conducting the soil-structure model dynamic test. Based on the findings from the present study, the following general conclusions are drawn:
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Proceedings of the 5th international conference on recent advances in geotechnical earthquake engineering and soil dynamics. San Diego (CA): NEES; 2010. [15] Tsinidis G, Pitilakis K, Madabhushi G, Heron C. Dynamic response of flexible square tunnels: centrifuge testing and validation of existing design methodologies. Geotechnique 2015;65(5):401–17. [16] Debiasi E, Gajo A, Zonta D. On the seismic response of shallow-buried rectangular structures. Tunn Undergr Space Technol 2013;38:99–113. [17] Conti R, Viggiani GMB. Evaluation of soil dynamic properties in centrifuge tests. J Geotech Geoenviron Eng 2011;138(7):850–9. [18] Tsinidis G, Pitilakis K, Madabhushi G. On the dynamic response of square tunnels in sand. Eng Struct 2016;125:419–37. [19] Chen Z, Liang S, Shen H, He C. Dynamic centrifuge tests on effects of isolation layer and cross-section dimensions on shield tunnels. Soil Dynam Earthq Eng 2018;109:173–87. [20] Kawamata Y, Nakayama M, Towhata I, Yasuda S, Tabata K. Large-scale experiment using E-defense on dynamic behaviors of underground structures during strong ground motions in urban areas. Proceedings of the 15th world conference of earthquake engineering. Lisbon. 2012. [21] Lanzano G, Bilotta E, Russo G, Silvestri F, Madabhushi SPG. Centrifuge modelling of seismic loading on tunnels in sand. Geotech Test J 2012;35(6):10–26. [22] Miao Y, Yao E, Ruan B, Zhuang H, Chen G, Long X. Improved Hilbert spectral representation method and its application to seismic analysis of shield tunnel subjected to spatially correlated ground motions. Soil Dynam Earthq Eng 2018;111:119–30. [23] Miao Y, Yao E, Ruan B, Zhuang H. Seismic response of shield tunnel subjected to spatially varying earthquake ground motions. Tunn Undergr Space Technol 2018;77:216–26. [24] Lu X, Li P, Chen Y, Chen B. Shaking table model testing on dynamic soil-structure interaction system. Proceedings of the 13th world conference on earthquake engineering. Vancouver, Canada. 2004. [25] Meymand PJ. Shaking table scale model tests of nonlinear soil-pile-superstructure interaction in soft clay Doctoral dissertation Berkeley: University of California; 1998 USA. [26] White FM. Fluid mechanics. eighth ed. New York, USA: McGraw Hill Education; 2015. [27] Seed H, Idriss I. Soil moduli and damping factors for dynamic response analyses. Report No. EERC-70-10. Berkeley (CA): Earthquake Engineering Research Center, University of California Berkeley; 1970. USA. [28] Griffiths SC, Cox BR, Rathje EM. Challenges associated with site response analyses for soft soils subjected to high-intensity input ground motions. Soil Dynam Earthq Eng 2016;85:1–10. [29] Yan X, Yu H, Yuan Y, Yuan J. Multi-point shaking table test of the free field under non-uniform earthquake excitation. Soils Found 2015;55(5):986–1001. [30] Huo H. Seismic design and analysis of rectangular underground structures Doctoral dissertation USA: Purdue University; 2005 [31] Yang L, Ji Q, Zheng Y, Yang C, Zhang D. Design of a shaking table test box for a subway station structure in soft soil. Front Archit Civ Eng China 2007;1(2):194–7. [32] Pacific Earthquake Engineering Research Center, PEER. User's manual for the peer ground motions data base web application. Berkeley (CA): The Peer Center, University of California; 2010https://ngawest2.berkeley.edu/.
1. From the free field test, the amplification effect at the field surface varied with the frequency of input motions. The quantitative relation of the ground motion amplification with input motion frequency was basically consistent with the analytical frequency domain solution by Kramer. The difference may be induced by the heterogeneity of the soil after shakings, such as the decreased shear velocity of the upper model soil. 2. Under the horizontal low-PGA (0.1 g) motions, the movement of the structure was constrained by the lateral surrounding soil, and the concordance was hardly affected by the frequency content of the motions. Under the horizontal high-PGA (0.5 g) motions, the maximum value of the acceleration of the structure and the surrounding soil was less than 0.5 g. Strong nonlinearity and damping of the soil attenuated rather than amplified the accelerations input from the base. 3. Rocking effect of the atrium subway station structure with zero buried depth was found under horizontal motions, which is inferred by antisymmetric distribution of the vertical acceleration about the centerline. The positive correlation of rocking with the frequency and PGA of motions has also been found, in which PGA has the larger sensitivity. It is believed that rocking should be taken into consideration for the seismic design of this type of structure. 4. When the soil-structure model was subjected to vertical (Z directional) motions, besides overall upward and downward acceleration, the vertical acceleration difference between different points of the beam was displayed, especially for the large-span beam in first level underground without columns. It may indicate the bending vibration of the beams. When the model was subjected to bidirectional record earthquake motions, the rocking contributed more than the bending vibration to vertical accelerations. 5. When subjected to bidirectional record earthquake motions, the horizontal component showed greater influence on the dynamic strain response than the vertical component. Furthermore, the weakest parts of the structure, in order from the greatest to least, were determined to be the ends of the top beams, then the middle beams, columns, and junction of the side wall and bottom plate. Acknowledgements The research has been supported by the funds from Natural Science Foundation of Shanghai, China (No. 19ZR1418700); Natural Science Foundation of Shanghai, China (No. 51208292 & 51678438 & 51478343 & 51778487); National Key Research and Development Plan of China (No. 2017YFC1500703 & 2018YFC0809602); and State Key Laboratory for c in Civil Engineering, China (No. SLDRCE15-02 and SLDRCE19-A-13). References [1] Iida H, Hiroto T, Yoshida N, Iwafuji M. Damage to daikai subway station. Soils and foundations, special issue on geotechnical aspects of the january 17 1995 hyogoken–nanbu earthquake. Japanese Geotechnical Society; 1996. p. 283–300. [2] Wang JN. Seismic design of tunnels: a simple state-of-the-art design approach. New York: Parsons Brinckerhoff; 1993. [3] Yu HT, Yuan Y, Liu X, Li YW, Ji SW. Damages of the Shaohuoping road tunnel near the epicentre. Struct Infrastruct Eng 2013;9(9):935–51.
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Response characteristics of an atrium subway station subjected to bidirectional ground shaking
T
Huiling Zhaoa, Yong Yuanb,∗, Zhiming Yea, Haitao Yuc,d,∗∗, Zhiming Zhange a
Department of Civil Engineering, Shanghai University, Shanghai, 200444, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China c Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China d Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai, 200092, China e Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Shaking table test Atrium subway station Rocking Bending vibration Earthquake
The stiffness distribution of an atrium subway station with zero buried depth spatially varies when columns in the first level underground are removed and lateral beams replace the middle part of the floor slabs. It is pertinent to the mechanism and effects of multidirectional ground shaking on such structures. In this paper, the response characteristics of an atrium subway station subjected to bidirectional ground motions in a shaking table test were presented. Under horizontal seismic shaking, the structure, without a soil cover, showed a non-negligible rocking mode coupled with the well-known racking of the structure. Under vertical seismic shaking, the lateral beams, without supporting columns, demonstrated an obvious bending vibration associated with an overall up and downward movement. Overall, the horizontal component contributed more to dynamic response of the structure than the vertical component.
1. Introduction Recently, underground structures in seismic active areas have undergone extensive damage [1–3]. Recent studies have focused on the effects of seismic excitation and earthquake-induced ground failures on the response of embedded rectangular structures, including tunnel [4–8] and subway station [9–12], which are inferior to circular structures. It also has been noted that shallow embedded structures in soft soil are more vulnerable to seismic shaking [13–15]. Shallow burial depth (low depth ratio) is often associated with large amplification of seismic ground motions as they travel from bedrock to the ground surface and also with the low confining pressure from the surrounding soil, hence increasing dynamic responses and leading to considerable racking and rocking [16]. In this paper, a typical two-story atrium station with zero burial depth in soft soil is presented. The first level underground is considered a beam-wall system, where the side walls are connected by large-span lateral beams. To maximize daylight and the view, the top floor slabs are replaced by lateral beams and the columns beneath are removed. The second level underground is beam-column-wall system with two rows of columns. Compared with traditional underground subway
∗
stations, the atrium station system has zero buried depth, removed top slabs and columns, large-span lateral beams, and strip bottom columns. However, these particularities have indefinite vulnerability to earthquakes due to irregularity of the structural stiffness, variation of the load transfer mechanism, and even uncertainty in the interaction between soil and structure. Therefore, it is necessary to acquire knowledge of the seismic soil-structure response to enhance the safety and resiliency of such underground structures. Experimental investigations, such as centrifuge tests and shaking table tests, provide an actual and comprehensive estimation of the dynamic responses of underground structures. In geotechnical engineering, centrifuge tests are a powerful approach to determine real stress conditions in the test ground and have been conducted to study soil-pile interaction and tunnels response [17–19]. However, a low scale factor often limits the expression of structural details, and instruments attached to the model may produce unwarranted dynamic effects. One common method to analyze structural response of complicated underground structures is a1g shaking table test [20]. For instance, Chen et al. [10,11] performed a series of shaking table tests for typical subway stations, which mainly focused on the dynamic soiltunnel interaction in liquefiable soil. Chen et al. [12] carried out a
Corresponding author. Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China. Corresponding author. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China. E-mail addresses: [email protected] (Y. Yuan), [email protected] (H. Yu).
∗∗
https://doi.org/10.1016/j.soildyn.2019.105737 Received 11 December 2018; Received in revised form 25 May 2019; Accepted 22 June 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.
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shaking table test on a six-story subway station under pulse-like seismic excitations. Results from both studies revealed that the columns are the most vulnerable structural component. Yet, atrium stations without top columns have attracted increasing interest as to which part of the station acquires the most severe damage. Some researches have shown that earthquake motion characteristics display significant effects on seismic responses of soil and structures [21–23], considering the frequency content, duration, intensity and spatial difference. Although the multidirectional nature of earthquakes is generally neglected, it is important for the structure with three-dimensional spatial variability. Several recent experimental and numerical results have shown the detrimental effects of multidirectional shaking, yet it is still unclear how these effects should be properly addressed in practice. Consequently, attention also needs to direct on how to consider and quantify the influence of intensity, frequency spectrum, and multi-direction of seismic excitations on the dynamic behaviors of such underground structures. This study presents a shaking table test performed on an atrium subway station model embedded in dry model soil. In the design of similitude ratio, consistency of the flexibility ratio (structure to soil between the prototype and model) was guaranteed to simulate interactions between the soil and structure. The system response was recorded with an extensive instrumentation array comprised of miniature accelerometers and strain gauges. The quantitative relation of the dynamic amplification was tested in free field model soil with depth and frequency and verified based on the analytic solution in the frequency domain. Structural dynamic responses reveal some unusual characteristics, including rocking when subjected to horizontal ground motions with sensitivity to frequency and intensity of motions, bending vibration of beams when subjected to vertical ground motions, and distinctive weak regions indicated by dynamic strain distribution when subjected to real bidirectional recorded earthquake motions.
Fig. 2. Illustration of the prototype structure and its dimensions (Unit: mm).
effects. Linear bearings were placed between the top steel plate and bottom of the rubber bucket, and universal joints were set between the top steel plate and the top laminar of the bucket to allow lateral displacement of the bucket. A gravel layer was set at the bottom of the container to make it rough, thereby reducing the relative slip at the interface between the soil and container. The boundary effect and attenuation of this container were previously investigated by Lu et al. [24]. Recorded responses of the structure are impervious to the container's lateral boundaries when the ratio of the diameter of soil to the width of structure in soil is no less than 5. 2.2. Model development
2. Shaking table test
2.2.1. Similitude ratio design The prototype structure in this study is a two-story atrium subway station with zero burial depth. As shown in Fig. 2, the cross section of the structure is 21.54 m wide and 15.89 m high. The first level underground is a beam-wall system, and the floor system is set up with oblique braces and beams. The second level underground is a beamcolumn-wall system with two rows of narrow columns. The columns are designed with a stripe cross section, 300 mm × 3040 mm, with a large height to width ratio for space efficiency. The floor system is composed of two side slabs and beams. The spacing of crossbeams, with a cross section 1500 mm × 1000 mm each, at the first level underground is 8900 mm. The crossbeams at the second level underground have the large spacing 22800 mm and with the cross section of 3040 mm × 800 mm. There are no slabs between crossbeams in order to bring natural light to the two levels. The geometric dimension of the model was 1/30 of the prototypical structure based on the size and bearing capacity of the shaking table and considering the boundary effect. Dimensional analysis, Buckingham-π theorem, and the method of governing equations are used for similitude design in geotechnical engineering [25]. Buckingham-π theorem [26] was adopted to define the similitude ratio. Geometry, density, acceleration, and elastic modulus were chosen as the fundamental factors governed by the similitude equation:
2.1. Shaking table and soil container The test was carried out in the State Key Laboratory on Disaster Reduction in Civil Engineering, located in Tongji University, Shanghai, China. The shaking table is three dimensional with six degrees of freedom, i.e., two horizontal and one vertical translational as well as three rotational degrees of freedom. The table is a 4 × 4 m2 square and is capable of applying motions with frequency between 0.1 and 50 Hz. The flexible laminar soil container is made from a cylindrical rubber bucket with a diameter of 3000 mm, height of 1800 mm, and thickness of 5 mm, as shown in Fig. 1. The container was reinforced with 34 4 mm-diameter steel rings with a spacing of 60 mm, which provided two dimensional horizontal motions without considerable boundary
Sa = SE /(Sl⋅Sρ)
(1)
where Sa , SE , Sl , and Sρ denote acceleration, elastic modulus, geometry, and density factor, respectively. The acceleration factor, Sa , was determined to be 1.0. The elastic modulus and density factor are material properties that guide the selection of the materials for model structure and soil. Previous studies [27]; Hashash 2010 [28], revealed that site response depends on the dynamic characteristics of the site soil, indicating the
Fig. 1. Schematic diagram of the soil container (Unit: mm). 2
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Table 1 Similitude scale factors of the soil-structural system model. Type
Physical quantity
Geometry properties Material properties Dynamic properties
Length Displacement Modulus Density Acceleration Duration time Frequency Strain
Similitude ratios Structure
Soil
1/30 1/30 0.14 0.75 1 0.18 5.48 1
1/30 1/30 0.12 0.40 1 0.18 5.48 1
Fig. 3. Variations of dynamic modulus and damping ratio with shear strain for model soil.
necessity to consider the similarity between the model soil and site soil. Model soil preparation was guided by Yan [29], and the model soil was made of sawdust and sand with a ratio of 1:2.5. Dynamic shear modulus and density of the model soil were determined to be 2.84 GPa and 700 kg/m3, respectively. The curves of the model soil and site soil in Fig. 3, Gd/ Gdmax -γd curves and ξ -γd curves, represent the variations in their dynamic shear modulus ratio and damping ratio as shear strain. It can be seen from the comparison that the dynamic properties of the model soil are similar to the prototype soil. Sand was poured in layers, while the model structure and instruments were properly positioned. The target material properties of the model need to be designed based on the previous scaling law. However, the 1 g-test facility and material tend to limit the specimen from achieving a fully-scaled down model of the prototype. It is also difficult to satisfy the similitude ratio derived from the scaling law for the elastic modulus and density. Since the seismic response and interaction effects are mainly affected by the relative flexibility between the soil and structure [2], the main target stiffness property of the model is determined by the relative flexibility ratio of the structure to soil. The flexibility ratio of the structure, denoted F, can be calculated as:
F=
GW SH
Fig. 4. Model structure for the atrium station.
2.2.2. Model structure As shown in Fig. 4, the structure of the model atrium subway station with two levels was manufactured using micro-concrete and galvanized steel wire nets. The structure has a longitudinal length of 1.25 m, width of 0.71 m, and height of 0.57 m. The amount of steel wire in the model was determined according to the same reinforcement ratio as the prototype, and diameters of the steel wire ranged 0.7–1.2 mm. The structure was placed in the center of the model box, and the outer wall of the model was 1.15 m away from the bucket wall.
(2)
where G denotes the shear modulus of soil; W , and H denote the width and height of the structure, respectively; and S is the unit racking stiffness, the reciprocal of the lateral racking deflection caused by a unit concentrated force. The relation between the shear modulus of the model soil and elastic modulus of the model structure is controlled by the flexibility ratio similitude governing equation:
SF = (SG SL)/(SS SL) = SG / SE = 1
2.3. Sensors layout A dense instrumentation array was implemented to monitor the soilstructure dynamic response. Miniature piezoelectric accelerometers were used to record the acceleration in the soil, structure, and shaking table. Strain gauges were attached to the sidewall, beams, columns, and joints to record strains and obtain data of the strain distributions at important locations. The model structure with zero buried depth was set at the center of the soil container, as shown in Fig. 5. Three cross sections, A-A, B–B, and C–C at mid-length, mid-beam of the first level, and mid-beam of the second level, respectively, were monitored to investigate the seismic response of the structure in horizontal and vertical directions, i.e. X and Z directions in the coordinate system in Fig. 5. According to Yang's research [31] when the distance of the cross section to the longitudinal end is larger than 0.38 times the structure width, the variation of internal force at the section, arising from the end effect, reaches 7% on average. In the test, the distance of sections A-A, B–B, and C–C to the longitudinal end were 0.87, 0.62 and 0.39 times the structure's width, respectively. In addition, the longitudinal end boundary effect can be neglected. The layout of the sensors is shown in Fig. 6, where the
(3)
According to the properties of the model soil and site soil, SG is 0.12. In order to satisfy eq. (3), a scaling factor for the elastic modulus of the model structure's material needs to be close to that of the model soil. In this work, the material was composed of micro-concrete, which contains water, cement, lime, and medium sand in volume ratio of 1.16:1:0.8:5. The elastic modulus and density of the micro-concrete were tested at 4.2 GPa and 1864 kg/m3, respectively. The density scale factor of the model structure does not conform to the scaling law. Since the atrium station structure has an incomplete and uneven floor slab, adding mass to the local plate confuses the relative dynamic characteristics between the members. Given that the structural dynamic response is weakly affected by its own inertial force [30], no additional mass was added to the structure. The detailed similitude ratios of the model structure and soil are listed in Table 1. 3
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denoted as the Z-axis. Table 2 shows a list of motions applied to the model. Two different kinds of acceleration time histories were selected as input motions: 1) a stepped sine motion and 2) record earthquake motions from the PEER Strong Motion Database [32]. According to Fourier amplitude spectra for 100 record ground motions from sites close to the prototype site, the average of the first dominant frequency was determined to be 1.2 Hz. The threshold was estimated as 0.2 Hz and 3.4 Hz in terms of the 5th and 95th percentiles, which are scaled to 1.1 Hz and 18.6 Hz based on the frequency similitude, respectively. Frequencies of the sine motions were selected as 1, 5, 10, 15, and 20 Hz, and the amplitude was 0.1 g. The horizontal component of Loma Prieta 1989 earthquake motion was recorded at the site where the shear velocity (Vs) was close to the prototype site with the distance of 24.6 km to the rupture surface (Rup). The modulated Loma Prieta motions with PGA 0.1 g, 0.3 g, and 0.5 g were selected to obtain the effect of ground motion intensity. The horizontal component of Kobe 1995 Earthquake motion (modulated PGA 0.1 g), recorded at the harder sites with Vs of 312 m/s and with a distance to a rupture surface of 0.9 km, was also selected as one of the input motions. Based on the Fourier amplitude spectra in Fig. 7, the Kobe (1995) motion has a greater energy, especially for frequency ranging from 6 to 8 Hz than the Loma Prieta motion. In order to consider the combined X and Z direction motions, the Northridge x, z (1994) motions were introduced as a relatively large vertical component, which promotes a high-frequency band distribution due to a small attenuation with a Vs of 550 m/s. The time history accelerations of the Northridge motion in the X and Z directions were applied synchronously to obtain the effect of bidirectional motion on the dynamic responses of the model.
Fig. 5. The soil-structure model on shaking table.
accelerometer and strain gauge are denoted A and S, respectively. Acceleration and strain measurements of the surrounding soil and structure were collected by a set of sensors during the shaking table tests. These sensors are: (1) Accelerometers A1s to A13s were set on the structure to collect accelerations in the horizontal direction. At some locations, two accelerometers were installed together to collect bidirectional accelerations simultaneously. For example, A7s, and Az7s denote the No.7 accelerometer recording acceleration in the horizontal and vertical directions, respectively. (2) Accelerometers A1 to A16 collect accelerations of the surrounding soil in the horizontal direction. A6, A8, A9, A11, and A12 were set at the same heights and close to A2s, A3s, A5s, A6s, and A9s on the sidewall of the structure to investigate the motion differences between the soil and structure. A1, A2, A4, A3, A5, A7, A10, and A14 were set to record the wave propagation from the base to surface. A13, A14, A15, and A16 were set to inspect the boundary effect. (3) Strain gauges S1 to S32 record strains of the structure. S1 to S16 were set to record stains at the sidewall and bottom slab. S17 to S24 record strains at the end of the columns. S25 to S32 record the strains at the end of the beams. S1 to S24, S25 to S28, and S29 to S32 strain gauges are located at the A-A, B–B, and C–C cross sections, respectively.
3. Free field verification 3.1. Surface amplification variation with frequency A series of analytical solutions to different kinds of site soil responses was obtained from the site response analyses in the frequency domain developed by Kramer (1996). The latter responses have been widely used to estimate or validate site dynamic effects. For uniform, damped soil on a rigid base, an amplification function (eq. (4)) was used to describe the ratio of the free surface motion amplitude to the base motion amplitude.
2.4. Input motions
F (z) =
Acceleration time history motions were input into the shaking table base to act on the model soil-structure system, with emphasis on the transversal cross section of the model structure. As shown in Fig. 5, the critical input motion direction is parallel to the cross section of the station, and denoted as the X-axis, while the vertical direction is
1 cos 2 (2 πωZ/ vs ) + [ξ(2 πωZ/ vs )]2
(4)
where ω denotes the frequency of base shaking; Z and vs represent depth and shear velocity of the soil, respectively; and ξ is the damping ratio assumed to be 0.05. The fundamental frequency is given as vs /4Z .
Fig. 6. Layout of sensors for the soil and structure. 4
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Table 2 Characteristics of the input motions. Name
Freq.
PGAx
PGAz
Name
Earthquake
PGAx
PGAz
1SIN-x0.1 5SIN-x0.1 10SIN-x0.1 15SIN-x0.1 20SIN-x0.1 5SIN-z0.2 10SIN-z0.2 20SIN-z0.2
1 Hz 5 Hz 10 Hz 15 Hz 20 Hz 5 Hz 10 Hz 20 Hz
0.1 g 0.1 g 0.1 g 0.1 g 0.1 g 0 0 0
0 0 0 0 0 0.2 g 0.2 g 0.2 g
K-x0.1 LP-x0.1 LP-x0.3 LP-x0.5 N-x0.2-z0.17 N-x0.3-z0.28 N-x0.4-z0.34
Kobe,1995 Loma Prieta,1989 Loma Prieta,1989 Loma Prieta,1989 Northridge,1994 Northridge,1994 Northridge,1994
0.1 g 0.1 g 0.3 g 0.5 g 0.2 g 0.3 g 0.4 g
0 0 0 0 0.17 g 0.28 g 0.34 g
Sine Sine Sine Sine
Fig. 7. Input record earthquake motions.
factors are 11.7 and 10.8, respectively. However, differences between the two results during the high-frequency domain may result from nonuniform shear velocity in the soil after vibrations. 3.2. Boundary effect of the soil container The soil-structure model on the shaking table appeared to be affected by the boundary condition of the soil container. Accelerations at the surface of the free field soil monitored by an array of points with different distances to the centerline were obtained to analyze the boundary effect of the soil container. The peak acceleration of these points in soil under 0.1 g sine motions with different frequencies are demonstrated in Fig. 9. It can be seen that the peak accelerations of the points in the soil were almost the same when their distance from the soil container wall exceeded 0.5 m with standard deviations of 0.007, 0.006, and 0.008 under sine motions with frequencies 5, 10, and 15 Hz, respectively. This result indicates the negligible boundary effect for these points.
Fig. 8. The variation of surface soil amplification with frequency by test and analytical solution.
In the free field test, white noise motion in the X direction was input to check the amplification variation in the soil with different frequencies. The amplification factor (AF in figures) at the surface was obtained using the ratio of the free surface motion amplitude to the shaking table motion amplitude. The influences of frequency on the soil response via test and analytical solutions are depicted in Fig. 8. The two curves are in good agreement with the low-frequency domain of the free field. The first natural frequency from the test and analytical solutions are as 6.8 Hz and 7.0 Hz, and the corresponding amplification
4. Dynamic response of the structure 4.1. Horizontal acceleration When the soil-structure model was subjected to horizontal 0.1 g sine motions, the acceleration peak of points in the structure were almost the same as that of points in the closest soil, as displayed in Fig. 10(a). In these low PGA cases, the structure and soil at the interface moved consistently, which was hardly affected by the frequency. When the 5
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was under bidirectional Northridge motion, the acceleration peak of points on the slab were larger than those of the side wall, implying the vibration difference between the different structural members at the same height. The large differences between responses of the structure and soil at the surface was mainly caused by the sensor at the soil surface. No enough constraints to the sensor at the soil surface resulting in the error of the data by this sensor. 4.2. Rocking effect Dynamical acceleration characteristics of the structure under horizontal motion were further analyzed. Although the horizontal acceleration is presented in Fig. 10, only the vertical acceleration was studied herein. The rocking mode of vibration was found when the structure was subjected to horizontal motion. Fig. 11 compares vertical acceleration distribution in the structure under horizontal 0.1 g sine motion with different frequencies, which were obtained by sensors Az1s, Az4s, Az7s, and Az8s. Accelerations by Az7s and Az8s located at the corners of the structure were the largest with opposite direction. Acceleration by Az1s located at the center of slab was the lowest and close to zero. Antisymmetric distribution of the vertical acceleration with respect to the centerline of the structure indicates the rocking vibration of the structure. It can be seen from Fig. 11(a) that rocking is more obvious under high-frequency motions than low-frequency. The vertical accelerations were too large to be compared with the input horizontal acceleration of 0.1 g. Fig. 11(b) shows that rocking increased with the PGA of the record earthquake motion. The acceleration at the centerline deviated from zero when PGA of the motion was 0.5 g, indicating that a slight overall up and down movement occurred in the structure. The rocking effect was also found to vary with the record
Fig. 9. The acceleration of the surface points with different distances to the centerline.
model was under horizontal 0.3 g and 0.5 g Loma motions, a significant difference between the structure and soil at interface occurred, as demonstrated in Fig. 10(b). Consequently, under the horizontal low-PGA motions, the movement of the structure was constrained by the lateral surrounding soil, even when the acceleration response was large (e.g. under 5 Hz motion), and the structure and soil moved consistently. The constraint effect of the soil on structural movement is mainly influenced by the PGA of input ground motions, rather than the frequency content. When under PGA 0.1 g motions, the soil around the structure amplified the motions, and the amplification effect became more obvious when the Fourier dominant frequency was closer to the soil fundamental frequency 6.8 Hz. As shown in Fig. 10(b), when PGA of the input motion was 0.5 g, the maximum accelerations of the soil was 0.35 g, indicating that the soil attenuated accelerations of the motion propagated from the base. The attenuation effect increased as PGA because the soil damping increased by the high PGA ground motion. When the model
Fig. 10. X-direction acceleration distribution of the structure points, side wall and closest soil. 6
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Fig. 11. Z-directional (vertical) acceleration distribution of the structure under horizontal motions.
Fig. 6(b) are depicted in Fig. 13. The axial strain at the ends of the beams, columns, and sidewall was approximately antisymmetrically distributed about the centerline of the structure under different horizontal motions, which indicates the lateral shear effect. Positive (tensile) strains at the left ends of beams were less than the negative (compressive) strains at the right ends of beams in both levels because the constrain from the surrounding soil provides reaction to the structural movement. Strains at the ends of the beam in the first level underground were the largest, followed by strains of the beam in second level. Strains at the ends of the column were also significant. It can be inferred that the weak parts of the structure were the ends of the top beams, middle beams, columns, and junction of the side wall and the bottom plate. As shown in Fig. 13(a), the strain response increased nonlinearly with the PGA. The strains under Loma motion with PGA 0.5 g were quite close to those with PGA 0.3 g. Strong nonlinearity and damping of the soil under the high-PGA motions decreased the movement of the model and suppressed the dynamic strain response. No obvious difference in strain response was found between Kobe and Loma earthquake motions with the same PGA 0.1 g. The strains under Kobe motion were slightly larger than the other two motions, which corresponds with the acceleration response in Fig. 11(b). As shown in Fig. 13(b), the strain response under 5 Hz sine motion was obviously larger than that of the other frequencies. 5 Hz is the closest to the fundamental frequency in the horizontal direction, resulting in amplification of the soil prominently. As demonstrated in Fig. 13(c), the axial strains of the structural members under Z directional (vertical) motions were less than those under X directional (horizontal) motions. The frequency of 10 Hz was closest to the fundamental frequency in the vertical direction; hence, a strain response under 10 Hz sine motion is obviously larger than the response of the other frequencies. The axial strains at the beam ends in the second level underground and the top ends of columns were
earthquake motions of different contents. For instance, the high-frequency content in Kobe motion caused more serious rocking than other earthquake motions. For the atrium subway station, no covered soil above the structure is also attributed to the rocking effect. This finding is in good agreement with the recent studies of Cilingir and Madabhushi [8] and Tsinidis et al. [15]. 4.3. Vertical bending vibration Dynamical vertical acceleration of the structure under the z-direction (vertical) sine motions with PGA of 0.2 g and bidirectional Northridge motions are represented in Fig. 12. It can be seen from Fig. 12(a) that the AF of the structure under 10 Hz sine motion is about 4, much larger than those under 5 and 20 Hz. This response is in accordance with the frequency domain analytic solution. The fundamental frequency of the soil under z-direction motion input was calculated to be 11.6 Hz by means of replacing the shear velocity with compress velocity in eq. (4). Because 10 Hz is the closest to the fundamental frequency, amplification of the ground motion in the test was significantly enlarged. The monitoring points of the slab and beam at the same height had the different accelerations, such as the group containing Az7s, Az10s, and Az8s and the group of Az4s, Az12s, and Az13s. Differences between accelerations (Az7s, Az10s, Az8s) at different locations of the large-span beam in first level underground are relatively large. It indicates the bending vibration of the large-span beam. When the bidirectional record Northridge earthquake motion acted on the model, the rocking contributed much more than the bending vibration to the vertical accelerations, as shown in Fig. 12(b). 4.4. Dynamic strain distribution Dynamic strain responses of the model obtained by sensors in
Fig. 12. Vertical accelerations of the structure under Z directional and bidirectional motions. 7
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Fig. 13. Dynamic strain distribution of the structure under horizontal motions.
similar to those under the X-0.4 g-Z-0.34 g motion, which was induced by the decreased amplification effect in the soil under high PGA motions.
approximately symmetrically distributed about the centerline of the structure, which may be induced by the bending vibration effect of beams and plates under Z directional motions. The axial strains at the beam ends in the first level underground showed approximate antisymmetric distribution, which may be attributed to the sensors that were set only on one sidewall. Unequal friction on both side walls resulted in an additional bending moment to the structure. Motions from the base propagated upwards, and the top beam was seriously affected by the additional bending. As demonstrated in Fig. 13(d), the axial strain distribution on the structure under bidirectional Northridge motions is neither antisymmetric distribution nor symmetric distribution. It is clear that the horizontal component contributed more to the dynamic strains than the vertical component. The strains under the X-0.3 g-Z0.28 g motion were
5. Conclusion This paper presents an experimental investigation on the seismic responses of an atrium subway station using a shaking table test of the soil-structure system. The unique features, including zero buried depth, removal of columns, and replacement of floor plates by lateral beams, of the system present challenges associated with capturing interactions between the soil and structure, with revealing dynamic response mechanism and weak parts of the structure under earthquake excitations, and also with quantifying correlation of these characteristics with input 8
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ground motions. These have been the focus of this study. Subsequently, the frequency content, intensity, and bidirectional were considered when conducting the soil-structure model dynamic test. Based on the findings from the present study, the following general conclusions are drawn:
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1. From the free field test, the amplification effect at the field surface varied with the frequency of input motions. The quantitative relation of the ground motion amplification with input motion frequency was basically consistent with the analytical frequency domain solution by Kramer. The difference may be induced by the heterogeneity of the soil after shakings, such as the decreased shear velocity of the upper model soil. 2. Under the horizontal low-PGA (0.1 g) motions, the movement of the structure was constrained by the lateral surrounding soil, and the concordance was hardly affected by the frequency content of the motions. Under the horizontal high-PGA (0.5 g) motions, the maximum value of the acceleration of the structure and the surrounding soil was less than 0.5 g. Strong nonlinearity and damping of the soil attenuated rather than amplified the accelerations input from the base. 3. Rocking effect of the atrium subway station structure with zero buried depth was found under horizontal motions, which is inferred by antisymmetric distribution of the vertical acceleration about the centerline. The positive correlation of rocking with the frequency and PGA of motions has also been found, in which PGA has the larger sensitivity. It is believed that rocking should be taken into consideration for the seismic design of this type of structure. 4. When the soil-structure model was subjected to vertical (Z directional) motions, besides overall upward and downward acceleration, the vertical acceleration difference between different points of the beam was displayed, especially for the large-span beam in first level underground without columns. It may indicate the bending vibration of the beams. When the model was subjected to bidirectional record earthquake motions, the rocking contributed more than the bending vibration to vertical accelerations. 5. When subjected to bidirectional record earthquake motions, the horizontal component showed greater influence on the dynamic strain response than the vertical component. Furthermore, the weakest parts of the structure, in order from the greatest to least, were determined to be the ends of the top beams, then the middle beams, columns, and junction of the side wall and bottom plate. Acknowledgements The research has been supported by the funds from Natural Science Foundation of Shanghai, China (No. 19ZR1418700); Natural Science Foundation of Shanghai, China (No. 51208292 & 51678438 & 51478343 & 51778487); National Key Research and Development Plan of China (No. 2017YFC1500703 & 2018YFC0809602); and State Key Laboratory for c in Civil Engineering, China (No. SLDRCE15-02 and SLDRCE19-A-13). References [1] Iida H, Hiroto T, Yoshida N, Iwafuji M. Damage to daikai subway station. Soils and foundations, special issue on geotechnical aspects of the january 17 1995 hyogoken–nanbu earthquake. Japanese Geotechnical Society; 1996. p. 283–300. [2] Wang JN. Seismic design of tunnels: a simple state-of-the-art design approach. New York: Parsons Brinckerhoff; 1993. [3] Yu HT, Yuan Y, Liu X, Li YW, Ji SW. Damages of the Shaohuoping road tunnel near the epicentre. Struct Infrastruct Eng 2013;9(9):935–51.
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