Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Dynamic centrifuge tests on effects of isolation layer and cross-section dimensions on shield tunnels
T
⁎
Zhiyi Chena,b, , Sunbin Lianga, Hao Shenc, Chuan Heb a
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, PR China Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Chengdu 610031, PR China c CCCC Highway Consultants CO., Ltd. (HPDI), Beijing 100088, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Dynamic centrifuge test Shield tunnel Seismic isolation effectiveness Cross-section dimensions
An isolation layer, consisting of a rubber layer wrapped around the outside of a tunnel lining, acts as a countermeasure to enhance the safety of a tunnel during an earthquake. The main objective of the present paper is to verify the seismic efficiency of isolation layers in shield tunnels, and to study the influence of cross-section dimensions on seismic isolation effectiveness. Two sizes of shield tunnel model (with and without isolation layers) are prepared, and six groups of dynamic centrifuge tests are conducted. The test results show that the isolation layer effectively decreases dynamic bending moments in both large and small cross-section tunnels. The smaller cross-section tunnel with smaller ratio of tunnel diameter to isolation layer thickness has a greater reduction of structural response, because more soil deformation is absorbed.
1. Introduction Tunnels are an important component of urban infrastructure. The damage information of recent earthquake events such as the Great Hanshin earthquake (Japan, 1995), the Chi-chi earthquake (Taiwan, 1999), the Düzce earthquake (Turkey, 1999), or the Wenchuan earthquake (China, 2008) show that tunnel structures are vulnerable to unrecoverable damage caused by earthquake [1,2]. Tunnels are difficult and expensive to repair if damaged in earthquake. Therefore, seismic analysis and structural control are key issues in engineering for disaster prevention and reduction. So far, the seismic isolation, one of the structural control methods, has been used successfully in surface structures. However, this advanced concept is not well known for underground structures. It is mainly because underground structures are strongly constrained by surrounding soils. Therefore, differing from surface structures, the dynamic behaviors of underground structures are mainly controlled by deformations of surrounding soils rather than natural vibration characteristics. Hence, further researches of seismic isolation in underground structures are necessary. Isolation layers are a relatively new countermeasure to enhance tunnel safety during earthquakes, so few studies have investigated the dynamic behavior of a tunnel with an isolation layer. Yamada et al. [3] conducted a series of centrifuge model tests of a flat cross-section tunnel and ground system with three different countermeasures in the transverse direction, and the
⁎
combination method (solidified ground and rubber membrane) was verified to be most effective. Kusakabe et al. [4] summarized physical modeling of the seismic response of tunnel structures, and emphasized the effectiveness of isolation layers and other countermeasures. These studies mainly concentrated on the influence of motion amplitude input on tunnel response, which takes isolation layers as countermeasures. The structural characteristics that influence the effectiveness of isolation layers, such as tunnel profile and dimensions, have not been investigated. Seismic behavior of underground structures varies with structural design and structure stiffness [4]. Unlike cut and cover tunnels or immersed tunnels, the linings of shield tunnels are usually constructed in segments that are secured together using circumferential and longitudinal bolts. The seams of shield tunnel reduce the stiffness and strength of the structure and have significant influence on structural seismic responses [5]. Shield tunnels are widely employed for transportation and municipal works in urban areas, where the cross-section dimensions are of great variety. Previous theoretical studies [6–8] have shown that the stiffness of a tunnel relative to the surrounding soil is a key factor when conducting seismic analysis. The cross-section dimensions, such as tunnel diameter and thickness, are the determining factors in tunnel stiffness and thus have important effects on structural seismic response. Liu et al. [9] conducted a parametric study of shield tunnels without an isolation layer using the time-history method, focusing on tunnel diameter and thicknesses. Their results indicated that
Corresponding author at: Department of Geotechnical Engineering, Tongji University, Shanghai 200092, PR China E-mail address:
[email protected] (Z. Chen).
https://doi.org/10.1016/j.soildyn.2018.03.002 Received 12 November 2016; Received in revised form 7 August 2017; Accepted 4 March 2018 0267-7261/ © 2018 Elsevier Ltd. All rights reserved.
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Therefore, the cross-section dimensions of a shield tunnel are believed to influence the seismic isolation effectiveness; thus, further research is needed. The main objective of the present paper is to verify the seismic efficiency of an isolation layer in a shield tunnel and to further study the influence of cross-section dimensions on seismic isolation effectiveness. For this purpose, two shield tunnel models with different cross-section dimensions (with and without an isolation layer) are prepared to conduct comparative dynamic centrifuge tests. 2. Dynamic centrifuge tests 2.1. Test facilities 2.1.1. Centrifuge machine and shaking table A TLJ-50 geotechnical centrifuge machine and an electro-hydraulic shaking table in Tongji University are used in the tests, which were manufactured by the Overall Engineering Institute of Chinese Academy of Engineering Physics. This shaking table can provide concise vibration at 50g centrifugal acceleration with a maximum payload of 300 kg. It can reproduce sinusoidal and actual earthquake waves of maximum 20g shaking acceleration with a maximum duration of 1 s. 2.1.2. Model soil container The design of container is the key factor in an effective centrifuge test. To minimize the boundary effect, a lamination box (Fig. 1) sized 500 mm × 400 mm × 550 mm was adopted in the tests. It is comprised of 22 rectangular cross-sectional aluminum frames. These frames can slide on the inner rail with little friction. The maximum slide displacement between two frames is 6 mm. A 1-mm-thick latex film is placed on the inner wall to prevent soil leakage from the gaps between the frames. The advantage of this kind of box is that it deforms together with the model soil in the shaking direction, reducing the reflection of P waves from the boundaries to a minimum level [10,11].
Fig. 1. Lamination box.
Table 1 Scaling factors for the centrifuge model. Parameter
Scaling factories (model/prototype)
Dimensions
Length Area Volume Stress Strain Mass Time (Dynamic) Velocity Acceleration Frequency
1/n 1/ n2 1/n3 1 1 1/n3 1/n 1 n n
L L2 L3 ML−1T−2 1 M T LT−1 LT−2 1/T
2.2. Scaling laws Geotechnical centrifuges are widely used in underground structure model tests because they can reproduce the actual stress and strain states of soil and structures. To explain the test results rationally, the test data need to be converted. The scaling law can be derived from dimensional analysis [12], as shown in Table 1. The geometric scaling factor is set as 1/n (n = 50), thus the centrifugal acceleration applied in these tests is 50g. The tunnel lining is an elastic shell structure, which bears both the bending moment and the axial force. According to different control equations, the bending deformation scaling law and axial deformation scaling law can be expressed in a different manner as Eq. (1) and Eq. (2), respectively. The scaling law when bearing bending deformation is
Table 2 Properties of prototype and model materials. Material
Modulus (GPa)
Prototype (Concrete) 35.5 Model (Aluminum) 70
Density (kg/m3)
Possion's ratio υ
Yield stress (MPa)
Ultimate stress (MPa)
2500 2700
0.2 0.33
– 500
– 600
2
Table 3 Physical properties of the model soil.
σp =
Parameter
Symbol
Value
Special gravity Maximum void ratio Minimum void ratio Maximum unit weight Minimum unit weight Maximum particle Friction angle
Gs emax emin γmax γmin dmax φ
2.67 1.039 0.682 1556 kN/m3 1283 kN/m3 2 mm 32°
1 − νp2 ⎛ nhm ⎞ ⎜ ⎟ σm 1 − νm2 ⎝ hp ⎠
(1)
where σ is the stress of lining, ν is Poisson's ratio, n is the centrifugal acceleration level, h is the thickness, and subscript p and m denote the prototype and model parameters, respectively. The scaling law when bearing axial deformation is
nh σp = ⎜⎛ m ⎟⎞ σm ⎝ hp ⎠
(2)
If the geometry was scaled by hp = n hm, and if the model and prototype had the same Poisson's ratio, then the bending and axial stresses in the model would equal the stresses in the prototype. Owing to material differences between the model tunnel and the prototype, these two equations cannot be satisfied simultaneously. Because
the dynamic bending moment and shear forces of shield tunnels have a positive correlation with the stiffness ratio, and that axial forces have a positive correlation with thickness and diameter of the lining structure. 174
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 2. Sand pourer equipment and S-shaped routine.
Fig. 3. Parametric curves of sand preparations.
flexural bearing capacity and bending deformation are the main factors in earthquake resilience, Eq. (1) is used in parameter conversion. 2.3. Materials properties
concrete and produces large strains due to low Young's modulus if compared with other common metal materials, such as steel. Table 2 shows the properties of prototype (concrete) and model (aluminum) materials.
2.3.1. Tunnel model properties Prototype tunnel segments are usually made from concrete using the sandwich method. The segments are made of internal and external steel plates, and filled with concrete in the middle. The surface steel plates are clamped firmly to the inner concrete using steel nails. The segments are connected by bolts through segment joints on both sides of the steel plates. The tunnel is assembled in staggered form to increase the longitudinal stiffness. Owing to the large number of segment joints in the shield tunnel, a reduction factor of stiffness η = 0.8 is adopted. Thus, the Young's modulus of prototype material is downscaled to 0.8 × 35.5 = 28.4 GPa. The homogeneous ring model is always adopted in the early design of shield tunnels in transverse direction. Although this is an empirical method, it is rational. In the present study, aluminum is adopted as the tunnel model material because, aluminum is easier than micro-concrete to fabricate precisely, owing to the very thin model lining. Aluminum has an advantage in data measurement and acquisition, since it has a smooth surface if compared with micro-
2.3.2. Model soil properties Reconstituted dry sand from the Shanghai area is used to simulated model soils, the properties of which are shown in Table 3. This kind of sand shows a grain size distribution close to fine sand with poor gradation, whose non-uniformity coefficient and curvature coefficient are 1.6 and 0.8, respectively. The relative density of the sand used in these tests is 40%, with a void ratio of 0.896. The volume of the tunnel models is approximately 0.0061 m3, and thus the sand used in the tests is 132.22 kg. To make the test repeatable and operable, sand properties can be controlled through the sand-rain pouring method. Fig. 2(a) shows the sand pourer equipment, which consists of a hopper, connection hose, spray head and sieve. When preparing the model soils, the sand is poured into the model box in an S-shaped pattern (see Fig. 2(b)) with the hopper at a controlled height. After every S-shape, the height of the hopper is adjusted according to the rising height of the sand surface in the model box, controlling the void ratios to be the same for different tests. The falling height of the sand and the diameter of sieve 175
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
6
150 Hz 5
Amplitude
4 3 2 1 0 0
20 00
400
600
800
1000
Frequeency(Hz) 20 0.6
El-Centro
15
0.5 0.4
5
Amplitude
Acceleration (g)
10
0 -5 -10
0.3 0.2 0.1
-15 -20 0.0
El-Centro
0.0
0.2
0.4
0.6
0
00.8
200 2
400
600
800
10000
Frequ uency(Hz)
Time (s) 20
Wolong g
15
0.6 0.5 0.4
5
Amplitude
Acceleration (g)
10
0 -5 -10
0.3 0.2 0.1
-15 -20 0.0
Wolong
0.0 0.2
0.4
0.6
0.8
0
200 2
Time (s)
400
600
800
10000
Frequ uency(Hz)
Fig. 4. Time histories and Fourier amplitude spectra of the input motions.
Table 4 Centrifuge tests details. Test ID
Outer diameter (mm)
Lining Thickness (mm)
Burial depth (mm)
Seismic Wave
Frequency(Hz)
Amplitude (g)
Duration (s)
T1 T2 T3 T4 T5 T6
120 120 120 60 60 60
5.0 5.0 5.0 2.9 2.9 2.9
140 140 140 140 140 140
Sinusoidal El-Centro Wolong Sinusoidal El-Centro Wolong
150 – – 150 – –
15 g 15 g 15 g 15 g 15 g 15 g
0.4 0.8 0.8 0.4 0.8 0.8
176
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 5. Model and transducer layout of small cross section tunnel (D = 60 mm).
the present paper is qualitative rather than quantitative. Given the main purpose of this experiment, which is to verify the effectiveness of the isolation layer in a shield tunnel and then further study the influence of cross-section dimensions on seismic isolation effectiveness, the test design is acceptable in this case. In addition, it is believed that the isolation layer can absorb dynamic deformation that transforms from the foundation to the underground structure, owing to its softness and low stiffness. Considering this, the Shore hardness of the silicon rubber is adopted as an important parameter to evaluate the material stiffness in the experiment. Silicon rubber with a Shore hardness of 45°, is adopted for the isolation layer.
control the void ratio of model soils, which must thus be determined by experiments before the sand preparation for centrifuge tests. Fig. 3(a) shows the relationships between the void ratios of model soils and the falling height of sand with different diameters of sieve. Fig. 3(b) depicts the relationships between the rising height of sand surface in model box and the falling height of sand with different diameters of sieve after every S-shape. In the experiments, the falling height of sand and the diameter of the sieve are determined as 900 mm and 7 mm, respectively. 2.3.3. Isolation rubber properties Silicon rubber (10 mm thick) is used as the isolation layer, and the corresponding prototype thickness is 500 mm. In practice, the thickness of an isolation layer, which is a modern silicone-based material, varies from 100 mm to hundreds of millimeters. Suzuki et al. [13] conducted indoor tests of silicone-based material and revealed that the shear modulus of the prototype material of the isolation layer decreases, whereas damping increases with the increase of shear strain. Because of the nonlinearity of the rubber material, the force-deformation relationship of the isolation layer used in practice could not be traced accurately by that of rubber material in the test. Thus, the research in
2.4. Test procedure Altogether, six groups of tests were carried out under 50g centrifugal acceleration. In Fig. 4, the graphs on the left show the time histories of the input motions, and the graphs on the right depict the corresponding frequency content information. The graphs clarify that the signals applied at the model base, which did not have constant amplitude, are not exactly harmonic. The frequency content was extended and larger than the design frequency, because some subsequent 177
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 6. Model and transducer layout of large cross section tunnel (D = 120 mm).
Fig. 7. Strain gauges’ layout.
the Wenchuan earthquake (China, 2008) respectively, are mainly in the range of 50–300 Hz, in the model scale. The prototypes are circular cross-section shield tunnels with different dimensions. The outer diameters of the two prototype tunnels are 3 m and 6 m and the lining thicknesses are 0.2 m and 0.35 m (2.9 mm and 5 mm for small and large model tunnels, respectively). To assure
frequencies were present up to around 1000 Hz. This extended frequency content was not noise recorded by instruments, but an effective energetic content and must not be eliminated with a filtering [14]. From the graphs on the right of Fig. 4, it can be also observed that the frequencies of the El-Centro wave and the Wolong wave, which are ground motion records of the El Centro earthquake (the US, 1940) and 178
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
under a 150-Hz sinusoidal wave are presented. The dynamic bending moments are calculated from the strains measured by a Wheatstone full bridge shown in Fig. 8. In Fig. 8, strain gauges R1 and R3 are stuck on the internal surface of tunnel lining, while R2 and R4 are stuck on the outside surface. Points A and B are connected to a power source. Thus, the voltage changes between C and D are in proportion to average strains, which can be calculated by Eq. (3).
ΔVCD K K = εm = (ε2 + ε4 − ε1 − ε3) VAB 4 4
(3)
where K is the coefficient of strain gauge, and ε1, ε2 , ε3 , and ε4 are the corresponding strains of R1, R2, R3, and R4, respectively. The circumferential normal strain consists of the bending moment normal strain and the axial force normal strain,
⎧ ε2 = ε4 = ⎨ ε1 = ε3 = ⎩
N (θ0) EA N (θ0) EA
+ −
M (θ0) t EI 2 M (θ0) t EI 2
(4)
where t is the thickness of model lining, E is the Young's modulus, A is the cross-section area, and I is the cross-section inertial moment, where A = tL, and I = (1/12)Lt3, L is per unit length. Combining Eq. (3) with Eq. (4), the bending moment can be calculated.
Fig. 8. Wheatstone full bridge.
the same test conditions when investigating the effectiveness of the isolation layer, two tunnels (one with and one without an isolation layer) are put in the laminar box during one flight. The tunnels are placed 20 mm apart to reduce unintended interactions. The detailed information about the test cases is presented in Table 4.
M (θ0) t ΔVCD =K VAB EI 2
(5)
Fig. 9 shows time histories of dynamic bending moment of the small cross-section tunnel (D = 60 mm), and Fig. 10 depicts those of the large cross-section tunnel (D = 120 mm). In these graphs, the dashed gray line and the solid black line represent time history of dynamic bending moment of the tunnels without and with an isolation layer, respectively. According to the sign convention of bending moment depicted in Fig. 11, the positive and negative bending moments, shown in Fig. 9 and Fig. 10, represent the lining bearing tension and compression respectively. From Fig. 9 and Fig. 10, either the large or the small crosssection tunnel, the isolation layer clearly reduces the values of dynamic bending moments, with the largest reduction rate of over 40%. Calculating from total five observation positions, the average reduction rates are about 25.6% and 12.4% for the small cross-section tunnel and the large cross-section tunnel, respectively. In addition to the remarkable seismic response reduction, the wave profiles of dynamic bending moments in the tunnels with or without isolation layer are basically consistent with each other. According to seismic wave field theory and seismic observation, the strain waveform of underground structures, such as pipelines, submarine tunnels and underground tanks, are similar to but not exactly the same as those of the surrounding media [15]. It can thus be inferred that the waveforms of the bending strains in the tunnels with or without an isolation layer in the tests should also be similar, which is in good agreement with the measured results (see Fig. 9 and Fig. 10). Fig. 12 and Fig. 13 show the time histories and Fourier amplitude spectra of the acceleration responses of the two tunnel cross-sections. The left panel of Fig. 12 shows the acceleration responses of small crosssection tunnels (with and without isolation layer) under the excitations of the 150-Hz sinusoidal wave, the El-Centro wave and the Wolong wave. The left panel of Fig. 13 shows the acceleration responses of large cross-section tunnels (with and without isolation layer) under the excitations of a the 150-Hz sinusoidal wave, the El-Centro wave and the Wolong wave. Whether an isolation layer is used or not, and independent of input motion, the acceleration response has little variation, so the inertial force of tunnels show little difference. Thus, this phenomenon illustrates that the isolation layer does not reduce the structural response by decreasing the inertial acceleration of
2.5. Layouts of model and transducers Based on the scaling law, the frequency and time in the dynamic centrifuge tests are n- and 1/n-times those of the prototype, respectively. Thus, the sampling frequency of the data acquisition is set to 5000 Hz. Fig. 5 and Fig. 6 are schematic diagrams of the experimental set-up of the small and large cross-section tunnels, respectively. The accelerations are directly measured by 607A11 accelerometers (PCB Piezotronics Inc.). Six accelerometers were arranged to measure horizontal accelerations at three levels: two at the bottom of the lamination box, two in the tunnels, and two in soils above the tunnels. Through this arrangement of accelerometers, the effects of the isolation layer on the acceleration response of the tunnel and of the soil above tunnel can be studied. Four custom-made linear varying differential transducers (Overall Engineering Institute, Chinese Academy of Engineering Physics) were placed on the outer surface of the laminar soil container to measure horizontal displacement. Another two linear varying differential transducers were placed on the ground surface to measure the settlement of the ground surface. As shown in Fig. 7, 20 strain gauges (BX-120-3AA; Zhejiang huangyan test instrument plant, China) were installed in five locations in the cross-section of each model. Numbers 1–5 represent the five locations on the cross-section of the small tunnel (D = 60 mm) with or without an isolation layer, and number 6–10 signify the corresponding locations on the cross-section of the large tunnel (D = 120 mm) with or without an isolation layer. 3. Test results and analysis 3.1. Effects of the isolation layer Results and data of the dynamic centrifuge tests in the following analysis are in the model scale. Considering space limitations, only the time histories of the dynamic bending moments of two tunnels with different cross-section dimensions (with and without an isolation layer)
179
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 9. Time histories of dynamic bending moment under the excitation of sinusoidal wave (D = 60 mm).
frequency content of the acceleration response, and illustrates that the reduction mechanism of the isolation layer is not filtering or absorbing any content of the input motion. The above results reveal the seismic reduction mechanism of the isolation layer，as illustrated in Fig. 14. The deformation of the
surrounding soils. In the right panels of Fig. 12 and Fig. 13, the corresponding Fourier amplitude spectra of acceleration responses are plotted. It can be seen that the isolation layer has a limiting effect on the amplitudes of acceleration response for tunnel, independent of input motion. It means the isolation layer has a minor influence on the
180
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 10. Time histories of dynamic bending moment under the excitation of sinusoidal wave (D = 120 mm).
deformations of the tunnel without and with an isolation layer, respectively, and Δ1 > Δ2. Thus, the seismic reduction mechanism of isolation layer is through absorbing soil deformation, thereby reducing deformation transferred from the soil to the shield tunnel. The seismic efficiency of an isolation layer in a shield tunnel is also verified. The
surrounding soil, rather than the vibration characteristics of the tunnel, dominates the seismic response of a tunnel. In the present study, the ground conditions around the two tunnels with different cross-section dimensions are almost identical; therefore, the foundation deformations show little difference as well. In Fig. 14, the Δ1 and Δ2 are the diameter
181
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
tunnel. Overall, increase of the tunnel cross-section may increase deformation and then internal forces in the tunnel. For example, in the present test, the moment of inertia of the large cross-section tunnel divided by that of the small cross-section tunnel is 5.12. The ratio of d2 of the large cross-section tunnel to d2 of the small cross-section tunnel is 4. The lining diametric deflection (Δ) of the large cross-section tunnel is 2.66 times that of the small cross-section tunnel under the same excitation, as calculated according to Hashash et al., [19]. Thus, in the present test, the dynamic bending moment of the large cross-section tunnel is much larger than that of the small cross-section tunnel. Fig. 16 shows the absolute dynamic bending moment reduction when an isolation layer is installed. For tunnels with different crosssection dimensions, the isolation layer has similar effects: better performance at X-shaped locations. For example, the absolute dynamic bending moment reductions at the 45° and 135° locations of the large tunnel under the El Centro wave are 10.8 and 12.8 Nm/m, respectively, while those at the 0° and 180° locations are 0.5 and 1.3 Nm/m, respectively (see the middle plot of Fig. 16). This phenomenon can be explained as follows. The rigidity of isolation layer rubber is much lower than that of the tunnel structure. The isolation layer absorbs more deformation at the locations where greater deformations occur; thus, tunnel deformation reduces, leading to a greater decrease in internal force. Additionally, although from the absolute value aspect, the isolation layer absorbs less deformation at the locations where less deformation occurs, from percentage reductions aspect, it is still effective in lowering the dynamic bending moment of the tunnel lining, and the reductions would be almost uniform at all locations. As mentioned before, the isolation layer reduces tunnel deformation through absorbing soil deformation; thus, it leads to smaller internal forces. Therefore, the rigidity and thickness of the rubber used influences its effects; a rigid and thin isolation layer will have little ability to absorb soil deformation. Thus, careful selection of rigidity and thickness of the isolation layer plays an important role in its actual effects. As mentioned above, dynamic bending moments at X-shaped locations are much greater, and a key factor for tunnel safety evaluation under seismic loadings; thus, and further discussion is needed. Reduction percentage R is defined as
Fig. 11. Sign convention of bending moment.
effectiveness of this isolation, as indicated by previous studies [17,18], is mainly dependent on Poison's ratio and thickness of the isolation layer and the relative stiffness of soils and the isolation layer. 3.2. Effects of cross-section dimensions Fig. 15 depicts the peak values of dynamic bending moment of the tunnels with two different cross-section dimensions with (solid line) and without (dashed line) an isolation layer under the excitations of the 150-Hz sinusoidal wave, the El-Centro wave, and the Wolong wave. In Fig. 15, the left semicircle and the right semicircle represent the small cross-section tunnel and the large cross-section tunnel, respectively. Theoretically, the maximum dynamic bending moments occur at the 45° and 135° locations of the circular cross-section tunnel [6–8,16], which are named X-shaped locations. Test results show good accordance with the theoretical analysis. Furthermore, Fig. 15 shows that the isolation layer has better performance at X-shaped locations for tunnels with different cross-section dimensions (this will be explained later). Considering that dynamic bending moments at X-shaped locations are much greater than those at other places, more attention should be paid to bending moments at these locations in practical seismic analysis and design. As depicted in Fig. 15, it is found that the peak values of dynamic bending moment of the large cross-section tunnel are much larger than those of the small cross-section tunnel, and are up to 2.85-times larger at X-shaped locations. This can be explained from the elasticity theory. Assuming a no-slip condition between the soil and structure, the solution for the moment in a circular tunnel during a seismic event is presented as [7]:
M (θ) = −
6EIΔ π cos 2(θ + ) d 2 (1 − υ2) 4
R = (M1 − M0)/ M1
(7)
where M0, and M1 are the peak bending moments of a tunnel with and without an isolation layer, respectively. For convenience, the thickness of isolation layer is considered identical, when conducting tests of tunnels with different cross-section dimensions. The d/t ratio is defined as the outer diameter of the tunnel divided by the thickness of the isolation layer. It thus is clear that the d/t ratios of small cross-section tunnel and large cross-section tunnel are 6 and 12 respectively. Fig. 17 shows the bending moment reduction at X-shaped locations under different excitations. From the test results under the excitations of a 150-Hz sinusoidal wave and a Wolong wave, it can be seen that smaller d/t ratio leads to greater reductions in dynamic bending moment, of up to 30.0% and 21.4% for the small and large cross-section tunnels, respectively. That is, the isolation layer is more effective in reducing dynamic bending moment of tunnels with a small cross-section than with a large cross-section. The isolation layer decreases the internal forces by absorbing the deformation of the surrounding soil. Because the thickness of the isolation layer is the same in the two tested situations, the influence of the isolation layer is greater on the smaller crosssection tunnel. Thus, smaller d/t ratio leads to better absorption of soil deformation and reduces structural response. It should be noted that the average reductions are about 22.7% and 19.6% at 45°location, and 11.5% and 14.5% at 135° location for small and large cross-section tunnels. Comparing the Fourier amplitude spectra of acceleration response
(6)
where Δ is the lining diametric deflection, E is the Young's modulus of the lining, v is the Poisson's ratio of the lining, d is the outer diameter of tunnel, θ is an angular position measured clockwise from the horizontal axis of cross-section, I = bt3/12 is moment of inertial of the tunnel cross-section in unit width, and b and t are unit width and thickness of the lining, respectively. In the present paper, E and v of tunnels with different cross-section dimensions are identical, because the same model material is used. Thus, seen from Eq. (6) directly, the moment in tunnel is proportional to I and Δ, and inversely proportional to d2. In practice design, t is about 5–6% of d, then I/d2 is about (1.04×10−5−1.8×10−5 ) d. On the other hand, the larger diameter the tunnel, the more flexible the structure. That leads to larger deformation (Δ) and then larger bending moments in larger tunnel than in smaller
182
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 12. Time histories and Fourier amplitude spectra of acceleration response of tunnel (D = 60 mm).
because the d/t ratio is smaller in the small cross-section tunnel, and the influence of the isolation layer is greater on the smaller cross-section tunnel with the thinner lining. This is in good accordance with the reduction in dynamic bending moment results.
of the large cross-section tunnel (see the right panel of Fig. 12) with those of the small cross-section tunnel (see the right panel of Fig. 13), it can be found that the effect of the isolation layer on acceleration frequency content of the small cross-section tunnel is much greater. This is
183
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 13. Time histories and Fourier amplitude spectra of acceleration response of tunnel (D = 120 mm).
4. Conclusions
comparative dynamic centrifuge tests. The following conclusions are drawn from six groups of centrifuge tests:
In the present paper, the seismic efficiency of isolation layer in a shield tunnel is verified and the influence of cross-section dimension on seismic isolation effectiveness are investigated by conducting
(1) The isolation layer decreases the dynamic bending moment of the shield tunnel. Seen from the absolute value, the maximum dynamic
184
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 14. Mechanism of isolation layer on shock absorption.
Fig. 15. Peak values of dynamic bending moments of different dimension tunnels with/without isolation layer.
may generally increase the dynamic bending moment owing to transverse stiffness reduction. Because the larger diameter the tunnel, the more flexible the structure. That mainly leads to larger deformation (Δ) and then larger bending moments in larger tunnel than in smaller tunnel. In the present test, the internal forces of large cross-section tunnel were up to 2.85-times greater than that of small cross-section tunnel at X-shaped locations. (4) For the same thickness of isolation layer, the smaller cross-section tunnel is more effective in decreasing structural response because
bending moment reductions occur at the X-shaped locations of the tunnel cross-section, where the maximum dynamic bending moments also occur. Seen from the percentage reductions, the reductions would be almost uniform at all locations. (2) The mechanism of isolation layer on structural response reduction is clarified. That is isolation layer absorbs surrounding soil deformation. Thus, it reduces the deformation of tunnel lining, and further decreases the dynamic bending moment of tunnel lining. (3) In practice, increasing the cross-section dimensions of the tunnel
185
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
Fig. 17. Reduction percentage of dynamic bending moment at X-shaped locations.
Acknowledgments This research was supported by the National Natural Science Foundation of China (Grant No. 41472246) and Key laboratory of Transportation Tunnel Engineering (TTE2014-01). Both supports are gratefully acknowledged. References [1] Wang W, Wang T, Su J, Lin C, Seng C. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi earthquake. Tunn Undergr Sp Tech 2001;16(3):133–50. http://dx.doi.org/10.1016/S0886-7798(01)00047-5. [2] SKLDRCE (State Key Laboratory for Disaster Reduction in Civil Engineering). Seismic hazards in Wenchuan earthquake. Shanghai: Tongji University Press; 2008(In Chinese). [3] Yamada T, Nagatani H, Ohbo N, Izawa J, Shigesada H, Kusakabe O. Seismic performance of flat cross-sectional tunnel with countermeasures. In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, B.C., Canada; 2004. No.706 〈http://www.iitk.ac.in/nicee/wcee/article/13_706.pdf〉. [4] Kusakabe O, Takemura J, Takahashi A, Izawa J, Shibayama S. Physical modeling of seismic responses of underground structures. In: Proceedings of the 12th international conference of international association for computer methods and advances in geomechanics, Goa, India; 2008. p. 1459–74. [5] Zhang WW, Jin XL, Yang ZH. Combined equivalent & multi-scale simulation method for 3-D seismic analysis of large-scale shield tunnel. Eng Comput 2014;31(3):584–620. http://dx.doi.org/10.1108/EC-02-2012-0034. [6] Penzien J, Wu CL. Stresses in linings of bored tunnels. Earthq Eng Struct Dyn 1998;27(3):283–300. http://dx.doi.org/10.1002/(SICI)1096–9845(199803) 27:33.0.CO;2-T. [7] Penzien J. Seismically induced racking of tunnel linings. Earthq Eng Struct Dyn 2000;29(5):683–91. http://dx.doi.org/10.1002/(SICI)1096–9845(200005) 29:53.0.CO;2-1. [8] Wang J. Seismic design of tunnels: a simple state-of-the-art design approach. Monograph 7. New York: Parsons, Brinckerhoff: Quade and Douglas Inc; 1993. [9] Liu LY, Chen ZY, Yuan Y. Seismic design and analysis of large-size shield tunnels. Part I: parametric study. Appl Mech Mater 2012;105–107:1299–303. http://dx.doi. org/10.4028/www.scientific.net/AMM.105-107.1299. [10] Yamada T, Nagatani H, Igarashi H, Takahashi A. Centrifuge model tests on circular and rectangular tunnels subjected to large earthquake-induced deformation. In: Proceedings of the 3rd symposium on geotechnical aspects of underground construction in soft ground; 2002. p. 673–8. [11] Takahashi A, Takemura J, Suzuki A, Kusakabe O. Development and performance of
Fig. 16. Absolute reduction of dynamic bending moment.
smaller tunnel has a larger t/d ratio and more soil deformation is absorbed. Thus, the isolation layer reduces the structural response of the small cross-section tunnel more effectively than of the large cross-section tunnel. The maximum reduction in dynamic bending moments were over 40% and 21.4% for the small cross-section tunnel and the large cross-section tunnel, respectively. It should be noted that, from the average reduction rate aspect, they were of 25.6% and 12.4% for the small cross-section tunnel and the large cross-section tunnel, respectively. 186
Soil Dynamics and Earthquake Engineering 109 (2018) 173–187
Z. Chen et al.
[12] [13]
[14]
[15]
[16] Hashash YMA, Park D, Yao IC. Ovaling deformations of circular tunnels under seismic loading, an update on seismic design and analysis of underground structures. Tunn Undergr Sp Technol 2005;20(5):435–41. http://dx.doi.org/10.1016/j. tust.2005.02.004. [17] Suzuki T, Tamura S. Proposal of evaluation method of seismic isolation effect on shield tunnel. J JPN Soc Civil Eng 1995;525:275–85. [In Japanese]. [18] Unjoh S, Hoshikuma JI, Suzuki T, Tanaka T. Seismic isolation system and seismic isolation design applied to underground structures. J Tunn Eng JSCE 1998;8:31–8. http://dx.doi.org/10.11532/journalte1991.8.31. [In Japanese]. [19] Hashash YMA, Hook JJ, Schmidt B, Yao IC. Seismic design and analysis of underground structure. Tunn Undergr Sp Technol 2001;16(4):247–93. http://dx.doi.org/ 10.1016/S0886-7798(01)00051-7.
an active type shear box in a centrifuge. Int J Phys Model Geotech 2001;1(2):1–17. http://dx.doi.org/10.1680/ijpmg.2001.010201. Taylor RN. Geotechnical centrifuge technology. London: Chapman & Hall; 1995. Suzuki T, Kasuda K, Kobayashi M, Fukuda K, Ikeno M. Experimental study on the silicone-based material for seismic isolation system for urban tunnels. J JPN Soc Civil Eng 1996;534:69–76. http://dx.doi.org/10.2208/jscej.1996.534_69. Brennan AJ, Thusyanthan NI, Madabhushi SPG. Evaluation of shear modulus and damping in dynamic centrifuge tests. J Geotech Geoenviron Eng 2005;131(12):1488–97. http://dx.doi.org/10.1061/(ASCE)1090-0241(2005) 131:12(1488). Shukla DK, Rizzo PC, Stephenson DE. Earthquake load analysis of tunnels and shafts. In: Proceedings of the symposium on rock mechanics 21st, rock mechanics: a state of the art, University of Missouri, Rolla; 1980. p. 622–31.
187
