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Model test study on the dynamic response of the portal section of two parallel tunnels in a seismically active area
Tunnelling and Underground Space Technology 26 (2011) 391–397
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Model test study on the dynamic response of the portal section of two parallel tunnels in a seismically active area Sun Tiecheng a,⇑, Yue Zurun a,1, Gao Bo b,2, Li Qiang a,3, Zhang Yungang a,4 a b
Shijiazhuang Tiedao University, Hebei, Shijiazhuang 050043, China Southwest Jiaotong University, Sichuan, Chengdu 610031, China
a r t i c l e
i n f o
Article history: Received 7 July 2010 Received in revised form 8 November 2010 Accepted 15 November 2010 Available online 21 December 2010 Keywords: Earthquake Two parallel tunnels Dynamic response Model test
a b s t r a c t A model test of the portals of two parallel tunnels is carried out to learn about the dynamic response of tunnel liner and the interaction between surrounding rock and liner in earthquakes. The experiment results show that: first, when the seismic acceleration traverses the model material, the low-frequency segment of seismic acceleration is magnified and the high-frequency segment of seismic acceleration is attenuated; second, the horizontal shear failure of the surrounding rock is caused by the interaction between the surrounding rock and the tunnel liner, and the cracks in the surrounding rock grow nearly in the same direction, however, because of the different constraints on the tunnel liner by the surrounding rock outside the tunnel, the destruction degree is different; third, the liner cracks of the left tunnel with short length appear mainly at the left tunnel entrance, the cracks of right tunnel with large length appear mainly at the right tunnel entrance and the tunnel cross-section nearly which is in the same vertical plane with the left tunnel portal, and the liner cracks are distributed mainly on the closer side of two liners between the two holes; finally, in the same vertical testing cross-section, the liner maximal strain at the inner sides between two tunnels is greater than outer sides. In addition, the cross-section maximal strain on the right tunnel decreases with the increasing distance between the tested cross-section and a reference vertical plane containing the left tunnel portal. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction It is well known that the analysis method for ground structures is not appropriate absolutely for the underground structures because the dynamic response of the ground and underground structures in earthquakes is quite different (Gao, 1996; Lin, 1990a,b; Lin and Liang, 1996). On May 12, 2008, a violent earthquake struck Wenchuan town and destroyed many tunnels to various degrees in the region, and the tunnel damage in the portal section was particularly serious (Wang et al., 2009). So, the dynamic response of underground structures to earthquakes emerges as significant research direction. Three methods are mainly used for the seismic study of underground structures: seismological observation, model tests and theoretical analysis. The model tests are divided into artificial seismic ⇑ Corresponding author. Tel.: +86 13315117871. E-mail addresses: [email protected] (T. Sun), [email protected] (Z. Yue), [email protected] (B. Gao), [email protected] (Q. Li), [email protected] (Y. Zhang). 1 Tel.: +86 13931120937. 2 Tel.: +86 13808019590. 3 Tel.: +86 15032693410. 4 Tel.: +86 15931193623. 0886-7798/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2010.11.010
focus tests and shaking table tests. Shaking table tests are divided into simple harmonic vibration tests and simulated earthquake shaking tests. Because the artificial seismic force is weak, it is difficult to reflect the nonlinear characteristics of structures and the influence on the earthquake response of underground structures by the foundation fracture when using artificial seismic focus tests and the method should not be adopted (Hu, 2004). In addition, the superposition principle cannot be used in nonlinear studies. Hence, the simulated earthquake shaking test is used for antiseismic studied in general. This test method is applied widely (Zhang et al., 2008; Liu et al., 2008; Wang et al., 2008) because it can help determine the seismic response characteristics of underground structures and the interaction with foundations. At the same time, the experiment cost is lower than other test methods. Although the tunnel type of two parallel tunnels with staggered distance between portals is adopted widely in highway tunnels, the dynamic response of this tunnel type and the tunnel slope of the surrounding rock under seismic loads are not well understood. A simulated earthquake test is carried out in the laboratory to study the dynamic response of this tunnel type. The tunnel model is based on a real tunnel which is located in a high-intensity earthquake area in the southwest. The tunnel model is shown in Fig. 1a and b.
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to single liner approach because the pouring of a composite liner is very difficult. On the basis of equivalent stiffness principle, the thickness of model liner is 2.0 cm, and C25 concrete is adopted. When the liner is made, it is difficult to include rebar because the model liner is too thin. There is no reinforcement in the tunnel portal, so, similarity ratio of rebar is not considered. Material parameters of the tunnel prototype were adopted from real engineering data. The material parameters which are used in model test are listed in Tables 2 and 3. The main items of the test are: (a) cracking along natural weakness line and development of ground crack; (b) cracking along natural weakness line and development of tunnel lining cracks; (c) strain of tunnel lining; and (d) acceleration of invert in tunnel entrance. 2.2. Test methods
(a) Design & geometry size of model The model casing has no cover, and its inner complete size is 2.5 m length, 2.5 m width and 2.0 m height. In the back end of the model casing, a 25 cm hole is set where the model liner is set in order to observe the development of liner cracks; in the center of the model casing front, a hatch which is as high as the top of the box is set for installing the tunnel model and materials easily, and its geometry size is 0.9 m width and 1.7 m height. The photo of the model casing front is shown in Fig. 2. The probability of encountering an earthquake in the building process of a tunnel is very low, so the model test does not simulate the excavation of the tunnel. The prefabricated liner is set in surrounding rock directly, and the filling material inside the space for the liner is cleaned up after the material simulating the surrounding rock is installed. The filling material inside liner space is mixed with wood sawdust and fine sand according to a certain proportion with water. If there were nothing in the inner space of liner, the liner model would be crushed by the surrounding rock material in the process of backfill. The seismic load acts in the horizontal direction and was perpendicular direction to the longitudinal tunnel. The measures
Acceleration transducer
(b) Completed model Fig. 1. The test-model (unit: mm).
2. Items and methods of test 2.1. Similarity rule and test items
Table 2 Rock parameters of the model and prototype.
The test was carried out in the laboratory and seven group parameters were simulated. The similarity ratios of the parameters are listed in Table 1, where physical variables with subscript p are used to describe the prototype, and physical variables with subscript m are used for the model. In the similarity ratios, two groups are used to simulate parameters of seismic waves, the others are used to simulate surrounding rock and liner material. A homogeneous material is used to simulate the actual surrounding rock material, while the stratum characteristic of the surrounding rock is not considered because of the complexity of the simulation test. In addition, the design grade of sprayed concrete is C20 (characteristic value of cubic concrete compressive strength is 20 MPa), and its thickness is 24 cm; the design grade of concrete is C25 (characteristic value of cubic concrete compressive strength is 25 MPa), and its thickness is 50 cm. The model liner is designed according
Name
Binding power c (kPa)
Friction angle u ð Þ
Young’s modulus E (MPa)
Density q (g/cm3)
Rock prototype Rock model
109.35 2.43
29.2 29.2
1.35e3 30.0
2.02 1.35
Table 3 Tunnel-liner parameters of the model and prototype. Name
Density q (g/cm3)
Poisson’s ratio l
Young’s modulus E (MPa)
Compression strength r (MPa)
Liner prototype Liner model
2.5 1.67
0.2 0.2
29.5e3 656
12.5 0.30
Table 1 Similarity ratio of the parameters in test. Name
Geometry similarity ratio C L ¼ Lmp
C E ¼ Emp
Cq ¼ q p
Binding power similarity ratio c C C ¼ cmp
30
45
1.5
45
L
Similarity ratio
Young’s modulus similarity ratio E
Density similarity ratio q
m
Friction angle similarity ratio u ð Þ
Acceleration similarity ratio C a ¼ Amp
C f ¼ fmp
1.0
1.0
0.1825
A
Frequency similarity ratio f
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Acceleration /g
(a) 0.8 0.4
0.0
-0.4
-0.8 0
10
20
30
40
Time /s (b)
8.0
Fig. 2. Front view of model casing.
welding the 5 cm 5 cm angle steel and covering the model casing bottom with gravels were adopted to assure synchronous vibration on the surrounding rock and model casing; in addition, the PVC plates which were used to absorb seismic wave caused by reflection of box are adhibited on the two inner sides of box. Considering that the length of tunnel model was finite, the perspex plate is set between the liners and the steel plate of model casing for decreasing boundary effect when the liners are emplaced. Before the perspex plate is emplaced, Vaseline is daubed on the double faces of perspex plate and the steel plate of model casing, which decreases the boundary effect to a certain extent. In the testing, the cracking along natural weakness line and development of ground cracks and liner cracks are recorded by high speed video; the micro-lens is used to observe the liner cracks which are located in the middle part of the liner, and the data are transported to a computer which is installed outside the shaking table for recording. Further observations and measurements were conducted when the vibration stopped. The load which is used in the test was provided by a design institute. The maximal amplitude of seism acceleration is 0.67 g, and the duration time of strong motion is 20 s. The curve of acceleration amplitude with time and the 3-D relationship surface which is gained by using the method of Hilbert–Huang transformation are shown in Fig. 3. From the 3-D figure, it is known that the frequency segment which contains more energy is wider. The seismic load input to the loading system needed to be transformed according to the frequency similarity ratio. The loading system is SCHENCK; the control system is: Tektronix TDS2022; the collection system of data is: DDS32 type digital dynamic signal collection system with 32 channels.
Amplitude / m s-2
6.0 7.5 5.0
4.0
2.5
0
0 0
10
2.0
Time /s
0.0
20 5
10
30 15
Frequency / Hz
40 20
25
50
Fig. 3. The curve of acceleration–time and 3-D relationship surface between acceleration amplitude, time, and frequency.
the liner collapses. The acceleration data of the inverted arch of tunnel and the model casing outside were recorded to the 4th load, and the data are transformed by means of the transformation method of time-frequency. The FFT curves are shown in Fig. 5. From Figs. 4 and 5 it can be seen: (a) The MCacc is diminishing with the increasing MaxMH, and then the value of MCacc tends to be 1.0. In addition, it was seen that the backfill of the model casing is closely-grained and contact closely with the tunnel model. (b) There is an amplification effect on the input acceleration by the model filling in the vibration process. (c) The spectrum characteristics of input load are changed obviously after it passes through the model filling. The amplitude is augmented in the range of 0–15 Hz, but is decreased in the range of high frequency. When the earthquake loads are the same, the MCacc remains the same if model casing is filled densely; or, the MCacc are not the same. For assuring the veracity of the test data, the model should be vibrated again until the MCacc becomes the same for the next test step when the earthquake loads are the same.
3. Test result analysis
3.2. Ground cracks
3.1. Model acceleration
The white markers are used to mark the location of ground cracks after the 6th load. The distribution location of cracks is shown in Fig. 6, and the effect picture of the crack distribution is shown in Fig. 7 in order to express the location of cracks clearly. From Figs. 6 and 7 it is known:
The seismic wave is loaded six times in the horizontal direction in order to observe the destruction of the tunnel model. The acceleration peak values of tunnel inverted arch and model casing outside are listed in Table 4 after the load application. If MaxTH =MaxMH is defined as magnification coefficient of acceleration (abbr.MCacc), the curve of MCacc and MaxMH is shown in Fig. 4. When the input acceleration is big, the testing acceleration can express reliably the dynamic characteristic of the tunnel before
(a) Although the development trend of the cracks located on the slope in the left tunnel is the same as the cracks in the right tunnel, they are different on the amount, the depth and the extending length of the cracks.
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Table 4 The acceleration peak values of every loading process (unit: g). Load order
Input
1 2 3 4 5 6
0.3 0.3 0.4 0.5 0.6 0.8
Inverted arch of tunnel
Outside of model casing
MaxTH
MinTH
MaxTV
MinTV
MaxMH
MinMH
MaxMV
MinMV
0.443 0.443 0.464 0.570 0.590 0.754
0.307 0.307 0.381 0.490 0.500 0.750
0.078 0.078 0.067 0.089 0.116 0.118
0.067 0.067 0.058 0.073 0.102 0.110
0.311 0.311 0.338 0.470 0.535 0.743
0.249 0.249 0.330 0.400 0.516 0.700
0.127 0.127 0.142 0.152 0.165 0.177
0.124 0.124 0.138 0.150 0.158 0.161
Explain: TH – horizontal direction of tunnel, TV – vertical direction of tunnel, MH – horizontal direction of model casing, MV – vertical direction of model casing.
MCacc
1.50 1.35 1.20 1.05 0.311
0.311
0.338
0.470
0.535
0.743
MaxMH / g
Amplitude / m s-2
Fig. 4. The curve of magnification coefficient of acceleration and input seismic load.
10.0 Fig. 6. The distribution of ground cracks after earthquake.
8.0 6.0 4.0 2.0 0 0
30
60
90
120
150
120
150
Frequency /Hz
Amplitude / m s-2
(a) FFT curve of liner 7.5 6.0 4.5 3.0 1.5 0
0
30
60
90
Frequency /Hz (b) FFT curve of model casing outside Fig. 5. FFT curves of test acceleration.
There are cracks which develop as the model ‘‘X’’ along 45° location in the surrounding rock at tunnel spandrel. On the slope of right tunnel, the amount of cracking is greater, and the extending length of crack is longer, and the depth and width is larger than the slope cracks which are located on the left tunnel. In addition, the width of this widest crack is 3.5 mm more or less in surrounding rock of right tunnel, and the width of the crack is 1.2 mm only in surrounding rock of left tunnel.
the stress concentration is more serious at the location where the left tunnel slope intersects with the right tunnel slope. With the increase of the vibration amplitude and the load duration of model casing, the surrounding rocks reach the limit state of the crack, and then the first crack appears here.
(b) The first crack of ground appears at the location where the left tunnel slope intersects with the right tunnel slope.
(c) The ground crack is less where the embedded depth of tunnel is deeper.
Because the constraint conditions on the liner by the surrounding rock is different between left tunnel and right tunnel, the dynamic stress concentration appears in the location where the geometry size of slope is changed when the vibration begins, and
The constraint condition on the liner by the surrounding rock is strengthened with increasing embedding depth of tunnel, and the constraint degrees of left tunnel and right tunnel tend to be equal. In addition, with the increase of the distance between the transect
Fig. 7. The distribution effect picture of ground cracks.
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3.3. Liner cracks The photos of tunnel structure on the whole cannot describe distinctly the distribution of cracks because the width of cracks is very narrow. The cracks in the liner are drawn in Fig. 8 according to the test results, and some conclusions can be drawn from Fig. 8: (a) There are distinct differences on the amount of cracks, the through degree of crack and the width of crack between left tunnel portal and right tunnel portal. Although the amount of cracks located at the left tunnel portal is bigger than it is at the right tunnel portal, the amount of through cracks which are located at the left tunnel portal are less and the crack width is smaller than at the right tunnel portal. The through cracking in the left tunnel portal is located at the upper side of the left spandrel, where there is only one through crack, and the widest
crack is 0.7 mm. The through cracks of the right tunnel portal are located at the left spandrel, the left arch springing and the right arch springing, and such through cracks are more than three, in addition, the widest crack is 1.5 mm. (b) The distribution laws of the liner cracks of the left liner and the right liner along tunnel portal are different. The cracks of left tunnel are distributed mainly on tunnel portal, and the liner cracks decrease with the increase in the embedment depth of tunnel. The cracks of right tunnel are distributed mainly on the tunnel portal and near the tunnel cross-section which is in the same vertical plane with the left tunnel portal, and the liner cracks decrease with the increase of the embedment depth of tunnel although the speed of the crack decrease is slower than it is in the left tunnel. (c) The crack distribution in the same liner cross-section is different between the left tunnel liner and the right tunnel liner. The left liner cracks are distributed mainly on right arch springing and the right hance; and the right liner cracks are distributed mainly on the left arch springing and the left hance. In other words, the liner cracks are distributed mainly on the closer side of two liners between the two holes. In earthquakes, the instantaneous force acting on a liner is more than the force in static loading because of the interaction between the liner and the surrounding rock. The liner will crack if the internal force is greater than the material strength of tunnel lining. As mentioned above, the geometry of the surrounding rock changes sharply near the left tunnel portal, and it has a great effect on the restriction degree of the right tunnel, which leads to the difference of the stress between different locations in earthquake. The forced state at the portal has some differences between left tunnel and right tunnel because of the interaction of the forces. By the macroscopic phenomenon the differences are shown as follows: (1) the right tunnel cracks are distributed mainly at the tunnel portal and the tunnel cross-section whose plane contains the left
(a)
th The 6th test The 4 test cross-section cross-section The 3rd test cross-section The 2nd test cross-section The 1st test cross-section
(b)
Strain gauge located on crown of arch Strain gauge located on right arch springing Strain gauge located on left arch springing
Acceleration transducer
Strain gauge located on left arch springing
The 5th test cross-section
Left tunnel
Right tunnel Acceleration transducer
Strain gauge located on inverted arch Fig. 8. The crack distribution of tunnel lining.
Fig. 9. The position of sensing probes.
Strain gauge located on right arch springing
of liner and the portal of tunnel, the effect which is induced by the difference of constraint degree on surrounding rock to tunnel portal is being weakened gradually to the left tunnel and the right tunnel. Finally, the interaction between the surrounding rock and tunnel structure is diminishing, and the interaction between the surrounding rock and left tunnel is the same with the interaction between the surrounding rock and right tunnel. So, at the location where the embedding depth size of tunnel is big, the ground crack is less and there is no difference between the left tunnel and the right tunnel. It is known that the surface cracks of the front elevation in tunnel slopes develop as ‘‘X’’ model and the cracks of the surrounding rock covering the top of tunnel develop as a ‘‘scissors’’ model. The development model of the cracks is a macroscopic phenomenon caused by the horizontal shear failure of surrounding rock because of the nonsynchronous vibration between the lining structure and the surrounding rock under earthquake loads. The nonsynchronous vibration is caused by the different stiffness between the tunnel liner and the surrounding rock. In earthquakes, the distortion of the right tunnel liner is bigger than the left tunnel liner because the constraint degree on the right tunnel liner by the surrounding rock is weaker than it is on the left tunnel lining. Therefore, the interaction between the surrounding rock and the right tunnel is greater than the left tunnel. As a result, the crack characteristics of the surrounding rock of the right and left tunnel are different.
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tunnel portal; (2) although the amount of all cracks located in left tunnel portal is bigger than it is in the right tunnel portal, the amount of through cracks located in the left tunnel portal is less and the width of cracks is smaller than it is in the right tunnel portal. In addition, there are some annular cracks in the liner, which are made by the fixed end effect of the boundary. 3.4. Liner strains In the test, the 5 mm 2 mm strain gauges were used for the strain of the liner, and their disposals are showed in Fig. 9. The curves of liner strain versus time during the 4th load are shown in Fig. 10, and the maximal strains at all locations are shown in Fig. 11. From Figs. 10 and 11, it is known that:
(a) The maximal strains at the closer sides of two holes are greater than they are at other sides when the strains are located at the same test cross-section. The restriction provided by the surrounding rock in the inner sides of the two liners is less than outer sides because of the existence of another tunnel. So the stress and the strains of the inner sides of the two liners are greater than outer sides. The result has been verified in the liner cracks. At the 2nd test cross-section, the maximal strain outside the left arch springing is 32.5 microstrains and the maximal strain outside the right arch springing is 27.5 microstrains; at 3rd test cross-section, the maximal strain outside the left arch springing is 31 microstrains and the maximal strain outside right arch springing is 17.0 microstrains.
35
15
5
Stress ( με )
Stress ( με )
25
15
5
-5
-15 -5 0
5
10
15
20
25
-25
30
0
5
10
15
20
25
30
Time /s (a) Left arch springing outside of the 2nd test cross-section
Time /s (d) Right arch springing outside of the 3rd test cross-section
10
35
2.5 20
Stress ( με )
Stress ( με )
-5.0 -12.5 -20.0
5
-10 -27.5 -25
-35.0 0
5
10
15
20
25
0
30
Time /s (b) Right arch springing outside of the 2nd test cross-section
5
10
15
20
25
30
Time /s (e) Inverted-arch outside of the 1st test cross-section 25
35
15
Stress ( με )
Stress ( με )
25
15
5
-5
5
-5
-15
-25 0
5
10
15
20
25
30
Time /s (c) Left arch springing outside of the 3rd test cross-section
0
5
10
15
20
25
30
Time /s (f) Arch-crown outside of the 2nd test cross-section
Fig. 10. The curves of strain–time.
T. Sun et al. / Tunnelling and Underground Space Technology 26 (2011) 391–397
Stress ( με )
35 28 21 14 7 The 1st test cross-section
The 2nd test cross-section
The 3rd test cross-section
The 4th test cross-section
Testing location Fig. 11. The maximum strain of testing cross-section.
(b) The cross-section maximal strain on the right tunnel diminishes with increasing distance between the testing crosssection and the reference vertical plane which contains the left tunnel portal. The distance between the 2nd and 3rd testing cross-section and the reference vertical plane is 25 cm and 55 cm respectively. The test results show that the maximal strains of the left arch springing and right arch springing at the 2nd test cross-section are greater than those at the 3rd test cross-section. For the tunnel portal of two holes, the left tunnel portal has influence on the right tunnel in a range. The range is related to many factors which need to be confirmed in more experiments or some numerical simulation. It is one of the emphases for future study. (c) The strain baseline at every testing point is offset in the loading process and the offset cannot be eliminated after the vibration loading. In addition, the perpetual plastic strain at the top of arch is smaller than at the inverted arch of tunnel. The main reason for the offset of the strain baseline is that the permanent deformation of the tunnel liner happened due to the earthquake load which produced additional strain in the tunnel structure. The restriction in the inverted arch of the tunnel portal by the surrounding rock is weakest in the tunnel because at the portal the tunnel covering is thinnest and the tunnel gate is free. However, the amplitude of earthquake loads is magnified, and as a result, the inverted arch of tunnel portal is one of the most precarious locations and its permanent plastic strain is greater than that at any other location. 4. Conclusion (a) The MCacc decreases with an increase of MaxMH. In addition, when the seismic acceleration traverses the model material, the low-frequency segment of seismic acceleration is magnified and the high-frequency segment of seismic acceleration is attenuated. (b) The interaction between lining structure and the surrounding rock leads to the horizontal shear failure of surrounding rock in earthquakes. The degree of destructive cracking of the surrounding rock is dissimilar at the different locations because of the different constraint on the surrounding rock of the left liner and the right liner although the development trend of rock cracking is similar. The constraint condition of surrounding rock to the liner is strengthened with increasing embedment depth of the tunnel, and the constraint degrees
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of left tunnel and right tunnel tend to be equal. The interaction between the surrounding rock and the tunnel structure diminishes, and the interaction between the surrounding rock and the left tunnel is similar to the interaction between the surrounding rock and the right tunnel. Therefore, at the location of the largest embedment depth of the tunnel, the amount of the ground cracking is small and there is no difference between the left tunnel and the right tunnel. (c) The distribution laws of the liner cracks at the same crosssection is different between the left tunnel liner and the right tunnel liner, and there are distinct differences in the amount of cracks, the degree of through cracks and the width of cracks between the left tunnel portal and the right tunnel portal. The liner cracks of the left tunnel concentrates mainly at the left tunnel entrance, and the cracks of right tunnel concentrates mainly at the right tunnel entrance and near the tunnel cross-section which is in the same plane with the left tunnel portal, and there are more liner cracks on the inner sides between two holes than the outer sides. (d) In the same vertical cross-section, the liner maximal strain at the inner sides between two holes is greater than the outer sides, and the cross-section maximal strain on the right tunnel decreases with the increase of distance between the test cross-section and the reference vertical plane containing the left tunnel portal. In addition, the inverted arch of the tunnel portal is one of the most precarious locations. (e) Rebar is not used in tunnel portal, so, the cracks width of tunnel lining and the liner strains are bigger than those when rebar is used in tunnel partal in the test result. In addition, there are some differences between the test result and the real situation because the stratum characteristic and the cranny of surrounding rock are not considered in the model test.
Acknowledgements Heartfelt thanks to my teachers, Ying-xue Wang, Yu-sheng Shen and Jia-mei Zhou in School of Civil Engineering of Southwest Jiaotong University, this study should not be performed perfectly if there were no selfless help from them. Thanks to the teachers of National Key Laboratory of Traction Power and Geotechnical Laboratory of Southwest Jiaotong University for providing a great deal of help. References Gao, Qu-qing, 1996. The Memoir on Tunnel & Underground Structure of Gao Quqing. China Railway Publishing House, Beijing. HU, Yuxian, 2004. Earthquake Engineering, second ed. Seismological Press, Beijing. Lin, Gao, 1990a. Summarization on antiseismatic analysis of under-ground structure (A). World Earthquake Engineering 6 (2), 1–9. Lin, Gao, 1990b. Summarization on antiseismatic analysis Of underground structure (B). World Earthquake Engineering 6 (3), 1–10. Lin, Gao, Liang, Qing-huai, 1996. Aseismic design of underground structures. China Civil Engineering Journal 29 (1), 15–24. Liu, Guang-lei, Song, Er-xiang, Liu, Hua-bei, et al., 2008. Dynamic centrifuge tests on seismic response of tunnel in saturated sandy foundation. Rock and Soil Mechanics 29 (8), 2070–2076. Zheng-zheng Wang, Bo Gao, Tie-cheng Sun, et al., 2008. Seismic response analysis of the tunnel with accumulated damage and crack effect in shaking table test. In: The 14th World Conference on Earthquake Engineering, Beijing, China, October 12–17. Wang, Zheng-zheng, Gao, Bo, Jiang, Yuan-jun, et al., 2009. Investigation and assessment on mountain tunnels and geotechnical damage after the Wenchuan earthquake. Science in China Series E: Technological Sciences 52 (2), 546–558. Zhang, Qing-song, Li, Li-ping, Li, Shu-cai, et al., 2008. Experimental study of blasting dynamic vibration of closely adjacent tunnels. Rock and Soil Mechanics 29 (10), 2655–2666.
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Model test study on the dynamic response of the portal section of two parallel tunnels in a seismically active area Sun Tiecheng a,⇑, Yue Zurun a,1, Gao Bo b,2, Li Qiang a,3, Zhang Yungang a,4 a b
Shijiazhuang Tiedao University, Hebei, Shijiazhuang 050043, China Southwest Jiaotong University, Sichuan, Chengdu 610031, China
a r t i c l e
i n f o
Article history: Received 7 July 2010 Received in revised form 8 November 2010 Accepted 15 November 2010 Available online 21 December 2010 Keywords: Earthquake Two parallel tunnels Dynamic response Model test
a b s t r a c t A model test of the portals of two parallel tunnels is carried out to learn about the dynamic response of tunnel liner and the interaction between surrounding rock and liner in earthquakes. The experiment results show that: first, when the seismic acceleration traverses the model material, the low-frequency segment of seismic acceleration is magnified and the high-frequency segment of seismic acceleration is attenuated; second, the horizontal shear failure of the surrounding rock is caused by the interaction between the surrounding rock and the tunnel liner, and the cracks in the surrounding rock grow nearly in the same direction, however, because of the different constraints on the tunnel liner by the surrounding rock outside the tunnel, the destruction degree is different; third, the liner cracks of the left tunnel with short length appear mainly at the left tunnel entrance, the cracks of right tunnel with large length appear mainly at the right tunnel entrance and the tunnel cross-section nearly which is in the same vertical plane with the left tunnel portal, and the liner cracks are distributed mainly on the closer side of two liners between the two holes; finally, in the same vertical testing cross-section, the liner maximal strain at the inner sides between two tunnels is greater than outer sides. In addition, the cross-section maximal strain on the right tunnel decreases with the increasing distance between the tested cross-section and a reference vertical plane containing the left tunnel portal. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction It is well known that the analysis method for ground structures is not appropriate absolutely for the underground structures because the dynamic response of the ground and underground structures in earthquakes is quite different (Gao, 1996; Lin, 1990a,b; Lin and Liang, 1996). On May 12, 2008, a violent earthquake struck Wenchuan town and destroyed many tunnels to various degrees in the region, and the tunnel damage in the portal section was particularly serious (Wang et al., 2009). So, the dynamic response of underground structures to earthquakes emerges as significant research direction. Three methods are mainly used for the seismic study of underground structures: seismological observation, model tests and theoretical analysis. The model tests are divided into artificial seismic ⇑ Corresponding author. Tel.: +86 13315117871. E-mail addresses: [email protected] (T. Sun), [email protected] (Z. Yue), [email protected] (B. Gao), [email protected] (Q. Li), [email protected] (Y. Zhang). 1 Tel.: +86 13931120937. 2 Tel.: +86 13808019590. 3 Tel.: +86 15032693410. 4 Tel.: +86 15931193623. 0886-7798/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2010.11.010
focus tests and shaking table tests. Shaking table tests are divided into simple harmonic vibration tests and simulated earthquake shaking tests. Because the artificial seismic force is weak, it is difficult to reflect the nonlinear characteristics of structures and the influence on the earthquake response of underground structures by the foundation fracture when using artificial seismic focus tests and the method should not be adopted (Hu, 2004). In addition, the superposition principle cannot be used in nonlinear studies. Hence, the simulated earthquake shaking test is used for antiseismic studied in general. This test method is applied widely (Zhang et al., 2008; Liu et al., 2008; Wang et al., 2008) because it can help determine the seismic response characteristics of underground structures and the interaction with foundations. At the same time, the experiment cost is lower than other test methods. Although the tunnel type of two parallel tunnels with staggered distance between portals is adopted widely in highway tunnels, the dynamic response of this tunnel type and the tunnel slope of the surrounding rock under seismic loads are not well understood. A simulated earthquake test is carried out in the laboratory to study the dynamic response of this tunnel type. The tunnel model is based on a real tunnel which is located in a high-intensity earthquake area in the southwest. The tunnel model is shown in Fig. 1a and b.
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to single liner approach because the pouring of a composite liner is very difficult. On the basis of equivalent stiffness principle, the thickness of model liner is 2.0 cm, and C25 concrete is adopted. When the liner is made, it is difficult to include rebar because the model liner is too thin. There is no reinforcement in the tunnel portal, so, similarity ratio of rebar is not considered. Material parameters of the tunnel prototype were adopted from real engineering data. The material parameters which are used in model test are listed in Tables 2 and 3. The main items of the test are: (a) cracking along natural weakness line and development of ground crack; (b) cracking along natural weakness line and development of tunnel lining cracks; (c) strain of tunnel lining; and (d) acceleration of invert in tunnel entrance. 2.2. Test methods
(a) Design & geometry size of model The model casing has no cover, and its inner complete size is 2.5 m length, 2.5 m width and 2.0 m height. In the back end of the model casing, a 25 cm hole is set where the model liner is set in order to observe the development of liner cracks; in the center of the model casing front, a hatch which is as high as the top of the box is set for installing the tunnel model and materials easily, and its geometry size is 0.9 m width and 1.7 m height. The photo of the model casing front is shown in Fig. 2. The probability of encountering an earthquake in the building process of a tunnel is very low, so the model test does not simulate the excavation of the tunnel. The prefabricated liner is set in surrounding rock directly, and the filling material inside the space for the liner is cleaned up after the material simulating the surrounding rock is installed. The filling material inside liner space is mixed with wood sawdust and fine sand according to a certain proportion with water. If there were nothing in the inner space of liner, the liner model would be crushed by the surrounding rock material in the process of backfill. The seismic load acts in the horizontal direction and was perpendicular direction to the longitudinal tunnel. The measures
Acceleration transducer
(b) Completed model Fig. 1. The test-model (unit: mm).
2. Items and methods of test 2.1. Similarity rule and test items
Table 2 Rock parameters of the model and prototype.
The test was carried out in the laboratory and seven group parameters were simulated. The similarity ratios of the parameters are listed in Table 1, where physical variables with subscript p are used to describe the prototype, and physical variables with subscript m are used for the model. In the similarity ratios, two groups are used to simulate parameters of seismic waves, the others are used to simulate surrounding rock and liner material. A homogeneous material is used to simulate the actual surrounding rock material, while the stratum characteristic of the surrounding rock is not considered because of the complexity of the simulation test. In addition, the design grade of sprayed concrete is C20 (characteristic value of cubic concrete compressive strength is 20 MPa), and its thickness is 24 cm; the design grade of concrete is C25 (characteristic value of cubic concrete compressive strength is 25 MPa), and its thickness is 50 cm. The model liner is designed according
Name
Binding power c (kPa)
Friction angle u ð Þ
Young’s modulus E (MPa)
Density q (g/cm3)
Rock prototype Rock model
109.35 2.43
29.2 29.2
1.35e3 30.0
2.02 1.35
Table 3 Tunnel-liner parameters of the model and prototype. Name
Density q (g/cm3)
Poisson’s ratio l
Young’s modulus E (MPa)
Compression strength r (MPa)
Liner prototype Liner model
2.5 1.67
0.2 0.2
29.5e3 656
12.5 0.30
Table 1 Similarity ratio of the parameters in test. Name
Geometry similarity ratio C L ¼ Lmp
C E ¼ Emp
Cq ¼ q p
Binding power similarity ratio c C C ¼ cmp
30
45
1.5
45
L
Similarity ratio
Young’s modulus similarity ratio E
Density similarity ratio q
m
Friction angle similarity ratio u ð Þ
Acceleration similarity ratio C a ¼ Amp
C f ¼ fmp
1.0
1.0
0.1825
A
Frequency similarity ratio f
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Acceleration /g
(a) 0.8 0.4
0.0
-0.4
-0.8 0
10
20
30
40
Time /s (b)
8.0
Fig. 2. Front view of model casing.
welding the 5 cm 5 cm angle steel and covering the model casing bottom with gravels were adopted to assure synchronous vibration on the surrounding rock and model casing; in addition, the PVC plates which were used to absorb seismic wave caused by reflection of box are adhibited on the two inner sides of box. Considering that the length of tunnel model was finite, the perspex plate is set between the liners and the steel plate of model casing for decreasing boundary effect when the liners are emplaced. Before the perspex plate is emplaced, Vaseline is daubed on the double faces of perspex plate and the steel plate of model casing, which decreases the boundary effect to a certain extent. In the testing, the cracking along natural weakness line and development of ground cracks and liner cracks are recorded by high speed video; the micro-lens is used to observe the liner cracks which are located in the middle part of the liner, and the data are transported to a computer which is installed outside the shaking table for recording. Further observations and measurements were conducted when the vibration stopped. The load which is used in the test was provided by a design institute. The maximal amplitude of seism acceleration is 0.67 g, and the duration time of strong motion is 20 s. The curve of acceleration amplitude with time and the 3-D relationship surface which is gained by using the method of Hilbert–Huang transformation are shown in Fig. 3. From the 3-D figure, it is known that the frequency segment which contains more energy is wider. The seismic load input to the loading system needed to be transformed according to the frequency similarity ratio. The loading system is SCHENCK; the control system is: Tektronix TDS2022; the collection system of data is: DDS32 type digital dynamic signal collection system with 32 channels.
Amplitude / m s-2
6.0 7.5 5.0
4.0
2.5
0
0 0
10
2.0
Time /s
0.0
20 5
10
30 15
Frequency / Hz
40 20
25
50
Fig. 3. The curve of acceleration–time and 3-D relationship surface between acceleration amplitude, time, and frequency.
the liner collapses. The acceleration data of the inverted arch of tunnel and the model casing outside were recorded to the 4th load, and the data are transformed by means of the transformation method of time-frequency. The FFT curves are shown in Fig. 5. From Figs. 4 and 5 it can be seen: (a) The MCacc is diminishing with the increasing MaxMH, and then the value of MCacc tends to be 1.0. In addition, it was seen that the backfill of the model casing is closely-grained and contact closely with the tunnel model. (b) There is an amplification effect on the input acceleration by the model filling in the vibration process. (c) The spectrum characteristics of input load are changed obviously after it passes through the model filling. The amplitude is augmented in the range of 0–15 Hz, but is decreased in the range of high frequency. When the earthquake loads are the same, the MCacc remains the same if model casing is filled densely; or, the MCacc are not the same. For assuring the veracity of the test data, the model should be vibrated again until the MCacc becomes the same for the next test step when the earthquake loads are the same.
3. Test result analysis
3.2. Ground cracks
3.1. Model acceleration
The white markers are used to mark the location of ground cracks after the 6th load. The distribution location of cracks is shown in Fig. 6, and the effect picture of the crack distribution is shown in Fig. 7 in order to express the location of cracks clearly. From Figs. 6 and 7 it is known:
The seismic wave is loaded six times in the horizontal direction in order to observe the destruction of the tunnel model. The acceleration peak values of tunnel inverted arch and model casing outside are listed in Table 4 after the load application. If MaxTH =MaxMH is defined as magnification coefficient of acceleration (abbr.MCacc), the curve of MCacc and MaxMH is shown in Fig. 4. When the input acceleration is big, the testing acceleration can express reliably the dynamic characteristic of the tunnel before
(a) Although the development trend of the cracks located on the slope in the left tunnel is the same as the cracks in the right tunnel, they are different on the amount, the depth and the extending length of the cracks.
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Table 4 The acceleration peak values of every loading process (unit: g). Load order
Input
1 2 3 4 5 6
0.3 0.3 0.4 0.5 0.6 0.8
Inverted arch of tunnel
Outside of model casing
MaxTH
MinTH
MaxTV
MinTV
MaxMH
MinMH
MaxMV
MinMV
0.443 0.443 0.464 0.570 0.590 0.754
0.307 0.307 0.381 0.490 0.500 0.750
0.078 0.078 0.067 0.089 0.116 0.118
0.067 0.067 0.058 0.073 0.102 0.110
0.311 0.311 0.338 0.470 0.535 0.743
0.249 0.249 0.330 0.400 0.516 0.700
0.127 0.127 0.142 0.152 0.165 0.177
0.124 0.124 0.138 0.150 0.158 0.161
Explain: TH – horizontal direction of tunnel, TV – vertical direction of tunnel, MH – horizontal direction of model casing, MV – vertical direction of model casing.
MCacc
1.50 1.35 1.20 1.05 0.311
0.311
0.338
0.470
0.535
0.743
MaxMH / g
Amplitude / m s-2
Fig. 4. The curve of magnification coefficient of acceleration and input seismic load.
10.0 Fig. 6. The distribution of ground cracks after earthquake.
8.0 6.0 4.0 2.0 0 0
30
60
90
120
150
120
150
Frequency /Hz
Amplitude / m s-2
(a) FFT curve of liner 7.5 6.0 4.5 3.0 1.5 0
0
30
60
90
Frequency /Hz (b) FFT curve of model casing outside Fig. 5. FFT curves of test acceleration.
There are cracks which develop as the model ‘‘X’’ along 45° location in the surrounding rock at tunnel spandrel. On the slope of right tunnel, the amount of cracking is greater, and the extending length of crack is longer, and the depth and width is larger than the slope cracks which are located on the left tunnel. In addition, the width of this widest crack is 3.5 mm more or less in surrounding rock of right tunnel, and the width of the crack is 1.2 mm only in surrounding rock of left tunnel.
the stress concentration is more serious at the location where the left tunnel slope intersects with the right tunnel slope. With the increase of the vibration amplitude and the load duration of model casing, the surrounding rocks reach the limit state of the crack, and then the first crack appears here.
(b) The first crack of ground appears at the location where the left tunnel slope intersects with the right tunnel slope.
(c) The ground crack is less where the embedded depth of tunnel is deeper.
Because the constraint conditions on the liner by the surrounding rock is different between left tunnel and right tunnel, the dynamic stress concentration appears in the location where the geometry size of slope is changed when the vibration begins, and
The constraint condition on the liner by the surrounding rock is strengthened with increasing embedding depth of tunnel, and the constraint degrees of left tunnel and right tunnel tend to be equal. In addition, with the increase of the distance between the transect
Fig. 7. The distribution effect picture of ground cracks.
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3.3. Liner cracks The photos of tunnel structure on the whole cannot describe distinctly the distribution of cracks because the width of cracks is very narrow. The cracks in the liner are drawn in Fig. 8 according to the test results, and some conclusions can be drawn from Fig. 8: (a) There are distinct differences on the amount of cracks, the through degree of crack and the width of crack between left tunnel portal and right tunnel portal. Although the amount of cracks located at the left tunnel portal is bigger than it is at the right tunnel portal, the amount of through cracks which are located at the left tunnel portal are less and the crack width is smaller than at the right tunnel portal. The through cracking in the left tunnel portal is located at the upper side of the left spandrel, where there is only one through crack, and the widest
crack is 0.7 mm. The through cracks of the right tunnel portal are located at the left spandrel, the left arch springing and the right arch springing, and such through cracks are more than three, in addition, the widest crack is 1.5 mm. (b) The distribution laws of the liner cracks of the left liner and the right liner along tunnel portal are different. The cracks of left tunnel are distributed mainly on tunnel portal, and the liner cracks decrease with the increase in the embedment depth of tunnel. The cracks of right tunnel are distributed mainly on the tunnel portal and near the tunnel cross-section which is in the same vertical plane with the left tunnel portal, and the liner cracks decrease with the increase of the embedment depth of tunnel although the speed of the crack decrease is slower than it is in the left tunnel. (c) The crack distribution in the same liner cross-section is different between the left tunnel liner and the right tunnel liner. The left liner cracks are distributed mainly on right arch springing and the right hance; and the right liner cracks are distributed mainly on the left arch springing and the left hance. In other words, the liner cracks are distributed mainly on the closer side of two liners between the two holes. In earthquakes, the instantaneous force acting on a liner is more than the force in static loading because of the interaction between the liner and the surrounding rock. The liner will crack if the internal force is greater than the material strength of tunnel lining. As mentioned above, the geometry of the surrounding rock changes sharply near the left tunnel portal, and it has a great effect on the restriction degree of the right tunnel, which leads to the difference of the stress between different locations in earthquake. The forced state at the portal has some differences between left tunnel and right tunnel because of the interaction of the forces. By the macroscopic phenomenon the differences are shown as follows: (1) the right tunnel cracks are distributed mainly at the tunnel portal and the tunnel cross-section whose plane contains the left
(a)
th The 6th test The 4 test cross-section cross-section The 3rd test cross-section The 2nd test cross-section The 1st test cross-section
(b)
Strain gauge located on crown of arch Strain gauge located on right arch springing Strain gauge located on left arch springing
Acceleration transducer
Strain gauge located on left arch springing
The 5th test cross-section
Left tunnel
Right tunnel Acceleration transducer
Strain gauge located on inverted arch Fig. 8. The crack distribution of tunnel lining.
Fig. 9. The position of sensing probes.
Strain gauge located on right arch springing
of liner and the portal of tunnel, the effect which is induced by the difference of constraint degree on surrounding rock to tunnel portal is being weakened gradually to the left tunnel and the right tunnel. Finally, the interaction between the surrounding rock and tunnel structure is diminishing, and the interaction between the surrounding rock and left tunnel is the same with the interaction between the surrounding rock and right tunnel. So, at the location where the embedding depth size of tunnel is big, the ground crack is less and there is no difference between the left tunnel and the right tunnel. It is known that the surface cracks of the front elevation in tunnel slopes develop as ‘‘X’’ model and the cracks of the surrounding rock covering the top of tunnel develop as a ‘‘scissors’’ model. The development model of the cracks is a macroscopic phenomenon caused by the horizontal shear failure of surrounding rock because of the nonsynchronous vibration between the lining structure and the surrounding rock under earthquake loads. The nonsynchronous vibration is caused by the different stiffness between the tunnel liner and the surrounding rock. In earthquakes, the distortion of the right tunnel liner is bigger than the left tunnel liner because the constraint degree on the right tunnel liner by the surrounding rock is weaker than it is on the left tunnel lining. Therefore, the interaction between the surrounding rock and the right tunnel is greater than the left tunnel. As a result, the crack characteristics of the surrounding rock of the right and left tunnel are different.
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tunnel portal; (2) although the amount of all cracks located in left tunnel portal is bigger than it is in the right tunnel portal, the amount of through cracks located in the left tunnel portal is less and the width of cracks is smaller than it is in the right tunnel portal. In addition, there are some annular cracks in the liner, which are made by the fixed end effect of the boundary. 3.4. Liner strains In the test, the 5 mm 2 mm strain gauges were used for the strain of the liner, and their disposals are showed in Fig. 9. The curves of liner strain versus time during the 4th load are shown in Fig. 10, and the maximal strains at all locations are shown in Fig. 11. From Figs. 10 and 11, it is known that:
(a) The maximal strains at the closer sides of two holes are greater than they are at other sides when the strains are located at the same test cross-section. The restriction provided by the surrounding rock in the inner sides of the two liners is less than outer sides because of the existence of another tunnel. So the stress and the strains of the inner sides of the two liners are greater than outer sides. The result has been verified in the liner cracks. At the 2nd test cross-section, the maximal strain outside the left arch springing is 32.5 microstrains and the maximal strain outside the right arch springing is 27.5 microstrains; at 3rd test cross-section, the maximal strain outside the left arch springing is 31 microstrains and the maximal strain outside right arch springing is 17.0 microstrains.
35
15
5
Stress ( με )
Stress ( με )
25
15
5
-5
-15 -5 0
5
10
15
20
25
-25
30
0
5
10
15
20
25
30
Time /s (a) Left arch springing outside of the 2nd test cross-section
Time /s (d) Right arch springing outside of the 3rd test cross-section
10
35
2.5 20
Stress ( με )
Stress ( με )
-5.0 -12.5 -20.0
5
-10 -27.5 -25
-35.0 0
5
10
15
20
25
0
30
Time /s (b) Right arch springing outside of the 2nd test cross-section
5
10
15
20
25
30
Time /s (e) Inverted-arch outside of the 1st test cross-section 25
35
15
Stress ( με )
Stress ( με )
25
15
5
-5
5
-5
-15
-25 0
5
10
15
20
25
30
Time /s (c) Left arch springing outside of the 3rd test cross-section
0
5
10
15
20
25
30
Time /s (f) Arch-crown outside of the 2nd test cross-section
Fig. 10. The curves of strain–time.
T. Sun et al. / Tunnelling and Underground Space Technology 26 (2011) 391–397
Stress ( με )
35 28 21 14 7 The 1st test cross-section
The 2nd test cross-section
The 3rd test cross-section
The 4th test cross-section
Testing location Fig. 11. The maximum strain of testing cross-section.
(b) The cross-section maximal strain on the right tunnel diminishes with increasing distance between the testing crosssection and the reference vertical plane which contains the left tunnel portal. The distance between the 2nd and 3rd testing cross-section and the reference vertical plane is 25 cm and 55 cm respectively. The test results show that the maximal strains of the left arch springing and right arch springing at the 2nd test cross-section are greater than those at the 3rd test cross-section. For the tunnel portal of two holes, the left tunnel portal has influence on the right tunnel in a range. The range is related to many factors which need to be confirmed in more experiments or some numerical simulation. It is one of the emphases for future study. (c) The strain baseline at every testing point is offset in the loading process and the offset cannot be eliminated after the vibration loading. In addition, the perpetual plastic strain at the top of arch is smaller than at the inverted arch of tunnel. The main reason for the offset of the strain baseline is that the permanent deformation of the tunnel liner happened due to the earthquake load which produced additional strain in the tunnel structure. The restriction in the inverted arch of the tunnel portal by the surrounding rock is weakest in the tunnel because at the portal the tunnel covering is thinnest and the tunnel gate is free. However, the amplitude of earthquake loads is magnified, and as a result, the inverted arch of tunnel portal is one of the most precarious locations and its permanent plastic strain is greater than that at any other location. 4. Conclusion (a) The MCacc decreases with an increase of MaxMH. In addition, when the seismic acceleration traverses the model material, the low-frequency segment of seismic acceleration is magnified and the high-frequency segment of seismic acceleration is attenuated. (b) The interaction between lining structure and the surrounding rock leads to the horizontal shear failure of surrounding rock in earthquakes. The degree of destructive cracking of the surrounding rock is dissimilar at the different locations because of the different constraint on the surrounding rock of the left liner and the right liner although the development trend of rock cracking is similar. The constraint condition of surrounding rock to the liner is strengthened with increasing embedment depth of the tunnel, and the constraint degrees
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of left tunnel and right tunnel tend to be equal. The interaction between the surrounding rock and the tunnel structure diminishes, and the interaction between the surrounding rock and the left tunnel is similar to the interaction between the surrounding rock and the right tunnel. Therefore, at the location of the largest embedment depth of the tunnel, the amount of the ground cracking is small and there is no difference between the left tunnel and the right tunnel. (c) The distribution laws of the liner cracks at the same crosssection is different between the left tunnel liner and the right tunnel liner, and there are distinct differences in the amount of cracks, the degree of through cracks and the width of cracks between the left tunnel portal and the right tunnel portal. The liner cracks of the left tunnel concentrates mainly at the left tunnel entrance, and the cracks of right tunnel concentrates mainly at the right tunnel entrance and near the tunnel cross-section which is in the same plane with the left tunnel portal, and there are more liner cracks on the inner sides between two holes than the outer sides. (d) In the same vertical cross-section, the liner maximal strain at the inner sides between two holes is greater than the outer sides, and the cross-section maximal strain on the right tunnel decreases with the increase of distance between the test cross-section and the reference vertical plane containing the left tunnel portal. In addition, the inverted arch of the tunnel portal is one of the most precarious locations. (e) Rebar is not used in tunnel portal, so, the cracks width of tunnel lining and the liner strains are bigger than those when rebar is used in tunnel partal in the test result. In addition, there are some differences between the test result and the real situation because the stratum characteristic and the cranny of surrounding rock are not considered in the model test.
Acknowledgements Heartfelt thanks to my teachers, Ying-xue Wang, Yu-sheng Shen and Jia-mei Zhou in School of Civil Engineering of Southwest Jiaotong University, this study should not be performed perfectly if there were no selfless help from them. Thanks to the teachers of National Key Laboratory of Traction Power and Geotechnical Laboratory of Southwest Jiaotong University for providing a great deal of help. References Gao, Qu-qing, 1996. The Memoir on Tunnel & Underground Structure of Gao Quqing. China Railway Publishing House, Beijing. HU, Yuxian, 2004. Earthquake Engineering, second ed. Seismological Press, Beijing. Lin, Gao, 1990a. Summarization on antiseismatic analysis of under-ground structure (A). World Earthquake Engineering 6 (2), 1–9. Lin, Gao, 1990b. Summarization on antiseismatic analysis Of underground structure (B). World Earthquake Engineering 6 (3), 1–10. Lin, Gao, Liang, Qing-huai, 1996. Aseismic design of underground structures. China Civil Engineering Journal 29 (1), 15–24. Liu, Guang-lei, Song, Er-xiang, Liu, Hua-bei, et al., 2008. Dynamic centrifuge tests on seismic response of tunnel in saturated sandy foundation. Rock and Soil Mechanics 29 (8), 2070–2076. Zheng-zheng Wang, Bo Gao, Tie-cheng Sun, et al., 2008. Seismic response analysis of the tunnel with accumulated damage and crack effect in shaking table test. In: The 14th World Conference on Earthquake Engineering, Beijing, China, October 12–17. Wang, Zheng-zheng, Gao, Bo, Jiang, Yuan-jun, et al., 2009. Investigation and assessment on mountain tunnels and geotechnical damage after the Wenchuan earthquake. Science in China Series E: Technological Sciences 52 (2), 546–558. Zhang, Qing-song, Li, Li-ping, Li, Shu-cai, et al., 2008. Experimental study of blasting dynamic vibration of closely adjacent tunnels. Rock and Soil Mechanics 29 (10), 2655–2666.