Numerical simulation of shaking table test on utility tunnel under non-uniform earthquake excitation

Tunnelling and Underground Space Technology 30 (2012) 205–216

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Numerical simulation of shaking table test on utility tunnel under non-uniform earthquake excitation Jun Chen a,b, Luzhen Jiang c, Jie Li b,⇑, Xiaojun Shi b a

Institute for Advanced Study in Civil Engineering, Tongji University, PR China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, PR China c School of Civil Engineering, Hebei University of Science and Technology, Shi Jiazhuang, PR China b

a r t i c l e

i n f o

Article history: Received 21 June 2010 Received in revised form 24 November 2011 Accepted 25 February 2012 Available online 3 April 2012 Keywords: Utility tunnel Shaking table test Non-uniform earthquake excitation Numerical analysis

a b s t r a c t This paper studies numerical simulation of shaking table test on utility tunnel model subjected to nonuniform earthquake excitation. The experimental work is first introduced with focuses on experimental strategy, structural model and soil, instrumentation and test cases. Followed are numerical modeling details of the shaking table tests, including modeling of shear box, soil–structure interaction and initial stress equilibrium. Numerical results are presented and compared with experimental records in terms of boundary effect of the shear box, soil and structure model acceleration response, soil displacement and structural strain responses. It is found that the utility tunnel has a bending deformation and its acceleration response is larger than the surrounding soil for high shaking intensity. The proposed numerical model is found to be satisfactory in predicting many details of the experimental results. The modeling methodology suggested in this paper is reasonable for representing the shaking table test and it can be used for further analysis. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction A utility tunnel is a kind of underground structure that accommodates various utilities as water, sewerage, gas, electrical power, telephone and heat supply, and also provides enough head-room to allow maintenance personnel to walk through and to perform maintenance tasks. The utility tunnels are linear and cut-and-cover structures whose cross sections are typically smaller than the traffic tunnel and larger than buried underground pipelines. The adoption of utility tunnel for construction and maintenance of underground utility pipelines has many advantages against the traditional digging-up manner, such as exempting streets from frequency traffic-blocking and providing easy access for maintenance and improvement. Therefore, utility tunnels have been widely constructed throughout the world after it first appeared in Paris in 1851. The safety and reliability of utility tunnels is of great importance for modern city since they contain pipelines of city’s lifeline system. Experiences from major earthquakes have shown that cut-and-cover tunnels are more vulnerable to earthquake damage than circular bored tunnels (Hashash and Hook, 2001). ⇑ Corresponding author at: State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, PR China. Tel.: +86 21 6598 3526; fax: +86 21 6598 6345. E-mail addresses: [email protected] (J. Chen), [email protected] (L. Jiang), [email protected] (J. Li), [email protected] (X. Shi). 0886-7798/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tust.2012.02.023

In 1995 Hyogoken–Nambu earthquake, for instance, different types of damages, such as longitudinal and transverse cracks, spalling of concrete and movement of tunnel joints, were observed on almost all the utility tunnels in the adjacent areas affected by the earthquake (JSCE, 1999; PWRI, 2001). Observations from major earthquake events have pointed out several reasons for causing severe damage to underground structures: slop instability, soil liquefaction, fault displacement and earthquake wave propagation (Hashash and Hook, 2001). On the other hand, shaking table tests have been carried out by many researchers to investigate the performance of underground structure and to check current design/ analysis methods. Ohtomo et al. (1973) conducted shaking table tests on 1:250 submerged tunnels model. Silicone rubber and gelatin gel material were used in the experiment for the tunnel model and the soil. The dimension of the soil container is 2.2 m by 1.0 m. Ohtomo et al. (2001, 2003) carried out shaking table experiments on a large tunnel model (3.0 m  1.75 m  0.97 m, scale ratio 1/ 3–1/4) to learn the soil–structure-interaction (SSI) based on the assumption of two-dimensional plane strain problem. A small sampling of some recent similar experimental research works includes Yang et al. (2003), Prasad et al. (2004), Huang et al. (2006), Shi et al. (2007, 2009), and Luzhen et al. (2010). All these research works have expanded our knowledge on performance of underground structures under earthquake attack. All the above mentioned experiments were performed on single shake table. Therefore only uniform earthquake excitation was simulated in the test. The spatial distribution of ground motion is

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J. Chen et al. / Tunnelling and Underground Space Technology 30 (2012) 205–216 Table 1 Material parameter of soil and structure.

Soil Structure

Density (kg/m3)

Elastic modulus (Mpa)

Poisson’s ratio

Inner friction angle (°)

Cohesion (kPa)

Dilation angle (°)

1800 2400

16.5 33,000

0.4 0.20

27.9 –

24.4 –

0 –

Fig. 1. Photo of the prototype utility tunnel. Fig. 3. Installation of the utility model on the shake tables.

considered as one of the main factors for causing damage to shallow buried tunnels (Hashash and Hook, 2001; Chouw and Hao, 2005, 2008). However, shaking table test on tunnel model using non-uniform earthquake excitation is very rare. The following two reasons are identified: (1) lack of test facility in the past; (2) with current available test facility as shaking tables array, it is still not an easy task to simulate the continuously changing earthquake wave acted along the tunnel. Consequently, few experimental results or numerical simulations were available in literature on performance of utility tunnel under non-uniform earthquake wave excitation. In view of this, we had designed and conducted a series of shaking table tests on a scaled utility tunnel model. Technical details of the test including test facility, experimental setup, soil and structural model, design and fabrication of the soil container and simulations of non-uniform earthquake excitation have already been presented in Chen et al. (2010). In this paper we further establish finite element model of the whole box–soil–tunnel system in order to simulate the shaking table test. The experimental results are used as a basis for verifying the numerical model. After a brief introduction of the shaking table test, numerical modeling details are presented and the numerical results as structural and model acceleration responses, structural strain responses and soil pressure are calculated and compared with the experimental records. 2. Overview of the shaking table tests

Fig. 2. 1:8 Scaled test model.

Main features of the shaking table test are outlined in this section for completeness and comparison purpose. In the test, a structural model was built after an existing utility tunnel with the geometrical scale of 1:8 (see Figs. 1 and 2). Unsaturated clay soil was adopted and placed in two soil containers which were in turn fixed on two shake tables (Fig. 3). Material properties of the tunnel model and the model ground were tested before the shaking table experiments, and the results are summarized in Table 1. The nonuniform earthquake was simulated in the experiment by applying two different input waves to two different shake tables, namely Tables A and B as demonstrated in Fig. 3. As can be seen from Fig. 3, two shear boxes were used in the test. The two boxes were of identical dimensions and each comprised sixteen steel frames that were stacked on each other. Each frame was made of rectangular

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207

Fig. 4. Locations of sensors used in the test (all dimensions in mm).

Table 2 Test cases for utility tunnel under transverse non-uniform earthquake excitation. Case No

1

2

Wave form PGA (g)

White noise

W1 for Table A, W2 for Table B 0.02 0.05 0.1 0.2 0.4 0.6

a

3

4

5

6

7

8

9

0.8

1.0

a

The frequency range is 1–55 Hz, and the maximum displacement value is 0.6 mm.

Table 3 Measured damping ratios of the soil. PGA (g)

0.1

0.2

0.4

0.6

0.8

1.0

Damping ratio

0.06

0.10

0.12

0.15

0.18

0.2

steel pipes. With help of linear rolling guides between adjacent frames, each frame could move freely in accordance with the input wave excitation in either longitudinal or transversal direction. Fig. 4a–d shows the arrangement of sensors in the test, including accelerometers, displacement transducers, earth pressure and strain gauges. A special laser displacement transducer D9 was used to measure settlement of ground surface in the test. The first letter

of the sensor name refers to the installation location, letter A, B and M means ‘in box A’, ‘in box B’ and ‘on the structural model’ respectively. The second letter of the sensor’s name denotes the type of sensor, letter A, D and S means accelerometer, displacement transducer and strain gauge respectively. In total, nineteen accelerometers, ten displacement transducers, twenty earth pressure (whose name starts with ‘EP’) and 26 strain gauges were utilized in the test to measure soil and structural responses. In Fig. 4, strain gauges in brackets were installed on the backside surface of the model. Both longitudinal and transversal earthquake excitation were applied to the structural model in the test. Experimental results for transversal earthquake excitation, which means the shaking table moves in the direction that is perpendicular to the longitudinal axis of the utility tunnel (see Fig. 4), are discussed in this paper. There were in total nine test cases had been carried out and Table 2 summarizes the excitation waveform and the input peak ground acceleration (PGA) for each case. 3. Numerical modeling of the shaking table test Finite element model of the soil–structure–shear box system is established in this section. Several important factors, like the lam-

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(a) Whole model

(a) Shear box A on shake table A

(b) Model of the shear box

(c) Structure element

(d) Soil element

Fig. 5. Finite element model of the whole system.

(b) Shear box B on shake table B

inar shear box, soil–structure interaction, initial stress field, and input of earthquake wave, are carefully considered in the numerical modeling.

FAS 2-norm deviation

There are several ways available in the literature to model the laminar shear box. Matsui et al. (2001) adopted the plane strain model for the soil container used in a shaking table test. The side boundary condition was idealized by horizontal rollers with a mass representing the effect of inertia force caused by the frame of laminar shear box. Chen et al. (2002) adopted shell elements for a flexible rubber soil box utilized in a soil–pipe interaction shaking table test. How the shell elements were connected to the soil had not been clearly documented. For modeling shear box in a shaking table tested on subway station in soft soil, Yang et al. (2003) used a rigid model that ignored the deformation of the box and fixed the movements of bottom surface and all the side walls. Prasad et al. (2004) reviewed the problems in the simulation of the laminar shear box and pointed out that the main factors were the inertia force, friction, membrane effect and the boundary effect. Huang et al. (2006) adopted shell elements to simulate the laminar shear box. The bottom of the box was fixed and the side surface was fixed except at the vibrated direction. Two requirements need to be satisfied in the numerical modeling of the laminar shear box. They are: minimizing the boundary effect and effectively simulating the shear deformation. We have tried and compared two different ways to model the shear box and found the following one was better. To satisfy the first requirement, the shell element with a thickness of

0.4 0.35 0.3

AA6/AA3 AA5/AA3 BA6/BA3 BA5/BA3

0.25 0.2 0.15 0.1 0.05 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.8

0.9

1

Input excitation peak (g)

(a) Experiment FAS 2-norm deviation

3.1. Laminar shear box

Fig. 6. Soil surface after test PGA = 1.0 g.

0.35 0.3 0.25 0.2 0.15 0.1 0.1

AA6/AA3 AA5/AA3 BA6/BA3 BA5/BA3

0.2

0.3

0.4

0.5

0.6

0.7

Input excitation peak (g)

(b) Numerical results Fig. 7. Boundary effect of the shear box and the numerical model.

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1 mm is used to model the steel frame. The weights of the frame are simulated by adding uniformly distributed mass element (126.3 kg) to the shell element. The Young’s module of the shell element is set the same as soil; Slippage and separation between soil and box are ignored. To satisfy the second requirement, we assume each steel frame (in total 16 frames) has only rigid movement in the vibration direction since the stiffness of the steel frame is much larger than the soil. Accordingly, the soil is assumed to be constrained within each frame layer. That means all nodes of the shell element in the same height have the same displacement along the vibration direction and no displacement on the perpendicular direction. Meanwhile, the vertical movements of boundary points are constrained. The bottom frame of the box was fixed on the table in the test, therefore it is assumed in the numerical model that no relative slippage between soil and box at the bottom boundary.

3.2. Soil and the structure model The extended Drucker–Prager model is used as soil constitutive model. The parameters are obtained from material test as follows: the soil density 1800 kg/m3, the elastic modulus 16.5 MPa, the Poisson’s ratio 0.4, the cohesion 24.4 KPa, and the inner friction angle 27.9° (see Table 1). Rayleigh damping model is adopted for the soil. The damping coefficients are calculated by the following equation using measured natural frequencies and damping ratios from the test.

a ¼ 2ðf1 =x1  f2 =x2 Þ=ð1=x21  1=x21 Þ; b ¼ 2ðf2 x2  f1 x1 Þ=ðx22  x21 Þ

where f1 ; f2 are damping ratios of the first two modes of vibration and are assumed to the same. The equivalent damping ratios of

0.03 FEM Experiment

0.1

Amplitude

Acceleration (g)

0.2

0 -0.1 -0.2

ð1Þ

0

1

2

3

4

5

6

FEM Experiment

0.02

0.01

0

7

0

5

10

15

20

25

30

35

40

Frequency (Hz)

Time (s)

(a) Results of Sensor BA1 0.025 FEM Experiment

0.1

Amplitude

Acceleration (g)

0.2

0 -0.1 -0.2 0

1

2

3

4

5

6

0.015 0.01 0.005 0 0

7

FEM Experiment

0.02

5

10

Time (s)

15

20

25

30

35

40

Frequency (Hz)

(b) Results of Sensor BA2 0.02

FEM Experiment

0.1

Amplitude

Acceleration (g)

0.2

0 -0.1 -0.2 0

1

2

3

4

5

6

0.01 0.005 0 0

7

FEM Experiment

0.015

5

10

15

20

25

30

35

40

Frequency (Hz)

Time (s)

(c) Results of Sensor BA3 0.015 FEM Experiment

0.1

Amplitude

Acceleration (g)

0.2

0 -0.1 -0.2 0

1

2

3

4

5

6

7

FEM Experiment

0.01

0.005

0

0

Time (s)

5

10

15

20

25

30

Frequency (Hz)

(d) Results of Sensor BA4 Fig. 8. Acceleration time history and corresponding spectrum of soil at different depth in shear box B (Input PGA = 0.1 g).

35

40

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the soil were identified by advanced parameter identification method (Chen et al., 2008). The identified damping ratios of the first mode for different input PGAs are given in Table 3. x1 and x2 are natural frequencies that were also identified from the experiment records as 5.80 and 30.0 Hz. The test structure is modeled by shell elements with the following parameters: the density 7800 kg/m3, the elastic modulus 210 GPa, and the Poisson’s ratio 0.2. Master–slave surfaces are employed to simulate the soil–structure contact effect, with a coefficient of 0.22 between soil and structure. Considering the stiffness difference, the master and slave surface is assigned to structure and soil surface respectively. Sliding between the two surfaces is allowed but no separation. The numerical modeling is performed via ABAQUS as a platform, soil and structure are modeled as 8node 3-D solid element and 4-node shell element respectively (see Fig. 5).

3.3. Initial stress equilibrium For modeling soil–structure dynamic interaction, the normal stress and Coulomb friction at the master–slave contact surface are significantly influenced by the initial stress in soil. Therefore, it is important to balance the initial stress in soil in the numerical modeling. For free filed analysis, the stress balance method is generally adopted for initial stress equilibrium (Wang et al., 2007). This method, however, is not applicable in this case due to the existence and large dimensions of the structure model. Otherwise, our trail calculations showed the vertical displacement of the whole soil–structure system could reach several millimeters, which was not reasonable. To solve this problem, we first applied gravity force only on the whole model first, then took the calculated stress of each element as initial conditions and applied them on the whole system again. This procedure produced an initial vertical displace-

0.2 FEM Experiment

0.5

Amplitude

Acceleration (g)

1

0 -0.5

FEM Experiment

0.15 0.1 0.05 0

-1 0

1

2

3

4

5

6

0

7

5

10

15

20

25

30

35

40

Frequency (Hz)

Time (s)

(a) Results of Sensor BA1 0.1 FEM Experiment

0.5 0 -0.5 -1

0.06 0.04 0.02 0

0

1

2

3

4

5

6

FEM Experiment

0.08

Amplitude

Acceleration (g)

1

7

0

5

10

15

20

25

30

35

40

Frequency (Hz)

Time (s)

(b) Results of Sensor BA2 FEM

0.5

Experiment

0 -0.5 -1 0

Experiment

0.05

0

1

2

3

4

5

FEM

0.1

Amplitude

Acceleration (g)

1

6

7

0

10

20

30

40

Frequency (Hz)

Time (s)

2 FEM

1

FEM

Amplitude

Acceleration (g)

(c) Results of Sensor BA3

Experiment

0 -1

Experiment

0.1 0.05 0

-2 0

1

2

3

4

5

6

7

0

5

10

15

20

25

30

Frequency (Hz)

Time (s)

(d) Results of Sensor BA4 Fig. 9. Acceleration time history and corresponding spectrum of soil at different depth in shear box B (Input PGA = 1.0 g).

35

40

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ment of 1.5 1:5  105 m, almost zero. Thus, the balance of initial stress was achieved in the numerical model.

4. Results and discussion 4.1. General observations in the test

3.4. Seismic wave input During the test, the laminar box behaved like rigid body for input PGA less than 0.1 g. For PGA larger than 0.2 g, relative movement between the two boxes was observed and story drift in each box was also observed. Fig. 6 shows the photo of soil surface after the PGA = 1.0 g. It is seen that the surface were broadly split

0

-0.5

-0.5

-1

-1

FEM Experiment

1

1.5

-0.5

-1

-1.5

-2

2

0.8

1

1.2

-2

1.4

0.8

1

Scale factor

(a) PGA=0.1g

(b) PGA=0.2g

(c) PGA=0.4g 0

-0.5

-0.5

-0.5

-1

Depth (m)

0

-1

-1.5

-1.5 FEM Experiment

0.6

0.6

Scale factor

0

-2

FEM Experiment

Scale factor

Depth (m)

Depth (m)

FEM Experiment

-1.5

-1.5

-2

0

Depth (m)

0

Depth (m)

Depth (m)

In the experiment, the laminar shear box was constrained on the shaking table with bolts. Therefore, measured time histories of acceleration of the shake table, i.e. AA7 and BA7, are applied directly to the base of the FEM model.

0.8

-2

1

-1

-1.5 FEM Experiment

0.6

0.8

1

-2

FEM Experiment

0.6

0.8

1

Scale factor

Scale factor

Scale factor

(d) PGA=0.6g

(e) PGA=0.8g

(f) PGA=1.0g

Fig. 10. Acceleration amplification factors for different PGAs. Table 4 Measured and computed peak acceleration results for different sensors (unit: g). Sensor

PGA = 0.1 g Measured

AA1 AA2 AA3 AA4 AA5 AA6 AA7 BA1 BA2 BA3 BA4 BA5 BA6 BA7 MA1 MA2 MA3 MA4 MA5

PGA = 0.2 g FEM

Measured

PGA = 0.4 g FEM

Measured

PGA = 0.6 g

PGA = 0.8 g

PGA = 1.0 g

FEM

Measured

FEM

Measured

FEM

Measured

FEM

0.51

0.77

0.59

0.93

0.72

1.10

0.42 0.50 0.55 0.49 0.46

0.61 0.48 0.62 0.49 0.44

0.50 0.65 0.72 0.62 0.57

0.74 0.58 0.79 0.59 0.54

0.59 0.79 0.88 0.75 0.68

0.89 0.69 0.96 0.68 0.63

0.59 0.58

0.59 0.67

0.79 0.74

0.79 0.81

0.99 0.93

0.99 0.93

0.47 0.52 0.68 0.55 0.52

0.44 0.49 0.69 0.50 0.51

0.57 0.72 0.95 0.74 0.67

0.57 0.65 0.96 0.64 0.61

0.63 0.91 1.17 0.89 0.82

0.67 0.78 1.23 0.76 0.70

0.71

0.71

0.65 0.48 0.49 0.42 0.63

0.54 0.46 0.41 0.42 0.54

0.97 0.87

0.98 0.66

1.25 1.08

1.25 0.77

0.61 0.62 0.56

0.56 0.52 0.53

0.71 0.74 0.68

0.67 0.61 0.62

0.87

0.72

1.11

0.87

0.16 0.12 0.12 0.09 0.13 0.12 0.09

0.17 0.13 0.15 0.13 0.15 0.14 0.09

0.28 0.22 0.20 0.18 0.21 0.20 0.19

0.28 0.23 0.24 0.24 0.23 0.21 0.19

0.44 0.33 0.33 0.37 0.33 0.31 0.39

0.55 0.43 0.37 0.42 0.35 0.31 0.39

0.18 0.13 0.12 0.10 0.12 0.12 0.09

0.15 0.11 0.15 0.11 0.14 0.15 0.09

0.29 0.20 0.21 0.21 0.22 0.21 0.22

0.25 0.16 0.23 0.23 0.21 0.22 0.22

0.45 0.36 0.39 0.43 0.39 0.36 0.46

0.48 0.29 0.38 0.45 0.37 0.38 0.46

0.14 0.11 0.09 0.08 0.12

0.16 0.14 0.11 0.09 0.17

0.27 0.19 0.16 0.14 0.24

0.26 0.23 0.18 0.15 0.26

0.44

0.41

0.33 0.32 0.28

0.36 0.28 0.29

0.45

0.41

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into three parts by two longitudinal ‘cracks’, which was perpendicular to the vibration direction. At the box longitudinal boundaries (marked as 1 and 2 in Fig. 6), a pounding phenomenon between soil and box was observed during the test for higher PGA values and soil there were smashed. From record of sensor D9, it was found that for PGA less than 1.0 g the settlement of soil was negli-

gible. For PGA = 1.0 g the measured maximum settlement of soil surface was less than 5 mm with an average values of about 2 mm. The result indicated that the soil density had not changed much during the test. After the test, the structure model was dug out and carefully checked, no cracks were found on the surface of the model.

0.1 FEM

1

Experiment

Amplitude

Acceleration (g)

1.5

0.5 0 -0.5 -1

0

1

2

3

4

5

6

Experiment

0.06 0.04 0.02 0

7

FEM

0.08

0

10

20

30

40

Frequency (Hz)

Time (s)

(a) Results of Sensor MA1 0.08 FEM

0.5

FEM

Experiment

Amplitude

Acceleration (g)

1

0 -0.5 -1

0

1

2

3

4

5

6

0.06

Experiment

0.04 0.02 0

7

0

10

Time (s)

20

30

40

Frequency (Hz)

(b) Results of Sensor MA2 0.08 FEM

FEM

0.5

Amplitude

Acceleration (g)

1 Experiment

0 -0.5 -1

0.06 0.04 0.02 0

0

1

2

3

4

5

6

Experiment

0

7

10

20

30

40

Frequency (Hz)

Time (s)

(c) Results of Sensor MA3 0.08 FEM

0.5

FEM

Experiment

Amplitude

Acceleration (g)

1

0 -0.5

0.06 0.04 0.02 0

-1 0

1

2

3

4

5

6

7

Experiment

0

10

20

30

40

Frequency (Hz)

Time (s)

(d) Results of Sensor MA4 0.15

FEM

1

Experiment

Amplitude

Acceleration (g)

1.5

0.5 0 -0.5 -1 0

1

2

3

4

5

6

7

FEM Experiment

0.1 0.05 0 0

10

20

Frequency (Hz)

Time (s)

(e) Results of Sensor MA5 Fig. 11. Peak structural acceleration response and comparison of soil response (input PGA = 1.0 g).

30

40

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where X0, Xi are quantities (acceleration in this paper) of reference sensor and target sensor respectively. Fig. 7a shows the l calculated using measured acceleration responses from AA3, AA5, AA6, BA3, BA5 and BA6 in the experiment, whilst Fig. 7b shows the corresponding index value using acceleration responses at the same location in the numerical model. It is observed in Fig. 7a that the index varies in a range of 0.05 to 0.36 for different PGA. The sensors close to the boundary, e.g. AA6 and BA6, have higher l value than that close to the center, e.g. AA5 and BA5. The numerical results of l have the similar variation range from 0.15 to 0.30. It is also observed in Fig. 7 that the variation trend of l value with the PGA amplitude is different between numerical and experimental results. The possible reason is that in experimental the earthquake excitation was applied successively therefore stress history, stress path and stress status of the soil were established and changed before and after each test, which would in turn affect the properties of the soil to some extent. In numerical mode, on the contrary, in initial stress status is the same for all test cases. Nevertheless, we have already demonstrated in Chen et al. (2010) that our shear box had the smallest boundary effect compared with several other similar tests, and the boundary effects of the numerical model are slightly smaller than the experimental value. In this connection, the numerical modeling of the shear box is reasonable and the boundary effect is successfully controlled. 4.3. Soil acceleration response Figs. 8 and 9 compares, in both time and frequency domain, the numerical results (dashed line) with the records of sensors (solid line) at different soil depth in shear Box B, i.e. BA1, BA2, BA3 and BA4, for PGA = 0.1 g and PGA = 1.0 g respectively. The acceleration amplification factors, defined as ratio of maximum acceleration of sensors in the soil with that of the shake table input, are depicted in Fig. 10 for different PGAs. It is seen from Figs. 8 and 9 that: for PGA = 0.1 g the soil acceleration responses increased from the bottom to the top. For PGA = 1.0 g, on the other hand, the soil acceleration responses in general decreases from bottom to the top. As for spectrum, for PGA = 0.1 g, one dominant frequency of about 7 Hz is observed. For PGA = 1.0 g the spectrum curve is more disperse than lower PGA case and there exists two dominant frequencies of about 3 Hz and 8 Hz. This phenomenon is due to the non-linear elastoplastic behavior of the clay material that can be further explained by results in Fig. 10. It is seen from Fig. 10 that for lower shaking intensity (PGA = 0.1 g) the amplification factor increases from box bottom to the top; whilst amplification factors decreases when the shaking intensity is creased (PGA > 0.2 g). For higher PGA excitation (say PGA = 0.6, 0.8 and 1.0 g), the amplification factor decrease with the depth, and amplification factors at the same depth become stable for different PGAs. The numerical results becomes closer to measured ones for higher PGAs (>0.4 g) than lower PGAs. The observations in shear box A are the same.

Acceleration peak (g)

ð2Þ

MA1 AA3 MA5 BA3

1.2 1 0.8 0.6 0.4 0.2 0

0

0.2

0.4

0.6

0.8

1

Input excitation peak (g) Fig. 12. Peak structural acceleration response and comparison of soil response.

Displacement (m)

kX i  X 0 k kX 0 k

4 FEM Experiment

2 0 -2 -4

0

1

2

3

4

5

6

7

Time (s)

(a) PGA=0.1g Displacement (m)

l¼

1.4

20 FEM Experiment

10 0 -10 -20

0

1

2

3

4

5

6

7

Time (s)

(b) PGA=0.4g Displacement (m)

Boundary effect of soil container is unavoidable in all soil structure interaction dynamic tests (Turan, 2008; Prasad et al., 2004; Pitilakis et al., 2008) and thus it is too an important aspect of the numerical model. To quantify the boundary effect of soil container in the test, an index l based on 2-Norms deviation has been introduced by the authors as follow (Chen et al., 2010):

It is seen from Figs. 8–10 that the suggested numerical model can well simulate the experimental records in time, frequency and amplitude domain. Table 4 further shows the measured and

20 FEM Experiment

10 0 -10 -20

0

1

2

3

4

5

6

7

Time (s)

(c) PGA= 0.6g Displacement (m)

4.2. Boundary effect

40 FEM Experiment

20 0 -20 -40

0

1

2

3

4

5

6

7

Time (s)

(d) PGA= 1.0g Fig. 13. Numerical and measured displacement responses of sensor AD1 under different PGAs.

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Table 5 Measured and computed peak displacement responses for different sensors (unit: mm). Sensor

PGA = 0.1 g

AD1 AD2 AD3 AD4 AD5 BD1 BD2 BD3 BD4 BD5

PGA = 0.2 g

PGA = 0.4 g

PGA = 0.6 g

FEM

Measured

FEM

Measured

FEM

Measured

FEM

Measured

FEM

Measured

FEM

2.75 2.39 2.33 2.15 2.04 1.76

2.87 2.79 2.72 2.59 2.69 2.63

5.87 5.02 4.83 4.58 4.39

5.20 5.06 4.89 4.89 5.11

11.33 10.16 10.09 9.26 8.89

10.80 10.50 10.19 10.17 10.57

16.88 15.38 15.23 13.96 13.56

15.15 14.71 14.27 14.38 15.09

23.57 21.67 20.81 18.93 18.24

21.26 20.64 20.067 20.17 20.91

31.34 28.99 27.31 24.06 22.79

26.33 25.53 24.78 24.91 25.66

1.99 1.60 1.74 1.77

2.54 2.44 2.27 2.09

4.10 3.96

5.19 4.96

9.28 7.56

10.51 10.06

13.72 11.22

14.15 13.52

17.51 15.70

20.31 19.53

24.47 20.94

24.67 23.78

3.33 3.89 3.78

4.66 4.19 3.89

6.69 7.71 7.71

9.53 8.75 8.45

10.18 11.65 11.41

12.88 11.66 11.21

13.13 15.25 15.05

18.72 17.65 16.91

16.55 19.80 18.91

22.75 21.49 20.25

70

0

60

-10 0

1

2

3

4

5

6

7

Time (s)

Strain (με)

Strain (με)

80

FEM Experiment

10

-20

(a) PGA=0.1g

Strain (με)

50 40

0.02g 0.05g 0.1g 0.2g 0.4g 0.6g 0.8g 1.0g

30 20 10

40 FEM Experiment

20

0 -2500

-2000

-1000

-500

0

(a) Frontal surface

-20 0

0

1

2

3

4

5

6

0.02g 0.05g 0.1g 0.2g 0.4g 0.6g 0.8g 1.0g

7

Time (s)

-20

Strain (με)

(b) PGA=0.4g 50 FEM Experiment

0

-50

-1500

Position (mm)

0

-40

Strain (με)

PGA = 1.0 g

Measured

20

-40

-60

0

1

2

3

4

5

6

7

Time (s)

-80 -2500

-2000

-1500

-1000

-500

0

Position (mm)

(c) PGA=0.6g

(b) Backside surface

100

Strain (με)

PGA = 0.8 g

Fig. 15. Measured strain distribution along the tunnel. FEM Experiment

50

well with the measured acceleration responses for all the sensors especially for higher PGA values.

0 -50 -100

0

1

2

3

4

5

6

7

Time (s)

(d) PGA=1.0g Fig. 14. Numerical and measured strain records of MS11 under different PGAs.

computed peak acceleration responses of different sensors in the soil. For each PGA, the measured maximum acceleration responses of sensor in box A and B are underlined in the table. It is seen from the table that the calculated acceleration responses match quite

4.4. Structure model acceleration response Fig. 11 shows the measured acceleration responses from sensors MA1, MA2 to MA5 for PGA = 1.0 g together with their corresponding power spectrum. The numerical results are also plotted in Fig. 11 for comparison. Note that the computational results agree well with the experimental results. Fig. 12 compares the peak responses of MA1, MA5 (on the structure model) with that of AA3 and BA3 (in the soil at the same location) for different PGAs. It is seen that the peak structural and soil acceleration response increase with the earthquake intensity. For lower PGA (<0.2 g), the

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Strain (με)

200

PGA, the maximum displacement (underlined values in table) occurs at the top of box A and B with one exception of PGA = 0.1 g for box B. It is seen from the table that the calculated displacement matches quite well with the measured value for most of sensors.

0.1g 0.2g 0.4g 0.6g 0.8g 1.0g

150 100

4.6. Structural strain

50 0

0

1

2

3

4

5

6

Position (m)

(a) Frontal surface

Strain (με)

200 0.1g 0.2g 0.4g 0.6g 0.8g 1.0g

150 100 50 0

0

1

2

3

4

5

6

Position (m)

(b) Backside surface Fig. 16. Distribution of structural strain along the tunnel (Numerical results).

differences between peak structural responses and surrounding soil responses are not significant. For PGA greater than 0.2 g, the structural responses are larger than soil responses, and the higher the earthquake intensity the more significant the difference. Table 4 further compares the measured and computed peak acceleration responses of MA1 to MA5. For each PGA, the measured maximum acceleration responses of sensor on the structure model are underlined in the table. It is seen from the table that the calculated acceleration responses match quite well with the measured acceleration responses for all the sensors on the structural model. 4.5. Displacement responses The displacement responses of model ground were measured in the test by sensors AD1 to AD5 for shear box A and BD1 to BD3 for shear box B. As an example, records of AD1 for PGA = 0.1, 0.4, 0.6 and 1.0 g are given in Fig. 13 together with the numerical simulated results. It is seen that the peak displacement response of model ground increase with increase of earthquake intensity. A good correspondence between the measured and calculated displacement time history at different height is achieved by the suggested numerical model. Table 5 compares the measured and computed peak displacement result of different sensors. For each

It was not an easy task to measure the strain responses of the structural model in the test. The strain gauges were buried in the soil and their data wires were also buried in the soil and ran out of the soil surface to data logger. In the test, several strain gauges were completely damaged in the test after PGA = 0.4 g case and the measurement noise due to the movement of data wire were more significant in strain records than displacement and accelerations. Therefore, all the structural strain records were screened and their qualities were carefully checked, and only reliable records were adopted for the following analysis. Fig. 14a–d shows the records of MS11 for PGA = 0.1, 0.4, 0.6 and 1.0 g respectively. Using records from MS1 to MS12 (all in shear box A), Fig. 15a and b shows the distribution of stain, for each PGA case, on the frontal and backside surfaces of the structure model when maximum compress strain value are reached. It is clear that the strain distributions at the frontal surface and backside surface of the utility tunnel are nearly symmetrical indicating that the tunnel is in bending deformation. The structural strain distribution along the utility tunnel is also calculated using the FEM model. Fig. 16 shows the absolute maximum strain values. The profile of strain distribution is similar to the experimental results. It is seen that the structural strain increase with the increase of earthquake intensity. The structural strain in the middle of shear box is larger than that at ends. The calculated structural strains are generally larger than the experimental measurements. Table 6 shows the measured and computed peak strain of sensors MS1 to MS12. For each PGA, the measured maximum strain of each sensor is underlined in the table together with the corresponding calculated values. It is seen from the table that for lower PGAs (PGA 6 0.4 g) the calculated structural strains are close to the measured values, for higher PGAs (PGA P 0.6 g) the numerical model gives higher strain value that the measured ones. 5. Concluding remarks The performance of utility tunnel under transverse non-uniform earthquake excitation is investigated in the paper through shaking table test and numerical simulations on a scaled structure model. In numerical simulation, factors as the laminar shear box, soil– structure interaction, initial stress field, element section and input of earthquake wave, are carefully considered in the finite element

Table 6 Measured and computed peak strain for different sensors (unit: le). Sensor

MS1 MS2 MS3 MS4 MS5 MS6 MS7 MS8 MS10 MS11 MS12

PGA = 0.1 g

PGA = 0.2 g

PGA = 0.4 g

PGA = 0.6 g

PGA = 0.8 g

Measured

FEM

Measured

FEM

Measured

FEM

Measured

FEM

Measured

3.08 3.24 10.57 10.74 13.34 12.41

8.01 7.93 8.65 9.58 10.17 14.15

4.62 4.18 14.23 14.35 18.78 16.75

13.46 13.35 11.78 12.39 17.95 22.57

7.99 7.26 21.29 22.29 28.29 25.81

21.44 24.43 20.36 17.72 35.78 36.32

10.74 9.84 27.28 28.82 36.30 33.95

29.24 34.83 27.32 24.85 55.84 53.15

13.08 13.72 31.25 35.09 44.90 40.25

14.15 13.12 11.13 7.57 7.44

10.17 14.15 20.29 17.29 20.29

19.11 17.83 14.69 10.63 10.19

17.95 22.57 35.97 31.03 35.97

29.61 28.17 23.95 17.12 17.14

35.78 36.32 60.88 66.18 60.88

37.86 36.24 30.62 22.33 22.98

55.84 53.15 105.02 84.84 105.02

45.81 43.65 36.07 27.85 27.92

PGA = 1.0 g FEM 39.317 45.42 33.50 27.37 77.54 70.98 77.54 70.98 158.33 105.57 158.33

Measured

FEM

16.54 14.54 36.08 38.51 49.02 44.47

53.55 51.54 35.21 34.03 89.19 94.19

51.04 48.57 41.54 30.34 30.87

89.19 94.19 215.11 157.75 215.11

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model. The results demonstrate that the designed laminar box does not impose significant boundary effect. The non-linear elastoplastic behavior of the soil under earthquake is well represented by the numerical model. The tunnel model experiences a bending deformation and its acceleration response is larger than the surrounding soil for high shaking intensity. Comparison of measured and calculated results demonstrate that the suggested numerical model is satisfactory and can thus be further used for numerical shaking table tests and numerical analysis of real life structures. Acknowledgments The authors gratefully acknowledge the financial support to this study from Key Project in the National Science & Technology Pillar Program (Grant NO. 2011BAK02B04) and Research Fund for Young Teacher supported by State Key Laboratory for Disaster Reduction in Civil Engineering (SLDRCE08-C-03). References Chouw, N., Hao, H., 2005. Study of SSI and non-uniform ground motion effect on pounding between bridge girders. Soil Dynamics and Earthquake Engineering 25, 717–728. Chouw, N., Hao, H., 2008. Significance of SSI and non-uniform near-fault ground motions in bridge response II: effect on response with modular expansion joint. Engineering Structures 30, 154–162. Chen, B., Lu, X.L., Li, P.Z., 2002. Modeling of dynamic soil–structure interaction by ANSYS program. Earthquake Engineering and Engineering Vibration 22, 126– 131 (in Chinese). Chen, J., Zhao, G.Y., Qi, X.Y., Li, J., 2008. A comparison of techniques for identifying soil dynamic properties. In: Proceedings of the Tenth International Symposium on Structural Engineering for Young Experts, October 19–21, 2008, Changsha, China. Chen, J., Shi, X.J., Li, j., 2010. Shaking table test of utility tunnel under non-uniform earthquake wave excitation. Soil Dynamics and Earthquake Engineering 30 (11), 1400–1416. Hashash, Y.M.A., Hook, J.J., 2001. Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology 16, 247–293. Huang, C., Zhang, H., Sui, Z., 2006. Development of large-scale laminar shear model box. Chinese Journal of Rock Mechanics and Engineering 25, 2128–2134 (in Chinese).

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