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Nonlinear dynamic failure process of tunnel-fault system in response to strong seismic event
Journal of Asian Earth Sciences 64 (2013) 125–135
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Nonlinear dynamic failure process of tunnel-fault system in response to strong seismic event Zhihua Yang a, Hengxing Lan a,⇑, Yongshuang Zhang b, Xing Gao a, Langping Li a a State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China b Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 17 May 2012 Received in revised form 6 December 2012 Accepted 12 December 2012 Available online 25 December 2012 Keywords: Nonlinear dynamic failure process Earthquake Dynamic response Tunnel-fault system 3DEC
a b s t r a c t Strong earthquakes and faults have significant effect on the stability capability of underground tunnel structures. This study used a 3-Dimensional Discrete Element model and the real records of ground motion in the Wenchuan earthquake to investigate the dynamic response of tunnel-fault system. The typical tunnel-fault system was composed of one planned railway tunnel and one seismically active fault. The discrete numerical model was prudentially calibrated by means of the comparison between the field survey and numerical results of ground motion. It was then used to examine the detailed quantitative information on the dynamic response characteristics of tunnel-fault system, including stress distribution, strain, vibration velocity and tunnel failure process. The intensive tunnel-fault interaction during seismic loading induces the dramatic stress redistribution and stress concentration in the intersection of tunnel and fault. The tunnel-fault system behavior is characterized by the complicated nonlinear dynamic failure process in response to a real strong seismic event. It can be qualitatively divided into 5 main stages in terms of its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. This study provides the insight into the further stability estimation of underground tunnel structures under the combined effect of strong earthquakes and faults. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The seismic behavior of underground structures (e.g., railway tunnels, road tunnels) differs from that of ground structures. Generally, underground structures usually suffer less damage compared with ground structures during a seismic event (Hashash et al., 2001; Mirko et al., 2011). However, under the strong earthquakes the damage to the underground tunnel structures is still remarkable. Numerous case studies have suggested such phenomena such as the Mw7.9 (USGS) Wenchuan earthquake in 2008, in Sichuan province, in China (Wang et al., 2009), the Hanshin earthquake in 1995 (Samata et al., 1997), the Chi-Chi earthquake in 1999 (Wang et al., 2001) and the Kocaeli earthquake in 1999 (Hashash et al., 2001). In such strong seismic events, the discontinuities (e.g., faults, joints and cracks) in rock masses play an important role in increasing its frictional instability and inducing ⇑ Corresponding author. Address: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 11A Datun Road, Chaoyang District, Beijing 100101, China. Tel.: +86 10 6488 8783. E-mail addresses: [email protected], [email protected] (H. Lan). 1367-9120/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jseaes.2012.12.006
tremendous potential threat to the stability capability of underground tunnel structures (Hashash et al., 2001). The seismic response of tunnel structures (e.g., highway tunnels, immersed tunnels) has been investigated by many researches using various methods (theoretical analysis, numerical simulation, physical model tests, et al.) (e.g., Mirko et al., 2011; Anastasopoulos et al., 2007, 2008; Genis, 2010; Sevim, 2011; Ichimura and Hori, 2009; Kirzhner and Rosenhouse, 2000; Kontoe et al., 2008; Pakbaz and Yareevand, 2005; Chen et al., 2010; Sun et al., 2011). The study results show that strong earthquakes have severe effect on the stability capability of tunnel structures. The underground tunnel structures shall become more vulnerable to strong earthquakes if affected by faults (Hashash et al., 2001; Pakbaz and Yareevand, 2005). The stability of tunnel will be reduced dramatically (Jeon et al., 2004; Anastasopoulos and Gazetas, 2010). While many researchers have mainly addressed the eventual stability of tunnel structures, the concerns are increasing on the complicated failure process of tunnel structures during a strong seismic event. The combined effect of underground tunnel structure and faults should be taken into account for optimizing structural design and improving the capability of tunnel structures resisting to strong seismic events.
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The Wenchuan earthquake caused tremendous damage to underground tunnel structures (Wang et al., 2009) and a large amount of secondary geological disasters (Yin et al., 2010; Dai et al., 2011; Dong et al., 2011; Qi et al., 2010, 2011). The results from field survey show the inner parts of investigated tunnels suffer moderate damages mainly due to fault displacements. Longmenshan fault is its major seismic fault. A section of the ChengLan Railway (from Chengdu to Lanzhou of China) was designed to cross longmenshan fault. The tunnel-fault system (underground tunnel structures crossed by active faults) was composed of the Dengjiaping Tunnel and Beichuan–Yingxiu Fault (BYF). Its dynamic response to the seismic event is investigated using a 3-Dimensional Discrete Element Code (Cundall, 1971). The real records of ground motion in the Wenchuan earthquake are used for its dynamic boundary input. Many key characteristics are examined, including stress distribution, strain, vibration velocity and failure process for a better understanding of dynamic response of the rock masses around the tunnel-fault system (RMTF). The results are expected to provide references for the engineering design and safety assessment of underground tunnel structures. 2. Study area The Longmenshan section of the Cheng-Lan Railway is located in the southeast edge of the Qinghai–Tibet Plateau characterized by complicated geological setting. For example, complicated lithology (the strata include the time period from upper Archean to Quaternary (Qi et al., 2011)) and developed active faults (e.g., Maoxian–Wenchuan Fault (MWF) (F1 in Fig. 1), Beichuan–Yingxiu Fault (BYF) (F2 in Fig. 1) and Jiangyou–Guanxian Fault (JGF) (F3 in Fig. 1). The complicated conditions of engineering geology shall bring remarkable difficulty to the construction of the Cheng-Lan Railway. The study emphasis is the tunnel-fault system that is composed of the Dengjiaping Tunnel (T2 in Fig. 1) and BYF. The Dengjiaping tunnel, a key project of the Cheng-Lan Railway, is located in the front zone of the Longmenshan cordillera and traverses the BYF.
The BYF is the central segment of Longmenshan faults system (trending NE-NNE, about 500 km long and 30–50 km wide). Fig. 2 shows the detailed engineering geological modeling section of the Dengjiaping tunnel. The entrance and exit of tunnel is located in Yangerping and Meizitan, respectively. The entire length and maximum buried depth of the tunnel is 10,534 m and 921 m, respectively. For the construction of such a long-buried railway tunnel, it is inevitable to confront some challenge of ensuring its safety. 3. Methodology 3.1. Numerical code The FEM (Finite Element Method) and FLAC (Fast Lagrangian Analysis of Continua) methods that have been used by many researchers (Anastasopoulos et al., 2007, 2008; Anastasopoulos and Gazetas, 2010; Jeon et al., 2004; Mirko et al., 2011) have the disadvantage in simulating the large deformation or displacement of rock masses. The state of plane stress in 2-dimensional model would constrain the spreading of seismic wave energy (Chen, 2000). So, the seismic response may be underestimated (Ichimura and Hori, 2009). 3DEC, which is developed to simulate the large displacement of discontinuous jointed rock masses (Cundall, 1971), overcomes these shortcomings. This method is based on the hypothesis of pseudo-rigid rock masses and the theoretic basis of Newton’s second law. So, in this paper, 3DEC is adopted to characterize the dynamic response of the tunnel-fault system to strong earthquakes. 3.2. Model 3.2.1. Geometric model According to the geological and tectonic conditions of the study area, a 3DEC geometric model with width 50 km, length 50 km and height 10 km (Fig. 3a) was constructed. The geometric model includes 11 strata (11 different color in Fig. 3a and b), one tunnel
Fig. 1. Geological and tectonic map of the Longmenshan section of the Cheng-Lan Railway (from Chengdu to Lanzhou of China). F1: Maoxian–Wenchuan Fault (MWF), F2: Beichuan–Yingxiu Fault (BYF), F3: Jiangyou–Guanxian Fault (JGF). T1: Longmenshan Tunnel, T2: Dengjiaping Tunnel.
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Fig. 2. Engineering geological section of the Dengjiaping tunnel. F2 is the modeled Beichuan–Yingxiu Fault (BYF).
Fig. 3. (a) Side view of the 3DEC geometric model. (b) Overlooking view of the 3DEC geometric model. (c) The block discretization of tunnel model. (d) Close-up of the partial block discretization of tunnel model cut by fault (F2), whose front face is the intersection interface of tunnel and fault. The black dots in (b) and (d) are the monitoring points to examine the dynamic response of rock masses during seismic loading. F1, F2 and F3 have the same meaning as Fig. 1. T (black dashed line) is the ground projection of the tunnel model. The lithology of strata is shown in Table 1 through the corresponding ID.
(T in Fig. 3b) and three faults (F1, F2 and F3 in Fig. 3a and b). The tunnel (T) and fault (F2) compose the tunnel-fault system that is the study emphasis in this paper. Three faults are also the boundaries of different strata. The entire model length of tunnel axis is 200 m with individual length about 100 m in 2 different strata (Fig. 3c). Relative to ground surface, the buried depth of tunnel axis is 800 m. The shape of tunnel is saddle-shape with width 10 m and height 9 m.
3.2.2. Parameters Rock masses and discontinuities adopted ‘‘Mohr–Coulomb plasticity’’ and ‘‘Coulomb slip’’ constitutive model, respectively. The parameters have been calibrated including the rock mass (Young’s modulus, Poisson’s ratio and density) and joint properties (stiffness, cohesion, friction angle, etc.) (Table 1 and Table 2). The initial properties were selected referring to related literatures (Starfield and Cundall, 1988; Lan and Wu, 2001), 3DEC manual (Itasca, 2007) and a number of the experiential material properties within the study area. The joint properties were assigned to both faults and beddings based on the estimation of their mobility characteristics. These parameters were then adjusted prudentially by examining the ground displacement of various monitoring points until
Table 1 Material properties of rock masses (ID: Strata ID in Fig. 3. E: Young’s modulus. m: Poisson’s ratio. q: Mass density). ID
Lithology
E (GPa)
m
q (kg/m3)
1 2, 6 3, 10 4 5,11 7 8 9
Sandstone, clay Limestone, dolomite Carbonatite, clastic rock Granite Sandstone, shale, dolomite Muddy shale, siltstone, sandstone Phyllite, slate Mudstone, siltstone
19.3 28.5 43.0 73.8 53.0 11.1 30.0 50.0
0.38 0.29 0.27 0.22 0.26 0.29 0.25 0.25
2200 2300 2400 2700 2450 2300 2600 2500
their displacement magnitude is agreeable to the field survey at the nearest locations. 3.2.3. Dynamic input The actual acceleration histories of ground motion during the Wenchuan earthquake measured by Qingping observation site, Sichuan province, China were adopted for dynamic analysis. The acceleration histories include three orientations: east–west orientation (EW), north–south orientation (NS) and vertical orientation (UD). Considering computational efficiency of 3DEC model, the
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Table 2 Material properties of discontinuities (Kn: normal stiffness. Ks: shear stiffness. C: cohesion. u: internal frictional angle. T: tensile strength. C0 : residual cohesion. u0 : residual internal frictional angle. F1, F2 and F3 are the fault models in Fig. 3). Discontinuities
Kn (GPa)
Ks (GPa)
C (MPa)
U (°)
T (MPa)
C0 (MPa)
u0 (°)
F1 F2 F3 Bedding
1.0 0.9 1.1 5.0
0.8 0.6 0.7 4.0
0.8 0.7 0.5 3.5
25 24 26 30
0.5 0.4 0.6 5.0
0.4 0.4 0.5 0.4
20 21 22 25
records between 30th and 80th second of the acceleration histories, in which most seismic energy distributes were selected for dynamic analysis. The selected acceleration history sections with duration 50 s were converted to stress histories (Itasca, 2007) (Fig. 4), which were added to 3DEC model as stress wave.
boundary, respectively. Finally, the dynamic calculation was achieved under the seismic loading using the stress histories.
3.3. Dynamic calculation
We carried out model validation using qualitative and quantitative validation methods. The qualitative method is to compare the fault’s rupture characteristics between modeled results and field survey. The Wenchuan earthquake induces abundant co-seismic ground rupture, of which one typical ground rupture at Qingping observation site near the BYF is shown in Fig. 5 (Chen et al., 2009). The modeled fault behaved in the same way of thrusting with right strike-slip (Fig. 15) as real faulting. The modeled damage pattern is also agreeable with that observed at filed survey. The modeled tunnel structure shows shear-tension damage characteristics which can be observed in many tunnels during the Wenchuan earthquake (Wang et al., 2009).
Based on the 3DEC geometric model and the calibrated parameters, numerical calculation was conducted. Firstly, the model was initially run to the static equilibrium under only gravity and initial field stress to equilibrate the body forces and the boundary forces prior to the seismic loading. Then, the model was subjected to various dynamic conditions. The model adopted Rayleigh damping to describe the energy loss of physical system. The coefficient of Rayleigh damping adopted the critical damping ratio 0.05 and the fundamental frequency 20 Hz. The bottom, top and four sides of model adopted viscous boundary, free boundary and free-field
3.4. Model validation
Fig. 4. The stress histories with duration 50 s from actual acceleration histories of the Wenchuan earthquake measured by the Qingping observation site, Sichuan province, China. (a) East–west orientation (EW). (b) North–south orientation (NS). (c) Vertical orientation (UD).
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Fig. 5. Co-seismic ground rupture and their measured topographic profiles on the main road (a) and on the third terrace (b) at Qingping observation site, Sichuan province, China (Chen et al., 2009).
The quantitative method is to statistically compare values of the ground motion displacement along the Beichuan–Yingxiu fault between modeled results and field survey. In terms of the field survey of ground motion after Wenchuan earthquake, along the BYF, the vertical displacement of ground rupture is between 1.6 m and 6.0 m with an average of 2.9 m, and the horizontal displacement of ground rupture is between 0.2 m and 6.5 m with an average of 3.1 m (Chen et al., 2009; Li et al., 2009). The modeled horizontal and vertical displacement values (Table 3) of the monitoring points in Fig. 3b were acquired, which were statistically compared with field survey (Fig. 6). The modeled average vertical displacement and horizontal displacement is 2.75 m and 3.18 m with error of 5.17% and 2.58% comparing with field survey, respectively. The coincidence or comparability between the modeled faulting displacement and field survey shows that the modeled numerical results have high reliability. 4. Results 4.1. Stress distribution In order to analyze the effect of fault on stress distribution and stress concentration in the RMTF under strong seismic excitation, the maximum principle stress distribution of four tunnel cross-sections in the 10th second of seismic loading, when there is considerable stress concentration, was acquired (Fig. 7). Many previous studies have shown that stress redistribution and stress concentration may occur in the RMTF under strong external disturbance (Moore and Guan, 1996). In the case of the absence of fault (Fig. 7a), the stress distribution is mainly affected by tunnel structures and free surface amplification of seismic waves propagation. The tensile stress concentration (red color in Fig. 7a) with a symmetric distribution can be observed on both side walls of tunnel. Simultaneously, the slight compressive stress concentration (blue color in Fig. 7a) can also be observed on the top of tunnel. So, the top and both side walls of tunnel are likely to encounter more damage.
Fig. 6. The comparison between real records in the Wenchuan earthquake and numerical modeled results of ground motion along the BYF.
The presence and dislocation of faults in rock masses (Fig. 7b– d) induced the reflection and refraction of seismic waves, and affected their propagation characteristics (Wang et al., 2006), which formed complicated seismic wave field. As a result, stress redistribution and stress concentration near faulting region in rock masses arose. The tensile stress concentration (red color in Fig. 7b–d) can be observed along the oblique faults in all three scenarios. Simultaneously, the compressive stress concentration (deep blue color in Fig. 7b–d) can also be observed in some regions. In addition, the area characterized by stress concentration in the circumstance of the presence of fault is much larger than that of the absence of fault. So, the difference of stress distribution between two scenarios of the presence and absence of fault can be attributed to the significant effect of faults on seismic wave propagation. In order to further analyze the effect of the tunnel-fault interaction on the stress distribution in RMTF under strong seismic excitation, the maximum principle stress distribution along tunnel and fault in the 10th second of seismic loading is acquired (Fig. 8). Then, the average maximum principal stress values along tunnel (the top and bottom of tunnel) (Fig. 9) and fault (Fig. 10) from the 7th to 15th second of seismic loading are acquired.
Table 3 Numerical modeled results of ground motion along the BYF (H: horizontal displacement. V: vertical displacement. A: average displacement).
H (m) V (m)
1
2
3
4
5
6
7
8
9
10
11
12
A (m)
4.68 3.59
4.71 2.93
4.53 3.28
4.55 3.64
4.66 3.51
4.08 3.21
3.73 3.74
1.41 1.85
1.86 2.47
1.31 1.74
1.45 1.64
1.45 1.41
3.18 2.75
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Fig. 7. Maximum principal stress distribution of four tunnel cross-sections in the tenth second of seismic loading. The dotted lines indicate the faults. The locations of tunnel cross-sections are shown in Fig. 8. Please note that there is some rupture failure and dislocation along faults (see red circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Stress (Pa)
Fig. 8. Maximum principal stress distribution along tunnel and fault in the tenth second of seismic loading. The oblique dotted line indicates the fault with length 200 m. The vertical dotted lines ((1) 112 m, (2) 100 m, (3) 92 m, (4) 84 m) indicate the locations of four tunnel cross-sections (a–d in Fig. 7, respectively. The black dots are the monitoring points to examine the dynamic response of rock masses during seismic loading.
4.5E+07 4.0E+07 3.5E+07 3.0E+07 2.5E+07 2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00
tunnel top tunnel bottom
0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
Length (m) Fig. 9. Average maximum principal stress along the top and bottom of tunnel from the 7th to 15th second of seismic loading.
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4.5E+07 4.0E+07 3.0E+07 2.5E+07
tunnel
Stress (Pa)
3.5E+07
2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00 0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
Length (m) Fig. 10. Average maximum principle stress along fault from the 7th to 15th second of seismic loading. The center of tunnel is located at 100 m. The 0 m and 200 m is the bottom and top of fault, respectively.
Fig. 11. Vibration velocity histories with duration 60 s of monitoring point c, e (a), p and r (b), as shown in Fig. 8, during the dynamic response of tunnel-fault system.
The obvious stress concentration (red1 color in Fig. 8) can be observed in the intersection of tunnel and fault. However, there is not obvious stress concentration away from the intersection of tunnel and fault. So, the phenomena of dramatic stress concentration in the intersection of tunnel and fault can be attributed to the intensive tunnel-fault interaction under strong seismic excitation. In addition, the values of the maximum principle stress, as shown in Fig. 9 and Fig. 10, as well as the area of stress concentration are larger in the top than in the bottom of tunnel. As a result, the intersection of tunnel and fault is likely to encounter more damage than other regions.
4.2. Vibration velocity The tunnel-fault interaction can also be reflected by the vibration behavior of rock masses along tunnel and fault. We analyzed the vibration behavior using the vibration velocity histories of the monitoring points along tunnel and fault, as shown in Fig. 8. The vibration velocity histories of monitoring point c, e, p and r are illustrated in Fig. 11. On the whole, the vibration action is more intensive from about the 5th to the 25th second when there are strong stress waves with high energy (Fig. 4). After the termination of seismic loading in the 50th second, the vibration velocity weak1 For interpretation of color in Figs. 8 and 15, the reader is referred to the web version of this article.
ens remarkably. The fluctuation trend of vibration velocity histories shows that the vibration motion of monitoring point e and p is more intensive than that of monitoring point c and r, respectively. So, the stress and strain at the monitoring point e and p response more intensively than other points since they are closer to the intersection of tunnel and fault than monitoring point c and r. The peak vibration velocity values of all monitoring points (in Fig. 8) are illustrated in Fig. 12. Along fault and the top of tunnel, the peak vibration velocity values gradually decrease with increasing distance to the intersection of tunnel and fault where there is intensive tunnel-fault interaction. That is to say, the effect of tunnel-fault interaction on dynamic response of tunnel-fault system gradually decreases with increasing distance to the intersection of tunnel and fault.
4.3. Tunnel failure process In this study, the tunnel failure process was examined though analyzing the dislocation displacement characteristics of the RMTF. Based on the motion characteristics of the monitoring points in Fig. 3d, the average horizontal and vertical displacement histories (Fig. 13), and the maximum principle strain rate history (Fig. 14) of the RMTF were acquired. Fig. 13 shows that, on the whole, the vertical displacement is larger than the horizontal displacement. From Fig. 13 and Fig. 14, we can observe that the nonconstant tan-
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Fig. 12. Peak vibration velocity of all monitoring points along tunnel (a) and fault (b), as shown in Fig. 8, during the dynamic response of tunnel-fault system.
(1 ) (2 )
3.500
(3 )
(4 )
(5 )
Displacement (m)
3.000 2.500 2.000 1.500 1.000
Vertical displacement
0.500
Horizontal displacement
0.000
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Time (s) Fig. 13. Dislocation displacement histories of the RMTF statistically resulted from monitoring points in Fig. 3d. The time sections (1–5) divided by dotted lines indicate five main stages of tunnel failure process (see Section 5).
(1 ) (2 )
1.200
(4 )
(5 )
0.98
1.000
strain rate
(3 )
0.800 0.600 0.400 0.200 0.000 0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Time (s) Fig. 14. Maximum principle strain rate history of the RMTF resulted from monitoring points in Fig. 3d. The time sections (1–5) have the same meaning as that in Fig. 13.
gent slope of displacement history curves and nonconstant strain rate, which shows that the dislocation displacement of the RMTF goes through non-uniform growth. Fig. 15 shows typical failure state and maximum principle stress distribution of the RMTF during seismic response of the tunnelfault system. Fig. 15a shows the initial static equilibrium state without obvious stress concentration and tunnel failure before seismic loading. The faulting regions are very likely weaker than surrounding rocks and thus are more responsive to the stress change induced by earthquakes (Duan, 2010). The red color (Fig. 15b–f) indicates the remarkable stress accumulation and stress concentration, which suggests the intensive tunnel-fault interaction in the intersection of tunnel and fault during seismic loading. When the accumulated stress in the RMTF (shear stress,
especially) exceeds the fault strength, the fault begins to rupture and the tunnel begins to fail which can be indicated by the dislocation displacement in the intersection of tunnel and fault in Fig. 15. In the 10th second of seismic loading, the dislocation displacement of the RMTF sharply increases (large tangent slope in Fig. 13), and the strain rate arrives at peak value (Fig. 14). Then, the accumulated stress begins to release, which can be indicated by the decreasing area with red color from Fig. 15c to f. With the gradual decrease of seismic loading, the tunnel-fault interaction in the intersection of tunnel and fault begins to weaken, and the dislocation displacement rate of the RMTF begins to decreases. After the termination of seismic loading in the 50th second, the dislocation displacement of the RMTF has no obvious increase and the tunnel-fault system gradually approaches to the
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Fig. 15. Typical failure state and maximum principal stress distribution of the RMTF during seismic loading. (a) is the initial statically balanced state before seismic loading. (b–f) are the typical scenario of five time sections (1–5) in Fig. 13 and Fig. 14, respectively. Relative to the intersection of tunnel axis and fault interface, the length, height and width of the RMTF are 120 m, 15 m and 15 m, respectively.
stable state with static equilibrium. The residual dislocation displacement can be found comparing the tunnel failure scenario in Fig 15a and f. 5. Discussion The tectonic structure of the tunnel-fault system that includes many geological and structural objects is considerably complicated. Lan et al. (2010, 2012) has suggested that the stress redistribution within the discontinuous rock masses plays an important role in their damage processes. The interaction between fault and tunnel structure dramatically amplify the effect of seismic event on the rock mass behavior during the development of progressive deformation and failure process. The initial static equilibrium of field stress in rock masses is disturbed by the strong seismic excitation, and then the initial field stress begins to redistribute. During the stress redistribution, the remarkable stress accumulation and stress concentration is observed in the intersection of tunnel and fault because of intensive tunnel-fault interaction and geological material-tunnel interaction. The local stress concentration results in the non-uniform stress distribution. From the different seismic response characteristics of key elements (stress, strain, displacement and rate) at the different location of rock masses, we can include that the seismic response in the intersection of tunnel and fault is more intensive. So, the intersection of tunnel and fault could have more damage and potential threat to the tunnel structures. Lan et al. (2012) investigated the damage evolution of in situ rock mass damage induced by mechanical–thermal loading and suggested that the failure process can be divided by a number of distinct stages. Similarly, based on the non-uniform growth of the dislocation displacement of the RMTF and associated stress, strain developing characteristics, we can conclude that the tunnel failure process is nonlinear under the combined effect of strong earthquakes and faults. The process can be qualitatively divided
into 5 main stages (see Fig. 13 and Fig. 14) based on its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. 5.1. Strain localization The preliminary stress concentration in the intersection of tunnel and fault induces the slight deformation, and then the intensive deformation concentration at some location of rock masses. The performance of non-continuous deformation development is named strain localization (Fig. 15b). The strain localization is the aura of severe rock masses failure. 5.2. Rupture initiation The severe strain localization changes the internal structure of rock masses, which dynamically reduces its frictional strength, and then increases its frictional instability. Small dislocation displacement occurs along the weak fault in the intersection of tunnel and fault (Fig. 15c), which indicates the formation of shear slide surface, as well as is the breakthrough point of the progressive failure of the entire RMTF. 5.3. Rupture acceleration With the high seismic loading in this stage, the accumulated stress rapidly grows. As a result, the dramatic rupture failure occurs along the weak fault in the intersection of tunnel and fault, and the dislocation displacement (Fig. 13) and failure area (Fig. 15d) rapidly increases. The principle strain rate arrives at peak value (Fig. 14). Due to the remarkable rupture failure of rock masses consumes some internal energy coming from accumulated stress, the accumulated stress in rock masses begins to release, and the area with high accumulated stress begins to decrease.
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5.4. Spontaneous rupture growth After the remarkable rupture failure occurrence, the rupture failure spontaneously grows mainly along the weak fault and other discontinuities in rock masses under the continuous seismic loading (Fig. 15e). Rupture propagation on a major active fault is controlled by the properties of slip-weakening friction law on the fault. Friction controls the initiation, development of rupture, and the healing of faults (Madariaga et al., 1998). 5.5. Stabilization In this stage, the seismic loading terminates, and the accumulated stress further releases. The tunnel-fault system comes into self-stabilization stage, and finally reaches the stable state with static equilibrium (Fig. 15f). The seismic induced residual dislocation displacement (residual deformation) can be observed in the post-earthquake equilibrium state (Fig. 15f) as compare with the initial statically balanced state (Fig. 15a). 6. Conclusions There are significant challenges to provide a better understanding of the tunnel-fault interaction and the tunnel failure process under the combined effect of strong earthquakes and faults. Nonetheless, 3-D discontinuous element modeling approach and abundant data acquired for the Mw7.9 Wenchuan earthquake occurred in May 12, 2008 provide an opportunity to investigate the dynamic responses of tunnel-fault system to the strong seismic event. The displacements from the numerical modeling were in reasonable agreement with the measured displacement along faulting system. The modeled distribution and evolution of key elements (stress, strain, displacement and rate) were capable of capturing the characteristics of these complicated dynamic processes. The dynamic failure process of tunnel-fault system is a stressdominant progressive process. The stress redistribution and evolution play a significant role in the development of failure process of the RMTF during the strong earthquake. The non-linear failure process of tunnel-fault system induced by strong seismic event is characterized by several different stages with different response characteristics. More complicated mechanism might be behind this process, e.g., the deterioration of friction and strength of rock masses. The comparison of tunnel-fault system to far-field rock mass behavior reveals basic characteristics of tunnel-fault interaction in response to strong seismic event. Despite the limitation of numerical modeling at such large scale, it appears to have captured many key elements of the failure processes of tunnel-fault system under strong seismic event. Understanding of these processes helps to link the seismic response of tunnel to its stability analysis. Acknowledgements This research was supported by the National Science Foundation of China (41072241) and Chinese geological survey program (1212010914025). The authors also wish to acknowledge the Chinese Seismic Bureau for providing the seismic ground motion data. References Anastasopoulos, I., Gazetas, G., 2010. Analysis of cut-and-cover tunnels against large tectonic deformation. Bulletin of Earthquake Engineering 8, 283–307. Anastasopoulos, I., Gerolymos, N., Drosos, V., Kourkoulis, R., Georgarakos, T., Gazetas, G., 2007. Nonlinear response of deep immersed tunnel to strong
seismic shaking. Journal of Geotechnical and Geoenvironmental Engineering 133, 1067–1090. Anastasopoulos, I., Gerolymos, N., Drosos, V., Georgarakos, T., Kourkoulis, R., Gazetas, G., 2008. Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking. Bulletin of Earthquake Engineering 6, 213–239. Chen, S.G., 2000. Discrete element modeling of an underground explosion in a jointed rock mass. Geotechnical and Geological Engineering 18, 59–78. Chen, G.H., Xu, X.W., Yu, G.H., An, Y.F., Yuan, R.M., Guo, T.T., Gao, X., Yang, H., Tan, X.B., 2009. Co-seismic slip and slip partitioning of multi-faults during the Ms8.0 Wenchuan earthquake. Chinese Journal Geophysics 25, 1384–1394 (in Chinese with English abstract). 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, 1400–1416. Cundall, P.A., 1971. A computer model for simulating progressive, large-scale movements in blocky rock systems. In: Proceedings of Symposium of International Society of Rock Mechanics. Nancy, France. Dai, F.C., Xu, C., Yao, X., Xu, L., Tu, X.B., Gong, Q.M., 2011. Spatial distribution of landslides triggered by the 2008 Ms 8.0 Wenchuan earthquake, China. Journal of Asian Earth Sciences 40, 883–895. Dong, Y.F., Li, Q., Dou, A.X., Wang, X.Q., 2011. Extracting damages caused by the 2008 Ms 8.0 Wenchuan earthquake from SAR remote sensing data. Journal of Asian Earth Sciences 40, 907–914. Duan, B.C., 2010. Inelastic response of compliant fault zones to nearby earthquakes. Geophysical Research Letters 2010 (37), L16303. http://dx.doi.org/10.1029/ 2010GL044150. Genis, M., 2010. Assessment of the dynamic stability of the portals of the Dorukhan tunnel using numerical analysis. International Journal of Rock Mechanics and Mining Sciences 47, 1231–1241. Hashash, Y.M.A., Hook, J.J., Schmidt, B., Yao, J.I.C., 2001. Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology 16, 247–293. Ichimura, T., Hori, M., 2009. Structural seismic response analysis based on multiscale approach of computing fault-structure system. Earthquake Engineering and Structural Dynamics 38, 439–445. Itasca, 2007. 3 Dimensional Distinct Element Code User’s guide, USA. Jeon, S., Kim, J., Seo, Y., Hong, C., 2004. Effect of a fault and weak plane on the stability of a tunnel in rock – a scaled model test and numerical analysis. International Journal of Rock Mechanics and Mining Sciences 41, 486. Kirzhner, F., Rosenhouse, G., 2000. Numerical analysis of tunnel dynamic response to earth motions. Tunneling and Underground Space Technology 15, 249–258. Kontoe, S., Zdravkovic, L., Potts, D.M., Menkiti, C.O., 2008. Case study on seismic tunnel response. Canadian Geotechnical Journal 45, 1743–1764. Lan, H.X., Wu, F.Q., 2001. The decision of mechanical parameters for numerical simulation of rock and soil mechanics. World Geology 20, 66–71 (in Chinese with English abstract). Lan, H.X., Martin, C.D., Hu, B., 2010. Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. Journal of Geophysical Research-Solid Earth 115, B01202. http://dx.doi.org/10.1029/ 2009JB006496. Lan, H.X., Martin, C.D., Andersson, J.C., 2012. Evolution of in situ rock mass damage induced by mechanical–thermal loading. Rock Mechanics and Rock Engineering. http://dx.doi.org/10.1007/s00603-012-0248-8. Li, Y., Huang, R.Q., Zhou, R.J., 2009. Geological background of Longmenshan seismic belt and surface ruptures in Wenchuan earthquake. Journal of Engineering Geology 17 (1), 3–18 (in Chinese with English abstract). Madariaga, R., Olsen, K., Archuleta, R., 1998. Modeling dynamic rupture in a 3D earthquake fault model. Bulletin of the Seismological Society of America 88, 1182–1197. Mirko, C., Laura, C., Carlo, G.L., Roberto, P., 2011. Seismic analysis of deep tunnels in near fault conditions: a case study in Southern Italy. Bulletin of Earthquake Engineering 9, 975–995. Moore, I., Guan, F., 1996. Three-dimensional dynamic response of lined tunnels due to incident seismic waves. Earthquake Engineering and Structural Dynamics 25, 357–369. Pakbaz, M., Yareevand, A., 2005. 2-D analysis of circular tunnel against earthquake loading. Tunneling and Underground Space Technology 20, 411– 417. Qi, S.W., Xu, Q., Lan, H.X., Zhang, B., Liu, J.Y., 2010. Spatial distribution analysis of landslides triggered by 2008.5.12 Wenchuan Earthquake, China. Engineering Geology 116, 95–108. Qi, S.W., Xu, Q., Zhang, B., Zhou, Y.D., Lan, H.X., Li, L.H., 2011. Source characteristics of long runout rock avalanches triggered by the 2008 Wenchuan earthquake, China. Journal of Asian Earth Sciences 40, 896–906. Samata, S., Ohuchi, H., Matsuda, T., 1997. A study of the damage of subway structures during the 1995 Hanshin-Awaji earthquake. Cement and Concrete Composites 19, 223–239. Sevim, B., 2011. Nonlinear earthquake behaviour of highway tunnels. Natural Hazards and Earth System Sciences 11, 2755–2763. Starfield, A.M., Cundall, P.A., 1988. Towards a methodology for rock mechanics modeling. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 25, 99–106.
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Contents lists available at SciVerse ScienceDirect
Journal of Asian Earth Sciences journal homepage: www.elsevier.com/locate/jseaes
Nonlinear dynamic failure process of tunnel-fault system in response to strong seismic event Zhihua Yang a, Hengxing Lan a,⇑, Yongshuang Zhang b, Xing Gao a, Langping Li a a State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China b Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 17 May 2012 Received in revised form 6 December 2012 Accepted 12 December 2012 Available online 25 December 2012 Keywords: Nonlinear dynamic failure process Earthquake Dynamic response Tunnel-fault system 3DEC
a b s t r a c t Strong earthquakes and faults have significant effect on the stability capability of underground tunnel structures. This study used a 3-Dimensional Discrete Element model and the real records of ground motion in the Wenchuan earthquake to investigate the dynamic response of tunnel-fault system. The typical tunnel-fault system was composed of one planned railway tunnel and one seismically active fault. The discrete numerical model was prudentially calibrated by means of the comparison between the field survey and numerical results of ground motion. It was then used to examine the detailed quantitative information on the dynamic response characteristics of tunnel-fault system, including stress distribution, strain, vibration velocity and tunnel failure process. The intensive tunnel-fault interaction during seismic loading induces the dramatic stress redistribution and stress concentration in the intersection of tunnel and fault. The tunnel-fault system behavior is characterized by the complicated nonlinear dynamic failure process in response to a real strong seismic event. It can be qualitatively divided into 5 main stages in terms of its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. This study provides the insight into the further stability estimation of underground tunnel structures under the combined effect of strong earthquakes and faults. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The seismic behavior of underground structures (e.g., railway tunnels, road tunnels) differs from that of ground structures. Generally, underground structures usually suffer less damage compared with ground structures during a seismic event (Hashash et al., 2001; Mirko et al., 2011). However, under the strong earthquakes the damage to the underground tunnel structures is still remarkable. Numerous case studies have suggested such phenomena such as the Mw7.9 (USGS) Wenchuan earthquake in 2008, in Sichuan province, in China (Wang et al., 2009), the Hanshin earthquake in 1995 (Samata et al., 1997), the Chi-Chi earthquake in 1999 (Wang et al., 2001) and the Kocaeli earthquake in 1999 (Hashash et al., 2001). In such strong seismic events, the discontinuities (e.g., faults, joints and cracks) in rock masses play an important role in increasing its frictional instability and inducing ⇑ Corresponding author. Address: State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 11A Datun Road, Chaoyang District, Beijing 100101, China. Tel.: +86 10 6488 8783. E-mail addresses: [email protected], [email protected] (H. Lan). 1367-9120/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jseaes.2012.12.006
tremendous potential threat to the stability capability of underground tunnel structures (Hashash et al., 2001). The seismic response of tunnel structures (e.g., highway tunnels, immersed tunnels) has been investigated by many researches using various methods (theoretical analysis, numerical simulation, physical model tests, et al.) (e.g., Mirko et al., 2011; Anastasopoulos et al., 2007, 2008; Genis, 2010; Sevim, 2011; Ichimura and Hori, 2009; Kirzhner and Rosenhouse, 2000; Kontoe et al., 2008; Pakbaz and Yareevand, 2005; Chen et al., 2010; Sun et al., 2011). The study results show that strong earthquakes have severe effect on the stability capability of tunnel structures. The underground tunnel structures shall become more vulnerable to strong earthquakes if affected by faults (Hashash et al., 2001; Pakbaz and Yareevand, 2005). The stability of tunnel will be reduced dramatically (Jeon et al., 2004; Anastasopoulos and Gazetas, 2010). While many researchers have mainly addressed the eventual stability of tunnel structures, the concerns are increasing on the complicated failure process of tunnel structures during a strong seismic event. The combined effect of underground tunnel structure and faults should be taken into account for optimizing structural design and improving the capability of tunnel structures resisting to strong seismic events.
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The Wenchuan earthquake caused tremendous damage to underground tunnel structures (Wang et al., 2009) and a large amount of secondary geological disasters (Yin et al., 2010; Dai et al., 2011; Dong et al., 2011; Qi et al., 2010, 2011). The results from field survey show the inner parts of investigated tunnels suffer moderate damages mainly due to fault displacements. Longmenshan fault is its major seismic fault. A section of the ChengLan Railway (from Chengdu to Lanzhou of China) was designed to cross longmenshan fault. The tunnel-fault system (underground tunnel structures crossed by active faults) was composed of the Dengjiaping Tunnel and Beichuan–Yingxiu Fault (BYF). Its dynamic response to the seismic event is investigated using a 3-Dimensional Discrete Element Code (Cundall, 1971). The real records of ground motion in the Wenchuan earthquake are used for its dynamic boundary input. Many key characteristics are examined, including stress distribution, strain, vibration velocity and failure process for a better understanding of dynamic response of the rock masses around the tunnel-fault system (RMTF). The results are expected to provide references for the engineering design and safety assessment of underground tunnel structures. 2. Study area The Longmenshan section of the Cheng-Lan Railway is located in the southeast edge of the Qinghai–Tibet Plateau characterized by complicated geological setting. For example, complicated lithology (the strata include the time period from upper Archean to Quaternary (Qi et al., 2011)) and developed active faults (e.g., Maoxian–Wenchuan Fault (MWF) (F1 in Fig. 1), Beichuan–Yingxiu Fault (BYF) (F2 in Fig. 1) and Jiangyou–Guanxian Fault (JGF) (F3 in Fig. 1). The complicated conditions of engineering geology shall bring remarkable difficulty to the construction of the Cheng-Lan Railway. The study emphasis is the tunnel-fault system that is composed of the Dengjiaping Tunnel (T2 in Fig. 1) and BYF. The Dengjiaping tunnel, a key project of the Cheng-Lan Railway, is located in the front zone of the Longmenshan cordillera and traverses the BYF.
The BYF is the central segment of Longmenshan faults system (trending NE-NNE, about 500 km long and 30–50 km wide). Fig. 2 shows the detailed engineering geological modeling section of the Dengjiaping tunnel. The entrance and exit of tunnel is located in Yangerping and Meizitan, respectively. The entire length and maximum buried depth of the tunnel is 10,534 m and 921 m, respectively. For the construction of such a long-buried railway tunnel, it is inevitable to confront some challenge of ensuring its safety. 3. Methodology 3.1. Numerical code The FEM (Finite Element Method) and FLAC (Fast Lagrangian Analysis of Continua) methods that have been used by many researchers (Anastasopoulos et al., 2007, 2008; Anastasopoulos and Gazetas, 2010; Jeon et al., 2004; Mirko et al., 2011) have the disadvantage in simulating the large deformation or displacement of rock masses. The state of plane stress in 2-dimensional model would constrain the spreading of seismic wave energy (Chen, 2000). So, the seismic response may be underestimated (Ichimura and Hori, 2009). 3DEC, which is developed to simulate the large displacement of discontinuous jointed rock masses (Cundall, 1971), overcomes these shortcomings. This method is based on the hypothesis of pseudo-rigid rock masses and the theoretic basis of Newton’s second law. So, in this paper, 3DEC is adopted to characterize the dynamic response of the tunnel-fault system to strong earthquakes. 3.2. Model 3.2.1. Geometric model According to the geological and tectonic conditions of the study area, a 3DEC geometric model with width 50 km, length 50 km and height 10 km (Fig. 3a) was constructed. The geometric model includes 11 strata (11 different color in Fig. 3a and b), one tunnel
Fig. 1. Geological and tectonic map of the Longmenshan section of the Cheng-Lan Railway (from Chengdu to Lanzhou of China). F1: Maoxian–Wenchuan Fault (MWF), F2: Beichuan–Yingxiu Fault (BYF), F3: Jiangyou–Guanxian Fault (JGF). T1: Longmenshan Tunnel, T2: Dengjiaping Tunnel.
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Fig. 2. Engineering geological section of the Dengjiaping tunnel. F2 is the modeled Beichuan–Yingxiu Fault (BYF).
Fig. 3. (a) Side view of the 3DEC geometric model. (b) Overlooking view of the 3DEC geometric model. (c) The block discretization of tunnel model. (d) Close-up of the partial block discretization of tunnel model cut by fault (F2), whose front face is the intersection interface of tunnel and fault. The black dots in (b) and (d) are the monitoring points to examine the dynamic response of rock masses during seismic loading. F1, F2 and F3 have the same meaning as Fig. 1. T (black dashed line) is the ground projection of the tunnel model. The lithology of strata is shown in Table 1 through the corresponding ID.
(T in Fig. 3b) and three faults (F1, F2 and F3 in Fig. 3a and b). The tunnel (T) and fault (F2) compose the tunnel-fault system that is the study emphasis in this paper. Three faults are also the boundaries of different strata. The entire model length of tunnel axis is 200 m with individual length about 100 m in 2 different strata (Fig. 3c). Relative to ground surface, the buried depth of tunnel axis is 800 m. The shape of tunnel is saddle-shape with width 10 m and height 9 m.
3.2.2. Parameters Rock masses and discontinuities adopted ‘‘Mohr–Coulomb plasticity’’ and ‘‘Coulomb slip’’ constitutive model, respectively. The parameters have been calibrated including the rock mass (Young’s modulus, Poisson’s ratio and density) and joint properties (stiffness, cohesion, friction angle, etc.) (Table 1 and Table 2). The initial properties were selected referring to related literatures (Starfield and Cundall, 1988; Lan and Wu, 2001), 3DEC manual (Itasca, 2007) and a number of the experiential material properties within the study area. The joint properties were assigned to both faults and beddings based on the estimation of their mobility characteristics. These parameters were then adjusted prudentially by examining the ground displacement of various monitoring points until
Table 1 Material properties of rock masses (ID: Strata ID in Fig. 3. E: Young’s modulus. m: Poisson’s ratio. q: Mass density). ID
Lithology
E (GPa)
m
q (kg/m3)
1 2, 6 3, 10 4 5,11 7 8 9
Sandstone, clay Limestone, dolomite Carbonatite, clastic rock Granite Sandstone, shale, dolomite Muddy shale, siltstone, sandstone Phyllite, slate Mudstone, siltstone
19.3 28.5 43.0 73.8 53.0 11.1 30.0 50.0
0.38 0.29 0.27 0.22 0.26 0.29 0.25 0.25
2200 2300 2400 2700 2450 2300 2600 2500
their displacement magnitude is agreeable to the field survey at the nearest locations. 3.2.3. Dynamic input The actual acceleration histories of ground motion during the Wenchuan earthquake measured by Qingping observation site, Sichuan province, China were adopted for dynamic analysis. The acceleration histories include three orientations: east–west orientation (EW), north–south orientation (NS) and vertical orientation (UD). Considering computational efficiency of 3DEC model, the
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Table 2 Material properties of discontinuities (Kn: normal stiffness. Ks: shear stiffness. C: cohesion. u: internal frictional angle. T: tensile strength. C0 : residual cohesion. u0 : residual internal frictional angle. F1, F2 and F3 are the fault models in Fig. 3). Discontinuities
Kn (GPa)
Ks (GPa)
C (MPa)
U (°)
T (MPa)
C0 (MPa)
u0 (°)
F1 F2 F3 Bedding
1.0 0.9 1.1 5.0
0.8 0.6 0.7 4.0
0.8 0.7 0.5 3.5
25 24 26 30
0.5 0.4 0.6 5.0
0.4 0.4 0.5 0.4
20 21 22 25
records between 30th and 80th second of the acceleration histories, in which most seismic energy distributes were selected for dynamic analysis. The selected acceleration history sections with duration 50 s were converted to stress histories (Itasca, 2007) (Fig. 4), which were added to 3DEC model as stress wave.
boundary, respectively. Finally, the dynamic calculation was achieved under the seismic loading using the stress histories.
3.3. Dynamic calculation
We carried out model validation using qualitative and quantitative validation methods. The qualitative method is to compare the fault’s rupture characteristics between modeled results and field survey. The Wenchuan earthquake induces abundant co-seismic ground rupture, of which one typical ground rupture at Qingping observation site near the BYF is shown in Fig. 5 (Chen et al., 2009). The modeled fault behaved in the same way of thrusting with right strike-slip (Fig. 15) as real faulting. The modeled damage pattern is also agreeable with that observed at filed survey. The modeled tunnel structure shows shear-tension damage characteristics which can be observed in many tunnels during the Wenchuan earthquake (Wang et al., 2009).
Based on the 3DEC geometric model and the calibrated parameters, numerical calculation was conducted. Firstly, the model was initially run to the static equilibrium under only gravity and initial field stress to equilibrate the body forces and the boundary forces prior to the seismic loading. Then, the model was subjected to various dynamic conditions. The model adopted Rayleigh damping to describe the energy loss of physical system. The coefficient of Rayleigh damping adopted the critical damping ratio 0.05 and the fundamental frequency 20 Hz. The bottom, top and four sides of model adopted viscous boundary, free boundary and free-field
3.4. Model validation
Fig. 4. The stress histories with duration 50 s from actual acceleration histories of the Wenchuan earthquake measured by the Qingping observation site, Sichuan province, China. (a) East–west orientation (EW). (b) North–south orientation (NS). (c) Vertical orientation (UD).
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Fig. 5. Co-seismic ground rupture and their measured topographic profiles on the main road (a) and on the third terrace (b) at Qingping observation site, Sichuan province, China (Chen et al., 2009).
The quantitative method is to statistically compare values of the ground motion displacement along the Beichuan–Yingxiu fault between modeled results and field survey. In terms of the field survey of ground motion after Wenchuan earthquake, along the BYF, the vertical displacement of ground rupture is between 1.6 m and 6.0 m with an average of 2.9 m, and the horizontal displacement of ground rupture is between 0.2 m and 6.5 m with an average of 3.1 m (Chen et al., 2009; Li et al., 2009). The modeled horizontal and vertical displacement values (Table 3) of the monitoring points in Fig. 3b were acquired, which were statistically compared with field survey (Fig. 6). The modeled average vertical displacement and horizontal displacement is 2.75 m and 3.18 m with error of 5.17% and 2.58% comparing with field survey, respectively. The coincidence or comparability between the modeled faulting displacement and field survey shows that the modeled numerical results have high reliability. 4. Results 4.1. Stress distribution In order to analyze the effect of fault on stress distribution and stress concentration in the RMTF under strong seismic excitation, the maximum principle stress distribution of four tunnel cross-sections in the 10th second of seismic loading, when there is considerable stress concentration, was acquired (Fig. 7). Many previous studies have shown that stress redistribution and stress concentration may occur in the RMTF under strong external disturbance (Moore and Guan, 1996). In the case of the absence of fault (Fig. 7a), the stress distribution is mainly affected by tunnel structures and free surface amplification of seismic waves propagation. The tensile stress concentration (red color in Fig. 7a) with a symmetric distribution can be observed on both side walls of tunnel. Simultaneously, the slight compressive stress concentration (blue color in Fig. 7a) can also be observed on the top of tunnel. So, the top and both side walls of tunnel are likely to encounter more damage.
Fig. 6. The comparison between real records in the Wenchuan earthquake and numerical modeled results of ground motion along the BYF.
The presence and dislocation of faults in rock masses (Fig. 7b– d) induced the reflection and refraction of seismic waves, and affected their propagation characteristics (Wang et al., 2006), which formed complicated seismic wave field. As a result, stress redistribution and stress concentration near faulting region in rock masses arose. The tensile stress concentration (red color in Fig. 7b–d) can be observed along the oblique faults in all three scenarios. Simultaneously, the compressive stress concentration (deep blue color in Fig. 7b–d) can also be observed in some regions. In addition, the area characterized by stress concentration in the circumstance of the presence of fault is much larger than that of the absence of fault. So, the difference of stress distribution between two scenarios of the presence and absence of fault can be attributed to the significant effect of faults on seismic wave propagation. In order to further analyze the effect of the tunnel-fault interaction on the stress distribution in RMTF under strong seismic excitation, the maximum principle stress distribution along tunnel and fault in the 10th second of seismic loading is acquired (Fig. 8). Then, the average maximum principal stress values along tunnel (the top and bottom of tunnel) (Fig. 9) and fault (Fig. 10) from the 7th to 15th second of seismic loading are acquired.
Table 3 Numerical modeled results of ground motion along the BYF (H: horizontal displacement. V: vertical displacement. A: average displacement).
H (m) V (m)
1
2
3
4
5
6
7
8
9
10
11
12
A (m)
4.68 3.59
4.71 2.93
4.53 3.28
4.55 3.64
4.66 3.51
4.08 3.21
3.73 3.74
1.41 1.85
1.86 2.47
1.31 1.74
1.45 1.64
1.45 1.41
3.18 2.75
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Fig. 7. Maximum principal stress distribution of four tunnel cross-sections in the tenth second of seismic loading. The dotted lines indicate the faults. The locations of tunnel cross-sections are shown in Fig. 8. Please note that there is some rupture failure and dislocation along faults (see red circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Stress (Pa)
Fig. 8. Maximum principal stress distribution along tunnel and fault in the tenth second of seismic loading. The oblique dotted line indicates the fault with length 200 m. The vertical dotted lines ((1) 112 m, (2) 100 m, (3) 92 m, (4) 84 m) indicate the locations of four tunnel cross-sections (a–d in Fig. 7, respectively. The black dots are the monitoring points to examine the dynamic response of rock masses during seismic loading.
4.5E+07 4.0E+07 3.5E+07 3.0E+07 2.5E+07 2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00
tunnel top tunnel bottom
0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
Length (m) Fig. 9. Average maximum principal stress along the top and bottom of tunnel from the 7th to 15th second of seismic loading.
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131
4.5E+07 4.0E+07 3.0E+07 2.5E+07
tunnel
Stress (Pa)
3.5E+07
2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00 0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
Length (m) Fig. 10. Average maximum principle stress along fault from the 7th to 15th second of seismic loading. The center of tunnel is located at 100 m. The 0 m and 200 m is the bottom and top of fault, respectively.
Fig. 11. Vibration velocity histories with duration 60 s of monitoring point c, e (a), p and r (b), as shown in Fig. 8, during the dynamic response of tunnel-fault system.
The obvious stress concentration (red1 color in Fig. 8) can be observed in the intersection of tunnel and fault. However, there is not obvious stress concentration away from the intersection of tunnel and fault. So, the phenomena of dramatic stress concentration in the intersection of tunnel and fault can be attributed to the intensive tunnel-fault interaction under strong seismic excitation. In addition, the values of the maximum principle stress, as shown in Fig. 9 and Fig. 10, as well as the area of stress concentration are larger in the top than in the bottom of tunnel. As a result, the intersection of tunnel and fault is likely to encounter more damage than other regions.
4.2. Vibration velocity The tunnel-fault interaction can also be reflected by the vibration behavior of rock masses along tunnel and fault. We analyzed the vibration behavior using the vibration velocity histories of the monitoring points along tunnel and fault, as shown in Fig. 8. The vibration velocity histories of monitoring point c, e, p and r are illustrated in Fig. 11. On the whole, the vibration action is more intensive from about the 5th to the 25th second when there are strong stress waves with high energy (Fig. 4). After the termination of seismic loading in the 50th second, the vibration velocity weak1 For interpretation of color in Figs. 8 and 15, the reader is referred to the web version of this article.
ens remarkably. The fluctuation trend of vibration velocity histories shows that the vibration motion of monitoring point e and p is more intensive than that of monitoring point c and r, respectively. So, the stress and strain at the monitoring point e and p response more intensively than other points since they are closer to the intersection of tunnel and fault than monitoring point c and r. The peak vibration velocity values of all monitoring points (in Fig. 8) are illustrated in Fig. 12. Along fault and the top of tunnel, the peak vibration velocity values gradually decrease with increasing distance to the intersection of tunnel and fault where there is intensive tunnel-fault interaction. That is to say, the effect of tunnel-fault interaction on dynamic response of tunnel-fault system gradually decreases with increasing distance to the intersection of tunnel and fault.
4.3. Tunnel failure process In this study, the tunnel failure process was examined though analyzing the dislocation displacement characteristics of the RMTF. Based on the motion characteristics of the monitoring points in Fig. 3d, the average horizontal and vertical displacement histories (Fig. 13), and the maximum principle strain rate history (Fig. 14) of the RMTF were acquired. Fig. 13 shows that, on the whole, the vertical displacement is larger than the horizontal displacement. From Fig. 13 and Fig. 14, we can observe that the nonconstant tan-
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Fig. 12. Peak vibration velocity of all monitoring points along tunnel (a) and fault (b), as shown in Fig. 8, during the dynamic response of tunnel-fault system.
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Time (s) Fig. 13. Dislocation displacement histories of the RMTF statistically resulted from monitoring points in Fig. 3d. The time sections (1–5) divided by dotted lines indicate five main stages of tunnel failure process (see Section 5).
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Time (s) Fig. 14. Maximum principle strain rate history of the RMTF resulted from monitoring points in Fig. 3d. The time sections (1–5) have the same meaning as that in Fig. 13.
gent slope of displacement history curves and nonconstant strain rate, which shows that the dislocation displacement of the RMTF goes through non-uniform growth. Fig. 15 shows typical failure state and maximum principle stress distribution of the RMTF during seismic response of the tunnelfault system. Fig. 15a shows the initial static equilibrium state without obvious stress concentration and tunnel failure before seismic loading. The faulting regions are very likely weaker than surrounding rocks and thus are more responsive to the stress change induced by earthquakes (Duan, 2010). The red color (Fig. 15b–f) indicates the remarkable stress accumulation and stress concentration, which suggests the intensive tunnel-fault interaction in the intersection of tunnel and fault during seismic loading. When the accumulated stress in the RMTF (shear stress,
especially) exceeds the fault strength, the fault begins to rupture and the tunnel begins to fail which can be indicated by the dislocation displacement in the intersection of tunnel and fault in Fig. 15. In the 10th second of seismic loading, the dislocation displacement of the RMTF sharply increases (large tangent slope in Fig. 13), and the strain rate arrives at peak value (Fig. 14). Then, the accumulated stress begins to release, which can be indicated by the decreasing area with red color from Fig. 15c to f. With the gradual decrease of seismic loading, the tunnel-fault interaction in the intersection of tunnel and fault begins to weaken, and the dislocation displacement rate of the RMTF begins to decreases. After the termination of seismic loading in the 50th second, the dislocation displacement of the RMTF has no obvious increase and the tunnel-fault system gradually approaches to the
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Fig. 15. Typical failure state and maximum principal stress distribution of the RMTF during seismic loading. (a) is the initial statically balanced state before seismic loading. (b–f) are the typical scenario of five time sections (1–5) in Fig. 13 and Fig. 14, respectively. Relative to the intersection of tunnel axis and fault interface, the length, height and width of the RMTF are 120 m, 15 m and 15 m, respectively.
stable state with static equilibrium. The residual dislocation displacement can be found comparing the tunnel failure scenario in Fig 15a and f. 5. Discussion The tectonic structure of the tunnel-fault system that includes many geological and structural objects is considerably complicated. Lan et al. (2010, 2012) has suggested that the stress redistribution within the discontinuous rock masses plays an important role in their damage processes. The interaction between fault and tunnel structure dramatically amplify the effect of seismic event on the rock mass behavior during the development of progressive deformation and failure process. The initial static equilibrium of field stress in rock masses is disturbed by the strong seismic excitation, and then the initial field stress begins to redistribute. During the stress redistribution, the remarkable stress accumulation and stress concentration is observed in the intersection of tunnel and fault because of intensive tunnel-fault interaction and geological material-tunnel interaction. The local stress concentration results in the non-uniform stress distribution. From the different seismic response characteristics of key elements (stress, strain, displacement and rate) at the different location of rock masses, we can include that the seismic response in the intersection of tunnel and fault is more intensive. So, the intersection of tunnel and fault could have more damage and potential threat to the tunnel structures. Lan et al. (2012) investigated the damage evolution of in situ rock mass damage induced by mechanical–thermal loading and suggested that the failure process can be divided by a number of distinct stages. Similarly, based on the non-uniform growth of the dislocation displacement of the RMTF and associated stress, strain developing characteristics, we can conclude that the tunnel failure process is nonlinear under the combined effect of strong earthquakes and faults. The process can be qualitatively divided
into 5 main stages (see Fig. 13 and Fig. 14) based on its stress, strain and rupturing behaviors: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth and (5) stabilization. 5.1. Strain localization The preliminary stress concentration in the intersection of tunnel and fault induces the slight deformation, and then the intensive deformation concentration at some location of rock masses. The performance of non-continuous deformation development is named strain localization (Fig. 15b). The strain localization is the aura of severe rock masses failure. 5.2. Rupture initiation The severe strain localization changes the internal structure of rock masses, which dynamically reduces its frictional strength, and then increases its frictional instability. Small dislocation displacement occurs along the weak fault in the intersection of tunnel and fault (Fig. 15c), which indicates the formation of shear slide surface, as well as is the breakthrough point of the progressive failure of the entire RMTF. 5.3. Rupture acceleration With the high seismic loading in this stage, the accumulated stress rapidly grows. As a result, the dramatic rupture failure occurs along the weak fault in the intersection of tunnel and fault, and the dislocation displacement (Fig. 13) and failure area (Fig. 15d) rapidly increases. The principle strain rate arrives at peak value (Fig. 14). Due to the remarkable rupture failure of rock masses consumes some internal energy coming from accumulated stress, the accumulated stress in rock masses begins to release, and the area with high accumulated stress begins to decrease.
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5.4. Spontaneous rupture growth After the remarkable rupture failure occurrence, the rupture failure spontaneously grows mainly along the weak fault and other discontinuities in rock masses under the continuous seismic loading (Fig. 15e). Rupture propagation on a major active fault is controlled by the properties of slip-weakening friction law on the fault. Friction controls the initiation, development of rupture, and the healing of faults (Madariaga et al., 1998). 5.5. Stabilization In this stage, the seismic loading terminates, and the accumulated stress further releases. The tunnel-fault system comes into self-stabilization stage, and finally reaches the stable state with static equilibrium (Fig. 15f). The seismic induced residual dislocation displacement (residual deformation) can be observed in the post-earthquake equilibrium state (Fig. 15f) as compare with the initial statically balanced state (Fig. 15a). 6. Conclusions There are significant challenges to provide a better understanding of the tunnel-fault interaction and the tunnel failure process under the combined effect of strong earthquakes and faults. Nonetheless, 3-D discontinuous element modeling approach and abundant data acquired for the Mw7.9 Wenchuan earthquake occurred in May 12, 2008 provide an opportunity to investigate the dynamic responses of tunnel-fault system to the strong seismic event. The displacements from the numerical modeling were in reasonable agreement with the measured displacement along faulting system. The modeled distribution and evolution of key elements (stress, strain, displacement and rate) were capable of capturing the characteristics of these complicated dynamic processes. The dynamic failure process of tunnel-fault system is a stressdominant progressive process. The stress redistribution and evolution play a significant role in the development of failure process of the RMTF during the strong earthquake. The non-linear failure process of tunnel-fault system induced by strong seismic event is characterized by several different stages with different response characteristics. More complicated mechanism might be behind this process, e.g., the deterioration of friction and strength of rock masses. The comparison of tunnel-fault system to far-field rock mass behavior reveals basic characteristics of tunnel-fault interaction in response to strong seismic event. Despite the limitation of numerical modeling at such large scale, it appears to have captured many key elements of the failure processes of tunnel-fault system under strong seismic event. Understanding of these processes helps to link the seismic response of tunnel to its stability analysis. Acknowledgements This research was supported by the National Science Foundation of China (41072241) and Chinese geological survey program (1212010914025). The authors also wish to acknowledge the Chinese Seismic Bureau for providing the seismic ground motion data. References Anastasopoulos, I., Gazetas, G., 2010. Analysis of cut-and-cover tunnels against large tectonic deformation. Bulletin of Earthquake Engineering 8, 283–307. Anastasopoulos, I., Gerolymos, N., Drosos, V., Kourkoulis, R., Georgarakos, T., Gazetas, G., 2007. Nonlinear response of deep immersed tunnel to strong
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