- Email: [email protected]
Seismic capacity assessment of cracked lining tunnel based on the pseudo-static method
Tunnelling and Underground Space Technology 97 (2020) 103281
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Seismic capacity assessment of cracked lining tunnel based on the pseudostatic method
T
Wenge Qiu, Bingtian Li⁎, Lun Gong, Xingxin Qi, Zhiheng Deng, Guang Huang, Hui Hu Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Seismic capacity Tunnel Permanent lining Crack Pseudo-static method Damage plastic
Crack is one of the most common lining deteriorations, which is generally regarded as an indicator of tunnel safety. The present study investigated the lining cracks of 11 tunnels which are 200 km away from the Longmenshan fault zone. In order to evaluate the seismic capacity of these tunnels with longitudinal cracks in the permanent lining, a modified deformation-based pseudo-static assessment method was developed. The propagation of lining cracks was simulated by a reconstructed damaged plasticity constitutive model of reinforced concrete. The analyses adopted a two-dimensional finite element model and took tunnel depth, initial crack position, and the interaction between soil and lining structures into account. The analysis results showed that the modified evaluation method could simulate the damage process of lining structures under the action of seismic shear wave well. The results also showed that the failure modes of tunnels with cracked permanent lining were different with different burial depth in an earthquake. The cracks in the spandrel had the greatest impact on the seismic capacity of tunnels and should be reinforced in time before the earthquake. In addition, the interaction between the temporary support and permanent lining had little effect on the damage process of linings but had an impact on the damage speed. This study can provide a reference for the safety assessment of cracked lining tunnels in seismically active areas and help to determine the reinforcement measures and time more reasonably.
1. Introduction
tunnel safety (Asakura and Kojima, 2003; Richards, 1998; Yuan et al., 2012). Cracks bring leakage, carbonization, and corrosion to the concrete structure, and even destroy the structural integrity, leading to spalling and collapse. Researchers have been carrying out extensive research on the root cause, evolution mechanism and safety assessment of the lining cracks. Wang (2010) and Chiu et al. (2017) studied lining crack evolution influenced by slope instability based on the long-term records and analysis of detailed anomaly variation in a mountain tunnel. Konagai et al. (2009) and Wang and Zhang (2013) analyzed the earthquake-induced cracks of tunnels due to the 2008 Wenchuan earthquake and the 2004 Mid-Niigata earthquake. Using a three-dimensional numerical simulation method, Xiao et al. (2014) studied the cracking mechanism of permanent lining for a shallow and asymmetrically-loaded tunnel in loose deposits. Song et al. (2019) studied the deformation evolution laws, cracking mechanism and failure process of the secondary lining for an existing highway tunnel in loess ground by carrying out field investigations and laboratory model tests. In addition, the tunnel maintenance guidelines of the United States, Japan, and China also provide the evaluation criteria for lining cracks (Federal Highway Administration, 2004; Japan Society of Civil Engineers, 2005;
A large number of tunnels have been built in the mountainous areas of western China. In the past 10 years, seismic activity in this area, including four intensive earthquakes: the 2008 Wenchuan Earthquake (Ms = 8.0), 2010 Yushu Earthquake (Ms = 7.1), 2013 Lushan Earthquake (Ms = 7.0) and 2017 Jiuzhaigou Earthquake (Ms = 7.0). Although underground structures are generally considered to be more seismic-resistant than overground structures, some relevant literature shows that tunnels can be damaged in strong earthquakes (Asakura, 1997; Shen et al., 2014; Wang et al., 2001; YASHIRO and KOJIMA, 2007). Therefore, as an important part of transportation infrastructure, the seismic performance of tunnels in seismically active areas is still an important issue. Tunnels generally satisfy the seismic design requirements in a long period after the construction. However, the time-dependent deterioration of rock masses and lining structures are sometimes inevitable, which may lead to degradation in operational tunnels, such as cracks, leakage and spalling. Lining cracks are the most common tunnel anomalies, which are frequently regarded as one of the indicators of
⁎
Corresponding author. E-mail address: [email protected] (B. Li).
https://doi.org/10.1016/j.tust.2020.103281 Received 30 May 2019; Received in revised form 16 December 2019; Accepted 2 January 2020 0886-7798/ © 2020 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
C25 was used for the temporary support with a design thickness of 0.2 m. The permanent lining was constructed of reinforced concrete C30 with a design thickness of 0.4 m. The compressive strength and tensile strength of concrete are 20.1 MPa and 2.01 MPa respectively. The diameter of the main steel bar is 22 mm and the reinforcement ratio is 0.95%. The inspect result indicated that lining cracks were the main anomalies of these tunnels. The tunnel length, max overburden depths, and lining crack statistics of these tunnels are summarized in Table 2. These cracks are mainly longitudinal cracks and a small number of circumferential cracks, oblique cracks, and reticular cracks. According to the tunnel maintenance guidelines of China (Ministry of Transport of the PRC, 2015), crack with length L c ≥ 5m and width Wc ≥ 1mm was defined to be a severe crack that needs to be strengthened in time. Penetrating crack was also considered to be of high risk. Other cracks were considered to have no impact on structural safety and do not need to be repaired. However, the influence of these minor cracks on the seismic capacity of the tunnel was not considered at that time.
Ministry of Transport of the PRC, 2015). However, little attention has been devoted to the influence of cracks on the seismic capacity of tunnel linings up to now. The vertically propagating shear wave is the prevailing form of earthquake load (Wang, 1993). The seismically induced ovaling or racking deformations rather than the inertial force has the most significant influence on the tunnel lining (Penzien, 2015). Therefore, tunnel seismic analysis was simplified as a pseudo-static form in many cases (Hashash et al., 2005; Iai, 2005; Lu and Hwang, 2017; Zou et al., 2017). Previous studies mostly analyzed concrete tunnel lining in linear elasticity. Through monitoring the internal force such as axial force and bending moment of structures, the possible location of cracks and the failure state of linings can be determined. However, for the analysis of cracked lining tunnels, such an approach cannot point out the evolution of structural damage and the path of crack propagation. The plastic damage analysis method was often more accurate and effective (Chen and Wei, 2012; Cui et al., 2015; Wu et al., 2015; Xu et al., 2017; Yan et al., 2018). The main objective of this paper is to study the effect of the lining cracks on the seismic response of tunnels. Based on the investigation of lining cracks of 11 tunnels in earthquake-prone areas of China, the typical analysis object was determined first. Then a modified deformation-based pseudo-static assessment method was developed, in which a reconstructed damaged plasticity constitutive model of reinforced concrete was proposed and used to simulated the damage evolution of cracked lining structures. The analyses adopted a two-dimensional finite element numerical model considering the impact of tunnel depth, initial crack position, and interaction between soil and lining structures.
3. Methodology 3.1. A damaged plasticity constitutive model of reinforced concrete There are several constitutive models for concrete crack analysis, such as the discrete crack model (Ayari and Saouma, 1990), the smeared crack model (Vargas-Loli and Fenves, 2010), and the plasticdamage model (Lee and Fenves, 1998). The conventional approach to account for the reinforced concrete by the plastic-damage model is to adopt a plastic-damage model for concrete and model the reinforcing bars with one-dimensional elements (Hamid et al., 2012; Qiu et al., 2019). This method costs a lot of computational work, and sometimes it is difficult to achieve the desired results because of the complex interaction between steel and concrete. Wu et al. (2015) proposed a simplified method for three-dimensional simulation, in which reinforcing bars were smeared into a membrane element and then embedded into a solid concrete element. Lee and Fenves (1998) developed a plastic-damage model for concrete subjected to cyclic loading using the concepts of fracture-energybased damage and stiffness degradation in continuum damage mechanics, as shown in Fig. 3. Reinforcing bars can improve the mechanical behavior of concrete structures, especially tensile behavior because the tensile strength of steel is much greater than that of concrete. Nefedov (2005) studied the stability of tensioned reinforced concrete in the process of cracking and pointed out that due to the different reinforcing radio and mechanical properties of materials, reinforced concrete has two different instability processes. Based on the hypothesis of strain compatibility and strength equivalence, the mechanical behavior of reinforcing bars can be incorporated into the
2. Engineering background Dazhou-Chengdu railway is located in Sichuan Province, China. It was built in June 1992 and opened to traffic in November 1997. Upgrading was completed in 2007 with a design speed of 200 km/h. In 2012, the lining quality of 11 tunnels near Nanchong was inspected by ground-penetrating radar (GPR) and laser scanning. The topography around these tunnels can be seen in Fig. 1. These tunnels are about 200 km away from the Longmenshan fault zone and the seismic peak ground acceleration (PGA) of the designed earthquake in this area is 0.05 g. The overburden depths range from 8 m to 115 m. The design data and geological investigation indicate that the ground formation which the tunnels pass through is mudstone mixed with sandstone, and the upper stratum to the surface is silt and silty clay with a thickness of about 0–3 m. The physical and mechanical properties of these formations are summarized in Table 1. These tunnels were built by the New Austrian tunneling method (NATM). The cross-section of the tunnels is shown in Fig. 2. Shotcrete
Fig. 1. The geographical locations of the tunnels and the surrounding topography. 2
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 1 The parameters of the mudstone mixed with sandstone, silt, and silty clay formations. Ground formation
Unit weight γ (KN/m3)
Young’s modulus E (MPa)
Cohesion c (kPa)
Friction angle ϕ (°)
Poisson’s ratioν
Shear wave velocity Vs (m/s)
Mudstone mixed with sandstone Silt Silty clay
2.2 1.85 1.95
920 10 15
100 12 25
35 7 12
0.35 0.23 0.30
393.6 46.9 54.4
σA = σc (A − A' ) + σs A'
(2)
where σc and σs are the average stress in concrete and reinforcing steel, respectively. In the elastic state: (3)
ERC A = Ec (A − A' ) + Es A'
(4)
where ERC is the equivalent elastic modulus of the reinforced concrete equivalent material element; ε is the nominal strain of the reinforced concrete equivalent material. The equivalent material can be explained as the superposition of concrete and reinforcing bars, as Fig. 4(b) shows. According to Eq. (3) and Eq. (4), the constitutive model of reinforced concrete equivalent material can be obtained. Fig. 7(a) shows the tensile behavior of reinforced concrete equivalent material, which is consistent with one of the two instability processes of reinforced concrete proposed by Nefedov (2005). On the segment OM, the equivalent material is in the elastic state, and the stress grows steadily. The concrete reaches yield strength at point M. Subsequently, the structure load gradually turns to be borne by reinforcing bars, corresponding to the segment MN. The roles of concrete and reinforcement are exchanged after the inflection point of the segment MN. Point N represents the stress in reinforcing bars reaches the yield strength and the strain of equivalent material increases rapidly. Fig. 7 (b) shows the compressive behavior of reinforced concrete equivalent material, similar to that of concrete, but with higher yield strength. The evolution of tensile and compressive damage variables of concrete can be obtained according to Wittke et al. (2006) as follows:
Fig. 2. The cross-section of the 11 tunnels.
equivalent constitutive model of reinforced concrete instead of being an independent material. This modified constitutive model can effectively reflect the mechanical behavior of reinforced concrete, simplify the calculation work, and is more suitable for engineering analysis. Section of the reinforced concrete lining structure studied in this paper is shown in Fig. 4(a). The cross-section area of reinforced concrete and reinforcing bars is A and A' . The reinforcing steel is assumed to be elastic-perfect plastic and the stress-strain relation of concrete damaged plasticity model is defined by GB-50010 (2010), as shown in Fig. 5 and Fig. 6. According to the hypothesis of strain coordination, it is assumed that the strain of concrete and reinforcing steel is equal:
(
d=
)
1 α
σ+
− 1 ε plE0
(
1 α
)
− 1 ε plE0
(5) (6)
ε pl = αε in ε pl
ε in
= ε − σ / E0 is the inelastic is the equivalent plastic strain; where strain; α is the constant factor with 0 < α < α1. Replace E0 in Eq. (5) with ERC and order α = 0.7 , the damage variables of the reinforced concrete equivalent material studied in this paper are obtained, as shown in Fig. 8. The tensile damage variables
(1)
εc = εs
σA = Ec εc (A − A' ) + Es εs A' = ERC εA
The nominal stress σ of the reinforced concrete equivalent material can be obtained:
Table 2 The tunnel length, max overburden depths, and lining crack statistics of 11 tunnels. Tunnel
Liangfuwan Goujiagou Ranjiawan Zhaizishan Chenjiawan Ranfangwan Zhangjiawan Wangjiawan Jiajiagou Nianzigou Xuejigou
Length (m)
620 590 670 105 463 787 188 223 106 238 252
Max overburden depths (m)
103 106 108 37 89 115 42 50 36 55 58
Longitudinal crack
L c ≥ 5 m and Wc ≥ 1 mm
L c ≤ 5 m or Wc ≤ 1 mm
15 23 26 1 25 43 17 11 9 8 0
16 10 7 4 26 38 8 4 2 7 6
3
Circumferential crack and Oblique crack
Reticular crack
Total
5 7 5 0 9 17 6 6 1 0 3
1 1 0 0 1 0 0 0 0 0 0
37 41 38 5 61 98 31 21 12 15 9
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 3. The response of concrete to uniaxial loading in tension and compression.
underground structure by imposing seismic racking deformation on structures. But the interaction between underground structure and the surrounding ground was not considered. The International Standard, ISO23469, presented a simplified equivalent static analysis method as a guideline for the seismic design of geotechnical works (Iai, 2005). The ground displacement, inertia force, and interface shear stress were taken into account, while the soil-structure interaction was simulated by a series of normal and shear springs. Lu and Hwang (Lu and Hwang, 2017) proposed a modified cross-section racking deformation (MCSRD) method which can automatically consider the nonlinear soil-tunnel interaction based on the FLAC2D program. Compared with the dynamic analysis, the pseudo-static analysis cannot accurately catch the real variation of the relative stiffness, nor consider the cumulative damage of structures during the earthquake. However, the pseudo-static analysis can reflect the ultimate seismic capacity of tunnel lining to a certain extent. The calculation time can be considerably reduced, and the analysis process can be greatly simplified. Therefore, the pseudo-static method was adopted in many studies, especially in engineering design and evaluation, and a good agreement was observed in most cases (Bilotta et al., 2014; Corigliano et al., 2011; Hwang and Lu, 2007; Kontoe et al., 2014; Lu and Hwang, 2018). This paper put forward a modified deformation-based pseudo-static method. Based on the damage plasticity constitutive model of reinforced concrete proposed in Section 3.1, the seismic capacity of the cracked lining tunnels described in Section 2 was evaluated by analyzing the damage evolution of the lining structure under different seismic shear strains. The analysis and assessment steps are summarized in Fig. 9 and described below:
Fig. 4. The cross-section of the reinforced concrete lining structure. (a) real, (b) equivalent.
1. Set up a numerical model with a suitable mesh domain; establish geostatic equilibrium; excavate rock mass and construct tunnels in the domain. 2. Apply seismic shear strain step by step with a fixed rate on the boundaries of the numerical simulation domain. 3. Monitor the stress-strain curves and the damage evolution of lining structural elements during shear strain application; compare them with the curves shown in Fig. 7 and Fig. 8. 4. Check damage state of lining under different input shear strains; correspond the damage state of lining with the failure process; and determine the seismic shear strain γ leading to tunnel failure which can be evaluated by the following equation (John and Zahrah, 1987).
Fig. 5. Stress-strain curves of reinforcing steel.
corresponding to the inflection point and point N on segment MN in Fig. 7(a) is 0.7 and 0.82, respectively. The compressive damage variable is 0.26 when the equivalent material reaches the compressive yield strength. 3.2. Pseudo-static method
γ = v / Vs
Pseudo-static analysis can either be deformation-based or forcebased (Sun and Dias, 2019). An early application of the deformationbased method was the cross-section racking deformation (CSRD) method developed by the San Francisco Bay Area Transit (SFBAT) in the 1960 s. This method simulated the seismic action on the
(7)
where v is the peak ground velocity (PGV) during earthquake shaking at the location; and Vs is the average shear wave velocity of the ground. The Chinese Seismic Intensity Scale (Standardization Administration of 4
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 6. Stress-strain curves of concrete (GB-50010, 2010).
of shotcrete C25 refer to the experiment in Cong et al. (2015). The damage plasticity constitutive model of reinforced concrete studied in Section 3.1 was used to simulate the mechanical behavior of the permanent lining, which can be defined by material behavior of Concrete Damaged Plasticity in ABAQUS. The parameters of tunnel lining are presented in Table 4. The lining cracks can be interpreted as that the permanent lining had taken part of confining stress as time went by. In order to reflect the stress state of tunnel lining structure at that time, the stress release of 30% was considered after the excavation of rock mass and the permanent lining was constructed simultaneously with the temporary support in this model. No slipping is allowed between the temporary support and the rock mass. The interaction between the temporary support and the permanent lining is difficult to obtain accurately. Two extreme cases: the full-slip and no-slip conditions were considered in the model, as the idealizations of real contact. The initial crack of permanent lining was simulated by seam cracks in ABAQUS. A seam defines an edge or a face in your model that is originally closed but can open during an analysis. ABAQUS places overlapping duplicate nodes along a seam when the mesh is generated. According to the in-situ data, the longitudinal initial crack was taken as the research target of this paper. Initial cracks in the vault, spandrel, and sidewall were considered in the model. The depth of the initial crack was defined as 20 cm, which is half the thickness of the permanent lining. A triangular displacement distribution was applied along the lateral boundaries and a uniform displacement was also applied along the top boundary and bottom boundary, as shown in Fig. 9. Both were applied
PRC, 2008) gives the relationship between PGV, PGA, and the seismic intensity, as shown in Table 3.
4. Numerical model description and validation 4.1. Pseudo-static model Fig. 10 shows the configuration of the pseudo-static numerical model in the XY plane. The burial depth of the tunnel, H', is the vertical distance from the free surface to the vault of the tunnel. Three burial depths of 20 m, 60 m, and 100 m are considered in this paper. B denotes the maximum horizontal diameter of the tunnel. The size of the computational domain is very important to the pseudo-static method, which not only affects the computational costs but also affects the accuracy of the analysis results. Lu and Hwang (2017) studied the influence of the boundary distance by analyzing the variation of vertical stress after excavation and the distribution of shear strain after imposing seismic shear-strain along the sidewall direction. Sun and Dias (2019) studied the boundary effects by considering the influence zone caused by tunneling and the effect of the model width on the lining forces. Based on the above study, the boundary distance to the centerline of the tunnel, L = 65 m , corresponding to the L/ B = 65 m/12.67 m = 5.13 was adopted in the present study. The height of the computational domain, H , was equal to the width of the computational domain. The rock mass and the temporary support were considered to be a Mohr-Coulomb material. Because the thickness of the silt and silty clay near the surface is less than 3 m, only the stratum of mudstone mixed with sandstone was considered in the numerical model. The shear strength parameters
Fig. 7. The constitutive model of reinforced concrete equivalent material. (a) Tensile behavior, (b) Compressive behavior. 5
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 8. The damage variables of the reinforced concrete equivalent material.
Fig. 9. Flow chart of analysis and assessment procedure.
shear strain is considered in both directions in these cases. Compared with the two-dimensional model, the three-dimensional model is more accurate in simulation but required more computational load and longer calculation period. Therefore, the tunnel structure was simplified to a plane strain model for analysis in some cases. In this paper, two-dimensional and three-dimensional finite element models were established in ABAQUS, and the situation of a 20 m depth tunnel with the initial crack at the spandrel of lining was analyzed and compared, as shown in Fig. 11 and Fig. 12. The three-dimensional model is 24 m along the longitudinal direction. The initial longitudinal crack is 5 m long and is in the middle of the lining model. Fig. 13 shows the failure process of the lining structure in threedimensional simulation. In the first stage, the initial crack propagated along the longitudinal direction of the lining. The damage at the crack tip was greater than that in other crack propagation areas. However, the initial crack and new cracks did not extend along the radial direction of the lining at this stage. In the second stage, the initial crack
Table 3 The corresponding relationship between PGV, PGA and seismic intensity. Intensity
VI VII VIII IX X
Seismic ground motion parameters in horizontal PGA(m/s2)
PGV(m/s)
0.63 (0.45–0.89) 1.25 (0.90–1.77) 2.50 (1.78–3.53) 5.00 (3.54–7.07) 10.00 (7.08–14.14)
0.06 0.13 0.25 0.50 1.00
(0.05–0.09) (0.10–0.18) (0.19–0.35) (0.36–0.71) (0.72–1.41)
at a uniform rate in the time step. The maximum shear strain γmax applied in the model is 0.00358. According to Eq. (7) and the shear wave velocity of the stratum, the PGV is 1.41 m/s, corresponding to the seismic intensity Ⅹ in Table 3. The initial cracks in the spandrel and sidewall make the model geometrically asymmetric, so the seismic 6
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
of failure started in the initial crack zone, which is the most dangerous area. The failure process of the lining structure in the two-dimensional model is similar to that in the three-dimensional model, as shown in Fig. 14. In general, the results of the two-dimensional analysis, as expected, are different from those of three-dimensional analysis. However, these differences can be allowed when the more effective and more realistic from an engineering point of view. Therefore, the twodimensional model was chosen for the later analysis in this paper. 4.2. The response of the displacement field Fig. 15 shows the global and local displacement field for the case of the 20 m deep tunnel when γ = 0.00358 is applied on the boundary of the pseudo-static model. The global displacement fields show that the pseudo-static model can simulate the shear deformation of the ground well. The local displacement fields show that the ground displacement near the tunnel is restrained by the tunnel and the interaction between the temporary support and permanent lining affects the seismic displacement response of the tunnel. The deflection of the displacement field near the permanent lining is more obvious under the condition of full-slip.
Fig. 10. Pseudo-static numerical model in the XY plane. Table 4 Properties of tunnel lining. Parameters
Temporary support
Permanent lining
Unit weight γ (KN/m3) Thickness t (cm) Young’s modulus E (GPa) Poisson’s ratioν Cohesion c (MPa) Friction angle ϕ (°) Compressive behavior Ultimate stress σ cu (MPa) Tensile behavior Initial yield strength σ1(MPa) Secondary yield strength σ2 (MPa)
2.2 20 23 0.2 3 55
2.35 40 32.9 0.2 – –
–
22.4
– –
2.13 3.98
4.3. Comparison with dynamic analysis for no-crack tunnel Representative dynamic analyses were performed with the two-dimensional model by the finite element code ABAQUS in order to compare and validate the results of the pseudo-static method for the nocrack tunnel. The width of the model was 20 times the diameter of the tunnel and the left and right boundaries were set to infinite element boundaries. The upper boundary of the model was a free surface. A harmonic wave was used in the analysis with a frequency of 2.5 Hz. The amplitude of the incident wave had to be chosen to produce the same maximum shear strain of the free-field ground as in the pseudo-static case. Referring to the analysis model proposed by Chen et al. (2012), the ratio of the element size to the wavelength of the incident wave was set to less than 1/10 to ensure the accuracy of the simulated displacements and stresses. And the analysis was terminated when the wave was reflected from the free surface and reached the bottom boundary to prevent disturbance of the stress state of the tunnel by further reflection from the bottom boundary. The dynamic responses of the vault and
propagated along the radial direction of the lining. The propagation started in the middle of the initial crack until the initial crack zone penetrated the lining along the radial direction. In the final stage, the penetrating crack extended along the longitudinal direction. All stages
Fig. 11. Two-dimensional pseudo-static model. 7
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 12. Three-dimensional pseudo-static model.
Fig. 13. Failure process of lining structure in three-dimensional simulation.
practical and efficient method to evaluate the seismic capacity of tunnels. But at the same time, it should also be noted that the pseudo-static method cannot simulate the real nonlinear and hysteretic characteristics of the tunnel under earthquake.
spandrel of the permanent lining were monitored. Fig. 16 shows the comparison of the internal forces at monitored points between dynamic analysis and pseudo-static method for tunnels with different depths. The general trends of the internal forces versus seismic shear strain were similar for both methods. The differences of the peak responses varied with the tunnel depth and the locations of the lining, but it was reasonably close in the engineering view. This suggests that the pseudo-static method can be regarded as a more simple, 8
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 14. Failure process of lining structure in two-dimensional simulation. Fig. 15. The global and local displacement fields under the application of γ = 0.00358. (a) no-slip, (b) full-slip.
5. Numerical result and discussion
and the permanent lining took the confining stress simultaneously, the deeper the buried depth, the greater the compressive stress on the lining structure. The failure process of no-crack linings under seismic shear deformation and corresponding shear strain are listed in Table 5. The tunnel located at 20 m depth was only damaged by tension under seismic shear deformation. The concrete cracked first near the spandrel of lining, then steel bars yielded in tension, leading to partial instability
5.1. Failure process of no-crack lining Fig. 17 shows the principal stress distribution of tunnels with different buried depths after construction. The principal stress of lining structures distributes along the circumferential direction, all of which is compressive stress. Due to the Consideration of the temporary support 9
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 16. The comparison of the internal forces at monitored points. (a) 20 m, (b) 60 m, (c) 100 m.
structure. The 100 m deep tunnel mainly suffered from compression damage under seismic shear deformation. In all three cases, the damaged zones did not penetrate the lining under γmax . In an earthquake, the shear deformation of the stratum leads to the ovaling of lining, as
of the structure. For the 60 m deep tunnel, both tensile damage and compressive damage occurred near the spandrel of the lining. The crush of reinforced concrete in the compression zone occurred earlier than the yield of steel bars in the tensile zone, leading to partial spalling of 10
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 16. (continued)
Fig. 17. Principal stress distribution of linings with different buried depths after construction. Table 5 Failure process of no-crack linings under seismic shear deformation. Buried depth
No-slip
Full-slip
Seismic shear strain γ
Description of damage
Seismic shear strain γ
Description of damage
20 m
0.173% 0.304%
Concrete near spandrel cracks obviously Steel bars in the tensile zone yield
0.182% 0.311%
Concrete near spandrel cracks obviously Steel bars in the tensile zone yield
60 m
0.221% 0.251%
Concrete near spandrel cracks obviously Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
0.225% 0.278%
Concrete near spandrel cracks obviously Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
100 m
0.243%
Reinforced concrete in the compression zone of spandrel crushed Concrete near spandrel cracks obviously
0.261%
0.326%
0.304%
11
0.309%
0.314%
Reinforced concrete in the compression zone of spandrel crushed Concrete near spandrel cracks obviously
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
the 60 m deep tunnel with lining cracks under seismic shear deformation. The initial crack in the vault and sidewall did not improve the damage level of the tunnel. But for the no-slip case of the cracked lining tunnel, the steel bars in the tensile zone yielded earlier. Compared with the no-cracked lining, both tensile damage and compression damage occurred earlier near the spandrel crack. With the increase of seismic shear strain, the crushing zone of reinforced concrete near the crack tip gradually enlarged and eventually penetrated the lining, leading to structural collapse, as shown in Fig. 19(b). Table 9 shows the failure process and corresponding shear strain of the 100 m deep tunnel with lining cracks under seismic shear deformation. The initial cracks in the vault and the sidewall had little effect on the seismic response of the tunnel. The initial crack in the spandrel was sensitive to seismic action. The crushing zone developed from the crack tip along the circumferential and radial direction and quickly penetrated the lining structure. The final damage state of lining is shown in Fig. 19(c). The seismic capacity of the tunnel was greatly reduced, especially under full-slip conditions. The numerical result indicates that cracks in vault and sidewall have a slight impact on the seismic response of linings under seismic shear wave conditions. There was little further development of damage near the initial cracks in these conditions. However, cracks in spandrel were in totally different situations and the seismic capacity of the tunnel was reduced. With the increase of seismic shear strain, structural damage developed rapidly near the initial cracks. In the case of the shallow tunnel, the cracking zone developed along the radial direction of lining from the crack tip and penetrated the structure. In the case of the deepburied tunnel, crushing zones firstly appeared near the initial crack in spandrel and then connected with it. Finally, the lining structure collapse along the oblique section.
Fig. 18. Deformation modes of tunnels under seismic waves (Hashash and Romero-Arduz, 2015).
shown in Fig. 18. This results in tension or compression concentration near the spandrel of the lining. The initial stress states of linings with different buried depth are different, so the failure modes are also different in seismic. Several typical failure processes of lining structures under the action of seismic shear deformation are classified in Table 6. The corresponding representative damage values based on Section 3.1 are also given. Considering that it has no impact on the normal use of tunnels, cracking of lining concrete is defined as minor damage. Yielding of steel bars in the tension zone or crushing of reinforced concrete in the compression zone is defined as moderate damage, which may lead to partial spalling of lining and endanger traffic safety. The lining may lose stability or even collapse when the cracking zone or crushing zone penetrates the structure. This damage state is defined as severe damage.
5.3. Effect of the interaction between temporary support and permanent lining The damage process of linings in the cases of no-slip and full-slip was similar, while the thresholds of different failure states were different. The development of damage states in the no-slip case was faster than that in the full-slip case for the no-crack lining. It demonstrates that the allowance of relative slip between the temporary support and permanent lining slows the damage state development under the same loading conditions, which is consistent with previous research (Lu and Hwang, 2018; Sedarat et al., 2009; Sun and Dias, 2019). The lining with cracks in vault and sidewall also conforms to the above-mentioned rules. However, the lining structure with cracks in the spandrel was more likely to lose stability and collapse under the condition of full-slip. This shows that the deformation of the permanent lining is limited by the no-slip condition under the seismic shear deformation. Therefore, the lining structure is less likely to have penetration damage under this condition.
5.2. Effect of the lining cracks on the seismic capacity of tunnels Table 7 shows the failure process and corresponding shear strain of the 20 m deep tunnel with lining cracks under seismic shear deformation. The lining with the initial crack in the sidewall has the same failure process as the no-crack lining. The initial crack in the vault developed slightly with the increase of seismic shear strain. However, there was no further damage to the structure. The initial crack in the spandrel of lining has a great impact on the seismic response and capacity of the tunnel. The cracking zone near the tip of the initial crack developed rapidly and eventually penetrated the lining. The final damage state of lining is shown in Fig. 19(a). Table 8 shows the failure process and corresponding shear strain of Table 6 Classification of failure characteristics of lining structures. Damage level
Description of damage
Effect on the capacity of structures
III
Concrete in the tensile zone cracking obviously (DAMAGETa 0.7)
Do not affect the normal use
Ⅱ
Steel bars in the tensile zone yield (DAMAGETa 0.82) Reinforced concrete in the compression zone crushed (DAMAGECb 0.26)
Part of the structure reaches the ultimate state of bearing capacity (partial spalling of structure)
Ⅰ
Cracking or crushing zone penetrates lining (DAMAGET 0.82& DAMAGEC 0.26)
Structure loses stability or collapse
a b
Tensile damage variable. Compressive damage variable. 12
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 7 Failure process of cracked linings under seismic shear deformation (20 m buried depth). Initial crack location
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.172% 0.271% 0.318% 0.185% 0.277% 0.336%
Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield
III III Ⅱ III III Ⅱ
0.158% 0.226% 0.263% 0.326% 0.147% 0.183% 0.282%
Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Cracking zone penetrates lining from the initial crack Initial crack propagating Concrete near spandrel cracks obviously (new cracks) Cracking zone penetrates lining from the initial crack
III III Ⅱ Ⅰ III III Ⅰ
0.167% 0.335% 0.220%
Concrete near spandrel cracks obviously (new cracks) Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks)
III Ⅱ III
Full-slip
Spandrel
No-slip
Full-slip
Sidewall
No-slip Full-slip
Fig. 19. Finial damage state of lining with the initial crack.
Table 8 Failure process of cracked linings under seismic shear deformation (60 m buried depth). Initial location of crack
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.213% 0.247% 0.305% 0.215% 0.261% 0.296%
Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
III Ⅱ Ⅱ III Ⅱ Ⅱ
0.188% 0.212% 0.257% 0.275% 0.356% 0.219% 0.221% 0.233% 0.275% 0.332%
Reinforced concrete near the initial crack crushed Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Crushing zone penetrating lining from the initial crack Concrete near spandrel cracks obviously (new cracks) Reinforced concrete near the initial crack crushed Initial crack propagating Steel bars in the tensile zone yield Cracking and crushing zone penetrating lining from the initial crack
Ⅱ III III Ⅱ Ⅰ III Ⅱ III Ⅱ Ⅰ
0.215% 0.258% 0.296% 0.232% 0.275% 0.319%
Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
III Ⅱ Ⅱ III Ⅱ Ⅱ
Full-slip
Spandrel
No-slip
Full-slip
Sidewall
No-slip
Full-slip
6. Conclusions
modified deformation-based pseudo-static analysis. This analysis employed a reconstructed damaged plasticity constitutive model of reinforced concrete to simulate the propagation of lining cracks. Based on the case study of 11 tunnels in earthquake-prone areas of western
This paper highlighted the important effect of the longitudinal cracks in the permanent lining on the seismic capacity of tunnels by a 13
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 9 Failure process of cracked linings under seismic shear deformation (100 m buried depth). Initial location of crack
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.284% 0.303% 0.286% 0.311%
Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed
III Ⅱ III Ⅱ
0.225% 0.264% 0.211% 0.254%
Reinforced concrete near the initial crack crushed Crushing zone penetrating lining near the initial crack Concrete near spandrel cracks obviously (new cracks) Crushing zone penetrating lining from the initial crack
Ⅱ Ⅰ III Ⅰ
0.293% 0.294% 0.303% 0.318%
Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks)
Ⅱ III Ⅱ III
Full-slip Spandrel
No-slip Full-slip
Sidewall
No-slip Full-slip
China, a two-dimensional finite element model was established considering the influence of tunnel depth, initial crack position, and interaction between soil and lining structures. The simulation results showed that the failure process of the reinforced concrete structure could be accurately simulated by the modified damaged constitutive model and identified by the damage variables. The analysis considered the contribution of permanent linings to the confining stress of operating tunnels. The initial stress state of the permanent lining was different with different depth, and the failure mode under the action of the seismic shear deformation was also different. However, for all three cases with different depths, the damage zone first appeared in the spandrel of linings. Cracks in vault and sidewall had a slight impact on the seismic response of linings, while cracks in spandrel were in totally different situations. With the increase of seismic shear strain, structural damage developed rapidly near the initial spandrel cracks. For shallow tunnel, the cracking zone developed along the radial direction of lining from the crack tip and penetrated the structure. For deep-buried tunnel, crushing zones were formed in a large area near the initial crack, resulting in the lining structure collapse along the oblique section. The seismic capacity of tunnels with lining cracks in the spandrel was greatly reduced. The interaction between the temporary support and permanent lining had little effect on the damage process of linings but had an impact on the thresholds of different failure states. The development of damage states in the no-slip case was faster than that in the full-slip case for no-crack lining, and so does for the lining with cracks in vault and sidewall. However, the allowance of relative slip slows the damage state development on the permanent lining under the same loading conditions but also increases its deformation capacity. Therefore, the lining structure with cracks in the spandrel was more likely to have penetration damage and lose stability under the condition of full-slip.
References Asakura, T., 1997. Mountain tunnels performance in the 1995 hyogoken-nanbu earthquake. International Symposium on Recent Advances in Exploration Geophysics. Asakura, T., Kojima, Y., 2003. Tunnel maintenance in Japan. Tunn. Undergr. Sp. Tech. 18, 161–169. Ayari, M.L., Saouma, V.E., 1990. A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Eng. Fract. Mech. 35, 587–598. Bilotta, E., Lanzano, G., Madabhushi, S.P.G., Silvestri, F., 2014. A numerical Round Robin on tunnels under seismic actions. Acta Geotechnica. 9, 563–579. Chen, C.-H., Wang, T.-T., Jeng, F.-S., Huang, T.-H., 2012. Mechanisms causing seismic damage of tunnels at different depths. Tunn. Undergr. Sp. Tech. 28, 31–40. Chen, Z., Wei, J., 2012. Correlation between ground motion parameters and lining damage indices for mountain tunnels. Nat. Hazards. 65, 1683–1702. Chiu, Y.-C., Lee, C.-H., Wang, T.-T., 2017. Lining crack evolution of an operational tunnel influenced by slope instability. Tunn. Undergr. Sp. Tech. 65, 167–178. Yu, C.O., Liang, K.O., Yingren, Z.H., 2015. Experimental study on shear strength of concrete. Concrete 5, 40–45. Corigliano, M., Scandella, L., Lai, C.G., Paolucci, R., 2011. Seismic analysis of deep tunnels in near fault conditions: a case study in Southern Italy. Bull. Earthquake Eng. 9, 975–995. Cui, X., Li, S., Lou, J., Wang, Z., Zhang, J., Tang, W., Gao, Z., 2015. Dynamic responses and damage analyses of tunnel lining and errant large vehicle during collision. Tunn. Undergr. Sp. Tech. 50, 1–12. Federal Highway Administration, 2004. Highway and Rail Transit Tunnel Maintenance and Rehabilitation Manual. GB-50010, 2010. Code for design of concrete structures. China Architecture and Building Press, Beijing. Hamid, S., Mahdi, S., Amir, H.A., Mohammad, A., Ali, S., 2012. Evaluation of reinforced concrete beam behavior using finite element analysis by ABAQUS. Sci. Res. Essays. 7. Hashash, Y.M.A., Park, D., Yao, J.I.C., 2005. Ovaling deformations of circular tunnels under seismic loading, an update on seismic design and analysis of underground structures. Tunn. Undergr. Sp. Tech. 20, 435–441. Hashash, Y.M.A., Romero-Arduz, M.I., 2015. Seismic Design of Tunnels. Hwang, J.-H., Lu, C.-C., 2007. Seismic capacity assessment of old Sanyi railway tunnels. Tunn. Undergr. Sp. Tech. 22, 433–449. Iai, S., 2005. International standard (ISO) on seismic actions for designing geotechnical works–An overview. Soil Dyn. Earthq. Eng. 25, 605–615. Japan Society of Civil Engineers, 2005. Tunnel Maintenance and Management. Japan Society of Civil Engineers, Tokyo, Japan. John, C.M.S., Zahrah, T.F., 1987. Aseismic design of underground structures. Tunn. Undergr. Sp. Tech. 2, 165–197. Konagai, K., Takatsu, S., Kanai, T., Fujita, T., Ikeda, T., Johansson, J., 2009. Kizawa tunnel cracked on 23 October 2004 Mid-Niigata earthquake: An example of earthquake-induced damage to tunnels in active-folding zones. Soil Dyn. Earthq. Eng. 29, 394–403. Kontoe, S., Avgerinos, V., Potts, D.M., 2014. Numerical validation of analytical solutions and their use for equivalent-linear seismic analysis of circular tunnels. Soil Dyn. Earthq. Eng. 66, 206–219. Lee, J., Fenves, G.L., 1998. Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124, 892–900. Lu, C.-C., Hwang, J.-H., 2017. Implementation of the modified cross-section racking deformation method using explicit FDM program: A critical assessment. Tunn. Undergr. Sp. Tech. 68, 58–73. Lu, C.-C., Hwang, J.-H., 2018. Damage analysis of the new Sanyi railway tunnel in the 1999 Chi-Chi earthquake: Necessity of second lining reinforcement. Tunn. Undergr. Sp. Tech. 73, 48–59. Ministry of Transport of the PRC, 2015. Technical Specification of Maintenance for Highway Tunnel. China Communications Press. Nefedov, S.S., 2005. Instability of reinforced concrete containment under internal pressure. International Conference on Structural Mechanics in Reactor Technology. Penzien, J., 2015. Seismically induced racking of tunnel linings. Earthquake. Eng. Struc. 29, 683–691. Qiu, W., Lu, F., Wang, G., Huang, G., Zhang, H., Zhang, Z., Gong, C., 2019. Evaluation of
CRediT authorship contribution statement Wenge Qiu: Conceptualization, Methodology, Supervision. Bingtian Li: Conceptualization, Methodology, Validation, Writing original draft, Writing - review & editing. Lun Gong: Writing - review & editing. Xingxin Qi: Investigation, Visualization. Zhiheng Deng: Investigation, Visualization. Guang Huang: Investigation, Visualization. Hui Hu: Investigation, Visualization.
Acknowledgments The authors gratefully acknowledge the financial support of the National Key R&D Program of China (2017YFC0806000), the National Natural Science Foundation of China (U1434206). 14
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Wang, Z.Z., Zhang, Z., 2013. Seismic damage classification and risk assessment of mountain tunnels with a validation for the 2008 Wenchuan earthquake. Soil Dyn. Earthq. Eng. 45, 45–55. Wittke, W., Pierau, B., Erichsen, C., 2006. New austrian tunneling method (NATM) stability analysis and design. WBN, Essen, pp. 2441. Wu, D., Gao, B., Shen, Y., Zhou, J., Chen, G., 2015. Damage evolution of tunnel portal during the longitudinal propagation of Rayleigh waves. Nat. Hazards. 75, 2519–2543. Xiao, J.Z., Dai, F.C., Wei, Y.Q., Min, H., Xu, C., Tu, X.B., Wang, M.L., 2014. Cracking mechanism of secondary lining for a shallow and asymmetrically-loaded tunnel in loose deposits. Tunn. Undergr. Sp. Tech. 43, 232–240. Xu, D.-P., Feng, X.-T., Chen, D.-F., Zhang, C.-Q., Fan, Q.-X., 2017. Constitutive representation and damage degree index for the layered rock mass excavation response in underground openings. Tunn. Undergr. Sp. Tech. 64, 133–145. Yan, Q., Xu, Y., Zhang, W., Geng, P., Yang, W., 2018. Numerical analysis of the cracking and failure behaviors of segmental lining structure of an underwater shield tunnel subjected to a derailed high-speed train impact. Tunn. Undergr. Sp. Tech. 72, 41–54. Yashiro, K., Kojima, Y., 2007. Historical earthquake damage to tunnels in japan and case studies of railway tunnels in the 2004 niigataken-chuetsu earthquake. Qr of Rtri. 48, 136–141. Yuan, Y., Bai, Y., Liu, J., 2012. Assessment service state of tunnel structure. Tunn. Undergr. Sp. Tech. 27, 72–85. Zou, Y., Liu, H., Jing, L., Cui, J., 2017. A pseudo-static method for seismic responses of underground frame structures subjected to increasing excitations. Tunn. Undergr. Sp. Tech. 65, 106–120.
mechanical performance and optimization design for lattice girders. Tunn. Undergr. Sp. Tech. 87, 100–111. Richards, J.A., 1998. Inspection, maintenance and repair of tunnels: International lessons and practice. Tunn. Undergr. Sp. Tech. 13, 369–375. Sedarat, H., Kozak, A., Hashash, Y.M.A., Shamsabadi, A., Krimotat, A., 2009. Contact interface in seismic analysis of circular tunnels. Tunn. Undergr. Sp. Tech. 24, 482–490. Shen, Y., Gao, B., Yang, X., Tao, S., 2014. Seismic damage mechanism and dynamic deformation characteristic analysis of mountain tunnel after Wenchuan earthquake. Eng. Geol. 180, 85–98. Song, W., Lai, H., Liu, Y., Yang, W., Zhu, Z., 2019. Field and laboratory study of cracking and safety of secondary lining for an existing highway tunnel in loess ground. Tunn. Undergr. Sp. Tech. 88, 35–46. Standardization Administration of PRC, 2008. The Chinese seismic intensity scale. Standardization Administration of People's Republic of China, China. Sun, Q.Q., Dias, D., 2019. Assessment of stress relief during excavation on the seismic tunnel response by the pseudo-static method. Soil Dyn. Earthq. Eng. 117, 384–397. Vargas-Loli, L.M., Fenves, G.L., 2010. Effects of concrete cracking on the earthquake response of gravity dams. Earthquake. Eng. Struc. 18, 575–592. Wang, J.-N., 1993. Seismic design of tunnels: a simple state-of-the-art approach. Parsons Brickerhoff Quade & Douglas Inc, New York. Wang, T.-T., 2010. Characterizing crack patterns on tunnel linings associated with shear deformation induced by instability of neighboring slopes. Eng. Geol. 115, 80–95. Wang, W.L., Wang, T.T., Su, J.J., Lin, C.H., Seng, C.R., Huang, T.H., 2001. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake. Tunn. Undergr. Sp. Tech. 16, 133–150.
15
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Seismic capacity assessment of cracked lining tunnel based on the pseudostatic method
T
Wenge Qiu, Bingtian Li⁎, Lun Gong, Xingxin Qi, Zhiheng Deng, Guang Huang, Hui Hu Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Seismic capacity Tunnel Permanent lining Crack Pseudo-static method Damage plastic
Crack is one of the most common lining deteriorations, which is generally regarded as an indicator of tunnel safety. The present study investigated the lining cracks of 11 tunnels which are 200 km away from the Longmenshan fault zone. In order to evaluate the seismic capacity of these tunnels with longitudinal cracks in the permanent lining, a modified deformation-based pseudo-static assessment method was developed. The propagation of lining cracks was simulated by a reconstructed damaged plasticity constitutive model of reinforced concrete. The analyses adopted a two-dimensional finite element model and took tunnel depth, initial crack position, and the interaction between soil and lining structures into account. The analysis results showed that the modified evaluation method could simulate the damage process of lining structures under the action of seismic shear wave well. The results also showed that the failure modes of tunnels with cracked permanent lining were different with different burial depth in an earthquake. The cracks in the spandrel had the greatest impact on the seismic capacity of tunnels and should be reinforced in time before the earthquake. In addition, the interaction between the temporary support and permanent lining had little effect on the damage process of linings but had an impact on the damage speed. This study can provide a reference for the safety assessment of cracked lining tunnels in seismically active areas and help to determine the reinforcement measures and time more reasonably.
1. Introduction
tunnel safety (Asakura and Kojima, 2003; Richards, 1998; Yuan et al., 2012). Cracks bring leakage, carbonization, and corrosion to the concrete structure, and even destroy the structural integrity, leading to spalling and collapse. Researchers have been carrying out extensive research on the root cause, evolution mechanism and safety assessment of the lining cracks. Wang (2010) and Chiu et al. (2017) studied lining crack evolution influenced by slope instability based on the long-term records and analysis of detailed anomaly variation in a mountain tunnel. Konagai et al. (2009) and Wang and Zhang (2013) analyzed the earthquake-induced cracks of tunnels due to the 2008 Wenchuan earthquake and the 2004 Mid-Niigata earthquake. Using a three-dimensional numerical simulation method, Xiao et al. (2014) studied the cracking mechanism of permanent lining for a shallow and asymmetrically-loaded tunnel in loose deposits. Song et al. (2019) studied the deformation evolution laws, cracking mechanism and failure process of the secondary lining for an existing highway tunnel in loess ground by carrying out field investigations and laboratory model tests. In addition, the tunnel maintenance guidelines of the United States, Japan, and China also provide the evaluation criteria for lining cracks (Federal Highway Administration, 2004; Japan Society of Civil Engineers, 2005;
A large number of tunnels have been built in the mountainous areas of western China. In the past 10 years, seismic activity in this area, including four intensive earthquakes: the 2008 Wenchuan Earthquake (Ms = 8.0), 2010 Yushu Earthquake (Ms = 7.1), 2013 Lushan Earthquake (Ms = 7.0) and 2017 Jiuzhaigou Earthquake (Ms = 7.0). Although underground structures are generally considered to be more seismic-resistant than overground structures, some relevant literature shows that tunnels can be damaged in strong earthquakes (Asakura, 1997; Shen et al., 2014; Wang et al., 2001; YASHIRO and KOJIMA, 2007). Therefore, as an important part of transportation infrastructure, the seismic performance of tunnels in seismically active areas is still an important issue. Tunnels generally satisfy the seismic design requirements in a long period after the construction. However, the time-dependent deterioration of rock masses and lining structures are sometimes inevitable, which may lead to degradation in operational tunnels, such as cracks, leakage and spalling. Lining cracks are the most common tunnel anomalies, which are frequently regarded as one of the indicators of
⁎
Corresponding author. E-mail address: [email protected] (B. Li).
https://doi.org/10.1016/j.tust.2020.103281 Received 30 May 2019; Received in revised form 16 December 2019; Accepted 2 January 2020 0886-7798/ © 2020 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
C25 was used for the temporary support with a design thickness of 0.2 m. The permanent lining was constructed of reinforced concrete C30 with a design thickness of 0.4 m. The compressive strength and tensile strength of concrete are 20.1 MPa and 2.01 MPa respectively. The diameter of the main steel bar is 22 mm and the reinforcement ratio is 0.95%. The inspect result indicated that lining cracks were the main anomalies of these tunnels. The tunnel length, max overburden depths, and lining crack statistics of these tunnels are summarized in Table 2. These cracks are mainly longitudinal cracks and a small number of circumferential cracks, oblique cracks, and reticular cracks. According to the tunnel maintenance guidelines of China (Ministry of Transport of the PRC, 2015), crack with length L c ≥ 5m and width Wc ≥ 1mm was defined to be a severe crack that needs to be strengthened in time. Penetrating crack was also considered to be of high risk. Other cracks were considered to have no impact on structural safety and do not need to be repaired. However, the influence of these minor cracks on the seismic capacity of the tunnel was not considered at that time.
Ministry of Transport of the PRC, 2015). However, little attention has been devoted to the influence of cracks on the seismic capacity of tunnel linings up to now. The vertically propagating shear wave is the prevailing form of earthquake load (Wang, 1993). The seismically induced ovaling or racking deformations rather than the inertial force has the most significant influence on the tunnel lining (Penzien, 2015). Therefore, tunnel seismic analysis was simplified as a pseudo-static form in many cases (Hashash et al., 2005; Iai, 2005; Lu and Hwang, 2017; Zou et al., 2017). Previous studies mostly analyzed concrete tunnel lining in linear elasticity. Through monitoring the internal force such as axial force and bending moment of structures, the possible location of cracks and the failure state of linings can be determined. However, for the analysis of cracked lining tunnels, such an approach cannot point out the evolution of structural damage and the path of crack propagation. The plastic damage analysis method was often more accurate and effective (Chen and Wei, 2012; Cui et al., 2015; Wu et al., 2015; Xu et al., 2017; Yan et al., 2018). The main objective of this paper is to study the effect of the lining cracks on the seismic response of tunnels. Based on the investigation of lining cracks of 11 tunnels in earthquake-prone areas of China, the typical analysis object was determined first. Then a modified deformation-based pseudo-static assessment method was developed, in which a reconstructed damaged plasticity constitutive model of reinforced concrete was proposed and used to simulated the damage evolution of cracked lining structures. The analyses adopted a two-dimensional finite element numerical model considering the impact of tunnel depth, initial crack position, and interaction between soil and lining structures.
3. Methodology 3.1. A damaged plasticity constitutive model of reinforced concrete There are several constitutive models for concrete crack analysis, such as the discrete crack model (Ayari and Saouma, 1990), the smeared crack model (Vargas-Loli and Fenves, 2010), and the plasticdamage model (Lee and Fenves, 1998). The conventional approach to account for the reinforced concrete by the plastic-damage model is to adopt a plastic-damage model for concrete and model the reinforcing bars with one-dimensional elements (Hamid et al., 2012; Qiu et al., 2019). This method costs a lot of computational work, and sometimes it is difficult to achieve the desired results because of the complex interaction between steel and concrete. Wu et al. (2015) proposed a simplified method for three-dimensional simulation, in which reinforcing bars were smeared into a membrane element and then embedded into a solid concrete element. Lee and Fenves (1998) developed a plastic-damage model for concrete subjected to cyclic loading using the concepts of fracture-energybased damage and stiffness degradation in continuum damage mechanics, as shown in Fig. 3. Reinforcing bars can improve the mechanical behavior of concrete structures, especially tensile behavior because the tensile strength of steel is much greater than that of concrete. Nefedov (2005) studied the stability of tensioned reinforced concrete in the process of cracking and pointed out that due to the different reinforcing radio and mechanical properties of materials, reinforced concrete has two different instability processes. Based on the hypothesis of strain compatibility and strength equivalence, the mechanical behavior of reinforcing bars can be incorporated into the
2. Engineering background Dazhou-Chengdu railway is located in Sichuan Province, China. It was built in June 1992 and opened to traffic in November 1997. Upgrading was completed in 2007 with a design speed of 200 km/h. In 2012, the lining quality of 11 tunnels near Nanchong was inspected by ground-penetrating radar (GPR) and laser scanning. The topography around these tunnels can be seen in Fig. 1. These tunnels are about 200 km away from the Longmenshan fault zone and the seismic peak ground acceleration (PGA) of the designed earthquake in this area is 0.05 g. The overburden depths range from 8 m to 115 m. The design data and geological investigation indicate that the ground formation which the tunnels pass through is mudstone mixed with sandstone, and the upper stratum to the surface is silt and silty clay with a thickness of about 0–3 m. The physical and mechanical properties of these formations are summarized in Table 1. These tunnels were built by the New Austrian tunneling method (NATM). The cross-section of the tunnels is shown in Fig. 2. Shotcrete
Fig. 1. The geographical locations of the tunnels and the surrounding topography. 2
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 1 The parameters of the mudstone mixed with sandstone, silt, and silty clay formations. Ground formation
Unit weight γ (KN/m3)
Young’s modulus E (MPa)
Cohesion c (kPa)
Friction angle ϕ (°)
Poisson’s ratioν
Shear wave velocity Vs (m/s)
Mudstone mixed with sandstone Silt Silty clay
2.2 1.85 1.95
920 10 15
100 12 25
35 7 12
0.35 0.23 0.30
393.6 46.9 54.4
σA = σc (A − A' ) + σs A'
(2)
where σc and σs are the average stress in concrete and reinforcing steel, respectively. In the elastic state: (3)
ERC A = Ec (A − A' ) + Es A'
(4)
where ERC is the equivalent elastic modulus of the reinforced concrete equivalent material element; ε is the nominal strain of the reinforced concrete equivalent material. The equivalent material can be explained as the superposition of concrete and reinforcing bars, as Fig. 4(b) shows. According to Eq. (3) and Eq. (4), the constitutive model of reinforced concrete equivalent material can be obtained. Fig. 7(a) shows the tensile behavior of reinforced concrete equivalent material, which is consistent with one of the two instability processes of reinforced concrete proposed by Nefedov (2005). On the segment OM, the equivalent material is in the elastic state, and the stress grows steadily. The concrete reaches yield strength at point M. Subsequently, the structure load gradually turns to be borne by reinforcing bars, corresponding to the segment MN. The roles of concrete and reinforcement are exchanged after the inflection point of the segment MN. Point N represents the stress in reinforcing bars reaches the yield strength and the strain of equivalent material increases rapidly. Fig. 7 (b) shows the compressive behavior of reinforced concrete equivalent material, similar to that of concrete, but with higher yield strength. The evolution of tensile and compressive damage variables of concrete can be obtained according to Wittke et al. (2006) as follows:
Fig. 2. The cross-section of the 11 tunnels.
equivalent constitutive model of reinforced concrete instead of being an independent material. This modified constitutive model can effectively reflect the mechanical behavior of reinforced concrete, simplify the calculation work, and is more suitable for engineering analysis. Section of the reinforced concrete lining structure studied in this paper is shown in Fig. 4(a). The cross-section area of reinforced concrete and reinforcing bars is A and A' . The reinforcing steel is assumed to be elastic-perfect plastic and the stress-strain relation of concrete damaged plasticity model is defined by GB-50010 (2010), as shown in Fig. 5 and Fig. 6. According to the hypothesis of strain coordination, it is assumed that the strain of concrete and reinforcing steel is equal:
(
d=
)
1 α
σ+
− 1 ε plE0
(
1 α
)
− 1 ε plE0
(5) (6)
ε pl = αε in ε pl
ε in
= ε − σ / E0 is the inelastic is the equivalent plastic strain; where strain; α is the constant factor with 0 < α < α1. Replace E0 in Eq. (5) with ERC and order α = 0.7 , the damage variables of the reinforced concrete equivalent material studied in this paper are obtained, as shown in Fig. 8. The tensile damage variables
(1)
εc = εs
σA = Ec εc (A − A' ) + Es εs A' = ERC εA
The nominal stress σ of the reinforced concrete equivalent material can be obtained:
Table 2 The tunnel length, max overburden depths, and lining crack statistics of 11 tunnels. Tunnel
Liangfuwan Goujiagou Ranjiawan Zhaizishan Chenjiawan Ranfangwan Zhangjiawan Wangjiawan Jiajiagou Nianzigou Xuejigou
Length (m)
620 590 670 105 463 787 188 223 106 238 252
Max overburden depths (m)
103 106 108 37 89 115 42 50 36 55 58
Longitudinal crack
L c ≥ 5 m and Wc ≥ 1 mm
L c ≤ 5 m or Wc ≤ 1 mm
15 23 26 1 25 43 17 11 9 8 0
16 10 7 4 26 38 8 4 2 7 6
3
Circumferential crack and Oblique crack
Reticular crack
Total
5 7 5 0 9 17 6 6 1 0 3
1 1 0 0 1 0 0 0 0 0 0
37 41 38 5 61 98 31 21 12 15 9
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 3. The response of concrete to uniaxial loading in tension and compression.
underground structure by imposing seismic racking deformation on structures. But the interaction between underground structure and the surrounding ground was not considered. The International Standard, ISO23469, presented a simplified equivalent static analysis method as a guideline for the seismic design of geotechnical works (Iai, 2005). The ground displacement, inertia force, and interface shear stress were taken into account, while the soil-structure interaction was simulated by a series of normal and shear springs. Lu and Hwang (Lu and Hwang, 2017) proposed a modified cross-section racking deformation (MCSRD) method which can automatically consider the nonlinear soil-tunnel interaction based on the FLAC2D program. Compared with the dynamic analysis, the pseudo-static analysis cannot accurately catch the real variation of the relative stiffness, nor consider the cumulative damage of structures during the earthquake. However, the pseudo-static analysis can reflect the ultimate seismic capacity of tunnel lining to a certain extent. The calculation time can be considerably reduced, and the analysis process can be greatly simplified. Therefore, the pseudo-static method was adopted in many studies, especially in engineering design and evaluation, and a good agreement was observed in most cases (Bilotta et al., 2014; Corigliano et al., 2011; Hwang and Lu, 2007; Kontoe et al., 2014; Lu and Hwang, 2018). This paper put forward a modified deformation-based pseudo-static method. Based on the damage plasticity constitutive model of reinforced concrete proposed in Section 3.1, the seismic capacity of the cracked lining tunnels described in Section 2 was evaluated by analyzing the damage evolution of the lining structure under different seismic shear strains. The analysis and assessment steps are summarized in Fig. 9 and described below:
Fig. 4. The cross-section of the reinforced concrete lining structure. (a) real, (b) equivalent.
1. Set up a numerical model with a suitable mesh domain; establish geostatic equilibrium; excavate rock mass and construct tunnels in the domain. 2. Apply seismic shear strain step by step with a fixed rate on the boundaries of the numerical simulation domain. 3. Monitor the stress-strain curves and the damage evolution of lining structural elements during shear strain application; compare them with the curves shown in Fig. 7 and Fig. 8. 4. Check damage state of lining under different input shear strains; correspond the damage state of lining with the failure process; and determine the seismic shear strain γ leading to tunnel failure which can be evaluated by the following equation (John and Zahrah, 1987).
Fig. 5. Stress-strain curves of reinforcing steel.
corresponding to the inflection point and point N on segment MN in Fig. 7(a) is 0.7 and 0.82, respectively. The compressive damage variable is 0.26 when the equivalent material reaches the compressive yield strength. 3.2. Pseudo-static method
γ = v / Vs
Pseudo-static analysis can either be deformation-based or forcebased (Sun and Dias, 2019). An early application of the deformationbased method was the cross-section racking deformation (CSRD) method developed by the San Francisco Bay Area Transit (SFBAT) in the 1960 s. This method simulated the seismic action on the
(7)
where v is the peak ground velocity (PGV) during earthquake shaking at the location; and Vs is the average shear wave velocity of the ground. The Chinese Seismic Intensity Scale (Standardization Administration of 4
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 6. Stress-strain curves of concrete (GB-50010, 2010).
of shotcrete C25 refer to the experiment in Cong et al. (2015). The damage plasticity constitutive model of reinforced concrete studied in Section 3.1 was used to simulate the mechanical behavior of the permanent lining, which can be defined by material behavior of Concrete Damaged Plasticity in ABAQUS. The parameters of tunnel lining are presented in Table 4. The lining cracks can be interpreted as that the permanent lining had taken part of confining stress as time went by. In order to reflect the stress state of tunnel lining structure at that time, the stress release of 30% was considered after the excavation of rock mass and the permanent lining was constructed simultaneously with the temporary support in this model. No slipping is allowed between the temporary support and the rock mass. The interaction between the temporary support and the permanent lining is difficult to obtain accurately. Two extreme cases: the full-slip and no-slip conditions were considered in the model, as the idealizations of real contact. The initial crack of permanent lining was simulated by seam cracks in ABAQUS. A seam defines an edge or a face in your model that is originally closed but can open during an analysis. ABAQUS places overlapping duplicate nodes along a seam when the mesh is generated. According to the in-situ data, the longitudinal initial crack was taken as the research target of this paper. Initial cracks in the vault, spandrel, and sidewall were considered in the model. The depth of the initial crack was defined as 20 cm, which is half the thickness of the permanent lining. A triangular displacement distribution was applied along the lateral boundaries and a uniform displacement was also applied along the top boundary and bottom boundary, as shown in Fig. 9. Both were applied
PRC, 2008) gives the relationship between PGV, PGA, and the seismic intensity, as shown in Table 3.
4. Numerical model description and validation 4.1. Pseudo-static model Fig. 10 shows the configuration of the pseudo-static numerical model in the XY plane. The burial depth of the tunnel, H', is the vertical distance from the free surface to the vault of the tunnel. Three burial depths of 20 m, 60 m, and 100 m are considered in this paper. B denotes the maximum horizontal diameter of the tunnel. The size of the computational domain is very important to the pseudo-static method, which not only affects the computational costs but also affects the accuracy of the analysis results. Lu and Hwang (2017) studied the influence of the boundary distance by analyzing the variation of vertical stress after excavation and the distribution of shear strain after imposing seismic shear-strain along the sidewall direction. Sun and Dias (2019) studied the boundary effects by considering the influence zone caused by tunneling and the effect of the model width on the lining forces. Based on the above study, the boundary distance to the centerline of the tunnel, L = 65 m , corresponding to the L/ B = 65 m/12.67 m = 5.13 was adopted in the present study. The height of the computational domain, H , was equal to the width of the computational domain. The rock mass and the temporary support were considered to be a Mohr-Coulomb material. Because the thickness of the silt and silty clay near the surface is less than 3 m, only the stratum of mudstone mixed with sandstone was considered in the numerical model. The shear strength parameters
Fig. 7. The constitutive model of reinforced concrete equivalent material. (a) Tensile behavior, (b) Compressive behavior. 5
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 8. The damage variables of the reinforced concrete equivalent material.
Fig. 9. Flow chart of analysis and assessment procedure.
shear strain is considered in both directions in these cases. Compared with the two-dimensional model, the three-dimensional model is more accurate in simulation but required more computational load and longer calculation period. Therefore, the tunnel structure was simplified to a plane strain model for analysis in some cases. In this paper, two-dimensional and three-dimensional finite element models were established in ABAQUS, and the situation of a 20 m depth tunnel with the initial crack at the spandrel of lining was analyzed and compared, as shown in Fig. 11 and Fig. 12. The three-dimensional model is 24 m along the longitudinal direction. The initial longitudinal crack is 5 m long and is in the middle of the lining model. Fig. 13 shows the failure process of the lining structure in threedimensional simulation. In the first stage, the initial crack propagated along the longitudinal direction of the lining. The damage at the crack tip was greater than that in other crack propagation areas. However, the initial crack and new cracks did not extend along the radial direction of the lining at this stage. In the second stage, the initial crack
Table 3 The corresponding relationship between PGV, PGA and seismic intensity. Intensity
VI VII VIII IX X
Seismic ground motion parameters in horizontal PGA(m/s2)
PGV(m/s)
0.63 (0.45–0.89) 1.25 (0.90–1.77) 2.50 (1.78–3.53) 5.00 (3.54–7.07) 10.00 (7.08–14.14)
0.06 0.13 0.25 0.50 1.00
(0.05–0.09) (0.10–0.18) (0.19–0.35) (0.36–0.71) (0.72–1.41)
at a uniform rate in the time step. The maximum shear strain γmax applied in the model is 0.00358. According to Eq. (7) and the shear wave velocity of the stratum, the PGV is 1.41 m/s, corresponding to the seismic intensity Ⅹ in Table 3. The initial cracks in the spandrel and sidewall make the model geometrically asymmetric, so the seismic 6
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
of failure started in the initial crack zone, which is the most dangerous area. The failure process of the lining structure in the two-dimensional model is similar to that in the three-dimensional model, as shown in Fig. 14. In general, the results of the two-dimensional analysis, as expected, are different from those of three-dimensional analysis. However, these differences can be allowed when the more effective and more realistic from an engineering point of view. Therefore, the twodimensional model was chosen for the later analysis in this paper. 4.2. The response of the displacement field Fig. 15 shows the global and local displacement field for the case of the 20 m deep tunnel when γ = 0.00358 is applied on the boundary of the pseudo-static model. The global displacement fields show that the pseudo-static model can simulate the shear deformation of the ground well. The local displacement fields show that the ground displacement near the tunnel is restrained by the tunnel and the interaction between the temporary support and permanent lining affects the seismic displacement response of the tunnel. The deflection of the displacement field near the permanent lining is more obvious under the condition of full-slip.
Fig. 10. Pseudo-static numerical model in the XY plane. Table 4 Properties of tunnel lining. Parameters
Temporary support
Permanent lining
Unit weight γ (KN/m3) Thickness t (cm) Young’s modulus E (GPa) Poisson’s ratioν Cohesion c (MPa) Friction angle ϕ (°) Compressive behavior Ultimate stress σ cu (MPa) Tensile behavior Initial yield strength σ1(MPa) Secondary yield strength σ2 (MPa)
2.2 20 23 0.2 3 55
2.35 40 32.9 0.2 – –
–
22.4
– –
2.13 3.98
4.3. Comparison with dynamic analysis for no-crack tunnel Representative dynamic analyses were performed with the two-dimensional model by the finite element code ABAQUS in order to compare and validate the results of the pseudo-static method for the nocrack tunnel. The width of the model was 20 times the diameter of the tunnel and the left and right boundaries were set to infinite element boundaries. The upper boundary of the model was a free surface. A harmonic wave was used in the analysis with a frequency of 2.5 Hz. The amplitude of the incident wave had to be chosen to produce the same maximum shear strain of the free-field ground as in the pseudo-static case. Referring to the analysis model proposed by Chen et al. (2012), the ratio of the element size to the wavelength of the incident wave was set to less than 1/10 to ensure the accuracy of the simulated displacements and stresses. And the analysis was terminated when the wave was reflected from the free surface and reached the bottom boundary to prevent disturbance of the stress state of the tunnel by further reflection from the bottom boundary. The dynamic responses of the vault and
propagated along the radial direction of the lining. The propagation started in the middle of the initial crack until the initial crack zone penetrated the lining along the radial direction. In the final stage, the penetrating crack extended along the longitudinal direction. All stages
Fig. 11. Two-dimensional pseudo-static model. 7
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 12. Three-dimensional pseudo-static model.
Fig. 13. Failure process of lining structure in three-dimensional simulation.
practical and efficient method to evaluate the seismic capacity of tunnels. But at the same time, it should also be noted that the pseudo-static method cannot simulate the real nonlinear and hysteretic characteristics of the tunnel under earthquake.
spandrel of the permanent lining were monitored. Fig. 16 shows the comparison of the internal forces at monitored points between dynamic analysis and pseudo-static method for tunnels with different depths. The general trends of the internal forces versus seismic shear strain were similar for both methods. The differences of the peak responses varied with the tunnel depth and the locations of the lining, but it was reasonably close in the engineering view. This suggests that the pseudo-static method can be regarded as a more simple, 8
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 14. Failure process of lining structure in two-dimensional simulation. Fig. 15. The global and local displacement fields under the application of γ = 0.00358. (a) no-slip, (b) full-slip.
5. Numerical result and discussion
and the permanent lining took the confining stress simultaneously, the deeper the buried depth, the greater the compressive stress on the lining structure. The failure process of no-crack linings under seismic shear deformation and corresponding shear strain are listed in Table 5. The tunnel located at 20 m depth was only damaged by tension under seismic shear deformation. The concrete cracked first near the spandrel of lining, then steel bars yielded in tension, leading to partial instability
5.1. Failure process of no-crack lining Fig. 17 shows the principal stress distribution of tunnels with different buried depths after construction. The principal stress of lining structures distributes along the circumferential direction, all of which is compressive stress. Due to the Consideration of the temporary support 9
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 16. The comparison of the internal forces at monitored points. (a) 20 m, (b) 60 m, (c) 100 m.
structure. The 100 m deep tunnel mainly suffered from compression damage under seismic shear deformation. In all three cases, the damaged zones did not penetrate the lining under γmax . In an earthquake, the shear deformation of the stratum leads to the ovaling of lining, as
of the structure. For the 60 m deep tunnel, both tensile damage and compressive damage occurred near the spandrel of the lining. The crush of reinforced concrete in the compression zone occurred earlier than the yield of steel bars in the tensile zone, leading to partial spalling of 10
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Fig. 16. (continued)
Fig. 17. Principal stress distribution of linings with different buried depths after construction. Table 5 Failure process of no-crack linings under seismic shear deformation. Buried depth
No-slip
Full-slip
Seismic shear strain γ
Description of damage
Seismic shear strain γ
Description of damage
20 m
0.173% 0.304%
Concrete near spandrel cracks obviously Steel bars in the tensile zone yield
0.182% 0.311%
Concrete near spandrel cracks obviously Steel bars in the tensile zone yield
60 m
0.221% 0.251%
Concrete near spandrel cracks obviously Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
0.225% 0.278%
Concrete near spandrel cracks obviously Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
100 m
0.243%
Reinforced concrete in the compression zone of spandrel crushed Concrete near spandrel cracks obviously
0.261%
0.326%
0.304%
11
0.309%
0.314%
Reinforced concrete in the compression zone of spandrel crushed Concrete near spandrel cracks obviously
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
the 60 m deep tunnel with lining cracks under seismic shear deformation. The initial crack in the vault and sidewall did not improve the damage level of the tunnel. But for the no-slip case of the cracked lining tunnel, the steel bars in the tensile zone yielded earlier. Compared with the no-cracked lining, both tensile damage and compression damage occurred earlier near the spandrel crack. With the increase of seismic shear strain, the crushing zone of reinforced concrete near the crack tip gradually enlarged and eventually penetrated the lining, leading to structural collapse, as shown in Fig. 19(b). Table 9 shows the failure process and corresponding shear strain of the 100 m deep tunnel with lining cracks under seismic shear deformation. The initial cracks in the vault and the sidewall had little effect on the seismic response of the tunnel. The initial crack in the spandrel was sensitive to seismic action. The crushing zone developed from the crack tip along the circumferential and radial direction and quickly penetrated the lining structure. The final damage state of lining is shown in Fig. 19(c). The seismic capacity of the tunnel was greatly reduced, especially under full-slip conditions. The numerical result indicates that cracks in vault and sidewall have a slight impact on the seismic response of linings under seismic shear wave conditions. There was little further development of damage near the initial cracks in these conditions. However, cracks in spandrel were in totally different situations and the seismic capacity of the tunnel was reduced. With the increase of seismic shear strain, structural damage developed rapidly near the initial cracks. In the case of the shallow tunnel, the cracking zone developed along the radial direction of lining from the crack tip and penetrated the structure. In the case of the deepburied tunnel, crushing zones firstly appeared near the initial crack in spandrel and then connected with it. Finally, the lining structure collapse along the oblique section.
Fig. 18. Deformation modes of tunnels under seismic waves (Hashash and Romero-Arduz, 2015).
shown in Fig. 18. This results in tension or compression concentration near the spandrel of the lining. The initial stress states of linings with different buried depth are different, so the failure modes are also different in seismic. Several typical failure processes of lining structures under the action of seismic shear deformation are classified in Table 6. The corresponding representative damage values based on Section 3.1 are also given. Considering that it has no impact on the normal use of tunnels, cracking of lining concrete is defined as minor damage. Yielding of steel bars in the tension zone or crushing of reinforced concrete in the compression zone is defined as moderate damage, which may lead to partial spalling of lining and endanger traffic safety. The lining may lose stability or even collapse when the cracking zone or crushing zone penetrates the structure. This damage state is defined as severe damage.
5.3. Effect of the interaction between temporary support and permanent lining The damage process of linings in the cases of no-slip and full-slip was similar, while the thresholds of different failure states were different. The development of damage states in the no-slip case was faster than that in the full-slip case for the no-crack lining. It demonstrates that the allowance of relative slip between the temporary support and permanent lining slows the damage state development under the same loading conditions, which is consistent with previous research (Lu and Hwang, 2018; Sedarat et al., 2009; Sun and Dias, 2019). The lining with cracks in vault and sidewall also conforms to the above-mentioned rules. However, the lining structure with cracks in the spandrel was more likely to lose stability and collapse under the condition of full-slip. This shows that the deformation of the permanent lining is limited by the no-slip condition under the seismic shear deformation. Therefore, the lining structure is less likely to have penetration damage under this condition.
5.2. Effect of the lining cracks on the seismic capacity of tunnels Table 7 shows the failure process and corresponding shear strain of the 20 m deep tunnel with lining cracks under seismic shear deformation. The lining with the initial crack in the sidewall has the same failure process as the no-crack lining. The initial crack in the vault developed slightly with the increase of seismic shear strain. However, there was no further damage to the structure. The initial crack in the spandrel of lining has a great impact on the seismic response and capacity of the tunnel. The cracking zone near the tip of the initial crack developed rapidly and eventually penetrated the lining. The final damage state of lining is shown in Fig. 19(a). Table 8 shows the failure process and corresponding shear strain of Table 6 Classification of failure characteristics of lining structures. Damage level
Description of damage
Effect on the capacity of structures
III
Concrete in the tensile zone cracking obviously (DAMAGETa 0.7)
Do not affect the normal use
Ⅱ
Steel bars in the tensile zone yield (DAMAGETa 0.82) Reinforced concrete in the compression zone crushed (DAMAGECb 0.26)
Part of the structure reaches the ultimate state of bearing capacity (partial spalling of structure)
Ⅰ
Cracking or crushing zone penetrates lining (DAMAGET 0.82& DAMAGEC 0.26)
Structure loses stability or collapse
a b
Tensile damage variable. Compressive damage variable. 12
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 7 Failure process of cracked linings under seismic shear deformation (20 m buried depth). Initial crack location
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.172% 0.271% 0.318% 0.185% 0.277% 0.336%
Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield
III III Ⅱ III III Ⅱ
0.158% 0.226% 0.263% 0.326% 0.147% 0.183% 0.282%
Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Cracking zone penetrates lining from the initial crack Initial crack propagating Concrete near spandrel cracks obviously (new cracks) Cracking zone penetrates lining from the initial crack
III III Ⅱ Ⅰ III III Ⅰ
0.167% 0.335% 0.220%
Concrete near spandrel cracks obviously (new cracks) Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks)
III Ⅱ III
Full-slip
Spandrel
No-slip
Full-slip
Sidewall
No-slip Full-slip
Fig. 19. Finial damage state of lining with the initial crack.
Table 8 Failure process of cracked linings under seismic shear deformation (60 m buried depth). Initial location of crack
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.213% 0.247% 0.305% 0.215% 0.261% 0.296%
Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
III Ⅱ Ⅱ III Ⅱ Ⅱ
0.188% 0.212% 0.257% 0.275% 0.356% 0.219% 0.221% 0.233% 0.275% 0.332%
Reinforced concrete near the initial crack crushed Concrete near spandrel cracks obviously (new cracks) Initial crack propagating Steel bars in the tensile zone yield Crushing zone penetrating lining from the initial crack Concrete near spandrel cracks obviously (new cracks) Reinforced concrete near the initial crack crushed Initial crack propagating Steel bars in the tensile zone yield Cracking and crushing zone penetrating lining from the initial crack
Ⅱ III III Ⅱ Ⅰ III Ⅱ III Ⅱ Ⅰ
0.215% 0.258% 0.296% 0.232% 0.275% 0.319%
Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield Concrete near spandrel cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Steel bars in the tensile zone yield
III Ⅱ Ⅱ III Ⅱ Ⅱ
Full-slip
Spandrel
No-slip
Full-slip
Sidewall
No-slip
Full-slip
6. Conclusions
modified deformation-based pseudo-static analysis. This analysis employed a reconstructed damaged plasticity constitutive model of reinforced concrete to simulate the propagation of lining cracks. Based on the case study of 11 tunnels in earthquake-prone areas of western
This paper highlighted the important effect of the longitudinal cracks in the permanent lining on the seismic capacity of tunnels by a 13
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Table 9 Failure process of cracked linings under seismic shear deformation (100 m buried depth). Initial location of crack
Interaction
Seismic shear strain γ
Description of damage
Damage level
Vault
No-slip
0.284% 0.303% 0.286% 0.311%
Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed
III Ⅱ III Ⅱ
0.225% 0.264% 0.211% 0.254%
Reinforced concrete near the initial crack crushed Crushing zone penetrating lining near the initial crack Concrete near spandrel cracks obviously (new cracks) Crushing zone penetrating lining from the initial crack
Ⅱ Ⅰ III Ⅰ
0.293% 0.294% 0.303% 0.318%
Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks) Reinforced concrete in the compression zone of spandrel crushed Concrete near vault cracks obviously (new cracks)
Ⅱ III Ⅱ III
Full-slip Spandrel
No-slip Full-slip
Sidewall
No-slip Full-slip
China, a two-dimensional finite element model was established considering the influence of tunnel depth, initial crack position, and interaction between soil and lining structures. The simulation results showed that the failure process of the reinforced concrete structure could be accurately simulated by the modified damaged constitutive model and identified by the damage variables. The analysis considered the contribution of permanent linings to the confining stress of operating tunnels. The initial stress state of the permanent lining was different with different depth, and the failure mode under the action of the seismic shear deformation was also different. However, for all three cases with different depths, the damage zone first appeared in the spandrel of linings. Cracks in vault and sidewall had a slight impact on the seismic response of linings, while cracks in spandrel were in totally different situations. With the increase of seismic shear strain, structural damage developed rapidly near the initial spandrel cracks. For shallow tunnel, the cracking zone developed along the radial direction of lining from the crack tip and penetrated the structure. For deep-buried tunnel, crushing zones were formed in a large area near the initial crack, resulting in the lining structure collapse along the oblique section. The seismic capacity of tunnels with lining cracks in the spandrel was greatly reduced. The interaction between the temporary support and permanent lining had little effect on the damage process of linings but had an impact on the thresholds of different failure states. The development of damage states in the no-slip case was faster than that in the full-slip case for no-crack lining, and so does for the lining with cracks in vault and sidewall. However, the allowance of relative slip slows the damage state development on the permanent lining under the same loading conditions but also increases its deformation capacity. Therefore, the lining structure with cracks in the spandrel was more likely to have penetration damage and lose stability under the condition of full-slip.
References Asakura, T., 1997. Mountain tunnels performance in the 1995 hyogoken-nanbu earthquake. International Symposium on Recent Advances in Exploration Geophysics. Asakura, T., Kojima, Y., 2003. Tunnel maintenance in Japan. Tunn. Undergr. Sp. Tech. 18, 161–169. Ayari, M.L., Saouma, V.E., 1990. A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Eng. Fract. Mech. 35, 587–598. Bilotta, E., Lanzano, G., Madabhushi, S.P.G., Silvestri, F., 2014. A numerical Round Robin on tunnels under seismic actions. Acta Geotechnica. 9, 563–579. Chen, C.-H., Wang, T.-T., Jeng, F.-S., Huang, T.-H., 2012. Mechanisms causing seismic damage of tunnels at different depths. Tunn. Undergr. Sp. Tech. 28, 31–40. Chen, Z., Wei, J., 2012. Correlation between ground motion parameters and lining damage indices for mountain tunnels. Nat. Hazards. 65, 1683–1702. Chiu, Y.-C., Lee, C.-H., Wang, T.-T., 2017. Lining crack evolution of an operational tunnel influenced by slope instability. Tunn. Undergr. Sp. Tech. 65, 167–178. Yu, C.O., Liang, K.O., Yingren, Z.H., 2015. Experimental study on shear strength of concrete. Concrete 5, 40–45. Corigliano, M., Scandella, L., Lai, C.G., Paolucci, R., 2011. Seismic analysis of deep tunnels in near fault conditions: a case study in Southern Italy. Bull. Earthquake Eng. 9, 975–995. Cui, X., Li, S., Lou, J., Wang, Z., Zhang, J., Tang, W., Gao, Z., 2015. Dynamic responses and damage analyses of tunnel lining and errant large vehicle during collision. Tunn. Undergr. Sp. Tech. 50, 1–12. Federal Highway Administration, 2004. Highway and Rail Transit Tunnel Maintenance and Rehabilitation Manual. GB-50010, 2010. Code for design of concrete structures. China Architecture and Building Press, Beijing. Hamid, S., Mahdi, S., Amir, H.A., Mohammad, A., Ali, S., 2012. Evaluation of reinforced concrete beam behavior using finite element analysis by ABAQUS. Sci. Res. Essays. 7. Hashash, Y.M.A., Park, D., Yao, J.I.C., 2005. Ovaling deformations of circular tunnels under seismic loading, an update on seismic design and analysis of underground structures. Tunn. Undergr. Sp. Tech. 20, 435–441. Hashash, Y.M.A., Romero-Arduz, M.I., 2015. Seismic Design of Tunnels. Hwang, J.-H., Lu, C.-C., 2007. Seismic capacity assessment of old Sanyi railway tunnels. Tunn. Undergr. Sp. Tech. 22, 433–449. Iai, S., 2005. International standard (ISO) on seismic actions for designing geotechnical works–An overview. Soil Dyn. Earthq. Eng. 25, 605–615. Japan Society of Civil Engineers, 2005. Tunnel Maintenance and Management. Japan Society of Civil Engineers, Tokyo, Japan. John, C.M.S., Zahrah, T.F., 1987. Aseismic design of underground structures. Tunn. Undergr. Sp. Tech. 2, 165–197. Konagai, K., Takatsu, S., Kanai, T., Fujita, T., Ikeda, T., Johansson, J., 2009. Kizawa tunnel cracked on 23 October 2004 Mid-Niigata earthquake: An example of earthquake-induced damage to tunnels in active-folding zones. Soil Dyn. Earthq. Eng. 29, 394–403. Kontoe, S., Avgerinos, V., Potts, D.M., 2014. Numerical validation of analytical solutions and their use for equivalent-linear seismic analysis of circular tunnels. Soil Dyn. Earthq. Eng. 66, 206–219. Lee, J., Fenves, G.L., 1998. Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124, 892–900. Lu, C.-C., Hwang, J.-H., 2017. Implementation of the modified cross-section racking deformation method using explicit FDM program: A critical assessment. Tunn. Undergr. Sp. Tech. 68, 58–73. Lu, C.-C., Hwang, J.-H., 2018. Damage analysis of the new Sanyi railway tunnel in the 1999 Chi-Chi earthquake: Necessity of second lining reinforcement. Tunn. Undergr. Sp. Tech. 73, 48–59. Ministry of Transport of the PRC, 2015. Technical Specification of Maintenance for Highway Tunnel. China Communications Press. Nefedov, S.S., 2005. Instability of reinforced concrete containment under internal pressure. International Conference on Structural Mechanics in Reactor Technology. Penzien, J., 2015. Seismically induced racking of tunnel linings. Earthquake. Eng. Struc. 29, 683–691. Qiu, W., Lu, F., Wang, G., Huang, G., Zhang, H., Zhang, Z., Gong, C., 2019. Evaluation of
CRediT authorship contribution statement Wenge Qiu: Conceptualization, Methodology, Supervision. Bingtian Li: Conceptualization, Methodology, Validation, Writing original draft, Writing - review & editing. Lun Gong: Writing - review & editing. Xingxin Qi: Investigation, Visualization. Zhiheng Deng: Investigation, Visualization. Guang Huang: Investigation, Visualization. Hui Hu: Investigation, Visualization.
Acknowledgments The authors gratefully acknowledge the financial support of the National Key R&D Program of China (2017YFC0806000), the National Natural Science Foundation of China (U1434206). 14
Tunnelling and Underground Space Technology 97 (2020) 103281
W. Qiu, et al.
Wang, Z.Z., Zhang, Z., 2013. Seismic damage classification and risk assessment of mountain tunnels with a validation for the 2008 Wenchuan earthquake. Soil Dyn. Earthq. Eng. 45, 45–55. Wittke, W., Pierau, B., Erichsen, C., 2006. New austrian tunneling method (NATM) stability analysis and design. WBN, Essen, pp. 2441. Wu, D., Gao, B., Shen, Y., Zhou, J., Chen, G., 2015. Damage evolution of tunnel portal during the longitudinal propagation of Rayleigh waves. Nat. Hazards. 75, 2519–2543. Xiao, J.Z., Dai, F.C., Wei, Y.Q., Min, H., Xu, C., Tu, X.B., Wang, M.L., 2014. Cracking mechanism of secondary lining for a shallow and asymmetrically-loaded tunnel in loose deposits. Tunn. Undergr. Sp. Tech. 43, 232–240. Xu, D.-P., Feng, X.-T., Chen, D.-F., Zhang, C.-Q., Fan, Q.-X., 2017. Constitutive representation and damage degree index for the layered rock mass excavation response in underground openings. Tunn. Undergr. Sp. Tech. 64, 133–145. Yan, Q., Xu, Y., Zhang, W., Geng, P., Yang, W., 2018. Numerical analysis of the cracking and failure behaviors of segmental lining structure of an underwater shield tunnel subjected to a derailed high-speed train impact. Tunn. Undergr. Sp. Tech. 72, 41–54. Yashiro, K., Kojima, Y., 2007. Historical earthquake damage to tunnels in japan and case studies of railway tunnels in the 2004 niigataken-chuetsu earthquake. Qr of Rtri. 48, 136–141. Yuan, Y., Bai, Y., Liu, J., 2012. Assessment service state of tunnel structure. Tunn. Undergr. Sp. Tech. 27, 72–85. Zou, Y., Liu, H., Jing, L., Cui, J., 2017. A pseudo-static method for seismic responses of underground frame structures subjected to increasing excitations. Tunn. Undergr. Sp. Tech. 65, 106–120.
mechanical performance and optimization design for lattice girders. Tunn. Undergr. Sp. Tech. 87, 100–111. Richards, J.A., 1998. Inspection, maintenance and repair of tunnels: International lessons and practice. Tunn. Undergr. Sp. Tech. 13, 369–375. Sedarat, H., Kozak, A., Hashash, Y.M.A., Shamsabadi, A., Krimotat, A., 2009. Contact interface in seismic analysis of circular tunnels. Tunn. Undergr. Sp. Tech. 24, 482–490. Shen, Y., Gao, B., Yang, X., Tao, S., 2014. Seismic damage mechanism and dynamic deformation characteristic analysis of mountain tunnel after Wenchuan earthquake. Eng. Geol. 180, 85–98. Song, W., Lai, H., Liu, Y., Yang, W., Zhu, Z., 2019. Field and laboratory study of cracking and safety of secondary lining for an existing highway tunnel in loess ground. Tunn. Undergr. Sp. Tech. 88, 35–46. Standardization Administration of PRC, 2008. The Chinese seismic intensity scale. Standardization Administration of People's Republic of China, China. Sun, Q.Q., Dias, D., 2019. Assessment of stress relief during excavation on the seismic tunnel response by the pseudo-static method. Soil Dyn. Earthq. Eng. 117, 384–397. Vargas-Loli, L.M., Fenves, G.L., 2010. Effects of concrete cracking on the earthquake response of gravity dams. Earthquake. Eng. Struc. 18, 575–592. Wang, J.-N., 1993. Seismic design of tunnels: a simple state-of-the-art approach. Parsons Brickerhoff Quade & Douglas Inc, New York. Wang, T.-T., 2010. Characterizing crack patterns on tunnel linings associated with shear deformation induced by instability of neighboring slopes. Eng. Geol. 115, 80–95. Wang, W.L., Wang, T.T., Su, J.J., Lin, C.H., Seng, C.R., Huang, T.H., 2001. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake. Tunn. Undergr. Sp. Tech. 16, 133–150.
15