1 Introduction

Driven by the increasing need of providing infrastructural facilities in mountainous regions, the construction of tunnels for highway and railway networks has witnessed a constant increase. Major tunneling projects are either being planned or being executed in more challenging and complex conditions than in the past. However, following recent seismic events, the traditional view with regard to earthquake resistant characteristics of tunnels as a whole have been challenged. Severe cases of damages of mountain tunnels have been reported in the 1995 Hyogoken-Nanbu (Japan), 1999 Chi-Chi (Taiwan), 2004 Mid-Niigata Prefecture (Japan) and the 2008 Wenchuan (China) earthquakes (Asakura and Sato 1998; Otsuka et al. 1997; Wang et al. 2001; Shimizu et al. 2007b; Jiang et al. 2010; Li 2012; Chen et al. 2012; Shen et al. 2014 etc.). Such poor performances have led scholars and engineers to take up research in the area of seismic behaviour of tunnel and underground facilities (Kontoe et al. 2008; Penzien 2000; Hashash et al. 2001; O’Rourke et al. 2001; Konagai 2005; Wang et al. 2009; Li 2012).

The present paper provides a review of the investigations carried out by various researchers with regard to the seismic performance of mountain tunnels. Some prominent cases of damages reported following recent earthquakes are discussed with special emphasis on the observed damage patterns. Moreover, the factors believed to be responsible for the damages have been explained. Based on the damage patterns and the influencing factors, probable mechanisms of seismic damage of mountain tunnels have been summarized.

Finally, numerical investigation is attempted to evaluate influence of some of the prominent parameters on the seismic performance of tunnels in blocky rock mass. In this regard, a discontinuum based numerical approach has been adopted to simulate the blocky nature of the rock mass. Such an approach towards the seismic analysis of tunnels is very promising especially for tunnels in weathered blocky rock mass as most of the investigations reported in literature are either based on continuum or idealized discontinuum approaches. The highlights of the seismic analyses carried out in the study may be pointed out as following.

  • Consideration of fractured nature of the rock mass by Voronoi tessellation scheme which is very rare in literature.

  • Explicit investigation of seismic response of tunnels considering wide frequency range (1–10 Hz). For this, seismic analyses with harmonic base excitations of different frequencies have been carried out.

  • Influence of Peak Horizontal Acceleration (PHA) on the dynamic forces induced in the tunnel liner has been investigated. This observation has also been correlated with the damages observed in the past case histories viz. 1999 Chi-Chi and 2008 Wenchuan earthquakes.

  • Effect of tunnel depth on the seismic response of tunnels has been investigated. The numerical results have also been corroborated with the past damages.

The present study is believed to advance the current understanding with regard to the seismic performance of mountain tunnels passing through blocky rock mass. This may be helpful for number of tunneling projects coming up for various infrastructural developments especially in mountainous regions.

2 Overview of Past Seismic Performances of Mountain Tunnels

Some of the prominent work documenting seismic damages of tunnels and underground facilities have been carried out by Dowding and Rozen (1978), Owen and Scholl (1980), Sharma and Judd (1991) and Power et al. (1998). Dowding and Rozen (1978) investigated 71 tunnels following earthquakes in America and Japan. Most of the tunnels investigated were part of railway or roadway network with majority of them passing through rocky terrain. Based on analysis of the available data, damages may be grouped as damages due to slope instabilities, damages related to poor geology and damages at shallow overburden sections arising due to unsymmetrical loading condition. Damage patterns included uplift of invert, spalling of concrete at the crown, failures of sidewalls and portal cracking. Relationship between seismic damage and peak ground acceleration was established and it was observed that major damages occurred in case of seismic events having a peak acceleration magnitude greater than 0.50 g. The database was further enlarged by Owen and Scholl (1980) documenting 127 cases of damages of underground facilities.

Subsequently, Sharma and Judd (1991) documented 192 cases of tunnel performance under 85 different earthquakes. Correlation of seismic induced damages was made with six parameters: tunnel overburden, type of subsoil, peak ground acceleration, magnitude of earthquake, epicentral distance and type of lining support. It was concluded that the vulnerability of tunnels increased when the depth of overburden was small. Moreover, earthquake parameters like magnitude, peak ground acceleration and epicentral distance had a significant impact on the overall stability. It was also found that the damage levels decreased for tunnels constructed in competent rocks. Similar observations were made by Power et al. (1998) with regard to the performance of underground facilities following the 1995 Hyogoken-Nanbu (Japan) and the 1995 Northridge (U.S.) earthquakes. Table 1 collates past seismic performances of tunnels highlighting the major observations and conclusions.

Table 1 Past seismic performances of tunnels
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3 Specific Discussion on Major Damages

In the present section, case histories of damages of mountain tunnels for earthquakes in Japan, Taiwan and China are discussed. For each of the cases, discussions are made with emphasis on the earthquake parameters, ground conditions and damage patterns documented by various researchers. Based on these case histories, predominant damage patterns and the factors affecting the seismic behaviour of tunnels have been identified.

3.1 Damage of Tunnels in Japan

Owing to the mountainous terrain of Japan, there is an extensive use of tunnels for highway and railway networks. A total of about 4500 tunnels for railways and 6500 tunnels for highways are in operation. In addition, tunnels and underground facilities are also utilized for hydroelectric projects, water supply and storage purpose.

As Japan is situated in a volcanic zone on the Pacific ring of fire, volcanic and earthquake events are quite frequent. Motions arising as a result of movement of Pacific, Philippine, Eurasian and the North American plates results in around 40 earthquake events of magnitude greater than 4.0 per month. As such, seismic damages of tunnel have been reported extensively. Table 2 summarizes cases of tunnel damages following various earthquakes in Japan. Subsequently, some of the major tunnel damages during few prominent earthquakes are discussed.

Table 2 Summary of tunnel damages following earthquakes in Japan.
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1923 Kanto earthquake The catastrophic event of Kanto in 1923 caused severe damages to mountain tunnels in Japan. Over 100 cases of tunnel damages were reported following the earthquake out of which 25 needed immediate repair and reinforcement measures. One of the most severely affected tunnel was the Nabuya tunnel which suffered damage from landslide. The landslide destroyed a portion of the tunnel lining leading to collapse of a tunnel section making it inoperative.

1930 Kita-Izu earthquake The 1930 Kita-Izu earthquake of magnitude 7.1 severely affected the Tanna railway tunnel. The earthquake had a focal depth of 11 km. The tunnel was situated at an epicentral distance of 15 km (Sharma and Judd 1991). The damages were maximum in the sections where the tunnel passed through the fault-fracture zone of the Tanna basin. A 60 m stretch of the tunnel without concrete cover was subjected to large earth pressure during seismic shaking. Consequently, large volume of earth (about 1200 m3) fell into the tunnel disrupting the operations. Cracking of the tunnel lining was also observed at other sections.

1978 Izu-Oshima-Kinkai earthquake This earthquake severely affected the railway network of the adjacent area as it caused extensive damages to nine railway tunnels (Kawakami 1984). Among them, the most severely affected was the Inatori tunnel which was a 906 m long single track railway tunnel passing through a deposit of volcanic mudflow. The damage was majorly caused due to movement along a fault resulting in damage of tunnel lining and distortion of track alignment along the longitudinal direction. Based on the survey conducted following the earthquake, relative displacement of 70 and 20 cm in the horizontal and vertical direction respectively was worked out.

1995 Hyogoken-Nanbu earthquake Asakura and Sato (1998) investigated 100 mountain tunnels following the 1995 Hyogoken-Nanbu earthquake and found that 24 tunnels were affected by the earthquake with 12 of them sustaining heavy damages. In most cases, damages occurred in the form of cracking of the linings in longitudinal, cross-sectional and circumferential direction highlighting the influence of interaction of the direction of seismic waves with the tunnel axis and cross-section. Shear and compressive failure of the sidewalls and the arch, heaving of the invert, cracking of the portal wall and collapse of portal sections were also reported (Asakura and Sato 1998; Kitagawa and Hiraishi 2004). Table 3 summarizes the observations of four most severely affected tunnels following this earthquake.

Table 3 Summary of few tunnels damaged in 1995 Hyogoken-Nanbu earthquake.
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In case of Nunobiki tunnel, cracking in the lining both in the cross-sectional and longitudinal directions were observed. In addition, spalling of concrete at the junction between the arch and the sidewall was also observed. However, the damage was confined to a short zone which was comparatively heavily fractured.

The damages in the case of Bantaki road tunnel was also confined to a short section of highly fractured zone characterized by buckling and bending of steel reinforcements. In addition, strong vertical ground motions and thrusting in the axial direction were held responsible for the uplift of the ground pavement.

The Rokko tunnel was a 16 km long railway tunnel constructed in Mesozoic granite with the alignment passing thorough five major faults—Koyo, Ashiya, Gosukebashi, Ohtsaki and Nunobiki faults. The poor geological condition arising from the frequent faulting and fracturing led to different configurations of failures. Some prominent patterns of failures observed included the development of shear cracks and spalling of concrete near the arch shoulders. Bottom heaving and uplift in the vicinity of the inverts were also reported. Major damages occurred in the poor and highly fractured geological zone encountered between the Gosukebashi and Ohtsaki faults.

One of the main factors leading to failures was the adverse geology associated with the damaged tunnel sections. This clearly highlights the adverse effects of discontinuities leading to amplified ground motion and relative movements among rock blocks (Roy and Sarkar 2015). Some of the other factors influencing the magnitude of relative displacement among blocks are degree of separation, direction of ground motion and topography.

2004 Mid-Niigata Prefecture earthquake The earthquake occurred on October 23, 2004 severely affecting the rail and road network of the area. The focal depth of the earthquake was about 13 km having a magnitude of 6.8. A series of strong aftershocks followed the main events with four of them having a magnitude of around 6 or greater in a span of 38 min (Konagai et al. 2005). The earthquake affected about 24 railway tunnels and even caused the derailment of a train. Among them, five tunnels—Uonama, Myoken, Wanatsu, Tenno and Shin-Enokitoge suffered severe damages and had to be closed for a long time for repair and restoration (Shimizu et al. 2007b, Yashiro and Kojima 2007; Jiang et al. 2010).

The Uonama tunnel located close to the epicenter (<10 km) suffered maximum damage. The damaged section had an overburden of about 60–100 m. Movement of sidewalls along with development of diagonal cracks was common. At one location, severe damage at the crown leading to lining collapse and exposure of steel reinforcements was observed. As shown in Fig. 1, right lateral shift of about 10–15 cm of the center ditch along the rails was also observed (Konagai et al. 2005).

Fig. 1
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Right lateral shift of about 10–15 cm in Uonama tunnel (Konagai et al. 2005)

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Even though landslide was prevalent during the earthquake, it is believed that it was not the major cause as the damaged sections were located at deeper depths. Based on the pattern of cracks observed, it has been concluded that the damage was caused by slipping of a fault segment intersecting the tunnel.

Another tunnel to be severely affected was Myoken tunnel. Failures in terms of heaving of the invert and compressive failure at the crown were observed. In case of Wanatsu tunnel, compressive failure at crown with subsequent exposure of steel supports was observed. For both Tenno and Shin-Enokitoge tunnels, cracking of tunnel lining resulting from failure of bedrock was reported (Shimizu et al. 2007b, Jiang et al. 2010). A list of tunnels affected by the earthquake along with the associated geology and damage patterns has been reproduced from the study of Jiang et al. (2010) in Table 4.

Table 4 Tunnels damaged in Mid-Niigata Prefecture earthquake (After Jiang et al. 2010)
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3.2 Damage of Tunnels in Taiwan

1999 Chi-Chi earthquake A 7.3 magnitude earthquake struck central Taiwan on September 21, 1999 at a depth of around 7.5 km causing catastrophic damage to infrastructural facilities. The earthquake is believed to be a result of reactivation of the Chelungpu fault (Wang et al. 2000). The seismic event produced very high ground motion with the free field instruments recording horizontal motion of 1.0 and 0.8 g at two locations (Wang et al. 2001).

Figure 2 shows the location of the tunnels in vicinity of the earthquake epicenter and the Chelungpu fault. Following the earthquake, an investigation of 57 tunnels was taken up by Wang et al. (2001) based on which 49 cases of damages were reported. Figure 3 presents number of different damage patterns observed in case of reported 49 cases of instabilities. From the figure it is evident that the damages of tunnel sections are mostly in forms of lining cracks, portal failure and spalling of concrete lining. Figure 4 shows the slope instability induced failure of the Ching-Shue tunnel following this earthquake.

Fig. 2
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Location of tunnels and Chelungpu Fault in vicinity of epicenter of Chi-Chi earthquake (Wang et al. 2001)

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Fig. 3
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Various tunnel damages observed in Chi-Chi (1999) Taiwan earthquake

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Fig. 4
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Damage to Ching-Shue tunnel. a Tunnel entrance before the Chi-Chi earthquake. b Closure and damage of tunnel entrance due to slope instability (Wang et al. 2001)

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Table 5 reproduced from Wang et al. (2001) lists the 57 tunnels which were investigated providing details about their geometry, epicentral distance and location with regard to the Chelungpu fault. Greater damages were observed for tunnels located on the hanging wall of the Chelungpu fault which experienced higher ground motion. It was observed that the damages are mainly concentrated in the vicinity of the faulted or fractured region.

Table 5 Tunnel investigated following the 1999 Chi-Chi earthquake (after Wang et al. 2001)
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3.3 Damage of Tunnels in China

2008 Wenchuan earthquake On May 12, 2008 a strong earthquake having a magnitude of 8.0 on Richter scale struck in the Longmenshan fault zone in the Sinchuan Province of China (Chen et al. 2012; Huang and Li 2009; Xu et al. 2009). The focal depth of the earthquake was estimated to be around 15 km with the seismic shaking period of 120 s. This earthquake is believed to be the most destructive seismic event to have struck China in the last 100 years affecting around 87,000 people and causing an economic loss of about 845 billion Yuan. Table 6 lists 30 tunnels having an epicentral distance less than 50 km which suffered damages during the earthquake (Wang and Zhang 2013; Zhang 2013; Zheng et al. 2009, 2012).

Table 6 Tunnel with an epicentral distance of less than 50 km in the 2008 Wenchuan earthquake (Wang and Zhang 2013)
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Li (2012) has carried out a more detailed investigation of the damages to the mountain tunnels of the Dujiangyan Wenchuan highway tunnels following the Wenchuan earthquake highlighting the damage patterns and the factors contributing towards the instabilities. Table 7 summarizes the findings of Li (2012) with regard to 11 tunnels of the Du Wen highway network which were affected by the earthquake. Details of some of the damaged tunnels are elaborately discussed in the following section.

Table 7 Tunnels of Du Wen highway affected by 2008 Wenchuan earthquake (after Li 2012; Wang et al. 2009)
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Longxi tunnel It is a twin tunnel system separated by a distance of 30 m. According to the rock mass classification system of Chinese highway tunnel, the alignment passes though two zones. About 29 % of the tunnel length passes through sandstone and granite rock which is hard and hence has good overall stability. However, 71 % tunnel passes through intensely jointed and fractured rock mass comprising of mudstone, mudstone-siltstone mixture, carbonaceous mudstone and thin coal layers. In such stretches the stability was poor. Following the earthquake, instabilities were manifested in terms of portal closure, cracking of pavement and tunnel linings (Li 2012; Chen et al. 2012; Shen et al. 2014).

Due to high and steep configuration of slope, rock falls obstructed the tunnel entrance and destroyed the slope protection works. Figure 5a shows a rock block which fell across the opening during the earthquake. Moreover, five cases of collapse of lining due to presence of weak mudstone at entrance sections were observed (Li 2012). The tunnel linings were sheared off at some locations as shown in Fig. 5b. In addition, transverse ring cracks as shown in Fig. 5c developed in a particular stretch of the tunnel. A maximum ground bulge of about 120 cm with heaving and bulging of tunnel invert was also observed. Figure 5d shows the cracks which developed at the pavement as a result of uplift of the bottom pavement.

Fig. 5
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Damages at Longxi tunnel during 2008 Wenchuan earthquake (modified after Tao et al. 2011): a Rockfall causing obstruction at tunnel entrance, b sheared off tunnel lining, c transverse ring cracks, d pavement cracks due to uplift

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Baiyunding tunnel The tunnel has a maximum overburden of 125 m and passes through limestone formation which is highly weathered. Intense fracturing in the area filled with moist and loose gravel soil has lead to poor quality of rock mass. A fault belt also exists about 45 m away from one of the portals intersecting the tunnel axis. During the Wenchuan earthquake, widespread damage was reported at the portal sections resulting from a landslide as shown in Fig. 6a. Settlement of basement, cracking of the flooring and an average dislocation of around 20 cm was noted for a damage length of about 30 m leading to an adverse impact on the functionality of the tunnel (Chen et al. 2012). Moreover, spalling of concrete lining and shearing failure was also observed at number of sections. Figure 6b shows a section where the reinforcement was exposed as a result of shearing off and spalling of concrete liner.

Fig. 6
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Damages at Baiyunding tunnel (modified after Tao et al. 2011): a portal section damage due to landslide, b sheared off tunnel liner

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Longchi tunnel The tunnel passes through limestone formation having a maximum overburden depth of 345 m. However, the terrain becomes steep at the portal regions with an overburden of about 50 m. Intense weathering of rock mass and presence of faults near portals contributed adversely during the earthquake leading to failures. Cracking of tunnel lining in transverse, longitudinal and inclined directions as shown in Fig. 7a, b were noted. Moreover, the cracking and undulation of the bottom pavement was also observed.

Fig. 7
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Damages at Longchi tunnel (modified after Tao et al. 2011): a transverse cracking of liner, b inclined cracks and pavement damage

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Youyi tunnel It is a 962 m long tunnel having maximum overburden of 215 m with flat terrains at the portal ends. The tunnel passes through carbonaceous shale, argillaceous shale and sandstone with the portal sections located in gravelly soil. Relative movement along the faults caused tunnel liner to be sheared off along with deformation and cracks. Subsequent landslide induced failure at the portal sections. Figure 8a shows a damaged portal section near one of the tunnel entrance. The exposure of reinforcements as a result of spalling of tunnel lining is shown in Fig. 8b.

Fig. 8
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Damages at Youyi tunnel (modified after Tao et al. 2011): a damage at portal section, b spalling of concrete from tunnel lining

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Shen et al. (2014) compiled the seismic response of 52 tunnels following the 2008 Wenchuan earthquake classifying the observed damage patterns into eight categories. Based on the data, Fig. 9 presents number of different damage patterns observed following the seismic event. From the figure it is evident that the damages of tunnel sections are mostly in forms of lining cracks and rock falls.

Fig. 9
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Various tunnel damages observed in Wenchuan (2008) China earthquake

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4 Summary of Failure Characteristics

4.1 Cracking of Tunnel Lining

The most frequent form of earthquake induced damages in tunnels is the cracking of the tunnel lining. Based on field observations of tunnel damages, the cracking have been classified as longitudinal, horizontal, oblique breakage, ring breakage and invert cracks. Figure 10 shows some of the crack patterns generally observed following recent past seismic events. Many tunnels severely damaged in 1923 Great Kanto earthquake developed longitudinal, horizontal and oblique cracks in the lining. Various forms of cracking have also been reported by Li (2012) for the tunnels of the Du Wen highway following the Wenchuan earthquake of 2008. In some cases, cracks developed at both sides of arch wall. Moreover, at some sections, extensive collapse of the concrete lining coupled with the exposure and buckling of steel reinforcements compromised the safe operation of the tunnels.

Fig. 10
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Different patterns of cracks in tunnel lining

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4.2 Shear Failure of Tunnel Lining

One of the most severe forms of earthquake damages is the shear failure of the tunnel lining. This type of failure results from the shear force acting on the lining near the faults and is characterized by the spalling of concrete coupled with exposure and detachment of steel reinforcements. The Tanna tunnel in Japan was severely affected by the shearing failure leading to severe cracks at several locations during 1930 Kita-Izu earthquake. For this particular case a horizontal displacement of 2.39 m and a vertical displacement of 0.6 m were observed near the Ena fault zone (Dowding and Rozen 1978).

More recently, the Longxi tunnel was severely affected in the 2008 Wenchuan earthquake and became inoperative following about 1 m up and down relative displacement at some locations leading to the collapse of the arch lining. Severe damages to the secondary lining of the Baiyunding tunnel leading to the loss of structural integrity have also been attributed to the shear failure of the lining.

Although the shearing failure of tunnel lining is generally expected for regions crossing the faults, some damages in tunnels with alignment not crossing the fault have also been reported. Prominent among them is the case of the Nagasaka tunnel which was damaged in the 1923 Great Kanto earthquake (Chen et al. 2012).

4.3 Portal Failure

Review of case histories highlights the fact that the portal sections are the most vulnerable part of the tunnel (Zhao et al. 2013). Instabilities in the form of rock falls, avalanches and sliding, cracking of head walls, arch rings, wing walls and expansion joints are the most noted failures following seismic events.

Rock falls occur in steep slopes consisting of relatively strong and unfractured rock masses. Such damages were observed in case of Longxi tunnel where the rock fall destroyed the slope protection measures (see Fig. 5a). In contrast, sliding failure occurs in vicinity of portal sections where the geological medium consists of highly weathered and fractured rock mass as in the case of the Longdongzi tunnel (Li 2012) during 2008 Wenchuan earthquake. The weathered nature of the geological medium coupled with the steepness of the slope and the presence of unfavorably dipping structural planes led to sliding of the rock material burying the right hand tunnel exit of the Longdongzi tunnel following the Wenchuan earthquake. Spalling and cracking of concrete lining on the arch side wall for the Taoguan tunnel with crack widths reaching up to 50 cm are also attributed to the slope instabilities in the portal region following the earthquake (Li 2012).

4.4 Heaving and Cracking of Tunnel Invert

A number of cases of heaving and cracking of tunnel invert has been reported (Shen et al. 2014; Duke and Leeds 1959). A typical characteristic of this type of failure is the development of transverse cracks. In case of the Longxi tunnel, deformations in both the horizontal and vertical directions of about 30 cm were noted. Also, a maximum uplift of 120 cm was reported in one of the sections (Shen et al. 2014). Following the 1923 Great Kanto earthquake, Namutani tunnel suffered enormous lining distortion due to the uplift of the bottom slab. The displacement ranged between 50 cm and 1 m along the axis of the tunnel (Duke and Leeds 1959). In case of Longdongzi tunnel also, an uplift of about of 2 cm was observed (Li 2012).

From a number of case studies, it was concluded that the uplift and cracking of tunnel inverts were more predominant in case of presence of center drainage. This is attributed to the concentration of shear force and stiffness mismatch near the tunnel invert. In addition, the abrupt changes in the cross section at the invert leading to stress concentration is also regarded as a cause for such damages (Shen et al. 2014).

5 Factors Affecting Mountain Tunnel Damage

5.1 Earthquake Parameters

The major earthquake parameters causing seismic damages of mountain tunnels include magnitude, epicentral distance and the depth of the earthquake source. In conjunction, the three major parameters define the severity of a seismic event. Any earthquake having a higher magnitude, lower epicentral distance and a shallower depth will be more intense and influence the tunnels to a greater extent.

Sharma and Judd (1991) collected and analyzed data for 192 tunnels from 85 different earthquakes based on which the influence of magnitude and epicentral distance on the seismic performances were summarized. Table 8 summarizes the effect of Richter magnitude on tunnel damages. It was observed that the number of cases of tunnel damage reaches about 50 % for magnitudes greater than 6.0. At lower magnitudes, the number of cases of damages was low. Recent damages of mountain tunnels reported in literature following 1999 Chi-Chi, 2004 Mid-Niigata Prefecture and 2008 Wenchuan earthquakes also conform to these findings with most of the damages associated with magnitude greater than 6.0 on the Richter scale (Wang et al. 2001; Shen et al. 2014; Shimizu et al. 2007a, b; Jiang et al. 2010).

Table 8 Summary relating damage with Richter magnitude (after Sharma and Judd 1991)
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With consideration to the epicentral distance, it is observed that the seismic vulnerability of the tunnels increases when they are situated closure to the source of the earthquake. In most of the reviewed cases, it has been found that the epicentral distance for the damaged tunnels was within 70 km (Asakura and Sato 1998; Otsuka et al. 1997; Wang et al. 2001). Table 9 summarizes the findings of Sharma and Judd (1991) relating tunnel damages with epicentral distance. However, review of recent case studies does not strictly conform to these observations. In some cases, tunnels located farther away (about 40 km) suffered greater damages in comparison to those located close to the earthquake source (Chen et al. 2012).

Table 9 Summary relating damage with epicentral distance (After Sharma and Judd 1991)
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5.2 Overburden Depth

Sharma and Judd (1991) analyzed the effect of depth of overburden for 132 cases and concluded that overburden plays major role in influencing tunnel damages. Based on the analysis of available data, they concluded that the damages are more with the tunnel depths less than 50 m. However, in contrast, few damages of mountain tunnels show deviation from the above mentioned conclusion. Prominent among these are the damage cases of the Rokko tunnel and the Longxi tunnel. In fact, in the case of the Longxi tunnel, serious damages were observed at a depth of 500 m in terms of collapse of a portion of the secondary concrete lining during 2008 Wenchuan earthquake (Li 2012).

5.3 Fault Location

Permanent ground displacements resulting from fault movements during earthquakes have caused a number of failures of tunnels. In such events, large shear forces act on the tunnel sections and cause relative movement in both horizontal and vertical directions. Some of the prominent cases of fault induced damages include the case of Uonama (2004 Mid-Niigata Prefecture), Inatori (1978 Izu-Oshima-Kinkai) and the Tanna (1930 Kita-Izu) tunnels.

A total of more than 40 tunnel damages related to fault movement have been identified following the 1999 Chi-Chi Taiwan earthquake (Wang et al. 2001; Chen et al. 2012). In addition, fault movements have also caused damages to tunnels situated in vicinity of faults by inducing permanent deformations of the surrounding ground. Such damages have been reported for the Longxi, Longdongzi and Zipingpu tunnels of the Du Wen highway network (Li 2012). Even though these tunnels did not cross the main fault, secondary effects of fault movement of 2008 Wenchuan earthquake led to severe damages. The cases of damages for Shanglongshan, Shaohuoping, Jiujiaya and the Jiangejianmen tunnels during recent earthquakes are also related to ground deformation induced by fault movement.

5.4 Geology

The geological configuration through which the tunnel passes has a very significant impact on its stability during seismic scenario. It is observed that seismic damages of mountain tunnels are concentrated at zones which are weathered and/or fractured. However, tunnel passing through competent rock mass seldom suffer any significant damage (Kumari and Sitharam 2012).

Observation of instabilities at the portal section arising due to rock falls, sliding and collapse have been widely documented. The high vulnerability of portals is attributed to the poor geological conditions and shallow overburden depth.

Generally, the portal sections are located in highly weathered rock formation or relatively loose quaternary deposits. Such ground conditions leads to amplification of seismic waves resulting in higher ground deformations. The increased seismic deformation demand exceeding the tunnel capacity leads to various forms of damages.

Seismic vulnerability also increases when the tunnel passes through a transition zone between hard and soft rocks. For example, in case of Longxi tunnel, greater seismic damage occurred for the portal region situated in mudstone in comparison to the zone passing through granite rock. Figure 11 illustrates the vulnerability of tunnel passing through a transition zone. In such geological condition, mismatch in both stiffness and seismic impedance leads to differential kinematic movement. This kinematic movement coupled with amplified ground motion due to the softer strata results in an additional horizontal force on the tunnel liner leading to the development of cracks at the junction between the arch shoulder and the sidewall as shown in Fig. 12. Such a mechanism is believed to have caused major damages to mountain tunnels as reported by Miyabayashi et al. (2008).

Fig. 11
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High vulnerability at interface between two types of rock mass

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Fig. 12
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Vulnerability near junction of hard and soft ground. a Amplified ground movement in softer strata, b development of crack at junction of shoulder and sidewall

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The influence of geological conditions has also been recognized for deeper tunnel sections. Damages observed for the Rokko tunnel during 1995 Hyogoken-Nanbu earthquake at sections having comparatively larger overburden depth are also attributed to the prevailing geological conditions. One of the major findings of the investigation was the fact that almost all the damaged sections were located in highly fractured zone.

6 Plausible Mechanisms of Seismic Damages from Literature

A wide range of tunnel lining failures has been identified based on the case studies of damaged mountain tunnels. A few mechanisms proposed to explain some of them are presented in this section. Figure 13 presents the case of seismic shear wave propagating along the diagonal directions which causes shear stresses on the tunnel cross section as shown by dashed lines. These shear stresses can be resolved into a set of horizontal and vertical stresses subjecting the tunnel cross section to compressive and tensile action. As a result of such an action, compressive failure at the arch crown and shear failure at the arch shoulder may occur.

Fig. 13
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Mechanism of compressive and shear failure of tunnel lining

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Figure 14 shows a case in which the diagonal stresses give rise to tensile and compressive forces in the horizontal and vertical direction respectively. Such an action causes the vertical compression of the tunnel cross section coupled with an extension of the sidewalls. Spalling of concrete at the sidewalls may be observed in such a scenario resulting in exposure of lining reinforcements.

Fig. 14
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Mechanism of spalling of tunnel lining

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With these basic understanding of mechanism of damages, different failure patterns of tunnel lining may be summarized considering seismic wave propagation as discussed below.

6.1 Longitudinal Cracks at Arch Shoulder

The cracking of tunnel lining along the arch shoulder in the longitudinal direction results from vertical propagation of S-waves parallel to the tunnel cross-section. It causes particle movement in a horizontal direction as shown in Fig. 15 resulting in stress concentration at the junction of the sidewall and the arch.

Fig. 15
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Longitudinal cracks of tunnel lining

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6.2 Transverse/Circumferential Cracks

Transverse cracks are a result of propagation of P-waves along the direction of tunnel axis. Under this condition, alternate tension and compression along with the pounding of construction joints leads to the development of cracks along the circumference of the tunnel as shown in Fig. 16.

Fig. 16
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Transverse crack due to propagation of P-wave along longitudinal direction

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6.3 Inclined Cracks

Propagation of S-waves in the vertical direction in a plane parallel to the longitudinal axis of the tunnel results in development of tensile forces resulting in inclined cracks as shown in Fig. 17.

Fig. 17
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Inclined cracks due to propagation of S-wave

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6.4 Pavement Cracks

The pavement cracks are a result of vertical propagation of high frequency P waves parallel to the cross section. Under such wave propagation pattern arching or bending of the bottom pavement occurs as shown in Fig. 18.

Fig. 18
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Cracking of bottom pavement under action of P-wave

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6.5 Shear Failure of Lining due to Fault Movement

The shearing failure of tunnel lining results from a relative movement of adjacent parts of the tunnel intersecting the fault plane. Generally the damages sustained in such cases are very severe and may result in complete collapse of the tunnel. Figure 19 illustrates the shear failure of lining induced due to fault movement.

Fig. 19
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Shear failure of tunnel lining due to fault movement

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7 Seismic Analysis of Lined Tunnel in Fractured Rock Mass

In the present section, a numerical investigation has been presented dealing with the seismic response of a circular lined tunnel passing through fractured rock mass. The influence of depth of tunnel, frequency and PGA of the dynamic wave on the dynamically induced axial force and bending moment in the tunnel liner has been discussed. The results of the numerical analyses have been corroborated with some of the patterns of seismic damages observed in the past.

7.1 Modeling and Analyses

The numerical modeling of a circular lined tunnel subjected to dynamic loads has been carried out in a discrete element based software package UDEC. The schematic representation of the numerical model considered in the present study is shown in Fig. 20. The model consists of a circular tunnel having a diameter D (10 m) located at a variable depth of d (75 and 150 m) below the ground surface. To simulate the fractured nature of the rock mass, Voronoi tessellation scheme (Lorig and Cundall 1989) has been used to represent the blocky nature of the rock mass. This feature has been utilized to create randomly sized polygons representing the blocky nature of the medium around the tunnel. Brittle fracturing is allowed to occur along the edge of these Voronoi blocks in the event of either the shear or tensile strength being exceeded. Both the intact rock and the voronoi joints have been modeled using the Mohr–Coulomb constitutive law. The properties adopted in the study have been listed in Table 10. The properties are representative of the fractured nature of rocks encountered in case of real tunnel projects (Lunardi 2008).

Fig. 20
figure 20

Schematic representation of numerical model

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Table 10 Properties adopted for numerical model in present study
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The lining around the circular tunnel has been simulated using beam elements. The density of the liner is 2500 kg/m3 having an elastic modulus of 30 GPa and Poisson’s ratio of 0.2 (Shen et al. 2014) To ensure no slippage between the liner and the surrounding geological medium, the properties of the interface has been set to very high values so as to effectively glue them together (Itasca Consulting Group Inc. 2004). Moreover, elastic behavior has been assumed for the liner.

The mesh size adopted in the numerical model has been finalized based on the following considerations:

  1. 1.

    Efficient simulation of propagation of waveforms of dominant frequency range associated with the adopted sinusoidal motions.

  2. 2.

    Simulation of the stress gradient in the geological medium close to the tunnel structure.

In order to ensure the first condition, the mesh size is kept smaller than 1/10th of the smallest wavelength of interest in the simulation. For meeting the second condition, a finer discretization has been selected for regions close to the tunnel structure which gradually becomes coarser subject to the condition that no distortion of the propagating seismic waves occurs in the simulation.

To minimize adverse boundary effects during dynamic analysis, free field boundary conditions has been invoked at the lateral sides. In addition, viscous dashpots have been used at the bottom boundary in both the normal and shear directions. Moreover, the dimensions of the model have been kept as 200 m (20D) × 300 m (30D) in all the analyses.

The use of dashpots at the bottom boundary requires the dynamic input to be converted into stress waves which has been achieved through Eq. (1).

$$ \sigma_{\text{s}} = 2\uprho{\text{C}}_{\text{s}} {\text{V}}_{\text{s}} ({\text{t}}) $$
(1)

where ρ represents the mass density of the material, Cs is the shear wave velocity and Vs(t) is the instantaneous horizontal input motion velocity. Sinusoidal acceleration with six different frequencies between 1 and 10 Hz has been utilized in the study. Prior to every dynamic analysis, an initial static in situ stress state has been invoked keeping K = 1.0.

7.2 Effect of Depth and Frequency of Input Motion

A plot of typical variation of dynamic axial force and bending moment along the tunnel liner has been shown in Figs. 21 and 22 respectively. It is seen that the variation in the liner axial force and moment is driven by the nature of dynamic input as the recorded response comprises of steady state cycles having sinusoidal nature during the action of the dynamic wave. At the end of the dynamic input, a residual value of force and moment remains in the liner.

Fig. 21
figure 21

Typical axial force time history

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Fig. 22
figure 22

Typical bending moment time history

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The variation of axial forces in the liner for tunnel at depths of 150 and 75 m are shown in Figs. 23 and 24 respectively. It is seen that the forces are greater in case of tunnel at a depth of 150 m. Moreover, the frequency of input motion also has an effect on the maximum axial forces recorded during dynamic analyses (Fig. 23).

Fig. 23
figure 23

Maximum dynamic axial force along liner (d = 150 m)

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Fig. 24
figure 24

Maximum dynamic axial force along liner (d = 75 m)

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Fig. 25
figure 25

Failed joint pattern around tunnel (d = 150 m, 1 Hz)

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For both tunnel depths, the maximum axial force is largest for the case of 1 Hz frequency. A subsequent increase in frequency of input motion shows a decrease in the axial forces. Such a phenomenon maybe attributed to the frequency filtering effect of the Voronoi joints incorporated in the present numerical model for representation of blocky nature of rock mass. The fractured nature of the rock mass acts as a low pass filter which allows only low frequency waves to pass through and blocks the higher frequency motions (Myer and Pyrak-Nolte 1990; Cai and Zhao 2000; Jiao et al. 2005).

The pattern of joints which have failed either in tension or shear in the vicinity of the tunnel has been shown in Figs. 25 and 26 respectively. Figure 25 corresponds to the case of tunnel at a depth of 150 m subjected to an input frequency of 1 Hz. It is observed that the stress exceeds the strength of the Voronoi joints resulting in development of fractures near the left shoulder and the lower right portion of the tunnel. This phenomenon explains the subsequent higher axial forces recorded in the tunnel liner (Fig. 23) at angles of 70°–120° and 240°–300°. Thus it is inferred with reasonable certainty that the Voronoi blocks replicate the additional degree of freedom associated in case of blocky rock masses resulting in subsequent higher forces (Fig. 27).

Fig. 26
figure 26

Failed joint pattern around tunnel (d = 150 m, 6 Hz)

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Fig. 27
figure 27

Maximum dynamic bending moment along liner (d = 75 m)

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Fig. 28
figure 28

Maximum dynamic bending moment along liner (d = 150 m)

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In contrast, the stresses along the Voronoi joints do not exceed the strength for the case of tunnel at a depth of 150 m subjected to motion of frequency 6 Hz. This behavior is observed in the failed joint pattern shown in Fig. 26. Similarly, the failure development was minimal for all the cases of tunnel at depth of 75 m suggesting the importance of overburden and the static stresses in governing rock block movements under dynamic action.

Figures 27 and 28 show the variation in maximum bending moment along the liner at various frequencies of input motion for tunnel at depth of 150 and 75 m respectively. It is observed that the moment is also maximum at 1 Hz frequency. However, at higher frequencies, variation of moment is minimal for the various frequencies of input motion considered in the present study.

From the ensuing discussion, it may be noted that deeper tunnel section passing through blocky rock mass subjected to low frequency excitations experiences higher dynamic forces and hence are more prone to damages. This may explain the failure of deep tunnel sections passing through fractured regions which manifest in terms of collapse of secondary concrete lining as reported in literature.

7.3 Effect of Peak Horizontal Acceleration (PHA)

To evaluate the influence of the peak ground motion on the seismic response of tunnels, analyses were carried out by employing sinusoidal motions having PHA of 0.2 and 0.5 g for tunnel located at a depth of 150 m.The analyses have been run for frequencies of 1 and 2 Hz only. The variation of the dynamic axial force in the liner for the case of 0.2 and 0.5 g has been presented in Figs. 29 and 30 respectively. Similarly, Figs. 31 and 32 highlight the variation of bending moment in the liner for excitations having PHA of 0.2 and 0.5 g respectively.

Fig. 29
figure 29

Maximum dynamic axial force along liner subjected to PHA of 0.2 g

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Fig. 30
figure 30

Maximum dynamic axial force along liner subjected to PHA of 0.5 g

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Fig. 31
figure 31

Maximum dynamic bending moment along liner subjected to PHA of 0.2 g

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Fig. 32
figure 32

Maximum dynamic bending moment along liner subjected to PHA of 0.5 g

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For the case of 1 Hz frequency, it is observed that the maximum dynamic axial force increases by 25 % as the PHA increases from 0.1 to 0.2 g. The percentage increase becomes 54 % when a PGA of 0.5 g is adopted. A similar trend of increase in the dynamic bending moment is noted where an increase of 92 and 271 % is observed for PHA of 0.2 and 0.5 g respectively. Similar trend of increase in the liner forces are observed for the case of 2 Hz. However, the percentage increase is lower in comparison to the case of 1 Hz frequency. Thus, it may be stated that the vulnerability of the tunnels subjected to dynamic loads are higher in case of low frequency motions having higher PHA values. Table 11 summarizes the maximum forces and percentage change for the cases considered in the study.

Table 11 Variation in maximum axial force and bending moment with PHA
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7.4 Effect of Peak Horizontal Acceleration on Observed Tunnel Damages

Based on the discussions presented in the preceding sections, it can be concluded that one of the major factors affecting damages is the energy reaching the location of the tunnel. In order to predict the level of ground shaking, a number of attenuation laws have been proposed in literature (Kramer 1996). In the present section, the attenuation relation suggested by Campbell (1981) has been used to evaluate the Peak Horizontal Acceleration (PHA) at tunnel locations reported to have been damaged following the 1999 Chi-Chi earthquake and 2008 Wenchuan earthquake. Equation (2) represents the attenuation relation expressing the PHA as a function of epicentral distance (R) and magnitude (M).

$$ \ln \,PGA(g) = - 4.141 + 0.868M - 1.09\ln [R + 0.0606\exp (0.7M)] $$
(2)

Using Eq. (2), the PHA at tunnel location for the 57 tunnels listed in Table 5 has been evaluated. The results have been summarized in Table 12 relating the number of tunnel damages with the PHA. It is noted that only 3 tunnels suffered damages in case the PHA predicted from the attenuation relation is within 0.1 g. However, a substantial increase of tunnel damages is noted for higher PHA. In a similar manner, the attenuation relation has been applied for the tunnels listed in Table 6 and the results have been summarized in Table 13. It is noted that no case of tunnel damages is observed in case of PHA being within 0.1 g. However, higher PHA of 0.2 g and above is associated with greater number of tunnel damages.

Table 12 Damage to tunnels for various PHA in 1999 Chi-Chi earthquake
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Table 13 Damage to tunnels for various PHA in 2008 Wenchuan earthquakes
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Table 14 combines the results of both the earthquake events of 1999 Chi-Chi and 2008 Wenchuan earthquakes. From Table 14, it can be observed that a PHA of 0.1 g has caused damages to 3 tunnels only. In comparison, a substantial increase in cases of tunnel damages is observed for a PHA of 0.2 g and higher. These observations compare well with the findings highlighted in Sect. 7.3 where a substantial increase in tunnel liner forces has been observed as the PGA increases from 0.1 to 0.2 g.

Table 14 Summary of damages to tunnels in 1999 Chi-Chi and 2008 Wenchuan earthquake relating PHA
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8 Summary and Discussion

In the present paper, wide collection of literature reporting seismic damages of mountain tunnels has been reviewed. Some major cases of damages have been highlighted based on which various patterns of instabilities have been recognized. Observations made from damages have clearly shown that tunnels are vulnerable in portal sections, near zones of high impedance contrast or when passing through blocky rock masses. Moreover, important parameters believed to have a major impact on the seismic performance of tunnels have been discussed. A short summary of the probable failure mechanisms proposed in literature has also been presented.

To gain greater insight into the seismic response of tunnels, a numerical investigation of dynamic behavior of circular lined tunnel in blocky rock mass has been carried out. The roles of frequency of input seismic wave and tunnel depth on the dynamically induced axial force and bending moment in the tunnel liner have been discussed. It is observed that lower frequency waves induce higher axial force in the tunnel liner and lead to greater extent of surrounding rock mass to fail either in tension or in shear. Such behavior may be attributed to the frequency filtering effect which allows only lower frequency waves to pass across them.

In addition, the role of PHA on tunnel vulnerability has also been studied. It is observed that increase in the PHA leads to a consequent increase in the dynamically induced axial force and bending moment in the tunnel liner which may lead to various types of tunnel liner failures. In this context, the PHA at locations of tunnels damaged following two recent earthquakes are evaluated using an attenuation relation. The results compare well with the observations made from the numerical simulations carried out in the present study.

From the review of past seismic damages of mountain tunnels and numerical investigations carried out in this study following major conclusions may be drawn.

  • Contrary to the popular belief, mountain tunnels are vulnerable to seismic damages as observed from various damages in tunnels in past earthquakes.

  • Frequency content of the earthquake motion is a guiding factor in inducing damage in the tunnel liner. With regard to this, impact of degree of weathering on the properties of blocky rock mass will be crucial in modifying the frequency content of the seismic motion. From the study, it is confirmed that lower frequency ground motion will be having greater effect on the seismic response of tunnels.

  • Peak Horizontal Acceleration (PHA) will be a critical parameter governing tunnel damages. Using attenuation relationship, PHA values were evaluated for the tunnels damaged in 1999 Chi-Chi and 2008 Wenchuan earthquakes. It shows good correlation with PHA and tunnel damage. Numerical investigation also confirmed the same.

  • The study shows that the increase in tunnel depth will induce more seismic forces in the tunnel liner in case of mountain tunnels especially in blocky rock mass. More investigation, including both field observation as well as numerical investigation is envisaged for coming out with generalized conclusion for the same.