Rapid Assessment and Classification for Seismic Damage of Mountain Tunnel Based on Concentric Circle Method

Concentric circle method (CCM), a new method based on analytic hierarchy process (AHP) and numerical discretization of 40 mountain tunnels damaged by Wenchuan earthquake in China, is proposed to rapidly assess the seismic damage level (SDL) of mountain tunnels. (e new method consists of four components. First, according to the type and degree of seismic damage of tunnel, the whole tunnel is divided into a number of successive sections. Second, four factors (i.e., slope and portal damage, lining damage, pavement damage, and earthquake collapse) are selected as the main controlling factor set, and then multilevel factor sets are proposed to establish the assessment system. (ird, the discretized assessment indexes and classification criteria are established for the rapid assessment of SDL of mountain tunnel. Finally, based on the comprehensive analysis on the SDL of each section, the SDL of the whole tunnel is calculated in terms of the seismic damage index and synthetic radius. With the assessment results shown on a straightforward concentric circle diagram, the proposed CCMmethod can rapidly and reliably assess the SDL of mountain tunnel to win over precious time for emergency rescue and provide references for the repair of damaged tunnel. In addition, the accuracy and applicability of the proposed method is verified by using a case study of Longxi tunnel located at the epicenter of the Wenchuan earthquake in China.


Introduction
A significant number of tunnels and underground structures have been damaged during earthquakes. In particular, the mountain tunnels located in high-intensity seismic area are more prone to serious damage because of closing to fracture zone. For example, 16% of the railway mountain tunnels located within the disaster area were seriously damaged during Hyogoken-Nanbu earthquake occurred in Japan in 1995 [1]; 26% of the 50 mountain tunnels located within 25 km of the earthquake fault were severely damaged, and 22% moderately damaged during the Chi-Chi earthquake occurred in Central Taiwan in 1999 [2]; 65% of the 40 mountain tunnels near the epicenter were damaged during the Wenchuan earthquake occurred in 2008 in Sichuan, China [3]. In addition, mountain tunnels suffered from extremely severe seismic damage usually blocked the traffic almost entirely, resulting in substantial difficulty in emergency rescue and disaster relief. erefore, a rapid assessment of seismic damage level (SDL) after earthquake would have significant importance on timely and efficient operation of emergency rescue and remedial measures in mountain tunnels.
Recently, an increasing number of researchers and engineers have carried out field investigation and mechanism analysis on seismic damage of tunnels and underground structures during earthquakes [4][5][6][7][8][9][10][11]. Regarding the current research on the seismic damage assessment, most researchers mainly focused on the identification of risk factors and evaluation of seismic damage of tunnels, but less attentions were paid to the SDL assessment. Wang et al. [2] conducted a systematic statistics and assessment of damage in mountain tunnels resulted from the 1999 Taiwan Chi-Chi earthquake and analyzed the potential factors. Using the least square method according to tunnel's traffic function and damage description based on the site investigation, Fang et al. [12] proposed an equation for the evaluation of tunnel seismic damage. Jiang et al. [13] analyzed the tunnel damage caused by the 2004 Mid Niigata Prefecture earthquake using Hayashi's quantification theory type II. Wang et al. [14] proposed a new classification criterion to classify the seismic damage and a risk-based assessment technique to quantify the seismic risk. Zang et al. [15] summarized the main influencing factors and put forward a fuzzy comprehensive evaluation method to study the seismic risk level of tunnel portals. Nevertheless, there are still some shortages so far. For instance, owing to the complex multi-index system, complicated calculations, and single assessment result, these methods stated above are not so simple, resulting in great difficulty in applying the rapid assessment to tunnel seismic damage. Moreover, the assessment methods mentioned above do not take the slope and portal damage into comprehensive consideration. As a result, the crews and vehicles for emergency rescue and disaster relief cannot pass through the damaged tunnels, whose accessibility is not assessed and guaranteed, but have to seek detours, which significantly slows down the emergency rescue. erefore, combining analytic hierarchy process (AHP) with numerical discretization, a new method called concentric circle method (CCM) is proposed to allow for rapid assessment of the SDL of mountain tunnels. Although the concept of CCM has been applied in different fields, such as camera calibration [16], the principle of those differs from the CCM in this paper. Besides, the CCM has not been introduced to the seismic damage assessment of mountain tunnels so far. e idea of AHP is to treat the object of interest as a system for deciding online with the way of thinking, viz., decomposition, comparative judgment, and comprehensive analysis [17,18]. e idea of the numerical discretization is dividing continuous values into several intervals, using mathematical methods [19,20]. Because of the conciseness and practicality, the two methods have been widely applied in various engineering fields, such as risk assessment of tunnel engineering and slope stability classification [14,21].
With the assessment results shown on a straightforward concentric circle diagram, the proposed method can rapidly and accurately assess the SDL of mountain tunnel to win over precious time for emergency rescue and provide references for the repair of damaged tunnel. Moreover, the accuracy and applicability of the proposed method was illustrated using the field data of damaged mountain tunnels in the 2008 Wenchuan earthquake, China.

Statistical Analysis on the Seismic Damage Type of Mountain Tunnels
Tens of mountain tunnels suffered from some degree of seismic damage during the 2008 Wenchuan earthquake in China. e typical seismic damages in the mountain tunnels include collapse and slide of slope, collapse of lining and surrounding rock, cracks of tunnel portal, cracks and displacement of lining, upheaval and cracks of tunnel invert [3,9,14,22]. A field investigation into 11 tunnels on the new Dujiangyan-to-Wenchuan highway found that 8 tunnels located near the epicenter were severely damaged. In particular, the Longxi tunnel suffered from destructive damage, involving extensive large-scale lining cracks, severely distorted steel arch and bar, large-scale lining peeling-off, lining collapse up to tens of meters, significant crack and upheaval as high as 120 cm from tunnel pavement, and totally five large-scale collapses in the whole tunnel. ereby, the statistical analyses on field investigation data of 40 damaged mountain tunnels during Wenchuan earthquake [3,9,14,21] have been carried out with regard to the types and degrees of seismic damage of mountain tunnels. e main seismic damage types of mountain tunnels are summarized in Table 1, which may provide a useful reference for establishing the seismic damage assessment system and selecting the appropriate assessment indexes. e tunnel portal section is generally more prone to seismic damage than the tunnel tube section, because of less confining force from the surrounding rock and larger seismic inertial force. In particular, the tunnel portal slope is prone to severe seismic damage due to the action of seismic surface wave and the ground acceleration amplification effect. e main types of seismic damage at the tunnel portal slope include rock falls, collapse, and landslide, which are likely to damage the portal structure or even block the tunnel portal, significantly hindering the emergency rescue after earthquake. According to the report about statistical analysis of the field investigation data of damaged mountain tunnels in the 2008 Wenchuan earthquake by Highway Planning, Survey, Design, and Research Institute of Sichuan Provincial Department [23], the seismic damage of portal slope and portal structure in the tunnel portal section is the most common type and occurred for 97.18% of all the seismic damages of this section ( Figure 1). erefore, the damage of portal slope and portal structure should be taken into careful consideration in establishing the assessment and classification system and in selecting assessment indexes. e seismic damage types and characteristics of tunnel tube are different from those of the tunnel portal due to different influencing factors, the surrounding rock conditions, and seismic inertial force. e mountain tunnels located on two highways (i.e., Dujiangyan-Yingxiu Highway and Dujiangyan-Yingxiu section of National Highway No. 213) near the epicenter suffered from extensive seismic damage during the Wenchuan earthquake. Statistical analyses of the seismic damage types and proportions of the damaged tunnel tube for these two highways showed that the main damage types are lining damages and road pavement damages ( Figure 2). e lining damages mainly include cracks (longitudinal, transverse, oblique, and radial), peeling-off, falling, collapsing, water leakage, and shear displacement, and the road pavement damages mainly include upheaval and cracks (longitudinal and transverse). e lining damages greatly reduce the strength and safety of tunnel. For the road pavement damages, the rescue vehicles may not pass through the damaged tunnel, which will 2 Shock and Vibration significantly delay emergency rescue. erefore, the lining damages and the road pavement damages are typical and severe in the seismic damage of tunnel tube and should be taken into significant consideration in establishing the assessment and classification system and in selecting the assessment indexes. e collapse of surrounding rock is the most severe damage type among all seismic damages for tunnels. Once happened, it hinders or even completely blocks the rescue vehicles, and also it takes high economic cost and long time to repair the collapsed surrounding rock. In Longxi tunnel during the Wenchuan earthquake, for example, it took tens of millions of RMB and duration of 3 months to repair five locations of the collapsed surrounding rock. It is recommended that the collapse of surrounding rock be given the highest level of seismic damage in the assessment and classification system for tunnels.
Some other seismic damages of tunnel, including dropping of decorative surface layer, road groove damage, accessory equipment damage, and others, are also introduced in Table 1. Because these seismic damages have lesser impact on the safety of tunnel structure and the rescue remedy, they are not taken into consideration in the rapid assessment system.

Rapid Assessment and Classification
Based on CCM

Assessment and Classification System of Tunnel Seismic
Damage. e tunnel is a linear system with certain length, consisting of the tunnel lining structure and surrounding rock. After earthquake, the type and degree of seismic damage are different at various sections of the tunnel due to varying properties of surrounding rock and supporting structure. erefore, based on the type and degree of seismic damage, the whole tunnel is divided into successive sections with certain length in longitudinal direction (l 1 , l 2 , l 3 , . . . , l n ) using the numerical discretization, with each section having uniform seismic damage. e influence of each index on the result can be quantified via a weight, to allow an explicit process. Based on the idea of AHP and statistical analysis on the field investigation data of 40 damaged mountain tunnels during Wenchuan earthquake, four main factors, i.e., the slope and portal damage, the lining damage, the pavement damage, and the earthquake collapse, are selected as the controlling factor sets of level 1 in the rapid assessment and classification system. Each controlling factor set is divided into secondary factor sets, which are then further divided into the next level factor sets. Finally, a set of effective assessment and classification system covering complete multilevel factor sets and specific quantitative parameters is established as shown in Figure 3.
Level-1 factor set: the assessment and classification for seismic damage of the whole tunnel is comprehensive analysis on the SDL of each tunnel section from entrance to exit. According to the type and degree of seismic damage, the damaged tunnel is divided into successive sections with certain length in longitudinal direction so as to establish the level-1factor set as follows: where U is the seismic damage of the tunnel as a whole and U i (i � l 1 , l 2 , l 3 , . . . , l n ) is the seismic damage of the respective tunnel section. Level-2 factor set: the main seismic damage types at various sections include the portal and slope damage, the lining damage, the road pavement damage, and the earthquake collapse, which have significant effect on the safety of tunnel structure and postearthquake emergency rescue, as described in Section 2. As a result, they are selected as the level-2 factor set as follows: where u 1 , u 2 , u 3 , and u 4 are the portal and slope damage, the lining damage, the road pavement damage, and the earthquake collapse, respectively. Level-3 factor set: the main type of portal and slope damage (u 1 ) includes crack, collapse, landslide and rock falls from slope, crack, and tilt of tunnel portal; the main type of tunnel lining damage (u 2 ) includes crack, peeling-off, water leakage, and shear displacement; the main type of pavement damage (u 3 ) include crack and upheaval; earthquake collapse (u 4 ) is surrounding rock collapse induced by earthquake. Herein, this study only takes the lining damage (u 2 ) as an example to establish the level-3 and level-4 factor sets, while other factor sets (u 1 , u 3 , u 4 ) of level 3 and level 4 are shown in Figure 3: where u 21 , u 22 , u 23 , and u 24 are crack, peeling-off, water leakage, and shear displacement, respectively. Level-4 factor set: it is obvious that different damage types have different characteristics, and thus, in order to reflect the attribute values of different damage types, the level-4 factor set is established to reflect the degree of the same seismic damage type. For example, u 21 can be expressed as follows: where n 1 , n 2 , n 3 , and n 4 are the length, width, density, and direction of crack, respectively.

Development of CCM.
e rapid assessment and classification of tunnel seismic damage based on the CCM is carried out according to the following thoughts. First, the seismic damage level (SDL) is discretized and quantified into five levels with the corresponding seismic damage descriptions and discrete values (0, 1, 2, 3, and 4), such that the initial CCM diagram is drawn with different radius (�1, 2, 3, and 4). Second, according to the type and degree of seismic damage, the to-be-assessed tunnel is divided into a number of sections with different lengths, and the length is proportionally allocated as an arc in the CCM diagram. ird, the SDL of each section (i.e., the radius in CCM diagram) is calculated according to the parameters of assessment indexes. Finally, based on the comprehensive analysis on the SDL of each section, the SDL of the tunnel as a whole is calculated by the seismic damage index and synthetic radius introduced in later section below, and then the assessment result can be clearly shown on the CCM diagram in a straightforward way. e procedure of establishing the CCM is described in detail as follows: Step 1: draw the initial CCM diagram. On the basis of statistical analysis of the data from the field investigation of tunnel seismic damage, the SDL is quantified to 5 levels (i.e., undamaged, slight, moderate, severe, and extremely severe) with their corresponding seismic damage description and discrete value (i.e., 0, 1, 2, 3, and 4) introduced in Section 4.5. As such, the initial CCM diagram is drawn with radius of 1, 2, 3, and 4, with the larger radius representing a greater SDL ( Figure 4).
Step 2: divide the whole damaged tunnel into sections. Using discretization, the whole tunnel (l) is divided to n successive sections. e type and degree of seismic damage are almost the same for one section. e length of the ith section is denoted as l i , which gives l � l 1 + l 2 + l 3 + · · · + l i + · · · + l n , where l is the total length of the tunnel and n is the total number of the divided sections.
Step 3: allocate the angle and arc of each section.
In the CCM diagram, the linear tunnel is treated as a 360°circle, so the ith section tunnel can be represented by an angle θ i , where θ i is the ratio of the length of the ith section to the total length of tunnel (equation (2) and l i is the length of the ith section (not the length of the corresponding arc of θ i in CCM diagram): where n is the total number of tunnel sections.
In this way, we can successively assess and classify the seismic damage of each section using the idea of AHP.
Once the sector domain with a specific angle θ i in the CCM diagram is allocated to the ith section ( Figure 5), the contribution of SDL of the ith section to the overall assessment and classification of tunnel seismic damage can be further confirmed. At the beginning of the whole assessment and classification process, the x-axis positive half shaft 0°is treated as the entrance portal of the tunnel. With the increase of counterclockwise angle, the longitudinal assessment for tunnel seismic damage is continuously carried out in the order of sections divided beforehand to the x-axis positive half shaft 360°, which is treated as the exit portal of the tunnel.
Step 4: determine the radius for the SDL of each section. e radius is determined by the SDL of each section. According to the seismic damage investigation data for the ith section, together with multilevel factor sets and specific quantitative parameters, the radius for the SDL of the ith section is calculated and denoted as r i . To illustrate how to calculate the radius in detail, the ith section of the tunnel is taken as an example. First, it is very important to sort out the field investigation damage data according to the four main seismic damage types and multilevel factor sets. Second, based on the sorted data, the indexes of four main seismic damage types are determinated for the multilevel factor sets of the ith section. As a result, the level of four main seismic damage types is independently assessed as five possible damage levels which, respectively, correspond to five discrete values (i.e., 0, 1, 2, 3, and 4). Finally, due to the independence of four main seismic damage types in the assessment system, the highest damage level among four types should be regarded as the damage level of the ith section and the discrete value corresponding to the highest damage level is then adopted as the radius (r i ). In other words, if the damage level of anyone seismic damage type for the ith section is assessed as extremely severe damage, this section should be regarded as extremely severe damage, and the damage level of other seismic damage types for this section is only a supplement to the damage level.
is method can not only take full consideration of the characteristics of tunnel seismic damage but also meet the need of rescue crews for urgently passing the damaged tunnel. erefore, the determined radius r i is calculated by where the vector x � (P i , L i , R i , C i ), i � 1, 2, 3, . . . , n, and n is the total number of the divided tunnel sections; P i , L i , R i , and C i are the discrete values of four main factors corresponding to the portal and slope damage, the lining damage, the road pavement damage, and the earthquake collapse, respectively; "‖x‖ ∞ " represents "∞−norm" of the vector x and is calculated by where m is the total number of elements in the vector x.
Step 5: draw the sector domain of each section. Drawing the sector domain is necessary for comprehensive assessment and classification, as it reflects the contribution of each divided section to the SDL of the whole tunnel; i.e., larger sector domain reflects more severe seismic damage of tunnel. Based on Steps 3 and 4, the sector domain of each section can be drawn easily in the CCM diagram. e area S i of each sector domain is calculated as where r i is the damage level of the ith tunnel section; θ i is the ratio of the length of the ith section to the total length of the tunnel; and n is the total number of sections.
Step 6: assess the SDL of the whole tunnel.
To obtain a more reasonable assessment for the SDL of the whole tunnel, all sector domains of each section in the CCM diagram should be comprehensively analyzed. Herein, another parameter, the sum of effective area (ΔS), is introduced to reflect the seismic damage of the tunnel as a whole. Clearly, ΔS is obtained by accumulating all the sector domains of each section as follows: ΔS is a geometrical meaning that can be shown in the CCM diagram as a shadow area in Figure 6. In the CCM diagram, each concentric circle represents a seismic damage level, and, if ΔS is located between two concentric circles, the SDL of the tunnel is regarded as the lower level represented by the inner circle. erefore, another parameter, α, which is the seismic damage index, is introduced to achieve the rapid assessment of SDL and is expressed as where S is the area of the largest circle with radius 4 in concentric circle diagram (S � π · r 2 max � 16π). If ΔS � S � 16π, the whole tunnel is extremely severely damaged and likely to threaten the safety of the crews and vehicles for emergency rescue. e corresponding relationship between seismic damage index and seismic damage level is shown in     Shock and Vibration classification criterion of tunnel seismic damage is described in Section 4.5.
In particular, to visually display the classification result, an important parameter called synthetic radius of the SDL (R s ) is introduced and expressed as follows: With the parameter R s , not only the assessment and classification result can be visually displayed in the CCM diagram, but also the close degree with higher level in the same level be obtained by comparing R s value. A sample CCM diagram displaying an assessment result of the SDL is shown in Figure 6.

Discretized Assessment Indexes and Classification Criterion
Selecting appropriate indexes is important for the assessment of the SDL of mountain tunnel, and therefore, some criteria for index selection are quite essential. First of all, the extremely important indexes which directly reflect characteristics of seismic damage and its degree should be selected. Second, the potential factors that can induce severe disaster after an earthquake should also be selected. According to the statistical analysis in the 2nd section on the damage types of mountain tunnels in Wenchuan earthquake, four main seismic damage types, i.e., the portal and slope damage (P), the lining damage (L), the road pavement damage (R), and the earthquake collapse (C), are selected to set up the damage index system. is system covers the main controlling factors affecting the safety of the tunnel structure and emergency rescue after earthquake. Moreover, the independency among indexes is taken into elaborative consideration.
Based on numerical discretization of continuous variables [7,20], the attribute value for the index of each seismic damage type is discretized into several different ranges which, respectively, correspond to the different assessment levels with designated discrete values. e index of each seismic damage type is assessed as five damage levels (i.e., extremely severe, severe, moderate, slight, and undamaged), corresponding to the discrete value of 4, 3, 2, 1, and 0. In detail, once an index (such as "P") for the ith section tunnel is assessed as certain damage level (e.g., "severe"), the corresponding discrete value (e.g., 3) is assigned to P i (e.g., P i � 3). In the same way other indexes (e.g., L i , R i , and C i ) are also determined, and then r i is calculated using equation (4). e seismic damage level can be identified by the seismic damage description and specific quantitative parameters.

Portal and Slope Damage (P).
e portal and slope damage always occurs at the entry or exit part of tunnel. Due to its location on the ground surface, the tunnel portal structure is subjected to strong earthquake inertial force and thus prone to be damaged. e seismic damage of the portal slope involves collapse, rock fall, landslide, and others and can easily block the tunnel portal and seriously hinder the emergency rescue. On the basis of the present study on the seismic damage of tunnel portal and slope [14,15], the index of seismic damage of tunnel portal and slope (P) is discretized by quantitatively and qualitatively assessing the degree of slope collapse, the volume of rock fall and landslide, and the seismic damage situation of the tunnel portal structure, as shown in Table 3.

Lining Damage (L).
e lining damage mainly includes crack, peeling-off, falling, and collapse. e quantitative characteristics of the damage reflect the seismic damage degree of the lining, and they are described by the density, the width and length of cracks, the scale and range of peeling-off, and collapse. On the basis of the present study on lining damage assessment [9,14], the index of seismic damage of the lining (L) is discretized by quantitatively and qualitatively assessing the length, width and density of crack, the scale and degree of peeling-off, the falling and collapse [24], and the situation of groundwater, as shown in Table 4. Shock and Vibration

Road Pavement Damage (R).
e road pavement damage, including crack and upheaval, can seriously hinder the emergency rescue and disaster relief after earthquakes. Reflecting the severity of the pavement damage, the quantitative characteristics of the damage includes the width, the length and extension direction of cracks, the upheaval height, and others. According to the field investigation data and the present study on seismic damage assessment of pavement [2,6], the index of seismic damage of road pavement (R) is discretized by quantitatively and qualitatively assessing the width, length and direction of crack, the height of upheaval [14,15,24], and the situation of ponding water, as shown in Table 5.Note: l � length of crack, w � width of crack or dislocation, and h � height of upheaval or dislocation.

Earthquake Collapse (C).
e tunnel collapse triggered by earthquake is the most severe damage type among all tunnel seismic damages and can hinder and even completely block the rescue vehicles and crews. It takes high cost and long time to repair the collapse of tunnel and surrounding rock. Based on the present study on tunnel earthquake collapse [25][26][27][28][29], the index of tunnel earthquake collapse (C) is discretized by quantitatively and qualitatively assessing the volume, the type and characteristics of collapse, the groundwater situation, and the degree of weathering or fracture of rocks, as shown in Table 6.

Classification Criterion of Tunnel Seismic Damage.
Although some criteria were introduced in different literature studies, up until now, to the knowledge of authors, there lacks a unified standard for the classification of tunnel seismic damage. Dowding and Rozan [30] classified three damage levels, i.e., no damage, minor damage, and damage. Huang et al. [28] and Wang et al. [2] improved the study of Dowding and Rozan's classification by further dividing the minor damage into slight damage and moderate damage. Since the 2008 Wenchuan earthquake, some new classification studies were proposed because extremely severe damages in mountain tunnels, including earthquake collapse and dislocation, have been reported [3,9]. As a result, a new five-level damage classification system (i.e., extremely severe, severe, moderate, slight, and undamaged) was proposed [2,9,14]. Based on the abovementioned studies on the assessment and classification of tunnel seismic damage and referred to the Chinese railway and highway industry standards for tunnel performance degradation [12,24,31], the SDL of mountain tunnel is discretized in this study as shown in Table 7.

Application of CCM
e Wenchuan earthquake caused severe damages to tens of mountain tunnels. Due to the lack of rapid and accurate assessment of tunnel seismic damage, the emergency rescue and damage repair after the earthquake were seriously hindered. In order to demonstrate the applicability and accuracy of the rapid assessment method of CCM proposed in this study, we chose the Longxi tunnel as an example to assess and classify the seismic damage. Longxi tunnel is located near the epicenter of Wenchuan earthquake as shown in Figure 7, being in the south of Chaping Mountain between Yingxiu Town and Longxi Town and to the left bank of the Minjiang River in Sichuan Province of China. e tunnel axis direction is northwest (NW), and mountain ridge direction is northeast (NE), namely, there exists a large intersection angle between the two axes. e distance between the tunnel exit and the Wenchuan earthquake epicenter (i.e., Yingxiu Town) is only 4 km.
Because of its typical geographical location and representative seismic damage type of Longxi tunnel during the Wenchuan earthquake, some scholars have investigated the seismic damage characteristics of Longxi tunnel and the associated mechanisms [3,9,[32][33][34][35][36][37]; however, systematic assessment and classification study on seismic damage of Longxi tunnel was rarely conducted. Although Longxi tunnel is a double-line tunnel, the field investigation on the right line tunnel could not be carried out as the right line encountered severe earthquake collapse during Wenchuan earthquake. erefore, only the left line of the tunnel is used here to conduct the SDL assessment, and the length to be assessed is 3492 m.
Based on the field investigation data for the left line of Longxi tunnel after earthquake, the relevant parameters of    Shock and Vibration 9 different tunnel sections are calculated using the proposed CCM rapid assessment (Table 8).
Based on the seismic damage description and discretized assessment parameters of SDL as shown in Table 8, the rapid assessment of SDL for the left line of Longxi tunnel is carried out according to the following procedure: Step 1: draw the initial CCM diagram.
Step 3: assign proportional angle and arc for each section according to its length ( Figure 8).
Step 4: calculate the SDL (r i ) of each section using equation (3) according to the comprehensive assessment system and indexes (P, L, R, and C) proposed in this paper, and the r i values are shown in Table 8.
Step 5: draw each sector domain in the CCM diagram to represent the seismic damage situation of each tunnel section.
Step 6: calculate the seismic damage index (α) and synthetic radius (R s ) by equations (6) and (7), respectively, which are equal to 0.584 and 3.06. It is clear that the value of α is located between 9/16 and 1 according to Table 2, which shows that the seismic damage of the left line of Longxi tunnel is severe. Namely, severe performance degradation of tunnel structure occurred and traffic safety was threatened, and remedial measures should be taken as soon as possible. e synthetic radius for the classification of seismic damage is labelled in the CCM diagram, and the result is visualized in Figure 9.
According to the field investigation data, the left line of Longxi tunnel suffered from severe seismic damage during Wenchuan earthquake, including slope collapse, rock falls, crack and collapse of lining, crack and upheaval of invert, large-scale surrounding rock collapse, and others ( Figure 10). e seismic damage significantly lowered the tunnel structural safety and traffic safety and hindered rescue and remedial work after the earthquake. Shown in this case study, the assessment results from the CCM are consistent with those of the field investigation, which verifies the Intensive cracks (10 m < l < 20 m, 1 cm < w > 5 cm); pavement upheaval (10 cm < h < 50 cm); local dislocation (1 cm < w > 5 cm, 5 cm < h < 10 cm); severe damage to pavement; extensive ponding water; cautiously passable traffic with high risk 3

Slight
Local cracks (l < 5 m, w < 0.5 cm); no pavement upheaval; few dislocation (w < 0.5 cm, h < 1 cm); little damage to pavement; local pavement covered by less ponding water; passable traffic but maintenance still needed 1 Undamaged No crack or upheaval; passable traffic; no abnormal phenomenon 0           accuracy and applicability of the CCM assessment method for the seismic damage level.

Conclusions
Based on the techniques of analytic hierarchy process (AHP) and numerical discretization, the concentric circle method (CCM) is proposed to rapidly assess the seismic damage level (SDL) of mountain tunnel. e proposed method can rapidly and accurately assess the SDL of mountain tunnel to win over precious time for emergency rescue and provide references for the repair of damaged tunnel.
According to the statistical analysis on the damage characteristics and types of 40 mountain tunnels during Wenchuan earthquake, a set of effective assessment and classification system covering complete multilevel factor sets and specific quantitative parameters is established. Four main damage types, including the slope and portal damage, the lining damage, the road pavement damage, and the earthquake collapse, are defined as the level-1 controlling factor sets. To target the feature of rapidity for the assessment of SDL of mountain tunnel, the discretized assessment index and classification criterion are introduced and fully considered in this study.
Using the proposed concentric circle method (CCM), the SDL of the left line of Longxi tunnel after Wenchuan earthquake is used as an example and is identified to be severe damage. e assessment results from the proposed rapid assessment method are consistent with the field investigation data, verifying the accuracy and applicability of the CCM for rapid assessment of seismic damage of mountain tunnel.

Data Availability
e data used to support the findings of this study are included within the article.