# Stability Assessment of Ground Surface along Tunnels in Karst Terrain Using Improved Fuzzy Comprehensive Evaluation

Authors: Kai Zhang; Zelin Zhou; Shougen Chen
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

The stability of ground surface along tunnels in karst terrain is influenced by complex factors, among which the karst features are the significant ones. Under the influence of karst, the ground surface along tunnels is very easy to collapse, thus causing great casualties and economic losses. To provide guidance for maintaining the stability of ground surface along tunnels, an analysis system is proposed for assessing the stability of ground surface along tunnels in karst terrain based on an improved fuzzy comprehensive evaluation. Based on the case analysis of ground collapse along tunnels in karst terrain and the review of the related researches, the evaluation index system for ground surface stability assessment was established. The ridge-shaped membership functions were constructed to calculate the membership degree for the evaluation indices. The comprehensive weighting method combining the Fuzzy Analytical Hierarchy Process and correlation analysis was applied to determine weights for evaluation indices. And the ground surface stability level was recognized based on the maximum membership principle. The proposed assessment system was applied to assess the ground surface stability along the tunnels of Guiyang Metro Line 1, and the assessment results agreed well with the regional ground collapse history, verifying the effectiveness and reliability of the assessment system. Combining with the assessment results, a series of measures were conducted to promote the ground surface stability before tunnel excavation. This system provides a valuable tool for assessing and guiding to improve stability of the ground surface along tunnels in karst terrain.


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## Body

## 1. Introduction

During tunneling in karst terrain, the excavation disturbance can easily cause instability of karst caves and then leads to the ground surface collapse. Because of the complex karst phenomena, the ground collapse in karst terrain has the characteristics of invisibility, burstiness, and mass occurrence [1, 2]. Once the ground collapse happens in the karst terrain, it may cause great casualties and economic losses [3–7]. Recently, more and more efforts have been made in the development and utilization of underground space, and thousands of tunnels have been constructed in karst terrain all over the world, resulting in the fact that hundreds of ground collapses caused by tunnel construction have happed [8–10]. For example, the construction of the Jinshazhou tunnel on the Wuhan-Guangzhou railway led to 19 ground collapses in the Jinshazhou area in Guangzhou, Guangdong Province in the Southern Karst region of China. As a result, the stability of up to 120000 m2 buildings on the ground was threatened, and more than 260 households were forced to relocate [11]. Another example is that the ground collapse caused by Wuhan metro tunnel excavation in the karst areas resulted in four people falling and died in the collapse pits and millions of RMB of economic losses. In addition, the ground collapse along the tunnel line can also bring problems for tunnel construction. Therefore, assessing the ground surface stability along tunnels is significant for guiding the prevention of ground collapse disaster.As one of the thorniest problems in the engineering geology field, karst ground surface stability has been given great emphasis, and numbers of related studies have been conducted. Based on the factors influencing ground surface stability, some mathematical analysis methods, including favorability functions approach [12], curvature analysis [13], geographically weighted regression [14], logistic regression [15, 16], and weights-of-evidence analysis [17], have been applied to assess stability or susceptibility of karst ground. Investigations on the karst phenomenon [18] and geological and hydrogeological conditions [19] were also used to assess the regional karst ground surface stability status. In addition, the numerical simulation methods, including FEM approach [20], DEM approach [21], and physical modeling method [22], have been used to study the stability of karst cavities. However, the researches on ground surface stability related to tunneling in karst terrain are limited. Song et al. [23] and Valenzuela et al. [24] assessed the influence of karst sinkholes on the construction of the Sol-a tunnel in South Korea and Pajares tunnels in Spain, respectively. He et al. [25] assessed the risk of ground collapse along tunnels based on expert judgment.The existing researches are valuable for studying karst ground surface stability. But for assessing the stability of ground surface along tunnels in karst terrain, there are still limitations. Most of the above-mentioned researches mainly focused on the approaches of data acquisition or data processing but little attention is paid to the recognition of stability degree. Geological and hydrogeological investigation is the most intuitive method for analyzing the stability of karst ground, but the reliability of the results mainly depends on the accuracy of data acquisition. And the investigations cannot be widely used considering the cost and site conditions. As the characteristics of karst are various in different regions, the research results from investigations for karst ground surface stability in specific regions lack universal applicability. Ground surface stability in karst terrain is influenced by complicated factors; the numerical and physical models cannot reflect the real situations of karst geology. And the assessment based on expert judgments was much subjective, making it lacking reliability.This paper aims to establish an analysis model for assessing the stability of ground surface along tunnels in karst terrain using an improved fuzzy comprehensive evaluation method. The evaluation index system is firstly established based on the analysis of ground collapse cases and review of related researches. The ridged membership functions are applied to calculate the membership degree of evaluation indices. The comprehensive weighting method combining the Fuzzy Analytical Hierarchy Process (FAHP) and correlation analysis is applied to distribute weights for evaluation indices, and the stability level is recognized based on the maximum membership principle. And the proposed assessment system was applied to assess the stability of the ground surface along the tunnel of Guiyang Metro Line 1 to verify its effectiveness and reliability. The proposed assessment system is of great significance for maintaining the stability of ground surface along tunnels in karst terrain.


## 2. Methodology

The fuzzy comprehensive evaluation is a significant method which can be applied to address the issues with uncertain and fuzzy boundary and has been widely used in fuzzy mathematics [26, 27]. The fuzzy comprehensive evaluation method is improved and applied to establish an assessment system for ground stability in this research and the main work consists of the following parts: establishment of evaluation index system, establishment of index and evaluation sets, membership functions and membership matrix, weights distribution for evaluation indices, and fuzzy comprehensive evaluation matrix [28–30].


### 2.1. Evaluation Index System

The stability of ground surface along tunnels in karst terrain is affected by complex factors, which can be divided into internal and external factors. The internal influence factors refer to these geological and hydrogeological conditions, while the external factors refer to the engineering ones.


#### 2.1.1. Karst Development Degree

Underground karst is the major factor influencing ground surface stability during tunneling. The percentage of number of boreholes that encountered karst in the total number of boreholes (PBK) is recommended to reflect the density of underground karst [31]. The higher the PBK, the higher the degree of underground karst development. Formation lithology is one of the major factors controlling underground kart development. The formation solubility coefficient (FSC) is defined to describe the solubility of the rock formations. The FSC is calculated by the formula FSC = 0.636t1 + 0.259t2 + 0.105t3, where t1, t2, and t3 are proportions of lithology with strong, medium, and weak solubility, respectively [32], and the formation lithologies with strong, medium, and weak solubility have been defined by Zhang et al. [33]. In general, the higher FSC always contributes to a higher karst development degree.


#### 2.1.2. Bedrock Covering State

The ground surface stability in karst terrain is closely related to the bedrock covering state. The thickness of bedrock covering (TBC) and structural features of bedrock covering (SFBC) are the two major factors seriously influencing ground surface stability. In general, the thinner bedrock covering contributes to a higher probability of ground collapse under specific geological and hydrogeological conditions. The velocity and scale of the ground collapse are highly influenced by the features of bedrock covering, among which the amount and permeability of the layers forming the bedrocks are the two major factors influencing the stability of the bedrock covering.


#### 2.1.3. Groundwater State

The groundwater state, including groundwater hydrodynamic condition (GHC) and distance between groundwater table and bedrock top (DGTB), also strongly influences the stability of ground in karst terrain. The higher content and better runoff conditions of the groundwater generally contribute to a higher degree of karst development. And the flowing groundwater can also wash away the soil particles and dissolved debris of the karst caves. In addition, fluctuation of groundwater table can change the physical and mechanical properties of surrounding rock or soil of karst caves, resulting in instability of underground cavities, and then induce ground surface stability.


#### 2.1.4. Geological Structure Conditions

The influences of geological structures, including fault and fold, are also other factors influencing the stability of ground in karst terrain. Under the influence of geological structures, numbers of joints and cracks are generated inside the rocks subjected to the in situ stress. The joints and cracks will increase the permeability of the rock and make it susceptible to dissolution and scouring of groundwater, providing favorable conditions for karst development. In addition, the underground caves are extremely unstable in the areas where faults and folds are easy to collapse under the function of external disturbances.


#### 2.1.5. Tunneling Engineering Features

Tunneling engineering features are the external factors influencing the stability of ground surface along the tunnels in karst terrain. Firstly, the excavation of the tunnel can cause a change in the groundwater table. The change of groundwater table can result in a change of buoyancy on the rock mass. The state of force balance state of the karst caves will be broken by the change of buoyancy, easily leading to the collapse of karst caves. The depth of the proposed tunnel also influences ground surface stability. The deeper the tunnel, the more stable the ground above the tunnel, no matter whether there are caves in the ground or not.Based on cases analysis of ground collapse in karst terrain and review of the related researches [14, 15, 28, 34–39], the following ten factors, PBK, FSC, TBC, SBC, GHC, DGB, width of fault and its influence zone (WFI), structural features of fold (SFF), depth of the proposed tunnel (DPT), and groundwater table change caused by excavation of the proposed tunnel (GCE), were selected to access stability of ground surface along tunnels in karst terrain. A hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain was constructed as presented in Figure 1. And the ten evaluation indices, I1–I10, were quantitatively graded as shown in Table 1 [11, 17, 25, 30–32, 40, 41].Figure 1
Hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain.Table 1
Grading standards for evaluation indices.
Evaluation indexStability levelv1v2v3v4I1PBK (%)0–1010–3030–5050–100I2FLC0–0.0420.042–0.1040.104–0.2540.254–0.636I3TBC (m)20–5010–205–100–5I4SBC0–2525–5050–7575–100Uniform structureDouble-layer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is higher than that of the lower layerI5GHC0–2525–5050–7575–100Groundwater runoff condition is poorGroundwater runoff condition is moderateGroundwater runoff condition is goodGroundwater runoff condition is very goodI6DGB (m)10–505–102.5–50–2.5I7WFI (m)0–33–55–1010–50I8SFF0–2525–5050–7575–100No fold or the tunneling area locates in the limb parts of flat and open foldsThe tunneling area locates in the limb parts of steep and tight foldsThe tunneling area locates in the hinge parts of flat and open foldsThe tunneling area locates in the hinge parts of steep and tight foldsI9DPT (m)50–10030–5010–300–10I10GCE (m)0–22–55–1010–50


### 2.2. Index and Evaluation Sets

Based on the selected evaluation indices, the evaluation index set for assessment of ground surface stability was constructed as follows:(1)I=I1,I2,…,In.As the evaluation indices and the ground surface stability have been divided into four levels as shown in Table1, the evaluation set was constructed as follows:(2)V=v1,v2,…,vm.


### 2.3. Membership Functions and Membership Matrix

There are several membership functions, including triangular, trapezoid, Gaussian, parabolic, and ridged, which can be used to calculate the membership degree for evaluation indices in a fuzzy comprehensive evaluation. Considering the characteristics of the evaluation indices of stability of ground surface along tunnels in karst terrain, the ridged membership function was applied to calculate the membership degrees for evaluation indices in this research [41]. The ridged membership functions consist of smaller, medium, and larger forms, which were presented as equations (3)–(5), respectively:(3)μi1x=1,x≤a1,12−12sinπa2−a1x−a1+a22,a1<x≤a2,0,x>a2,(4)μijx=0,x≤−a2,12+12sinπa2−a1x−a1+a22,−a2<x≤−a1,1,−a1<x≤a1,12−12sinπa2−a1x−a1+a22,a1<x≤a2,0,x>a2,(5)μi4x=0,x≤a1,12+12sinπa2−a1x−a1+a22,a1<x≤a2,1,x>a2,where 1≤i≤10, 1≤j≤4, μijxis the membership degree of evaluation index Ii with regard to evaluation level vj, and a1 and a2 are interval thresholds. Figure 2 shows curves of smaller, medium, and larger ridged membership functions, respectively, where t is the critical value of the range corresponding to a stable level for each evaluation index. The interval thresholds a1 and a2 are determined using the coefficient amplification method, which was presented as follows:(6)a1=t1−η,a2=t1+η,where t is the critical value of the index value range and η is the amplification coefficient which is determined according to the related regulations and expert judgments and generally is taken as 0.05–0.3 [42]. In this research, the proportion for enlarging and reducing was determined as 0.2 based on actual situations and the expert judgments.Figure 2
Ridged membership function curves: (a) partial small-scale, (b) middle-scale, and (c) partial large-scale.
(a)(b)(c)Based on the grading standards for evaluation indices shown in Table1, the membership functions for the ten evaluation indices were constructed and the curves were presented in Figure 3.Figure 3
Ridged membership functions for evaluation indices.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)When the values of the evaluation indices are obtained, the membership degrees of the evaluation indices can be calculated by substituting the evaluation index values into the above membership functions. Then, a membership matrix can be constructed as follows, wheren = 10 and m = 4 in this research:(7)U=u11⋯uim⋱un1unm.


### 2.4. Weights for Evaluation Indices

The weights for evaluation indices reflect the contribution of the index to the object to be evaluated; the weight matrix of the evaluation indices for ground surface stability is defined as follows:(8)W=w1,w2,…,wn,where wi is the comprehensive weight of evaluation index Ii, and the weights are assigned through the combination weighting method. The comprehensive weight for the evaluation index consists of subjective and objective weight as shown in equation (14):(9)wi=wioko+wisks,ko+ks=1,where wis and wio are subjective and objective weights, respectively, and ks and ko are proportion coefficients of subjective weight and objective weight, respectively.


#### 2.4.1. Subjective Weight

The subjective weights for evaluation indices are determined based on the FAHP proposed by Chang [43]. In FAHP, the triangular fuzzy number (TFN) in Table 2 is recommended to represent the relative importance scale between objects [30, 44, 45].Table 2
Explanation of triangular fuzzy number.
Fuzzy numberExplanationTFNInverse TFN1˜One object is equally important to the other(1, 1, 1)(1, 1, 1)3˜One object is slightly important than the other(1, 3, 5)(1/5, 1/3, 1)5˜One object is moderately important than the other(3, 5, 7)(1/7, 1/5, 1/3)7˜One object is strongly important than the other(5, 7, 9)(1/9, 1/7, 1/5)9˜One object is extremely important than the other(7, 9, 11)(1/11, 1/9, 1/7)2˜Intermediate values between the above two adjacent judgments(1, 2, 4)(1/4, 1/2, 1)4˜(2, 4, 6)(1/6, 1/4, 1/2)6˜(4, 6, 8)(1/8, 1/6, 1/4)8˜(6, 8, 10)(1/10, 1/8, 1/6)Based on the FAHP, the subjective weights of evaluation indices are determined by the following steps. Firstly, the evaluation indices inF- and I-criterion levels were pairwise compared according to their contributions to their father node, and the comparison matrixes were constructed as shown in Tables 3–4. Then, the consistency ratio (CI) was computed to verify the consistency of the pairwise comparison matrixes [46]. Thirdly, the weights of evaluation indices in each comparison matrix were calculated fowling the FAHP. As the FAHP has been recorded in literature [33, 44, 45], the weight calculation process is omitted in this research and only the calculation results were presented in Tables 3–4. Finally, the global weights for all the evaluation indices were synthesized and presented in Table 5. So, the subjective weight set for evaluation indices was established as follows:(10)ws=0.2087,0.1037,0.1099,0.1099,0.0883,0.0883,0.0478,0.0238,0.0730,0.1467.Table 3
Weight analysis of indices atF-criterion level.
Evaluation indexF1F2F3F4F5WeightF1(1, 1, 1)(1, 3, 5)(1, 3, 5)(3, 5, 7)(1, 3, 5)0.3124F2(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197F3(1/5, 1/3, 1)(1/4, 1/2, 1)(1, 1, 1)(1, 3, 5)(1/4, 1/2, 1)0.1765F4(1/7, 1/5, 1/3)(1/5, 1/3, 1)(1, 3, 5)(1, 1, 1)(1/5, 1/3, 1)0.0716F5(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197CI = 0.027 < 0.1, meeting the consistency requirement.Table 4
Weight analysis of indicesI1–I10.
Evaluation indexI1I2WeightI1(1, 1, 1)(1, 2, 4)0.6679I2(1/4, 1/2, 1)(1, 1, 1)0.3321I3I4I3(1, 1, 1)(1, 1, 1)0.5000I4(1, 1, 1)(1, 1, 1)0.5000I5I6I5(1, 1, 1)(1, 1, 1)0.5000I6(1, 1, 1)(1, 1, 1)0.5000I7I8I7(1, 1, 1)(1, 2, 4)0.6679I8(1/4, 1/2, 1)(1, 1, 1)0.3321I9I10I9(1, 1, 1)(1/4, 1/2, 1)0.3321I10(1, 2, 4)(1, 1, 1)0.6679CI = 0 < 0.1, meeting the consistency requirement.Table 5
Subjective weights for evaluation indices.
Evaluation indexF-level index weightSubjective weightF1F2F3F4F50.31240.21970.17650.07160.2197I10.66790.2087I20.33210.1037I30.50000.1099I40.50000.1099I50.50000.0883I60.50000.0883I70.66790.0478I80.33210.0238I90.33210.0730I100.66790.1467


#### 2.4.2. Objective Weights

The objective weights for evaluation indices are determined through correlation analysis of the values of evaluation indices.Firstly, the evaluation indices should be nondimensionalized to reduce the influence of difference units on the assessment results and make the different indices comparable. In this research, the evaluation index values were linearly nondimensionalized using the following forms:(a)
If the larger values contribute to the higher evaluation levels, take(11)x˜i=xibiP−aiP,a˜ij=aij−aiPbiP−aiP,b˜ij=bij−aiPbiP−aiP.(b)
If the larger values contribute to the lower evaluation levels, take(12)x˜i=xiaiP−biP,a˜ij=aiP−aijaiP−biP,b˜ij=aiP−bijaiP−biP.Here,x˜i, a˜ij, and b˜ij are the nondimensionalized values of xi, aij, and bij, aiP,biP is the value range of evaluation indices Ii, and aij,bij is the value range of indices Ii for the stability level vj.Secondly, the correlation degree between index valuex˜i and the interval v˜ij=a˜ij,b˜ij is defined as follows:(13)Kijx˜i,v˜ij=2x˜i−a˜ijb˜ij−a˜ij,x˜i≤a˜ij+b˜ij2,2b˜ij−x˜ib˜ij−a˜ij,x˜i≥a˜ij+b˜ij2,and the maximum correlation degree is defined as follows:(14)Kijmaxx˜i,v˜ijmax=maxj=1mKijx˜i,v˜ij,where j meets 1≤j ≤ m.Thirdly, a coefficientri is calculated by the following forms:(a)
If the larger index measurexi contributes to the higher evaluation level, take(15)ri=jmax×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,jmax×0.5,Kijmaxx˜i,v˜ijmax<−0.5.(b)
If the larger index measurexi contributes to the lower evaluation level, take(16)ri=m−jmax+1×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,m−jmax+1×0.5,Kijmaxx˜i,v˜ijmax<−0.5.Finally, the weight of the evaluation index can be obtained according to the following equation:(17)wis=ri∑i=1nri.


### 2.5. Fuzzy Comprehensive Evaluation Matrix

Based on the weights and membership degrees of evaluation indices, the comprehensive evaluation matrix for ground surface stability can be constructed as follows:(18)C=W⋅U=w1,w2,…,wn⋅u11⋯uim⋱un1unm.Then, the level of ground surface stability can be recognized based on the maximum membership degree principle, which is expressed as follows:(19)vs=cmvm⟶maxi=1mci,where vs is the evaluation level of the object, cm is the maximum element in the comprehensive evaluation matrix, and vm is the corresponding evaluation level in the evaluation set.


## 2.1. Evaluation Index System

The stability of ground surface along tunnels in karst terrain is affected by complex factors, which can be divided into internal and external factors. The internal influence factors refer to these geological and hydrogeological conditions, while the external factors refer to the engineering ones.


### 2.1.1. Karst Development Degree

Underground karst is the major factor influencing ground surface stability during tunneling. The percentage of number of boreholes that encountered karst in the total number of boreholes (PBK) is recommended to reflect the density of underground karst [31]. The higher the PBK, the higher the degree of underground karst development. Formation lithology is one of the major factors controlling underground kart development. The formation solubility coefficient (FSC) is defined to describe the solubility of the rock formations. The FSC is calculated by the formula FSC = 0.636t1 + 0.259t2 + 0.105t3, where t1, t2, and t3 are proportions of lithology with strong, medium, and weak solubility, respectively [32], and the formation lithologies with strong, medium, and weak solubility have been defined by Zhang et al. [33]. In general, the higher FSC always contributes to a higher karst development degree.


### 2.1.2. Bedrock Covering State

The ground surface stability in karst terrain is closely related to the bedrock covering state. The thickness of bedrock covering (TBC) and structural features of bedrock covering (SFBC) are the two major factors seriously influencing ground surface stability. In general, the thinner bedrock covering contributes to a higher probability of ground collapse under specific geological and hydrogeological conditions. The velocity and scale of the ground collapse are highly influenced by the features of bedrock covering, among which the amount and permeability of the layers forming the bedrocks are the two major factors influencing the stability of the bedrock covering.


### 2.1.3. Groundwater State

The groundwater state, including groundwater hydrodynamic condition (GHC) and distance between groundwater table and bedrock top (DGTB), also strongly influences the stability of ground in karst terrain. The higher content and better runoff conditions of the groundwater generally contribute to a higher degree of karst development. And the flowing groundwater can also wash away the soil particles and dissolved debris of the karst caves. In addition, fluctuation of groundwater table can change the physical and mechanical properties of surrounding rock or soil of karst caves, resulting in instability of underground cavities, and then induce ground surface stability.


### 2.1.4. Geological Structure Conditions

The influences of geological structures, including fault and fold, are also other factors influencing the stability of ground in karst terrain. Under the influence of geological structures, numbers of joints and cracks are generated inside the rocks subjected to the in situ stress. The joints and cracks will increase the permeability of the rock and make it susceptible to dissolution and scouring of groundwater, providing favorable conditions for karst development. In addition, the underground caves are extremely unstable in the areas where faults and folds are easy to collapse under the function of external disturbances.


### 2.1.5. Tunneling Engineering Features

Tunneling engineering features are the external factors influencing the stability of ground surface along the tunnels in karst terrain. Firstly, the excavation of the tunnel can cause a change in the groundwater table. The change of groundwater table can result in a change of buoyancy on the rock mass. The state of force balance state of the karst caves will be broken by the change of buoyancy, easily leading to the collapse of karst caves. The depth of the proposed tunnel also influences ground surface stability. The deeper the tunnel, the more stable the ground above the tunnel, no matter whether there are caves in the ground or not.Based on cases analysis of ground collapse in karst terrain and review of the related researches [14, 15, 28, 34–39], the following ten factors, PBK, FSC, TBC, SBC, GHC, DGB, width of fault and its influence zone (WFI), structural features of fold (SFF), depth of the proposed tunnel (DPT), and groundwater table change caused by excavation of the proposed tunnel (GCE), were selected to access stability of ground surface along tunnels in karst terrain. A hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain was constructed as presented in Figure 1. And the ten evaluation indices, I1–I10, were quantitatively graded as shown in Table 1 [11, 17, 25, 30–32, 40, 41].Figure 1
Hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain.Table 1
Grading standards for evaluation indices.
Evaluation indexStability levelv1v2v3v4I1PBK (%)0–1010–3030–5050–100I2FLC0–0.0420.042–0.1040.104–0.2540.254–0.636I3TBC (m)20–5010–205–100–5I4SBC0–2525–5050–7575–100Uniform structureDouble-layer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is higher than that of the lower layerI5GHC0–2525–5050–7575–100Groundwater runoff condition is poorGroundwater runoff condition is moderateGroundwater runoff condition is goodGroundwater runoff condition is very goodI6DGB (m)10–505–102.5–50–2.5I7WFI (m)0–33–55–1010–50I8SFF0–2525–5050–7575–100No fold or the tunneling area locates in the limb parts of flat and open foldsThe tunneling area locates in the limb parts of steep and tight foldsThe tunneling area locates in the hinge parts of flat and open foldsThe tunneling area locates in the hinge parts of steep and tight foldsI9DPT (m)50–10030–5010–300–10I10GCE (m)0–22–55–1010–50


## 2.1.1. Karst Development Degree

Underground karst is the major factor influencing ground surface stability during tunneling. The percentage of number of boreholes that encountered karst in the total number of boreholes (PBK) is recommended to reflect the density of underground karst [31]. The higher the PBK, the higher the degree of underground karst development. Formation lithology is one of the major factors controlling underground kart development. The formation solubility coefficient (FSC) is defined to describe the solubility of the rock formations. The FSC is calculated by the formula FSC = 0.636t1 + 0.259t2 + 0.105t3, where t1, t2, and t3 are proportions of lithology with strong, medium, and weak solubility, respectively [32], and the formation lithologies with strong, medium, and weak solubility have been defined by Zhang et al. [33]. In general, the higher FSC always contributes to a higher karst development degree.


## 2.1.2. Bedrock Covering State

The ground surface stability in karst terrain is closely related to the bedrock covering state. The thickness of bedrock covering (TBC) and structural features of bedrock covering (SFBC) are the two major factors seriously influencing ground surface stability. In general, the thinner bedrock covering contributes to a higher probability of ground collapse under specific geological and hydrogeological conditions. The velocity and scale of the ground collapse are highly influenced by the features of bedrock covering, among which the amount and permeability of the layers forming the bedrocks are the two major factors influencing the stability of the bedrock covering.


## 2.1.3. Groundwater State

The groundwater state, including groundwater hydrodynamic condition (GHC) and distance between groundwater table and bedrock top (DGTB), also strongly influences the stability of ground in karst terrain. The higher content and better runoff conditions of the groundwater generally contribute to a higher degree of karst development. And the flowing groundwater can also wash away the soil particles and dissolved debris of the karst caves. In addition, fluctuation of groundwater table can change the physical and mechanical properties of surrounding rock or soil of karst caves, resulting in instability of underground cavities, and then induce ground surface stability.


## 2.1.4. Geological Structure Conditions

The influences of geological structures, including fault and fold, are also other factors influencing the stability of ground in karst terrain. Under the influence of geological structures, numbers of joints and cracks are generated inside the rocks subjected to the in situ stress. The joints and cracks will increase the permeability of the rock and make it susceptible to dissolution and scouring of groundwater, providing favorable conditions for karst development. In addition, the underground caves are extremely unstable in the areas where faults and folds are easy to collapse under the function of external disturbances.


## 2.1.5. Tunneling Engineering Features

Tunneling engineering features are the external factors influencing the stability of ground surface along the tunnels in karst terrain. Firstly, the excavation of the tunnel can cause a change in the groundwater table. The change of groundwater table can result in a change of buoyancy on the rock mass. The state of force balance state of the karst caves will be broken by the change of buoyancy, easily leading to the collapse of karst caves. The depth of the proposed tunnel also influences ground surface stability. The deeper the tunnel, the more stable the ground above the tunnel, no matter whether there are caves in the ground or not.Based on cases analysis of ground collapse in karst terrain and review of the related researches [14, 15, 28, 34–39], the following ten factors, PBK, FSC, TBC, SBC, GHC, DGB, width of fault and its influence zone (WFI), structural features of fold (SFF), depth of the proposed tunnel (DPT), and groundwater table change caused by excavation of the proposed tunnel (GCE), were selected to access stability of ground surface along tunnels in karst terrain. A hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain was constructed as presented in Figure 1. And the ten evaluation indices, I1–I10, were quantitatively graded as shown in Table 1 [11, 17, 25, 30–32, 40, 41].Figure 1
Hierarchy structure for assessing the stability of ground surface along tunnels in karst terrain.Table 1
Grading standards for evaluation indices.
Evaluation indexStability levelv1v2v3v4I1PBK (%)0–1010–3030–5050–100I2FLC0–0.0420.042–0.1040.104–0.2540.254–0.636I3TBC (m)20–5010–205–100–5I4SBC0–2525–5050–7575–100Uniform structureDouble-layer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is lower than that of the lower layerMultilayer structure and permeability of the upper layer is higher than that of the lower layerI5GHC0–2525–5050–7575–100Groundwater runoff condition is poorGroundwater runoff condition is moderateGroundwater runoff condition is goodGroundwater runoff condition is very goodI6DGB (m)10–505–102.5–50–2.5I7WFI (m)0–33–55–1010–50I8SFF0–2525–5050–7575–100No fold or the tunneling area locates in the limb parts of flat and open foldsThe tunneling area locates in the limb parts of steep and tight foldsThe tunneling area locates in the hinge parts of flat and open foldsThe tunneling area locates in the hinge parts of steep and tight foldsI9DPT (m)50–10030–5010–300–10I10GCE (m)0–22–55–1010–50


## 2.2. Index and Evaluation Sets

Based on the selected evaluation indices, the evaluation index set for assessment of ground surface stability was constructed as follows:(1)I=I1,I2,…,In.As the evaluation indices and the ground surface stability have been divided into four levels as shown in Table1, the evaluation set was constructed as follows:(2)V=v1,v2,…,vm.


## 2.3. Membership Functions and Membership Matrix

There are several membership functions, including triangular, trapezoid, Gaussian, parabolic, and ridged, which can be used to calculate the membership degree for evaluation indices in a fuzzy comprehensive evaluation. Considering the characteristics of the evaluation indices of stability of ground surface along tunnels in karst terrain, the ridged membership function was applied to calculate the membership degrees for evaluation indices in this research [41]. The ridged membership functions consist of smaller, medium, and larger forms, which were presented as equations (3)–(5), respectively:(3)μi1x=1,x≤a1,12−12sinπa2−a1x−a1+a22,a1<x≤a2,0,x>a2,(4)μijx=0,x≤−a2,12+12sinπa2−a1x−a1+a22,−a2<x≤−a1,1,−a1<x≤a1,12−12sinπa2−a1x−a1+a22,a1<x≤a2,0,x>a2,(5)μi4x=0,x≤a1,12+12sinπa2−a1x−a1+a22,a1<x≤a2,1,x>a2,where 1≤i≤10, 1≤j≤4, μijxis the membership degree of evaluation index Ii with regard to evaluation level vj, and a1 and a2 are interval thresholds. Figure 2 shows curves of smaller, medium, and larger ridged membership functions, respectively, where t is the critical value of the range corresponding to a stable level for each evaluation index. The interval thresholds a1 and a2 are determined using the coefficient amplification method, which was presented as follows:(6)a1=t1−η,a2=t1+η,where t is the critical value of the index value range and η is the amplification coefficient which is determined according to the related regulations and expert judgments and generally is taken as 0.05–0.3 [42]. In this research, the proportion for enlarging and reducing was determined as 0.2 based on actual situations and the expert judgments.Figure 2
Ridged membership function curves: (a) partial small-scale, (b) middle-scale, and (c) partial large-scale.
(a)(b)(c)Based on the grading standards for evaluation indices shown in Table1, the membership functions for the ten evaluation indices were constructed and the curves were presented in Figure 3.Figure 3
Ridged membership functions for evaluation indices.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)When the values of the evaluation indices are obtained, the membership degrees of the evaluation indices can be calculated by substituting the evaluation index values into the above membership functions. Then, a membership matrix can be constructed as follows, wheren = 10 and m = 4 in this research:(7)U=u11⋯uim⋱un1unm.


## 2.4. Weights for Evaluation Indices

The weights for evaluation indices reflect the contribution of the index to the object to be evaluated; the weight matrix of the evaluation indices for ground surface stability is defined as follows:(8)W=w1,w2,…,wn,where wi is the comprehensive weight of evaluation index Ii, and the weights are assigned through the combination weighting method. The comprehensive weight for the evaluation index consists of subjective and objective weight as shown in equation (14):(9)wi=wioko+wisks,ko+ks=1,where wis and wio are subjective and objective weights, respectively, and ks and ko are proportion coefficients of subjective weight and objective weight, respectively.


### 2.4.1. Subjective Weight

The subjective weights for evaluation indices are determined based on the FAHP proposed by Chang [43]. In FAHP, the triangular fuzzy number (TFN) in Table 2 is recommended to represent the relative importance scale between objects [30, 44, 45].Table 2
Explanation of triangular fuzzy number.
Fuzzy numberExplanationTFNInverse TFN1˜One object is equally important to the other(1, 1, 1)(1, 1, 1)3˜One object is slightly important than the other(1, 3, 5)(1/5, 1/3, 1)5˜One object is moderately important than the other(3, 5, 7)(1/7, 1/5, 1/3)7˜One object is strongly important than the other(5, 7, 9)(1/9, 1/7, 1/5)9˜One object is extremely important than the other(7, 9, 11)(1/11, 1/9, 1/7)2˜Intermediate values between the above two adjacent judgments(1, 2, 4)(1/4, 1/2, 1)4˜(2, 4, 6)(1/6, 1/4, 1/2)6˜(4, 6, 8)(1/8, 1/6, 1/4)8˜(6, 8, 10)(1/10, 1/8, 1/6)Based on the FAHP, the subjective weights of evaluation indices are determined by the following steps. Firstly, the evaluation indices inF- and I-criterion levels were pairwise compared according to their contributions to their father node, and the comparison matrixes were constructed as shown in Tables 3–4. Then, the consistency ratio (CI) was computed to verify the consistency of the pairwise comparison matrixes [46]. Thirdly, the weights of evaluation indices in each comparison matrix were calculated fowling the FAHP. As the FAHP has been recorded in literature [33, 44, 45], the weight calculation process is omitted in this research and only the calculation results were presented in Tables 3–4. Finally, the global weights for all the evaluation indices were synthesized and presented in Table 5. So, the subjective weight set for evaluation indices was established as follows:(10)ws=0.2087,0.1037,0.1099,0.1099,0.0883,0.0883,0.0478,0.0238,0.0730,0.1467.Table 3
Weight analysis of indices atF-criterion level.
Evaluation indexF1F2F3F4F5WeightF1(1, 1, 1)(1, 3, 5)(1, 3, 5)(3, 5, 7)(1, 3, 5)0.3124F2(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197F3(1/5, 1/3, 1)(1/4, 1/2, 1)(1, 1, 1)(1, 3, 5)(1/4, 1/2, 1)0.1765F4(1/7, 1/5, 1/3)(1/5, 1/3, 1)(1, 3, 5)(1, 1, 1)(1/5, 1/3, 1)0.0716F5(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197CI = 0.027 < 0.1, meeting the consistency requirement.Table 4
Weight analysis of indicesI1–I10.
Evaluation indexI1I2WeightI1(1, 1, 1)(1, 2, 4)0.6679I2(1/4, 1/2, 1)(1, 1, 1)0.3321I3I4I3(1, 1, 1)(1, 1, 1)0.5000I4(1, 1, 1)(1, 1, 1)0.5000I5I6I5(1, 1, 1)(1, 1, 1)0.5000I6(1, 1, 1)(1, 1, 1)0.5000I7I8I7(1, 1, 1)(1, 2, 4)0.6679I8(1/4, 1/2, 1)(1, 1, 1)0.3321I9I10I9(1, 1, 1)(1/4, 1/2, 1)0.3321I10(1, 2, 4)(1, 1, 1)0.6679CI = 0 < 0.1, meeting the consistency requirement.Table 5
Subjective weights for evaluation indices.
Evaluation indexF-level index weightSubjective weightF1F2F3F4F50.31240.21970.17650.07160.2197I10.66790.2087I20.33210.1037I30.50000.1099I40.50000.1099I50.50000.0883I60.50000.0883I70.66790.0478I80.33210.0238I90.33210.0730I100.66790.1467


### 2.4.2. Objective Weights

The objective weights for evaluation indices are determined through correlation analysis of the values of evaluation indices.Firstly, the evaluation indices should be nondimensionalized to reduce the influence of difference units on the assessment results and make the different indices comparable. In this research, the evaluation index values were linearly nondimensionalized using the following forms:(a)
If the larger values contribute to the higher evaluation levels, take(11)x˜i=xibiP−aiP,a˜ij=aij−aiPbiP−aiP,b˜ij=bij−aiPbiP−aiP.(b)
If the larger values contribute to the lower evaluation levels, take(12)x˜i=xiaiP−biP,a˜ij=aiP−aijaiP−biP,b˜ij=aiP−bijaiP−biP.Here,x˜i, a˜ij, and b˜ij are the nondimensionalized values of xi, aij, and bij, aiP,biP is the value range of evaluation indices Ii, and aij,bij is the value range of indices Ii for the stability level vj.Secondly, the correlation degree between index valuex˜i and the interval v˜ij=a˜ij,b˜ij is defined as follows:(13)Kijx˜i,v˜ij=2x˜i−a˜ijb˜ij−a˜ij,x˜i≤a˜ij+b˜ij2,2b˜ij−x˜ib˜ij−a˜ij,x˜i≥a˜ij+b˜ij2,and the maximum correlation degree is defined as follows:(14)Kijmaxx˜i,v˜ijmax=maxj=1mKijx˜i,v˜ij,where j meets 1≤j ≤ m.Thirdly, a coefficientri is calculated by the following forms:(a)
If the larger index measurexi contributes to the higher evaluation level, take(15)ri=jmax×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,jmax×0.5,Kijmaxx˜i,v˜ijmax<−0.5.(b)
If the larger index measurexi contributes to the lower evaluation level, take(16)ri=m−jmax+1×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,m−jmax+1×0.5,Kijmaxx˜i,v˜ijmax<−0.5.Finally, the weight of the evaluation index can be obtained according to the following equation:(17)wis=ri∑i=1nri.


## 2.4.1. Subjective Weight

The subjective weights for evaluation indices are determined based on the FAHP proposed by Chang [43]. In FAHP, the triangular fuzzy number (TFN) in Table 2 is recommended to represent the relative importance scale between objects [30, 44, 45].Table 2
Explanation of triangular fuzzy number.
Fuzzy numberExplanationTFNInverse TFN1˜One object is equally important to the other(1, 1, 1)(1, 1, 1)3˜One object is slightly important than the other(1, 3, 5)(1/5, 1/3, 1)5˜One object is moderately important than the other(3, 5, 7)(1/7, 1/5, 1/3)7˜One object is strongly important than the other(5, 7, 9)(1/9, 1/7, 1/5)9˜One object is extremely important than the other(7, 9, 11)(1/11, 1/9, 1/7)2˜Intermediate values between the above two adjacent judgments(1, 2, 4)(1/4, 1/2, 1)4˜(2, 4, 6)(1/6, 1/4, 1/2)6˜(4, 6, 8)(1/8, 1/6, 1/4)8˜(6, 8, 10)(1/10, 1/8, 1/6)Based on the FAHP, the subjective weights of evaluation indices are determined by the following steps. Firstly, the evaluation indices inF- and I-criterion levels were pairwise compared according to their contributions to their father node, and the comparison matrixes were constructed as shown in Tables 3–4. Then, the consistency ratio (CI) was computed to verify the consistency of the pairwise comparison matrixes [46]. Thirdly, the weights of evaluation indices in each comparison matrix were calculated fowling the FAHP. As the FAHP has been recorded in literature [33, 44, 45], the weight calculation process is omitted in this research and only the calculation results were presented in Tables 3–4. Finally, the global weights for all the evaluation indices were synthesized and presented in Table 5. So, the subjective weight set for evaluation indices was established as follows:(10)ws=0.2087,0.1037,0.1099,0.1099,0.0883,0.0883,0.0478,0.0238,0.0730,0.1467.Table 3
Weight analysis of indices atF-criterion level.
Evaluation indexF1F2F3F4F5WeightF1(1, 1, 1)(1, 3, 5)(1, 3, 5)(3, 5, 7)(1, 3, 5)0.3124F2(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197F3(1/5, 1/3, 1)(1/4, 1/2, 1)(1, 1, 1)(1, 3, 5)(1/4, 1/2, 1)0.1765F4(1/7, 1/5, 1/3)(1/5, 1/3, 1)(1, 3, 5)(1, 1, 1)(1/5, 1/3, 1)0.0716F5(1/5, 1/3, 1)(1, 1, 1)(1, 2, 4)(1, 3, 5)(1, 1, 1)0.2197CI = 0.027 < 0.1, meeting the consistency requirement.Table 4
Weight analysis of indicesI1–I10.
Evaluation indexI1I2WeightI1(1, 1, 1)(1, 2, 4)0.6679I2(1/4, 1/2, 1)(1, 1, 1)0.3321I3I4I3(1, 1, 1)(1, 1, 1)0.5000I4(1, 1, 1)(1, 1, 1)0.5000I5I6I5(1, 1, 1)(1, 1, 1)0.5000I6(1, 1, 1)(1, 1, 1)0.5000I7I8I7(1, 1, 1)(1, 2, 4)0.6679I8(1/4, 1/2, 1)(1, 1, 1)0.3321I9I10I9(1, 1, 1)(1/4, 1/2, 1)0.3321I10(1, 2, 4)(1, 1, 1)0.6679CI = 0 < 0.1, meeting the consistency requirement.Table 5
Subjective weights for evaluation indices.
Evaluation indexF-level index weightSubjective weightF1F2F3F4F50.31240.21970.17650.07160.2197I10.66790.2087I20.33210.1037I30.50000.1099I40.50000.1099I50.50000.0883I60.50000.0883I70.66790.0478I80.33210.0238I90.33210.0730I100.66790.1467


## 2.4.2. Objective Weights

The objective weights for evaluation indices are determined through correlation analysis of the values of evaluation indices.Firstly, the evaluation indices should be nondimensionalized to reduce the influence of difference units on the assessment results and make the different indices comparable. In this research, the evaluation index values were linearly nondimensionalized using the following forms:(a)
If the larger values contribute to the higher evaluation levels, take(11)x˜i=xibiP−aiP,a˜ij=aij−aiPbiP−aiP,b˜ij=bij−aiPbiP−aiP.(b)
If the larger values contribute to the lower evaluation levels, take(12)x˜i=xiaiP−biP,a˜ij=aiP−aijaiP−biP,b˜ij=aiP−bijaiP−biP.Here,x˜i, a˜ij, and b˜ij are the nondimensionalized values of xi, aij, and bij, aiP,biP is the value range of evaluation indices Ii, and aij,bij is the value range of indices Ii for the stability level vj.Secondly, the correlation degree between index valuex˜i and the interval v˜ij=a˜ij,b˜ij is defined as follows:(13)Kijx˜i,v˜ij=2x˜i−a˜ijb˜ij−a˜ij,x˜i≤a˜ij+b˜ij2,2b˜ij−x˜ib˜ij−a˜ij,x˜i≥a˜ij+b˜ij2,and the maximum correlation degree is defined as follows:(14)Kijmaxx˜i,v˜ijmax=maxj=1mKijx˜i,v˜ij,where j meets 1≤j ≤ m.Thirdly, a coefficientri is calculated by the following forms:(a)
If the larger index measurexi contributes to the higher evaluation level, take(15)ri=jmax×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,jmax×0.5,Kijmaxx˜i,v˜ijmax<−0.5.(b)
If the larger index measurexi contributes to the lower evaluation level, take(16)ri=m−jmax+1×1+Kijmaxx˜i,v˜ijmax,Kijmaxx˜i,v˜ijmax≥−0.5,m−jmax+1×0.5,Kijmaxx˜i,v˜ijmax<−0.5.Finally, the weight of the evaluation index can be obtained according to the following equation:(17)wis=ri∑i=1nri.


## 2.5. Fuzzy Comprehensive Evaluation Matrix

Based on the weights and membership degrees of evaluation indices, the comprehensive evaluation matrix for ground surface stability can be constructed as follows:(18)C=W⋅U=w1,w2,…,wn⋅u11⋯uim⋱un1unm.Then, the level of ground surface stability can be recognized based on the maximum membership degree principle, which is expressed as follows:(19)vs=cmvm⟶maxi=1mci,where vs is the evaluation level of the object, cm is the maximum element in the comprehensive evaluation matrix, and vm is the corresponding evaluation level in the evaluation set.


## 3. Case Study

### 3.1. Engineering Background

The Guiyang Metro Line 1 (GML1) with a total length of 33.90 km belongs to the urban rail transit system of Guiyang, a city locates in the Southwest karst region of China. The sixth working section of GML1 with a length of 2284.8 m (23689.0 m–25973.8 m) is located in the limb parts of the Guiyang syncline, and no fault crosses the tunneling area. The strata in the tunneling area consist of block stones, red clay, argillaceous dolomite, and limestone. The groundwater is mainly recharged by infiltration of surface water and groundwater table is higher than metro tunnel floor. Preliminary surveys indicate that karst features are widely distributed in the tunneling area. The ground surface along the metro line is prone to collapse due to the tunnel excavation. To ensure the safety of metro tunnel construction and protect citizens, roads, and facilities on the ground, it is essential to assess the stability of the ground surface along the metro terrain line before construction.


### 3.2. Evaluation Indices

Before metro tunnel construction, geological and geophysical surveys were conducted. Based on the survey results, the values of the evaluation indices,I1– I10, were obtained. According to the change of values of evaluation indices, the tunneling area along the sixth section of GML1 was divided into 32 chainage sections and the values of evaluation indices were presented in Table 6.Table 6
Values of the evaluation indices.
Chainage section numberChainage (m)Evaluation indexPBK (%)FSCTBC (m)SBCGHCDGB (m)WFI (m)SFFDPT (m)GCE (m)123689.0–23832.535.70.1052.4010452.100354.605.08223832.5–23874.735.70.1052.7085451.400354.305.08323874.7–23887.835.70.1053.4010450.900354.305.08423887.8–24108.89.50.1055.2085453.3403517.105.08524108.8–24195.09.50.1056.3085450.1803518.535.08624195.0–24260.09.50.1056.3085452.7703519.625.08724260.0–24288.09.50.1057.9090457.9003514.965.08824288.0–24366.39.50.10511.90854511.903514.515.08924366.3–24489.39.50.1054.8030458.1403511.135.081024489.3–24544.69.50.1052.8010450.1003517.375.081124544.6–24607.19.50.1050.5615452.4403516.655.081224607.1–24616.617.60.1050.5615602.4403516.655.081324616.6–24631.217.60.1057.1570605.980353.325.601424631.2–24656.717.60.1055.4280603.120353.115.601524656.7–24687.017.60.1056.7490601.730355.375.601624687.0–24721.217.60.1051.4615604.0403510.045.601724721.2–24775.317.60.1057.9020600.5003515.075.601824775.3–24779.617.60.1055.7315603.4502017.764.651924779.6–24840.717.40.1059.6080602.2902028.044.652024840.7–24871.617.40.1053.7015609.7202027.254.652124871.6–24900.017.40.1053.3420603.0502024.584.652224900.0–24939.417.40.1052.6080602.7702019.984.652324939.4–25000.017.40.1050.7820601.6402010.904.652425000.0–25056.417.40.1059.2080604.5502017.584.652525056.4–25100.017.40.1058.5080606.4002018.554.652625100.0–25153.217.40.1056.4080602.6602021.894.652725153.2–25230.517.40.1058.0080603.8302021.944.652825230.5–25285.617.40.1057.7080603.5302022.214.652925285.6–25340.017.40.1053.5085601.2602020.774.653025340.0–25400.017.40.1057.0085602.1302022.374.653125400.0–25467.317.40.1057.1085601.4402021.954.653225467.3–25973.817.40.1057.4085602.0802020.804.65(20)U=00.00150.9985000.46230.537700001.00001.000000000.85360.14640000.02450.97551.000000001.0000000001.000000.43730.56270.


### 3.3. Extension Assessment Results

Based on the values of evaluation indices, the stability of the ground surface along the metro tunnel line of the sixth section of GML1 was assessed by using the analysis model proposed in this research.


#### 3.3.1. Assessment of Ground Surface Stability at Chainage Section 1

The assessment of ground surface stability at chainage section 1 (chainage 23689.0–23832.5 m) was presented to demonstrate the assessment process. The values of evaluation indices at Section1 were presented in Table 7.Table 7
Values of evaluation indices at chainage section 1.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Firstly, the values in Table8 were substituted into the membership functions (Figure 2) to calculate the membership degrees for the evaluation indices, based on which the evaluation matrix was established as shown in equation (20).Table 8
Nondimensional values of evaluation indices.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Secondly, the objective weights for evaluation indices were determined by using relation analysis. The values of evaluation indices were nondimensionalized according to equations (11) and (12) and the results were presented in Table 8. The objective weights of evaluation indices for chainage section 1 were distributed according to equations (13)–(17) and the results were presented in Table 9.Table 9
Correlation analysis for objective weights of evaluation indices.
IndexKijKijmaxjmaxriwioN1N2N3N4c1−5.1400−0.57000.5700−0.57200.570034.7100.1153c2−3.0000−0.03230.0133−0.78010.013333.0400.0744c3−1.1733−1.5200−1.04000.96000.960047.8400.1919c40.8000−1.2000−3.2000−5.20000.800011.8000.0441c5−1.60000.4000−0.4000−2.40000.400022.8000.0686c6−0.3950−1.1600−0.32000.32000.320045.2800.1293c70.0000−3.0000−2.0000−0.50000.000011.0000.0245c8−0.80000.8000−1.2000−3.20000.800023.6000.0881c9−1.8160−2.5400−0.54000.92000.920047.6800.1880c10−3.0800−0.05330.0320−0.24600.032033.0960.0758Combining the subjective weights presented in Table5, the comprehensive weights of evaluation indices for Section 1 were synthesized according to equation (9), where the proportion coefficients of objective weight and subjective weight are valued as ks = ko = 0.5 considering the same importance of objective weight and subjective weight for comprehensive weight of evaluation index. So, the weight set was presented as follows:(21)w=0.1620,0.0891,0.1509,0.0770,0.0784,0.1088,0.0361,0.0560,0.1305,0.1112.Finally, the comprehensive evaluation matrix was established as the following form according to equation (17). And the ground surface stability level was recognized as v4 according to equation (19).(22)C=0.11310.21300.28640.3876.


#### 3.3.2. Assessment of Ground Surface Stability for the Sixth Working Section of GML1

The stability of ground surface for other chainage sections was assessed in the same way used for stability assessment for chainage section 1, and the assessment results for ground surface stability along tunnels in the sixth working section of GML1 were presented in Figure4.Figure 4
Assessment results of ground surface stability along tunnels in the sixth working section of GML1.


### 3.4. Regional Ground Collapse History

From the stability assessment results, it could be seen that the ground surface stability was medium (N2) only in chainage sections 7–9 while the stability was low (N3) or extremely low (N4) at the rest of chainages. The amount of chainage sections with low or extremely low ground surface stability (28) takes 87.5% of the total section numbers (32). And the length of chainages with low or extremely low ground surface stability (1906.8 m) takes 83.46% of the total length of the sixth working section of GML1 (2284.8 m). The assessment results indicated that the ground surface stability along the metro tunnel was relatively low as a whole.Correspondingly, the statistics show that more than 50 ground collapses, whose collapse pit diameter (d) is larger than 5 m, caused by human activity had occurred in the urban area of Guiyang city induced by 1998, including about 30 medium-scale collapses (5 m < d < 10 m), 12 large-scale collapses (10 m < d < 20 m), and 8 huge-scale collapses (d > 20 m). According to the design, the sixth working section of GML1 would pass through the areas where ground collapse had occurred. It indicated that the ground collapse was prone to occur during the excavation of the metro tunnel. So, the assessment results of ground surface stability agreed well with the history of ground collapse at the sixth working section of GML1, which confirmed the effective and reasonable effectiveness and rationality of the fuzzy comprehensive evaluation system for ground surface stability proposed in this research.


### 3.5. Engineering Countermeasures

Based on the assessment results of ground surface stability, a series of measures were taken to maintain the stability of the ground surface during the construction of the tunnel of GML1:(1)
The displacement of the ground surface along the entire metro tunnel line was closely monitored, and the ground-penetrating radar was applied to preliminarily detect the underground caves.(2)
Grouting was conducted on the ground in the areas with low or extremely low stability. The grouting borehole diameters were 159 mm and distances were 2.5 m. The grouting slurry consisted of cement slurry and water glass and their volume ratio was 1 : 0.6.(3)
Grouting on the tunnel face was conducted in the areas where the ground surface stability was extremely low. The grouting holes had a diameter of 10 cm and spacing of 30 to 60 cm. The grouting slurry was composed of cement slurry and water glass, and their volume ratio was 1 : 0.6.


## 3.1. Engineering Background

The Guiyang Metro Line 1 (GML1) with a total length of 33.90 km belongs to the urban rail transit system of Guiyang, a city locates in the Southwest karst region of China. The sixth working section of GML1 with a length of 2284.8 m (23689.0 m–25973.8 m) is located in the limb parts of the Guiyang syncline, and no fault crosses the tunneling area. The strata in the tunneling area consist of block stones, red clay, argillaceous dolomite, and limestone. The groundwater is mainly recharged by infiltration of surface water and groundwater table is higher than metro tunnel floor. Preliminary surveys indicate that karst features are widely distributed in the tunneling area. The ground surface along the metro line is prone to collapse due to the tunnel excavation. To ensure the safety of metro tunnel construction and protect citizens, roads, and facilities on the ground, it is essential to assess the stability of the ground surface along the metro terrain line before construction.


## 3.2. Evaluation Indices

Before metro tunnel construction, geological and geophysical surveys were conducted. Based on the survey results, the values of the evaluation indices,I1– I10, were obtained. According to the change of values of evaluation indices, the tunneling area along the sixth section of GML1 was divided into 32 chainage sections and the values of evaluation indices were presented in Table 6.Table 6
Values of the evaluation indices.
Chainage section numberChainage (m)Evaluation indexPBK (%)FSCTBC (m)SBCGHCDGB (m)WFI (m)SFFDPT (m)GCE (m)123689.0–23832.535.70.1052.4010452.100354.605.08223832.5–23874.735.70.1052.7085451.400354.305.08323874.7–23887.835.70.1053.4010450.900354.305.08423887.8–24108.89.50.1055.2085453.3403517.105.08524108.8–24195.09.50.1056.3085450.1803518.535.08624195.0–24260.09.50.1056.3085452.7703519.625.08724260.0–24288.09.50.1057.9090457.9003514.965.08824288.0–24366.39.50.10511.90854511.903514.515.08924366.3–24489.39.50.1054.8030458.1403511.135.081024489.3–24544.69.50.1052.8010450.1003517.375.081124544.6–24607.19.50.1050.5615452.4403516.655.081224607.1–24616.617.60.1050.5615602.4403516.655.081324616.6–24631.217.60.1057.1570605.980353.325.601424631.2–24656.717.60.1055.4280603.120353.115.601524656.7–24687.017.60.1056.7490601.730355.375.601624687.0–24721.217.60.1051.4615604.0403510.045.601724721.2–24775.317.60.1057.9020600.5003515.075.601824775.3–24779.617.60.1055.7315603.4502017.764.651924779.6–24840.717.40.1059.6080602.2902028.044.652024840.7–24871.617.40.1053.7015609.7202027.254.652124871.6–24900.017.40.1053.3420603.0502024.584.652224900.0–24939.417.40.1052.6080602.7702019.984.652324939.4–25000.017.40.1050.7820601.6402010.904.652425000.0–25056.417.40.1059.2080604.5502017.584.652525056.4–25100.017.40.1058.5080606.4002018.554.652625100.0–25153.217.40.1056.4080602.6602021.894.652725153.2–25230.517.40.1058.0080603.8302021.944.652825230.5–25285.617.40.1057.7080603.5302022.214.652925285.6–25340.017.40.1053.5085601.2602020.774.653025340.0–25400.017.40.1057.0085602.1302022.374.653125400.0–25467.317.40.1057.1085601.4402021.954.653225467.3–25973.817.40.1057.4085602.0802020.804.65(20)U=00.00150.9985000.46230.537700001.00001.000000000.85360.14640000.02450.97551.000000001.0000000001.000000.43730.56270.


## 3.3. Extension Assessment Results

Based on the values of evaluation indices, the stability of the ground surface along the metro tunnel line of the sixth section of GML1 was assessed by using the analysis model proposed in this research.


### 3.3.1. Assessment of Ground Surface Stability at Chainage Section 1

The assessment of ground surface stability at chainage section 1 (chainage 23689.0–23832.5 m) was presented to demonstrate the assessment process. The values of evaluation indices at Section1 were presented in Table 7.Table 7
Values of evaluation indices at chainage section 1.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Firstly, the values in Table8 were substituted into the membership functions (Figure 2) to calculate the membership degrees for the evaluation indices, based on which the evaluation matrix was established as shown in equation (20).Table 8
Nondimensional values of evaluation indices.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Secondly, the objective weights for evaluation indices were determined by using relation analysis. The values of evaluation indices were nondimensionalized according to equations (11) and (12) and the results were presented in Table 8. The objective weights of evaluation indices for chainage section 1 were distributed according to equations (13)–(17) and the results were presented in Table 9.Table 9
Correlation analysis for objective weights of evaluation indices.
IndexKijKijmaxjmaxriwioN1N2N3N4c1−5.1400−0.57000.5700−0.57200.570034.7100.1153c2−3.0000−0.03230.0133−0.78010.013333.0400.0744c3−1.1733−1.5200−1.04000.96000.960047.8400.1919c40.8000−1.2000−3.2000−5.20000.800011.8000.0441c5−1.60000.4000−0.4000−2.40000.400022.8000.0686c6−0.3950−1.1600−0.32000.32000.320045.2800.1293c70.0000−3.0000−2.0000−0.50000.000011.0000.0245c8−0.80000.8000−1.2000−3.20000.800023.6000.0881c9−1.8160−2.5400−0.54000.92000.920047.6800.1880c10−3.0800−0.05330.0320−0.24600.032033.0960.0758Combining the subjective weights presented in Table5, the comprehensive weights of evaluation indices for Section 1 were synthesized according to equation (9), where the proportion coefficients of objective weight and subjective weight are valued as ks = ko = 0.5 considering the same importance of objective weight and subjective weight for comprehensive weight of evaluation index. So, the weight set was presented as follows:(21)w=0.1620,0.0891,0.1509,0.0770,0.0784,0.1088,0.0361,0.0560,0.1305,0.1112.Finally, the comprehensive evaluation matrix was established as the following form according to equation (17). And the ground surface stability level was recognized as v4 according to equation (19).(22)C=0.11310.21300.28640.3876.


### 3.3.2. Assessment of Ground Surface Stability for the Sixth Working Section of GML1

The stability of ground surface for other chainage sections was assessed in the same way used for stability assessment for chainage section 1, and the assessment results for ground surface stability along tunnels in the sixth working section of GML1 were presented in Figure4.Figure 4
Assessment results of ground surface stability along tunnels in the sixth working section of GML1.


## 3.3.1. Assessment of Ground Surface Stability at Chainage Section 1

The assessment of ground surface stability at chainage section 1 (chainage 23689.0–23832.5 m) was presented to demonstrate the assessment process. The values of evaluation indices at Section1 were presented in Table 7.Table 7
Values of evaluation indices at chainage section 1.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Firstly, the values in Table8 were substituted into the membership functions (Figure 2) to calculate the membership degrees for the evaluation indices, based on which the evaluation matrix was established as shown in equation (20).Table 8
Nondimensional values of evaluation indices.
Evaluation indexPBKFSCTBCSBCGHCDGBWFISFFDPTGCEValue0.3570.1650.9520.1000.4500.9580.0000.3500.9540.102Secondly, the objective weights for evaluation indices were determined by using relation analysis. The values of evaluation indices were nondimensionalized according to equations (11) and (12) and the results were presented in Table 8. The objective weights of evaluation indices for chainage section 1 were distributed according to equations (13)–(17) and the results were presented in Table 9.Table 9
Correlation analysis for objective weights of evaluation indices.
IndexKijKijmaxjmaxriwioN1N2N3N4c1−5.1400−0.57000.5700−0.57200.570034.7100.1153c2−3.0000−0.03230.0133−0.78010.013333.0400.0744c3−1.1733−1.5200−1.04000.96000.960047.8400.1919c40.8000−1.2000−3.2000−5.20000.800011.8000.0441c5−1.60000.4000−0.4000−2.40000.400022.8000.0686c6−0.3950−1.1600−0.32000.32000.320045.2800.1293c70.0000−3.0000−2.0000−0.50000.000011.0000.0245c8−0.80000.8000−1.2000−3.20000.800023.6000.0881c9−1.8160−2.5400−0.54000.92000.920047.6800.1880c10−3.0800−0.05330.0320−0.24600.032033.0960.0758Combining the subjective weights presented in Table5, the comprehensive weights of evaluation indices for Section 1 were synthesized according to equation (9), where the proportion coefficients of objective weight and subjective weight are valued as ks = ko = 0.5 considering the same importance of objective weight and subjective weight for comprehensive weight of evaluation index. So, the weight set was presented as follows:(21)w=0.1620,0.0891,0.1509,0.0770,0.0784,0.1088,0.0361,0.0560,0.1305,0.1112.Finally, the comprehensive evaluation matrix was established as the following form according to equation (17). And the ground surface stability level was recognized as v4 according to equation (19).(22)C=0.11310.21300.28640.3876.


## 3.3.2. Assessment of Ground Surface Stability for the Sixth Working Section of GML1

The stability of ground surface for other chainage sections was assessed in the same way used for stability assessment for chainage section 1, and the assessment results for ground surface stability along tunnels in the sixth working section of GML1 were presented in Figure4.Figure 4
Assessment results of ground surface stability along tunnels in the sixth working section of GML1.


## 3.4. Regional Ground Collapse History

From the stability assessment results, it could be seen that the ground surface stability was medium (N2) only in chainage sections 7–9 while the stability was low (N3) or extremely low (N4) at the rest of chainages. The amount of chainage sections with low or extremely low ground surface stability (28) takes 87.5% of the total section numbers (32). And the length of chainages with low or extremely low ground surface stability (1906.8 m) takes 83.46% of the total length of the sixth working section of GML1 (2284.8 m). The assessment results indicated that the ground surface stability along the metro tunnel was relatively low as a whole.Correspondingly, the statistics show that more than 50 ground collapses, whose collapse pit diameter (d) is larger than 5 m, caused by human activity had occurred in the urban area of Guiyang city induced by 1998, including about 30 medium-scale collapses (5 m < d < 10 m), 12 large-scale collapses (10 m < d < 20 m), and 8 huge-scale collapses (d > 20 m). According to the design, the sixth working section of GML1 would pass through the areas where ground collapse had occurred. It indicated that the ground collapse was prone to occur during the excavation of the metro tunnel. So, the assessment results of ground surface stability agreed well with the history of ground collapse at the sixth working section of GML1, which confirmed the effective and reasonable effectiveness and rationality of the fuzzy comprehensive evaluation system for ground surface stability proposed in this research.


## 3.5. Engineering Countermeasures

Based on the assessment results of ground surface stability, a series of measures were taken to maintain the stability of the ground surface during the construction of the tunnel of GML1:(1)
The displacement of the ground surface along the entire metro tunnel line was closely monitored, and the ground-penetrating radar was applied to preliminarily detect the underground caves.(2)
Grouting was conducted on the ground in the areas with low or extremely low stability. The grouting borehole diameters were 159 mm and distances were 2.5 m. The grouting slurry consisted of cement slurry and water glass and their volume ratio was 1 : 0.6.(3)
Grouting on the tunnel face was conducted in the areas where the ground surface stability was extremely low. The grouting holes had a diameter of 10 cm and spacing of 30 to 60 cm. The grouting slurry was composed of cement slurry and water glass, and their volume ratio was 1 : 0.6.


## 4. Conclusion

This study has established an evaluation system for assessing the stability of ground surface along tunnels in karst terrain using a fuzzy comprehensive evaluation method. The major conclusions were drawn as follows.The works of stability assessment of ground surface along the tunnel in karst terrain mainly contain establishment of evaluation index system, establishment of membership functions for evaluation indices, weights distribution for evaluation indices, and fuzzy comprehensive evaluation of ground surface stability. The selection and quantitatively grading for evaluation indices were conducted based on related case analysis and review of related researches. The evaluation index weights were determined by a comprehensive weighting method combining the FAHP and correlation analysis. These characteristics make the proposed evaluation system a reliable tool for assessing the stability of ground surface along tunnels in karst terrain.The comprehensive weighting method was applied to distribute weights for evaluation indices. The evaluation indices were nondimensionalized during the determination of objective weights for evaluation indices. The nondimensionalization can eliminate the differences of evaluation indices units and make these indices comparable. The comprehensive weighting method combining FAHP and correlation analysis considers not only human subjective cognition but also factual information of objects, which can highly reduce the errors generated by using a single weighting method and significantly improve the accuracy of evaluation indices weights.The proposed fuzzy comprehensive evaluation system was applied to assess the stability of the ground surface along the metro tunnel of the sixth working section of GML1. The assessment results agreed well with the history of regional ground collapse, indicating that the assessment results were reliable. The proposed evaluation system provides a valuable tool for assessing and guiding to improve stability of ground along tunnels in karst terrain, and the methodology proposed in this research can be also referred to solve other decision-making problems in engineering, such as water inrush risk, slope stability analysis, and method selection for tunnel construction.The proposed evaluation system inevitably has limitations. Some of the evaluation indices are quantitatively graded with certain subjective. As the membership functions are closely related to grading standards of the evaluation indices, the evaluation index system highly affects the assessment result, which should be improved in the future research.



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*Source: 5523668-2021-03-18.xml*