A Study of Safety Coefficient Determination and Support Parameter Optimization Based on Vulnerability Preevaluation

Institute of Disaster Prevention, Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment, Langfang 065201, China Key Laboratory of Building Collapse Mechanism and Disaster Prevention, China Earthquake Administration, Langfang 065201, China North China Institute of Science and Technology, Langfang 065201, China School of Mine, China University of Mining and Technology, Xuzhou 221116, China


Introduction
Due to the influence of complex natural stress field in the surrounding rock, deep mining will face more intricate engineering rock mechanics problems than shallow mining [1]. Generally speaking, the limit of the transition from shallow to deep is called the limit depth, and the gateway whose depth exceeds the limit depth is called a deep gateway. e surrounding rock support of gateways above the limit depth is relatively simple and easy to maintain, but it is relatively difficult below. With the increase of mining depth, high stress environment, soft rock, large deformation, and other issues affect the stability of roadway surrounding rock and threaten the safety production of coal mine [2]. erefore, many support methods, such as steel support, anchor rod, anchor cable, and shotcrete, are applied to the surrounding rock control of the deep gateways. In particular, bolt support, due to the advantages of good support effect, low support cost, simple technology, and low labor intensity, has gradually become the main means of coal mine gateway support.
As a key in bolt support of coal mine gateway, reasonably designed support parameters can maximize the advantages of bolt support and achieve the safety of gateway. Due to the complex underground geological environment, a safety coefficient is often included in the anchor design to ensure the safety construction. However, the safety coefficient is usually identified based on the empirical value.
is approach is featured with randomness [3]. An overly high safety coefficient tends to lead to an unnecessarily high support strength, jeopardizing the construction progress and increasing the cost accordingly. On the other hand, an underestimated safety coefficient can result in insufficient bolt support strength, risking the construction safety [4]. erefore, it is of great significance to select a reasonable safety coefficient for the purpose of efficient operation of anchor bolts and construction safety [5].
Generally speaking, the determination of the safety coefficient of the gateway needs to refer to the damage degree of the surrounding rock of the gateway, which can be expressed by the degree of vulnerability [6]. Vulnerability can be used to describe the vulnerability of relevant systems and their components. Insufficient bearing capability will degrade the system to its original state [7]. Furthermore, vulnerability is often considered and analyzed together with sensitivity and stability in the field of underground gateway engineering [8][9][10][11]. However, under most of cases, qualitative results are often drawn from the analysis. Since the gateway stability evaluation fails to correlate with the support parameters of the surrounding rock directly, it can only provide qualitative guidance to the gateway support parameters design and optimization instead of quantitative calculation guidance. Meanwhile, the optimization of the gateway support tends to occur in the case of major gateway deformation observed, which easily attracts the attention of researchers [12][13][14]. However, for gateways with small deformations, due to various safety risk concerns and the lack of quantitative evaluation methods, reducing the excess support strength is often overlooked with little optimization. Maintaining the status quo is preferred by the authorities.
is mindset and approach slow down the excavation speed and increase the cost related to the supporting system, jeopardizing the goal of high production and efficiency.
In this paper, the preevaluation to the vulnerability of the surrounding rocks is proposed as one of the reliable indicators of the safety coefficient of gateway support and a foundation to optimize the support design parameters. Taking the surrounding rocks, stress, geological environment, and service time into consideration, a vulnerability preevaluation model is established through the analytic hierarchy process method. Following the theory of composite rock-bolt bearing structure, the bolt support parameters are identified through the quantitative calculation. e proposed approach has been applied to the gateways with both major deformations and small deformations, proving to be effective in reducing overly estimated bolt support strength.

Instability Criterion of Composite Rock-Bolt Bearing Structure
In order to maintain the stability of the surrounding rock stable, preloaded bolts are installed to reinforce the roof and two ribs of gateway. e preloaded bolts of proper dimensions and materials, together with the supporting accessories, form a bearing structure to the gateway surrounding rock, providing some strength and bearing capability. e geometric form of composite rock-bolt bearing structure is shown in Figures 1(a) (arch) and 1(b) (rectangle). e strength of composite rock-bolt bearing structure can be calculated by [15,16] where p i is the bolt support strength, d refers to the diameter of bolt, σ b indicates the tensile strength of bolt, C s stands for the column spacing of bolt, and R s shows the row spacing of bolt. If the gateway shape is arch, where R means the radius of arch gateway, and b indicates the thickness of composite rock-bolt bearing structure, which can be calculated by the sum of the thickness of internal nonuniform compression band (b 0 ) and the thickness of uniform compression band b 1 . Bolt length is supposed to be l. b 0 and b 1 can be calculated by If the gateway shape is arch, where R 1 stands for the outer boundary curve radius of composite rock-bolt bearing structure for rectangle gateway, β is the center angle corresponding to outer boundary curve of composite rock-bolt bearing structure for rectangle gateway, and B indicates the width of gateway. R 1 and β can be calculated by e gateway strata weight is mainly borne by the deep surrounding rock, while the formed composite rock-bolt bearing structure mainly bears the weight of the loose strata of the gateway. According to the field damage conditions of the underground gateway and related research, when the external load exceeds the strength of the composite rock-bolt bearing structure, serious roof falling and excessive deformation will be observed in the gateway. erefore, in order to ensure the stability of the composite rock-bolt bearing structure during the service life of the gateway, calculating the weight of the potential loose overlying rocks and determining the external load borne by the composite rockbolt bearing structure become crucial. According to the relevant researches, the thickness h of the potential loose rock layer of the gateway roof is calculated as follows [17]: 2 Shock and Vibration where φ is the internal friction angle of the roof stratum, and λ refers to the lateral pressure coefficient. Following the method mentioned above, the evenly distributed load on the composite rock-bolt bearing structure is calculated, and its strength is tested. When the upper evenly distributed load is less than the strength of the composite rock-bolt bearing structure, the composite rock-bolt bearing structure is stable with limited displacement. Under the event that the upper evenly distributed load is greater than the load limit of the composite rock-bolt bearing structure and a low shrinkage of the bearing structure, the bearing structure tends to fail, resulting in the gateway roof collapse. On the other hand, a bearing structure with a high shrinkage rate can cause dramatic deformation and eventually lead to the gateway failure. Considering a reasonable safety coefficient, the instability evaluation of composite rock-bolt bearing structure should be based on where n refers to the safety coefficient, whose value is determined by the vulnerability preassessment of the gateway surrounding rock. Whenq < nch, the composite rock-bolt bearing structure is most likely to fail during the service period. However, due to volatility of the geological conditions, drastic deformations occur more commonly to the bearing structure.

e Vulnerability Evaluation System and Indicators.
According to the analysis on the factors that affect the vulnerability of the gateway surrounding rocks, the indicators are selected to evaluate the vulnerability of the gateway surrounding rocks. Based on the Analytic Hierarchy Process (AHP) [9], the indicators were divided into three levels, as shown in Figure 2. e scores and evaluation level are listed below: (1) Scores for the characteristics of the surrounding rocks (i) e integrity of the surrounding rocks e integrity of the surrounding rocks can be influenced by the number of rock planes, shape, spacing, and roughness of the surrounding rock structure. e surrounding rock integrity is rated based on RQD for various integrity level and shown in Table 1.

Shock and Vibration 3
compressive strength of the roof rock mass. e surrounding rock strength is rated and presented in Table 2. (iii) Roof rock layer e reinforcement effect of the bolts varies depending on various rock layers, such as the rock roof, coal roof, and composite roof, making the rock layer an important factor to evaluate the roof stability. e impact of the rock layer characteristics on the stability evaluation is rated and presented in Table 3. (iv) Gateway type e gateway type refers to the combination of various surrounding rocks of the gateway including the rock gateway, the coal gateway, and the semicoal gateway. e gateway type is rated and presented in Table 4.
(v) e inclination angle of the surrounding rock e inclination angle of the surrounding rock is considered as one of the important factors to evaluate the vulnerability of the gateway surrounding rock, which is rated and presented in Table 5.
(2) e stress (i) e vertical stress e vertical stress is a fundamental factor to the deformation and failure of the gateway surrounding rock. e vertical stress is rated by the buried depth and presented in Table 6.
(ii) e horizontal stress        Shock and Vibration e influence of horizontal stress on the surrounding rock can be represented by the maximum principle horizontal stress and the angle between the axis of the gateway and the orientation of the maximum principal horizontal stress, which are often considered as key factors to evaluate the stability of the gateway surrounding rocks. e maximum horizontal principal stress and the angle between the gateway axis and maximum principal horizontal orientation are rated and presented in Tables 7  and 8, respectively. (iii) e construction disturbance During the service period of gateway, the surrounding rock vulnerability is affected by the disruptions generated by the excavation or mining [18]. During the excavation, the width of the protective coal pillar often leads to the stress redistribution, which can be used to indicate the disruption received by the surrounding rocks. e abutment pressure σ z was considered to consist of stress increment ( σ i ) and geostatic stress (σ q ), as shown in Equations (9)-(11) [19].
where σ i (i � 1 − n)is for the abutment stress transmitted from the suspended part of a key layer to solid coal, and n refers to the number of key layers.
where σ imax is the maximum abutment stress transmitted from the suspended part of ith key layer to solid coal, σ i max � Q i /H i cot α, Q i is the gravity of half of the suspended part of ith key layer, Q i � L i M i c/2L i refers to the suspended length of the center line of ith key layer in thickness direction,cL i � 2I + 2H i cot αindicates the strata bulk density, M i is the thickness of ith key layer, H i means the distance from coal floor to the center line of ith key layer in thickness I refers to half of the gob width, and His the buried depth of coal. According to Equations (9)-(11) and curve of abutment pressure distribution shown in Figure 3, the stress on the solid coal was divided into four parts, and the vulnerability of gateways driven in different areas was listed from low to high: IV < I < III < II [19]. Besides, retaining gateway along gob (pillar width is 0 m) was considered as a specific condition without coal pillar and was more difficult to control the stability of surrounding rock [20]. e construction disturbance degree is rated by the protective pillar widths and presented in Table 9.
e scores corresponding to various states of disturbance times are shown in Table 10.
Common geological structures in coal mine include folds, faults, and collapse columns. e influence of geological structure on the surrounding rock is evaluated based on the quantity and scale of geological structures within a radius of 50 m around the area to be assessed [21]. e scale of structure is rated into three levels, small (S), medium (M), and large (L). e scores of various geological structures are shown in Table 11. (v) Section parameter e section parameter comprises the section type and section size, which exert significant impact on the stress distribution and stress concentration of the gateway surrounding rock. e scores for the section type and section size are shown in Tables 12 and 13 separately. (3) Geological Environment (i) Underground water Water accumulations in the boreholes degrade not only the strength of the anchor bolts, but also the strength of the surrounding rock, which jeopardizes the stability of the gateway surrounding rock. Besides, due to the softening property, the inhaled water tends to degrade the rock strength [22]. e scores of the groundwater are shown in Table 14.
(ii) Underground temperature e temperature around the borehole can influence the resin anchor-hold [23]. e scores of the underground temperature are provided in Table 15. conducted by machines and auto systems, such as borehole stress meters, deep displacement meters, and data storage equipment. Smart monitoring indicates the smart data monitoring and analysis [24]. e scores of inspections and maintenance are shown in Table 16.
(ii) Service time With the increased service time, the gateway surrounding rock often develops the creep deformation, which escalates the internal damage, resulting in higher vulnerability of the gateway surrounding rock [25]. e scores of service time are shown in Table 17.

Confirmation of Weighted Values. (1) Calculation Steps.
Taking expertise of various experts into consideration, according to the principles of AHP, a judgement matrix was developed. E is defined as the comparative matrix, as shown in In the judgement matrix, E ij refers to the ratio between magnitude E j and magnitude E j under condition E: where E i is to evaluate the ith factor, and E j is to evaluate the jth factor, and Factors E i and E j E j are evaluated and compared via the judgement matrix by following a 1-9 scale method, as shown in Table 18.
irdly, both maximum eigenvalues λ max and the corresponding eigenvectors included in the judgement matrix were calculated via MATLAB software.
Fourthly, a judgement matrix consistency test was conducted. Since both subjective and approximate evaluations are included during the development of the judgement matrix, deviations are possible. us, a consistency test is required. e CR ratio can be calculated by where CR is the consistency ratio, CI represents the consistency indicator, CI � (λ max − t)(λ max − t)/(t − 1)t displays the order of the matrix, and RI refers to the mean random consistency index, which is shown in Table 19.
Both CI and CR must be below 0.1 [22][23][24][25]. Lastly, the weight of each indictor was calculated. After the consistency test, the weight values were determined by following the steps listed in Figure 4.
(2) Calculation Results. In order to demonstrate the weight value calculation process, the indicators for layer-1 are explained in detail below. e judgement matrix built is shown as      Table 20.

Vulnerability Evaluation.
e value of a gateway surrounding rock's vulnerability evaluation can be calculated according to the weight listed in Table 19 and Eq. (16). "e" denotes "excavation disturbance" and "m" refers to "mining disturbance". "1e" indicates the gateway suffering once excavation distribution, while "2e and 1m" mean the gateway suffering twice excavation distribution and once mining distribution.        where V j− 1 is the comprehensive score of layer-j, V 0 is the vulnerability score, s ij is the evaluate score of ith factor in layer-j, andw ij is the weight of ith factor in layer-j.

Vulnerability Score and Safety Coefficient.
After calculating the vulnerability score, the vulnerability of surrounding rock can be rated into five levels. e corresponding safety coefficients are exhibited in Table 21.

e Case of Increasing the Density of the Bolt Support
System. In order to examine the feasibility and effects of increasing the density of the bolt support, Gucheng coal mine of Luan Group, located in Shanxi Province, China, was selected. No water flooded into the tunnel when the main inclined shaft penetrated the soil surface and weathered bedrock section. However, after the main shaft entered into the bedrock section and reached certain depth, water was detected and even burst in the anchor boreholes. e anchor cable pull-out tests revealed that the anchor force dropped by nearly 32% and the anchor-hold was decreased by about 15%, which indicates that the water flooding and burst severely degraded the support for the main inclined shaft, resulting in a 100 mm deposition of the gateway roof with local cracks. is change significantly jeopardizes the 65year designed gateway surrounding rock support.    Based on the survey and the field investigation to the boreholes and the drainage holes, two new aquifers were identified between gateway mileage points 580 m and 740 m. During the gateway construction, cracks were generated around the anchor cable when the cable went through the aquifer and the middle-layer surrounding rock, which allowed the water to flow out from the anchor cable boreholes ad anchor bolt boreholes. Due to the tight schedule and the lacking of the emergency response plan, the project supervisor decided to replace the anchor cable with the anchor support. erefore, the vulnerability evaluation should be conducted to the gateway surrounding rock and develop optimization to the anchor bolt support parameters. e evaluation parameters of the main inclined shaft are shown in Table 22. e main inclined shaft gateway penetrates different rock strata with a vertical depth of around 40 meters for this section. In order to ensure the gateway safety, the most unfavorable parameters to the stability of the rock strata are taken. e main inclined shaft is jointly supported by anchor cable and a 150mm thick shotcrete. From the perspective of conservative estimation, without taking the bearing load of 150 mm thick shotcrete into account, the detailed parameters of the main inclined shaft are shown in Table 23.
According to Table 22 and Equation (11), the vulnerability score of the main inclined shaft is rated at 5.67, and the vulnerability preevaluation level is identified as IV with a safety coefficient of 5.2. e instability criterion for the main inclined shaft is illustrated as Based on the information listed in Table 23 and Equation (1), the strength of the composite rock-bolt bearing structure of the main inclined shaft is 1.5 MPa, which is below 1.55 MPa calculated by vulnerability preevaluation. is result is further validated by the increased deformation of the gateway roof and the cracks found in the shotcrete.
Based on the existing bolt types, reducing the distance among anchor bolts was recommended to increase the strength of the composite rock-bolt bearing structure. When the distance among anchor bolts was 824 mm, the strength of the composite rock-bolt bearing structure reached 1.55 MPa. Considering the safety construction, 800 mm was selected for the distance among anchor bolts, which provided 1.567 MPa as the composite rock-bolt bearing structure. e optimized supporting parameters can be viewed in Figure 5.
After the optimization, a deformation observation station is set at gateway mileage 594 m. As the deformation curve and the image of the completed optimization demonstrated in Figure 6, the control and support to the surrounding rock are improved. e observation for continuous 40 days suggests that the gateway roof deposition is 27 mm, and the heave at the bottom of the inclined shaft is measured at 6 mm. In addition, the deformation between two ribs is limited to 38 mm. e deformation rate grows lower on the eighth day after the excavation, indicating that the deformation of the main inclined shaft has been effectively controlled. More specifically, water has a great impact on the safety of underground engineering, especially the long-term use of underground engineering. In order to further reduce the influence of water on the stability of surrounding rock, the grouting reinforcement measure was applied in the main inclined shaft. Parameters and effect of grouting reinforcement are shown in Figure 7.

4.2.
e Case of Reducing Bolt Support Density. N1303 working face is located at Gucheng No. 1 mining zone, which mainly mines Coal seams #3 with a 6 m thickness through a fully mechanized caving technology. e tunnel for the conveyer in N1303 was excavated 600 m ahead the tailgate N1303.
e deformation of conveyer tunnel is well controlled during excavation with low excavation speed (only 6.4 m/d), resulting in a high construction cost. Gateway layout of N1303 working face is shown in Figure 8.
In order to increase excavation speed and reduce the cost of the supporting system, the vulnerability preevaluation method was adopted to identify the safety coefficient of the tailgate N1303 and develop an optimization plan. e evaluation parameters of tailgate N1303 are shown in Table 24.
e detailed parameters of tailgate N1303 are shown in Table 25.
According to Table 24 and Equation (11), the vulnerability score of tailgate N1303 is rated at 3.88, the vulnerability preevaluation level is identified as II, and the safety coefficient is 3.95. erefore, the instability criterion of tailgate N1303 is expressed as Based on Table 25 and Equation (1), the strength of the composite rock-bolt bearing structure in tailgate N1303 is identified as 1.094 MPa, higher than the 0.969 MPa calculated by vulnerability preevaluation. Considering the existing bolt types, increasing the bolt column spacing and row spacing is recommended to lower the strength of composite rock-bolt bearing structure. With a 900 mm bolt row distance and a 1015 mm row spacing, the composite rock-bolt bearing structure strength reached 0.969 MPa. Considering the safety construction, 1000 mm was selected for the distance among anchor bolts, which provided 0.973 MPa as the composite rock-bolt bearing structure. e optimized supporting parameters can be viewed in Figure 9.  After the optimization, a deformation observation station A is set at mileage 50 m to measure the deformation during excavation period (as shown in Figure 10(a)), while an observation station B is set at mileage 1690 m to measure the deformation during mining period (as shown in Figure 10(b)). e observation for continuous 40 days suggests that the tailgate N1303 roof deposition is 55 mm, and the heave at the tailgate bottom is measured at 6 mm. In addition, the deformation between two ribs is limited to 77 mm. e deformation rate grows lower on the tenth day after the excavation, indicating that the deformation of the tailgate N1303 has been effectively controlled.
As demonstrated in Figure 8(b), the deformation started to increase in the surrounding rock of the N1303 tailgate when the distance between the measuring station and the coal wall was at 93 m. When the distance was decreased to   35 m, the deformation increased drastically. During the excavation, the roof deposition reached 272 mm with a heave of 102 mm at the bottom. In addition, the deformation between two ribs is limited to 326 mm, suggesting that the deformation of the N1303 tailgate meets the desired specification. e N1303 conveyer tunnel and tailgate N1303 are compared in Table 26 in terms of technology and economy.
As the data shows in Table 26, the total amount of roof deformation increased by 40.9%, the total amount of floor deformation increased by 92.4%, and the total amount of two ribs deformation increased by 35.2%. e average stress of bolt       during excavation increased by 55.5%, and the average stress of anchor during excavation increased by 104%. Although the percentage of growth is relatively large, the absolute value of growth is not large, and the total deformation of N1303 tailgate is still within the acceptable limit. In addition, after the optimization, the excavation speed increased by 40.6%, and the cost decreased by 25.6%. erefore, the optimized support scheme can improve the driving speed and reduce the support cost on the premise of ensuring the gateway deformation.

Conclusion
(1) In this study, taking the surrounding rock, stress conditions, geological environment, and service time into consideration, a vulnerability preevaluation model is established by adopting the analytic hierarchy process. (2) A vulnerability preevaluation method to the surrounding rock is proposed as the basis to evaluate the gateway support safety coefficient and optimize the design of the support system. e safety coefficient is obtained based on the vulnerability scores of the surrounding rock through the vulnerability preevaluation model. Applying the safety coefficient factor to the composite rock-bolt bearing structure for the instability evaluation, a required strength of the composite rockbolt bearing structure can be identified quantitively with the optimization of the anchor bolt support. (3) is method has been successfully adopted to optimize the anchor bolt support in the gateway water pool area of the main inclined shaft located in the Gucheng Coal Mine. e application suggests that this method can effectively maintain the stability of the surrounding rock and lower the support strength of the anchor bolt in N1303 tailgate, resulting in lower cost and increased excavation speed. is method provides reliable basis for the gateway bolt support optimization in coal mining industry.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.