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Due to the uncertain nature of tunneling projects and the need for optimum disbursement of the resources, risk management of these projects is ¬of great importance, and a key element of the accuracy of this management process is rating of the risks with the aim of identifying the priority of each risk for ¬ proper planning on the part of decision makers in allocating the resources to deal with risks .
Tunneling projects are consistently associated with a high percentage of risk due to related uncertainties, and minimizing the probability of risk occurrence or negative impacts of it on implementation of these projects require accurate and timely management of subsequent risks, ¬which are frequently neglected. For example, in a global survey on tunneling projects , 30 to 50 percent increase in time and costs has been reported due to faulty management. Based on another survey (among English companies in 1994), 40% of the projects have surpassed the specified time or budget, and in more than 60% of them, the risk management of the organization has been evaluated as poor .
In recent years, risk assessment in tunneling projects has become considerably important, and several studies in this field have been reported. In the studies conducted by the International Tunneling Association, the product of the probability of an event has been used to define the concept of risk .
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In these studies, risk assessment results are not reliable and realistic due to the use of risk 'effect' and 'probability' indices in the form of probability-impact risk rating matrix (I-P Matrix) , since by using this matrix and considering the high probability and low impact risks equivalent with low probability and high impact ones may ignore low probability and high impact risks, resulting in systematic error . Therefore, further studies with respect to several risk factor indices have been conducted.
The indices of "organization's ability to respond to risk"  and "estimation uncertainty"  have been addressed for assessment and rating in some projects. Baccarini & Archer have applied probability and degree of impact on time, cost and quality of the project in risk rating . Waterland et al have used the three criteria of occurrence, severity of impact and tracking for risk assessment . In addition to probability and impact matrices, Haimes used risk management capabilities and risk exposure to prioritize the risks . In some project control software, the two complementary indicators of accessibility and proximity of risk occurrence have been considered . In other sources, socio-economic and environmental impact indicators have been applied .
Today, prioritization of multivariate decision-making units based on their relative importance and applying the experiences of individuals ¬with expertise, skills, and scientific perspectives has become important. Group and multivariate decision making techniques (e.g., linear assignment method) are appropriate tools to rate risk and make correct decisions in this field . In these techniques, using the aggregation of several expert opinions instead of a single one involves more details in decision-making analyses .
In this study, the main risks in construction operations of Golab water tunnel, which is excavated by TBM, have been identified, assessed and ranked. Risk identification is the first step in risk management process, and risk breakdown structure technique has been used to identify and group the risks in this study. Risk breakdown structure (RBS) is a hierarchical structure of project risks, which can be used for structuring and guiding the risk management process . Given the large number and variety of risks affecting the tunneling projects, efficient and effective risk management is not virtually possible without identification and preparation of RBS. On the other hand, any measure to understand and deal with risks is difficult without a systematic and accurate procedure for the identification and management of risks. ¬ Using RBS can contribute to this, since it presents an effective tool for targeted and classified risk identification . Afterwards, group decision making procedure has been used to gather expert opinions, and average agglomeration method was used to aggregate the expert opinions. In addition, linear assignment has been used as a multi-criteria decision making method to rate the risks.
1.2 Linear assignment method
Multivariate decision ¬making methods are used to select the optimum choice from among m available options, and a distinctive feature of them is presence of a few numerable options in advance. The best option in a multi-criteria model will be the option providing the most preffered value from each available characteristic. Modeling is based on development and formation of contingency tables .
Linear assignment is among these important methods. The basis of rating ¬in linear assignment method is the total of assumed options of a problem from each index option, and the final rank of the options is specified by a linear compensation process. In this way, based on the property of simplex solution space, while considering all the arrangements implicitly, optimal solution is extracted within a convex simplex space. Moreover, the compensatory effect of indexes results from exchange between ranks and options, although the index weight vector is obtained based on expert opinion. The main Advantage of this multi-criteria decision making method is taking advantage of both hard and soft (combination) skills. In soft decision making techniques, model expression is based on a contingency table, while in hard decision making techniques, the model is defined based on a system of mathematical equations. Combination decision-making techniques apparently follow the logic of soft techniques, and are defined according to contingency table but take advantage of methematical equations system practically in the solution process; therefore, they have the strengths of both hard and soft techniques . On the one hand, this method causes exchange between indices and lacks complicated calculations using a simple rating for the options, and on the other hand, there is no requirement for measuring scales, and the indices can be of any scale .
This method of rating is applied in the following steps : ¬
- Determining the risk rating for each index: formation of a matrix (m × m), in which the row indicates rank and the column shows index.
- Formation of allocation matrix or matrix-gamma (γ): formation of a square matrix (m × m) with line as I showing risk and column as k showing rank. Components of γ matrix ( ) are the total weight of indices whose ith risk has the kth rank.Gamma matrix is an allocation matrix giving the optimal solution using any of the allocation methods (transport, Hungarian method, grid method and linear zero and one programming method). The most common solution method in linear assignment is the linear programming method.
- Rating based on linear programming: Rating is done according to the following models.
2.2 Shannon entropy method
This is an appropriate technique to extract the coefficient of indices in problem solving procedure using linear assignment method, which is done in the following steps :¬
- Converting the value of entry (decision matrix) to :
- Calculation of value of the jth characteristic entropy:
- Calculation of vakue for each characteristic:
- Calculation of weight of kth characteristic:
To apply an importance coefficient for each index ( ), weight is calculated according to the below equation:
3. Risk assessment criteria
In general, validity of the risk assessment results are subject to the comprehensiveness of studied factors, although in most studies for tunnels, a comprehensive set of risk assessment criteria have not been simultaneously introduced and used. Table 1 shows risk assessment criteria in two categories, primary and secondary (complementary) with associated symbols. In this table, the positivity of impact aspect of each criterion indicates higher criticality of that risk and vice versa. Another important point in this table is independence of criteria from each other and lack of logical significant correlation between the indices.
Table 1. Risk assessment criteria along with sign and impact aspect
Definition Impact aspect Symbol criterion
Indicates that the estimator expects the occurrence of risk. Positive C1 Likelihood of risk
Capacity of predicting the risk occurrence and exposure of risk during occurrence Negative C2 Risk discovery rate
Indicative of replication rate and risk exposure during project implementation Positive C3 Exposure to risk
Indicative of the capacity to predict risk occurrence and ability to manage and respond to it Negative C4 Management of risk-taking
Indicative of the uncertainty of analyst from risk assessment values Positive C5 Uncertainty of estimates
Indicative of the negative effect of risk on the timing of project Positive C6 The effect of risk on time
Indicative of the negative effect of risk on project costs Positive C7 The effective of risk on cost
Indicative of the negative effect of risk on quality of project Positive C8 The effect of risk on quality
Indicative of the negative effect of risk on the rang of project activities Positive C9 The effect of risk on the range
4. Risk assessment of water tunnel of Golab
4.1 - Golab water tunnel introduction
Golab water tunnel and access tunnel in continuation of it with a total length of 11 kilometers from the eastern slopes of Zayanderud River under Corun Plain has been designed and implemented to supply water for Kashan County. Geographically, the tunnel is located 110 km to northwest of Isfahan, and is located geologically in part of Sanandaj-Sirjan zone. The main tunnel has been excavated using a full section mechanized TB458/TS model excavation machine with dual (telescopic) shield and prefabricated hexagonal concrete wall coverage towards the junction of the access tunnel .
4.2 Identifying the risks of tunnel excavation operations
As noted above, the first step in risk assessment and management is identifying the project risks; therefore, the main risks of Golab water tunnel were classsified using RBS method (Table 2). This table has followed the Work Breakage Structure (WBS), and presents a hierarchical structure of risks associated with excavation operations of Golab water tunnel. The designed structure includes three levels. In the first level, the overall risks of Golab water tunnel in three sets of internal, external-internal and external have been classified. In the second level, the risks have been classified based on RBS method in the form of five subsets, and in the third level in the form of 25 main risks (risk factors). We have attempted to analyze and classify the risks as comprehensive as possible to minimize their interface, and present the risks in an appropriate understandable form compatible with risk and project management.
Table 2: Hierarchical structure of risks of Golab tunnel at 3 levels (including 25 main risks)
Level zero Level 1 Level 2 Level 3
Risks associated with excavation of Golab tunnel using TBM TBM Internal risk Technical risks Alignment of the machine in the wrong path R1
Low rate of machine progress R2
Electrical and mechanical problems in the machine R3
Segment not preventing water entry R4
Crack and breaks in segmen R5
Workforce risks Low experience staff R6
Workforce clash and accident R7
Management risks Defective equipment R8
Delayed equipment and support of the instrument R9
Internal-external risks Operation risks TBM shield arrest R10
Instrument cutter head clog R11
Fire or explosion event R13
Segment ring distortion R14
External risks Environmental risks Unstable walls and ceiling of the tunnel R15
Work front unstability R16
Seepage and groundwater influx R17
Gas leak R18
Excessive wear of cutting tools
Injury or damage caused by mental ¬ orientation R20
Chemical corrosion R21
Realizability crush (Crush)
Swelling of clay rocks
Mixed work front R24
Sticky clay soils and rocks
5.2 Rating steps of tunnel risks
5.2.1 Collection and aggregation of experts' opinions
First, due to the main identified risks of the third level (R1 to R25) and nine assessment criteria (Table 1), a questionnaire was designed, and expert opinions were collecting by taking advantage of group decision making techniques. Table 3 shows the scoring range for each of the studied risk indices.
Table 3: Scoring range and linguistic variables for criteria values for each risk 
Very high High The average high Average Average low Low Very low Variable expression
10 9 7 5 3 1 0 Value
Thus, the decision matrix containing 225 entries includes 25 rows (main risks) and 9 columns (assessment indices) was formed, and the entry values were the average of scores collected from experts (Table 4).
2.2.5 Calculation of the weight of indices
At this point, the weight of each of the nine indices (W i) was obtained by combining expert views and Shannon entropy method according to equations 1 to 5, which is shown in Table 5.
Table 5: Calculation of final weight of each index by combining expert opinions and Shannon entropy
5.2.3- Rating the risks
Risk rating (R1 to R25) was done based on nine indicators in three steps using linear assignment method. Firstly, the rank of each risk for any of the available indices was calculated as a matrix (9 × 25), of which the row indicates rank and column indicates the index, and the results are shown in Table 6.
Table 6: Risk rating for each one of the indices
Secondly, the allocation matrix or gamma matrix ( ) was formed as a square 25 × 25 matrix, the row of which showed the i risk and the column shows k rank. The components of this matrix ( ) consisted of the set of index weights, in which the ith risk had the kth rank. The results of this step are presented in Table 7.
In the third step, risk rating was done¬ using linear programming method and the model presented in equations 1-3. In this study, given the high load of computing (625 decision variables), LINGO software was used. Since the decision variables have the value of 0 or 1, the output of this program for values of 1 indicates the rank of the risk under study. For example, h (15, 5) indicates rate 5 for risk No.15, and h (11, 8) indicates rate 8 for risk No.11. Accordingly, the risk rating ¬is presented in Table 8.
As can be seen, R22 and R17 have the lowest rating (first and second, respectively), and are identified as the most critical risks in this study. Therefore, project management must give priority to ¬solving and controlling these risks in its reaction and management measures, and the other risks have a lower rank in terms of criticality.
Finally, to rank the level 2 risks (five risk categories), the rate of each category can be determined by calculating the rate of main risks (Table 9). As can be seen, management risks have the lowest rate.
Table 9: Rating the five main risk categories according to the rank of the main risks
Risky construction projects such as tunneling require necessary meaures for risk managament and solution through correct identification and rating of the vital risky factors. In this study, we have dealt with rating the studied risk factors by linear assignment method considering both traditional risk assessment criteria (including probability and risk impact) and complementary indices by identifying the risk factors of Golab water tunnel and aggregating the expert opinions. Higher validity of the results of this method relative to the traditional method is due to additional assessment indices, simultaneous consideration of a few indices, considering different weights for indices, exchange between the indices, flexibility of the method and more analytic results. In this case study, crush ¬realizability (crush), leakage and flow of ground water and overerosion of cutting tools have respectively the lowest and highest criticality of risk, and should be in priority of reactionary and risk management measures.
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