Developing a cloud model based risk assessment ... - Springer Link

Stoch Environ Res Risk Assess (2015) 29:513–526 DOI 10.1007/s00477-014-0878-3

ORIGINAL PAPER

Developing a cloud model based risk assessment methodology for tunnel-induced damage to existing pipelines Limao Zhang • Xianguo Wu • Queqing Chen Miroslaw J. Skibniewski • Jingbing Zhong

•

Published online: 13 April 2014 Springer-Verlag Berlin Heidelberg 2014

Abstract This paper presents a cloud model (CM) based approach with step-by-step procedures for risk assessment of existing pipelines in tunneling environments (RAEPTE), where CM provides a basis for uncertainty transforming between qualitative concepts and their quantitative expressions. An evaluation index system of multiple layers and attributes is established for RAEPTE based upon the tunnelinduced pipeline failure mechanism analysis. The evaluation result is assessed by the correlation with CMs of each risk level. A confidence indicator is proposed to illustrate the reliability of evaluating results. Risk analysis for ten underground buried pipelines adjacent to the construction of Wuhan Metro Line Two in China is shown in a case study. Comparisons between different evaluation methods are further discussed according to results. The proposed approach is verified to be a more competitive solution, where the uncertainties of fuzziness and randomness are incorporated in the risk assessment system. This approach can serve as a decision tool for the safety risk assessment in other similar projects, and to increase the likelihood of a successful project in an uncertain environment. Keywords Cloud model Risk assessment Existing pipelines Tunneling environments Case study L. Zhang X. Wu (&) Q. Chen J. Zhong School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China e-mail: [email protected] L. Zhang M. J. Skibniewski Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742-3021, USA M. J. Skibniewski Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Warsaw, Poland

1 Introduction Due to an increase in urbanization all over the world, tunneling has become a preferred construction method for subway transportation and underground utility systems. The exploitation of urban underground space presents several geotechnical engineering problems, one of which is the impact of tunnel construction on existing pipelines (Yang et al. 2008; Yu et al. 2009; Zhang and Huang 2012). Urban underground areas are congested with underground municipal pipelines that support gas transmission, water supply electric power, and telecommunications. Many pipelines are too brittle to sustain additional deformations caused by aging and corrosion effects over the term of their service. The excavation of a new tunnel generates ground movement around nearby pipelines, which may deform or damage pipelines. Tunneling-induced ground movements cause pipeline deformation that may disrupt the conveyance of important services and resources, and then threaten the safety and security of urban inhabitants (Wang et al. 2011). Therefore, to ensure the operation and maintenance of underground buried pipelines, it is necessary to make a risk assessment of existing pipelines in tunneling environments (RAEPTE), aiming to provide support on corresponding preventive measures for pipelines at different risk levels ahead of time. Tunnel-soil-pipeline interaction is considered as a highly complicated process, where the soil is usually represented by an elastic continuum or by a Winkler model (Yu et al. 2013). In recent years, finite element numerical analyses have been widely applied to investigate the tunneling-induced impacts on existing buried pipelines in engineering practices (Vorster et al. 2005; Zhang et al. 2012). However, this approach will lead to long central processing unit (CPU) times since the simulation of the process may be slow, especially when a large number of adjacent pipelines have to be assessed (Chen

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et al. 2011; Ding et al. 2014; Zhang et al. 2012). Meanwhile, in order to simplify the computation process, comparatively few critical factors are chosen as input parameters in the numerical analyses, regardless of the contributions of other relevant factors (Wang et al. 2011; Yu et al. 2013). However, most existing pipelines are aging and do not have complete load-bearing capability designed, and some kinds of structural damages are likely to occur in existing pipelines in the process of long-term operation. The health condition of an existing pipeline itself provides a basis as to how much the additional deformation or loads it is able to bear (Laiarinandrasana et al. 2011; Weon 2010). This aging factor is rarely considered in previous numerical approaches owing to the complicity and essential characteristics of the aging facilities. Thus, the accuracy of final results is affected to some extent, leading to insufficiency for the total safety management in construction practices. A comprehensive evaluation method should have a capacity of taking all related factors into account, and calculating the contribution of each factor (Ji et al. 2013; Li et al. 2013; Shi et al. 2013). Current comprehensive evaluation methods can broadly be grouped into the following three categories: (1) approaches based on fuzzy mathematics theory (Tangari et al. 2008), such as fuzzy analytic hierarchy process (FAHP) and fuzzy fault tree analysis (FFTA); (2) approaches based on probability and statistics theory, such as osculating value method (OVM) and Bayesian networks (BNs) (Zhang et al. 2013b); (3) approaches based on artificial intelligence (Doukas et al. 2009), such as neural networks (NNs), support vector machines (SVM), genetic algorithms (GA) and rough sets (RS). It is known that the construction data is difficult or nearly impossible to collect in engineering practice, since contractors are unwilling to publish their performance and behavior based data to the public, especially for the safety violation data. Due to a lack of sufficient data, some limitations exist in applications of the statisticsbased approaches or artificial intelligence tools. Thus, a group decision making method is generally employed for safety risk analysis. The uncertainties existing in experiential data can be considered in term of intervals or fuzzy numbers (Horcik 2008). However, in conventional fuzzy-based approaches, the sectional fuzzy function, including its type, boundary and parameters, should be determined individually concerning each evaluation factor. This process is laborious and susceptible to human error, and can affect the accuracy and reliability of the calculated results. This paper is intended to present an innovative approach based on cloud model (CM) to address these deficiencies. CM provides a powerful tool in uncertain transforming between qualitative concepts and their quantitative expressions. CM was proposed by Li et al. (1995) based upon traditional fuzzy set theory and statistics and probability techniques. It has a capability of expressing fuzziness and

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Stoch Environ Res Risk Assess (2015) 29:513–526

randomness existing in human knowledge representation, acquirement and inference. In the past 10 years, CM has been widely applied in many areas, such as inexact knowledge representation, intelligent control and system evaluation data mining. Taking advantages of CM, a risk assessment approach has been developed for RAEPTE in this research. The safety status of an existing pipe adjacent to tunneling excavation is evaluated into five different levels using the embedded correlation calculation. The uncertainty of randomness existing in experimental data is addressed by means of a confidence indicator h. Finally, the proposed approach is applied to the risk assessment of adjacent pipelines along the route of Wuhan Metro Line Two (WMLT) in a case study. The comparisons between the proposed approach and other traditional methods are further discussed accordingly. The remainder of the paper is organized as follows. Section 2 is devoted to the fundamental theory of CM, and a CMbased safety risk assessment approach with step-by-step procedures is developed. In Sect. 3, the safety risk mechanism of tunnel-induced pipeline damage is investigated, providing a basis for the risk modeling and decision support. In Sect. 4, the proposed approach is applied to safety risk analysis in a tunnel case study. The conclusion is drawn in Sect. 5.

2 Methodology 2.1 Cloud model Aiming to eliminate the fuzziness and randomness inherent in human cognition, CM is defined as follows: supposing U is the quantitative domain expressed by accurate numbers and C is a quality concept in U, there exists a corresponding certainty degree l(x) to C for arbitrary x [ U. As shown in Eq. (1), x is a random realization of the quality concept C. l(x) is a random number with a stable tendency that is called a cloud drop. l : U ! ½0; 1;

8x 2 U;

x ! lðxÞ

ð1Þ

A CM can be characterized with three digital characteristics C = (Ex, En, He). The expected value ‘‘Ex’’ represents the typical point which best characterizes the quality concept, which is the center value of the qualitative concept. The entropy ‘‘En’’ is the uncertainty distribution of the concept representing the range of values that could be accepted in the domain. In addition, ‘‘En’’ reflects the fuzziness of the qualitative concept, and can be used to measure the randomness of cloud drops. The larger ‘‘En’’ is, the larger fuzziness and randomness of the concept is. The hyper-entropy ‘‘He’’ is a measure of the randomness and fuzziness of the entropy ‘‘En’’, which can be used to reflect the dispersion of cloud drops and determine the thickness of the cloud directly. The larger ‘‘He’’ is, the


Membership

Ex

515

is [6, 12] for the example, and the other contribution beyond the interval is negligible. This is also known as ‘‘3En criterion’’, which means that the elements beyond [Ex - 3En, Ex ? 3En] can be disregarded (Chen et al. 2012).

He

2.2 Cloud generator 3En

Cover Depth (m) Fig. 1 Cloud model ‘‘Very Shallow’’ for the ‘‘Cover Depth’’

larger the randomness of membership degree and the thickness of cloud drops is (Chen et al. 2012). Formed by choosing different probability distribution functions, there are various kinds of CMs, such as normal cloud, trapezium cloud, half-down cloud, and half-up CM. A normal CM is built on normal distribution and Gauss membership function. This kind of CM (also called the Gauss cloud) plays a prominent role in application due to its universality and stability (Li et al. 2009), and is therefore adopted in this research. The CM also has the above three numerical characteristics, and is described as follows: let U be the universe of discourse and A~ be a qualitative concept in U. If x [ U is a random realization of concept A~ which satisfies Eq. (2), the certainty degree of x belonging to the concept A~ satisfies Eq. (3). Then the distribution of x in the universe U is regarded as a normal cloud (Li 2004). ( x N Ex; En02 ð2Þ En0 N En; He2 ! ðx ExÞ2 ð3Þ y ¼ exp 2En02

Cloud generator establishes the mapping relationship between qualitative concept and quantitative characteristic. There are primarily two kinds of generators, namely forward cloud generator and backward cloud generator (Chen et al. 2012). The forward cloud generator maps qualitative concept to quantitative characteristic, where the generator can produce as many cloud drops as required when the three quantitative characteristics (Ex, En, He) and the required number of cloud drops are given, as seen in Fig. 2a. The forward cloud generator algorithm is presented in Algorithm 1. In contrary to the forward cloud generator, the backward cloud generator maps quantitative characteristic to qualitative concept, where three quantitative characteristics of (Ex, En, He) can be achieved to represent the corresponding qualitative concept from a given cloud drops sample, as seen in Fig. 2b). The backward cloud generator algorithm is presented in Algorithm 2.

For example, the factor ‘‘Cover Depth’’ plays a major role in describing the impact of tunneling excavation on the building damage. ‘‘From 6 to 12 m’’ is the common expression to describe the status such as ‘‘Very Shallow’’ for the ‘‘Cover Depth’’. Figure 1 shows the CM with parameters Ex = 9, En = 2, He = 0.3 and n = 40,000. It can be seen that in this CM, the contribution of cloud drops to qualitative concepts is mainly focused on [Ex - 3En, Ex ? 3En], that Fig. 2 Cloud generators. a Forward cloud generator, b backward cloud generator

(a) Ex

En He

(b)

CG

Drop( x, µ ( x))

Drop( x, µ ( x))

CG

−1

Ex En He

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models of all the evaluation factors of different risk states, denoted as Rij = (Exij, Enij, Heij) (i = 1,2,…,M; j = 1,2,…,N) can be obtained using Eq. (4) in RAEPTE. 8 cij ðLÞ þ cij ðRÞ > > > < Exij ¼ 2 cij ðRÞ cij ðLÞ ði ¼ 1; 2; . . .; M; j ¼ 1; 2; . . .; N Þ > Enij ¼ > > 6 : He ij ¼ s ð4Þ Where, ‘‘Exij’’ is the expectation of the normal cloud of the jth interval for the ith evaluation factor, ‘‘Enij’’ is the entropy, and ‘‘Heij’’ is the hyper entropy. ‘‘s’’ is a constant which used to illustrate the uncertainties of corresponding factors existing in the interval recognition of evaluations factors. The higher the value of ‘‘s’’ is, the larger the atomized feature of the cloud drops is. Li et al.(2009) indicated ‘‘s’’ should have a value ranging from 0 to ‘‘Enij’’ in computation, since the cloud drops can be too widely scattered to process the subsequent computation if ‘‘Heij’’ is greater than ‘‘Enij’’. The value of ‘‘s’’ can be chosen based on the engineers’ estimation, and adjusted according to actual conditions. 2.3.2 Step 2: correlation calculation 2.3 Development of a CM-based risk assessment approach RAEPTE is a typically complicated evaluation problem concerning multiple layers and attributes. Currently, various evaluation methods have been presented to deal with this problem, such as FAHP (Ho 2012), OVM (Peiyue et al. 2010) and NNs (Wang et al. 2013). However, due to a lack of sufficient statistical data and an ambiguity of expert knowledge, great uncertainties of randomness and fuzziness exist during the evaluation process, which can affect the accuracy and reliability of finally evaluation results to some extent (Zhang et al. 2013a). Considered as a powerful a qualitative and quantitative transformation model, CM provides a possible way to address the potential fuzziness and randomness inherent in human cognition. Thus, a CMbased risk assessment approach is developed in this research, which consists of the following five steps. 2.3.1 Step 1: evaluation factors division RAEPTE involves various evaluation factors xi (i = 1,2, …,M), and each evaluation factor xi can be further divided into different risk states xij (i = 1,2,…,M; j = 1,2,…,N). Meanwhile, each risk state corresponds to one closed double-restriction interval, represented by [cij(L), cij(R)] (i = 1,2,…,M; j = 1,2,…,N). The transformation from the double-restriction interval [cij(L), cij(R)] to a normal cloud model (Exij, Enij, Heij) is calculated by Eq. (4). Then, cloud

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Correlation is used to measure the relative degree between a specific pipeline and CMs of each risk level Rij (i = 1,2,…,M; j = 1,2,…,N). Correlation calculation plays a critical role in the safety risk assessment when the CM is adopted. Assuming a specific pipeline denoted as P, pi (i = 1,2,…,M) represents the actual value of ith evaluation factor for P. In the safety risk assessment process, original data can be entered into the model without a normalization procedure. In traditional safety risk analysis approaches, the normalization is routinely used in the treatment of original data, even though there might be some loss of information in the normalization process (Hu and He 2006). For instance, as for a selected sample, the dimension of each attribute varies greatly, and then the value of a specific attribute will be transformed into nearly zero after the normalization if the dimension of that attribute is very low. As a result, the diversity information existing in original data will be lost inevitably. Thus, the proposed approach is able to avoid the potential information loss. Compared with the CM of the j level denoted as Rij = (Exij, Enij, Heij) (i = 1,2,…,M; j = 1,2,…,N), the actual value pi is viewed as a cloud drop. Its correlation denoted as qij (i = 1,2,…,M; j = 1,2,…,N) can then be calculated using Eq. (5). The correlation matrix of the specific pipeline P, represented by Q, can be then obtained using Eq. (6). Herein, as seen in Eq. (5), En0ij is a random number produced by a generator which satisfies En0ij * N(Enij, He2ij). However, the randomness existing in


517

the correlation calculation of matrix Q can be eliminated by a vast amount of repeated computations 0 1 2 B pi Exij C qij ¼ exp@ 2 A; ði ¼ 1; 2; . . .; M; 0 ð5Þ 2 Enij j ¼ 1; 2; . . .; NÞ 2 q11 q12 6 q21 q22 6 Q¼6 . .. .. 4 .. . . qM1 qM2

q1N q2N .. .

3 7 7 7 5

ð6Þ

qMN

2.3.3 Step 3: weight determination The contribution of each evaluation factor varies noticeably in the evaluation system, causing a driving force for weight setting of each factor. Currently, there are two different kinds of weights, namely subjective weights and objective weights. Analytic hierarchy process (AHP) is the most common method to determine the subjective weights. The main idea is to break down the evaluation system into hierarchy structure and compare each element according to a principle, acquire the compare matrix elements, and then calculate the weight of each attribute. However, the practical distribution patterns of the objective value regarding each attribute are not taken into account in traditional AHP. Considered as a suitable method to decide the objective weights of attributes, the entropy weighting method passively determines attribute weights without decision-makers conscious intention. Thus, the opportunity to learn during the attribute weighting process is eliminated which in turn may reduce both the understanding and expectance. In most cases, both subjective and objective factors involve in the risk assessment index system. Therefore, an innovative integration of the AHP and entropy weighting method could potentially serve as a comprehensive solution for weight setting in this situation. Assuming there are m attributes in the risk assessment index system, AHP is used to calculate the subjective weight of each attribute ci (i = 1,2,…,M), represented by the vector g. See details in Appendix 1. Then, the Entropy weighting method is used to calculate the objective weight of each attribute, represented by the vector d. See details in Appendix 2. Finally, Eq. (7) is used to calculate the comprehensive weight of each attribute ci (i = 1,2,…,m). All the comprehensive weights constitute the weight matrix W in the assessment index system, as seen in Eq. (8) g di wi ¼ PM i ; i¼1 ðgi di Þ W ¼ ½w1 ; w2 ; . . .; wM

ði ¼ 1; 2; . . .; MÞ

ð7Þ ð8Þ

2.3.4 Step 4: safety risk assessment Effective management of project risk can improve project performance (Kuo and Lu 2013). Based on the weight matrix W and the correlation matrix Q, the comprehensive evaluation vector, denoted by B, can be calculated by Eq. (9). The weighted mean method can then be used to conduct the final comprehensive risk level K, as seen in Eq. (10). Accordingly, the value of K can be used as an indicator to evaluate the potential safety risk level of the specific pipeline P. For example, if K has a value of 3.1, this specific pipeline is assessed to be at a level of ‘‘IV’’, yet with certain tends towards a level of ‘‘III’’ B ¼ W Q ¼ ½b1 ; b2 ; . . .; bN PN j¼1 ðbj jÞ K ¼ PN j¼1 ðbj Þ

ð9Þ ð10Þ

Due to the randomness existing in the correlation calculation of matrix Q, a series of the K set (K1, K2, …,Kt) appears after repeated computations using Eqs. (5) and (6) for t times. Herein, in order to satisfy the demand for real-time data processing and analyzing, the value of t is chosen to be 1,000 in practical applications. As for the K set, the expectation denoted by Ex(K) and standard deviation denoted by En(K) can then be calculated by Eqs. (11) and (12), respectively. Ex(K) reflects the average of the risk level of the specific pipeline P, while En(K) reflects the degree of dispersion among those evaluation results. A confidence indicator h is proposed to measure the reliability of evaluation results, which is calculated by Eq. (13). h is one when the evaluation result is perfectly reliable. The closer the value of h approaches one, the more significant the predominant tendency of the evaluation results. In this way, the reliability of the evaluation results can be secured K1 þ K2 þ þ Kt t sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t 1X EnðKÞ ¼ ðKi ExðKÞÞ2 t i¼1

ExðKÞ ¼

h¼1

EnðKÞ ExðKÞ

ð11Þ ð12Þ ð13Þ

2.3.5 Step 5: sensitivity analysis Due to complexities in tunneling environments, great fuzziness and randomness exist during the determination of the observed value for a specific evaluation factor. For instance, geological variables usually suffer from errors, which can be of the order of magnitude of the values themselves. Considering that the parameters may fluctuate

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around a mean value due to uncertainties and errors, it is therefore useful to perform a sensitivity analysis. Sensitivity refers to how sensitive a model’s performance is to minor changes in the input parameters. Sensitivity analysis is particularly useful in investigating the performance of each input factor’s contribution to the occurrence of an output event. The most natural way of performing sensitivity analysis is to change the values of the input parameters, and then monitor the effects of changes on the output result. In this research, the observed value of each evaluation factor ci (i = 1,2,…,M) is assumed to suffer from a fluctuation of -30, -20, -10, 0, ?10, ?20, ?30 % of its initial value, and then, based up the above steps 1–4, the result of the safety risk assessment will be accordingly changed, represented by Exi ðKÞ1 , Exi ðKÞ2 , Exi ðKÞ3 , Exi ðKÞ4 , Exi ðKÞ5 , Exi ðKÞ6 , Exi ðKÞ7 , respectively. A performance-based indicator, Sensitivity Measure (SM) is proposed to measure the contribution of each evaluation factor ci to the final safety risk level, aiming to help decision-makers identify key factors which should be paid more attention so as to reduce the risk limit. The SM of each input evaluation factor ci, represented by SM (ci), can i ðKÞ is the arithmebe calculated by Eq. (14). Herein, Ex j tic average value of Exi ðKÞ (j = 1, 2,…,7), and can be calculated by Eq. (15) vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 7 u1 X i ðKÞ 2 ; i ¼ 1; 2; . . .; M Exi ðKÞ j Ex SM ðci Þ ¼ t 7 j¼1 ð14Þ i ðKÞ ¼ 1 Ex 7

7 X

Exi ðKÞ j :

ð15Þ

j¼1

3 Risk mechanism analysis for existing pipelines 3.1 Failure of underground buried pipelines Pipeline failure refers to the situation where leakage or structural damage occurs in the underground buried pipelines, which can affect their normal usage. Figure 3 illustrates a section diagram for the tunneling-induced pipeline deformation, in which a new tunnel is excavated under an existing pipeline. The tunnel excavation generates soil settlement around the pipeline, and then the pipeline is forced to deform and suffer additional bending moments. This kind of failure is commonly found in existing pipelines, such as drainage pipe, water supply pipe, and others. Under the function of additional stress, the rotational joints can be adjusted to deal with the pipeline deformation. However, the phenomenon of pipeline crack and even

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Surface ground settlement

Deformed pipeline

Volume loss

X

Tunneling

Z

Fig. 3 Section deformation

diagram

of

the

tunneling-induced

pipeline

failure is likely to occur when the additional deformation exceeds a certain threshold. In order to ensure the safety of underground buried pipelines, several indicators serving as the safety control standards are put forward, including surface ground settlement (O’Rourke and Trautmann 1982), joint rotation angle (Attewell et al. 1986), and pipeline settlement (Wang 2008). For one thing, using the surface ground settlement to assess the safety of underground buried pipelines is abstract and indirect, regardless of the interaction of pipelines and surrounding soils. For another thing, in engineering practice, the value of pipeline settlement is much easier to obtain than that of joint rotation angle. Therefore, the value of pipeline settlement is more representative to assess the safety status of existing pipelines in tunneling environments, and is usually used as an indicator in some technical specifications. An industry standard, ‘‘Technical Specification for Engineering of Foundation Excavation’’ (DB42/159-2004) was introduced in August 2004 in China, in which the deformation of the pipeline settlement should be monitored under a prescribed frequency. The allowable value for the maximum pipeline settlement is 30 mm, and early warning signals can be released once the allowable standard is exceeded. The value of the pipeline settlement is becoming a basic means for safety assurance of existing pipelines in metro tunnel construction. Numerous researchers studied various methods, including finite element modeling and NNs, to predict a single value of the final pipeline settlement (Moghaddas Tafreshi and Tavakoli Mehrjardi 2008; Vorster et al. 2005). Then the security and stability of the existing pipelines could be analyzed by comparing the difference between the predicted value and control standard. As a matter of fact, the actual observed value turns out to be random due to the uncertainties and complexities in complex real conditions. Therefore, a single predicted value has


significant limitations, and we divide the predicted value into several ranges based on the fuzzy mathematical theory. The safety status of existing pipelines induced by tunneling excavation is assessed by analyzing the chance of the predicted value within each range. In regard to the pipeline settlement with a general settlement range of 0–70 mm, we divide the predicated value into the following five ranges based upon current engineering practices: namely I (Very Safe, 0–20 mm), II (Safe, 20–30 mm), III (Dangerous, 30–40 mm), IV (Very Dangerous, 40–50 mm), and V (Extremely Dangerous, 50–70 mm).

519

Ratio (c7) and Pipe Materials (c8), are all closely related to the quality of the pipe preservation conditions. To be exact, Pipe Cover-span Ratio stands for the ratio between pipe burial depth and pipe diameter, while Pipe Service-life Ratio stands for the ratio between the pipe age and its economic lifetime. 3.2.4 Technical and managerial variables

In real projects, various influential variables are involved in tunnel-soil-pipe interaction, and contribute to failures of underground buried pipelines. Based on engineering practices and theoretical analysis, four types of variables concerning the safety of existing pipelines are descripted as follows.

Construction management is a dynamic process associated with an organic integration of man, material, machine, method and environment (4M1E) in project sites (Yihua and Tuo 2011). Generally, the complexity of the Construction Technologies (c9) plays a prominent role in the difficulty of the safety management for adjacent pipelines. Furthermore, high Management Quality (c10) and professional Monitoring Engineers (c11) are also the relevant factors in order to guarantee the safety of adjacent pipelines in tunneling environments.

3.2.1 Spatial neighbor relationship

3.3 Risk level gradation

The spatial neighbor relationship between the tunnel structure and adjacent pipelines plays a significant role in tunnel-induced pipeline deformation. Horizontal Both Relative Distance (L/D) (c1) and Vertical Relative Distance (H/D) (c2) are frequently used to represent the neighbor relationship. Herein, D stands for the diameter of the tunnel designed; L stands for the horizontal distance between the tunnel and the pipeline; and H stands for the vertical distance. In most cases, the value of the tunnel-induced pipeline settlement will slow down as Horizontal Relative Distance (or Vertical Relative Distance) increases.

Among the above 11 influential variables in RAEPTE, some are objective, like c1, c2,…c7, and the others (c8, c9, c10, c11) are subjective. Both the objective and subjective factors are gathered together to quantify the level of the safety risk for existing pipelines due to tunneling excavation. To be specific, the objective variables are measured by the observed values in real projects, while the subjective variables are measured by evaluated values from domain experts using a 100-mark system (Wang et al. 2012). Each variable contributes to the final safety risk level during RAEPTE, and it is therefore necessary to analyze and evaluate the safety status of those influential variables. In this paper, the safety status of each variable is divided into five different levels, 1–5. The higher the level, the higher the risk for each variable. However, due to complexities in tunneling environments, great fuzziness and uncertainty exist during the risk interval recognition where the boundary of each risk interval is vague in determination (Zhang et al. 2013a; Zhu et al. 2013). With the increased construction of metro tunnels worldwide, especially in China, large amounts of scattered knowledge are being accumulated from actual practices, such as monitoring records, standard specification, technical manuals and research reports. Also, numerous scholars have built simulation models for safety analysis, providing valid references for discovering relationships between various risks/risk factors (Ding et al. 2011; Keshuan and Lieyun 2008). These resources provide a prior knowledge for the understanding of evolutionary patterns of potential risk factors. Taking the factor of Horizontal Relative Distance (c1) for an example, based on

3.2 Influential variables

3.2.2 Geological variables Acting as an intermediary in tunnel-soil-pipeline interaction, the geological conditions also play a crucial role in tunnel-induced pipeline damages. Liao et al. (2009) indicated that the tunnel excavation in soft ground inevitably would lead to soil displacement, which subsequently would have an impact on existing surface or subsurface structures. The parameters compression modulus (c3), soil cohesion (c4) and friction angle (c5) are the three variables commonly used to illustrate the geological conditions. 3.2.3 Pipe related variables The condition of the pipe plays an important decisive role for the pipeline safety because it has a direct effect on the capacity of the pipe itself to resist external loads or additional deformations in tunneling environments. The variables, such as Pipe Cover-span Ratio (c6), Pipe Service-life

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districts, as seen in Fig. 5. As aforementioned, the safety risk assessment and management of existing pipelines adjacent to WMLT was considered a challenging task due to the complex interaction and failure mechanism. Among hundreds of crowded pipes around the tunnel, ten drainage pipes (DP1#, DP2#,…,DP10#) were randomly chosen for a case study. A systematic investigation was first carried out, covering all evaluation factors in RAEPTE. Integrated with the expert decision-making information simultaneously, the observed values of 11 evaluation factors for those ten adjacent drainage pipes are presented in Table 2. Fig. 4 Fitting curve between ‘‘Horizontal Relative Distance’’ and ‘‘Maximum Pipeline Settlement’’

large numbers of monitoring records obtained from the early warning web-based systems developed by scholars at Huazhong Univ. of Science and Technology (HUST) (Ding and Zhou 2013; Ding et al. 2013), the fitted curve between ‘‘Horizontal Relative Distance’’ and ‘‘Maximum Pipeline Settlement’’ is displayed in Fig. 4. Herein, the value of ‘‘Maximum Pipeline Settlement’’ can be regarded as an index to show the safety status of the factor of Horizontal Relative Distance in RAEPTE. As seen in Fig. 4, the relationship between Horizontal Relative Distance and ‘‘Maximum Pipeline Settlement’’ is approximately linear within a certain range. The pattern of the ‘‘Maximum Pipeline Settlement’’ tends to be slowed down when the Horizontal Relative Distance reaches up to three. In the past 7 years, researchers at HUST have developed safety control systems for metro construction and operation tasks for Shenyang, Zhengzhou, Shenzhen and Wuhan Metro systems. The researchers have also developed early warning web-based systems for safety control of each project. Large amounts of monitoring records have been accumulated during the progress of the work on these projects (Ding and Zhou 2013; Ding et al. 2013; Zhang et al. 2013b). Based on the early warning web-based systems and prior expert knowledge, the results of risk level gradation of the above 11 evaluation factors in RAEPTE are presented, as seen in Table 1.

4 Case study 4.1 Background Wuhan is the largest city in central China with a population of 10.12 million (2012 data). In order to relieve the urban traffic jam across the Yangtze River, the construction of WMLT formally started on August 28, 2006. The 27.7 km route with 21 stations and a total investment of nearly US $3.2 billion ran mainly underground on a northwestsoutheast alignment between the Hankou and Wuchang

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4.2 Analysis of results The pipe DP1# was taken as an example to illustrate the detailed computation process due to the space restriction. The correlation matrix of DP1#, denoted by Q1, was calculated using Eqs. (5) and (6). According to Appendices 1 and 2, both subjective and objective weights of 11 evaluation factors in RAEPTE can be obtained, as seen in Table 3. Based upon Eqs. (7) and (8), the comprehensive weight matrix was developed as represented by W = [0.1231 0.1134 0.0775 0.0996 0.0871 0.1093 0.1162 0.0858 0.0622 0.0595 0.0664]. Subsequently, Eq. (9) was used to calculate the comprehensive evaluation vector of the DP1#, represented by B1 = W 9 Q1 = [0.0205 0.1016 0.2258 0.1235 0.0880]. Then, Eq. (10) was employed to conduct the final comprehensive risk level K1 = 3.35. Next, 1,000 times of repeated computations were used to eliminate the randomness existing in the correlation matrix Q1. Finally, the expectation Ex(K) was calculated by Eq. (11) to be 3.35, which would be rated in the Level IV (Very Dangerous). Using Eqs. (12) and (13), the confidence indicator h was calculated to be 0.9635 approaching one, which indicated that the calculated result was significantly reliable. According to the sensitivity analysis method, the impacts of the fluctuations of evaluation factors’ values on the final comprehensive risk level are illustrated in Fig. 6. Eqs. (14) and (15) were used to calculate the sensitivity of each evaluation factor [SDM (ci)] in RAEPTE, as shown in Fig. 7. Furthermore, in the same way, the evaluation results of other nine adjacent pipes were obtained and presented, as seen in Table 4. Accordingly, the analysis of results is made as follows: 1.

From the perspective of the sensitivity of evaluation factors, the same magnitude of a fluctuation for the observed value of either the same evaluation factor or different evaluation factors may lead to different results. In other words, the sensitivity of each evaluation factor varies, depending on the current value and type of the evaluation factor. As for DP1# (see Fig. 7),


521

Table 1 Risk level gradation of the evaluation factors related to RAEPTE Variables

Factors

Description

States I (1)

Spatial neighbor relationship Geological variables

Pipe related variables

Technical and managerial variables

II (2)

III (3)

IV (4)

V (5)

c1

Horizontal Relative Distance (L/D)

[3, 5]

[2, 3]

[1.5, 2]

[1, 1.5]

[0, 1]

c2

Vertical Relative Distance (H/D)

[2.5, 4]

[1.5, 2.5]

[1, 1.5]

[0.5, 1]

[0, 0.5]

c3

Compression Modulus (MPa)

[40, 60]

[20, 40]

[10, 20]

[5, 10]

[0, 5]

c4

Soil cohesion (KPa)

[20, 25]

[15, 20]

[10, 15]

[5, 10]

[0, 5]

c5

Friction angle ()

[25, 45]

[15, 25]

[10, 15]

[5, 10]

[0, 5]

c6

Pipe cover-span ratio

[3, 5]

[2, 3]

[1, 2]

[0.5, 1]

[0, 0.5]

c7 c8

Pipe service-life ratio Pipe materials (score)

[0, 0.2] [80, 100]

[0.2, 0.4] [60, 80]

[0.4, 0.6] [40, 60]

[0.6, 0.8] [20, 40]

[0.8, 1] [0, 20]

c9

Construction technologies (score)

[80, 100]

[60, 80]

[40, 60]

[20, 40]

[0, 20]

c10

Management quality (score)

[80, 100]

[60, 80]

[40, 60]

[20, 40]

[0, 20]

c11

Monitoring engineers (score)

[80, 100]

[60, 80]

[40, 60]

[20, 40]

[0, 20]

Fig. 5 Route map of Wuhan Metro Line Two (WMLT)

2.

c1, c6, and c7 were remarkably sensitive to the high risk level in RAEPTE. Therefore, more control measures should be taken to ensure the rational status of these three construction parameters. From the perspective of risk rank, the top two adjacent pipes (DP4# and DP10#) were both rated Level V (Extremely Dangerous). Accordingly, those two pipes

turn out to be the core protected pipes during the practical construction progress. As for DP4#, the main causes leading to such a high risk level lay in a close Horizontal Relative Distance (c1 = 0.42, q15 = 0.8911) and a high Pipe Service-life Ratio (c7 = 0.89, q75 = 0.9477). As for D10#, the main causes lay in a close Vertical Relative Distance (c2 = 0.30, q25 = 0.8458) and a high Pipe

123

522


Table 2 Values of 11 evaluation factors in RAEPTE for ten adjacent pipes ID

DP1#

DP2#

DP3#

DP4#

DP5#

DP6#

DP7#

DP8#

DP9#

DP10# 0.85

c1

0.63

1.53

1.28

0.42

1.49

4.11

2.61

0.60

0.63

c2

1.54

1.26

3.20

0.45

1.89

3.86

2.32

1.52

2.94

0.30

c3

10

32

10

37

18

22

53

21

15

22

c4

16

16

23

11

14

19

17

22

12

19

c5

4

7

27

25

22

12

8

25

26

31

c6

4.66

0.46

2.89

0.78

2.58

1.24

4.24

3.60

4.13

0.35

c7

0.32

0.74

0.13

0.89

0.83

0.76

0.61

0.75

0.66

0.88

c8

14

36

16

36

42

16

14

35

43

60

c9

65

80

86

26

86

72

75

64

55

45

c10

83

70

19

26

69

74

50

28

35

58

c11

55

39

65

50

86

77

41

29

10

42

3.

Service-life Ratio (c7 = 0.88, q75 = 0.8504). Therefore, it is necessary to carry out field test experiments and numerical simulation analyses for safety risk analysis before tunneling excavation, aiming to provide support for both construction scheme optimization and emergency response proposals. Furthermore, the confidence indicator h of each pipeline was substantially approaching one, indicating all calculated results were robustly reliable. From the perspective of the safety status as a whole, six adjacent pipes (including DP4#, DP10#, DP1#, DP9#, DP8#, DP2#) out of ten were rated Level IV or above. These ten pipes were randomly selected from hundreds of pipes adjacent to the WMLT. Therefore, we have sufficient reasons to believe, the comprehensive risk of all adjacent pipes along the tunnel route was markedly high, rather than low or median. In fact, this deductionwasconsistent with the actual situation. WMLT, known as ‘‘the first metro tunnel across the Yangtze River in China’’, came across several challenging problems, such as complicated geological conditions, crowded surface and subsurface pipe systems, and shallow buried depth. Due to a lack of sufficient experience in similar projects, the risk was accordingly enlarged subjectively to some extent. In construction, efficient and reasonable preventive measures for adjacent pipes at different risk levels were developed and then strictly implemented. On February 26, 2012, WMLT ran successfully through the whole route on schedule. No adjacent pipes were damaged during the construction of the entire tunnel.

4.3 Discussions In order to further verify the feasibility of the proposed risk assessment approach in this research, three typical

123

evaluation methods among the aforementioned three categories, namely FAHP based on fuzzy mathematics theory, OVM based on probability and statistics theory and NNs based on artificial intelligence, were chosen to work out evaluation results based on the previous case, respectively. These three methods are the most typical representatives of the traditional comprehensive evaluation methods. For space limitation, the detailed computation procedures for FAHP can be referred by Ho (2012), the detailed computation procedures for OVM can be referred by Peiyue et al. (2010), and the detailed computation procedures for NNs can be referred by Wang et al. (2013). Subsequently, the obtained risk assessment results based on these four different methods are listed in Table 5. Discussions are presented as follows: 1.

2.

As seen in Table 4, the evaluation results calculated by the proposed approach were fairly consistent with the other three traditional evaluation methods, indicating the proposed approach was considerably reliable and efficient. The exceptions were DP2# [Ex(K) = 3.05] and DP3# (Ex(K) = 1.95), which were calculated to be Level IV and II, respectively. These two adjacent pipes both showed a considerable tendency to move towards Level III. To investigate the reason, the deflections inevitably existed due to the slight difference on risktaking attitudes or data processing among different evaluation methods. However, this slight deviation was acceptable and understandable in risk assessment of actual projects. Compared with the other three traditional evaluation methods, the proposed CM-based approach appeared to be a more competitive solution for addressing uncertainties. When dealing with the objective data, OVP and NN display a bigger superiority during the risk analysis and assessment. However, when the subjective date is incorporated, the problem of inefficiency often occurs due to the subjectivity and


523

Table 3 Weights of 11 evaluation factors in RAEPTE Weights

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

g

0.1299

0.1156

0.0771

0.0946

0.0874

0.1143

0.1132

0.0848

0.0596

0.0583

0.0653

d

0.0125

0.0111

0.0074

0.0091

0.0084

0.011

0.0109

0.0082

0.0057

0.0056

0.0063

w

0.1231

0.1134

0.0775

0.0996

0.0871

0.1093

0.1162

0.0858

0.0622

0.0595

0.0664

and quality of training data. However, the process of obtaining great amounts of training data was laborious and expensive in engineering practices. Due to a lack of sufficient data from construction, the expert knowledge, which was subjective and ambiguous, played a crucial role in the risk evaluation and management. In the conventional FAHP method, the sectional fuzzy function, including its type, boundary and parameters, should be determined individually concerning each evaluation factor. This process was laborious and susceptible to human error, which would affect the accuracy and reliability of the calculated results. The proposed CM-based approach can directly use the original data without a normalization procedure, effectively avoiding the potential information loss. Furthermore, the uncertainty of randomness existing in experiential data was addressed in the proposed approach by means of a confidence indicator h, which was not considered in the other three methods.

Results of the safety risk assessment

4.0 3.9 3.8

c1 c2

3.7

c3

3.6

c4

3.5

c5

3.4 3.3

c6 c7

3.2

c8

3.1

c9

3.0

c10

2.9

c11

2.8 -30%

-20%

-10%

0%

10%

20%

30%

Fluctuations of the observed values of evaluation factors

Standard Deviation Measure (SDM)

Fig. 6 Impacts of fluctuations of evaluation factors’ values on the final comprehensive risk level

0.24 0.22 0.20 0.18

5 Conclusions

0.16 0.14 0.12 0.10 0.08 0.06 0.04 c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

Evaluation factors in RAEPTE

Fig. 7 Sensitivity of each evaluation factor [SDM (ci)] in RAEPTE

ambiguity of the expert knowledge. In fact, the expert knowledge plays a crucial role in the safety evaluation and management because of the complexities in actual project environments. In regard to OVM and NN, high requirements needed to be met with both the quantity

Table 4 Evaluation results of ten existing pipes adjacent to WMLT

ID

DP4#

DP10#

DP1#

In recent years, RAEPTE has attracted broad attention due to the rapid development of underground transport systems. An evaluation index system of multiple layers and attributes for RAEPTE is proposed according to failure mechanism analysis of existing pipelines in tunneling environments. A CM-based risk assessment approach with detailed step-by-step procedures was then developed. The evaluation result is assessed by the correlation to the CM of each risk level. The proposed approach was applied to the safety evaluation of existing pipes in the construction of WMLT in China. The results have proved to be consistent with the actual situation. Compared with the other three traditional evaluation methods, the proposed CM-based approach was verified to

DP9#

DP8#

DP2#

DP7#

DP6#

DP5#

DP3#

Ex(K)

4.24

4.16

3.35

3.20

3.14

3.05

2.43

2.25

2.10

1.95

h

0.9615

0.9768

0.9635

0.9799

0.9681

0.9877

0.9553

0.9589

0.9662

0.9583

Rank

1

2

3

4

5

6

7

8

9

10

123

524


Table 5 Comparison of evaluation results by four different methods

Table 6 AHP scale of nine points used in the paired comparatives

ID

Numerical assessment

Definitions

1

Equally important

3

Moderately more important Strongly more important

FAHP (risk level)

OVM (risk level)

NN (risk level)

Proposed approach Ex(K)

Risk level

h

DP1#

IV

IV

IV

3.35

IV

0.9635

5

DP2#

IV

III

IV

3.05

IV

0.9877

7

Very strongly important

DP3# DP4#

II V

II V

III V

1.95 4.24

II V

0.9583 0.9615

9

Extremely more important

2, 4, 6, 8

Intermediate values of importance

DP5#

III

III

III

2.10

III

0.9662

1/9,1/8,…,1/2

Reciprocal values (inverses)

DP6#

III

III

III

2.25

III

0.9589

DP7#

III

III

III

2.43

III

0.9553

DP8#

IV

IV

IV

3.14

IV

0.9681

DP9#

IV

IV

IV

3.20

IV

0.9799

DP10#

V

V

V

4.16

V

0.9768

be a more competitive solution under uncertainty. This approach can directly use the original data without a normalization procedure, avoiding the potential information loss. Unlike other artificial intelligence tools, there is no need for large amounts of training data in the modeling process. The uncertainty of randomness existing in experimental data is addressed in the proposed approach by means of a confidence indicator h, which is usually not considered in other methods. Also, this approach can be used as a decision tool for the risk assessment of other similar projects, in order to increase the likelihood of a successful project in an uncertain environment. Acknowledgments The National Science and Technology Support Plan (No. 51378235), Wuhan City Construction Committee Support Project (No. 201208) and China Scholarship Council (CSC) are acknowledged for their financial support of this research.

2

C ¼ ðcij Þmm

1 6 1=c12 ¼6 4 ... 1=c1m

c12 1 ... 1=c2m

3 . . . c1m . . . c2m 7 7 ... ... 5 ... 1

ð16Þ

In this research, AHP is used to determine subjective weights for the safety risk factors in RAEPTE. At first, m criteria are set up in the rows and columns of m 9 m matrix. Then, pair-wise comparisons of all the criteria are performed using the fundamental scale (see Table 6). When more than one decision-maker is involved in the evaluation process, it is necessary to add up and average the judgments of the various decision-makers. Mikhailov (2004) and Escobar et al. (2004) suggested using the geometric median as an average, when the personal assessments of the decision-makers are added up in a matrix of final decision, as shown in Eq. (17). Finally, the average over normalized columns is used to estimate the Eigen values of the matrix, and the weight of all the factors, represented by g [see Eq. (18)] can be obtained according to the eigenvector of the matrix Cm9m 1=p cij ¼ cij1 cij2 cijp ð17Þ

Appendix 1: Analytic hierarchy process

g ¼ ½g1 ; g2 ; . . .; gm

AHP, developed by Saaty (1988), structures the decision problem in levels which correspond to one understands of the situation: goals, criteria, sub-criteria and alternatives. The main idea is to break down the evaluation system into a hierarchy structure and compare each element according to a principle, and then acquire the compare matrix elements by pair-wise comparison method. In pair comparison of criterion, if the priority of an element i compared to element j is equal to cij, then the priority of the element j compared to element i is equal to 1/cij. The priority of element compared to it is equal to one. Table 6 shows the scale used to make the paired comparisons with the AHP. Assuming M factors (ci, i = 1,2,…,m) involves in the evaluation index system, the matrix Cm9m of the paired comparisons is shown in Eq. (16)

One of the advantages of the AHP is that it allows identifying and taking into account the inconsistencies of the decision-makers, since they are rarely consistent in their judgments. Therefore, a Consistency Index (CI) and a Consistency Relationship (CR) are incorporated into the analysis. The CI, which is used to measure the quality of the judgments made by a decision-maker, is estimated by Eq. (18). Herein, kMAX stands for the largest eigenvalue of the matrix Cm9m. A CI lower than 0.10 is considered acceptable; if it is higher, it will be necessary to ask the decision-maker to make the assessments or judgments once again. The CR, which is used to represent a measure of the error made by the decision-maker, is estimated by Eq. (19). A CR depends on the value of CI and Random Index (RI). The value of CR should be lower than 10 % of the RI. The value of RI for 3–12 attributes is presented in Table 7.

123

ð18Þ

Stoch Environ Res Risk Assess (2015) 29:513–526 Table 7 Consistency random index (RI)

525

m

3

4

5

6

7

8

9

10

11

12

RI

0.58

0.90

1.12

1.24

1.32

1.41

1.45

1.49

1.52

1.54

kMAX m m1 CI CR ¼ RI CI ¼

ð19Þ ð20Þ

Appendix 2: Entropy weighting Entropy concept, proposed by Shannon (1963), is a measure of uncertainty in information formulated in terms of probability theory. Since the entropy concept is well suited for measuring the relative contrast intensities of criteria to represent the average intrinsic information transmitted to the decision maker (Zeleny and Cochrane 1982), the entropy weighting is used to decide the objective weights of attributes. Given a decision matrix with column vector xi = (xi1, xi2,…,xin) that shows the contrast of all alternatives with respect to ith attribute, an attribute has little importance when all alternatives have similar outcomes for that attribute. Moreover, if all alternatives are the same in relation to a specific attribute then that attribute should be eliminated because it transmits no information about decision-makers preferences. In contrast, the attribute that transmits the most information should have the greatest importance weighting. Mathematically this means that the projected outcomes of attribute i, denoted by Pij, are defined by Eq. (21). The entropy Ei of the set of projected outcomes of attribute i is defined by Eq. (22) xij Pij ¼ Pn

j¼1 xij

n 1 X Ei ¼ Pij In Pij In n j¼1

ð21Þ

ð22Þ

where n is the number of alternatives, Ei lies between zero and one. The degree of diversification di of the information provided by outcomes of attribute i can be defined by Eq. (23). Hence, the entropy weighting of an attribute, denoted by d, is calculated by Eqs. (24) and (25) d i ¼ 1 Ei

ð23Þ

di di ¼ Pm

ð24Þ

i¼1

di

d ¼ ½d1 ; d2 ; . . .; dm

ð25Þ

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