Use of multi-criteria decision-aids for risk zoning and management of large area subjected to mining-induced hazards

The end of iron-mining operations in France’s Lorraine region has raised the problem of post-mining management. Collapses and subsidence have recently occurred in this region, which focused on the necessity to develop a specific methodology for risk zoning. The proposed methodology is based on the multi-criteria decision-aid approach called ‘ELECTRE TRI’, with aim to assign zones at risk into predefined classes. It allows experts opinions, qualitative and quantitative criteria and uncertainties to be taken into account. 2003 Elsevier Ltd. All rights reserved.


Introduction
Mine subsidence events have recently occurred in the Lorraine iron-mining basin (North-eastern France) causing major damages to surface buildings and infrastructures (Deck et al., 2003). These events have raised widespread awareness of the severity of human, technical, financial and legal risks due to the end of mining activities. The Lorraine iron-mining basin, which covers a surface area of 1150 km , had been mined for more 2 than a century (Varoquaux, 1995) up until 1997 by reliance upon the 'room and pillar' caving method under urban areas in order to prevent the ground from subsidence. This 'technical' prevention strategy, however, has failed several times throughout history and, consequently, it has now become necessary to establish a 'managerial' prevention strategy based on risk analysis. According to natural hazard theory, risk appears wherever and whenever assets are subjected to hazards; it is usually defined as 'the expected potential loss due to a particular hazard for a given area and reference period' (UN, 1992) and can be mathematically defined as the combination of hazard and vulnerability (UN, 1992; *Corresponding author. E-mail address: thierry.verdel@mines.inpl-nancy.fr (T. Verdel). Varnes, 1984). In France, Risk Prevention Plans (RPPs) have been adopted to control risks due to ground movement (MATE, 1999). Such plans consist of producing four principal outputs: an informative report about the natural phenomena; a hazard map (gives the contours of the area subjected to given levels of hazards); an assets evaluation (whether formalized or not on a map); and a risk map (superimposition of hazard and assets maps). In practice, RPPs are commonly prepared using the 'typical configurations' method (Didier, 1999), which entails identifying within the study area a limited number of rupture scenarios, called 'configurations'. A hazard level is then ascribed to each configuration. Afterwards, homogeneous zones are established according to these configurations in order to produce a hazard map. Despite the advantages associated with the 'typical configurations' method, which serves to formalize expert approach, some imperfections still remain. Firstly, when this method is placed into practice, it only provides a hazard map, not a risk map. Secondly, the hazard map established is extremely dependent upon the knowledge and experience held by the engineer in charge. Thirdly, the method has been developed for low extended area (quarries) rather than large extended area (mining basin). Lastly, uncertainties, inaccuracies and  incomplete knowledge are not explicitly identified nor taken into account. In order to overcome these shortcomings, we are proposing herein another method, based on a multi-criteria decision-aid approach, for prioritising zones at risk.

Multi-criteria, decision-aid methods for risk analysis
The zones at risk studied lie in urbanized areas within France's Lorraine region, which had been mined using the 'rooms and pillars' method. These zones span a land area of over 20 km . The 'rooms and pillars' method 2 consists of extracting ore in the rooms and then leaving pillars to support the weight of the overlying ground (see Fig. 1).
Mining works, however, can present a danger to people and buildings when pillars fail to withstand ground loads. Such a rupture can induce a gradual settlement of the surface, called subsidence (Fig. 2a), or a more brutal settlement called collapse (Fig. 2b), which consists in an instantaneous drop of the entire overlying ground (Whittaker and Reddish, 1989). These phenomena may, in certain instances, produce dramatic consequences (ruin) on surface buildings (Fig. 3) and infrastructures.
Within such a context, risk analysis proves to be a complex decision-making problem where the available information is uncertain (missing information, such as geological data) and imprecise (mining works maps) and where knowledge is incomplete (e.g. soil-structure interaction). Multi-criteria, decision-aid methods can help overcome these limitations because they basically include mathematical mechanisms to manage these aspects. One such method called ELECTRE (Roy, 1985;Roy and Bouyssou, 1993) is widely used in France and Europe for resolving decision-type problems involving institutions and experts (Roy and Bouyssou, 1993). We would like to emphasize the feasibility, advantages and difficulties encountered when adapting the ELECTRE method to the prioritisation of zones subjected to mining subsidence or collapse. The application of the proposed methodology requires the assistance of a committee of experts to handle complexity issues. The general principle underlying this methodology has been depicted in Fig. 4.
The committee of experts called upon for the present purposes has defined four risk classes, given that an appropriate monitoring device must be set up for the identified zones as a function of estimated risk level. By convention, Class 1 corresponds to the highest risk level and Class 4 to the lowest. A permanent monitoring system must be introduced for all Class 1 zones, while only reference levelling (topographic surveys) is required for Class 4 zones (see Table 1). The aim of this method is to identify and categorize homogeneous zones into these four predefined risk classes.
The first step consists in selecting the studied risk (collapse or subsidence) among those available (collapse, subsidence, pollution, sinkholes, slope instabilities, etc.). This choice will then influence the second step, which entails choosing the criteria applied to provide information on the risk and, similarly, to identify homogeneous zones over the study area; homogeneous zones are those whose intrinsic characteristics (i.e. values of the selected criteria) are identical (see Figs. 5 and 6). The last step consists of choosing a prioritisation method for analysing these homogeneous zones, i.e. moving from a partial evaluation of the zone on each criterion to a global evaluation of the entire zone (level of risk) (Fig. 7) based on all criteria. In the following sections, we will examine in greater detail how risk zones are selected, how a set (family) of criteria and sets of weights are defined, and how the 'ELECTRE TRI' method is integrated for prioritising zones at risk.

Selection of zones at risk and choice of evaluation criteria and weighting sets
The procedure used to select zones at risk is illustrated in Fig. 8. In addition to this schematic approach, the zones must satisfy two selection tests defined by the committee of experts: (1) the stress applied on pillars must be greater than or equal to 7.5 MPa (no pillar rupture is expected below this value); (2) zone width must exceed 0.9=H, where H represents depth from the operating wall (no significant effects on surface below this value). If these conditions are not fulfilled, it is considered that the selected zone presents no danger and monitoring is not necessary in such cases. The same conclusions are valid for zones with no surface assets.
Let Z be the set of zones at risk and Z be a zone i such that Z gZ, with is1, «, m, where m represents i the number of zones. The data available for each zone can be either quantitative (stress applied to pillars, depth, zone extent, etc.) or qualitative (presence of faults, superposition of pillars, sensitivity to flooding, etc.). The risk due to mining subsidence is therefore represented in a multicriteria form. Due to the extent of the basin studied and the objectives inherent in risk mapping, relevant data are synthesized through a family of criteria that may be defined on each zone selected for the prioritisation study. These criteria are implemented in conjunction with and under the supervision of a committee of experts. These criteria taken as a whole form a consistent family (Roy, 1985), meaning that: -Two zones with identical criteria values are assigned to the same risk class: the criteria family is said to be exhaustive; -A zone on which the value on one criterion is reduced (in terms of decreasing risk) cannot be assigned to a lower class (higher risk) than that initially assigned: the criteria family is said to be consistent; -A zone cannot be assigned to a class when one criterion is removed from the criteria family: the criteria family is said to be non-redundant.
The various criteria used have been grouped into two headings: 'susceptibility of the mine to collapse' and 'surface sensitivity' (see Table 1). The first refers to the 'probability of rupture' and the second to both the 'intensity of the rupture' and the 'value and vulnerability of assets'.
Let g be a criterion within the family of criteria, j where js1,«n and n is the number of criteria. A qualitative or quantitative scale is then defined for each criterion g . The quantitative criteria g , g , g , g j 1.  (Roy, 1985) and other coding systems, such as (6, 7, 8), could also be used. Two types of surface assets are considered for each zone Z : buildings and infrastructures. This distinction i makes it necessary to apply different criteria to evaluate the risk for Z according to surface occupancy. If Z is i i a zone with buildings, then the criteria used would be g to g and g to g . Table 3 gives a detailed 2.1 2.4 2.5.2 2.5.5 example of the evaluation of a zone with buildings. Note that due to the ultimate 'Public safety' purpose of this risk analysis, buildings have been considered more sensitive than infrastructures. If both buildings and infrastructures are present on a given surface zone Z , i then the criteria for zones with buildings are to be employed.

Choice of a method for prioritising zones at risk
Several multi-criteria, decision-aid methods can be used to progress from a partial evaluation of the risk on  (Roy, 1985;Roy and Bouyssou, 1993). One of the most frequently used methods is the 'weighted mean method', which provides a complete order and enables differentiating the weight of criteria. It is possible, for example, to ascribe a particular criterion g with a greater j weight, hence a greater role in determining the class assignment. This method, however, imposes certain strict constraints, such as the numerical evaluation on each criterion g and leads to compensation effects since j equal evaluation differences correspond to equal risk variation measurements (Roy, 1985). Furthermore, the weighted mean method does not easily accommodate uncertainties and inaccuracies. These elements make 'ELECTRE'-type methods and 'ELECTRE TRI' in particular, applicable. ELECTRE TRI is appropriated to sort zones Z into four predefined, mutually exclusive i and ordered risk classes (Roy, 1985;Yu, 1992).  Each risk class h (hg{1,2,3,4}) is delimited by a threshold profile Pr (see Fig. 9). A class profile Pr is h h a virtual zone representing an entry standard into a risk class. Each profile Pr takes a value on each criterion h g (Fig. 10) Fig. 11).
In order to assign zones to risk classes (to go from a partial assignment to a global assignment), we have chosen the 'ELECTRE TRI' pseudo-disjunctive procedure (see Appendix A). This procedure is based on the calculation of a credibility index s and its comparison with a parameter l. Intuitively, l represents a desired majority of decision-making criteria (Roy and Bouyssou, 1993). There are only three possible situations (Yu, 1992

Choice of weighting sets for the criteria family
The choice of criteria-specific weightings requires the input of expert opinion. Two methods were used to determine such weighting sets. The first consists of holding a meeting of the expert committee and discussing the criteria until a consensus is reached regarding the weight of each criterion. The second, known as the 'cards method' (Arondel and Girardin, 2000;Roy and Figuera, 2002), is well-adapted to ELECTRE-type methods and facilitates communication and discussion between experts. The operating approach consists of associating a card with each criterion. Experts are then individually asked to: sort the criteria from the least important to the most important, with the possibility of placing criteria at the same rank; insert blank cards to indicate the relative importance among criteria from one rank to the next; and specify the ratio of the highest weight to the least weight assigned the criteria. This revised Simos method (Roy and Figuera, 2002) has many advantages, namely preventing criteria from being eliminated by a zero-weight assignment and incorporating the various weightings ascribed by participants as a function of their interests and skills. This method was used to obtain one weighting set for zones with buildings and another set for zones with infrastructures (see Table  4). The weight of criterion j is denoted k . j The weights listed in Table 4 demonstrate that the   weights of 20 and 10, respectively, which represent 43% and 22% of total criteria family weight. Such a decision suggests that these two criteria play a determinant role in the choice of the risk class. Note that a single criterion with a low weight may be sufficient to change the decision made by the 'strongest' criterion in the family, provided it is contradictory and imposes a 'veto' (Roy, 1985;Yu, 1992), as shown below.

Implementation of the 'ELECTRE TRI' method
This section will describe the prioritisation method for zones at risk through a ten-zone sample ( Table 5). In practical terms, the method is capable of handling many more zones; up until now, we have actually applied it on over 300 zones.
All ten zones included in Table 5 contain buildings. Parametric studies have allowed identifying indifference and preference thresholds for each quantitative criterion.
In order to specify the appropriate monitoring system for each zone in Table 5, it is necessary to define entry conditions for risk classes. A statistical data analysis of an assignment sample of 52 zones under buildings and 69 zones under infrastructures helped establish these conditions which have then been validated by the committee of experts.
The ELECTRE TRI method was used in conjunction with the ELECTRE TRI software, Version 2.0 (Mousseau et al., 1999). This software relies upon two procedures for risk class assignment: the pessimistic procedure and the optimistic procedure. The pseudo-disjunctive procedure mentioned above (Section 4.1) corresponds to the optimistic procedure in the software.
The two credibility indices s(Z ,Pr ) and s(Pr ,Z ) were calculated for each of the ten zones and are presented in Table 6. These credibility indices are then compared to parameter l (see Section 4.1) which must be greater than 0.5. This value of l means that at least 50% of the criteria family accredits the entry of the zone Z into the i considered risk class. In practice, the value of l has to be greater than (1-highest weightytotal weight), i.e. above 0.57 in our case. With this minimum l value, assignment of a zone to a risk class needs the agreement of more than one criterion within the criteria family (this value prevents the most weighted criterion from being the only one to decide the assignment class). No value of parameter l higher than 0.57 is better than another. In this example, we have tested six values: 0.60, 0.65, 0.70, 0.75, 0.80 and 0.85.
For purposes of illustration, let's consider zone Z 8 and ls0.65. We first calculate the credibility indices and then proceed with risk class assignment. The comparison procedure begins with the low profile Pr of 3 Class 3. Z and Pr assume the values 11.2 MPa and 8 8 3 MPa on criterion g , respectively. From Table 5    as Z ' (Pr S Z ) as shown on Table 7.
Since no veto has been used in the present study (see Appendix A), all disagreements are equal to 0 ( Table  7). The credibility indices s(Z ,Pr ) and s(Pr ,Z ) Z can then be assigned to Class 1 (according to the 1 pseudo-disjunctive procedure). By proceeding in the same manner for all zones with ls0.65, zones Z , Z , Z and Z are assigned to Class 1 2 6 9 1, zones Z and Z to Class 2, Z to Class 3, and zones 3 4 7 Z , Z and Z to Class 4.

8 10
The robustness of the classification must, however, be demonstrated by analysing the sensitivity to the change of parameter l, the weighting sets, the thresholds and profiles (Roy and Bouyssou, 1993). The results from such a study are summarized in Table 8, which reveals that the classification of zones Z , Z and Z 3 4 1 0 remains insensitive to parameter changes. The classification of other zones oscillates between two successive classes (see Table 8).
We have only shown results for ls0.65. If l were ascribed too high a value (e.g. 0.85), the principle of maximum caution would become exacerbated. Under such conditions, most comparisons conducted between zones and profiles would conclude with their incomparability and would assign zones to Class 1 by virtue of the pseudo-disjunctive procedure.

Conclusion
In early risk-related decision-making phases, methods and tools are necessary to manage incomplete, inaccurate and heterogeneous information. However, all this available information must be combined in a rational way capable of assisting the decision-maker in risk prevention efforts (Dikau et al., 1996;Montovani et al., 1996;Soeters and Van Westen, 1996;Wu et al., 1996). Decision-aid methods are helpful in using and formally presenting available information in order to provide decision-makers and users with a common basis for discussing and resolving problems. In the case of the Lorraine iron-mining basin, analysis of the risk due to mining subsidence is a limited-data decision problem, in which the decision consists of choosing appropriate monitoring systems for all zones concerned. The 'ELEC-TRE TRI' multi-criteria, decision-aid method is of considerable utility in this context for prioritising zones at risk. Analyses have been based on several parameters and are therefore inherently multi-criteria. The ELEC-TRE TRI approach is based on comparison between study zones and the entry conditions (profiles) of predefined risk classes. This comparison is conducted for each criterion (partial comparisons) and all criteria are then synthesized into a single global conclusion regarding the entry (or non-entry) of a zone into a class. The reliability of the results provided is an important point for further study. The robustness of risk-zoning depends on several factors, including the accuracy of inputs, the definition of profiles and preference thresholds, and the weighting set. Sensitivity analyses are easy to carry out with ELECTRE TRI, which have up until now enabled classifying over 320 zones within the Lorraine iron-mining basin. greater than that for Z ) (Roy, 1985;Yu, 1992); i -If the preference threshold p is not equal to the j indifference threshold q , the interval between these j two values represents an ambiguity range over which it is presumed that the risk is higher even though the difference Ng (Z )yg (Pr )N cannot be genuinely conj i j h sidered as significant. It will then be stated that the risk for zone Z is slightly higher than that for the i low profile of class h, Pr (otherwise, the risk for h Pr is strictly higher than that for Z ) (Roy, 1985;Yu, h i 1992). By convention, if a zone is indifferent with a low profile in a given class, the zone is assigned to this class; it will be said that the risk class is closed at the bottom.

Nomenclature
In ideal cases, where the evaluation of zone Z on i each criterion is between the evaluation of Pr and h Pr , then Z is assigned to class h. However, this case hy1 i is rarely encountered (Roy, 1985). This is why we introduce the credibility index.

A.2. Credibility index
This index is built with all criteria and used to estimate the credibility of the assertion: 'the risk level of Z is at least as high as that of Pr ' (Z S Pr ) (or i hi h 'the risk level of Pr is at least as high as that of Z ' h i (Pr S Z )). It is denoted s(Z ,Pr ) (or s(Pr ,Z )) and may be equal to values lying between 0 and 1 (Roy, 1985). When this index equals 0, the assertion is completely rejected either because no criterion satisfies it or because a criterion is in a position to veto. If the index equals 1, the assertion is completely accepted, which means that no criterion is in opposition. Between 0 and 1, the credibility index is based on two other component indices: an agreement index and a disagreement index (see Fig. 12). The agreement index is a weighted mean of the partial agreement indices and is calculated as follows: where F is the set of criteria numbers and c the partial j agreement index on criterion j (Fig. 12). When the assertion 'the risk for Z is at least as high i as that for Pr ' is rejected for a criterion, the partial h agreement index for this criterion is equal to 0. The agreement index therefore only takes account of those criteria for which this assertion is not rejected.  (Yu, 1992) (Fig. 12).
In light of the above discussion, the credibility index is determined as follows:

A.3. 'ELECTRE TRI' assignment procedures
Two extreme rationales may be called upon when assigning a zone to a particular risk class: either Z is i assigned to the lowest class given by a criterion or Z i is assigned to the highest class given by a criterion. These two rationales correspond to a principle of caution, which is minimized in the first case and maximized in the second. ELECTRE TRI offers two assignment procedures to attenuate these two extremes, namely a pseudo-conjunctive procedure and a pseudo-disjunctive procedure. The pseudo-disjunctive procedure, inspired from the maximum caution rationale, is therefore well adapted to risk prioritisation. According to this procedure, the entry of a zone into a class is accepted if the zone is preferred (higher risk level), indifferent (equivalent risk level) or incomparable (risk level not comparable) to the low profile of the class. With the pseudo-conjunctive procedure, the zone may enter into a class only if it is preferred or indifferent to the low profile of the class. The treatment of incomparability differs from one procedure to the other.