Ensuring the Human Right to Water in Dam Break Scenarios Using Geoprocessing and Multicriteria Analysis

Abstract

The high incidence of mining dam failures in recent decades and the socio-environmental aspects related to these events demand improvements in disaster risk management in the mining sector. One of the impacts related to mining dam failures is the alteration in water quality downstream of the breach. This chapter presents a methodology to determine critical points regarding the assurance of the right to access safe water, signaling locations that deserve special attention, and demonstrating practical application through the case study of the Piracicaba River. Geotechnology solutions, such as the use of multicriteria analysis associated with geoprocessing, play a prominent role in spatial studies related to environmental impacts, such as those caused by mining dam failures. The overlay of various layers of information, whether they are related to environmental or anthropogenic factors, provides coherent and consistent data concerning the reality presented in the particularity of each studied location. The assessment of the impact of a dam breach on surface water catchments carried out through this technology, provides a ranking of the potential damages caused and, consequently, allows for better decision-making for mitigation or even the prevention of future damages caused by the interruption of water supply from potentially affected watercourses.

1. Introduction

In recent decades, mining dam failures worldwide have raised new questions in both political and academic contexts regarding the safety of these structures. In a bibliographic survey conducted by [1], 250 events of tailings dam failures were identified between 1910 and 2010, with a significant portion occurring between 1960 and 1980. These events have their risk of occurrence further amplified by natural events, as observed by [2], a concern that intensifies with climate change. The El Cobre Dam failure, a copper mining dam complex in Chile in 1965, was caused by an earthquake in the region, leading to the destruction of the city. Another natural event caused by heavy rains and thaw contributed to a dam failure in Maramures County, Romania, in 2000 [3].

One of the impacts related to mining dam failures is the alteration in water quality downstream of the breach. There is a knowledge gap in terms of methodologies focused on predicting the impact on water catchments.

A thorough historical data survey [4], points out the vulnerability in verifying information related to such impacts, as a significant portion of dam failure studies do not provide data on the impacts on water quality/supply. Some real examples of impacts on water quality and supply in dam breach events are listed in Figure 1.

Figure 1.

List of dam breach events with recorded impacts on water quality and supply. Source: adapted from [4].

Still regarding the Fundão dam break, [5] reported that the increase in turbidity and inorganic substances temporarily rendered the water unsuitable for human consumption and agricultural use. The event resulted in the downstream transport of approximately 50 million cubic meters of mining tailings. The resulting mud traveled 600 km through the Doce River basin (southeast Brazil) and reached the Atlantic Ocean after 16 days [6]. According to the author, all 41 cities [7] that relied on the river had to suspend water catchments. This vulnerability can be identified before a dam failure event, thereby allowing for the mitigation of predicted impacts and, consequently, safeguarding the right to safe water.

Flood or dam break studies are employed to characterize potential impacts resulting from flooding due to the rupture or malfunction of a mining dam, aiming to safeguard human lives, properties, and environmentally sensitive areas [8]. Hence, flood maps are crucial in Emergency Action Plans, providing dam owners and emergency management authorities with information about the affected areas in the event of a breach, as well as flood wave arrival times, facilitating timely notification and evacuation of potentially affected areas, and planning measures to minimize wave-related impacts [9]. Additionally, the use of methods to predict water quality even before an eventual dam failure, identifying impacts on water quality and access, is of utmost importance for identifying and mitigating the impacts on water supply for affected communities. This allows both the entrepreneur and the state to plan emergency response actions effectively. Spatial analysis and multicriteria analysis methods are potential tools to aid in the identification of water catchments that may be impacted in the event of a dam failure, requiring structural interventions (such as treatment station reinforcement or possibly new works) or that may have an emergency response plan involving water trucks.

Spatial analysis comes with the fundamental need to understand various layers of information that, when combined, yield a range of results. The interaction between society and the environment is not simplistic, and to comprehend these interactions that are constantly evolving and improving, geoprocessing tools come into play. In [10], geoprocessing is referred to as the implementation of a process that brings progress to Earth representation. This progress goes beyond mere representation, making it possible to envision future realities through event and fact modeling methods, data, and information that project into estimates, scenarios, and probabilities, as depicted in Figure 2.

Figure 2.

Representation of dam breach scenarios and their relationship with water supply. Source: developed by the authors.

An example of such a method is multicriteria analysis, which involves characterizing phenomena through the numerous variables that make up reality. Organizing these variables into data, categorizing this data into layers, and applying these layers in combined flows simplify the complex spatial reality, making it possible to systematize natural and/or anthropogenic processes and consequently enabling spatial modeling that presents alternatives for future events.

Environmental studies related to hypothetical mining dam failures benefit from techniques like this. By using methods such as multicriteria analysis, overlaying variables of interest in this study, it is possible to prioritize surface water catchment points based on the complexity of data attributed to each point. Defining appropriate scores and weights for each layer of information is the key to defining a prognosis consistent with the desired purpose. Systematizing a methodology within the multicriteria analysis method allows for confident decision-making regarding the security of ensuring human rights to access safe water.

This chapter will present a methodology that utilizes multicriteria analysis to determine critical points, signaling locations that deserve special attention in Public Water Supply Plans, or even in emergency cases of mining dam failures, situations that require extreme agility in making decisions to solve the water supply problems resulting from the dam failure event.

2. Methodological definition

Geographic analyses greatly benefit from a systemic view of reality, achieved through an understanding of the various elements that comprise the environment, whether natural or anthropogenic, enabling the perception of an organized system [11]. When this system is dissected based on its different spatial characteristics, it allows us to select and utilize elements of interest in methodologies, such as the one chosen for this study.

The choice of the multicriteria analysis methodology was driven by the feasibility of utilizing specific elements that were deemed relevant in the systematization of a scenario of water scarcity resulting from a mining dam breach. Determining which spatial characteristics will be used and their respective levels of importance within the context serves as the starting point for the development of this methodology, summarized in Figure 3.

Figure 3.

Methodological flowchart. Source: developed by the authors.

As determined in [12], when conducting a multicriteria analysis to establish a hierarchy of importance among different locations, it is suggested to employ the technique known as “Weights of Evidence” (WE). This method involves a preliminary selection of relevant variables for the analysis, as well as data preparation to enable manipulation through map algebra operations. This preparation applies to both the format of vector elements (such as points, lines, polygons, and rasters) and the normalization of quantitative and qualitative data within a standard numerical scale, establishing a minimum and maximum interval, for example, from 0 to 1 or from 0 to 10.

Subsequently, it is necessary to perform a pairwise integration of the variables, validating them through mathematical models, such as the Analytic Hierarchy Process (AHP) model developed in [13], which is the model employed in this study. The obtained results are then verified through comparisons with observed real-life situations, process calibrations, and result validations to ensure their reliability. Finally, the analysis results are used to support decision-making processes.

2.1 Definition of variables

The stage of defining variables requires special attention, as it is where the layers to be overlaid to obtain the model’s result are determined. To define variables that are relevant to the study, various items that could be determinants in the impact analysis of a disruption of surface water catchments were verified, always considering the feasibility and reliability of the data to be obtained and their relevance in the overall context of the analysis. The chosen variables are presented in Figure 4, in descending order of impact on the study:

Figure 4.

Infographic depicting variable definitions according to their importance in the study. Source: developed by the authors.

For the first variable, “Population served by the affected water catchment”, it is essential to delineate the area affected by the interruption of the water supply from a specific catchment point. To determine the affected population, a survey must be conducted on-site using either census data (primary data) or publicly available information from the most recent census (secondary data). If the affected area’s boundaries are not available, an alternative is to estimate the affected population by dividing the daily catchment flow by the average daily consumption of an adult (200 L/day).

The criterion “Use of the water” is directly related to the catchment point and aims to give greater relevance to “human consumption” use, correlating with the “Flow rate of the affected catchment point” variable. Different types of use should be reclassified, considering the various purposes listed in the water rights database. Four classes were defined to meet the main objectives of this study: human consumption, irrigation, animal watering, and others. The latter incorporates other use purposes not included in the first three classes, as their impact is more significant due to their direct effect on the population’s quality of life.

The “Supply scope: public or individual” variable is directly related to the previous variable and aims to give more importance to “human consumption” use, correlating with the “Flow rate of the affected catchment point” variable. Surface catchments considered of insignificant use by the responsible water resources agency are classified as individual supplies. Non-insignificant water rights that have a flow rate equal to or lower than those classified as individual supplies are also considered individual supplies. All other human consumption catchments with flow rates above this established limit are considered public supplies.

The “Flow rate of the affected catchment point” is a quantitative variable representing the amount of water that needs to be regulated in case of an interruption of the catchment. This flow rate is determined based on the authorized flow rate for the catchment point, or in the case of unregistered catchments, it is established through flow tests. The flow rate is directly related to the catchment point and is considered a single value for the entire impacted area. It is important to consider the periods of catchment use when calculating the average value of the authorized flow rate based on the number of hours per day and days per year that the catchment operates.

Regarding the “Proximity of the affected area to loading points” variable, the existing road network from a central point in the affected area to previously mapped loading points for water trucks should be considered. This quantitative variable is calculated based on the distance for water transportation, seeking the shortest feasible distance along existing routes. For this purpose, route calculation tools in geoprocessing software are utilized, such as the tool pgRouting, an extension of the open-source software QGIS, for example. The values can be calculated based on coverage radii from the catchment point, generating buffers of 25 and 50 km from the affected catchment and identifying the existence of auxiliary water catchment points within these radii. The latter method should be used if location information for the affected area is not available. Whenever possible, it is recommended to prioritize route calculations using existing roads to increase the study’s accuracy.

Similarly to the previous item, the “Slope of access routes in the affected area” considers the accessibility of the affected area. This variable aims to assess the viability of access to the impacted region for water truck circulation and other vehicles required in the process of regulating the water supply. The slope of the access routes in the affected area may restrict some supply alternatives, making it an important variable in the overall analysis. It is obtained by using high-resolution Digital Elevation Models (DEMs) to calculate the slope of the road layer in the affected area. It is essential to use high-resolution DEMs to identify the specific slope of the road. To obtain a single value for the entire affected area, the steepest slope occupying more than 10% of the total area of the accesses is assigned to the entire region.

Finally, the “Types of accesses present in the affected area” variable also considers the accessibility of the affected area. This variable aims to classify the existing accesses in the affected region as rural roads (unpaved rural roads), paved rural roads, or urban roads. This classification is adapted from the Brazilian Traffic Code [14] and aims to grade the levels of local access difficulty, which, like the previous variable, may represent a challenge for the proposed supply alternatives. The determination of values should also be standardized for the entire affected area, with the predominant access type determining the assigned values.

2.2 Definition of variable components

To proceed with the multicriteria analysis, it is essential to normalize the components of each variable on a common scale of analysis. Both quantitative and qualitative attributes must be converted into numerical values, using a standardized scale that reflects the degree of relevance of each item in the variable. This approach is known as “Weight of Evidence.” [13].

Through the Weight of Evidence methodology, it is possible to generate a ranking of standardized variation for each component, which will be subsequently combined through a weighted average with specific weights assigned to each variable.

To normalize the components of each variable, it is necessary to follow the logic presented below. This step is essential to ensure that all data are comparable and that there are no distortions in the final analysis.

The data for the variable “Population served by the affected water catchment” are numerical and are reclassified by grouping the magnitudes of the affected population into three categories: a population less than 30,000 inhabitants, a population between 30,000 and 100,000 inhabitants, and a population greater than 100,000 inhabitants. For areas analyzed without correlation to water rights characterized as “human consumption” use, the component is denoted as “no population data.” The importance rating for each item is represented by scores on a logical scale, as exemplified in Table 1.

Criterion	Components	Scores
Population served by the affected water catchment	No population data	0
	Population less than 30,000 inhabitants.	1
	Population between 30,000 and 100,000 inhabitants.	5
	Population greater than 100,000 inhabitants.	10

Table 1.

Scores for the components of the “Population served by the affected water catchment” criterion.

Source: developed by the authors.

For qualitative data regarding “Use of the captured water,” the assignment of scores was based on the importance of each component of the variable. The scores were assigned according to the logic of the level of impact on the population’s life, organized as listed in Table 2.

Criterion	Components	Scores
Use of the captured water	Others*	0
	Irrigation*	5
	Animal Watering	7
	Human Consumption	10

Table 2.

Scores for the components of the criterion “use of the captured water”.

*

Lower ratings, considering that other uses beyond human consumption and animal watering may be subject to eventual compensation.

Source: developed by the authors.

The classification of “Supply scope: public or individual”, also a qualitative variable, is divided into three components. A lower value is assigned to water rights data that are not for human consumption, an intermediate value for individual consumption (flow rate stipulated by the responsible water resources agency of the locality), and the highest value for public supply, considering the significant impact caused by a possible interruption. The values are distributed as presented in Table 3.

Criterion	Components	Scores
Supply scope: public or individual	Other uses other than human consumption	0
	Individual Supply	5
	Public Supply	10

Table 3.

Scores for the components of the criterion “supply scope: public or individual”.

Source: developed by the authors.

To define scores for the “Flow rate of the affected catchment point,” which is a numerical variable, we use the statistical calculation of quartiles based on data with non-zero values. Data with a value of zero is considered as “Undetermined flow rate” and receives a specific value in the components of the variable. The other values that compose the quartile statistics (Minimum, Q1, Q2, Q3, and Maximum) are used to determine the boundaries of each component.

In their study, [15] defines that quartiles divide an ordered set of data equally. The second quartile (Q2), also known as the median, divides the set into two subsets with the same number of elements, while the first quartile (Q1) divides the first half into two equal parts, and the third quartile (Q3) divides the second half.

When dealing with a significant amount of data, it is advisable to use the following Excel formula to calculate the values of Q1, Q2, and Q3: “=QUARTILE.INC(array, quart)”. Where “array” is the cell range of numerical values from which you want to obtain the quartile value, and “quart” indicates the value to be returned (1 for Q1, 2 for Q2, and 3 for Q3).

Table 4 presents the assignment of scores following the logic of data separation into quartiles.

Criterion	Components	Scores
Flow rate of the affected catchment point	Flow rate not determined	0
	Minimum	2
	Minimum to Q1	4
	Q1 a Q2	6
	Q2 a Q3	8
	>Q3	10

Table 4.

Grades for the components of the criterion “flow rate of the affected catchment point”.

Source: developed by the authors.

The criterion “Proximity of the affected area to loading points” is divided into three components defined by previous experience in the elaboration of emergency plans for public water supply. The data is distributed quantitatively based on the distance from a central point of the affected area to the loading point of the tanker trucks, or, in the absence of information about the affected area, qualitatively based on the presence of any supply point within buffers of 25 and 50 km delimited from the catchment point. Obtaining data from the supply system with the responsible authorities, especially regarding the distribution network, location, and volume of reservoirs, is of fundamental importance. Table 5 demonstrates the hierarchically assigned scores to provide minimum/medium/maximum weights:

Criterion	Components	Scores
Proximity of the area without supply to loading points	Distance less than 25 km	0
	Distance between 25 and 50 km	5
	Distance greater than 50 km	10

Table 5.

Scores for the components of the criterion “proximity of the affected area to loading points”.

Source: developed by the authors.

For the variable “Slope of access routes in the affected area,” with the steepest slope value already normalized for the entire affected area, the slope classification proposed in Ref. [16] was adopted, as shown in Table 6. The slope scores were assigned following equal intervals, with higher weights for steeper slopes.

Criterion	Components	Scores
Slope of access routes in the affected area	0 a 3%	0
	3 a 6%	2
	6 a 12%	4
	12 a 20%	6
	20 a 45%	8
	Above 45%	10

Table 6.

Grades for components of the criterion “slope of access routes in the affected area”.

Source: developed by the authors.

As the last criterion, assigning scores to the “Types of accesses present in the affected area” was based on the road classes present in the area, categorizing them according to their drivability conditions. The highest score is given to the predominance of rural roads (representing higher difficulty of access), while the lowest score is reserved for urban roads (indicating easier access) (Table 7).

Criterion	Components	Scores
Types of accesses present in the affected area	Predominance of urban roads	0
	Predominance of paved rural roads	5
	Predominance of dirt roads	10

Table 7.

Notes for the components of the criterion “types of accesses present in the affected area”.

Source: developed by the authors.

2.3 Definition of weights for criteria

After normalizing the values of the variables’ components, the next step in the analysis is the assignment of weights to each adopted criterion. These weights aim to combine the variables in a way that considers their relative contribution to the result.

The method of integrating variables adopted is pairwise, as verified through the AHP model (Analytic Hierarchy Process) developed in [13], which considers the relative degrees of importance of the criteria according to Table 8.

Intensity of Importance	Definition	Explanation
1	Equal importance	Equal contribution to both factors regarding the study objective
3	Moderate importance	Slightly more important than the other factor for the analysis
5	Essential importance	The importance of one factor is significantly greater than the other
7	Demonstrated importance	Greater relevance strongly demonstrated compared to the other factor
9	Extreme importance	Highest possible order of differentiation in relevance between factors
2, 4, 6, 8	Intermediate values between judgments	Possibility of additional trade-offs

Table 8.

Intensity of importance for variable comparison.

Source: adapted from [17].

Considering all the variables in this study and comparing them in a correspondence matrix, where: A = Population served by the affected water catchment; B = Use of the captured water; C = Supply scope: public or individual; D = Flow rate of the affected catchment point; E = Proximity of the affected area to loading points; F = Slope of access routes in the affected area; and G = Types of accesses present in the affected area, the defined importance is assigned based on the knowledge of the relationship between the criteria.

The correspondence matrix consists of comparing the variables and assigning importance to this comparison (according to the values in Table 8). The importance of the criterion in the row is compared to that in the column, and for equal criteria (e.g., A/A), the value of 1 is assigned. The comparison should follow the increasing order of importance of the variables, in the columns from left to right (from the most important to the least important criterion), and in the rows from top to bottom (from the most important to the least important criterion). Following this logic, the comparison should occur between the criterion in the first row and all the criteria in the columns, from the most relevant to the least relevant (e.g., A/A, A/B, A/C, … A/n). From the second row onwards, the importance assignments, according to Table 8, are given based on equal criteria (e.g., B/B, C/C), with the values inverse to those previously inserted in the previous fields. The value of B/A will be the inverse of the one assigned to A/B, for example (if the importance assigned to the comparison of criteria A/B is 3, the value of B/A will be 1/3).

By making the comparisons according to the logic described above, Table 9 is obtained.

	A	B	C	D	E	F	G
A	1,00	2,00	4,00	5,00	6,00	8,00	8,00
B	0,50	1,00	2,00	5,00	7,00	7,00	7,00
C	0,25	0,50	1,00	2,00	5,00	5,00	5,00
D	0,20	0,20	0,50	1,00	3,00	4,00	4,00
E	0,17	0,14	0,20	0,33	1,00	3,00	3,00
F	0,13	0,14	0,20	0,25	0,33	1,00	1,00
G	0,13	0,14	0,20	0,25	0,33	1,00	1,00

Table 9.

Correspondence matrix.

Source: developed by the authors.

After assembling the matrix, it is necessary to sum the columns to obtain total values for each of them, as shown in Table 10.

	A	B	C	D	E	F	G
A	1,00	2,00	4,00	5,00	6,00	8,00	8,00
B	0,50	1,00	2,00	5,00	7,00	7,00	7,00
C	0,25	0,50	1,00	2,00	5,00	5,00	5,00
D	0,20	0,20	0,50	1,00	3,00	4,00	4,00
E	0,17	0,14	0,20	0,33	1,00	3,00	3,00
F	0,13	0,14	0,20	0,25	0,33	1,00	1,00
G	0,13	0,14	0,20	0,25	0,33	1,00	1,00
Total	2,37	4,13	8,10	13,83	22,67	29,00	29,00

Table 10.

Sum of columns in the correspondence matrix.

Source: developed by the authors.

With the values summed for each column, the obtained totals (Table 10) should be divided by each weight from the correspondence matrix (Table 9), as shown in Table 11.

	A	B	C	D	E	F	G
A	1/2,37 = 0,4219	2/4,13 = 0,4843	4/8,1 = 0,4938	5/13,83 = 0,3615	6/22,67 = 0,2647	8/29 = 0,2759	8/29 = 0,2759
B	0,5/2,37 = 0,211	1/4,13 = 0,2421	2/8,1 = 0,2469	5/13,83 = 0,3615	7/22,67 = 0,3088	7/29 = 0,2414	7/29 = 0,2414
C	0,25/2,37 = 0,1055	0,5/4,13 = 0,1211	1/8,1 = 0,1235	2/13,83 = 0,1446	5/22,67 = 0,2206	5/29 = 0,1724	5/29 = 0,1724
D	0,2/2,37 = 0,0844	0,2/4,13 = 0,0484	0,5/8,1 = 0,0617	1/13,83 = 0,0723	3/22,67 = 0,1323	4/29 = 0,1379	4/29 = 0,1379
E	0,17/2,37 = 0,0717	0,14/4,13 = 0,0339	0,2/8,1 = 0,0247	0,33/13,83 = 0,0239	1/22,67 = 0,0441	3/29 = 0,1034	3/29 = 0,1034
F	0,13/2,37 = 0,0549	0,14/4,13 = 0,0339	0,2/8,1 = 0,0247	0,25/13,83 = 0,0181	0,33/22,67 = 0,0146	1/29 = 0,0345	1/29 = 0,0345
G	0,13/2,37 = 0,0549	0,14/4,13 = 0,0339	0,2/8,1 = 0,0247	0,25/13,83 = 0,0181	0,33/22,67 = 0,0146	1/29 = 0,0345	1/29 = 0,0345

Table 11.

Product of the correspondence matrix by the totals from Table 10.

Source: developed by the authors.

Next, the calculation of the Eigen vector is performed. “The Eigen vector represents the relative weights among the criteria and is obtained approximately through the arithmetic mean of the values of each criterion” [18]. The calculation is done by summing the rows of Table 11 and dividing by the number of criteria, as shown in Table 12.

Table 12.

Calculation of the Eigen vector.

Source: developed by the authors.

The values of the Eigen vector represent the weights of each criterion for the final calculation of the multicriteria analysis. Next, the result of each row in Table 12 should be multiplied by the corresponding totals from Table 10, and then the sum of these values should be calculated, generating the principal Eigen number, as shown in Eq. (1).

$$\begin{array}{c}\left(0,3683\ast 2,37\right)+\left(0,2647\ast 4,13\right)+\left(0,1514\ast 8,1\right)+\left(0,0964\ast 13,83\right)+\\ \left(0,0579\ast 22,67\right)+\left(0,0307\ast 29\right)+\left(0,0307\ast 29\right)=7,6204\end{array}$$E1

Next, the principal Eigen number should be validated using a consistency index (CI), expressed by [17] in Eq. (2).

$$\mathit{CI}=\frac{\mathit{\text{λmax}}-n}{n-1}$$E2

where CI is the Consistency Index; λmax is the largest eigenvalue of the matrix, equivalent to the principal Eigen number, and n is the number of criteria in the correspondence matrix.

Eq. (3) presents the Consistency Index for the values used here.

$$\mathit{CI}=\frac{7,6204–7}{7-1}=0,1034$$E3

The value of the Consistency Index should be used to calculate the Consistency Ratio (CR), which is the ratio between CI and the Random Consistency Index (RI), resulting in a value of less than 0.1. The Random Consistency Index is a constant value that depends on the number of variables (N) and was developed by [19], as shown in Table 13.

N	1	2	3	4	5	6	7	8	9	10
RI	0	0	0,58	0,90	1,12	1,24	1,32	1,41	1,45	1,49

Table 13.

Random consistency index (RI).

Source: [18].

Given Eq. (4),

$$\mathit{CR}=\frac{\mathit{CI}}{\mathit{RI}}<0,1$$E4

it is presented that the Consistency Ratio should be less than 0.1 to validate the consistency of the weight assignment.

After applying the formula, we have CR = 0.1034/1.32 = 0.0783, confirming the validity of the values applied to the matrix and the consequent consistency of the weights assigned to the criteria.

In summary, with the association of information from the table of Intensity of Importance for variable comparison, the correspondence matrix is obtained, and by applying the methodology from [19], it is possible to calculate the Eigen Vector (P) reflecting the weights of each criterion. With this information associated with the scores of each variable’s components and the number of criteria, it is possible to classify each capture point on the maps that will be developed based on the need for structural actions or not. Furthermore, with the information on CI (Consistency Index), RI (Random Consistency Index), and CR (Consistency Ratio), it was possible to validate the developed weight determination methodology, as CR was found to be less than 0.1. This information proves that the classification of weights for defining actions as proposed in the study can be applied and has been demonstrated to be effective.

2.4 Creation of the spatial results layer

Given the values for each component of the variable, normalized on the standard analysis scale, and after calculating the weights for each variable, the final step of the study involves map algebra, which consists of combining spatial layers (associating points, lines, polygons, or rasters) performed using geoprocessing software.

In the attributes of the vector layers, the respective scores for the original values of each component of the variable in question (quantitative or qualitative initial values) must be inserted. In the case of working with raster layers, the raster should be reclassified so that its original value is replaced by the normalized value with the variable’s scores.

Next, the combination of vector or raster layers should be done through weighted and quantitative integration [12]. Weighted average should be applied to each feature’s value following the logic of Eq. (5) below:

$$\frac{\left(V1\cdot P1\right)+\left(V2+P2\right)+\left(V3+P3\right)+\dots +\left(\mathit{Vn}+\mathit{Pn}\right)}{n}$$E5

where V is the score of the variable component (already normalized); P is the specific weight of the criterion (value from the Eigen vector, Table 12); and n is the number of criteria.

This result should be calculated using map algebra, performed in geoprocessing software (in this case, ArcGIS 10.2 was used), where the overlay of layers from different normalized variables, using the calculated weights and the weighted average described above, will result in a new layer with features represented by numbers that express the result of Eq. (5).

Finally, the resulting values are grouped into three criticality classes: Low, medium, and high criticality. It should be noted that the classification method to be used in geoprocessing software is natural breaks. The three classes can be linked, in a study of supply alternatives, to decision-making classes in emergency situations. For example, scenarios classified as low criticality may receive supply through water trucks, while locations classified as high criticality would require structural supply actions, and the intermediate class would have mixed supply alternatives.

3. Case study of the Piracicaba River

The method described is based on the fundamental premise of its applicability in practical situations. Areas with the presence of dams, regardless of the level of rupture risk, can make use of the methodology, as its application for possible damage prevention in a hypothetical breach is both feasible and recommended.

The practical application of the proposed method for prioritizing and determining the level of actions to be taken in the event of interruption of water supply due to the unsuitability of surface water catchments in a specific watercourse was realized in the Piracicaba River case. The study considered a hypothetical situation of a rupture of any of the 41 tailings or waste dams present in the river basin, which, if ruptured, could compromise the water quality of part or all of the watercourse. Therefore, all surface water catchments from the main river of the basin were surveyed for classification.

The Piracicaba River was chosen for this case study due to the large number of dams located within its watershed. The river originates in the municipality of Ouro Preto and flows into the Doce River, on the border of the municipalities of Ipatinga and Timóteo, approximately 150 km from the capital of the State, Belo Horizonte. The studied section is approximately 240 km in length.

Data on water use permits and registrations for insignificant use of surface water catchments were collected from the Spatial Data Infrastructure of the State Environmental and Water Resources System (IDE-Sisema), a corporate and shared management model for geospatial data, standards, and technologies of Minas Gerais State Secretariat for Environment and Sustainable Development (Semad). These compiled data from permits and registrations provided the necessary information to represent the analysis criteria listed below.

It is important to highlight that the data obtained from this source are not primary data, which imposed limitations on the analysis, restricting it to the four criteria listed above. It was not possible to obtain the location of the area affected by the possible interruption of the water supply or to perform a previous mapping of the points for the water truck supply. The consequent restriction in the number of criteria used does not make the study unfeasible, but it is worth considering that the use of all layers described in the methodology enhances the consistency of the analysis, as well as encompassing other factors that are significant to represent reality.

1. Population served by the affected water catchment, obtained by calculating the quotient of the daily catchment flow by the average daily consumption of an adult (200 L/day), resulting in an estimated value. Exact values were not obtained due to the unavailability of a census or registry of the affected area;

2. Use of the captured water, regrouped into two categories: human consumption and others (other uses related to the criteria components in the methodology were not identified in the catchments of the Piracicaba River);

3. Supply scope: public or individual, obtained by verifying the flow rates of human consumption permits (for this case study, only individual supply points and other uses that are not for human consumption were considered);

4. Flow rate of the affected catchment point, provided in L/s (with the subdivision of component classes done using quartile statistics for the values of each catchment).

The criteria “Proximity of the affected area to loading points,” “Slope of access routes in the affected area,” and “Types of accesses present in the affected area” irrevocably require the location and spatialization of the affected areas, and thus cannot be used in the case study. They are disregarded in the steps of calculating weights for criteria and layer combinations. Once again, it emphasizes the relevance of incorporating the aforementioned criteria in the application of the proposed methodology, and their non-use is viable only when data is unavailable.

Using the methodological approaches described in this study and disregarding the criteria with unavailable data, the selected set of criteria and their respective ratings for the variable components were obtained, as shown in Table 14.

Criteria	Components	Scores
Population served by the affected water catchment;	No population data available	0
	Population less than 30,000 inhabitants	1
	*Population between 30,000 and 100,000 inhabitants	5
	*Population greater than 100,000 inhabitants	10
Use of the captured water;	Others	0
	*Animal Watering	3
	*Irrigation	7
	Human Consumption	10
Supply scope: public or individual;	Other uses besides human consumption	0
	Individual supply	5
	*Public supply	10
Flow rate of the affected catchment point;	No determined flow rate	0
	Values equal to 0.00007 L/s	2
	Values between 0.00007 L/s and 0.00149 L/s	4
	Values between 0.00149 L/s and 0.00226 L/s	6
	Values between 0.00226 L/s and 0.02762 L/s	8
	Values above 0.02762 L/s	10

Table 14.

Scores for the components of the criteria.

*

components not present in the data of the Rio Piracicaba catchments, but kept in the table to preserve the logic of the valuation of grades.

Source: developed by the authors.

During this phase, the data was quantitatively normalized following Table 14. Specifically, for the flow classification, the values were calculated using basic quartile statistics, using a specific Excel formula developed for this purpose. After assigning ratings to the variable components, weights were assigned to the criteria, adopting the Analytical Hierarchy Process (AHP) methodology [13]. Table 15 presents the values assigned in the comparison matrix for calculating the weights, where A = Population served by the affected water catchment; B = Use of the captured water; C = Supply scope: public or individual; D = Flow of the affected catchment point.

	A	B	C	D
A	10,000	30,000	60,000	90,000
B	0,3333	10,000	30,000	70,000
C	0,1667	0,3333	10,000	30,000
D	0,1111	0,1429	0,3333	10,000

Table 15.

Correspondence matrix.

Source: developed by the authors.

The weights assigned to the criteria differ according to the number of variables used in the study; therefore, the values presented here are not the same as those shown in the methodology. However, the weights still follow the methodology described in Table 8.

From the matrix, the calculation of the column sums was performed to obtain the total values shown in Table 16.

	A	B	C	D
A	10,000	30,000	60,000	90,000
B	0,3333	10,000	30,000	70,000
C	0,1667	0,3333	10,000	30,000
D	0,1111	0,1429	0,3333	10,000
Total	16,111	44,762	10,3333	20,0000

Table 16.

Sum of columns in the correspondence matrix.

Source: developed by the authors.

Next, the values of the weights are divided by the calculated total for each column to normalize the values for the subsequent determination of the CI (Consistency Index), as shown in Table 17.

	A	B	C	D
A	1/16111 = 0,6207	3/44762 = 0,6702	6/10,3333 = 0,5806	9/20 = 0,45
B	0,3333/16111 = 0,2069	1/44762 = 0,2234	3/10,3333 = 0,2903	7/20 = 0,35
C	0,1667/16111 = 0,1034	0,3333/44762 = 0,0745	1/10,3333 = 0,0968	3/20 = 0,15
D	0,1111/16111 = 0,069	0,1429/44762 = 0,0319	0,3333/10,3333 = 0,0323	1/20 = 0,05

Table 17.

Product of the correspondence matrix (Table 15) by the totals of Table 16.

Source: developed by the authors.

The next step is the calculation of the Eigen vector by computing the arithmetic mean of the rows in Table 17, as shown in Table 18.

Table 18.

Calculation of the Eigen vector.

Source: developed by the authors.

Once the values of the Eigen vector (which represents the weights of each criterion) were obtained, the calculation of the principal Eigen number (Eq. 6) was performed. This involves multiplying the results of each row in Table 18 by the corresponding totals for each criterion in Table 16, and then summing these values to generate the principal Eigen number, as expressed below:

$$\left(0,{5804}^{\ast }1,6111\right)+\left(0,{2677}^{\ast }4,4762\right)+\left(0,{1062}^{\ast }10,3333\right)+\left(0,{0458}^{\ast }20\right)=\mathbf{4},\mathbf{1459}$$E6

Next, the validation of this value was done through the Consistency Index (CI), expressed by [17] in Eq. (7).

$$\mathit{CI}=\frac{\mathit{\text{λmax}}-n}{n-1}=\frac{4,1459-4}{4-1}=\mathbf{0},\mathbf{04865}$$E7

In which CI is the Consistency Index; λmax is the largest eigenvector of the matrix, equivalent to the principal Eigenvalue; and n is the number of criteria in the correspondence matrix.

The value of the Consistency Index was used to calculate the Consistency Ratio (CR), which is the ratio between CI and the Random Consistency Index (RI), given by [19] in Table 13. For the weights assigned to each criterion to be consistent, the CR value must be less than 0.1. Using the data presented here, the value for the Consistency Ratio is CR = 0.04865 /0.9 = 0.05406, confirming the validity of the values applied to the matrix and the consequent consistency of the weights assigned to the criteria.

Having established the feasibility of assigning weights, it was necessary to assign values to each component of the variable in their respective vector layers, normalized on the standard analysis scale. Subsequently, a map algebra was created, which involves the combination of spatial layers by integrating the point vectors related to each potentially affected grant. This integration was performed through the weighted average of the values for each component of the variable, calculated in the geoprocessing software, ArcGIS 10.2, considering the respective criteria weights.

As a result of this process, we obtained a final vector layer with a specific value for each grant, representing the weighted average as described above. These values were grouped into three distinct classes of criticality, defined in the ArcGIS software using natural breaks, resulting in a map, presented in Figure 5.

Figure 5.

Map representing the criticality hierarchy for surface water catchments in the Piracicaba River in case of mining dams failure. Source: Developed by the authors.

The application in the case of the Piracicaba River allowed the demonstration of more critical points, which would require special attention in the development of an Integrated Supply Plan. From the delineation of the critical points identified, it is possible to define strategies to avoid interruptions in water supply, ensuring the right to water use.

4. Conclusion

The use of geotechnologies in socio-environmental analysis has once again proven to be capable of providing solutions and pointing out paths that would be extremely difficult to visualize without such tools. By employing Multi-Criteria Analysis to overlay various space-modifying factors, it was possible to identify starting points for strategic decision-making regarding water use and the need to reduce vulnerabilities in water supply systems.

The application of the methodology enables the ranking of potentially affected surface water catchment points in the event of a dam rupture or waste disposal within the studied area. Such ranking provides satisfactory support for emergency decision-making, and the methodology can also be applied for risk assessment, enabling the prioritization of structural actions to mitigate future damages, as demonstrated in the practical application in the case of the Piracicaba River.

In summary, based on the data obtained from the application of the demonstrated methodology, it is expected that its utilization will assist both public authorities and private institutions in maintaining and improving water resources management, thereby preventing or mitigating impacts on the population from possible future events related to mining dam ruptures.

Abbreviations and symbols

AHP	Analytic Hierarchy Process
ArcGIS	Geoprocessing software
CI	Consistency Index
CR	Consistency Ratio
DEMs	Digital Elevation Models
IDE	Sisema - Spatial Data Infrastructure of the State Environmental and Water Resources System
n	Number of criteria
P	Specific weight of the criterion
pgRouting	QGIS geoprocessing application’s routing tool
Q1	First quartile (statistical calculation of quartiles)
Q2	Second quartile or median (statistical calculation of quartiles)
Q3	Third quartile (statistical calculation of quartiles)
QGIS	Open-source geoprocessing software
RI	Random Consistency Index
Semad	Minas Gerais State Secretariat for Environment and Sustainable Development
V	Score of the variable component
WE	Weights of Evidence
λmax	Principal Eigen number