Economic damage and life-loss estimates provide important
insights for the elaboration of more robust alerts and effective emergency
planning. On the one hand, accurate damage analysis supports decision-making
processes. On the other hand, the comparison of different flood alert
scenarios through modeling techniques is crucial for improving the
efficiency of alert and evacuation systems design. This work evaluates the
use of flood damage and life-loss models in floods caused by tailings dams
through the application of these models in the real case of the São
Francisco dam failure, which occurred in January 2007 in the city of
Miraí in Brazil. The model results showed great agreement with
observed damage and loss of life. Furthermore, different simulations were
done in order to measure the impact of increasing and decreasing alert
system efficiency on life-loss reduction. The simulated scenarios exploring
the inefficiency of flood alert and evacuation revealed that life loss could
have reached the maximum rate of 8.7 % of the directly exposed population
when considering the more pessimistic and uncertain scenario instead of the
actual null life loss achieved. The results of this work indicate that the
models could represent both the observed accident and different
alert and evacuation efficiency impacts. It highlights the importance of
developing and implementing robust alert and evacuation systems and
regulations in order to reduce flood impacts.
Introduction
The benefits provided to society by the construction of dams of different
types and purposes are undeniable. However, the failure of these structures
may represent high damage potential to downstream valleys (Proske, 2018).
From 1915 to 2022, 257 tailings dams worldwide suffered accidents, accounting
for 2650 fatalities (Piciullo et al., 2022). The rate of tailings dam
failures (1.2 %) is 2 orders of magnitude higher than the value of
0.01 % reported for conventional dams (ICOLD, 2001; Azam and Li, 2010).
In addition to the fact that tailings dams are historically more vulnerable
than conventional dams (Rico et al., 2008a), these dams generally present a
much more significant risk to the environment due to the physicochemical
characteristics of materials that may be stored in their reservoirs (Kossoff
et al., 2014; Fernandes et al., 2016; Rotta et al., 2020; Guimarães et
al., 2022).
North America and Europe are the continents with higher records of accidents
involving these structures (Rico et al., 2008b; Azam and Li, 2010). However,
from 2000 to 2023, Brazil alone accounted for 11 tailings dam accidents,
with consequences of different orders (economic, socio-environmental and
cultural). Three of these accidents took place in 2019, including the
Brumadinho dam failure, where 270 victims, including dead and missing
persons, were reported (Project Chronology of Major Tailings Dam Failures,
2023).
Potential flood impact assessment is an extremely effective tool for
supporting emergency planning and decision-making processes (Apel et al.,
2004; Merz et al., 2010). Specifically in flood events, the main socially
relevant impacts are loss of life and economic damage, which are both
objectively quantifiable and more relevant in the public perception of
disasters (Jonkman et al., 2003). Several methods are available for
evaluating the loss of life and economic damage related to floods. Comprehensive
literature reviews were realized by Merz et al. (2010) for flood economic
damage evaluation and by Jonkman et al. (2016) for flood loss of life
evaluation. Since then, other relevant studies and models were achieved for
economic damage (Gerl et al., 2016; Bombelli et al., 2021) and loss of life
evaluations (Huang et al., 2017; Li et al., 2019; Mahmoud et al., 2020; Ge
et al., 2021, 2022; Jiao et al., 2022; Alabbad et al., 2023). In addition,
recent computational advances and software developments allow for the
performance of more robust impact simulations (e.g., LifeSim and the Life Safety
Model). However, international studies that focused on tailings dam impact
assessments are rare. Lumbroso et al. (2021) performed life-loss simulations
related to the Brumadinho (Brazil) tailings dam failure. No studies focused,
jointly, on both tailings dam failure economic and loss of life assessments
were identified. This is one of the main topics explored in this paper.
We analyzed the São Francisco mining tailings dam rupture in Miraí
city, Minas Gerais state (Brazil). This accident took place in 2007. It
caused several damages in the downstream valley, including the flooding of
around 300 to 500 dwellings, generating economic and environmental losses.
Although a high risk was observed, the identification of the hazard and
evacuation procedures adopted during the event led to the absence of
fatalities. This accident represents an opportunity for research purposes
once it presents a particular case of efficiency of evacuation, and it was
the object of some important data gathering in national studies (Pimenta de
Ávila, 2007; Rocha, 2015; Veizaga et al., 2017) and media coverage,
which provides relatively detailed data concerning the real flood extent
and its consequences.
Even when considering natural floods, few studies compare damage estimates
with actual surveys (Molinari et al., 2019). The application of predictive
models for estimating impacts under these conditions is of great scientific
interest. It allows for validating the use of models against observed data
and estimating potential impacts in more or less favorable conditions with
the success of the observed evacuation through the simulation of
hypothetical scenarios.
In this context, this paper evaluates how accurate life-loss and damage
models may be for estimating tailings dam failure flood impacts and alert
and evacuation efficiency for loss of life alleviation. Furthermore, it
performs the application of models to estimate economic damage and loss of
life together. In addition to the objective of representing the real
accident, we simulated different scenarios for warning and evacuation,
validating and comparing the results with actual observed data and revealing
the benefits of using models to guide flood warning and evacuation system
implementation.
Case study – the Miraí accident in 2007
The São Francisco dam was a structure for storing tailings from the
effluent generated in the bauxite washing process of Mineração Rio Pomba Cataguases Ltda. The dam was located
8 km from the urban center of Miraí, a city located in the
Zona da Mata of Minas Gerais state (Fig. 1). The
breach wave directly impacted this city. The São Francisco tailings dam
reservoir was 34 m high, with a length of 90 m, a width of 9 m, and a capacity of approximately 3.8 million cubic meters.
Location map of the São Francisco dam in Miraí
city (MG) – Brazil.
The Miraí accident occurred on 10 January 2007, and its description,
with all available details concerning flood wave propagation, reservoir
characteristics, and impacts, was obtained from Rocha (2015). At around 03:00 LT, the water level in the reservoir rose rapidly due to an intense
rainfall of 121.3 mm, which lasted 4 h. The water overtopped the
dam's crest, starting to overflow through the surface spillway and through
the contact of the massif with one of the dam abutments, causing the dam to
collapse due to the rapid erosion caused by the volume and speed of the
water. According to local estimates, the collapse began around 03:30 LT,
with a sharp increase in the breach until 05:30 LT that day. About 82 %
of the volume of mud stored in the reservoir spread through the Fubá
River (which crosses the urban area of Miraí city) and continued beyond
the confluence with the Muriaé River. Figure 2
shows the Miraí accident and the extent of the observed inundation
area, outlined using satellite images and aerial photographs.
Observed inundation area after the São Francisco dam breach,
Miraí (MG).
According to local studies, during the rainfall event period, the dam
watchman noticed the rapid rise in the water level in the structure and
notified the military police about the imminent danger of rupture when the
water level of the reservoir was about 30 cm from the crest of the dam.
After receiving the warning, approximately at the same time as the beginning
of the dam collapse, the local military police went through the streets of
Miraí city, helping to evacuate the whole population during the night
successfully. Regarding the economic damage to the infrastructure of the
city, the municipal government estimated a value of approximately BRL 74 million (USD 14.149 million, using the average exchange rate for the first
half of 2022 with a value of 5.23), which is around 9 times the city's
annual budget. This estimate did not include the damage to residents due to
the loss of personal objects, furniture, and household structure. Other
consequences of the event were the death of fish and the interruption of
water supply in several cities downstream.
Method for achieving the potential evaluation of flood impacts
Several methods exist for analyzing and quantifying economic damage (Merz et
al., 2010). Nevertheless, due to the difficulty in specifying indirect and
intangible damage, the methods usually focus on direct tangible damage. For
estimating this type of damage, Merz et al. (2010) consider the following
aspects: characterization and classification of assets at risk,
quantification of impacts on flood-exposed assets at risk, and association
of the potential damage to assets through the use of damage models which
relates assets typology and flood characteristics to damage economic
potential.
The methods for assessing loss of life rely on behavioral assessment and
macroeconomic indicators (Jongejan et al., 2005). However, the monetary
specification of loss of life is complex due to the intangible
characteristic of this type of damage. Risk assessments usually address
fatalities directly and quantitatively, without monetary attribution
(Jonkman et al., 2003). Potential quantification of direct loss of life
comprises three main factors: first, the number of people potentially at
risk; then, the effectiveness of evacuation and shelter strategies, thus
determining the number of people who may be exposed to the event; and,
finally, the fatality rate estimate, which is the ratio between the number
of fatalities and the number of flood-exposed people (Jonkman et al., 2008).
Depending on the model, these main factors are represented by many other
specific factors (e.g., flood and people characteristics and when the flood
occurred).
There are several available life-loss models in the literature, as presented
by Jonkman et al. (2016). Among these models, we highlight LifeSim (Aboelata
and Bowles, 2005), an agent-based model used in this research. LifeSim
simulates the outcomes of event exposure, and its methodology links the loss
of life to the evacuation of people or their success in finding a safe shelter.
Besides, the model allows the estimation of economic damages. The full
version of the model is integrated into HEC-LifeSim v.1.0.1 (USACE, 2019).
This version, which was developed by the U.S. Army Corps of Engineers
(USACE), is the most used in North American consultancy and insurance
companies (Needham et al., 2016), and it is also being widely used worldwide
(Risher et al., 2017; Hill et al., 2018; Kalinina et al., 2018; Leong-Cuzack
et al., 2019; Wang, 2019; Tomura et al., 2020; El Bilali et al., 2021; Kalinina
et al., 2021; Silva et al., 2021; El Bilali et al., 2022). A more recent
version, LifeSim v.2.0, has been implemented (USACE, 2021). However, some
issues in this version, reported to the Risk Management Center (RMC) of the
USACE, prompted our decision to utilize the HEC-LifeSim v.1.0.1.
Based on these principles, the impact assessment methodology presented in
this article consists of three parts (Fig. 3):
(1) using accident data to model the amplitude of the tailings flood wave,
to map the flood extent, and to delimit the affected region; (2) estimating
damage and loss of life based on the analysis of exposure and vulnerability
of the urban area of Miraí city and the observed evacuation process;
and (3) developing scenarios for warning and evacuation to estimate the
efficiency of different measures that were or could be achieved during the
flood event.
Methodological parts and their interrelationships.
Dam breach modeling and flood wave mapping
In the HEC-RAS (Hydrologic Engineering Center – River Analysis System)
model, the propagation of the flood wave is given by solving the shallow-water equations (Brunner, 2020). In two-dimensional modeling using the
HEC-RAS version 6.3, the channel and the floodplain were subdivided into
nonoverlapping cells to form a grid for solving the equations. The digital
elevation model (DEM) used to generate the numerical grid was obtained by
the Shuttle Radar Topography Mission (SRTM), with 1 arc-second spatial
resolution (30 m). The Fubá River channel was inserted using the
AGREE method (Hellweger and Maidment, 1997), with later correction of the
river profile and insertion of topobathymetric points. This correction
reduced the average error from 3.6 m (DEM) to 1.2 m
(topobathymetric survey).
This grid can be structured by cells of any shape, with a maximum of eight
faces. These cells can be orthogonal or not; however, if there is
orthogonality in all or part of the grid, the solution of the applied
numerical method has an advantage in computational speed. A hybrid
discretization scheme that combines finite differences and finite volumes is
used to solve the shallow-water equations. Furthermore, the shallow-water
equations can be simplified, resulting in the diffusive wave model. However,
simplification is not recommended for the present study since it addresses a
dam failure, which denotes highly dynamic flood waves (Brunner, 2020). The
variation in speed in these situations can be highly drastic in space and
time, and diffusion wave simplification does not include the terms of local
acceleration (change of speed over time) and convective acceleration (change
of speed over space). The grid in this study was structured with 10 m
cells, being refined to 5 m in the region of the Fubá River
channel (Fig. 4). The Eulerian–Lagrangian method
was used to solve the shallow-water equations on flood propagation. The
databases used for constructing the model and the maps were obtained by
Rocha (2015) in a detailed local analysis of the accident.
Structuring of the numerical grid used in HEC-RAS.
Through several experiments performed on mud flow samples, O'Brien and
Julien (1985) defined classes of flow type by volumetric solid
concentration. The authors noticed that the volumetric solid concentration
in the waste stream is usually higher than 20 %. In these cases, there is
a variation in fluid viscosity, the flow being considered non-Newtonian
(Gildeh et al., 2021). Some studies present techniques to model the flow
resistance of non-Newtonian fluids (Jeyapalan et al., 1983; Jin and Fread,
1999; Rico et al., 2008a; Bernedo et al., 2011; Gildeh et al., 2021;
Larrauri Concha and Lall, 2018; Piciullo et al., 2022). Studies on the
applicability of some of these techniques (Travis et al., 2012; Melo, 2013;
Martin et al., 2015; Rocha, 2015; Machado, 2017) demonstrate the capacity
and limitations of tailings flood wave modeling adopting a Newtonian fluid.
For the case under study, analyses from a minor incident in 2006 during dam
raising showed that the reservoir sludge had a volumetric solid
concentration of 12 %, which consequently allows for the representation of
the flow as aqueous according to the definition proposed by O'Brien and
Julien (1985). Therefore, no technique was used to represent tailings flow
resistance without prejudice to the simulation.
As done for traditional flood modeling, different Manning coefficients were
determined for each class of land use and occupation determined by the
maximum likelihood method, using the Landsat 5 image (orbit 217 and point 75) of
15 October 2005, supplied by the U.S. Geological Survey (USGS, 2005). The classes
considered were (Fig. 5) dense vegetation, sparse
vegetation, exposed soil, urbanized area, and water body, with respective
coefficients of 0.160, 0.035, 0.025, 0.100, and 0.040, as proposed by the
Natural Resources Conservation Service (NRCS, 2016).
Map of land use and occupation – Manning coefficients.
The affluent hydrograph to the São Francisco dam reservoir was developed
considering the rainfall accumulation of 121.3 mm in 4 h, the
estimate of effective rainfall by the curve number (CN) method (NRCS, 1997),
and the transformation of this effective rainfall into a runoff by the
synthetic unit hydrograph method. The reconstruction of the accident (Rocha,
2015) led to the conclusion that the gap was 34 m high, 70 m wide
at the top, and 4 m wide at the bottom, and it developed in 4.5 h. Considering the affluent hydrograph calculated with a peak of
72 m3 s-1, the quota-volume curve with 18 % of the material
retained in the reservoir, and the quota-discharge curves of the spillway,
the breach hydrograph was developed by the author starting at 3 h 30 min,
with a peak flow of 422 m3 s-1 and peak and base times of 1 h
and 57 min and 3 h and 54 min, respectively. This breach
hydrograph was used as the upstream boundary condition of the model. As
the downstream boundary condition, normal depth was adopted in a section
approximately 220 m away from the urban area under analysis (the most
fitted flow condition), not influencing the study area.
Regarding the spread of the tailings flood wave, the simulated inundation
boundary comprised 1.171 km2, equivalent to 89.4 % of the total
observed (1.310 km2). Figure 6 shows the
envelope of the simulated inundation area, highlighting the urban region of
Miraí.
Inundation boundary simulated with HEC-RAS and observed from the
São Francisco dam breach.
Despite having similar percentages, the inundation boundary shows noticeable
differences. The simulation area an overestimation and underestimation of
16.0 % and 26.3 %, respectively, when compared to the observed flood
map. These discrepancies are a consequence of inaccuracies related to the
DEM used, which tends to overestimate altimetry in areas with buildings and
more robust vegetation, consequently reducing flood depths in these areas.
Meanwhile, due to the low resolution of the model, the lack of details on
altimetric obstacles that could obstruct wave propagation may lead to the
overestimation of hydraulic parameters in flat areas (Paiva et al., 2011;
Yamazaki et al., 2012; Saksena and Merwade, 2015; Jarihani et al., 2015).
Analyzing the flood hydrograph propagation through the sections indicated in
Fig. 6, one can perceive greater damping of the
peak flow in flatter regions. These regions provide an increase in flood
wave spread compared to regions of high slopes with embedded valleys, which,
in turn, provide higher propagation speeds (Fig. 7). The reach between CS-0 and CS-01 comprises two large areas of flatland
floodplain and an extensive floodplain. Such topographic characteristics are
also observed to a lesser extent in the stretch between CS-03 and CS-05. In
turn, the reach between CS-01 and CS-03 comprises a high-slope region. In
the urban region, between CS-05 and CS-06, there was no significant damping
of the peak flow, only a delay in peak time. This is probably because the
flood wave already reached the urban area of Miraí city damped with low
flow speeds. Table 1 presents the synthesis of the
results for each cross-section analyzed.
Breach hydrograph of the tailings wave propagation.
Synthesis of the results of the tailings wave propagation.
Cross sectionLocation downstreamPeak flowMaximum depthMaximum speedArrival timeTime to maximumof the dam (m)(m3 s-1)(m)(m s-1)(min)depth (min)CS-004223.96.40117CS-0130043265.24.683163CS-0250053224.14.1108172CS-0369943217.11.7132186CS-0499962915.64.0155260CS-0512 0062226.11.5179278CS-0614 0172164.42.1229295
Even though some differences between simulation and observation were
highlighted, the spread of the flood wave was consistent with the actual
event that occurred in 2007. Witnesses reported that the evacuation in the
first neighborhood of the urban region took place at dawn.
Table 1 shows that the arrival time in the section
closest to the start of the urban area (CS-04) occurs around hour 2.5 of
the simulation, equivalent to 06:00 LT on the event day.
For the urban area of Miraí city, the object of the analysis of
subsequent consequences, there were also discrepancies between the simulated
and actual boundary (Fig. 8). As for the entire
study region, the simulated and the observed area differed noticeably,
totaling 0.488 and 0.579 km2, respectively. Area
overestimation and underestimation in the simulation corresponded to 10.8 % and 26.5 %, respectively, again evidencing the consequences of
inaccuracies related to the DEM used.
Cutout of the envelope of the inundation boundary simulated and
observed from the São Francisco dam breach in Miraí city.
Potential damage and expected loss of life modeling
The agent-based life-loss estimation model used (HEC-LifeSim v.1.0.1) is
structured using a modular modeling system (Zhuo and Han, 2020). Each module
exchanges information with other modules through a database that includes
multiple layers and tables of the geographic information system (GIS) in
this system. The model also presents the uncertainty module, which allows for
the insertion of uncertainty boundaries in several input parameters.
Propagation of these uncertainties occurs with Monte Carlo simulations. The
four modules present in the methodology are “flood routine”, which
contains a set of networks representing flood characteristics throughout the
inundated area and period; “shelter loss”, which simulates the exposure of
people and buildings during each event as a result of building submergence
and potential structural damage; “warning and evacuation”, which simulates
the distribution of the population at risk after the warning issuance; and
“loss of life”, which estimates fatalities through probability
distributions (USACE, 2019). The inputs in the four modules are summarized
in Table 2 and are further elaborated on below.
Summary of HEC-LifeSim module inputs.
ModuleInput/parameterData/valueFlood routineHydraulic dataDam failure flood modeling performed in HEC-RAS 2DLoss of shelterStructural inventoryFeature layer set by aerial images and characterized by the Brazilian demographic censusDamage modelUSACE (1985) for building stability criteria and Nascimento et al. (2007) for monetary damage estimationWarning and evacuationHazard communication delayUniform distribution [-30, 0] min from dam failure startingWarning issuance delayTriangular distribution (0, 15, 30) minWarning dissemination time and mobilization timeBased on Sorensen and Mileti's (2015b, 2015e) recommendations, given the characteristics of the eventRoad networksOpenStreetMapDestinationsSet in high places outside the extent of the floodplain and close to roadsPedestrian speed1.79 m s-1Vehicle speedMaximum speed defined by the class of the road determined by the Census Bureau's Census Feature Class Codes and the speed of traffic conditions simulated by the modified transport model of Greenshields et al. (1935)Fraction of the people in vehicles0.5Loss of lifeFatality ratesFatality distribution curves for chance, compromised and safe zones, obtained by McClelland and Bowles (2002) and updated by USACE (2019)
Exposure and vulnerability analyses were carried out to prepare an inventory
of buildings presenting and characterizing the structures and populations at
risk in the flood-affected region. The following information was
consolidated for buildings and population in the shelter loss module:
dwellings location, occupation type, construction material, number of
floors, and population under and over 65 years of age (mobility criterion).
The affected population and number of households were determined by a set of
regular statistical grids integrating data from different sources and
aggregated in incompatible geographic units (IBGE, 2016). For each grid in
the flood-affected region (Fig. 9), households
were geographically allocated with the aid of satellite images, and the
population per household was considered homogeneously across the entire
grid. Once residential buildings majorly occupy the impacted area and
because the breach occurred during the night, outside business hours, other
types of construction were not considered in the study.
Statistical grid in the flood-affected region.
The exact number of buildings directly impacted by the flood wave in 2007
was not recorded. In local studies, it is possible to estimate that the
number of buildings directly affected is between 300 and 500. The observed
estimated flood boundary indicates that 358 households may have been
directly affected (354 in the urban area and 4 in the rural area). The
simulated flood boundary indicates 311 buildings (308 in the urban area and
3 in the rural area) (Fig. 10).
Zoom-in of the urban area of Miraí city indicating the
households potentially affected by the observed and simulated inundation
boundary.
In order to characterize households and the population obtained by the
statistical grid, samples of households and people existing in the 2010
Brazilian Demographic Census microdata were used, which are the main
reference for characterizing the population in Brazilian urban areas. For
the confidentiality of research informants, the smallest geographic unit for
identifying microdata is the weighting area, which is formed by grouping
census sectors (IBGE, 2011). Therefore, the results obtained considering the
weighting areas of interest were arranged proportionally and distributed
evenly in the affected region. Each sample element was multiplied by its
sample weight to represent the population.
The sample of households also enabled the determination of construction
material, occupation type, and social class, which is essential for damage
evaluation purposes. The construction materials considered were masonry and
wood. Occupation types were adopted considering the building codes presented
by Gutenson et al. (2018): single-family home (RES1), temporary
accommodation (RES 4), institutional dormitory (RES 5), and asylum or
orphanage (RES 6). The social class was defined using the average monthly
family income defined for each class as proposed in the Brazil Economic
Classification Criterion 2010 from the Brazilian Association of Research
Companies (ABEP, 2012). The sample of people enabled the determination of
the population under and over 65 years of age that were present at home at
night using the variable “return home”.
Statistical grids showed that 1537 households were affected by the flood,
corresponding to a population of 4675 people. The microdata analysis
considered the only weighting area existing for Miraí city. A total of
4209 households were obtained in the considered weighting area, in which
there is a predominance of single-family residential typology, masonry
construction material, and social classes C and D
(Table 3). The total population in the weighting
area was 13 808, with 94.6 % being at home at night
(Table 4).
Data obtained from the 2010 Brazilian Demographic Census microdata
on households in the affected region of Miraí city.
Type of dataOccupation typeaConstruction material ClassbRES1RES4RES5RES6WoodMasonryABCDMicrodata4132022550420914147815532037%98.20.00.51.30.0100.03.411.436.948.4Region of interest150908200153751175567744
a RES1: single-family home, RES 4: temporary accommodation, RES 5: institutional dormitory and RES 6: asylum or orphanage, defined according to Gutenson et al. (2018). b Socio-economic classes A, B, C and D, with A being the highest and D the lowest, according to criteria established by ABEP (2012).
Data obtained from the 2010 Brazilian Demographic Census microdata
on the population in the affected region of Miraí city.
Type of dataPopulation at home at night Total< 65 years> 65 yearsMicrodata13 06211 7241338%94.684.99.7Region of interest44223969453
By the analysis performed, the directly affected population at night was
1033 and 868 for the extent of observed and simulated flooding,
respectively. In order to minimize the possible effects of overestimating
and underestimating the extent of the flood on the number of buildings and
people directly affected, we constructed an alternative scenario of exposure
and vulnerability analysis. In this scenario, the number of people allocated
to the residences within the simulated inundation boundary was increased to
equal the number of people affected according to what was found in the
observed area. This excess number of 165 people was randomly allocated to
the affected households according to the extent of the simulated flood,
keeping the percentages in Table 4.
For building submergence in HEC-LifeSim, three flood head limits physically defined by the interaction between existing shelter and
depths thresholds are proposed: “chance zone”, “compromised zone”, and “safe zone”.
Chance zone refers to a condition where flood victims are typically swept
downstream or trapped underwater, and survival depends largely on chance.
Compromised zone refers to a condition where the shelter has been severely
damaged, increasing the exposure of flood victims to violent floodwaters. On
the other hand, the safe zone is typically dry, and the life-loss
probability is virtually zero. Stability is defined by the speed and depth
criteria for structural damage in buildings, considering occupation type,
construction material, and the number of floors. HEC-LifeSim allows the use
of several stability criteria, among these the criteria of USACE (1985) and
RESCDAM (2000).
The warning and evacuation module represents the distribution and behavior
of the population during the flood event, including each emergency planning
zone (EPZ) in the affected area. This process has several milestones that
are separated by time lag intervals, as shown in the timeline in
Fig. 11.
Warning and evacuation timeline. Source: USACE (2019).
The timeline starts from the identification of the imminent threat and
presents the first delay in communicating the threat to managers. In both
situations, no studies assist in determining these values; therefore, the
user must determine the time considering the characteristics of the case
under study. In contrast, the choice of time in the other three subsequent
delays is supported by the studies and equations of Sorensen and Mileti (2015a–e). These authors analyzed many disaster
cases with data available for evacuation, not only about floods but also
about chemical and fire accidents, adjusting models through the historical
cases and defining coefficients to represent a certain type of existing
warning system and population characteristics. Besides, in the
identification of the threat and all delays, it is possible to insert
uncertainty in the input data.
For the dynamics of evacuation, the modified transport model of Greenshields
et al. (1935) is used to represent the effects of traffic density and road
capacity on vehicle speed, and the short path algorithm of Dijkstra (1959)
is used to determine the path with the shortest travel time to the
destination. The user can insert the road network or import directly by
OpenStreetMap. If the flood reaches the vehicle or people during the
evacuation, the stability criteria defined by Aboelata and Bowles (2005) are
used. If these criteria are exceeded, the affected population is allocated
to the chance zone; if it is not exceeded, the population is allocated to the safe
zone. Other evacuation parameters, such as the fraction of the population in
vehicles vs. on foot, are presented in Table 2.
For the representation of the warning and evacuation timeline, the delays
for each step in Fig. 11 were determined. Based on
the information regarding the watchman's perception of the imminent danger
before the breach, the period between the hazard identification time and the
communication to the emergency planning zone was determined as a uniform
distribution from 0 to 30 min before the dam breach. This interval
corresponds to the period between the perception of the watchman and the
start of the dam's collapse. For warning issuance delay, a triangular
probability distribution was adopted with the minimum, most likely, and
maximum values of 0, 15, and 30 min, respectively. The other two stages,
with their respective uncertainties, were defined through the relationship
between the characteristics of the warning that occurred at the event and
the recommendations of Sorensen and Mileti (2015b, e).
Figure 12 shows the 90 % confidence interval for
the percentage of the population mobilized after the alert was issued (which
is the sum of these last two delays). By the median, the entire population
starts evacuating 150 min after the alert is issued.
Combined dissemination and mobilization time for the evacuation
scenario in the Miraí accident.
The fatality distribution curves, obtained by McClelland and Bowles (2002)
and updated by USACE (2019) through the analysis of historical cases of
mainly dam breach floods, were applied in the loss of life module. In order
to determine the economic damage, the empiric national equations of
Nascimento et al. (2007) were inserted into HEC-LifeSim for each social class
affected by the flood. The curves relate the depth (h) in meters to the
damage in BRL m-2 (reals per square meter of built projected area) to
the property structure and its contents. The built area of the affected
households was estimated in the function of national social classes, as
defined by Nascimento et al. (2006). Table 5
presents the equations and ranges of built area for each social class. These
equations were proposed in 2007, and for their use it needs a correction of
the values by some inflation index.
Model for economic damage and the most frequent range of built area
as obtained by Nascimento et al. (2007) for each social class.
After 1000 interactions (value used in studies applying HEC-LifeSim), the
economic damage was estimated at BRL 1.01 million to BRL 1.95 million
for the 311 households affected directly by the simulated flood. Corrected
by a factor of 169.12 % (based on the Broad National Consumer Price Index
– IPCA in June 2022), this value corresponds with BRL 2.72 million to
BRL 5.23 million in 2022 (USD 521 thousand to USD 1.00 million).
According to the public registry, 500 lawsuits related to property
material damage were filed by residents against the mining company following
the accident. Several of these lawsuits, judged between 2012 and 2013,
resulted in indemnities ranging between USD 956 and USD 1530 (STJ,
2014). Assuming that this indemnity range was allocated to each household
and applying it to all 311 affected households, a range between BRL 1.56
million and BRL 2.49 million is obtained in 2012. By using the IPCA-based
correction factor of 89.67 %, this value corresponds with BRL 2.95
million to BRL 4.72 million in 2022 (USD 564 thousand to USD 902 thousand). Thus, on average, this range of indemnity values was close to the
simulated economic damages for households (between BRL 4.64 thousand and BRL 8.92 thousand per household impacted according to the corrected value for the year
2012) (USD 888 thousand to USD 1.71 thousand). Table 6
summarizes the results of flood economic damage estimation.
Summary of economic damage using the Broad National Consumer Price
Index – IPCA to update the value to 2022.
ValueSimulatedSimulatedIndemnitiesIndemnitiesdamage in 2007damage in 202220122022(million BRL dollars)(million BRL dollars)(million BRL dollars)(million BRL dollars)Minimum1.012.721.562.95Maximum1.955.232.494.72
Regarding the estimated loss of life, the values obtained following the
actual event have a median of zero fatalities. On average, 99.97 % of the
population escaped the flood. Fatalities were estimated in only 67 of the
1000 interactions, the frequency of occurrence of which was one fatality in 65
interactions, two fatalities in one interaction, and three fatalities in one
interaction.
For the alternative scenario of exposure and vulnerability, fatalities were estimated in 65 interactions, the frequency of occurrence of which was
one fatality in six interactions, two fatalities in 58 interactions, and
three fatalities in one interaction. This result indicates that the model
fitted the real event, and the difference in the population directly
affected by the extent of observed and simulated flooding did not influence
the estimated loss of life.
Furthermore, in all 66 interactions in the base scenario that resulted in one
or two fatalities, the loss of life concerned the population over 65 years
of age, who were not mobilized for evacuation and, therefore, were allocated
to some of the flood risk areas. The same result was noticed in 62 of 64
iterations in the alternative scenario. This behavior indicates the impact
on the divergent submergence thresholds defined by Aboelata and Bowles (2005) to represent the mobility criterion. For the chance zone, the
threshold is 4.58 and 1.82 m for people under and over 65 years of age,
respectively. As expected, the simulated flood extent uncertainty
highlighted before did not influence the life-loss estimates.
Analysis of warning and evacuation efficiency
An effective warning system depends on several factors and is essential for
selecting appropriate emergency management (Rogers and Sorensen, 1989;
Lumbroso and Davison, 2018; Tonn and Guikema, 2018; Kolen et al., 2020). To
assess the success of the warning and evacuation with a view to a good
representation of the simulations in comparison with the observed data, we
developed, beyond the actual “optimistic” scenario that occurred, three
more scenarios: “pessimistic”, “moderate”, and “unknown”
(Table 7). The simulations were executed for both
base and alternative scenarios of exposure and vulnerability. The period
between the time of identification of the hazard and the communication to
the emergency planning zone was considered null. The three remaining steps,
warning issuance delay, warning dissemination, and mobilization time
(Fig. 11), were defined through the
recommendations of Sorensen and Mileti (2015a, b, e) for issuance
and dissemination of the warning and mobilization of the population.
Description of each modeled scenario of warning and evacuation
efficiency.
ScenarioDescriptionOptimistic (actual)It represents the real scenario that occurred in the event on 10 January 2007, and it is characterized by reports that detailed the accident, as described in Sect. 3.2. In this scenario, the evacuation was successful, with the entire population mobilizing, on average, 150 min after the alert was issued.PessimisticIt represents the worst possible scenario, using limited alerting technologies. Therefore, any emergency response necessarily involves improvisation. Affected communities are unlikely to believe they have a severe threat or may face events requiring a rapid response.ModerateIt represents an intermediate scenario, using only a combination of traditional technologies. About the population, it indicates the situation that most represents a community, given a mix of existing factors. However, it considers that this community does not have effective emergency planning.UnknownIt represents a scenario in which the existing alert system in the affected region is unknown. Therefore, the range of uncertainty inserted in the stages of the alert and evacuation process is greater, resulting in expected high variability in the estimate of the loss of life.
When simulating these three additional alert and evacuation scenarios,
differences were found between the two exposure and vulnerability scenarios
(Fig. 13). In all simulations, the median of the
alternative scenario was higher by two fatalities compared to the base
scenario: respectively, for the base and alternative scenarios, it was
computed to be 21 and 23 losses for the pessimist alert and evacuation scenario, 13
and 15 losses for the moderate, and 15 and 17 losses for the unknown. In
addition to verifying the high impact of the level of efficiency of the
alert and evacuation system, the observed and adopted optimistic scenario in
the evacuation process was confirmed in the real representation of the event
that occurred in 2007. In all the standard curves of Sorensen and Mileti (2015a, b, e) used to represent the delay in the issuance of the
alert, the dissemination of the alert, and the mobilization, the estimates
of the loss of life were higher than those obtained throughout these
scenarios.
Life-loss estimation for different scenarios of warning and
evacuation efficiency.
Results discussion
For a priori analyses of dam failure consequences, considering several
uncertainties in flood modeling is ideal for better representing the event
in flood risk assessment. Despite specific disparities between simulation
and observation, the flood wave propagation exhibited congruence with the
factual occurrence in 2007. Although there is a difference, it is essential
to note that most of the differences observed in terms of area are not
highly relevant for the study's purposes. These differences are mainly
observed in areas without buildings or population, except in a central area
where adaptations were made to improve the representation of the observed
risk by addressing vulnerability and exposure.
Even though the flood extent uncertainty was not the main focus of the
study, considering its relevance to the whole evaluation process, this
uncertainty was partially incorporated into the evaluation by contemplating
different scenarios. We evaluated the impacts of the flood model
uncertainties on the impacted population estimates using two different
vulnerability scenarios designed according to the observed and simulated
extent of the flood. It consisted of compensating the differences between
simulated and real event flood extent regarding the number of people
exposed. We spatially increased and reduced the amount of the population exposed
in the buildings nearby areas where differences were observed between
simulations and the real event. Considering these two scenarios, we noticed
that these uncertainties did not significantly impact the life-loss
estimates.
The comparative analysis between actual accident records and simulation
results yielded favorable outcomes in the examined case study, providing
evidence of the successful implementation of alert and evacuation measures.
Notably, the evacuation process proved effective, with an average of
99.97 % of the population successfully escaping the flood. This success
can be attributed to the relationship between the flood timeline and the
warning and evacuation.
The analysis of the tailings flood wave's spread revealed that it reached
the urban area's initial (CS-04) and final (CS-06) points in approximately
2.5 and 4 h, respectively. This ample timeframe allowed for
adequate mobilization of the population. Even when considering the most
pessimistic scenario involving the longest warning and evacuation periods,
the entire population could be fully mobilized within approximately 3 h.
Despite the inherent uncertainties associated with the tested models, the
calibrated models exhibited precise evaluation capabilities in terms of
economic damage and loss of life. These findings underscore the significant
potential of these tools in facilitating proactive and strategic development
for prevention and planning purposes.
Furthermore, the hypothetical scenarios of alert and evacuation allowed us
to demonstrate that, as performed by Lumbroso et al. (2021), flood
consequences may significantly increase or decrease depending on the
system's efficiency. For the specific case study, loss of life could have
been much more catastrophic. The simulated scenarios, exploring the
inefficiency of flood alert and evacuation under poor conditions, revealed
that life loss could have reached the maximum rate of 3.5 % of the
exposed population (pessimistic scenario) instead of the null actual
life loss recorded. Taking into account other uncertainty, we identified
that life loss could have reached the maximum rate of 8.7 %, considering
the unknown scenario. The fragile circumstances that led to the successful
evacuation in this case study, which relied on the actions of just one
professional (the watchman), could have turned into a much more
catastrophic accident, highlighting the great importance of developing and
implementing robust and secure alert systems for this kind of structure.
Conclusions
Risk assessment is an effective tool to assist in the emergency planning
requested for tailings storage structures under Brazilian law. This work
aimed to verify the application of consequence models by comparing their
real and estimated outcomes using the dam failure event that occurred in
São Francisco dam in Mirai, Brazil, in 2007. It was possible to collect
the real event data mainly based on local technical reports and information
collected from local authorities and post-event local studies. The breach
characteristics, arrival time at the city, and flood extension are
examples of this data.
The hydrodynamic modeling showed satisfactory results mainly due to the
similarity in the time the flood wave arrives, which is one of the main
parameters in loss of life modeling since it correlates with the time
available for evacuation of the population at risk. The modeling of the
economic damage was similar to the indemnity values per household. The model
was also capable of representing the loss of life estimates and the success of
evacuation in the event that occurred. However, in this specific case, the
low concentration of solids in the flow may have been one of the factors
that contributed to the success of the results obtained. We emphasize the
need to carry out studies of this type for other real accidents with greater
solid loads so as to expand the possibilities raised in this study.
The estimates acquired throughout the development of this case study were
adherent to observed data, which sustained the great potential of the use of
these modeling techniques for planning purposes. Besides, one of the great
advantages of HEC-LifeSim is the possibility of dynamically simulating the
evacuation of the population. The best suitability of this model in tailings
dam failure events can be achieved by changing the model standards. Several
criteria are editable, and changes in these criteria could assist in
representing the physicochemical characteristics of the tailings. It is
possible to adapt the representation of alert and evacuation to incorporate
specific characteristics for a specific case (as we did in this work). Furthermore, life loss rates can be modified to account for the impact of debris and other characteristics in potential interactions between tailings and humans.
In addition to HEC-LifeSim showing the ability to simulate the
non-occurrence of fatalities like the one that occurred in the event, the
model also made it possible to speculate on scenarios that take into account
lower alert and evacuation efficiencies, which resulted in much more
catastrophic scenarios in terms of loss of life.
Finally, this study explored models to estimate economic damage and loss of
life in floods at the same event of tailings dam failure. In this sense, it
shows the potential efficiency of the widely used models for flood
simulation. A greater understanding of the application of these models in
tailings flow can subsidize Brazilian and international legislation on dam
safety by considering these consequences in risk assessments.
Code and data availability
The code and data will be made available on request.
Author contributions
AFRS developed the case study, performed the analysis, and wrote
the paper. JCE supervised the work and wrote and revised the paper.
Competing interests
The contact author has declared that neither of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “Hydro-meteorological extremes and hazards: vulnerability, risk, impacts, and mitigation”. It is a result of the European Geosciences Union General Assembly 2022, Vienna, Austria, 23–27 May 2022.
Acknowledgements
The authors acknowledge the kind support provided by the Coordination for the Improvement of Higher Education Personnel (CAPES), the support by the National Council for
Scientific and Technological Development (CNPq), and the Foundation for
Research Support of the State of Minas Gerais (FAPEMIG) for the financial
resources.
Review statement
This paper was edited by Francesco Marra and reviewed by Darren Lumbroso, Lukas Riedel, and one anonymous referee.
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