Modeling the Impact of Groundwater Pumping on Karst Geotechnical Risks in Sete Lagoas (MG), Brazil

Abstract

Karst terrains can undergo geotechnical issues like subsidence and collapse, occurring both naturally and anthropogenically. The municipality of Sete Lagoas, in the State of Minas Gerais, Brazil, is notable for overexploiting a karst aquifer, resulting in adverse effects such as drying lakes and geotechnical problems. This study aims to assess the progression of geotechnical risk areas in the central urban area from 1940 to 2020 and simulate future scenarios until 2100. To achieve this, historical hydraulic head data, a three-dimensional geological model, and a karst geotechnical risk matrix were used to develop a calibrated FEFLOW numerical model. Results show that before the installation of the first pumping well in 1942, the natural groundwater flow direction was primarily northeast. However, in the 1980s, a cone of depression emerged in the city, creating a zone of influence (ZOI) with a surface area of around 30 km². Between 1940 and 2020, twenty geotechnical collapse events occurred in defined risk zones, often in regions where limestone outcrops or is mantled in association with the ZOI. In future scenarios, if the 2020 total annual groundwater pumping rate (Q = 145,000 m³/d) remains constant until 2100, the geotechnical risk zones will continue expanding laterally. To establish a sustainable risk state, a 40% decrease in the pumping rate (Q = 85,500 m³/d) is necessary.

1. Introduction

Karst terrains have the potential to experience geotechnical issues such as subsidence and collapse. These issues can occur both naturally, because of the failure of the bedrock caprocks overlying karstified zones, or anthropogenically, because of human activities that induce or accelerate the process [1,2,3]. Anthropogenic collapses are common in urban, industrial, or mining areas, often occurring abruptly, leaving affected populations insufficient time to prepare for material or human losses [4].

Induced geotechnical problems are mainly the result of subsurface groundwater withdrawal, surficial civil works, or a combination, especially over karst terrains [5]. In urban karst aquifers, groundwater depletion from droughts and increased water demands due to urban growth can be particularly hazardous, leading to the formation of enlarged cones of depression with radii of influence reaching kilometers and water tables dropping dozens of meters [6]. Subsurface erosion can occur through pumping or dewatering, transporting materials to underlying voids, and collapse can happen when the void’s roof becomes too thin to support overlying layers [4].

The use of numerical models [7] in karst terrains can organize and synthesize field data, enabling the understanding of existing hydrogeological and geotechnical phenomena. A well-calibrated model can be used to evaluate the progression of groundwater cones of depression, as well as verify the progression of geotechnical risk areas over the years. Furthermore, it can predict different situations and interventions that may impact such systems, helping to develop and adapt management strategies to ensure long-term sustainability [8,9,10,11,12].

However, deterministic models can have certain inherent limitations, especially those developed in karst terrains, that must be considered when examining the results. The sources of uncertainties may come from hydrodynamic parameters, hydraulic heads and flow data, scale effects, rock formation geometry limitations, and karst heterogeneity. The numerical stability of Monte Carlo-based simulations associated with stochastic models is a method to employ when dealing with those uncertainties in complex aquifers, which can minimize localized areas with highly inherent uncertainties [13].

China is one of the countries with the greatest number of reported karst-induced collapses, particularly in its northern regions [14]. This is largely due to declining groundwater levels. Pumping collapses in urban areas are reported in 20 northern regions, accounting for 58% of artificial collapses [14]. In the USA, states like Missouri, Minnesota, Pennsylvania, Florida, and Kentucky have reported induced sinkholes, posing hazards in developed and developing areas [15,16,17,18,19]. Other cities worldwide, including Kamloops in Canada [20], West Driefontein in North Spain [21,22], Southern Belgium [23], Great Britain [19], and South Africa [24], have also reported induced collapses related to aquifer withdrawal in urban areas.

In Brazil, various municipalities, including Cajamar (São Paulo), Almirante Tamandaré and Colombo (Paraná), Teresina (Piaui), Lapão (Bahia), Lagoa Santa, Montes Claros, and Sete Lagoas (Minas Gerais), host significant urban karst areas [6]. An evaluation of susceptibility to terrain collapse and subsidence in the karst area of Iraquara, Chapada Diamantina (Bahia), was conducted, and a hazard index was proposed [25]. In João Pessoa (Paraíba), the capital city, karst collapse risk areas were mapped based on karst geological structures and high levels of urbanization and human activities [26].

Sete Lagoas, in the State of Minas Gerais, is a medium-sized municipality situated on developed karst terrain, considered the largest “karst city” studied in Brazil [27]. Historically reliant on groundwater from a karst aquifer, the city, with its heavy industry, shifted to alternative surface water from the Velhas River in 2015 [28]. The urban central area, featuring a concentration of pumping wells, is experiencing increasing groundwater exploitation, resulting in adverse effects such as shallow karst conduits in unsaturated zones [6], collapse issues, particularly in the central area [29], and drying lakes [30].

This study area is over a graben filled with karstified limestone rocks covered by unconsolidated sediments, hosting two main solutionally enlarged bedding planes and a large groundwater reservoir. According to [6], geotechnical issues are conditioned by geological factors (unconsolidated sediments over limestones) and groundwater abstractions leading to the dewatering of karst conduits. These areas are the most susceptible to subsidence and collapse, and at least 20 episodes have been reported since the 1980s, increasing with water demand [31].

The goal of this paper is to model the impact of groundwater pumping on karst geotechnical risks in the central urban area of the municipality of Sete Lagoas from the 1940s (when the first pumping well was installed) to 2020. Additionally, two future scenarios until 2100 are simulated to determine potential consequences under different pumping scenarios (equal to the 2020 rate and a 40% reduction). The model integrates hydraulic head data from the 1940s to the 2000s, a three-dimensional geological model, and the karst geotechnical risk matrix to delineate risk levels, resulting in a calibrated FEFLOW numerical model [32]. The results of this study add a novel contribution to understanding the potential evolution of karst geotechnical risks posed by the overexploitation of aquifers in cities like Sete Lagoas.

2. Site Description

Sete Lagoas is a municipality located in the south-central region of the state of Minas Gerais, Brazil (Figure 1), approximately 70 km from the capital city, Belo Horizonte. Since the 1950s, the municipality has undergone rapid urbanization, leading to the establishment of a significant industrial sector, including steel plants, and significant production of dairy, pig iron, and limestone [33]. Sete Lagoas has a population of approximately 250,000 inhabitants living in an area of around 540 km² [34]. The area studied encompasses 146 km², including the central urban area, which is more developed, and has the highest population density and, as a result, the highest water demand (Figure 1).

The city’s water supply primarily comes from groundwater, obtained from 187 public pumping wells (a total of Q = 7060 m³/h) managed by the Water Supply and Sewage Service (SAAE—Serviço Autônomo de Água e Esgoto), whereby 135 wells are located within the study area (a total of Q = 3900 m³/h) (Figure 1). Additionally, there are 232 private wells in the municipality, 147 of them within the study area [31]. The current overall water demand within the modeled area (red line in Figure 1) is 6080 m³/h, supplied by SAAE’s wells (3900 m³/h) and private wells (2180 m³/h).

The region is humid tropical with a mean annual precipitation of 1320 mm, characterized by two well-defined seasons: rainy, from October to March, which accounts for 90% of the annual precipitation (mean 1184 mm); and dry, from April to September, with a mean value of 135 mm. The local annual mean temperature is 21.3 °C, with July having the lowest average value (17.5 °C) and February being the one with the highest average value (22.9 °C) [35].

The area is geologically over the São Francisco Craton [36,37], where Neoproterozoic sediments were deposited, resulting in the Bambuí Group [37], which is represented, from base to top, by the Sete Lagoas and Serra de Santa Helena formations, which are over gneissic and granitoid rocks from the Belo Horizonte Complex basement (Figure 2). The Sete Lagoas Formation is divided into two members: (1) the Pedro Leopoldo (base), composed of fine-grained limestones, with dissolution features developed in bedding planes and in subvertical fractures; and (2) the Lagoa Santa (top), composed of calcarenites and calcisiltites, with dissolution structures in horizontal caves. The Serra de Santa Helena Formation is constituted essentially of metapelites. Covering these formations are Cenozoic unconsolidated sediments, which occur primarily in the central area of the city [27].

The geology and climate combined have resulted in a typical karst morphology featuring several lakes (located mainly in the central area), caves, sinkholes, and closed drainage basins, coupled with a poor drainage pattern [38]. Areas with well-developed drainage networks are related to the Santa Helena ridge foothills in the center, basement outcrops in the south, and metasediments in the north.

The Sete Lagoas Formation serves as the main aquifer in terms of regional flow and storage capacity, referred to as the Sete Lagoas Karstic Aquifer System (SLKAS). Positioned directly above the Basement Fractured Aquifer System, the SLKAS is either confined or semiconfined by the upper rocks of the Serra de Santa Helena Aquiclude. Groundwater reservoir and circulation are conditioned by dual porosity, characterized by fractures and well-karstified bedding planes [6]. A shallow and thick karstified zone (1–8 m thick) is vertically located near the contact with the overlying unconsolidated sediments. Below, a thinner dissolution zone, located 10–20 m below the surface, exhibits conduits ranging from 20 cm to 1 m thick within the SLKAS [28].

Recharge areas occur both autogenically, in outcropping karst and less karstified limestone features, and allogenetically, via unconsolidated sediments overlying limestones. The primary outflow from the SLKAS occurs via pumping wells, leading to the formation of a local cone of depression spanning approximately 30 km² and disrupting the previous natural groundwater flow to the northeast. Further details on the hydrostratigraphic and geological structural relationships can be found in the works of [6,27,28,29,31,39].

3. Material and Methods

The work was conducted in five stages: (1) database construction, (2) hydrogeological conceptual model integration, (3) numerical modeling and simulation of past/future water level scenarios, (4) karst geotechnical risk matrix development, and (5) simulation of past and future risks. The stages will be presented in sequence, followed by a discussion of the data integration approach.

3.1. Database Construction

The database consolidates data from various studies conducted within the region. The 3D integrated conceptual (hydro)geological model was developed by [28] using the Geomodeller 4.0.x software (French Geological Survey, BRGM, www.geomodeller.com, accessed on 20 December 2019) and was based on regional geological–structural and geophysical maps (scale 1:25,000), 161 lithological well logs, and 30 optical televiewer logs.

The SLKAS’s hydraulic parameters (hydraulic conductivity, K; storativity, S; and specific storage, Ss) from small to regional scale were obtained from [6]. Pumping rates, static and dynamic groundwater levels, and potentiometric surface maps for the years 1980, 1990, 2010, and 2020 were constructed using hydraulic head data from 282 wells and compiled from the studies of [6,29,31,40].

Maps of recharge zones/rates were derived from [31], who adapted the APLIS method [41] that consists of mapping the spatial distribution of groundwater recharge rates by combining five parameters: altitude, slope, lithology, infiltration, and soil. The location, construction data, and discharge rates of the wells used in the models were based on previous studies. The karst geotechnical risk matrix was reassessed according to the method of [6]. All data were compiled in a GIS database and georeferenced in QGis Prizren 3.34.7 software (QGIS Association. http://www.qgis.org, accessed on 27 November 2021). The coordinate system was Universal Transverse Mercator (UTM) projection, Zone 23, datum Sirgas 2000, with units in meters.

3.2. Integrated Hydrogeological Conceptual Model

The hydrogeological conceptual model comprises an area of about 146 km² and considers the regions with geological contacts of the Sete Lagoas Formation with the basement and local hydrographic sub-basin dividers (S, SW, NW regions) (Figure 1 and Figure 2). In areas without defined geological contacts or sub-basin dividers (N, NE, W regions), the potential continuity of groundwater flow was considered. In the case of the basement, its generally impermeable features led to the neglect of hydraulic connections with the SLKAS. The unconsolidated sediments over the SLKAS were assumed to indirectly represent SLKAS recharge and discharge zones. For the Serra de Santa Helena Aquiclude, despite its low hydraulic conductivities, a small recharge was considered, with details given below.

The SLKAS was divided into three hydrogeological units with the following thicknesses [28]: (1) epikarst (0 to 90 m), (2) karst zones (0 to 130 m), and (3) limestone matrix (0 to 220 m). Horizontal model domains align with Sete Lagoas Formation’s geological contacts with basement and sub-basin dividers, while N and NW boundaries act as a regional groundwater sink. Vertical domains span from land surface to the aquifer contact with the basement (Figure 2).

The hydrodynamic parameters for these units are hydraulic conductivity (K) for epikarst and karst zones (which are hydraulically connected) = 1 to 36 m/d; and for matrix = 1.6 × 10⁻⁵ to 3.5 × 10⁻³ m/d; storativity (S) = 1.3 × 10⁻² to 1.6 × 10⁻⁵ [29]. Effective porosities (n_ef) for the limestone matrix and epikarst were compiled from other karst aquifers with similar hydraulic features, studied by [42,43,44] Bolster et al., 2001, Panagopoulos 2012; and Rose et al., 2018, with values between 5.4 × 10⁻⁵ and 8.6 × 10⁻¹ (Figure 3).

Five springs and streams combined with a total flow of 88 m³/h were considered as known natural discharge (Figure 2) [41]. The Jequitibá stream, representing 31% of the modeled area, had a mean baseflow of 11,772 m³/h (~103 Mm³/y) between 1976 and 1990 (Figure 1). Artificial discharge, related to well pumping rates, ranged from 148 m³/h (1.3 Mm³/y in 1942) to 6881 m³/h (60 Mm³/y in 2015). The 2020 estimated demand was 6080 m³/h (53 Mm³/y), lower than 2015 due to well deactivation. Dug wells, accounting for 5%, had a pumping rate of 305 m³/h (2.7 Mm³/y) in 2020 for domestic use only [30].

Autogenic recharge, which comprises 55–75% of precipitation (725–989 mm/y), occurs in areas with karstic features (cave entrances, sinkholes, and lakes) or in unkarstic limestone outcrops with low lineament density (35–55%, 461–725 mm/y). Allogenic recharge areas have values of 35–55% (461–725 mm/y) in unconsolidated sediments near lineaments and low slopes, with values of 25–35% (329–461 mm/y) occurring in areas with lower lineament density and high slopes. The recharge rate in areas where the Serra de Santa Helena Aquiclude covers the SLKAS is estimated to be 1–5% (13–66 mm/y). As previously noted, ref. [31] adapted the APLIS method [41] to obtain these recharge rates and spatial distributions.

In general, the potentiometric surface maps from the years 1980, 1990, 2010, and 2020 indicate that groundwater flow is generally towards the northeast, following the topographic slope of the basin. However, from the 1990s, there is a progressive and consistent lowering of groundwater levels within the central urban area because of high pumping rates. In specific sectors, where pumping rates exceed 1200 m³/h per km², this leads to the formation of a cone of depression covering approximately 30 km² by the year 2010 and beyond [29,31].

3.3. Numerical Model

The numerical model was implemented in FEFLOW^® 7.2 using the finite element solver, described by the following partial differential equation for transient, heterogeneous, and anisotropic conditions [32,44,45].

$$\frac{\partial }{\partial x}\left(K_x\frac{\partial h}{\partial x}\right)+\frac{\partial }{\partial Y}\left(K_y\frac{\partial h}{\partial y}\right)+\frac{\partial }{\partial z}\left(K_z\frac{\partial h}{\partial z}\right)=S_s\frac{\partial h}{\partial t}-W$$

(1)

where K_x, K_y, and K_z are saturated hydraulic conductivity (L/t) tensor of the respective axis x, y, z; h is the hydraulic head (L); S_s is specific storage; W corresponds to a such flow rate as sources and sinks (L³/t); and t is time [t].

The model developed in this study considered only the water flow of the SLKAS. The model domain covers an active cell surface area of 135 km² and it is configured with the automatic triangle option [46], generating a mesh with 71,189 triangles and 35,874 nodes based on the geometry of the hydrogeological conceptual model. The diameter of the generated elements ranges from 5 to 129 m, with a mean of 53 m, with refinements around wells to better represent hydraulic gradients generated by pumping.

To represent hydrogeological unit distributions, the geological model [28] was transferred to define the numerical grid. Four model layers were represented (Figure 3): (1) the basement, corresponding to the Belo Horizonte Complex as the model base; (2) the Sete Lagoas Formation matrix, composed of the limestone’s primary porosity; (3) the karstified zones of the Sete Lagoas Formation as a dual porosity system, representing the connection between sinkholes, caves, fractures, and conduits; and (4) the overlying epikarst zone, indicating weathered shallow limestone.

The representation of the flow domains of the karst system is a double-continuum porous equivalent (DCPE) [47,48,49], which is valid when modeling processes at spatial (semiregional) and temporal (annual/decennial) scales [50]. Despite the presence of fractures and karst conduits that may locally affect the flow and transport distributions in some way, requiring more detailed fracture/conduit networks, the use of the DCPE approach combined with the large database mentioned above makes the model particularly applicable to the current study of long-term changes in karst risk.

The boundary conditions were based on the following assumptions (Figure 2 and Figure 3) [51]: (1) Type 1 (Dirichlet) (specified head), representing only water outlets in karst springs and in streams over limestone or over unconsolidated sediments overlying limestone; (2) Type 2 (Neumann) (specified flow, Q = 0, no flow), south and east limits of the area (lithological contact between Sete Lagoas Formation and basement, and outcropping basement); west limit (Santa Helena ridge’s topographic divider). These zones are inactive cells; (3) Type 3 (Cauchy) (flux as a function of potential), adopted in the N and NE regions, with hydraulic heads based on previous potentiometric surface maps (1980, 1990, 2010, 2020) from 169 pumping wells within the modeled area; (4) recharge zones distributed using their respective rates, where the model considers the recharge being injected directly into the upper layer of the aquifer.

In FEFLOW models, a standard practice for simulating underground outflow in watercourses involves implementing specified head conditions with maximum flow restrictions, permitting the exit of water from the domain. This is commonly employed in the modeling of springs and drainages, whether they have direct contact with limestone or indirect contact through unconsolidated sediments overlying limestones. The assumption is made that these zones serve as outlets for the system, even in cases where specific discharge values are not precisely known [52,53]. For discharge calibration, values measured in situ from the conceptual model were used to validate the model. In the model’s groundwater outlet regions with no data of discharge, these were obtained with the output of the numerical model.

3.4. Calibration and Validation

Model calibration considered both steady-state and transient regimes [7] based on 257 water levels from 169 pumping wells. An estimate of the natural groundwater conditions of the SLKAS before significant pumping began in the 1940s was generated. The predevelopment potentiometric surface for transient regime calibration was generated using an adjustment in the steady-state model considering 10 well-known records of static water level from wells from 1942-1970 (PT-01 in 1942; PT-37 in 1968; PT-49 in 1968; PT-169 in 1966; PT-182 in 1966; PT-05 in 1970; PT-12 in 1970; PT-51 in 1970; PT-155 in 1970; PTP-187 in 1970), a period in which pumping discharge rates were relatively lower (415 m³/h overall), and the effects of pumping were more restricted. After the calibration, its statistical data were compared with data from the conceptual model, such as recharge and discharge rates/zones, as well as hydrodynamic parameters and storage, and potentiometric surface patters for validations.

Recharge rates, hydraulic conductivities (K), storativity (S), and effective porosities (n_ef) were adjusted in sequential model runs via a trial-and-error calibration procedure [7]. The parameter values considered were in accordance with the hydrogeological conceptual model, with K values ranging from 10 to 16 m/d for regional scale, 1 to 36 m/d for well scale, and 10⁻⁴ to 10⁻³ m/d for small scale. The analyzes were both qualitative (evaluation of flow patterns and parameters) and quantitative (statistical measures of differences between observed and simulated water levels) [54]. For statistical analyses, the root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were used. For hydraulic gradient statistical analyses, the normalized RMSE were calculated. Furthermore, the discrepancies in the mass balance resulting from the calibrations were evaluated, which resulted in differences between water inputs and outputs calculated by the model of <0.02 [54] (Figure 4).

In the steady-state calibration, complementing the trial-and-error calibration procedure, the parameter estimation software PEST 7.2 [55] was employed for optimal values within specific ranges for each hydraulic parameter. Higher calibration weights were defined for PT-01, the well with the oldest water level records (since 1942), and for wells PT-37 and PT-51, both in areas further from PT-01, without its pumping influence. Thus, errors between simulated and observed water levels in the PT-01 were also used as a criterion for evaluating the quality of the calibration.

A sensitivity analysis was also performed using the one-at-a-time (OAT) method [56]. This involved testing various recharge configurations within the ranges specified by [30]. While maintaining the hydraulic conductivity (K) of the matrix constant, the K values for the epikarst and karst zones were systematically adjusted to be 2, 5, and 10 times smaller and larger than the calibrated values. Similarly, the impact of changes in the matrix K was evaluated while keeping the K values of the epikarst and karst zones constant. Additionally, a variation in K values was explored while keeping the recharge (R) constant.

Figure 4. Comparison between calculated and simulated hydraulic heads in wells (A,B); the geographical spatial distribution of errors (C); table of the statistical analysis of calibration (D); and table with the hydraulic parameters versus calibration adjustments (E) [27,28,29,30,31,42,43,44,45,57].

Figure 4. Comparison between calculated and simulated hydraulic heads in wells (A,B); the geographical spatial distribution of errors (C); table of the statistical analysis of calibration (D); and table with the hydraulic parameters versus calibration adjustments (E) [27,28,29,30,31,42,43,44,45,57].

3.5. Scenario Analysis

Past (1940–2020—calibration stage) and future (2040–2100) scenarios were simulated to generate SLKAS hydraulic heads, with 20-year intervals, to generate potentiometric surface maps. In these maps, zones of influence (ZOIs), which are the surface area of the groundwater affected by pumping wells resulting in water depletion, were recognized as a condition required by the karst geotechnical risk index method [6] (next section). Values of recharge, K, S, and boundary conditions for the SLKAS were maintained in all simulation scenarios as defined during the calibration process.

Past scenarios were compared with potentiometric surface maps from previous works for verification purposes. Two situations were considered for the future scenarios: (1) a constant global pumping rate from 2020 until 2100, set at the 2020 level (Q₂₀₂₀ = 145,000 m³/d); and (2) a reduction in the total 2020 pumping rate by 40% (Q_<40% = 85,500 m³/d), that remains constant until 2100.

The value of 40% reduction was adopted after a first attempt with a 20% reduction in the total pumping rate; however, with 20% the drawdown in the central area did not reduce, being doubled to 40%, resulting in a reduction in drawdown and stabilization of the cone of depression in the central portion. Values above 40% were not considered in other future scenarios because they would be impossible to adopt by the city due to its water demand necessity.

For future precipitation values, on an 80-year future timescale (2020–2100), assessing climate change impact, including different scenarios and precipitation patterns, is important for understanding potential effects on hydraulic behavior and associated risks. Additionally, the possibility of increased pumping under climate change may render reduction impractical. However, due to limited predictability regarding climate change in the region, the value was kept constant during calibration to run all the future scenarios.

3.6. Karst Geotechnical Risk Mapping

The karst geotechnical risk evaluation is an index method proposed by [6] to categorize the various risk factors that can lead to subsidence or collapse, which was directly developed based on local hydrogeological context and geotechnical information for Sete Lagoas. The method is divided into two categories of risk factors (geological and hydrological), where each one is further divided into risk values of different weights (Figure 3), resulting in two risk factor raster maps. The risk categories for the two maps are the following.

Geological risk map (factors and weights): (1) Limestone outcrops and limestone covered by unconsolidated sediments (highest risk value = 5); (2) limestones covered by competent rocks (metapelites from the Serra de Santa Helena Formation) divided into two categories: (i) areas in contact with the above factors considering a buffer of 500 m beyond (risk value = 3), and (ii) outside the 500 m buffer (risk value = 1); and (3) basement outcrops (negligible risk value = 0).

Hydrological risk map (factors and weights), applicable within the ZOI: (1) Potentiometric surface (m.a.s.l.) < 720 m (highest risk value = 5); (2) between 720 and 740 m (risk value = 3); (3) between 740 and 760 m (risk value = 2); (4) >760 m (risk value = 1); and (5) outside the ZOI (negligible risk = 0).

By overlaying the geological and hydrological raster risk maps, the final karst geotechnical risk map was obtained, with risk values ranging from zero (negligible risk) to ten (high risk): The risk levels were then divided into five categories: 8–10 (high risk), 5–7 (considerable risk), 3–4 (moderate risk), 1–2 (low risk), and 0 (negligible risk) (Figure 3). The weight values and assumptions adopted by [6] were determined by comparing the relative importance of each factor (geological and hydrological), checking them on local (hydro)geological features, and based on the back analysis. This study involved the creation of five historic risk maps at 20-year intervals, from 1940 to 2020, to represent the modeled evolution of risk areas up to the present time. Additionally, four future risk maps were developed for each future scenarios 1 and 2 (years 2040, 2060, 2080, 2100) to determine the possible worsening of existing risk areas, resulting in a total of eight risk maps.

4. Results

4.1. Model Calibration and Validation

At the regional scale in this complex karst hydrogeology, the model results are deemed acceptable, as most of the observed and predicted values, respectively, demonstrate a close proximity to the 1:1 line [7] (Figure 4A,B). In the majority of wells in the model (58%), errors are less than 10 m, primarily located in the central region, where more information about lithological and well logs is available. Conversely, errors greater than 30 m are present in peripheral areas with more limited information (Figure 4C).

The values of RMSE and MAE, when considering all hydraulic heads, are 16 m and 11 m, respectively (as shown in the second row of the table in Figure 4D). For years with more than 10 records, the RMSE varies between 5 m and 19 m, while the MAE ranges from 4 m to 23 m. The correlation coefficients (R) are greater than 0.79, with the majority being above 0.90 (Figure 4D). When normalized to the highest hydraulic gradient of 195 m, NRMSE results are between 2% and 12%, being acceptable for regional-scale models [7] (Figure 4D).

The presence of errors greater than 30 m in peripheral areas does not mean a less efficient calibration, but, rather, that the refinement of the edge elements is not enough in their contours. However, as seen in Figure 2, the modeled area boundary conditions were defined by the following assumptions: south, west, and east limits do not show flux exchange; while for the northern limit, despite having flux, the number of monitoring data decreases towards the north, which would increase the model error due to the absence of calibration data. When observing the calibration graph, disregarding the 10% of wells closest to the edge, NRMSE values between 2% and 12% are obtained (Figure 4D).

Figure 4E illustrates that the best recharge rates coincide with the highest values estimated by [30], yielding a mean annual recharge between 1942 and 2020 of 29% of precipitation (51 Mm³/y, or 12 L/s/km²). The calibrated values of K are 2 m/d for epikarst zones, 20 m/d for karstified zones, and 3.5 × 10⁻³ m/d for limestone matrix, all within the range of 1–36 m/d obtained from pumping tests and capture zone method [6]. These values result in MAE and RMSE of 7.8 m and 9.4 m, respectively.

PT-01 was included in the analysis as it is the first well installed in the city in 1942. The error between the hydraulic head measured in 1942 and the simulated value is 2.6 m (Figure 4E). The flow representation in the transient calibration demonstrated the best adjustments for Sy of 1.5 × 10⁻², 5.0 × 10⁻¹, and 2.5 × 10⁻¹ for limestone matrix, karstified epikarst and zones, respectively, Ss of 4.5 × 10⁻³ m⁻¹ for limestone matrix, and 9.0 × 10⁻³ m⁻¹ for epikarst and karstified zones. The adjustments resulted in MAE and RMSE values of 11.4 m and 15.7 m, respectively, in transient regime, and 7.8 m and 9.4 m, respectively, in steady state, with a PT-01 error of 1.9 m, relative to the hydraulic head measured in 2012 and simulated (Figure 4E).

Before the first well PT-01 in 1942, simulated recharge rates were stablished at 12 L/s/km², with outputs distributed to rivers (37 Mm³ or 9 L/s/km²) and external boundaries (14 Mm³ or 3 L/s/km²), resulting in a null annual net balance. in the period between 1942 and 2020, simulated recharge varied from (18 to 76 Mm³/y or 4 to 18 L/s/km²), allocated to rivers (13 to 40 Mm³/y or 3 to 9 L/s/km²), external boundaries (6 to 17 Mm³/y or 1 to 4 L/s/km²), and pumping wells (1 to 59 Mm³/y or 0.2 to 14 L/s/km²). Thus, the mean numerical error in mass balance estimation was below 2%. During 1976–1990, the period analyzed by Pessoa (1996), the model indicated a mean river discharge of 27 Mm³ (6 L/s/km²), constituting 26% of the total Jequitibá River’s baseflow (103 Mm³/y or 7 L/s/km²), corroborating the specified criteria (model mean baseflow <31% of total Jequitibá baseflow).

4.2. Past and Future Scenarios of Potentiometric Surfaces

The predevelopment regional groundwater direction of the SLKAS is generally towards the northeast (Figure 5). The groundwater flow begins in the topographically higher regions in the south (elevation close to 900 m) with a general direction towards the north (hydraulic heads, h, between 840 m and 800 m) until the central region (elevation around 800 m) where the direction changes to a northeast trend (with h between 780 m and 740 m). In the extreme west, h values between 800 m and 780 m are observed, but the groundwater flow direction tends to be west–east due to the high altitudes above 900 m in the foothills of the Santa Helena ridge. In the northeast–east portion, downgradient flexures with increased potentiometric contour values between 740 m and 760 m are noted. All the flow directions lead to the northeast region of the modeled area, with the lowest h of 720 m. This general characteristic is consistent with all predevelopment potentiometric surface maps developed in the region by [6,28,29,31,40].

By analyzing the evolution of the potentiometric surfaces over time (Figure 6), the 1940 map can be considered an estimation of the SLKAS’s natural flow system, as the first well was not drilled until 1942 (PT-01). The 1960 map indicates the same groundwater flow trends as seen in 1940, with no consequences of groundwater withdrawals altering the natural flow directions (despite the presence of five wells and a total pumping rate of 6057 m³/d). The 1980 map indicates the incipient development of a cone of depression in the central area, with relatively low h values of around 740 m (71 wells and a total pumping rate of 48,816 m³/d), which increases from the 2000s (163 wells and 124,737 m³/d) and is consolidated by 2020 (251 wells and 145,000 m³/d), with potentiometric contour values around 720 m (Figure 5). Some groundwater flow directions, which previously flowed to the northeast between 1940 and 1980, now converge towards the center of the municipal cone of depression, which is located inside the ZOI, resulting in negative water table variations (Figure 6).

For the future scenarios, the regional flow direction of the SLKAS groundwater remains towards the northeast (Figure 5). However, a significant portion of the groundwater converges towards the central cone of depression initiated in 1980. Under future scenario 1, where the global pumping rate remains constant at the 2020 pumping rate of 145,000 m³/d until 2100, the cone of depression and ZOI increase further. The potentiometric contour values of 740 m and 720 m expand in surface area over the decades, and a new upgradient flexure is observed, resulting in h values below 700 m in 2100 (Figure 6).

The north–northeast portion of the area, compared to the 1940 aquifer natural flow map, indicates a reduction of at least 20 m in the general hydraulic heads (as seen in the equipotential line of 720 m in the north–northeast portion of the 1940 map, and the same area in the maps for future scenario 1). The southern region remains largely unchanged in h values, as it is outside the ZOI. Under future scenario 2, where the 2020 global pumping rate is reduced by 40% until 2100 (Q = 85,500 m³/d), the cone of depression and ZOI tend to reduce starting in 2040. The configuration of the central potentiometric surfaces returns to something close to that seen on the 2000 map, tending to stabilize its hydraulic head. Only in the north–northeast region of the area the values not return to the previous 720 m, remaining close to 700 m (Figure 5 and Figure 6).

4.3. Geologic and Hydrologic Risks

The geologic risk map (Figure 7) exhibits the following distributions of factors and weights: (1) limestone outcrops or mantled, represented by a red risk value of 5, are primarily in the central, western, southern, and eastern portions, covering an area of 30.46 km² or 20.88% of the total area; (2) limestones covered only by competent rocks (Serra de Santa Helena Formation’s metapelites) within a buffer of 500 m, which are represented by an orange risk value of 3, encompass 66.62 km², representing 45.66% of the total area; (3) the same rocks but outside the 500 m buffer, represented by a green risk value of 1, occupy 41.24 km² and represent 28.27% of the total area; (4) lithologic basement outcrops, which are represented by a negligible risk value of 0, occupy the remaining 7.47 km² or 5.19% of the area.

The past hydrologic risk map (Figure 7) considers maps from 1960 onwards, as the 1940 map represents the aquifer’s natural flow before the installation of pumping wells. In 1960, areas with groundwater elevations between 740 m and 760 m, represented by a yellow risk value of 2, and areas greater than 760 m, represented by a green risk value of 1, were observed, representing a total ZOI area of 29.55 km² or 20.25% of the modeled area. By 1980, the ZOI area remained similar in terms of size (29.86 km² or 20.47%), but an orange risk value of 3 was added, with a central potentiometric contour value of 740 m and an individual area of 0.21 km². In 2000, the ZOI area expanded, and the respective risk values 1, 2, and 3 increased, totaling 40.07 km² or 27.47% of the entire study area. Note that the yellow area in the 1960 and 1980 maps was replaced by the orange risk factor. In 2020, the ZOI reached its largest area of occurrence (42.17 km² or 28.91%), with risk factor values 1, 2, and 3 being quite similar in terms of area to in 2000, but with the addition of a central red risk factor value of 5 (elevations < 720 m) with an area of 0.56 km². The bottom table in Figure 6 provides information on the km² and % occurrence of each risk factor or ZOI area.

Regarding the future hydrological risk maps (Figure 7), future scenario 1 (Q = 145,000 m³/d) confirms and expands the ZOI, leading to an increase in the red risk area. This risk factor reaches an area of 8.83 km² in 2040 and a maximum of 15.10 km² in 2100. The orange risk area reaches 14.37 km² in 2040 and tends to decrease over time, reaching 7.91 km² in 2100. The yellow areas tend to stabilize around 6.6 km², decreasing from 9.71 km² in 2020, while the green area increases from 19.38 km² in 2020 to values around 23 km² over time. Future scenario 2, which reduces the 2020 global pumping rate by 40% (85,500 m³/d), leads to a reduction in the ZOI area as early as 2040, and the configuration and respective hydrologic risk areas return to those seen in the 2000 map (Figure 7).

4.4. Karst Geotechnical Risk

The results of the geologic and hydrologic risk maps are presented in Figure 7, Figure 8 and Figure 9 as karst geotechnical risk maps. The high-risk areas, indicated by red, are in regions where limestone outcrops or is mantled within the ZOI, coupled with groundwater elevations less than 720 m. The considerable risk areas, represented by orange, are found where the limestone outcrops or is mantled outside the ZOI and/or is associated with competent rocks from the Serra de Santa Helena Formation within the ZOI. Yellow areas represent moderate risk zones and are situated 500 m beyond limestone outcrops outside the ZOI or in regions with thin competent rocks within the ZOI. The low-risk zones, denoted by green, are characterized by competent rocks covering limestones. The negligible zones, depicted by white, are constituted by basement outcrops with little potential for subsidence or collapse.

The evolution of the risks from 1940 to 2020 (Figure 8) reveals that most geotechnical events (82%, or 14 out of 17 events) occurred in high-risk zones, with the remaining issues reported in considerable-risk zones. From 1940 to 1960, there were no high-risk zones, with the first incipient area of high risk appearing in 1980 with a total area of 0.21 km². This area expanded to 3.78 km² in 2000 and almost doubled to 6.07 km² in 2020. From 1960 onwards, considerable-risk zones began to increase in the center, from 32.40 km² to 35.10 km² in 2020. The moderate-risk zones decreased from 64.31 km² in 1960 to 56.63 km² in 2020. The low-risk zones have remained relatively unchanged over the decades, with an area of approximately 40 km². Nine geotechnical events were reported between 1988 and 2000, with an additional eleven events reported between 2001 and 2020 (see Table in Figure 8).

Future scenarios of geotechnical risks (Figure 9) were also analyzed. In future scenario 1 (Q = 2020), high-risk zones are confirmed and expanded. In 2040, these zones may reach a total area of 13.22 km², a 118% increase from the 6.07 km² in 2020. The maximum area may be 17.18 km² in 2100, an increase of 183% from 2020. The considerable-risk areas may have a total area of 34 km² in 2040 and 29.92 km² in 2100, although there may be a decrease compared to 2020. Moderate- and low-risk areas are expected to stabilize around 51 km² and 38.9 km², respectively. In future scenario 2 (40% reduction in pumping rate), high-risk areas may experience a significant reduction for the next 20 years, from 6.07 km² in 2020 (Table in Figure 8) to 3.69 km² in 2040 (Table in Figure 9), a decrease of 61%, having a configuration like the 2000 map (Figure 8). From then onwards, high-risk and other-risk areas are expected to stabilize, with values of around 36 km² (considerable), 59 km² (moderate), and 40 km² (low) (Figure 9).

5. Discussion

5.1. Mechanisms That Control Geotechnical Risks

To date, all subsidence or collapse events that have occurred within the central urban region of Sete Lagoas are situated in high- or considerable-risk zones. According to [6,28], these zones are located over outcropping limestones from the Sete Lagoas Formation or can be covered by Cenozoic unconsolidated sediments in a central graben region. From a review of 161 well construction logs and 30 optical televiewer logs, two continuous bedding planes, which have been enlarged due to karst dissolution, have been identified: (1) a shallower, thicker zone of 1–8 m of dissolution near the contact with unconsolidated sediments, and (2) a thinner zone of 20 cm to 1 m of dissolution located 10–20 m below the shallow zone. The shallowest karst zone is, in some regions, unsaturated or has a water table close to this state, as confirmed by an optical televiewer log in PT-01 in 2012 [6].

These locations coincide with the zone of influence (ZOI) caused by groundwater extractions from wells with intermediate (500–2000 m³/d) and high pumping rates (>2000 m³/d). For example, drawdown evolutions in some wells over the decades have been recorded, showing depletions of tens of meters. The well PT-01, the first well drilled in the municipality in 1942, had an original static water level of 14 m. With a mean pumping rate of 3600 m³/d, the static water level reached 62 m in 2012, resulting in a depletion of 48 m. PT-11, from the 1960s, reached a drawdown of 30 m in five decades. In the 1970s, 1980s, and 1990s, some wells reached drawdowns between 10 and 38 m. In general, several decades of pumping have resulted in groundwater elevation decreases of about 40 m in the central urban area.

All subsidence or collapse events are located within the ZOI boundary and within the central graben area, filled with limestone deposits and two enlarged bedding planes either outcropping or covered by unconsolidated sediments, or within 500 m beyond these areas. The combination of a karstified geological setting and severe groundwater extraction has likely led to the emergence or acceleration of subsidence or collapse, with conduits likely unsaturated prior to a geotechnical event. It is important to highlight that the geologic risk factors for Sete Lagoas are interpreted as static risk, including geological contacts, structural relationships, and thicknesses of bedrock layers, which remain unchanged in human timescales. However, hydrologic risk factors are linked to groundwater extractions and, therefore, to the geometry and elevation of potential cones of depression. An increase in extractions will increase the dimension of the risk areas, as the karst geotechnical risk index method proposed by [6] considers both geologic and hydrologic risk factors.

5.2. Evolution of Karst Geotechnical Risks from 1940 up to 2010

The municipality of Sete Lagoas was established in 1867 and primarily engaged in agricultural activities that utilized surface water sources, such as local lakes, ponds, and streams, for water supply. In 1896, the inauguration of the Sete Lagoas Railway Station resulted in the expansion of several industries, particularly in the textile and dairy sectors, leading to rapid economic and population growth. Consequently, alternative water demand also grew, and by 1940, the population of Sete Lagoas had surpassed 10,000. In response to this increase in demand, the first 110 m deep tubular well (PT-01) was drilled in 1942, followed by PT-02 and PT-03 in 1948. By the end of the 1960s, the number of wells installed in the region had only increased to 11, resulting in low variations in the hydrologic risk factors and, hence, in karst geotechnical risk areas.

However, the situation changed in the 1980s, when the region experienced a significant socioeconomic expansion due to the pig iron industry. As a result, a total of 71 tubular wells were pumping almost 49,000 m³/d. Thus, the behavior of the SLKAS started to respond to the progressive increase in groundwater extractions, especially in the central urban area, and an incipient development of a cone of depression altered the geotechnical risk factors (Figure 5).

In the 2000s, industrial activities were well consolidated, and a total of 163 wells were extracting around 125,000 m³/d to meet demand. This increase in demand, along with a growing economy and population, resulted in a decline in the mean aquifer recharge rate and a 20 m drawdown in central groundwater levels. The global pumping rate continued to increase from 2010 onwards, reaching 251 wells and 144,675 m³/d in 2020, leading to a well-defined cone of depression with an area of influence of around 30 km². In 2016, the Velhas river was utilized as a supplementary source of surface water.

This socioeconomic evolution has had a significant impact on the potentiometric surface of the SLKAS and the evolution of karst geotechnical risks over the decades. The central area is predominantly situated over limestone outcrops or limestone covered by thin competent rock layers, and the presence of a cone of depression with groundwater elevations below 740 m has led to an increase in geotechnical events. The first collapse, reported in 1988 with a diameter of 20 m and a depth of 20 m [58] (Figure 1), was initially concluded to be a natural phenomenon without anthropic influence. However, given its location in the zone of greatest pumping and drawdown, it is possible that the process was accelerated by groundwater extractions. In 2023, during a visit to the same location, a reactivation of the collapse was observed, resulting in dimensions like those of 1988 in terms of diameter and depth. The correlation between drawdown and the evolution of high-considerable-risk zones becomes increasingly evident in the 1990s, with five additional incidents. Between 2000 and 2020, 14 new events were recorded (Table in Figure 8), totaling 20 issues, most of which occurred in the highest risk zone.

5.3. Future Scenarios on Karst Geotechnical Risks

The scenario that maintains the current total groundwater pumping rates from 2020 until 2100 is likely to generate additional karst geotechnical events, as the expansion of high- and considerable-risk zones is confirmed. The location of these zones over karstified limestone outcrops or covered by unconsolidated sediments associated with an enlarged cone of depression intensifies the vulnerability to subsurface erosion, resulting in the transport of materials down to underlying voids [4,6]. In extreme cases, a collapse may occur when the roof of the void is too thin to support overlying layers, and collapses like 1988 [58] can be repeated, as happened in 2023.

In a scenario of reducing the 2020 global pumping rate by 40% (from 145,000 m³/d to 85,500 m³/d), the high- and considerable-risk zones may significantly reduce areas stabilizing in terms of occurrences. This is considered the best situation for the expansion of geotechnical risk to be contained. This optimal value represents about 61% of the modeled area’s global recharge and it is close to the discharge exploited in the mid-1980s [12], before the beginning of the most significant changes in the levels of the aquifer.

Thus, there is a significant correlation between the intensification of groundwater pumping and the rate of land subsidence and sinkhole formation. This paper indicates that proper management and reduction in groundwater pumping is necessary to mitigate the negative effects of overexploitation on land stability and prevent further sinkhole occurrences. These findings have practical applications as both a planning tool for organizing the city’s urban space and as a means of managing groundwater extraction.

A post-audit of the model results in the next decade can be evaluated relative to predicted head levels and observed collapse features that are generated. This can be utilized to further refine the model results and utilize the results to evaluate groundwater extraction management strategies. The results of historical modeling suggest that waiting for a post-audit will likely result in collapse features developing in the intervening period. Thus, efforts to maintain the groundwater elevation in the high-geologic-risk areas are required to minimize the karst hazards in Sete Lagoas.

5.4. Limitations and Considerations

This deterministic model has certain limitations that must be considered when examining the results. The sources of uncertainties may come from both the database and the numerical model. The model’s hydrodynamic parameters were simplified, being based on four factors: (1) the features of the available water level and flow data, (2) the extensive represented area of 146 km², (3) the limited knowledge regarding the geometry and its of dual porosity of the SLKAS, and (4) different geological heterogeneous setups. Due to these, the model only reflects effects on a semiregional scale and cannot be applied at a more detailed scale.

For future works, with more data available, it will be possible to incorporate new data and apply this model to analyze scales with greater precision. This can be achieved by refining and adjusting the mesh and the representation of karst elements. Another suggestion is to run new future scenarios considering global values above the current rate (Q = 145,000 m³/d), as well as considering alternative sources of water in the future.

An interesting way is considering the numerical stability of Monte Carlo-based simulations to be employed in an FEFLOW stochastic model, according to [13], to minimize localized areas with possible highly inherent uncertainties in this study’s model. These stochastic simulations in groundwater-related issues can be also employed in the work’s geotechnical risk uncertainties.

6. Conclusions

This study, conducted in the central urban area of Sete Lagoas, Brazil, modeled the impact of groundwater pumping on karst geotechnical risks from 1940 to 2020 and simulated two future scenarios until 2100. The results indicated that groundwater overexploitation has altered the natural flow system of the karst aquifer, creating a cone of depression and a zone of influence that affects the geotechnical stability of the karst terrain.

The geologic risk map of Sete Lagoas, Minas Gerais, Brazil, indicates the natural risks of terrain subsidence or collapse, such as karst lakes/ponds or sinkhole formations. These risks are considered a static setting for the municipality. However, the hydrologic risk map is directly related to current human activities, particularly groundwater extraction. The more the pumping increases, the more the groundwater level decreases, increasing the risks of subsidence or collapse. The karst geotechnical risk is the cumulative effect of both factors, but changes in the risk over time are largely due to groundwater extraction.

Before the installation of the first well in 1942, the natural flow direction of groundwater was predominantly towards the northeast. In the 1980s, clustered pumping wells in the central area caused the development of a cone of depression, which resulted in the convergence of flow directions towards the center and the formation of a zone of influence (ZOI) with a radius of approximately 30 km².

The result suggests that karst geotechnical events in the central urban area of the city of Sete Lagoas are triggered and accelerated by depletion of groundwater in the ZOI, which encompasses a graben area filled with outcropping karstified limestones and may also be overlaid with unconsolidated sediments in certain areas or up to 500 m beyond these areas (high- and considerable-risk zones). All 20 geotechnical events reported from 1940 to 2020 correlate to these mapped risk zones.

For future scenarios, if the current global well pumping rate from 2020 (Q = 145,000 m³/d) persists until 2100, the areas of high and considerable geotechnical risks will continue to expand. Achieving a sustainable state, characterized by the reduction and stabilization of these risk zones, would require an approximately 40% decrease in the global discharge rate (Q = 85,500 m³/d).

The numerical model and the karst geotechnical risk matrix developed in this study can be useful tools for water management and risk mitigation in urban karst areas. These findings contribute to the understanding of the impact of groundwater pumping on geotechnical risks in karst terrains and provide valuable insights for future water management strategies.