Slope geometry optimization considering groundwater drawdown scenarios at an open-pit phosphate mine, southeastern Brazil

The design of open-pit mines should balance safety and economy. However, safe geotechnical conditions generally involve redesigning the geometry of slopes and groundwater drawdown, significantly increasing the costs of mining operations. The use of numerical models to simulate groundwater drawdown and slope stability can be an alternative to assess cost–benefit trade-offs for decision-making. This study documents a mining plan using groundwater drawdown scenarios that illustrate how geotechnical, economic, and environmental indicators can be combined to obtain optimum slope geometry for open-pit mining. The optimization approach analyzed different scenarios of groundwater drawdown for the final pit of a phosphate mine to improve the pit slopes stability. The groundwater simulation scenarios included the combination of deep horizontal drains and pumping wells. Stability analyses using the limit equilibrium method were used to obtain the bench, inter-ramp, and overall factors of safety of different representative sections. The factors of safety obtained, the drawdown costs and the water table elevation of each section were selected as indicators for obtaining the optimal drawdown scenario using a multi-objective tool. The groundwater control system obtained with 11 horizontal drains and 1 pumping well was considered the most adequate from the geotechnical and economic perspectives. Slope geometry optimization obtained with this drawdown scenario led to adequate inter-ramp and overall safety factors for the final pit design, reducing the barren-to-ore ratio to 0.38, much less than the present ratio (≈ 3). The results are important for optimizing the slope geometry of open-pit mines and can be replicated in other regions.


Introduction
The geometry of open-pit slopes should provide a good compromise between safety, economy, and sustainability (Read and Stacey 2009). In fact, the use of gentle slopes warrants stable conditions for mining operations, since factors of safety (FoS) remain sufficiently large to minimize the chances of slope failure. However, this favorable geotechnical condition comes at the expense of the increased costs associated with mining the ore (Sperling et al. 1992). Furthermore, the larger the volume of rock waste (barren material) extracted during mining operations, the higher the carbon footprint and energy use (Utili et al. 2022), and the lower the land savings (Guo et al. 2021). Therefore, optimization of slope geometry is a prerequisite for mine design, construction, operation, and maintenance. This frequently requires multi-objective analysis to identify optimum geometries for bench, inter-ramp, and overall slopes considering geotechnical and economic trade-offs.
Although bench failures generally have a less economic impact on production, the consequences of inter-ramp and overall slope failures can be much more significant (Santos et al. 2019). In fact, production losses (Wyllie and Mah 2004), cleanup costs (Jele and Dunn 2019), injuries and fatalities (Terbrugge et al. 2006), and damage to equipment (Golestanifar et al. 2018) are some of the major problems involved in inter-ramp and overall slope failures. For these reasons, slope stability at these spatial scales must be closely controlled in open-pit mines. As such, much research has been devoted to slope geometry optimization using deterministic and probabilistic slope stability analyses (e.g., Islam and Faruque 2013;Ulusay et al. 2014;Rem et al. 2020) One of the most common methods applied to stability analysis in open-pit mines is the Limit Equilibrium Method (LEM), which provides a basis for computing FoS (Du et al. 2022). These stability approaches use as the main objective the maximization of FoS and can adequately predict stable conditions for slopes, thereby enabling optimization of the local (open-pit) geometry (Ahmadi et al. 2019;Zhou et al. 2020). For example, Bye and Bell (2001) used detailed geological and geotechnical data to optimize the final overall angle at the Sandsloot open pit, South Africa. Their study resulted in an improved slope geometry, with an increase in the ultimate angle of the wall by 7°. In the same line of research, field observations and stability analyses with the 2D LEM Slide software package by Cooper et al. (2019) were used to recommend an increase in the overall slope angle of the Cobre Las Cruces mine, Spain, from 28° to 31°. Still, these FoS-based optimization methods have their drawbacks, since they do not explore technical, economic, and environmental issues in a single integrated framework. An alternative methodology is a risk-cost-benefit analysis, in which the economic impacts of possible slope failures are used as decision variables to optimize the mine geometry (Contreras 2015;Zevgolis et al. 2018).
It is well known that the groundwater table exerts a strong control on the stability of the pit walls through pore pressures generated within the slope, reducing the shear strength of the geomaterials (Read and Stacey 2009). Unfortunately, the drawdown of groundwater in openpit mines, largely by pumping, might demand relatively high operational costs (Mallios and Tsiarapas 2022). Consequently, some researchers resort to risk-cost-benefit analyses that take into consideration the groundwater control strategy, which not only provide optimum slope geometries that are more representative of the actual mine-scale water dynamics but also enable the selection of a cost-effective groundwater control program. In fact, the study by Sperling et al. (1992) illustrated that the combination of horizontal drainage and slope flattening produced the lowest risk and the highest profits. Although installation and operating costs were involved in the water table drawdown, the authors showed the benefits of the institution of a groundwater control program. Therefore, optimization of slope geometry in open-pit mines should balance the benefits of numerical simulations of slope stability and the costs associated with drawdown scenarios.
Groundwater control systems often require vertical (deep) pumping wells installed behind the pit face and/or (sub-) horizontal drains positioned from slope benches. To develop these dewatering strategies in mines, engineers often make use of groundwater flow simulations from conceptual hydrogeological models . However, since the interiors of mines are difficult and costly to illuminate and access, the conceptual hydrogeological model of many mines is unknown to a great extent (Masoud et al. 2016). In the absence of detailed information about the water table level, hypothetical groundwater scenarios that take into account different depths of groundwater can be useful for stability assessments (Solak et al. 2017). Despite hypothetical scenarios do not represent the reality of hydrogeological conditions, slope stability analysis considering groundwater drawdown by horizontal drains showed significant improvements in FoS (Saeed et al. 2015;Widodo et al. 2018). Powerful groundwater simulation and optimization models have been used in many different fields (Gorelick and Zheng 2015), but further research may be useful to investigate groundwater drawdown scenarios in mining studies (Jiang et al. 2013). An example is the work by Argunhan-Atalay et al. (2021), who simulated drawdown scenarios using horizontal drains. Although they did not collect field data from the drains and did not assess the stability of the open-pit mine, the authors reported a 15-37% increase in mine water discharge. The authors also argued that the assessment of horizontal drains in open pit mines has been overlooked in the literature.
Pore pressure is the strength-conditioning parameter that is more easily controlled and modified within the geomaterial. As such, early findings suggested the installation of an efficient drainage system might promote strength gains, enabling the re-design and optimization of the pit geometry, including reduction of costs, reduction of the risk of mass instability, and improvement of the operational safety of the mine. Additionally, literature findings showed that the definition of optimal slope geometries is not trivial (Chaves et al. 2020) and more studies are needed to better understand how multiple and conflicting elements can be combined to improve decisionmaking in open-pit mines (Golestanifar et al. 2018). Several noted that optimization algorithms facilitate more rapid and reliable decision-making. In fact, optimization approaches have the advantage of dealing with a significant amount of information to provide the best drawdown scenario. For instance, Mohan et al. (2007) combined numerical simulations of a seven-layer three-dimensional groundwater model using the popular MODFLOW package with an optimization framework based on the simulated annealing technique. Their merged simulation-optimization model provided an optimum depressurization strategy while maintaining local and regional hydrogeological impacts within acceptable limits. Jiang et al. (2013) investigated the drawdown system of an open-pit coal mine in China using a genetic algorithm. The authors aimed to minimize the sum of total pumping and seepage, concluding that FoS increased after the drawdown simulation and that the mine drainage system should be improved. Using a similar optimization approach, Widodo et al. (2018) studied horizontal drainage scenarios. By maximizing groundwater drawdown and minimizing installation costs, their investigation attempted to determine an optimum drain hole system in terms of number, location, and length. One should be particularly careful, however, not to use excessive pumping rates in mine drainage, as this significantly affects groundwater resources (Zhao et al. 2017). In fact, Peksezer-Sayit et al. (2015) simulated the impacts of dewatering on groundwater resources in three open pits located in western Turkey. Their results showed that the drawdown during 21 years of the mining operation would not affect water supply wells but would drastically reduce the natural discharge of the springs around the mine. Therefore, optimization of the use of water resources is crucial for the sustainability of mine operations (Yin et al. 2016).
Despite the interest and importance of optimizing the geometry of open-pit mine slopes, some questions have not yet been fully addressed in the literature, such as which performance indicators should be selected for the simulation of drawdown scenarios; and it is also unclear if and how the selection of the optimal drawdown scenario should use geotechnical, economic, and environmental trade-off analysis. As an example, the depth of groundwater should be minimized from a geotechnical standpoint, but this conflicts with the largely ignored environmental viewpoint (Xu et al. 2021;Zolghadr-Asli et al. 2021), as the depth of groundwater should be maximized. The present study embraces these research gaps to propose and explore a simple and comprehensive approach to obtaining optimum slope geometry for an open-pit phosphate mine, in southeastern Brazil. For this purpose, this study investigates a mining plan that explores groundwater drainage scenarios, including the combination of deep horizontal drains and pumping wells. Slope stability analyses using the LEM are used to estimate FoS for different representative sections of a phosphate open-pit mine in Brazil. A multi-objective multi-criteria framework using compromise programming is implemented to select a slope geometry for the final pit with the help of four indicators and multiple perspectives. The framework presented herein provides a practical tool for mining-related water management problems and can be applied to other regions with similar geologic settings and climate conditions.

Study area
The investigations were carried out at the Morro da Oficina mine, in the city of Araxá, state of Minas Gerais, southeastern Brazil ( Fig. 1(a)). The geographic location of the field site, the Barreiro pit, is shown in red in Fig. 1(b) on the simplified geological map. A more detailed view of the study area is shown in Fig. 1(c).
Local geology consists of quartzites, fenitized schists, and carbonatite bodies that occur as a complex system of dikes and veins of some millimeters to several meters in thickness, crosscutting metasomatic phlogopitites (Traversa et al. 2001). The main type of carbonatite is dolomitic, medium to coarse-grained, that contains subordinate amounts of calcite, ankerite, barite, apatite, magnetite, perovskite, pyrite, phlogopite, sodic amphibole, isokite, barium pyrochlore, and strontianite (Issa Filho et al. 1984). Subordinately, calcite carbonatite dikes occur in the NW portion of the complex. This heterogeneous geology, also known as the Araxá Complex, is covered by a variety of unconsolidated materials, such as saprolites and sediments, up to 230 m thick (Rodrigues and Santos 1984). Since the horizons of the unconsolidated mantle have been individualized throughout the years (Grasso 2000), this stratigraphic subdivision has guided the planning and operation of the mine and the dressing of the ore.
The Araxá Complex is well known for its phosphate reserves and for the largest niobium reserve in the world. In the study mine, a phosphate deposit was discovered in 1939, but mining operations only started in 1973. Nevertheless, systematic mapping work was only carried out after 2002. The study mine was completely excavated in a thick unconsolidated mantle, involving saprolites (here referred to as isalterites, as defined by Delvigne (1998)) and sedimentary covers (colluvia). The unconsolidated mantle of the Morro da Oficina pit was mapped on a scale of 1:5000, thereby enabling the identification of several isalteritic and sedimentary cover units.
The study area is inserted into the tropical zone, which is slightly warm most of the year. The hydrological year is divided into a rainy (wet) season from October to March and a dry season from April to September ( Fig. 2(a)). Due to such seasonality, rainfall data are essential for hydrogeological studies, both to corroborate the data obtained from the monitoring and to predict aquifer recharges. The mean pluri-annual rainfall, according to the data series from 2002 to 2020, is 1541.2 mm/year; on average, the rainy season corresponds to approximately 85% of all annual rainfall.

Methods
In this article, a framework is developed for slope design at the studied open-pit mine. The approach uses tradeoff evaluations between geotechnical, economic, and environmental criteria and encompasses four main blocks: (i) field assessment and data collection, (ii) drawdown scenarios, (iii) slope stability simulations, and (iv) optimization framework.

Field assessment and data collection
Based on field observations and mapping since 2002, the mine was divided into three major domains: sedimentary covers, isalterites (saprolites), and rock masses. Sedimentary covers occur on the upper benches of the pit and constitute the barren materials of the mine. Seven isalterite units were identified based on their mineralogic, textural, and structural properties. These units were developed from alkaline rocks and are characterized by preserving the structure of the rocks and concentrating supergene minerals, such as magnetite and apatite. The rock mass domain is characterized by outcrops of fresh or partially weathered rock, namely phlogopitite and carbonatite (Fig. 1). This rock domain is not involved in landslide processes that affect the unconsolidated mantle. The transition from these rocks to the isalterites is irregular and usually occurs between elevations 980 and 1040 m. Table 1 summarizes all the relevant information on the identified geotechnical units. The first column of Table 1 identifies the major groups, the second column their corresponding units, and the third column briefly describes some geological features of the present pit. As can be seen, 15 geotechnical units were mapped in the Morro da Oficina pit, including barren material, ores, and rocks.
Based on the geotechnical map for the present mining conditions (2020), a total of 17 locations within the mining limits were carefully chosen as representative of the different units (Fig. 3). The disturbed and undisturbed samples were then collected for laboratory tests to investigate the soilmantled mine. The tests included Atterberg limits (ABNT 2016c, d), grain size distribution (ABNT 2016b), and specific gravity (ABNT 2016a). These tests were developed according to the requirements of the Brazilian standards. Furthermore, samples collected from unconsolidated mantle units were prepared for isotropically consolidated undrained  triaxial tests (CIU), with pore water pressure measurements according to ASTM method D4767 (ASTM 2011). These tests provided values for the strength parameters (cohesion, c and friction angle, ϕ) of the Mohr-Coulomb failure criterion, adopted here for slope stability analyses (of which more will be provided later). Since this failure criterion is commonly used for soils, the method is deemed appropriate for unconsolidated materials (Vallejo and Ferrer 2011). In addition to the geotechnical map derived for the present pit conditions (2020), updated geotechnical maps were derived for the mid-term (2025) and long-term or final pit (2030). This mapping was based on the corresponding topographic map but was restricted to the sections under drawdown and slope stability analyses.

Groundwater drawdown data and simulation scenarios
The region where the mine occurs has been the subject of some hydrogeological studies ( Using this numerical approach, water table drawdown simulations in the mining complex can help to (re)design the underground drainage system. In this study, water level drawdown data is used to help plan for the medium-and long-term mines from 2025 to 2030 (final pit). Data covered periods defined according to local seasonality (wet and dry periods as shown in Fig. 2(a)), from January 2020 to December 2030.
Four simulation scenarios were used to assess the impact of different drawdown situations on the stability of the soilmantled open pit mine (Fig. 4). The first scenario (top-left panel) constitutes the current field condition at the Morro da Oficina mine. A total of seven deep (sub)horizontal drains (DHD's) have been installed in the pit for groundwater drainage (green circles). The drainage system (both superficial and underground) is built simultaneously with the expansion of the pit, as a set of drainage channels that direct the flow of water to a sump (pond), from which water is continuously pumped to a lake, located outside the pit domain. In this scenario, the 2025 and 2030 mine plans consider a gradual reduction of water flow in the DHD's of approximately 2% from the present condition until 2025 and 7% until 2030.
The second scenario assumes the same drainage system as the first (present) case scenario. However, a deep pumping well (DPW) is included outside (upstream) of the mine boundary (purple circle). The DPW location was chosen to avoid potential seepage face on the downstream slope of the mine pit. Another reason for the DPW installation was to evaluate the potential water flow rate reduction of existing DHD's. In the numerical simulations, a flow rate of 55 m 3 /h was considered for the DPW, which was gradually reduced (approximately 5% each year) from the present condition until 2030. The third scenario includes the components of the first and second scenarios, but incorporates four additional DHD's, as indicated by the black dashed crosssection in Fig. 4. These new DHD's, added along the cross section, were positioned 5 m below the topographic surface (i.e., surface level). In the fourth scenario, the components of the first and second scenarios were incorporated. However, three additional DPW's were included, as indicated in Fig. 4. These new DPW's were positioned very close to the first installed DPW, ideally to intensify the reduction of the upstream incoming flux. Table 2 summarizes the number of DHD's (column 2), DPW's (column 3), and installation and operating costs (column 4) of each simulation scenario (column 1).
The simulated flows of horizontal drains (Q DHD ), pumping wells (Q DPW ), and global discharge (Q Global ) drained to the mine pond are shown in Fig. 2(b-d). The positive correlation between the rainfall amount ( Fig. 2(a)) and the drainage system discharge is consistent with previously reported data (Fernãndez-Rubio and Singh 1983).

Slope stability analyses
The identification of the potential failure mechanisms is a fundamental prerequisite for slope stability analysis. In general terms, the slopes of the Morro da Oficina pit are cut in thick unconsolidated material layers that are easily scarifiable, very friable, and isotropic. In fact, as these soil layers are very weathered, the discontinuities of the fresh rock do not interfere in the material strength. This explains the predominant instabilization mechanism, i.e., rotational sliding.  Here, the LEM was used with the aid of the Slide2 software (Rocscience Inc.), which benefits from the auto-refine search method for rotational slides. This method works with an effective algorithm for iteratively refining the search area on the slope, until the critical surface is located. As a calculation model, the Spencer method, applied to any rupture surfaces and explained in detail by Duncan et al. (2014), was adopted. This method is one of the most theoretically rigorous methods of slices, since it satisfies both the force and the moment equilibrium of the failure mass. The slope stability analyses were carried out using a deterministic method, i.e. without resorting to the inherent uncertainty of soil and hydrogeologic properties. Slope stability analyses were performed for 3 years of the mine plan, that is, using four representative cross sections of the current pit (2020), two in 2025, and five in 2030 (Fig. 5). As also schematically illustrated in Fig. 5, bench, inter-ramp, and overall slopes were investigated in each cross-section. Individual bench stability analyses were performed for all geotechnical units in Fig. 3. To accomplish this task, the typical mine section was adopted as standard, with individual benches 10 m high and with a face angle of 60°, in the sections with natural moisture and at 50°, when the geotechnical units were under saturated conditions. The soil moisture conditions of each cross section varied according to the groundwater drawdown scenarios described in "Groundwater drawdown data and simulation scenarios". Thus, the safety factors of the pit slopes were determined using geological-geotechnical, hydrogeological data, and strength parameters of the different units identified in the mine (Fig. 3).
Below 1030 m to the bottom of the pit, the geometry consists of 20 m-wide berms and a slope angle of 45°. For the 2030 mine plan, stability analyses were also carried out considering different berm widths for the regions below the 1030 m elevation: 9 m, 10 m, and 12 m-wide berms.
Despite the area of the Morro da Oficina pit is not seismically active, an analysis of the possible consequences of stresses caused by seismicity on slope stability is recommended. Among the methods of analysis of the influence of seismic activity, the pseudo-static has been chosen for its simplicity (Duncan et al. 2014;Vallejo and Ferrer 2011). In this method, the seismic effect is considered by adding static forces in each slice of the limit equilibrium method. Because seismic monitoring data are inexistent for the study area, dynamic analysis was performed adopting project criteria recommendations for dams in Brazil (Eletrobras 2003). According to these recommendations, seismic loads should be adopted considering an acceleration of 0.05 g in the horizontal direction and of 0.03 g in the vertical direction. As such, pseudo-static analyses were performed to analyze the influence of seisms on the global (overall) slope stability of the 2030 mine plan conditions. The inter-ramp and overall safety factors obtained in the stability analyses were further used to propose improvements in the pit geometry considering geotechnical, environmental, and economic trade-offs, as detailed in the next section.

Performance indicators
Four performance indicators were adopted in this work to investigate the optimum drawdown scenario of the Morro da Oficina pit, in a multi-objective methodology. The indicators are the inter-ramp factor of safety FoS (I) , the overall factor of safety FoS (O) , the water table elevation (WTE), and the drawdown cost. Here, WTE is taken as the average depth of the water table in the section under study. This is convenient for the optimization process, as it converts a vector of groundwater depths into a single scalar. Costs include costs of installation and operation of each drawdown scenario. These important decision variables for the mining sector are indicated in Table 3. It is important to note that the costs involve the installation and annual maintenance value of the DHPs and wells and the annual energy costs to pump the wells at varying rates over the simulation period. The most likely environmental In this work, we assumed that these four performance indicators are sufficient to adequately describe the optimum drawdown condition using different simulation scenarios and perspectives. Yet, the use other informative performance indicators, if available, may be convenient to improve the optimization process.

Compromise programming-based scenario analysis
The decision-making process of drawdown scenarios often requires a multi-objective optimization (Sperling et al. 1992;Jiang et al. 2013;Widodo et al. 2018;Mallios and Tsiarapas 2022). In this manuscript, compromise programming (CP) was used as a mathematical approach to select scenarios. The CP method is a multi-criteria, multi-objective framework that makes use of a normalized distance, L p , to identify the best-compromise scenario as the closest scenario with respect to the ideal solution (Zeleny 1973(Zeleny , 1974. The CP method can be formulated using the family of normalized L p metrics as follows (Yu 1985;Romero and Rehman 2003). and where f i (x) represents the i-th objective to be optimized, f * i and f * * i denote the best and worst case for the i-th objective, = { 1 , ⋯ , n } indicates a user defined weight vector and highlights the relative weight of the i-th objective in a particular decision situation, and p is a model parameter that specifies which of the family of L p metrics will be used. The variable f * i is a proxy of the "good" solution, and the counterpart f * * i represents the "bad" solution in the decisionmaking process. The L p metrics can assume values from 0 to 1. L p = 0 means that positive ideal solutions of the objectives are obtained. In contrast, L p = 1 implies that the objective functions are equal to the negative ideal solutions. Hence, the essence of this method is to minimize the distance from the ideal point ( f * i ). In the CP method, the best compromise solution is affected by the parameter p and the weights . Users must provide values for p and to execute the optimization framework. The L p distances are limited between the L 1 -metric and the L ∞ -metric, and the L 2 -metric denotes the Euclidean distance (Romero and Rehman 2003). In this work, it is assumed that the vector p = {1, 2, 3, ∞} is adequate to characterize an efficient compromise solution (Ringuest 1992;Abrishamchi et al. 2005;Roozbahani et al. 2015). Sections S1 to S5 of 2030 (see Fig. 5) were chosen as representative of the mine plan. Therefore, the drawdown scenarios in these sections were investigated using different weights , considering geotechnical, environmental, and economic perspectives.

Geotechnical, environmental, and economic perspectives
The optimal drawdown scenario was investigated through a multi-objective compromise considering different preferences. Geotechnical, environmental, and economic perspectives are conflicting on many occasions, so different weights should be conveniently attributed to the indicators adopted in the optimization approach. Here, the weights were assigned using a three-level linguistic scale (Low, Medium, and High), which were further converted into numeric values: 1, 2, and 3. Higher weights indicate superior importance of the criterion for each different viewpoint. Table 3 lists the direction of optimization and weights the different perspectives.
From a geotechnical point of view, the factor of safety is by far the most critical part of an open-pit design. Of course, from any perspective, the objective is to maximize the factor of safety. Therefore, the highest weights were attributed to FoS (I) and FoS (O) . When considering the WTE indicator, there is a conflict of objectives (direction of optimization) between the geotechnical and environmental perspectives. While minimization of WTE is relevant for pore pressure reduction, excessive drawdown causes environmental impacts (Yin et al. 2016). The most likely environmental impact associated with the drawdown investigated in this study is a decrease in the natural discharge of springs around the mine. Therefore, since the maximization of WTE is of utmost importance from a sustainable point of view, this indicator received the greatest weight from the environmental perspective. The construction and maintenance costs of each drawdown system are much more important from an economic perspective. From an environmental point of view, manufacturing and transportation of a larger number of drainage devices entail additional adverse impacts. Given that the main objective of mining owners is to maximize overall profits, the costs related to the drawdown system should be minimized from an economic perspective. For completeness, another optimization run was considered assuming equal weights for each performance indicator (see the last two columns of Table 3). In the optimization approach, all five cross sections of 2030 were selected as representative of the pit. As an illustrative example, the performance indicator values for "Introduction" are listed in the last four columns of Table 2.

Geotechnical units and sampling in the Morro da Oficina Pit
The specific weights and the Mohr-Coulomb strength parameters of each geotechnical unit are summarized in Table 4, under natural moisture and saturated conditions. The specific weight of the samples varied between 17.5 (WD) and 24.0 (RM) kN/m3 under natural moisture, and between 19.5 (OBIS) and 25.0 (RM) kN/m3 under saturated conditions. The reported values are in agreement with a range of young, mature, and saprolitic residual soils found in southeastern Brazil (Gomes et al. 2022). While the friction angle values did not vary much, the values of the cohesion parameter were distributed between 10 and 100 kPa. The listed Mohr-Coulomb strength parameters were found to be slightly higher than weathered marls (Cooper et al. 2019) and quaternary deposits (Fan et al. 2015) of mines excavated in unconsolidated materials, but are similar to values used in modeling rainstorm-induced soil landslides in southeastern Brazil (Gomes 2017). These parameters were used next to assess the impact of different groundwater drawdown scenarios on the stability of the soil-mantled open-pit mine.

Groundwater drawdown simulations in the Morro da Oficina pit
To provide information on the differences in the groundwater table for each simulation scenario, consider Fig. 6 which contains a cross-section with elevation and WTE values for different years and drawdown scenarios as detailed in "Groundwater drawdown data and simulation scenarios". Figure 6(a) shows mine plans for the years 2020, 2025, and 2030, with different colors for better visualization. As expected, the largest excavation takes place in the year 2030, as can be seen in the lower elevations of the cross-section ( Fig. 6(b)). The WTE of the current pit is shown in Fig. 6(c). One can note that, without a groundwater control strategy, some lower parts of the mining front are below the water table level, which is undesirable from a trafficability point of view (Sperling et al. 1992). Finally, Fig. 6(d) summarizes in one graph the WTE values for each drawdown scenario of 2030. The large black rectangle is zoomed inset on the smaller rectangle (Fig. 6(d) of the sideslope, between distances of 450 and 500 m) and much better illustrates the effect of the different drawdown scenarios on the water table.
It is clearly visible in the inset that scenarios 3 and 4 provide the greatest drawdown, with scenario 4 providing the largest drawdown in the side slope. However, as previously shown in "Groundwater drawdown data and simulation scenarios", in the third scenario, DHD's were included 5 m below the topographic surface, thereby allowing a greater lowering of the water table at the lowest levels of the mine. In relation to the four simulated drawdown scenarios, results of Fig. 2 showed that the highest flows for 2025 and 2030 were obtained for scenario 4 (417 and 797 m 3 /h), followed by scenario 3 (409 and 709 m 3 /h), scenario 2 (398 and 707 m 3 /h) and scenario 1 (388 and 671 m 3 /h). Additionally, the differences in global flows of scenarios 2, 3, and 4 should decrease from December 2023 on, due to the gradual reduction of the flow in the pumping wells and the slower advance of the pit towards saturated portions of the aquifer. Scenario 1 represents the operation of drainage structures only in August 2020. In scenario 2, with the inclusion of well PP01, an expansion of the dewatering influence area is observed in the southern portion of the pit. The drawdown is more intense close to the PP01 well, located in the southern sector of the mine, and its influence gradually decreases towards the north. In scenario 3, drawdown intensification is evident in the pit area, reflecting the insertion of drains 5 m below the pit topography. In 2030, a larger radius of influence of the drawdown is observed. In scenario 4, drawdown is more pronounced near the wells located in the southern portion of the mine. In scenario 3, it is possible to maintain the groundwater level 5 m below the final pit topography, without the installation of new pumping Fig. 6 Drawdown simulation scenarios: a identifies the 2020 topography, and the 2025 and 2030 pit plans. The black cross-section is visualized in the remaining plots. In (b), the different topographies of the three periods are shown. In (c), the initial water table condition (i.e., year 2020 and scenario 1) is highlighted and in (d), the final 2030 pit plan with its different drawdown scenarios is shown wells. The implementation of DHD's was chosen due to the experience and proven effectiveness of the method already used in the Morro da Oficina pit. Moreover, this technique is considered a low-cost installation and maintenance drainage system. The results indicate that the gain of the drained flows of scenario 4 compared to scenario 3 is not significant. Despite this good sign that scenario 3 would be the best drawdown scenario, this result still needs to be confirmed with the slope stability analysis and finally with the proposed optimization method.

Slope stability analysis of the pre-final Morro da Oficina pit
To assess the intermediate operating conditions before the final pit is excavated, slope stability analyses were performed for the pit geometry of 2020 and for the 2025 mine plan. In general, the overall slope angles for 2020 and the projected angles for 2025 are low, because there are several wide berms along the slopes, and thus the overall slope angles vary between 20° and 23°. Therefore, the analysis resulted in high safety factors, between 1.60 and 2.00 (not shown), reflecting the stable conditions observed in the field. To provide an example of the stability analyses performed, consider Fig. 7, which shows the different slope geometries, geotechnical profiles, water table positions, and the corresponding bench, inter-ramp and overall FoS values for the 2020 representative cross sections (Fig. 5) with initial groundwater level (scenario 1).
It can be seen in Fig. 7 that bench analyses were performed for superficial materials under natural moisture conditions, such as sedimentary covers (RSC) and orange isalterite (OIS), units that were always considered dry on the slopes of the pit. For isalterites such as ISML, ISM, ISMV, and ISV, which occur at the lower levels of the pit, the analyses were performed under natural moisture and saturated conditions, considering the most critical situation. For materials under natural moisture conditions with a face angle of 60° and under saturated conditions with a face angle of 50°, FoS values much greater than 1.30 were obtained. According to Read and Stacey (2009), the deterministic slope stability analysis approach must comply with the project acceptance criteria. Since the level of acceptance of a project failure depends on the consequence of the failure, slope angles must be evaluated considering the safety and economic impacts. A FoS of 1.2 or 1.3 is acceptable for slopes in pits that are not disturbed by crushing plants or where the main access ramps are not immediately behind the crest. For more critical situations, the FoS must be greater than 1.5. Therefore, current mine conditions would allow for higher slopes of individual benches under both natural and saturated moisture conditions.

Slope stability analysis of the final Morro da Oficina pit
For the evaluation of the final pit predicted for 2030, water level drawdown simulations were performed for the four scenarios. For the final pit, a significant lateral advance is predicted in the pit toward the south and southwest, making it necessary to lower the water level in this direction as well. The location of the five sections analyzed for the 2030 pit is indicated in Fig. 5.
The geometry of the mine plan for the final pit, represented in sections S1 to S5 is 12 m-wide berms and a face angle of 50° for saturated materials, and 10 m-wide berms Fig. 7 Example of slope stability analysis for the 2020 pit geometry with initial groundwater level (scenario 1): a "Introduction"; b "Study area"; c "Methods"; d "Results". The analyses include bench, interramp and overall slope failures Page 13 of 18 164 and a face angle of 60° for materials under natural moisture conditions. For sections S2, S3, and S4, up to elevation 1030 m, the geometry is 9 m-wide berms and a face angle of 50°. Below 1030 m to the bottom of the pit, the geometry is 20 m-wide berms and a slope angle of 45°. For the waste dump that occurs in sections S3, S4, and S5, slopes with a face angle of 26° and berms of at least 8 m of width are predicted. Figure 8 exemplifies the results of the slope stability analysis for section S3 of the 2030 mine plan with different drawdown scenarios: (a) scenario 1, (b) scenario 2, (c) scenario 3, and (d) scenario 4. Although with a slight advantage to the FoS obtained in scenario 3, results of the slope stability analysis for "Methods" indicate satisfactory safety factors (> 1.45), for both inter-ramp and global (overall) failure circles for the four scenarios analyzed. On the basis of the results presented here, it is concluded that it is possible to re-design both face angles and berm widths.
To further verify the slope stability results, additional pseudo-static analyses were performed for the 2030 mine plan to analyze the influence of seisms on overall stability. As an illustrative example, Fig. 8(e) shows the pseudo-static analysis of cross-section S3 modeled with the drawdown scenario 3 and 20 m-wide berms. Additionally, the pit geometry of section S3 was redesigned, now with face angles of 50° and berm widths of 9 m below 1030 m. This led to the results of the conventional stability analysis for 9 m-wide berms (Fig. 8(f)), and pseudo-static analysis for 9 m-wide berms ( Fig. 8(g)). Even with the incorporation of a seismic coefficient (Ducan et al. 2014), FoS obtained from the pseudo-static analysis was 1.30 and 1.41 for the inter-ramp and overall safety factors of section S3 with 20 m-wide berms, respectively (Fig. 8(e)). This result inspired confidence in testing new geometries for the final pit. As can be seen in Fig. 8, the use of a shorter berm hardly changed the results of both conventional stability analysis (Fig. 8(f)) and pseudo-static analysis ( Fig. 8(g)). This finding is important because the oxidized ore is of high quality, so any gain in processing is significant from both the operational and economic viewpoints. The results show a safety factor of 1.40 for more global failures, and a FoS of 1.33 for the first bench, which is the minimum stability threshold. Table 5 summarizes the inter-ramp, overall and seismic FoS obtained for the five sections and four scenarios of the final pit geometry. As the safety factors are fairly similar for the four scenarios, the successful choice of a groundwater control strategy must consider other economic and environmental issues. Therefore, once the safety factors for each section investigated and drawdown scenario have been defined and analyzed, what is left in the present study is to Fig. 8 Example of stability analysis for the 2030 mine plan. The plots compare inter-ramp and overall safety factors of section S3 considering different drawdown scenarios: a scenario 1; b scenario 2; c scenario 3; and d scenario 4. Also, the slope stability analysis of crosssection S3 modeled with the drawdown scenario 3 for the 2030 mine plan: e pseudo-static stability with 20 m-wide berms, f conventional stability analysis with 9 m-wide berms, and g pseudo-static analysis with 9 m-wide berms define the optimum drawdown scenario based on the proposed optimization framework. Table 6 lists the results of the optimization approach considering the different perspectives for section S3. The L p -values obtained for all drawdown scenarios are rounded to two decimal places. The lower the value of L p , the closer the scenario is to the ideal solution. Values in bold highlight the lower L p -values acquired for each p-value. The geotechnical and economic perspectives indicate that scenario 3 is the optimal drawdown alternative for all values of p . This is also true when equal weights were used in the optimization run. Yet, the environmental perspective suggests that scenario 2, involving a larger WTE and consequently a lower cost (see Table 2), would be the optimal drawdown scenario. The same exercise was performed for all five sections investigated. The result is shown in Table 7. The analyses highlighted that the pit slope design process is a complex one. Even using a decision-making technique, including trade-off analysis and assessment of drawdowns, there is still some degree of uncertainty in choosing the best scenario. For example, with a sufficiently high safety factor, the lowest cost, and a smaller amount of groundwater drawdown, scenario 1 was considered the optimal solution for sections S4 and S5 from an environmental point of view. While under such specific conditions scenario 1 provides adequate optimum from a sustainable standpoint, scenario 3 is apparently the most suitable from a geotechnical, economic, and equal weight point of view, scenario 3 is apparently the most suitable from a geotechnical, economic, and equal weight point of view. Hence, scenario 3 was considered the optimal drawdown scenario for the Morro da Oficina pit, as the proposed groundwater control would benefit not only the safety of the mine slopes, but also the trafficability of the mine.

Optimum drawdown scenario
Lastly, since the open-pit design must take into account geological conditions within the mine area, which may   Geotechnical  4  4  3  3  3  Environmental  2  2  2  1  1  Economic  2  3  3  3  3  Equal weights  2  3  3  3  3 require different slope designs around the pit (Read and Stacey 2009), this article concludes with the ultimate slope design for the investigated sections of the 2030 mine plan (Table 8). With this optimized geometry, the released ore mass would be about 680,000.00 tons, corresponding to nine months of the current average production. The corresponding mass of barren material to be moved would be 260,000.00 tons, equivalent to approximately a month and a half for the removal of this material. Without optimization, the amount of barren material to be extracted would be much higher (2.045.000 tons) for the same amount of ore mass. Therefore, the barren material-to-ore ratio obtained from these masses is 0.38, which is much less compared to the present ratio, close to 3, and thereby much expected for the mine operation. The cost of implementing the groundwater control system for slope depressurization is estimated to be USD 600,000 (scenario 3, Table 2) and the savings associated to this program (barren material reduction) would be of USD 1.8 million approximately. These values are similar to those found in other mines, where slope depressurization resulted in significant economic gains (Sperling et al. 1992;Read and Stacey 2009). In this paper, the importance of assessing the influence of groundwater drawdown was thus highlighted, taking into account slope stabilization and, consequently, mining pit optimization. However, continuous monitoring of hydrogeological conditions and slope stability analysis in the study area is strongly recommended. This will confirm the adequacy of the slope design proposed here. Despite our efforts to consider representative drawdown scenarios of the study mine, there are indeed other opportunities that go beyond the simulations of this work. The approach presented here, while focused on four drawdown simulations, could also be extended to a wide variety of numerical simulations. More research is needed to couple subsurface flow and slope stability programs with other optimization techniques or decision support tools, such as the cost benefit analysis (Merisalu et al. 2021). What is more, by combining a hydrogeological model with a more advanced optimization procedure (e.g., Jiang et al. 2013;Widodo et al. 2018), drawdown can be considerably reduced while complying with groundwater management targets, such as constraints of permitting processes, land subsidence, and stakeholder concerns.

Summary and conclusions
In mining enterprises, groundwater drainage studies have become much more important. Groundwater is one of the main agents that triggers open-pit mine slope instability mechanisms, especially when these mines are excavated in thick soil layers, such as the one in the Morro da Oficina pit, investigated in this work. Therefore, slope geometry optimization is a determining factor in the design of the mine, which has a major impact on the barren materialto-ore ratio.
In the present work, a practical framework was proposed to optimize the slope geometry of open-pit mines considering four groundwater drawdown scenarios that included the use and combination of deep horizontal drains (DHD's) and deep pumping wells (DPW's). The approach merges groundwater flow simulations and slope stability using the Limit Equilibrium method with compromise programming to select the optimal drawdown scenario based on geotechnical, economic, and environmental trade-off analysis. The inter-ramp factor of safety (FoS), the overall FoS, the drawdown cost, and the water table elevation (WTE) were used as technical indicators. While the WTE indicator should be minimized from a geotechnical point of view, this perspective conflicts with environmental and economic viewpoints, as WTE should be maximized. Therefore, different optimization directions were tested and distinct weights were assigned for the indicators, including equal weights.
The framework was applied in an open-pit phosphate mine in southeastern Brazil for different years of the pit design: the current pit topography (2020), pre-final pit (2025) and final pit (2030). The following conclusions were drawn: • Geotechnical investigation and slope stability analysis indicated that current and pre-final slope geometries with wide berms and high overall slope angles (between 20 and 23°) resulted in relatively high safety factors and encouraged stability analyses with different geometries for the final pit design. • The proposed optimization approach honors geotechnical, economic, and environmental perspectives using compromise programming, providing a relatively simple way to merge geological data and field expertise in pursuit of the so desired best drawdown scenario. • Scenario 3, with 11 DHDs and 1 DPW, was considered the most adequate from a geotechnical, economic, and Face angle (°) S1 10 10 10 50 S2 10 9 10 50 S3 10 9 10 50 S4 10 9 10 50 S5 10 12 10 50 equal weight point of view because efficient drawdown is achieved with low-cost installation and maintenance. Therefore, slope optimization was obtained by adopting the water level of this scenario. • Drawdown optimization based only on the total mine water drainage flow rate might provide an inappropriate optimum groundwater control system from a sustainable standpoint. In fact, scenario 4, with a larger number of pumping wells, did not result in the optimal drawdown scenario. • The ultimate slope design proposed for five representative sections of the final pit included berms of 10 m above elevation 1030 m, berms ranging from 9 to 12 m below elevation 1030 m, bench heights of 10 m, and an overall face angle of 50°. • The inter-ramp and overall FoS obtained for these 2030 optimized sections were higher than 1.25 and 1.40, respectively. The pseudo-static analysis further supported the stability of the new slope geometries, which inspires confidence in the findings of the paper. • With the proposed optimized geometry, the barren material-to-ore ratio was calculated as 0.38, much less than the present ratio, close to 3, implying significant economic gains. • The results of the suggested methodology are important for preventing soil landslides in open-pit mines and can be adapted to regions with similar geological settings and climate conditions.