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Pit Slope Optimization Based on Hydrogeologic Inputs

Pit Slope Optimization Based on Hydrogeologic Inputs

Pit Slope Optimization Based on Hydrogeologic Inputs

G. Evin, F. Henriquez, V. Ugorets SRK Consulting (U.S.), Inc., Lakewood, Colorado, USA

ABSTRACT With the variability of commodity prices and the constant increase of mining costs, it has become increasingly important to optimize pit slopes of mines, taking into consideration the complexity and the uncertainties presented by ground conditions. The variables in slope stability, , rock mass strength, structural defects, inherent and induced stresses, rock weathering, alterations, and , are known, as are their impacts on slope performance. Most variables cannot be changed to optimize slopes. However, groundwater is one variable that can be managed during pit excavation, to reduce the effect of pore on slope stability. Hydrogeologists and rock mechanics engineers combine their efforts in order to quantify, simulate, and control the effect of groundwater on pit slope performance. Based on comprehensive field hydrogeological data collection and interactive numerical groundwater and geotechnical modeling, it is possible to evaluate the pore pressure effect on the pit slope, to provide an efficient depressurization strategy to meet the targets, and thus to develop cost-effective mine plans. This paper discusses how proper management of groundwater conditions can contribute to mine planning and operations, through pit slope optimization. We show a complete approach from collection of hydrogeological data in the early stages of a project to design of an appropriate depressurization plan, taking into account the rock mass conditions, the mining plan, and the time to achieve an optimal pit slope.

1 INTRODUCTION 2.1 Changes of Effective Stresses Groundwater water in open pit mines affects In its simplest definition, the water pore normal operations in many ways. Excessive pressure is the pressure of groundwater held water inflow into the pit can significantly within a or rock in gaps between impact the mine operations by reducing particles (pores). is used equipment performance and increasing in calculating the stress state in the ground loading and haulage time. Water in the pit using Terzaghi's expression could result in incremental increases in for the of a soil (below). mining cost, reduction of mining Soil or rock can be pictured as a frame performance, the need for special blasting of soil particles enclosing continuous voids products, increases in drilling time, and containing fluids (water, air, gas etc.) as mechanical damage of mine equipment, etc. shown in Figure 1. In fully saturated soil, A poor knowledge of the hydraulic parameters could also have a negative impact water is considered to be incompressible, so on the slope design and stability performance that a reduction in volume is possible only if of the pit, which could result in an over or some of the water can escape from the voids. underestimation of the mine design; directly In dry or partially saturated soil a reduction impacting, negatively, the net present value in volume is always possible due to the (NPV) of the business. compression of air in the voids which allows It is clear that a good understanding of the opportunity for the rearrangement of groundwater conditions and their effects on particles within the soil. In 1923, Terzaghi the mine operation and mine design can help presented the principle of effective stress. mining companies optimize their business. The principle applies only to fully saturated Several authors have developed and relates the following three stresses: methods of data collection, interpretation and (a) total normal stress σN, (b) pore water modeling of groundwater conditions to pressure (u) and effective normal stress (σ’), provide recommendations for pore pressure which represents the stress transmitted reduction and mine (Read & through the soil skeleton only. The Terzaghi Stacey, 2009; Beale & Read, 2013; and principle is expressed by the following others). This paper does not intend to review equation (Eq.1). and comment about the current data collection and modelling technics, the σN= σ’ + u (Eq.1) objective of this paper is to discuss how the integration of the and geotechnical disciplines can optimize the mine operations. The paper intends to demonstrate the importance of good data collection, interpretation, and groundwater numerical modeling on slope stability as an optimization tool.

2 EFFECT OF GROUNDWATER ON SLOPE STABILITY

The literature lists different ways in which groundwater can affect open pit mine excavations, including (a) changes of effective stresses and/or (b) saturation, both contributing factors of slope stability. Figure 1. Interpretation of effective stresses.

Figure 1 shows a Normal force P applied particle forces; therefore, if the effective on an area A, resisted by inter particle forces normal stresses are zero then the shearing and the pressure located in the pore water. resistance must be zero (at least there is cementation between the particles) and the The physical model indicates that the forces value of effective (c’) would be at each point are in contact with the true zero. plane XX, which can be split into two The physical model indicates that each components; Normal Effective N’ and point in contact on the true plane XX, the tangential T forces, then the Effective Normal Effective N’ and tangential T forces, Normal stress can be defined by the will be reduced and potentially reach a critical combination of normal and shear following equation (Eq. 2): stresses over the failure envelop establishing the failure. σ’ = ΣN’ / A (Eq. 2)

Given the fact that the Total Normal stress is: 2.3 Water Pore Pressure in Slope Engineering σ = P / A (Eq. 3) The pore pressure in slope engineering is one Then the points in contact between the of the contributing factors in slope stability. particles should have a total pore pressure The groundwater changes, effective stresses, acting on the plane (entire area A), reaching and increased density of the materials cause the equilibrium in direction normal to XX changes in hydrostatic loading (Read & plane given by: Stacey, 2009). There are several different techniques to simulate water pore pressure in P = ΣN’ + u x A (Eq. 4) slope analyses; computer simulations can provide a good approach to analyze the or groundwater effect on slope performance. P/A = ΣN’ / A + u (Eq. 5) For saturated or partially saturated slopes, rock engineering experience establishes that a reduction of pore water Therefore, σN= σ’ + u or σ’ = σN – u pressure will improve the results of the slope performance parameters creating the 2.2 Shear Failure opportunity to optimize slope designs. In practice, the time required to achieve the In simple terms, failure occurs within the reduction of pore pressure must be material when the shear stress becomes equal considered, as well as the flexibility in the to the , expressed by mining plan to allow enough time for getting Coulomb’s principles (Das, Braja, 2011) in the depressurization targets established by the lineal failure envelope, given in the the pit slope engineer. following equation:

τ = c + σN x tan φ (Eq. 6) 3 MINE DEWATERING AND PIT SLOPE DEPRESSURIZATION where: One of first steps in pit slope stability analyses is to understand the water pore τ = shear stress; pressures in the pit slopes as the result of c = material cohesion; mining and planned dewatering. As soon as the pit floor reaches levels below the water σN =normal stress; and table, natural drainage of the wall will φ = internal angle of the material. usually occur due to seepage and with response to mining which induces relaxation In other words, there are critical of the rock mass (Beale & Read, 2013). The combinations between shear and normal natural drainage in conjunction with active stresses that produce failure. However, dewatering (if implemented) will cause a shearing resistance is developed by the inter- reduction of pore pressures in the rock walls. The second step is to evaluate an effect of x = distance; and additional pore pressure reduction on the pit erfc (α) – function which increases when slopes and the necessity of implementing a α decreases and decreases when α depressurization program. In some cases, the increases. pore pressure dissipation achieved by passive and active dewatering is adequate for This simple relationship (Eq. 7) indicates targeting the desired pore pressure goals. In that slope depressurization depends on other cases, to achieve the dewatering goals, hydraulic parameters, time of dewatering, a dedicated pit slope depressurization and distance from the dewatering (or program is needed. depressurization) system. The hydraulic Pit dewatering is a necessary element parameters need to be known. Time and of any mining that occurs below the water distance are the only two variables which table. Pit slope depressurization is an allow control of the pit slope optional method for additional reduction of depressurization. pore pressure within pit walls if this is Figure 2 indicates that for the given required for geotechnical reasons. Table 1 hydraulic parameters (K and Ss) the degree of shows a comparison of general mine depressurization increases with time and dewatering and pit slope depressurization. decreases with distance from the dewatering Table 1. Comparison of mine dewatering and system. Figure 3 shows that more successful pit slope depressurization depressurization is potential for more Parameter Mine Dewatering Slope Depressurization permeable rock and shorter distances from Material/rock High permeability Low permeability the dewatering system. Equation (7) illustrates the mechanism for pore pressure Decrease effective stress of Target Lower the slope materials reduction but it should be noted that it is based on various assumptions (linear flow, Volume of water Often high Normally low homogeneity, isotropy) that are unlikely to Often local to a specific be met in practice, given the complex Area of implementation Normally pit-wide slope sector hydrogeological conditions surrounding

By horizontal drain holes many mine sites. By in-pit sump or gravity flowing drains in A key factor for designing a slope Most common method and vertical conjunction with general depressurization program in poorly- mine dewatering permeable materials is the time required to achieve the target pore pressure profile for The ability to reduce pore pressure to the critical sector of the pit. Slopes excavated achieve the desired target depends on in higher-permeable rocks typically require hydraulic parameters, on timing, and on the less time for the depressurization to be effectiveness of dewatering and effective. depressurization methods. In poorly-permeable weak rock environments, such as an operation with deep weathered zones or thick zones of 3.1 Depressurization Parameters argillic () altered rock, it can take months Major depressurization parameters and pore to years to depressurize the slopes to desired pressure reduction can be illustrated by a targets (Beale & Read, 2013). Depending on simple 1-D Flow (or Diffusivity) Equation: the time available, it may be necessary to advance a general dewatering program to −(1/ 2)  4Kt  lower the water table and to provide ∆ = ∆   additional time for drainage of less h(x,t) hoerfc 2   Ss x  permeable pit sectors.

(Eq. 7) where: ∆h = change in ;

∆ho = initial hydraulic head; K = ; Ss = ; t = time; most commonly applied method worldwide for locally reducing pore pressures behind open pit slopes. To install the drain holes, specific targets need to be identified. These targets may include: • The water contained in low permeable material. • Water trapped in permeable but compartmentalized fractures behind the pit slope. • Water “dammed” behind geological structures. Figure 2. Pore pressure reduction vs. time • New geological units which will be and distance from dewatering (K=10-8 m/s, encountered in pushbacks as the pit is -5 Ss=10 1/m) expanded.

The effectiveness of the depressurization system from horizontal drain holes depends on the success of intersecting the defined targets and, in case of a low permeable pit slope, timing, distance between drain holes and their depth, hydraulic parameters, and the ability to discharge more water than recharged from precipitation and surface-water bodies.

3.3 Hydrogeological Characterization and Data Analysis Figure 3. Pore pressure reduction as function Hydrogeological parameters affecting pit of hydraulic conductivity and distance for 90 slope stability include: days of dewatering • Water levels; • Distribution of hydraulic conductivity 3.2 Depressurization Methods of rock within pit slope; • Groundwater storage parameters; and There are different methods of pit slope • Recharge from precipitation and depressurization, which include: surface-water bodies. 1. Seepage from face and pumping from sumps. These parameters need to be 2. Horizontal drain holes. determined during hydrogeological studies. 3. Gravity-flowing vertical drains. Where it is possible, hydrogeological data 4. Pumping wells. should be collected during the early stages of 5. Drainage with sub-vertical drain the project and in conjunction with holes. geotechnical studies. Table 2 summarizes The first method is very common and used content of hydrogeological studies for for passive dewatering or as part of active different stages of the project and targeted dewatering to intercept residual passive level of data confidence. groundwater inflow coming to the open pit. The other methods allow for the addition of Table 2. Hydrogeological study and targeted the reduction of pore pressures in the pit level of data confidence slopes to achieve the desired Targeted Project Level of depressurization target. The choice of the Hydrogeological Study Stage Data best depressurization option, or a Confidence combination thereof, depends on the site Regional groundwater survey; water specific hydrogeological, geological, level data collection in exploration Conceptual holes; identification of >20% structural, and geotechnical conditions which hydrogeological units based on define the depressurization targets. Geological Model The use of horizontal drains or sub- horizontal drain holes (second method) is the Mine scale airlift, pumping, packer predict pore pressure distributions within the testing and installation; initial hydrogeological parameters pit slopes. Therefore, 2-D cross sectional or and groundwater flow understanding; 3-D (strip or asymmetrical) and more initial hydrogeological database and Pre-Feasibility 30-50% conceptual model established; detailed pore pressure models are used along preliminary and critical pit sections as “windows” within the sensitivity analysis; initial regional groundwater model. These models assessment of dewatering and depressurization requirements use the hydraulic heads from the regional Targeted pumping and airlift testing; model to incorporate boundary conditions piezometer installation; (sometimes variable in time) within pore enhancement of hydrogeological Feasibility database and 3D model; 40-65% pressure models. It should be noted that pore advancement of assessments of pressures in pit slopes and their changes as a dewatering and depressurization requirements result of depressurization should be predicted Installation of dewatering wells and in time due to the fact that steady state ; refinement of Design and calculations tend significantly to over predict hydrogeological database, 3D 65-75% Construction model, depressurization and dewatering and depressurization effects. dewatering requirements To evaluate the effect of Ongoing management of depressurization parameters on pit slope piezometers and dewatering well Operations network; continued refinement of >75% stability through the calculation of the Factor hydrogeological database and 3D of Safety (FoS), the authors developed a model series of 3-D strip models. These models Note: Table modified by authors from Read and Stacey (2009) assume excavation of a 45 degree open pit to depths of 300m, 600m, and 1000m, in 3, 6, 4 GROUNDWATER MODELING AS A and 10 years (Figure 4 shows the finite- element mesh for the 1,000m pit). TOOL TO PREDICT PORE Hydraulic conductivity values were PRESSURES varied from 10-9 m/s to 10-5 m/s (with an Numerical groundwater modeling is widely increase by a factor of 10; a total of 5 values used to simulate groundwater inflow to open were evaluated). Specific yield and specific pits for relatively complex hydrogeological storage were kept constant and equal to 0.05 conditions. The modeling process includes and 10-6 1/m, respectively. development of a conceptual The initial hydraulic heads were hydrogeological model, grid discretization, assumed to be 50m below the ground surface assigning of hydraulic parameters and with constant-head boundary conditions at a boundary conditions, model calibration, and significant distance (6km), from the center of prediction. Predictions very often include the pit. Depending on the time and geometry two scenarios: of the excavations, different water levels can • Passive inflow (or how much water be predicted. Figure 4 shows the predicted will enter into the pit during its water table (P=0 kPa curve) at the end of 10 excavation without active years of excavation of the 1,000 m open pit, dewatering/depressurization). for different hydraulic conductivity values. • Active dewatering to reduce residual passive inflow to the pit or active depressurization to reduce pore pressure for pit slope stability. The active dewatering scenario is used when the rock within the pit slope is permeable and the amount of passive inflow cannot be managed safely during the mine operation. The active depressurization scenario is used when the rock within the pit slopes has low permeability, and high seepage face and pore pressures that are causing slope stability problems. The numerical groundwater models used for dewatering predictions are typically 3-D and developed at the regional Figure 4. Predicted water table (P=0 kPa) at scale with additional discretization around end of open pit excavation used for slope the pit both laterally and vertically. The stability analysis discretization of regional dewatering models very often is not sufficient to precisely The numerical simulation provides the pore pressure distribution in the slope, which easily can be used for the , as showed in Figure 5.

Figure 5. Pore pressure distribution at year 10 of pit excavation, K=10-8 m/s

Based on these models, the FoS of each pore pressure distribution was Figure 6. Relationship between FoS and determined in order to demonstrate the effect hydraulic conductivity, obtained by using a of the hydraulic conductivity on pit slope test model. stability. For this exercise, the simplified stability models considered the single rock The results of the test model indicate: mass medium to be continuous, isotropic, • Reduction of the hydraulic and lineally elastic, and assumed the lineal conductivity results in incremental Mohr & Coulomb failure criteria to be valid increase of pore pressure within pit and a good estimation of the rock mass slopes. Therefore a reduction of the strength. FoS is expected. Even though the described rock mass • Slopes less than 300m could be conditions are rarely found in the real world, considered stable for rock with any this condition will be assumed valid for the hydraulic conductivity values, median purpose of this exercise. pits (H is about 600m) requires Changes of hydraulic conductivity additional depressurization for K<10-7 have a strong effect on the FoS. Figure 6 m/s, however for deep slope (1,000m) shows the FoS for 300m, 600m, and 1,000m the FoS could be reduced to values pit slopes (excavated in 3, 6, and 10 yrs., below the limit of equilibrium (it respectively) as function of hydraulic should be noted that this statement is conductivity. The geometry and the rock valid for only the test model used). mass strength parameters were fixed for this • In low permeable rock (K from 10-8 example and a variable range of the m/s to 10-9 m/s) increasing of FoS by hydraulic conductivity values were used to additional pore pressure reduction simulate the pore pressure field for each could be not achievable due to case. required timing of depressurization This example does not intend to and change of slope angle might be discuss the acceptability of the FoS given required, and should be reviewed in different pore pressure conditions; the chart, more detail. rather, shows the impact of the water pore • Figure 6 shows that the stability of the pressure field, based on a large range of slope could depend upon the hydraulic hydraulic conductivity, on the slope conductivity at different heights. This performance. example shows, for a medium size slope (H>600m), that a wrong assignment of the hydraulic conductivity can over or under estimates the slope angle, resulting in extra capital cost, NPV of the project and/or safety issues, mining difficulties, negative impact on the mining plan and could jeopardize the Engineer needs to identify potential effects mine reserves and the business. of pore pressure on slope stability, allowing the Hydrogeologist to characterize geotechnically important hydrogeological 5 HYDROGEOLOGICAL AND units. Data collected in the field need to be GEOTECHNICAL INTEGRATION sufficient to develop reliable conceptual The success of an open pit mine design is hydrogeological and numerical groundwater based on quality, quantity and distribution of flow models to predict pore pressures in pit the geotechnical and hydrogeological data. slopes during excavation and dewatering. At Also, interpretation and modeling plays a late stages of project development, these “key” role in the final results. Today, mining models should be sufficient to predict companies have a clear understanding of the additional pit slope depressurization options importance of data requirements, and (if they are necessary) and to define the extensive budgets are assigned to this task required time for pore pressure reduction. during different stages of the project. These models, along with comprehensive Unfortunately, there can be disconnection sensitivity analysis of remaining between the geotechnical and uncertainties, should provide an input for hydrogeological disciplines, affecting the cost-benefit analysis of implementation of pit final results. For example, hydrogeologists slope depressurization. Numerical test very often focus on dewatering and not on modeling completed for this study indicates water pore-pressure modelling, placing more that for a medium- and high-permeable rock attention on high permeability units and not in a medium size slope (200 – 500 m height), considering, in detail, the low permeable there is significant impact of hydraulic units, which might present problems for conductivity on slope performance. This slope stability. Another example of this indicates that the accuracy of the disconnect is reflected in the geotechnical hydrogeological inputs, and the design constraints; sometimes the interpretation and the modelling of the geotechnical engineer’s design assumes hydrogeological conditions are essential certain hydrogeological conditions, which during the geotechnical investigation. are not achievable in reasonable time. For saturated or partially saturated The disconnect between disciplines slopes, rock engineering experience normally results in extra cost for drilling, establishes that a reduction of water pore opportunities lost for data collection, pressure will improve the results of the slope misunderstanding of the geotechnical performance parameters, creating the requirements, use of non-achievable opportunity to optimize slope designs. assumptions, missuses of the Unfortunately, in some cases the slope hydrogeological models, over or under depressurization requirements are not estimation of the slope designs or excessive properly assessed due to lack of costs for missed selection of appropriate hydrogeological understanding, slope depressurization systems. hydrogeological modelling objectives and, in To minimize the negative impacts, it is some cases, due to miscommunication important to recognize the need for the between the Hydrogeologist and rock integration of both disciplines during each mechanics Engineers. This disconnection stage of the project. between the hydrogeological and rock Figure 7 below shows an integrated mechanics teams results in a potential of over chart of geotechnical and hydrogeology or under estimation of slope designs. In processes for slope stability analysis order to avoid this, it is useful to consider the recommended by the authors. following questions: • What will pore pressures be in the ultimate pit slope and how will they 6 CONCLUSIONS change in time during planned mining/dewatering? Integration of geotechnical and • What would be the effect of pore hydrogeological studies during different pressure reduction on slope stability? stages of the mining project can provide • How much time is required to reduce required hydrogeological input for slope pore pressure? stability analysis and pit optimization. At early stages of the project the Geotechnical

Figure 7. Integration of geotechnical and hydrogeological studies during different stages of the project (PFS: Prefeasibility Study, FS: Feasibility Study)

• Is the time required for depressurization in alignment with the mine plan and life of the mine? • Is the knowledge regarding the hydraulic parameters sufficient for constructing a detail model to simulate the depressurization requirements? • Does the mine plan have the flexibility to develop a proper depressurization plan? • What depressurization method is the best for site specific hydrogeological conditions? • What is the cost-benefit of implementation of pit slope depressurization?

These questions must be addressed in detail before moving forward to more detailed engineering. Slope engineering is a common effort between different disciplines, and the understanding of each of the disciplines is critical in determining the final results. Also, the design process should be considered as an iterative process, where the integration between Geotech - Hydrogeology and Mine plan areas is a key in the mining cycle.

REFERENCES

Das, Braja (2011). Principles of Engineering. Stamford, CT: Cengage Learning. ISBN 9780495668107. Guidelines for evaluation of water in pit slope stability/edited by John Read and Geoff Beale, CSIRO, 2013. Read J and Stacey P (Eds) (2009) Guidelines for Open Pit Slope Design. CSIRO Publishing, Melbourne.

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