Data driven approaches to designing large open pit slopes - OnePetro

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Data driven approaches to designing large open pit slopes – lessons from engineering geology Kaunda, R.B. Mining Engineering Department, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401, USA

Wang, F. Mining Engineering Department, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401, USA Copyright 2016 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 50th US Rock Mechanics / Geomechanics Symposium held in Houston, Texas, USA, 26-29 June 2016. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: As mine open pits become increasingly aggressive and deep (beyond 400 m) due to exhaustion of near-surface resources or implausibility of underground excavation, significant challenges emerge using standard slope stability analysis techniques. Typically during overall failure analysis, factor of safety calculations are conducted. Although quite useful and despite recent advances in characterizing insitu stresses, the factor of safety approach has its inadequacies. For example, single factor of safety values cannot characterize an entire pit sector under varying geotechnical and environmental conditions. In this paper we draw on lessons learned from large dataset techniques in engineering geology to assess landslides. The proposed approach utilizes the emerging field of deep learning using artificial neural networks. Deep learning uses data-driven tools to continually update algorithms used to conduct computations resulting in high levels of accuracy and precision. Using our results and relevant examples from the literature, we discuss the benefits and shortcoming of the proposed approach, the appropriate conditions and types of environments for application and suggested modifications and improvements.

1. INTRODUCTION AND BACKGROUND Rock mass slope stability analysis is one of the most important undertakings during the design of surface mine open pit slopes. Typically select cross section profiles from a three dimensional geological model are created and assigned material and geotechnical properties for analytical calculations of factors of safety. In two dimensional limit equilibrium analysis using one of the methods of slices, the factor of safety is expressed as a ratio of the sum of the resistive forces to that of the destabilizing forces. A factor of safety less than 1.0 is indicative of unstable conditions, while a value greater than 1.0 represents stable conditions. For surface mine slopes, both interramp and overall slope stability analyses are undertaken under both static and pseudostatic conditions. The interramp angles are defined by bench face angles, bench heights and bench widths (Figure 1). The overall slope angle is defined by interramp sections separated by wide step-outs for haulage roads or mine infrastructure. In general, except for slopes of high failure consequence, a design factor of safety of 1.2 is adopted (Read and Stacey, 2009). Slopes of high failure consequence are those slopes that are critical to mine operations, such as hosting major haul roads, those providing ingress or egress points to the pit,

or those underlying essential infrastructure. Those slopes identified as having high failure consequences tend to have relatively higher factors of safety up to 1.5 (Read and Stacey, 2009). In addition, certain adverse geologic environments do not favor high interramp angles due to rock fall and bench overbreak, and hence design angles tend to be flattened to provide wide catch benches. The Mine Safety and Health Administration (MSHA), Title 30 of the Code of Federal Regulations, Section 56.3130 requirements for open pit slopes demand that adequate benches must be in place to retain rockfall above work or travel areas. A major short coming of using two dimensional cross sections is that both field and laboratory data usually show a high degree of variability in rock strength and geological structure. There is a possibility that the limited available data may not be representative of conditions encountered at pit limits.

Fig. 1. Main features of open pit slope

Another challenge is that most drilling is conducted for exploration purposes and targets the mineralization - not future open pit highwalls. In contrast, geotechnical drilling is specifically geared towards acquiring information needed for the geotechnical design and tends to be slower and more expensive as the process is sensitive to handling and transportation of the recovered rock core. As a result the amount of available geotechnical data on projects tend to be limited. Other issues include the absence of accurate assessments of anticipated degree of production blasting related damage to the rock mass along pit highwalls at the prefeasibility stage. The amount of rock mass disturbance due to blasting is typically included in slope stability analysis prior to slope design. In addition assumptions have to be made about ground water conditions near the rock mass (i.e. effective depressurization or not) for the slope stability analysis. In this paper we draw on lessons learned from datadriven techniques used in engineering geology to assess slope instabilities for very large landslides. The new approach utilizes the emerging field of deep learning using artificial neural network works. Unlike conventional computational techniques, deep learning uses data-driven tools to continually update the algorithms used to conduct the computations resulting in high levels of accuracy and precision. Using relevant examples from the literature and our own results, we discuss the benefits and shortcoming of the proposed approach, the appropriate conditions and types of environments for application and suggested modifications and improvements for future deployment.

2. LIMITATIONS OF USING ONLY FACTORS OF SAFETY IN SLOPE DESIGN Assessment of slope instabilities using factors of safety has been widely used to design slopes for a long time. Factors of safety can be calculated with more than one method of limit equilibrium analysis. Before a safety

factor for a slope is determined, several factors must be considered and analyzed. The higher the factor of safety, the more stable a slope is likely to be. However, usually the most economic safety factors are chosen to meet the basic safety requirements in an open pit mine, which implies that the margin of safety is relatively small. Typically more than one design safety factor is usually applied in different sections of a large open pit mine, to not only ensure stability and safety, but also to reduce costs of excavation, transportation and storage of waste rock. However, a small margin of factor of safety cannot always ensure safe slopes, as small uncertainties in geotechnical parameters may be sufficient to unpredictability trigger slope failures. There are many limitations in the application of safety factors to slope stability analysis and design. First, a design safety factor is not always in accordance with the actual safety factor on the project or construction, because many factors will decrease its effectiveness, including quality assurance of construction, engineering design, presence of undetected weak rock layers, and so on. The common cases are the removal of earth below the toe, loading on the crest, presence of water or drainage in the slope, and overcut of the slope benches (Pradeep, 2012). Second some limitations can be closely tied to the limitations of the widely used limit equilibrium methods. Researchers such as Krahn (2003) have highlighted the major shortcomings of limit equilibrium methods and their resulting slope factors of safety. These include missing physics in the form of material stress-strain relationships along localized failure surfaces, prone to abuse or misuse if limitations not understood (e.g. the method is based on statics and says nothing about displacements),incorrect results where stress concentrations exist within the sliding mass due to the shape of the failure surface or material-structure interaction, and in cases where complex geological processes and systems are at play resulting in unusual stress conditions. Third, the widely known and important influencing factors on rock slope stability include unit weight, cohesion, internal friction angle, slope height, slope angle and water condition. It is well known that any of these parameters can vary with both time and location. Mechanisms such as surface erosion, weathering, extension of tension cracks, water intrusions into the cracks, joints sets or faults, and modification of slope benches, can all influence effective safety factor values by changing the nature equilibrium between resisting forces and driving force in the failure planes. (Pradeep, 2012). Finally and most importantly, designing a slope with safety factors from slope stability analysis is a good

technique; however it is difficult to manage or monitor the slope stability with safety factors when the depth and scale of an open pit mine scale is very large (e.g. Figure 2). The increasing depths and scales make the slope stability monitoring much more complicated and challenging for additional geotechnical structures and higher stress conditions. In addition, features and properties such as joints sets, weak rock layers, vegetation, ground water tables, outcrop erosion and intense rainfall can also have important effects on the stability of slopes.

Fig.2. Example of large open pit slopes

However it is difficult to account for all the influencing factors at the same time. Further, the exact role of certain factors have not been thoroughly or clearly understood by engineers precluding their consideration in systematic slope stability calculations (Sakellariou and Ferentinou, 2005). Analyzing many safety factors from two dimensional slope stability analyses for a large open pit mine, section by section, sector by sector, may not be the most efficient use of time for the practicing slope engineer. On the other hand safety factor calculations using limit equilibrium methods have been in use for many years and developed a high level of faith and confidence with practitioners, marked by experience and observations of slope performance.

3. HAZARD ZONATION MAPPING IN ENGINEERING GEOLOGY Large-scale natural slopes, such as those undergoing gradual season movements or landslides can be characterized by complex stress and geological conditions. A practical approach commonly used by engineering geologists to assess potential slope instabilities is hazard zonation mapping. This technique has been successfully adopted by several researchers. For example, Neaupane and Achet (2004) developed a backpropagation neural network (BPNN) to predict landslide movement based on many documented landslide case history at Okharpauwa, Nepal. Eighty

percent of the land in Nepal is mountainous, leading to the frequent occurrence of several landslides in the past. The BPNN architecture consisted of six parameters in the input layer, two hidden layers and one output layer. The input variables were antecedent rainfall, rainfall intensity, infiltration coefficient, shear strength, groundwater and steepness, and the output parameter was the predicted movement (mm/day) of the slope during the monsoon season (June-August). The correlation coefficient between the predicted data with the observed data was 0.89, demonstrating the viability of the BPNN model as a tool in mapping landslide susceptibility accurately. Yesilnacar and Topal (2005) reported a landslide occurrence and damage to a segment (from 60 km to 83 km) of natural gas pipeline to the Eregli Steel Factory, which created a three-day fire in the Hendek region in Turkey. A landslide susceptibility map was created using both logistic regression analysis and neural networks because it was difficult to model landslide susceptibility and inducing inducing factors for such a large area. The input data for both approaches were fault density, elevation, slope angle, profile curvature, plan curvature, distance to roads, slope length, drainage density, land cover, distance to ridges, geology, road density, surface area ratio, distance to drainage, topographic wetness index, distance to fault, stream power, sub watershed basins, aspect. The output data for the landslide susceptibility level was classified as: 0–0.25 Very Low, 0.25–0.5 Low, 0.5–0.75 High and 0.75–1 Very High. By taking the 14 independent variables into consideration, the overall success of the landslide susceptibility prediction had an accuracy of 79.5%, while the neural network model had an accuracy of 82.12% on test data. In addition, the neural network approach predicted more zones with “high” and “very high” levels of landslide susceptibility. These results demonstrated the practicality of the method in producing realistic landslide susceptibility maps. Pradhan B. and Lee S. (2009) applied a data driven method to analyze landslide hazard risk on Penang Island, Malaysia, where heavy rains occasionally trigger landslides. Field data collecting tools, Geographic Information System (GIS) and artificial neural network (ANN) were used to collect, process, and analyze the factors indicating landslide susceptibility. These factors include slope angle, slope aspect ratio, slope curvature, distance from drainage, soil type, lithology types, distance from fault lineaments, land cover, NDVI (the normalized difference vegetation index), and precipitation. A total area of 285 km2 with a grid of 10×10m was mapped and interpreted to obtain the topography, lithology and land cover data. From this area, 463 landslides were identified and included in the database to evaluate landslide susceptibility, and 21

more active landslides were used to validate and test the data driven approach. This approach classified the landslide risk area into four groups by percentage: No risk area-60%; Moderate risk area-20%; High risk area10% and Very High risk area-10%. The validation and test results from the 21 cases validated the accuracy of this method, making landslide hazard and risk analysis for the entire area compelling and practical. Kaunda et al. (2009) applied back propagation artificial neural networks to study slope movements along seasonal active landslides near Lake Michigan. The inputs used were soil type, temperature, groundwater elevations and records of previous displacements. Established model features were six hidden neurons, a learning rate of 0.01 with 50 iterations. A sigmoid output function was used on a training set with 33 records and 15 test data. The neural network model outperformed multiple regression analysis to locate failure surfaces and predict slope movements in specific locations of the shoreline bluffs. Yilmaz I. (2009) compared the accuracy of frequency ratio (FR), logistic regression and artificial neural networks in assessing landslide susceptibility in Kat County, Turkey. The site is located on a mountain side, influenced by the North Anatolian Fault Zone, and is frequently subjected to landslide hazard and risk. The frequency ratio model was based on the assumption that landslides with similar conditions to previous landslides would occur in future. Landslide inducing factors were weighted in all the three methods, and these factors include elevation, slope angle, slope aspect, stream power index (SPI), topographic wetness index (TWI), faults, drainage, and geology. The area under the curve (AUC) was regarded as a good indicator to evaluate the prediction performance, and the area values of 0.826, 0.842 and 0.852 for frequency ratio (FR), logistic regression and artificial neural networks respectively showed that artificial neural network had a slightly better performance and accuracy in the landslide susceptibility map. These examples show that large areas susceptible to landslides or active slope movements can be reasonably characterized using engineering geology techniques from field observations and measurements. The next section discusses how select cases where similar techniques have been applied in mid-to-large open pit surface mines using data driven approaches.

4. DATADRIVEN MODELING APPLICATIONS IN OPEN PIT MINE CASE STUDIES A convenient approach to applying data-driven modeling in rock engineering is through machine learning or artificial neural networks ANNs. Sakellariou and Ferentinou (2005) applied an ANN method to

investigate slope stability. Since slope stability can be related to several geotechnical parameters, these parameters were utilized to develop and build four ANN models. Two ANN models were built to predict stability based on a circular failure mechanism, while two additional models were developed to predict wedge type failure behavior. The parameters selected for circular failure included unit weight, cohesion, angle of internal friction, slope angle, slope height, and pore water pressure. The parameters used for wedge failures were unit weight, cohesions and friction angles for two different joint sets A and B joint sets, their angle intersection, slope angle and slope height. The investigation included 46 slope cases for circular failure mechanism, among which half involved dry rock or soil slopes with 13 failed cases. The other half consisted of wet slopes with 16 failed cases. For the wedge failure analysis, 14 rock slope case studies were used and all cases were under dry conditions with eight failed cases (Sah et al., 1994). The results showed important relationships between the input and output data, and that the safety factors from ANNs had high consistency with the results from standard analytical methods. Monjezi and Dehghani (2008) applied ANNs to evaluate the instability of local benches through back break analysis. The ANN model consisted of 15 neurons in the first hidden layer and 25 neurons in the second hidden layer utilized burden (m), charge per delay,(kg/ms), last row charge per total charge ratio, powder factor (kg/ton), spacing to burden ratio, stemming to burden ratio, and number of rows to predict backbreak (m). The mean average error and mean relative error for the ANN performance were 0.14 m and 1.3% respectively. In addition to predicting bench failures, the ANN model was useful as a practical tool in readjusting the blast design patterns such that back break was reduced from 20 to 4m. Naghadehi et al (2013) used an extensive database of global open pit slope stability case histories and ANN modeling to develop a new predictive mine slope instability index. The new slope index was used to define slope instability hazard levels and compared with actual, observed slope behavior of 12 independent case histories. The 18 input parameters included rock type, intact rock strength, Rock Quality designation (RQD), weathering, tectonic regime, groundwater, number of joint sets, persistence, spacing, orientation, aperture, roughness, filling, overall slope angle, overall slope height, blasting method, precipitation and previous instability. The coefficients and weights from the 18 x 36 x 36 x 18 neural network architecture were used to derive the slope instability index using a Rock Engineering System (RES) approach and interaction matrix. The test results using the new index showed promise for future large scale applications.

It can be seen therefore that lessons can be drawn from engineering geology in large landslide cases and applied to large open pit slopes using data driven modeling methods. Caution should be exercised however in understanding differences and limitations stemming from the fact that open pit slopes are anthropogenic structures in contrast to active/passive landslides from natural slopes.

the scheme discussed by Einstein (1988, 1996), and Karam et al. (2015) for slope and tunneling problems (Figure 3).

5. HOW TO DEVELOP SPECIFIC ANN TOOL The goal of building an ANN model is to find several connection weights, Wij, such that the ANN learns to accurately map Input/Output data pairs with minimal error. Once the optimum weights have been determined, the developed ANN model is tested on an independent dataset. This ANN model development method is termed supervised learning. During ANN model development, each artificial neuron computes a weighted sum of the inputs from the preceding layers as shown in Equation (1): ∑



(1)

where = the output, f (x) = nonlinear transfer function such as the sigmoid function, = input, and = a constant called the bias. The ANN training occurs by minimizing an error function defined as:

∑ ∑

where p = pattern number,

(2) = target output value,

= neural network output value The error function is minimized iteratively using partial derivatives applied with respect to the weights and biases. In this study, the back propagation algorithm was implemented using MATLAB (Mathworks, 2014). The specific input parameters used and parameters are described in detail in Section 6.

6. LESSONS FROM ENGINEERING GEOLOGY AND EXAMPLE APPLICATION The slope failure risk assessment approach advocated in this paper draws lessons from both engineering geology zonation mapping and data driven modeling techniques. Each of these methods have their shortcomings and restrictions, but when properly understood appropriate modifications can be made. The predictive powers and limitations of data-driven modeling can be illustrated by

Fig. 3. Decision Analysis Cycle (after Einstein, 1988)

In this performance analysis based framework, the first step is identification and collection of information pertinent to slope stability. The importance of this step in data-driven modeling cannot be overemphasized, nor can the need for a highly reliable methodology (via technology or expert) for the data acquisition. The next step which is the deterministic identification of potential instabilities, requires a level of expertize or training. Next the uncertainties in the available information are addressed using probabilistic analysis and risk assessment through the quantification of likelihood of failure. Finally decisions (or predicted “performances”) are made based on a set of alternatives. The most important phase in the entire decision making cycle is the updating of each step as new data or information is acquired leading to modifications and improved decisions/predictive capabilities. A similar framework can be adopted to combine the basic concepts from engineering geology and data driven modeling. For example the data acquired during the exploration phase of mining projects or during expansion of existing surface mines could be used in an ANN model to predict “performance” of slopes under various conditions or designs. The collected data including geologic maps, geophysics surveys, photographs, diamond core drilling logs, topographical data, weather data and visual observations (Figure 4) can potentially be useful to provide information about anticipated slope performance.

Fig. 4. Visual inspections of exposed outcrops can provide useful information about anticipated performance of future slopes

A simplified schematic is shown in Figure 5 to illustrate how site specific information collected during a prefeasibility program can be used in conjunction with historical records to build the framework.

local rock mass conditions. The rock core collected from various locations and depths at the site could be classified using one of the standard rock mass classification systems from the geotechnical logs. Using published previous slope failure cases (Figure 6), a site specific hazard zonation map showing high risk areas (Figure 7) was created with a back propagation ANN model. The ANN inputs were the ratings for intact rock strength, joint conditions, joint spacing and rock quality designation under dry conditions. The predicted output was the optimum slope angle likely to result in stability under the specific logged rock mass conditions. To build the ANN model a Levenberg-Marquardt (damped least squares) training algorithm was implemented with an architecture of 4 input neurons, 10 hidden neurons and 1 output neuron (Figure 8). Performance metrics for the ANN during training and testing indicate relatively low errors and an excellent fit to observed data (Figures 9 – 10).

Fig. 5. Schematic showing one example of proposed framework

The idea is illustrated by using an example from a real mine in North America, “Mine X”, where an extensive geotechnical drilling program was conducted. Field engineers carefully logged and collected the standard geotechnical information required to characterize the

Fig. 6. Failure case histories for slopes (after Orr, 1992).

Fig. 7. Site specific hazard zonation map predicted by the ANN model showing recommended slope design angles.

Fig. 8. Backpropagation ANN model architecture showing four inputs and one output used in this study.

Fig. 9. Error values for the ANN model during training, validation and testing.

Fig. 10. ANN model performance on test data.

7. CONCLUSIONS Slope stability analysis is the most important and fundamental techniques in designing the open pit slopes. One approach heavily relies on factors of safety, especially limit equilibrium methods. As discussed in this paper, under certain conditions these techniques are subject to a number of challenges when applied to the design of open pit mines, especially at a large scale. The

challenges include small margins of safety factors under complex geology and geotechnical conditions, large scales and depths, and over long periods of time. The approach advocated for in this study emphasizes more advanced data driven approaches to complement two dimensional, factors of safety approach or other alternatives such as numerical modeling. The framework borrows from the field of engineering geology where typically large scale active landslides are carefully characterized to construct hazard zonation maps. The major advantage of the proposed slope design method is that the framework is not static, but subject to continual updates as more site specific data and information is acquired thereby increasing confidence in the model results. Using previous case studies from the literature and a new example from a specific mine site computed in this study, the preliminary results seem encouraging.

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