Contreras Paper

�Slope Stability Santiago Chile, November 2009

Value and Risk in Slope Design

This paper presents a review of the concepts behind the data confidence categorization for slope design suggested by Steffen (1997). The codes used to qualify the data used in mineral resource estimation as measured, indicated and inferred according to a decreasing order of confidence, should be equally applied to slope engineering. Data for slope design includes geology, structures, rock mass properties, the groundwater regime and in situ stress conditions. Normally the level of uncertainty of these sets of information is progressively reduced along with the project development, as more information is gathered and analyzed during the successive project stages. Once the confidence of the data is assessed, the corresponding classification of the slope design can be made as proven, probable and possible. The concept of confidence categorization is particularly suitable when probabilistic methods of design are used, as engineering judgment is frequently applied in this methodology for the definition of variances in data. The normal process of data gathering can be optimized by assessing the relative influence of data sets on consequences of slope instability. This provides a rational approach to the site investigation planning. The concept of data confidence categorization is illustrated in the paper.

Abstract

P J Terbrugge, L-F Contreras,

O K H Steffen

SRK CONSULTING, SOUTH AFRICA

INTRODUCTION

Slope design for large open pit mines presents unique challenges to the engineer that is captivated in the oft quoted maxim that “the objective is to have the slope fail the day after the last truckload of ore leaves the pit rim”. This infers that the maximum benefit has been extracted from the mineral resource. The engineer however, has to provide a design that is functional and economic at an acceptable risk. The great attraction of the geotechnical discipline is that it relies on different engineering, geological and hydro-geological disciplines to achieve the above objectives.

Uncertainty and variability of properties within a rock mass provides the first challenge: How much data do we need to adequately describe the rock mass properties? Codes for data adequacy have been established for the minerals industry to define geological certainty. It is proposed in this paper that the same logic can be applied to geotechnical data that is also derived from the geological environment.

The paper presents a guideline to geotechnical data requirements and a process that can distinguish for different study levels. Using logic diagrams, the relative importance of different parameters can be identified early in the study programme and effort and cost can be focused on the more critical parameters, instead of the common “populate the data base” procedures.

GeOTeChNICal DaTa GUIDelINes

General Data Requirements Bieniawski (1991, 1992) dealt with the issues of engineering design in the rock mechanics field, and defined a series of design principles

that encompass a design methodology, the second design principle which includes the “minimum uncertainty of geological conditions”.

The rock masses in which mining takes place are extremely variable, with the rock engineering and the mine design therefore taking place in an environment of considerable uncertainty. In mining, which is almost always tightly cost controlled, there is usually an aversion to spending money on geotechnical investigations, with the result that geological/geotechnical conditions are often unknown, or at best, little known. In many mines, designs are carried out with inadequate knowledge of the in situ stresses, the rock material, defect strengths and deformational properties, and the rock mass behavioural conditions together with knowledge on the groundwater regime. The minimization of uncertainty will provide an environment in which more confidant designs can be carried out with the resulting reduction in risk. The remaining uncertainties must be taken into account in the design method.

In assessing the data requirements for a pit slope design, it is an imperative of the data gathering programme that sufficient data is collected to minimize uncertainty. Wong (2005) suggests that “Reliability cannot be predicted without statistical data; when no data is available, the odds are unknown”. To this end, it is recommended that prior to embarking on a pit slope design, a predictive model of the likely pit is generated together with the best estimate of geology, including macro and minor structures, intact rock strengths, rock mass strengths as well as defect strengths. Best estimates of the regional groundwater regime should also be input to the model.

With this model to hand, a series of pit slope sensitivity analyses should be carried out on the critical slopes in the pit in order to evaluate the impact of the range of parameters on pit stability. These analyses would allow for the identification of the critical parameters

� Santiago Chile, November 2009 Slope Stability

having the major impact on stability, with a site investigation programme being drawn up accordingly. The process will then alleviate the requirement for precise data sets where they may not be needed with the concomitant saving of time and costs in the process. The analyses can be carried out using Fault Tree methodology, where the impact of the various input parameters can be measured in terms of probability of failure.

The possibility to influence a project is normally largest in its early phases, with an important feature for large open pits, the early site investigation, performed as a means to identify and quantify hazards. Early information allows for sufficient time to deal with identified hazards from a technical point of view, with the trade off on when information is sufficient, a decision problem, Back and Christiansson (2009). The benefit of more investigations depends on how much is known at the time of decision with the higher the level of knowledge, the less impact additional information will have on the decisions affecting slope designs. The value of additional information depends on how effective the investigation is, with no investigation of geotechnical conditions being perfect, and hence there will always be remaining uncertainties, meaning that decisions must be made under uncertainty. If additional investigations of certain properties only slightly decrease the uncertainty, they may not be worthwhile pursuing even if the uncertainty as such, is judged to be quite large.

Data ClassificationHaving defined the relevant levels of data required for analysis, the following general guidelines for possible, probable and proven slope

angles in an open pit design are given;

Possible slope angle Corresponds to application of typical slope angles based on experience in similar rock types. Quantification will be on the basis of

rock mass classification and a reasonable inference of the geological and groundwater conditions within the affected rock mass.

Probable slope angle Corresponds to a design based on information which allows a reasonable assumption to be made on the continuity of stratigraphic

and lithologic units. Some structural mapping will have been carried out using estimates of joint frequencies, lengths and conditions. All major features and joint sets should have been identified. A small sample of testing for the physical properties of the in situ rock and defect surfaces will have been carried out. Similarly, groundwater data will be based on water intersections in exploration holes with very few piezometer installations. Data levels will be such as to allow simplified design models to be developed to allow sensitivity analyses to be carried out.

Proven slope angle Requires that the continuity of the stratigraphic and lithological unit within the affected rock mass is confirmed in space from adequate

intersections. Detailed structural mapping of the rock fabric is implied, which can be extrapolated with high confidence for the affected rock mass, and that strength characteristics of the structural features and the in situ rock determined by the appropriate testing procedures should allow reliable statistical interpretations to be made. Groundwater pressure distributions within the rock mass should have been measured using piezometer installations to allow high confidence in the groundwater model. Data reliability should be at a confidence level of 85% for the design to be effective.

For each of the slope classes the reliability of the design is quantified by the probability of failure, determined by calculation using the available geotechnical information at the level appropriate to the particular level of study.

With rock slopes occurring in natural materials, by definition, there will be a multitude of variables. There will be different lithologies, degrees of alteration and weathering, and structures, and within each rock type there will be variation in the strength and deformation properties. With this in mind it can be seen that very little will be known about the rock mass in which the slope exists or is to be excavated, and that there will be no single value for a parameter, but rather a variation in each parameter which may be described by a statistical distribution. This variability and uncertainty can then be taken into account in slope analysis and design by using a probabilistic approach.

GeOTeChNICal DesIGN CRITeRIa

Slope design improvement through project stagesDifferent phases of feasibility studies require different levels of confidence, usually expressed in terms of accuracy of estimates. For

example: Profile engineering ± 35%, pre-feasibility study ± 25%, feasibility study +15/-10 %. What is really meant by these estimation accuracies is the accuracy of capital and operating costs at each stage. It should really mean the variance accepted on the NPV calculated for the project, which means the estimation of price comes into reckoning. However, because of the over-riding influence of price on the NPV and the price volatility, it has become accepted that the level of study accuracy required is only applicable to the cost i.e. capital and operating costs, which are the only elements that are in the control of the study engineers.

In mines, the primary risks are associated with the resource estimation, geotechnical confidence and process recoveries. It is not surprising that all these main contributors to risk result from confidence in the geological information. Of course there are many other contributors to risk that should not be ignored, among which infrastructure and environmental constraints are paramount. In the case of resources, the classification according to different codes has become the measure of confidence and risk and a similar route has been followed for geotechnical confidence.

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In the case of different levels of study in open pit mining, a single number for the slope angle is utilized in determining the reserves within the final pit, even though at the extremity of pit depths it is likely that only inferred resources are available. Certainly this is the case for the conceptual study, but in most cases also for the feasibility or ‘detailed engineering’ studies. How best to handle the estimation of slope angles through these different study phases is the main objective of the proposed data confidence characterization with an obligation to conform to the accuracy requirements of the study objectives.

Conceptual study level From the limited knowledge that exists at the conceptual phase, a best estimate of the maximum angle possible is made. Then for the

particular mine and orebody, the variation in slope angle that produces an outcome of ± 35% of the cost of production is determined. Hence for the conceptual phase it is necessary to be confident that sufficient information exists to be accurate within the range of slope angles so determined. The variability of the slope angle is then introduced into the economic model for the pit design, using either a uniform distribution over the range of slope angles (or a beta distribution tending towards a uniform with only slightly less likelihood at the extreme values) and the risk to achievement of the mine plan due to slope designs then evaluated.

Pre Feasibility study level As the project progresses into the more detailed studies, requiring higher degrees of confidence, so the sensitivities will determine a

narrower range of acceptable slope angles leading to the specification of additional data required to achieve this objective. Here the classification of slopes provides the basis for additional geotechnical data specification. Once again the impact of the slope design uncertainty is determined using the mine risk model. At pre-feasibility level, the most important outcome has to be the opportunities and risk associated with alternative mine plans. Hence, at this stage, the first high level pass of the rigorous risk model is used in determining best option ramp layouts, push back sequences, etc.

Feasibility study level At final bankable feasibility, slope design classification should correspond to resource classification and again meet the criterion of

accuracy of +15/-10% cost impact. It should be noted that this refers to the Net Present Cost, so a higher variability in the latter years is acceptable within the accuracy requirements. At this stage the full detailed risk approach to the design of slope angles needs to be applied per domain and per slope performance requirement. The final design stage is carried out during the mine life when sufficient data becomes available to ensure that only proven slopes are mined at any stage. The process is presented diagrammatically in Figure 1.

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Figure 1 - Slope design improvement with additional data (case 1, allowance for uncertainty larger than actual geotechnical variability)


There is a question on whether the different slope classifications could be applied to the different study classes respectively, with the assumption that the slope angle would increase with each phase of study. While it is true that at every stage it is the geotechnical objective that the maximum slope angle be targeted for the study and also that the information is gradually improved with more detailed studies, it is not always the case that a steeper slope angle is determined as the project progresses. This is because more information reduces the so called ‘epistemic’ uncertainty which is related to the lack of knowledge on project conditions, revealing in more detail the actual ‘random’ uncertainty which is associated with the natural variability of geotechnical factors. If a conservative selection of the slope angle is made at the beginning of the project, the allowance for uncertainty might result in a larger than actual variability of geotechnical factors determined at later stages from the investigations, and a steeper angle is obtained as illustrated in Figure 1. Conversely, if an optimistic selection of the slope angle is made at an early stage, the allowance for uncertainty is likely to be insufficient to cover the true variability of geotechnical factors defined with the project investigations, and a flatter angle will be obtained at later stages as illustrated in Figure 2.

Figure 2 - Slope design improvement with additional data (case 2, allowance for uncertainty smaller than actual geotechnical variability)

It is clear that the reduction of the geotechnical uncertainty should be one of the main objectives of the planned investigations as the project progresses, as the achievement of this target leads to an increased confidence in the slope angle defined. The ranking of geotechnical factors according to their relative effect on the likelihood of slope failures and the severity of their consequences is, therefore, essential to achieve a rational planning of the investigations required throughout the various project stages. This approach results in a cost effective reduction of the geotechnical uncertainty.

Ranking of geotechnical factorsThe ranking of geotechnical factors can be achieved within the risk approach for pit slope design and different elements of the model

can be used for this purpose. They include logic diagrams used to represent the slope design process, event trees to evaluate the consequence of failures and tornado diagrams used after a Monte Carlo simulation to rank risk factors according to their relative influence on target variables of analysis.

Logic diagrams for analysis of probability of failureIn the analysis of variability of risk sources, it is common to use logic diagrams to represent the slope design process. These diagrams

define logic relationships between source variables leading to a top variable whose variability needs to be assessed. One type of these diagrams is known as a source response diagram (SRD) and it is very useful when other sources of uncertainty not accounted for in the


design of the slopes need to be incorporated into the analysis. Typically the probabilistic methods of design of the slopes only consider the variability of strength parameters for the calculation of the “model probability of failure”, as opposed to the “total probability of failure” where all possible sources of uncertainty are incorporated as required for the analysis of consequences of failure. Figure 3 shows a typical SRD, corresponding to the case of deviation in the water conditions of a pit slope.

In these diagrams the effect of the deviations from normal conditions on the model probability of failure of the slope are evaluated with a slope stability model, for example, one based on a limit equilibrium approach. The methodology enables the consideration of both, favourable and unfavourable variations of the aspect under analysis, as well as the possible responses to these variations during operation. Therefore, both threats to and opportunities for the stability condition of the slope can be incorporated into the analysis. With this methodology the ranking of geotechnical factors is based on their relative contributions to the total probability of failure of the slope.

The SRD methodology is appropriate for those situations where there is not abundant hard data on those aspects having an influence on the stability of the slopes, although some knowledge exists on the effect of these aspects based on broad experience or on observed performance of the operation or on any other source of non formal information. It is clear that in these situations the uncertainty is large, but at least it can be incorporated into the analysis.

Figure 3 - Example of a SRD for deviation of water conditions of a pit slope

Event trees for consequence analysisEvent trees are normally used for the analysis of consequences of slope failure. The event tree is a diagram that connects the starting

event (failure of the slope) with the ultimate consequence under evaluation (fatality, equipment loss, Force Majeure, etc) through a series of intermediate events based on a cause-effect relation. The events are quantified in terms of their likelihood of occurrence, thus enabling the assessment of the end outcomes in terms of their probabilities of occurrence, following the appropriate rules to operate the AND/OR gates. Figure 4 shows an example of the event tree developed for the evaluation of an economic impact of failure of pit slopes.

During the early stages of a project it is useful to assess the sensitivity of the achievement of the mine plan to the consequences of slope failure, as they are ultimately the events that determine the acceptability criteria for design. For example, it might be the case in a particular mine that eventual slope failures might be acceptable in a particular slope because they can be safely anticipated with a monitoring system, or because they would have little impact on the normal operation of the mine. This result would move down in the ranking of factors the elements associated with this particular slope, in favour of other items in another area of the pit that might require more attention during the project development.


Figure 4 - Example of event tree for the analysis of an economic impact of slope failure

Tornado graphs from Monte Carlo AnalysisIn a slope design process it is customary to calculate the probability of occurrence of events like failure of the slopes or impacts of those

failures using a Monte Carlo analysis. In this technique many simulations (“realizations”) are made using randomly chosen values from parent distributions of the different uncertain variables (“assumptions”) represented in the analysis, with the results grouped to construct a probability distribution of the target variable of interest (“forecast”). Typically several thousand realizations are required to determine the probability of performance of the variable modelled.

The Monte Carlo simulation can be used for the analysis of logic diagrams, event trees or performance models, but whatever the application, the results will be presented in the form of a probability distribution of the target variable under analysis and a tornado graph depicting the relative influence of the various uncertainties on the variance of this target variable. Figure 5 shows an example of these products for the case of an analysis of probability of failure of a slope. In this example, it is clear that the main contributing factor to the stability of the slope is related to the water conditions and this would be the primary target for the next investigation programme for that slope.

Figure 5 - Example of tornado graph from a Monte Carlo analysis for calculation of probability of slope failure


Optimization of exploration programmeOnce the more relevant geotechnical factors for the achievement of the mine plan have been identified and ranked, they will be the

base for the design of the most appropriate exploration programme specific for the project and for the stage of study. Obviously, the programme should target those factors causing the largest uncertainty in the slope angle, so that when the next phase of study is reached, those factors are proven to be adequate for the required performance of the slope, or are declared to be problematic to support a design to the required level. In the latter case, the investigations can be re-routed on time to look for alternatives while the project is still flexible enough to permit this type of adjustment.

CONClUsIONs

The approach to geotechnical data collection suggested in the paper provides a rigorous process that allows exploration programmes to be rationalized and cost-justified. Whilst experienced judgment, embraced in the definition of the ‘competent person’, remains the anchor to success, the process suggested enhances such judgment decisions. Areas to be considered when embarking on the various study levels to meet the relevant risk criteria to the project are:

Sufficiency of data for classification purposes;Insufficient statistical data to define the boundaries of the classifications;Risk process (sensitivity analyses)is the method to identify shortcomings in data;Must be cost effective in terms of defining Geotechnical exposure programme;Requirement for competent person to review effective programme; and Confidence levels taken through to LoM plans.

Benchmarking data and processes against practical experience of slope performance is of paramount importance for defining the different levels of confidence, viz. measured, indicated and inferred. The authors have embarked upon a systematic recording of information quality at different sites onto data templates to improve the estimates of data required for different classes of geological complexity.

These issues lie at the core of the engineer’s dilemma of a design that is ‘functional and economic at an acceptable risk’. For this reason, risk must be quantified as practiced in other engineering disciplines.

RefeReNCes

1. Bieniawski, Z.T. 1991. In search of a design methodology for rock mechanics, In Rock Mechanics as a Multidisciplinary Science, Proc. 32nd U S Symp. On Rock Mech., Ed Roegiers, Balkema.

2. Bieniawski, Z.T. 1992. Invited Paper: Principles of engineering design for rock mechanics, Rock Mechanics, Proc. 33rd U S Symp. On Rock Mech., Ed Tillerson & Wawersik, Balkema.

3. Steffen, O.K.H. 1997. Planning of open pit mines on a risk basis. Journal of SAIMM, March / April 1997.

4. Christian, J.T. 2003. Geotechnical Engineering Reliability: How Well Do We Know What we Are Doing?, The Thirty-Ninth Karl Terzaghi Lecture, Presented at the ASCE 2003 Annual Convention. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, October 2004.

5. Wong, W. 2005. How did that happen? – Engineering Safety and Reliability, Professional Engineering Publishing Limited, London and Bury St Edmonds, UK.

6. Contreras, L.F., R. LeSueur and J. Maran. 2006. A Case Study of Risk Evaluation at Cerejon Mine. In Proceedings of the International Symposium on Stability of Rock Slopes in Open Pit Mining and Civil Engineering Situations, 3-6 April 2006, Cape Town, South Africa. SAIMM. Symposium Series S44, Johannesburg, South Africa.

7. Tapia, A., L.F. Contreras, O. Steffen. 2007. Risk Evaluation of Slope Failure at the Chuquicamata Mine. In Slope Stability 2007, Proceedings of the 2007 International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering, 12-14 September 2007, Perth, Australia. Ed. Yves Potvin, Australian Centre for Geomechanics, Perth, Australia.

8. Steffen, O., L.F. Contreras, P.J. Terbrugge, J. Venter. 2008. A Risk Evaluation Approach for Pit Slope Design, 42nd US Rock Mechanics Symposium, 2ns US-Canada Rock Mechanics Symposium, ARMA, San Francisco, USA, June 30 – July 2 2008.

9. P-E Back, R Christiansson, 2009. Value of information analysis for site investigation programmemes accounting for variability, uncertainty and scale effects with the Äspö HRL prototype repository as an example. International Journal of Rock Mechanics & Mining Sciences.

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Contreras Paper