THE USE OF CUSUMS AS A TOOL TO AID IN THE INTERPRETATION OF SLOPE MONITORING DATA WITH SPECIFIC EXAMPLES FROM AN OPERATING OPEN PIT MINE

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1 THE USE OF CUSUMS AS A TOOL TO AID IN THE INTERPRETATION OF SLOPE MONITORING DATA WITH SPECIFIC EXAMPLES FROM AN OPERATING OPEN PIT MINE W.Sarunic 1 and P.A.Lilly 2 1 Snowden Mining Industry Consultants, Western Australia 2 WA School of Mines, Curtin University of Technology, Western Australia ABSTRACT In most cases, slope movement monitoring data are collected on a temporal basis and displacement or velocity is plotted against time in order to assist the engineer to make judgements about slope behaviour. Once an unusual behaviour pattern has been established, the data are then analysed to estimate when the key inflection points occur in the data, when the slope movements start to accelerate and, ultimately, when the slope is expected to collapse. The identification of these inflection points is sometimes difficult to achieve with the naked eye. This paper presents the application of a trend analysis technique, known as cusums, to assist in this process. The authors have presented a range of data from various real life examples which highlight the effectiveness of the cusums technique. A key aspect of the cusums technique is the use of a constant (K) against which data trends are assessed. This constant is best derived from slope performance data at each site, as each rock mass will behave in its own unique way. The authors have experienced slopes that have had threshold values ranging from.1mm/day through to 1mm/day, and therefore a conservative approach should be adopted when assessing the performance of slopes. 1. INTRODUCTION The monitoring of open pit mine slopes is an important part of the slope engineering process. It forms that stage of the engineering loop that collects data on slope performance that, in turn, establish whether slope behaviour is similar to or different from that originally planned and designed. There is a range of techniques available to monitor the performance of slopes, some of which are listed below: Survey prisms Visual monitoring (berm walking) Crack extensometers Borehole shear strips Borehole extensometers Borehole inclinometers Radar scanning Laser scanning Microseismic monitoring Page 231

2 In most cases, data are collected on a temporal basis, and displacement or velocity is plotted against time in order to assist the engineer to make judgements about slope behaviour. Once an unusual behaviour pattern has been established, the data are then analysed to estimate when and why the key inflection points occur in the data, when and why the slope movements start to accelerate and, ultimately, when the slope is expected to collapse. This process, and the engineering judgements associated with it, can be relatively complex for the following reasons (Sullivan, 1993): In a large slope, it is necessary to have a large number of monitoring stations/points. There are significant practical constraints in relation to locating monitoring points in the right places at the right times to capture the movement history. In large slopes, the geological regime is often complex and/or the failure mechanism is multifaceted, which leads to non-uniform and sometimes erratic movements and movement rates. Once substantial movement has commenced, access to the monitoring sites may be dangerous. Added to this is the error that is inherent in many of the techniques used for monitoring slopes, particularly prisms (which are also the most commonly used blanket pattern slope monitoring technique used in mining). Consequently, it is often difficult to identify the times at which displacement or velocity changes from the data collected. However, if trend analysis is used, it can make the selection of inflection points (times) more meaningful and less subjective. 2. THE CUSUMS TECHNIQUE Whilst Cusums has been used for other purposes for many years, it is the authors understanding that it was used for the first time in mining geomechanics applications by Piteau (197) to assist in the demarcation of geotechnical/structural domains within rock masses. In this case, the purpose was to delineate spatial, rather than temporal, trends in data. Cusums involves plotting the cumulative sum of the differences between a constant value and each data point in the sequence of a particular variable. That is: Let x 1, x 2, x 3,.. x n be the series of values measured in sequence. Select a constant, K. The mean of the data set for which the analysis is being undertaken is often chosen as the value of K so that trends can be tracked relative to the mean (rather than some arbitrary) value. Subtract K from each value in the sequence and then add the differences in a series of partial sums; that is: S 1 = x 1 K; S 2 = (x 1 - K) + (x 2 - K) = S 1 + (x 2 - K); and S n = S n-1 + (x n - K) = x 1 + x 2 + x x n nk. Page 232

3 The S values represent a cumulative sum series (or cusum) and S is plotted versus position in the sequence. Table 1 and Figure 2 show a simple example (in which the trends are obvious to the naked eye) to clarify the points outlined above. Table 1: Cusums example where K = 1 Value of variable (x n ) Difference (x n K) Position in Sequence (n) Figure 2 Cusum plot for data in Table 1 Cusum (S n ) Cusum Position in sequence If there is no trend in the values, then the negative values of S will more or less cancel out the positive values and the cusum will be more or less constant (that is, the plot will be more or less horizontal). However, if the local mean value is greater than K, more of the differences will be positive and the cusum curve will slope upwards. This can be seen in the first three values in Table 1 and Figure 2, where the cusum trend is upwards because all three values are greater than K=1. The reverse will occur where the local mean is less than K, which can be seen in the final two values in Table 1 and Figure 2. The steeper the cusum line, the greater the difference between the local mean and K. In the case of slope monitoring, the mean value of displacement or velocity may not have any practical significance, particularly as these mean values change with time. It may be more useful, therefore, to select a value of K that has some physical meaning to the engineer. For example, Zavodni (2) suggests that velocities in large slopes in Page 233

4 poor quality rock masses of the order of 4mm/day are indicative of initial response or on-going failure without acceleration to collapse. Thus K in such an application might be selected as 4, and local means and trends measured relative to this value. 3. APPLICATION TO SLOPE MONITORING DATA The first case example relates to slope displacement based on prism monitoring with three prisms presented. Figure 3 and 4 present the incremental displacement and velocity respectively. Attempting to interpret slope movement from this data is difficult primarily due to the scatter. As such any early stages of slope acceleration (potential failure) may not be detected Figure 3 Incremental Displacement Incremental Displacement (mm) P1 Disp P2 Disp P3 Disp Figure 4 Velocity Velocity (mm/day) P1 Vel P2 Vel P3 Vel Page 234

5 As noted above, a key consideration for the assessment of displacement monitoring data is the definition of the K constant. This with respect to prism data should relate to the threshold value for displacement (or velocity) at which a change of state occurs (for example, moving to a progressive mode). Using the example presented by Zavodni (2), where 4mm/day represents a critical change in state for a slope, some interpretations of the performance of the slope with respect to this threshold value can be made. Figure 5 presents the cusums velocity for the same data presented in Figures 3 and 4 and based on a 4mm/day threshold. Figure 5 CUSUM 4mm/day CUSUM Velocity (mm/day) P1 P2 P3 Based on Figure 5 some key interpretations of the performance of the slope can be made, these include: Prism 1 to 6 initially shows steady state velocities at 4mm/day (i.e. line approximately horizontal) 6 to 65 - a brief phase of velocities at greater than 4mm/day indicated by a positive slope 65 to 9 steady state velocities at 4mm/day 65 to 18 velocities less than 4mm/day (indicated by a negative slope) 18 to 21 slight increase in velocity above 4mm/day indicated by the approximately horizontal line Prism 2 Day 53 Monitoring commences 6 to 8 Movement at velocities greater then 4mm/day 8 to 18 velocity at approximately 4mm/day 18 to 21 velocity greater than 4mm/day Prism 3 Day 94 Monitoring commences Page 235

6 94 to 18 velocity less then 4mm/day 18 to 21 velocity greater than 4mm/day A useful application for slope monitoring data is the ability to vary the K or threshold value and the same data using a 1mm/day threshold is presented in Figure 6 to highlight this point. Note that all prisms are moving at velocities greater than 1mm/day and Prism 2 has the greatest velocity based on the steepest cusums velocity plot. Figure 6 CUSUM 1mm/day CUSUM Velocity (mm/day P1 P2 P3 The authors wish to highlight that the 4mm/day criterion should be used as a guide only, as experience from slopes we have been involved with have had threshold values ranging from.1mm/day to, in some cases, as high as 1mm/day. We suggest that the engineer develops his or her own value, based on data from his or her particular site, or initially use a relatively conservative estimate until sufficient data exist to establish a more reliable criterion. Furthermore, triggers to slope acceleration are easier to interpret when the cusums technique is applied. Figure 7 presents the same data as earlier but now with rainfall statistics highlighting that the significant rainfall event at approximately day 58 has triggered the acceleration in Prisms 1 and 2. Additionally, based on the data presented in Figure 7, it can be seen that the acceleration in all prisms at approximately day 18 was not triggered by rainfall events. Page 236

7 Figure 7 CUSUM 4mm/day 25 CUSUM Velocity (mm/day) Rainfall (mm) P1 P2 P3 Rainfall Some further examples of the application of cusums assessment of slope monitoring data has been applied to that of extensometer displacement data presented in Figure 8. Note that both the cumulative displacement data as well as the cusums displacement data is presented. Based on the threshold value of 4mm/day it is evident that extensometers 3 and 4 are moving at a faster rate, while 1 and 2 are indicating approximately 4mm/day displacement. 3 Figure 8 Extensometer Monitoring Data Threshhold set at 4mm/day 4 Displacement (mm) /5 31/5 7/6 14/6 21/6 CUSUM Displacement (mm) DATE Exto 1 Exto 2 Exto 3 Exto 4 Cusum 1 Cusum 2 Cusum 3 Cusum 4 Page 237

8 CONCLUSION The usefulness of the cusums technique when applied to temporal data cannot be understated. The authors have presented some examples to highlight this point. Based on these examples the authors believe that the application of cusums to the assessment of slope monitoring data is extremely valuable in the early detection of changes or trends in slope behaviour. REFERENCES Piteau, D.R. Engineering Geology Contribution To The Study Of Stability Of Slopes In Rock With Particular Reference To De Beers Mine. Unpubl. PhD thesis, The University of the Witwatersrand, Johannesburg, 197. Sullivan, T.D. Understanding pit slope movements, in Geotechnical Instrumentation and Monitoring in Open Pit and Underground Mining, T.Szwedzicki (ed.), Balkema, pp Zavodni, Z.M. Time-dependent movements of open pit slopes, in Slope stability in surface mines, Hustrulid and others (eds), SME, 2. pp Page 238