Q Risk
It is crucial to the safe and economic operation of a quarry to be able to quantify the risks presented to quarry personnel, equipment and infrastructure, as well as to the public, by an excavated rock face. The ability to rate the level of risk to personnel, equipment and infrastructure will not only allow comparison with other slope orientations in the same domain, slopes with different rock types, different areas of weathering, and slopes with different geometries or ages of exposure, but also permit a financial value to be applied to the risk. Both of these aspects significantly increase the value of a geotechnical risk assessment to the quarry manager and operating company, allowing them to make adjustments to their current operating practices, and short-term and long-term planning, based on a potential cost benefit.
QRisk has been developed by geotechnical engineers within SRK specifically for the quarrying industry, reflecting SRK’s worldwide experience in quarry and open-pit mine geotechnics over the last 25 years. The programme was principally developed to provide a systematic approach to geotechnical appraisal and assessment of quarry faces, which would be useful for compliance with the Quarries Regulations 1999.
QRisk is a probabilistic spreadsheet-based tool that calculates the risk of injury (safety risks) and the risk of damage to equipment and infrastructure (financial risks) in quarry excavations. QRisk can be carried out in a production environment on faces where there is some form of activity nearby, such as drilling, blasting, loading, haulage, tipping, stockpiling, pedestrian access etc, or where there is infrastructure close to the crest or the toe of the slope. Alternatively, QRisk can be used for planning purposes at the initial design stage, during short-term planning of excavation campaigns, or for closure.
The quantification of risk is based on a visual assessment of geotechnical instability hazards on the slope face and the exposure in terms of proximity, duration and financial value of quarry and public personnel, equipment and infrastructure within the area of risk. Domains for assessment can be chosen by rock type, rock mass quality, orientation of faces or different levels of exposure. The risk is calculated using empirically derived relationships between assessed conditions, exposure and consequences of potential failure.
APPROACH OF Qrisk
QRisk relies on the judgement of the geotechnical engineer to identify instability hazards in the slope. These are assessed visually, but it is important to take into account any supporting information from maps, survey information, inspections, previous reports, etc. The hazards are identified independently of the exposure level of the slope. The exposure information is based on the measured geometry of the quarry slope, the actual operating conditions observed, and usually from discussions with the quarry manger or operations manager. It is also useful to have knowledge of the interim and final designs of the slope.
QRisk has been designed for efficient data entry on specially designed field sheets and to produce concise results for rapid assessment. All the QRisk calculations are transparent to the user; it is not a ‘black-box’ approach. The user has access to the full details of interim calculations and results.
Input parameters are collected on field data sheets and entered into QRisk using on-screen dialogue boxes (figures 1 and 2). Using simple probabilistic models, QRisk calculates risk of rockfall, single-bench, multi-bench, and overall slope failure. The most likely failure mechanism is returned and, depending on the exposure at the toe of the slope, a risk rating in the range of 0 (no risk) to 100 (extremely high risk) is calculated. QRisk also identifies whether the risk is a safety risk or a financial risk and, depending on the monetary values provided, the financial value of the risk is also estimated. It is possible to undertake sensitivity analyses on the data to identify parameters that can be changed to reduce the risks cost-effectively.
METHOD OF ANALYSIS
The geotechnical engineer’s assessment identifies instability hazards. The consequences of instability are then evaluated using empirical rules and analytical techniques. Finally, the risk is calculated from event probabilities and consequences.
The geotechnical risks include:
- small-scale rock falls, blastinduced rockfalls
- bench-scale failure along joints (planar, wedge, toppling)
- multiple-bench failure along major structures (faults, joints, bedding, dykes)
- deep-seated failure affecting the entire slope (rock-mass failure).
- employee/contractor and public safety
- damage to quarry/contractor and public equipment
- damage to quarry and public infrastructure.
DATA INPUTS
Since QRisk relies entirely on the field-assessment sheets as input, a qualified geotechnical engineer, who is familiar with quarry and rock slope stability issues, should conduct the assessment. QRisk simply combines the different inputs to perform the necessary calculations for risk determination.
The geotechnical engineer subdivides the slope into domains with similar geological, geotechnical, geometrical or operational characteristics. Several categories of data input are required for each domain and there are special data sheets for data collection, which are completed for each domain. The input data are entered into dialogue boxes and transferred to the appropriate locations in a spreadsheet, where the risk is calculated and the results presented. Typical parameters can be included for the whole slope or specific values entered for each individual bench. The input dialogue boxes for slope geometry and toe exposure are shown in figures 1 and 2.
The data inputs can be subdivided into five categories.
- Geometric inputs:
—orientation
—overall slope angle
—bench face angles
—bench height
—berm width
—face roughness profile
—berm effectiveness
—edge-protection height
—accessibility to the toe of the slope
- Rock mass data inputs
These conform to the Rock Mass Rating of Bieniawski (1989)1. The parametric ratings are recorded in the field and entered directly into QRisk.
- Stability assessment
A stability assessment of rock-fall potential, single-bench- scale kinematic instability potential (such as toppling, wedge, planar failure) and multi-bench-scale kinematic instability potential is made using simple rating systems, as shown in table 1. Estimates are also made of the potential magnitude of instability and the degree of weathering and erosion on the face which may impact instability, as shown in table 2.
- 4.Blasting effectiveness and slope remediation
The quality of blasting and the effectiveness of any installed remedial measures such as rock bolting and catch fencing will reduce the risk of slope instability. Ratings to account for these parameters are shown in table 3. - 5.Exposure inputs
Exposure of persons, equipment and infrastructure on benches and behind crest of slope including:
—number, standoff and percentage daily presence for persons
—value, standoff and percentage daily presence for equipment
—value, standoff and slope parallel length for buildings and permanent infrastructure.
RISK CALCULATION PROCEDURES
Calculation of rockfall risk
Rockfall risks are generally associated with individual rolling rocks that may strike a person, equipment or infrastructure. The probability of spatial coincidence is first calculated to determine the probability that rolling rocks will actually reach the object (person, equipment or infrastructure). The spread of rolling rocks is determined using a relationship between the bench height, face angle and face profile. The overlap distance, that is the distance that the rocks will roll past the object, is determined and calculated from the standoff distance. This quantity is used to determine the proportion of rolling rocks that can hit the object.
The probability that the object is hit by a rolling rock is calculated assuming the rocks are spread in a triangular distribution, with the most rocks lying at the toe of the face. The probability that a rolling rock will hit an object is calculated as:
P(hit) = (Overlap/Spread)2
The annual frequency of falling rocks is determined from the geotechnical engineer’s rating of the stability (table 1). The fall frequency for each failure mode is first visually estimated for a 30m strike length of bench. The relationship between failure frequency (F30) and rating (R) for rockfalls is:
F30 = 10(R-3)
The potential for rocks to spill from an upper bench on to the bench being evaluated is determined by calculating and summing the percentage of rolling rocks that are likely to be ejected over the edge of each bench.
The annual frequency of rolling rocks along the entire strike length of the bench is calculated as:
F = F30/30 S
where S is the strike length of the bench.
A number of adjustments are made to the annual frequency to account for:
- The effectiveness of any remedial measures.
- The probability that an object will occupy the same space at the same time as a falling rock, the temporal coincidence, which is based on the exposure duration.
- The probability that an object will be in the path of a rock when it falls, the spatial coincidence, which is a function of the length of the object to the total strike length of the slope.
The frequency calculations are repeated for employees, public, equipment and infrastructure.
The probability that an incident caused by rolling rocks will occur is calculated from the maximum frequency of the different types of failures. It is assumed that the discrete events follow a Poisson distribution (as they should) and the probability of one or more events occurring in the stated time interval (one year) is given by:
P= 1- e-F
Bench-scale failure
The annual frequency of failures along ubiquitous joints, resulting in bench-scale failures, is calculated for wedge, plane and toppling failure modes. The approximate volume of the failure is calculated from the potential failure dimensions estimated by the geotechnical engineer. The volume is used to calculate the spillage of rocks from one bench to the next. The spillage of rock from one bench to the next is calculated using the procedure described previously for rockfalls.
The annual frequency of failure on a particular bench is calculated as follows:
F = 10R-4 Hf / Hs
where R is the failure rating, Hf is the height of the failing block and Hs is the height of the entire slope. This assumes that a failure may occur at any vertical location on the slope, and the probability that it will occur at a particular location depends on the ratio of the failing block to the height of the slope. The failure frequencies associated with the failure ratings are one order of magnitude lower than the values used for rockfalls. For example, if the failure rating is 2, the estimated height of a failure is 15m and the slope height is 45m, the annual failure frequency F would be 0.045, which is one failure in 22 years.
The frequency of objects being affected by bench-scale failure is determined by the product of the frequency of failure, temporal coincidence and spatial coincidence. Temporal coincidence is calculated as for rockfalls. The spatial coincidence is calculated as the ratio of the width of the expected failure to the strike length of the bench. For example, if a person is located on a bench with a strike length of 200m and a 10m wide wedge failure occurs, the probability that they will be in the path of the failure will be 5%.
The probability of a bench-scale failure occurring is calculated in the same way as for rolling rocks using the Poisson distribution.
Failure along major structures
The failure frequency along individual major structures, such as faults, is calculated in a similar way as for ubiquitous joints. The calculation procedure for bench-scale failures is followed. The only difference between the calculations is that the failure frequencies associated with the failure ratings are one order of magnitude lower than for bench-scale failures, as shown below.
F = 10R-5 Hf / Hs
The probability of a failure along a major structure occurring is calculated in the same way as for rolling rocks using the Poisson distribution.
Deep-seated failure
The probability of deep-seated failure of an entire slope is determined from the Haines & Terbrugge2 slope-design chart, which is based on the MRMR (Laubscher)3rock-classification system. The MRMR is calculated from the RMR by applying adjustments for blasting, weathering and orientation of jointing. The spreadsheet calculates the required angle for a factor of safety of 1.2. The difference between the required angle and the actual slope angle is used to determine the annual probability of deep-seated failure, as follows:
P=0.0017e -0.32ß
where ß is the difference between the required angle and the actual angle. This relationship was developed on the assumption that the recommended slope angle implies a 5% annual failure probability. The resulting failure probabilities are illustrated in figure 3. For example, if the slope angle exceeds the recommended angle by 10o, the failure probability would be 27%.
The approximate failure width is assumed to be equal to one half the slope height and the failure depth one-third the width. The failure width is used to calculate the spatial coincidence.
The probability of an incident occurring as a result of deep-seated failure is calculated in a similar way as the failure frequencies are calculated for the previously discussed failure modes. In this case the probability of an incident is directly calculated as the product of the failure probability, the temporal coincidence and the spatial coincidence.
Calculation of potential financial risk
Financial losses (financial risks) to quarry-owned or public infrastructure and equipment are determined separately. The consequences of rockfall events are calculated separately from the remaining failure modes.
The probabilities of bench-scale, major structure and deep-seated failure are summed. Since these are relatively large-scale events, they are likely to have severe effects on equipment and infrastructure should failure occur. The probability of a major loss will be greater than that of a minor loss, which in turn will be greater than if only inconvenience occurs. The relative cost of a major loss, a minor loss and inconvenience are defined as decreasing fixed percentages of the total value of the object. The potential loss, in monetary terms, is calculated as:
L = P x V x (P[Loss]xV%)
where V is the monetary value of the object, P is the probability of an incident occurring and the summation is the product of a probability of loss and its relative cost for major and minor losses and inconvenience.
A similar approach is used to calculate the losses caused by rockfalls, except that the distribution of losses is inverted, as inconvenience is more likely than a major loss in these circumstances. The total financial losses are the sum of the losses from the larger-scale failures and the small-scale rockfalls.
Calculation of risk index
The safety risk index is calculated separately for employees and public to reflect the difference between ‘voluntary’ risk of employees and ‘involuntary’ risk of the public. The ‘voluntary’ risk is an order of magnitude higher than the ‘involuntary’ risks. For employees the risk index (Ie) is calculated as:
Ie = 90e 0.3log P
and for the public the risk index (Ip) is:
Ip = 100e 0.3logP
where P is the annual probability of an incident.
The financial risk index (If) is calculated from the potential financial loss as follows:
If = 12In(L)
where L is the potential financial loss in £x1,000. A loss of £1 million has an index of about 80, while a loss of £100,000 has an index of about 50.
DATA OUTPUT
A typical summary data output screen for QRisk is illustrated in figure 4. This is an example of the phased development of a fictitious slope and shows the change in rating depending on the prevailing geotechnical and exposure conditions. The Phase 2 and Phase 4 excavation profiles are illustrated in figures 5 and 6 and show the risk ratings for each bench and the financial value of the risk.
The significance of the risk rating in this case is related to an initial geotechnical assessment of a quarry where there is little previous knowledge of the performance of slopes and history of any instability. The time frame for reassessment can be modified to take account of the level of monitoring, inspection, planned exposure etc, in the coming months and should be agreed upon with the quarry manager and the operating company’s geotechnical experts, if available.
Once these results have been produced, the detailed results for each geotechnical domain can be inspected and the input parameters changed, if appropriate. This allows a sensitivity analysis to be performed with respect to the geotechnical assessment, the operational procedures and the quarry plan, and is a very useful tool for aiding decision-making.
In addition, the recommendations based on the risk level can be modified to reflect different aspects other than a geotechnical assessments schedule, such as a particular operating procedure, initiation of remedial measures, or changes in the inspection and monitoring schedule. The essence of QRisk is that it can be used as a management tool and can be modified in consultation with the quarry manager and the operating company so that the significance of the risk ratings is agreed upon with regards to the dynamic operating environment and the short-term and long-term quarry plans.
CONCLUSIONS
The purpose of the system is to provide a quantification of the risks presented to quarry personnel, equipment and infrastructure, as well as to the public, by an excavated rock face. The rating system allows direct comparison with other slopes of different orientations, with different rock types, different rock-mass characteristics and different levels of exposure.
The monetary rating aspect allows remedial measures to be planned on a cost-benefit basis.
The combination of safety and financial risk ratings allows quarry operators to make timely adjustments to their current operating practices, and short-term and long-term planning, as well as helping to schedule geotechnical appraisals and assessments. The programme can be used as an effective management tool covering all rock slope geotechnical aspects.
QRisk is not, however, intended to be a substitute for rigorous geotechnical analysis and the geotechnical input parameters are based on the judgement and experience of the engineer. QRisk requires a geotechnical engineer or engineering geologist with experience of the assessment of rock slope instability to carry out the survey and monitor the results.
References
- BIENIAWSKI, Z.T.: ‘Engineering Rock Mass Classifications’, Wiley, New York, 1989, 251 pp.
- HAINES, A., and P.J. TERBRUGGE: ‘Preliminary estimation of rock slope stability using rock mass classification systems’, Proc. 7th Congress on Rock Mechanics, ISRM, Aachen, Germany, 2nd edition, Wittke W, Balkema, Rotterdam, 1991,
pp 887–892. - LAUBSCHER, D.H.: ‘A geomechanics classification system for the rating of rock mass in mine design’, South African Institute Mining Metallurgy, vol. 90, no. 10, Oct 1990, pp 257–273.
The authors, Richard Oldcom and Neil Marshall, are with SRK (UK), and Essie Esterhuizen is with SRK (US)
