Synthetic slope profiles to assess rockfall hazard on open pit: influence of topography uncertainties

Synthetic Slope Profiles to Assess Rockfall Hazard on Open Pit: Influence of Topography Uncertainties *Maddalena Marchelli1 and Anna Giacomini2 1 Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, Turin, Italy *[email protected] 2 Centre for Geotechnical Science and Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia [email protected] Abstract. Rockfall represents one of the most dangerous landslide phenomena, with serious impacts on infrastructure and work areas. In open pit mining, the occurrence is increased by unforeseen adverse structural conditions during mining operations or poor blasting practices. At the design stage, the geometric outlines of the benches are generally chosen to minimize the impact of rockfalls. In standard practice, trajectory analyses are conducted using the ideal initial geometry to assess potential hazards in advance and determine effective mitigation measures. During mining activities, variations from the design profile, such as crest loss, flattening of the edge, and accumulation of debris at the toe of a bench, are frequently observed. In these cases, the catch capacity of the benches is reduced, leading to potential increase of block run-out distances and impact energies. In this study, we numerically investigate the impact of uncertainties related to slope topography, using more realistic slope profiles. The results are compared with those obtained for the ideal design geometry, providing powerful insights for preliminary rockfall hazard assessment and open pit slope design. A comparison with a real case is presented. Keywords: Rockfall hazard, Open pit design, sensitivity analysis, realistic slope profiles. 1 Introduction Rockfall is a significant hazard in both natural environments and working areas such as open pit mining, posing risks to structures, infrastructure, and personnel at all stages, including intermediate, final, and closure phases [1]. Ensuring slope stability is crucial to prevent fatalities, equipment damage, production losses, and restricted access to reserves [2]. While major failures at the overall slope scale are a primary focus, rockfalls also represent frequent instabilities at a bench slope scale [3]. Rockfall events are generally associated with structural conditions, meteorological events, weathering, and slope degradation, but they can also result from inadequate design implementation, such as uncontrolled procedures for blasting and/or © The Author(s) 2025 R. Hammah et al. (eds.), Proceedings of the Rocscience International Conference 2025 (RIC 2025) , Atlantis Highlights in Engineering 40, https://doi.org/10.2991/978-94-6463-900-1_48 482 M. Marchelli and A. Giacomini scaling, or unpredicted structural conditions ahead of mining. Effective catch bench design is thus essential to prevent rocks from reaching working areas [4]. The design process, balancing exploitation and safety, should account for geological, parameter, and model uncertainties affecting stability and performance of the pit slopes. While the modified Ritchie criterion is commonly used as a guide for rockfall design [3], the adoption of process-based trajectory analyses reduces model uncertainties related to material parameters and slope roughness conditions by applying a probabilistic approach. Several empirical formulations and charts have been recently proposed with this intent [4,5,6], including a 2023 study by the authors [7]. These approaches consider ideal 2D profiles, introducing a slope roughness factor to account for variability in the local surface angle of slope segments. However, real slope geometry often significantly deviates from the initial design due to unexpected geological variability that could affect the extent of back break, i.e., the horizontal distance between the planned toe and the actual mined crest of the final bench slope, at each mining level [4]. Despite good blasting and excavation control, mining activities and rock face degradation further alter the design profile, such as crest loss, flattening of the bench face angle, and accumulation of debris at the toe of a bench, reducing catch capacity and increasing run-out distances and impact energies [8]. Although iterative hazard assessment during operation is advisable, the ability to foresee possible deviations and assess their effects on the rockfall trajectory could significantly reduce production interruptions and delays. Since variations in the slope profile cannot be adequately represented by merely adding a general roughness parameter, this study proposes and applies a procedure to examine the impact of topography variations on multiple bench geometries using the same numerical technique reported in [7] for the ideal case. Aiming for a bench width that is sufficient to prevent rockfall, to contain spillage from higher benches, and to provide long-term access, results are compared with ideal geometry in terms of run-out distance and impact velocity on the pit floor. The study provides insights into block retention capacity and includes a comparison with a real-case scenario, followed by conclusions and future perspectives. 2 Methodology To evaluate the influence of slope variations from the ideal design profile before or during operations, we propose and perform a procedure based on a series of rockfall trajectory analyses. To minimize the number of variables, a 2D lumped-mass approach, commonly used in the initial stages of design [3], is adopted. A specific Matlab (R2023b) code, in combination with RocFall software (RocScience Suite), has been developed to perform multiple analyses, collect, and manage all output quantities, accounting for their distributions. The analyses start from a multiple benches ideal geometry, i.e. a synthetic profile representing the so called “design”, defined by bench height, ℎ𝑏, bench width wb, and bench slope angle β. According with what observed in real cases [3,4,8], given the profile three are the principal possible deviations from the original design that should be considered: (i) bench width and associated bench slope angle reduction (namely, 483Synthetic Slope Profiles to Assess Rockfall Hazard on Open Pit: … BR); (ii) crest loss and flattening of the edge (namely, F); and (iii) accumulation of debris at the toe, i.e. muckpiles (namely, M). Such profile modifications can be associated to blast-induced side effects (BR and M cases) or to weathering effects (F case) [4]. It is worth noting that the size of the back break can be predicted based on the structural features of the site. In the present study, for a 5-bench slope, several initial ideal geometries are considered, as reported in Table 1. The modified geometries are obtained as follows. For the BR case, the berm reduction has an equal probable percentage width reduction, from the “design” case, in the range 10-50%. Thus, For the F case, a constant back break of 1.5 m, i.e. ≈15 −20% of the investigated bench widths, is applied together with a fillet of 45° to the underlaying bench, without varying the slope angle. In the M case, a muckpile with a maximum height of 1.5 m is assumed [9]: considering an internal friction angle of the deposited waste rock material of 35°, as suggested by [10], a length of about 2.15 m is obtained. Fig. 1 shows an example of ideal (the design profile) and its variations. It should be noted that while the simultaneous occurrence of these alterations is not considered, the techniques to account for each case could be eventually merged to consider specific cases. Fig. 1. Example of an open pit ideal profile and the applied geometrical variations. In the zoom the ideal profile is slightly shifted to be visualized. To account for parameter (mainly material) uncertainties associated with the rockfall phenomenon, as proposed in the Eurocodes [11], trajectory analyses are carried out in a probabilistic framework. According with what suggested by [5], a normal distribution is assigned to slope roughness and to block-open pit interaction parameters, i.e. the normal and tangential restitution coefficients, 𝑅𝑛 and 𝑅𝑡 respectively, and the friction angle 𝜙. Table 1 report the adopted values. The different values of ℎ𝑏, wb, and β lead to 8 different design geometries, as further highlighted. For each geometry, the ideal (I) and the three modified (BF, F, M) cases were analysed. A Monte-Carlo sampling technique is adopted with 6000 throws per analysis. The source zone is inserted in the highest point of the pit slope. The run-out and the velocity of the blocks are recorded at the 484 M. Marchelli and A. Giacomini pit floor and at two control points of infinite height inserted in the pit floor at a distance from the toe, 𝑥𝑝 , equal to 10 and 20 m, respectively. Table 1. Input parameters for the bench geometry and the block-open pit interaction. Parameter Value Parameter Value ℎ𝑏 (𝑚) 15; 20 𝑅𝑛 (−) 0.35 ± 0.03 𝑤𝑏 (𝑚) 7; 10 𝑅𝑡 (−) 0.85 ± 0.03 𝛽 (°) 55°; 85° 𝜙 (°) 30° ±1° Roughness (°) ±1° 3 Results and discussion Considering the pit retention capacity as an important parameter in the slope design, the run-out distance on the pit floor 𝑑𝑝 is recorded considering 90th, and 95th percentiles. The minimum value is also registered. A similar approach is adopted for the impact velocity on the pit 𝑣𝑝. These values agree with the acceptance criteria proposed by [3]: at a bench scale, the maximum probability of failure is 20-10%, i.e. an 80-90% reliability, while at the overall slope scale a reliability up to 5% is required if the expected consequences of failure are high. Moreover, for protective measure design, the Eurocodes suggest considering the 95th percentiles of the distributions of the output variable as the characteristic values to be coupled with partial safety factors [12]. Fig. 2 reports the range of 𝑑𝑝 and 𝑣𝑝 from the minimum to the 95th percentile, highlighting with vertical markers also the 90th percentile, for all the geometrical configurations and variations. To evaluate the shape of the distributions the 50th percentile is reported too. Considering first 𝑑𝑝, the ideal case (I) generally represents the best scenario since blocks reach the pits in only three configurations, all with 𝛽 = 55°. This means that at 𝛽 = 85°, the design bench width is enough to catch all blocks, since they tend to experience free fall, to rebound almost perpendicular to the catch bench, and to stop at the first catch bench. For 𝛽 = 55°, as in [7], a less inclined slope favours sliding and rebounding along the bench surface and consequent impacts on the catch bench with a tangential component that it is higher than the corresponding quantity for 𝛽 = 85°. Since 𝑅𝑡> 𝑅𝑛, this leads to further motions. Although all deviations from case I entail a reduction in length of flat part of the catch bench, it is interesting to note that for 𝛽 = 55°, case F represents the best scenario: the curved edge reduces the number of blocks encountered during bounce and free fall and promotes sliding. Comparing with the I scenario, where present, a reduction up to 15% (ℎ𝑏=15 𝑚, 𝑤𝑏= 7 𝑚) of the 95th percentile of the run-out distance is observed. However, for 𝛽 = 85°, the experienced berm reduction is not sufficient to keep the blocks on the first bench, as in case I. This is due to the flattening of the edge from which blocks are thrown, which promotes farther trajectories on steep benches. It is worth noting that in these situations 𝑑𝑝 has a fattailed distribution, with very large values for the 95th, but median and minimum values even lower than in other cases of geometric variation, i.e. very disperse results are present. In contrast, in BR case the worst situation occurs when 𝛽 = 55°, which mimics 485Synthetic Slope Profiles to Assess Rockfall Hazard on Open Pit: … and emphasises the observations for case I. Comparing with the I scenario, an increase from 20 to 74% (ℎ𝑏=20 𝑚, 𝑤𝑏= 7 𝑚) of the 95th percentile of the run-out distance is observed. When 𝛽 = 85°, instead, no block arrives on the pit. Finally, in case M, blocks reach the pit for almost all geometric configurations (except ℎ𝑏=15 𝑚, 𝑤𝑏= 10 𝑚, 𝛽 = 55°). The presence of a muckpile at the toe of each bench, with a slope greater than the block-open pit friction angle, promotes rebounds and subsequent falls on the benches below. In the configuration with ℎ𝑏=20 𝑚, 𝑤𝑏= 7 𝑚, 𝛽 = 55°, the M case shows an 86% increase in the 95th percentile compared to the I configuration. Table 2 reports the % of blocks arriving on the pit, from which the retention capacity can be derived. Considering a 90% as target reliability value for block retention, i.e. the probability of having blocks reaching the pit is ≤10%, the only geometrical configurations for which this target is achieved independently from the alterations on the profile are those with ℎ𝑏=15 𝑚, 𝑤𝑏=10 𝑚. For higher benches, an increase in bench width is required to address this target. Hence, considering not only ideal geometry would lead to a probability of reaching the pit higher than the threshold value (10%). Looking at the velocity distributions at pit 𝑣𝑝, it could be observed that for 𝛽 = 55°, cases I, BR and M have a left-skewed distribution (the median is higher than the mean), while in the F case they are variable, with similar values for the higher percentiles (a variation less than 3% for the 95th percentile), about 20-25 m/s. For 𝛽 = 85°, the muckpile (M) geometry generates higher velocities than the flattening (F) geometry. It is worth noting that an opposite trend is observed for the run-out distance 𝑑𝑝. Fig. 2. Run-out distance (left) and impact velocity (right) at the pit floor. Vertical markers indicate the values corresponding to the minimum and to the 50th, 90th and 95th percentiles of the distribution of the results, for all the geometrical configurations. 2. 486 M. Marchelli and A. Giacomini Table 2: Percentage of blocks arriving on the pit. For the configurations refer to Fig. % of block on the pit Configuration A B C D E F G H 𝐼 0 94 0 16 0 43 0 0 𝐵𝑅 0 100 0 74 0 44 0 1 𝐹 99 74 0 16 90 36 0 0 M 100 99 71 5 100 76 2 0 Mean increment (%) 66.3 -3 23.6 15.7 63.3 9 0.7 0.3 Fig. 3. 95th percentile of the velocity at two control points in the pit floor at a distance 𝑥𝑝 equal to 10 (left) and 20 m (right), for all the geometrical configurations. Fig. 3 reports the 95th percentile of the velocities at the two control points in the pit floor, useful for mitigation measures design. With the same ℎ𝑏 and 𝑤𝑏, values are higher for 𝛽 = 85° than 𝛽 = 55°. With 𝛽 = 85° blocks arrive at the control points in M and F cases only. Maximum values are observed for ℎ𝑏=20 𝑚, 𝑤𝑏= 7 𝑚, 𝛽 = 85°, up to 35-40 m/s. No other specific trends are observed, either for 𝛽 = 55° or 𝛽 = 85°. In most of the geometrical configurations, case I represents the best scenario, while the worst scenario can occur almost randomly in cases BR, M or F. Hence, neglecting the study of the geometrical variations could lead to an underestimation of rockfall risk. 3.1 Application to a case study The study reported in [13] has been considered to assess the validity of our approach by analysing rockfall trajectories on ideal and actual slope geometries (cases BR, F, and 487Synthetic Slope Profiles to Assess Rockfall Hazard on Open Pit: … M). Full-scale rockfall tests were conducted in 2023 in a Nevada open pit gold mine to evaluate the probability of blocks impacting a prototype rockfall barrier system. Fiberreinforced concrete boulders were dropped from a 116 m highwall with four 24.4 m high double benches and a partial bench (16 m). The bench was approximately 10 m wide with a 65° slope angle. Deviations from ideal topography included a 1 m berm reduction at the 4th bench top and waste rock accumulation at its toe. Of 300 throws, only three blocks hit the barrier on the pit floor, 5 m from the 5th bench toe. Two blocks arrived rolling/sliding, and one impacted the barrier at 11.9 m/s. The trajectory analysis reported in [13] indicated that crest loss at the 4th bench caused a bypass of the catch bench, impacting the muckpile and rebounding with increased horizontal velocity. In the present study, trajectory analyses are performed on ideal and actual geometries (BR, F, and M), considering the same 𝑅𝑛= 0.32 ± 0.03 and 𝑅𝑡= 0.80 ± 0.03 as in [13]. Results showed that cases I and M have blocks stopping on the 4th catch bench, while cases BR and F have 20% and 1.5% of blocks reaching the pit floor, respectively. Pit floor velocities range from 8.7 to 21 m/s, with 95th percentiles of 20.4 and 13.3 m/s for cases BR and F, respectively. Run-out distances are 1.7 to 14.6 m for case BR and 8.1 to 8.2 m for case F. At the barrier position, the 95th percentiles of velocities are 8.4 and 5.9 m/s for cases BR and F, respectively. Despite the simulated geometrical variations differ from the real case, results confirmed significant effects of topography variation on rockfall trajectory and block propagation, especially for crest loss. Fig. 4. Trajectory analyses in the I, BR, F and M cases. The red cross represents the release point, the light-blue lines the trajectories, the magenta stars the ending points, the blue line the barrier. 𝐻𝑡𝑜𝑡 is the total height of the pit. 488 M. Marchelli and A. Giacomini 4 Conclusions This study examines how geometric deviations from the design profile of an open-pit mine affect rockfall propagation and kinematics. During mining, crest loss, bench face angle flattening, and debris accumulation at the bench toe reduce catch capacity, altering predicted rockfall run-out distances and energies. Trajectory analyses on ideal and modified profiles show significant variations in run-out distances, especially with steep bench slopes. The worst scenarios involve flattening and muckpile presence. Applied to a real case, field tests revealed an increase of runout distance due to reduced catch bench capacity. Results emphasize the need to assess rockfall risk considering potential geometric variations, as the ideal design often underestimates these effects. Future work will explore more realistic scenarios and develop design charts for various conditions. Acknowledgements This work was supported by Marie Curie Postdoctoral Fellowship 2022 (Call HorizonMSCA-2022-PF-01, grant GA101103401 - RIDETHERISK project) and by the Australian Research Council (DP210101122). References 1Marchelli, M., Coltrinari, G., Degan, G. A., & Peila, D.: Towards a procedure to manage safety on construction sites of rockfall protective measures. Safety science, 168, 106307, (2023). . 2Darling, P. (Ed.): SME mining engineering handbook, vol. 1. 3rd edn. SME, Littleton (2011). . 3Read J, Stacey P.: Guidelines for open pit slope design. 1st end. 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