A typical workflow of a rockfall trajectory study that may incorporate the use of statistical analysis programs, such as RocFall, was developed by Dorren et al. [10] and can be divided into six phases including: (1) preparation phase, (2) definition of the release scenarios, (3) rockfall simulation, (4) plausibility check/validation of the simulated results, (5) fixation of the model results, and (6) transformation into rockfall process maps. Mine sites have utilized this workflow in some form or another to gain a better understanding of rockfall behavior with respect to their specific bench design.

Through the years, RocFall has continually been upgraded with more sophisticated analysis tools, such as the use of the lump mass versus rigid body models. With the lump mass model approach, each rock is modeled as a very small spherical particle and the rocks are not considered to have any size, only mass. With the rigid body approach, the shape of the rocks is accounted for by selecting from a wide variety of pre-defined smooth or polygonal shapes in the program’s rock type library, and the mass of the rock determines the actual size of the rock shape. Additional details on the differences between the aforementioned modeling methods can be found on Rocscience’s website [11].

With regards to mine sites utilizing the program, a literature search shows that users either apply the lump mass approach [5, 12, 13, 14, 15] or the rigid body approach [8, 16] but rarely use both. Additionally, field experience and extensive use of RocFall in both mining and civil applications has helped identify key variables, additional to bench height, that affect the runout distance of rocks along a designed catch bench slope [14, 16, 17, 18, 19] ; however, there is less clarity on how results can differ between the available RocFall models. This prompted researchers at the Spokane Mining Research Division (SMRD) of the U.S. National Institute for Occupational Safety and Health (NIOSH) to reach out to industry partners, conduct an analysis of 90% rock runout distance according to changes in slope height, slope angle, slope material, and rock size for both lump mass and rigid body models, and compare/contrast the results with the MRC bench design criterion according to each designed test. This research is part of the NIOSH Highwall Safety project which started in October of 2021.

In October of 2021, the Geomechanics Team at NIOSH SMRD started the Highwall Safety project, which will run for 5 years. This project is a continuation of a pilot project conducted by Warren et al. [20] where one of the main goals is to quantify the performance of available criterion for rockfall catchment bench design in a variety of bench configurations and optimize said criterion based on field calibration. As shown in Equation 1, the MRC only considers bench height in determining catch bench width; however, field testing and statistical analysis programs show that additional variables related to geology and operational practices play a role in rockfall runout distance and necessary catch bench width.

Therefore, as a starting point for the NIOSH Highwall Safety project, the modeling executed in this paper is a first attempt at a sensitivity analysis looking into the various factors that influence how far rocks roll on a single bench to gain insight into required catch bench width to achieve safe mining conditions.

Within each individual RocFall test, differences in distribution of runout distance were easily identifiable between lump mass and rigid body models. For example, the specific tests shown in Figure 2 and Figure 3 show that, while runout distance of each rock size in the lump mass model were confined to distances between 10 feet and 27 feet from the toe of the slope, the runout distance of the same rock sizes ranged between 0 feet (not getting past the toe of the slope) and 29 feet for the rigid body model. These differences in runout distribution between each model were seen throughout the entirety of RocFall testing. This illustrates the effect of how the rigid body model accounts for the shape of the rocks. It is important to note that, for Figure 2 and Figure 3, while the runout distribution is vastly different between each model, the 90% runout distance only differs by a maximum of 2 feet. Therefore, the rock percentage retained at the calculated MRC width for each individual test is also noted (Figure A3) as this provides a better indication of runout distribution and whether this type of test would meet the criterion of catching 90% at the MRC.

Figures A4 and A5 help provide an initial indication of which independent variables have a more significant influence over rockfall runout distance. For both lump mass and rigid body models, the slope height and slope angle have a greater influence than slope material and rock size, demonstrating that as the bench height increases and the slope angle decreases, the 90% rockfall runout distance increases. This is further exemplified by the correlation coefficients shown in Table 3. In this case, the correlation coefficient shown for slope angle is negative because, as previously stated, with shallower slope angles there will be higher rockfall runout. Based on previous literature associated with rockfall testing within the civil and mining industries, these findings are relatively common knowledge; however, this helps reiterate that the MRC should account for more than just bench height.

With regards to slope material and rock size, it was anticipated that both factors would have more influence than the results show. It is important to note that a roughness factor was not incorporated into the RocFall tests carried out in this study. As field testing occurs throughout the duration of the NIOSH Highwall Safety project, notes will be taken to further calibrate the RocFall models to the real-world tests with similar geometry so that factors such as slope roughness may be considered. Additionally, previous rockfall field testing by the NIOSH SMRD team showed that rock size had a higher effect on runout distance than the RocFall results in this study [20]. While it was expected that the lump mass model would show little difference in runout distance according to rock size, the rigid body also demonstrated relatively minor difference apart from certain tests at a bench height of 80 feet as shown in Figure A5. While these tests in RocFall mark a starting point in investigating the effect of certain parameters on rockfall runout, field testing will help further illustrate what changes need to occur to better link modeling to the real-world tests.

The contour plots developed in MATLAB based on the resulting data help identify combinations of the bench geometry where the rockfall runout is significantly high and the calculated MRC bench width does not come close to catching 90% of the rocks. Once the bench height reaches 40 feet and above, slope angles of 50 and 60 degrees create rockfall runout scenarios that far surpass the calculated MRC width with extreme cases of the rock percentage retained being 1% to 4% at a bench height of 80 feet and slope angle of 50 degrees. While this and some other bench configurations shown in this study may not be common in industry, these statistical modeling results indicate that the performance of the MRC is not consistent. Any criterion used in the mining industry for slope design should be relatively uniform in its performance expectation.

Through the NIOSH Highwall Safety project, field testing of bench configuration scenarios similar to those tested in this study will develop a more concrete correlation between not only bench height, but additional variables related to geology and operational practices, so that the MRC can be further updated for improved confidence and safety at mine sites.