New model for predicting the erosional performance of rehabilitated mine sites

To avoid rill/gully erosion on steep rehabilitated mine hillslopes, mine waste can be redistributed to be less steep and have fewer areas where runoff is concentrated. In addition, the shear strength of a rehabilitated mine site surface can be increased with riprap and/or vegetation. Figure 1 Oblique-shaded relief image of a 350-m-long tailings dam hillslope located in Pinal county, AZ with superimposed blue-white-red elevation change map of the erosion (blue) and deposition (red) that occurred during an Aug. 8, 2022 rain event that lasted approximately 30 minutes. The mine-site rehabilitation community lacks mathematical models that predict the likely erosional performance of such rehabilitations so that they can be implemented cost-effectively and with confidence that they will work to prevent rill/gully erosion under both modern and future climates. This article describes a new mathematical model (Rillgen2D) for predicting rill/gully erosion that is informed by studying hillslope erosion processes in the laboratory and in the field at study sites in Arizona in the United States and Queensland in Australia. It highlights advances both on the forcing side of the problem (how rainfall generates runoff) and the resistance side (how certain properties of riprap contribute to shear strength). It documents three validation studies across a range of study sites (including with and without riprap, continuous-slope and benched-slope designs), which demonstrate that Rillgen2D accurately predicts where and when rills and gullies are likely to form. The intent is for this model to be widely used to predict the erosional performance of alternative rehabilitation designs to optimize performance and save money. Problem statement Mining activities often result in piles of waste rock and soil bounded by long, steep hillslopes that are highly susceptible to rill/gully erosion. A key goal of mine-site rehabilitation is to prevent rill/gully development and the associated transport of mine waste on such hillslopes. Rehabilitated mine hillslopes in dryland regions can be especially susceptible to rill/gully erosion because the sparse vegetation cover in such climates can limit the shear strength that resists erosion. As such, it is often necessary to modify mine-waste topography (for example, reduce slope steepness/length) and/or cover the waste material and soil cap with riprap to prevent rill/gully development. Such interventions can be costly and do not always work even when carefully implemented. Figure 1 illustrates the rill/gully erosion that can occur on steep rehabilitated mine hillslopes. This example is a tailings embankment 350 m (1,150 ft) long and 100 m (330 ft) tall located in Pinal county, AZ. The colors represent the erosion and deposition measured by differencing high-resolution (2 cm/pixel) drone-based photogrammetric surveys of the embankment before and after a rain event that lasted approximately 30 minutes on the evening of Aug. 8, 2022 when the site experienced a peak 15-minute-duration rainfall intensity of 174 mm/h. Despite the presence of riprap with median diameter of 10 cm on the lower two-thirds of the hillslope, gullies more than 2 m (7 ft) deep formed during this event, exposing and transporting waste material to the bottom of the slope. Figure 2 Comparison of how rills and gullies are modeled in (a) WEPP and (b) Rillgen2D. In WEPP, the user prescribes the spacing and width of rills/ gullies and WEPP implicitly routes runoff to each, as shown by the arrows in (a). In Rillgen2D, rill/gully initiation is modeled from shearstress hot spots — for example, the circled areas in (b) — that are explicitly resolved. Preventing erosion of the kind illustrated in Fig. 1 in future rehabilitated mine sites requires that proposed rehabilitation designs be assessed in terms of their potential for rill/ gully development under modern and future climate scenarios. Historically, the most widely used mathematical model for rill/gully erosion on hillslopes has been the water erosion prediction project (WEPP) model (Flanagan and Livingston, 1995). Although WEPP has many positive traits, it has a limited ability to model rill/gully erosion because the user must prescribe the spacing of rills/gullies a priori — otherwise, WEPP assumes all rills/gullies to have 1-m spacing (Fig. 2a). Clearly, the widths and spacings of rills/ gullies cannot be known for any hillslope that has not yet been constructed. Rills/gullies form in response to the incipient steering of runoff into microtopographic depressions (Fig. 2b) that deepen if a threshold shear stress is exceeded, further localizing runoff in a self-enhancing feedback. The colors in Fig. 2b represent the effective slope length: that is, the upslope length that would be conveying flow to that point on the hillslope if the hillslope was planar and uniform sheetflow was occurring. Effective slope lengths greater than 350 m (1,150 ft) can occur in places where runoff has been steered and concentrated. Effective slope lengths of up to 1,000 m (3,280 ft) occur in this example on the lower half of the hillslope and are associated with approximately a factor-of-three increase in shear stress relative to the case of uniform sheetflow. The fact that microtopography can result in enhanced shear stresses on hillslopes as illustrated in Fig. 2 and that such shear stress hot spots tend to be where rills/gullies initiate is widely recognized, but the literature contains inconsistent solutions to representing the runoff convergence/divergence that leads to such shear stress hot spots. The U.S. Nuclear Regulatory Commission (U.S. NRC, 2002, p. 41), for example, recommends that the effective slope length be estimated as the horizontal distance from the top of the slope multiplied by three, while the U.S. Environmental Protection Agency (EPA, 2012, p. 46) recommends that the same value be estimated as the horizontal distance from the top of the slope, L, multiplied by L/4. Rillgen2D models flow localization explicitly, avoiding any need to apply ad hoc adjustment factors. Recently, the CAESAR-Lisflood model (Coulthard et al., 2013) has been used to model rill/gully erosion on hypothetical rehabilitated mine hillslopes (Slingerland and Dressler, 2022). One advantage of CAESARLisflood over WEPP is that it explicitly routes runoff on hillslopes, including the effects of microtopography, similar to that of Fig. 2b. CAESAR-Lisflood does not explicitly include the protective effects of riprap, however, and it is unclear whether CAESAR can make predictions consistent with data from a real-world hillslope. A new approach In this study, field and laboratory measurements (Fig. 3) and remote sensing (for example, Fig. 1) of rainfall, runoff, erosion and related parameters (such as the angle of internal friction) were used to develop a new mathematical model (Rillgen2D) for rill/ gully erosion on hillslopes. Rillgen2D accepts data for rainfall, topography (including microtopography), soil and land cover (riprap and/or vegetation) to predict where and when rills/gullies are likely to form on rehabilitated mine hillslopes (actual or proposed designs). In the following, we emphasize two novel elements of Rillgen2D and outline the work that went into its development. Improvements in quantifying the runoff associated with intense rainfall Runoff data from monitoring plots (collected using the equipment illustrated in Figs. 3b-c) have been used to develop an empirical model predicting runoff based on its primary controlling factors in our Arizona study sites. In this model, runoff measured at a five-minute duration, R5 (mm/h), is a power-law function of rainfall intensity measured at a 15-minute duration, I15 (mm/h), rainfall intensity measured at a one-hour duration, I60 (mm/h), and drainage area, A (m2): I15 and I60 control R5 because more intense shortterm rainfall triggers more infiltration-excess runoff, and more runoff is also likely to occur when the short-term peak rainfall occurs within a high-intensity rainfall of longer duration (one hour) that tends to saturate the soil prior to the arrival of the peak-intensity rainfall. Equation (1) was validated using runoff data from the Walnut Gulch Experimental Watershed (open circles in Fig. 4), which have similar soil types to those of our Arizona study sites. Equation (1) can be readily applied to simulating event-based runoff for hundreds or thousands of years using the weather generator CLIGEN included in WEPP, assuming current climatic conditions. Figure 4b illustrates a simulated 100-year time series of the coefficient, ar = 0.008〖I15 1.44 I60 0.75 that predicts water discharge for the example station of Miami, AZ at every point on a landscape and for every event in a 100-year period when multiplied by A0.87. The value of A at every point can be determined using several algorithms widely used for this purpose. Rillgen2D allows users to choose between the Freeman (1991) algorithm and a new algorithm developed for this project that accounts for runoff depth in addition to groundsurface slope when simulating surface water flow. Simulating possible changes in the duration and intensity of future rain events is an area of active research, but Rillgen2D users can prescribe possible or expected increases in precipitation intensities based on estimates of these changes from the published literature (for example, Prein et al., 2017). Figure 3 Examples of equipment used in the Arizona study sites: (a) laboratory: a tilt table for measuring the angle of internal friction of layered riprapover- soil covers, (b) field: instrumentation at the base of hillslope-scale plots used for measuring coarse sediment load (collected in a bottom trough and subsequently weighed), runoff and fine sediment loads (measured using a tipping bucket outfitted with a turbidity sensor) and (c) field: instrumentation for measuring runoff and fine sediment in small-watershed-scale plots (including wingwalls that concentrate the runoff into a Parshall flume). Improvements in quantifying the shear strength associated with riprap Several empirical models have been developed to quantify the shear strength associated with riprap. Historically, such models have been developed using the Abt et al. (2013) database, which includes 102 measurements of the threshold unit water discharge or shear stress (unit discharge and shear stress on steep slopes can be related by Eq. (7) of Eli and Gray, 2008) required for riprap failure when a filter layer is present. The most accurate current empirical model for riprap failure was proposed by Haws and Erickson (2020). Their model relates the threshold unit discharge of runoff, qf (m2/s) to the median riprap particle diameter, d50 (m) and slope angle, θ. An alternative model was developed that explicitly includes the angle of internal friction, ϕ: The value of c is 2.6 for riprap layers that include a filter layer and 1.3 for riprap layers that do not have a filter layer (the riprap is placed directly on top of soil, as is generally the case for largescale mine rehabilitations). The factor-of-two difference between the two values of c is based on preliminary experiments of riprap failure with and without a filter layer. The root-mean-squared errors of the logarithms (base 10) of qf predicted by the model of Haws and Erickson (2020) and Eq. (2) are 0.195 and 0.171, respectively, demonstrating the superiority of Eq. (2) (Fig. 5). Typical angles of internal friction for angular particles are greater than 33°, but small-scale laboratory experiments we have performed on riprap layers over soil (Fig. 3a) reveal that friction angles can be as low as 30° because of the layered nature of riprap-over-soil cover systems. Three degrees of difference may seem slight, but this difference can lead to large reductions in shear strength even for slopes substantially less steep than the angle of internal friction because the denominator in the parenthetical expression in Eq. (2) approaches zero as θ approaches ϕ. The literature on mine-site rehabilitation recommends against designs steeper than 3H:1V (Weeks and Sulfate, 2007), but they cannot always be avoided (such as when embankments abut land ownership boundaries). Figure 4 (a) Predicted versus observed values of R5, as predicted by Eq. (1), for our rehabilitated mine study sites in Arizona and the Walnut Gulch Experimental Watershed (WG). (b) Simulated time series of the coefficient, ar , that predicts water discharge when multiplied by A0.87, for the example station of Miami, AZ. Figure 5 Plots of the predicted versus observed unit water discharge that triggers rock armor failure, qf, from (a) Haws and Erickson (2020) and (b) Eq. (2) for rip-rap layers with (solid line) and without (dashed line) a filter layer. Validations of Rillgen2D to rehabilitated mine sites in Arizona and Australia Three validation tests of Rillgen2D are documented to extreme rain events at the study sites in Arizona and Queensland, where approximately 1 minute per sample rainfall intensity data and approximately 0.5 m per pixel surveys of the erosion and deposition that resulted from that rainfall (similar to Fig. 1) are available. Rillgen2D uses a time series of runoff predicted by Eq. (1) (or a user-prescribed runoff, if preferred) to relate drainage area to water discharge from runoff. Where and when the water discharge exceeds the threshold for rill/gully development, the rill/gully erosion rate at that location is modeled as the product of a rill/gully-erodibility coefficient, Kr, and the amount that the shear stress exceeds the critical value determined by Eq. (2) or, if riprap is not present, the shear strength associated with soil and/or vegetation. Figure 6 presents the results of Rillgen2D for the rain event that occurred on Aug. 8, 2022, whose effects are illustrated in Fig. 1. The time series of runoff for this simulation was constructed using Eq. (1) and by interpolating the I15 and I60 values measured by four tipping-bucket rain gauges located across the study site. The first simulation used d50 = 10 cm, as specified in the as-built report for the rehabilitation. The value of Kr required to match the sediment yield measured by repeat photogrammetric survey (179 t/ ha) was determined by trial and error to be Kr = 0.14 s/m. Figure 6d compares the distribution of rill depths predicted by Rillgen2D (in red) to the observed distribution (in black) for this simulation. Figure 6 (a) Color map of the effective slope length, illustrating how zones of water flow convergence tend to be where rills/gullies form. Comparison of the erosion maps (b) observed and (c) predicted by Rillgen2D for the tailings embankment illustrated in Fig. 1. Probability distributions of observed and predicted rill/gully depths for the Rillgen2D cases that best match the observed sediment yield using (d) d50 = 10 cm and (e) d50 = 9 cm. Using d50 = 10 cm and Kr = 0.14 s/m, the percent of the study area that is rilled/gullied is underpredicted by Rillgen2D: that is, 5 percent versus the observed 6 percent. To determine whether a smaller value of d50 could better match the observed data, a Rillgen2D simulation using d50 = 9 cm and the value of Kr (0.06 s/m) that best matches the measured sediment yield was performed. This set of d50 and Kr values resulted in Rillgen2D predictions that precisely match the observations both in terms of the percent area rilled/gullied (6 percent) and sediment yield (179 t/ha). Allowing a modest variation in the value of d50 in this validation test is reasonable considering that d50 can be expected to vary by 10 percent due to construction vagaries and the likely redistribution of riprap since rehabilitation in 2007. The distribution of rill depths for the d50 = 9 cm and Kr = 0.06 s/m simulation matches the observed rill-depth distribution closely (Fig. 6e). In contrast, the distribution of rill depths for the d50 = 10 cm and Kr = 0.14 s/m case underpredicts rill depths for shallow rills and overpredicts rill depths for deeper rills (Fig. 6d). Figure 7 Results for the two Queensland study sites, comparing the observed erosion maps (c) and (e) to the Rillgen2D-predicted maps in (d) and (f) using best-fit parameters τc and Kr. Figure 7 illustrates the analogous results for two locations in Queensland without riprap, one with a continuous-slope design and one with a benched slope design with laterals and down drains. In theory, benched hillslopes with laterals and down drains minimize the likelihood of erosion because slope lengths are short relative to continuous-slope designs. In practice, however, such systems may be less resilient to extreme rain events because even more erosion can occur than in continuous-slope designs if the laterals and down drains do not convey water as intended. The best-fit parameter values for the Queensland site 1 are τc = 5 Pa and Kr = 0.0057 s/m, and and those for the Queensland site 2 are τc = 9 Pa and Kr = 0.0032 s/m. Qualitatively, the spatial distribution of rills predicted for both sites (Figs. 7d and 7f) are consistent with the patterns measured by repeat topographic survey (Figs. 7c and 7e). In particular, Rillgen2D successfully identifies areas of topographic convergence as particularly susceptible to rill erosion. Discussion and conclusions Although not documented in this article, we have carefully studied the statistics of the microtopography that results from modern construction/landforming practices and developed a workflow for simulating such topography (given prescribed construction tolerances) for input into Rillgen2D to aid in the design-selection process. Work remains to successfully apply Rillgen2D to the widest range of applications. The ability to predict the shear strength associated with different vegetation types and densities is limited, for example. We would appreciate hearing from anyone interested in applying Rillgen2D to understanding why existing mine-site rehabilitations did not work as intended, choosing the optimal rehabilitation design among several alternatives, and improving our ability as a community to parameterize how cover conditions translate into model parameters such as the critical shear stress for rill/gully initiation and the rill/gully erodibility coefficient. References Abt, S. R., Thornton, C. I., Scholl, B. A., and Bender, T. R., 2013, Evaluation of overtopping riprap design relationships. Journal of the American Water Resources Association, v. 49(4), pp. 923–937. https://doi.org/10.1111/jawr.12074 Coulthard, T. J., Neal, J. C., Bates, P. D., Ramirez, J., de Almeida, G. A. M., and Hancock, G. R., 2013, Integrating the LISFLOOD-FP 2D hydrodynamic model with the CAESAR model: implications for modelling landscape evolution. Earth Surface Processes and Landforms, v. 38, pp. 1897–1906. https://doi.org/10.1002/esp.3478 Eli, R. N., and Gray, D. D., 2008, Hydraulic performance of a steep single layer riprap drainage channel, Journal of Hydraulic Engineering, v. 134(11), pp. 1651–1655. https://doi. org/10.1061/(ASCE)0733-9429(2008)134:11(1651) Flanagan D. C., and Livingston, S. J., 1995, Water Erosion Prediction Project (WEPP) Version 95.7 User Summary, NSERL Report No. 11, https://www.ars.usda.gov/ ARSUserFiles/50201000/WEPP/usersum.pdf Freeman, G. T., 1991, Calculating catchment area with divergent flow based on a rectangular grid, Computers & Geosciences, v. 17, pp. 413– 422. https://doi.org/10.1016/0098-3004(91)90048-I Prein, A. F., Rasmussen, R. M., Ikeda, K., Liu, C., Clark, M. P., and Holland, G. J., 2017, The future intensification of hourly precipitation extremes, Nature Climate Change, v. 7, https:// doi.org/10.1038/nclimate3168 Slingerland, N. and Dressler, S., 2022, Evaluating construction tolerances and tailings dam shape for closure using the CAESARLisflood landscape evolution model, in Fourie, A.B., Tibbett, M. and Boggs, G. (eds.), Mine Closure 2022: 15th International Conference on Mine Closure, Australian Centre for Geomechanics, Perth, pp. 1117-1130. https://doi.org/10.36487/ACG_repo/2215_82 U.S. EPA, 2012, Closing Small Tribal Landfills and Open Dumps, U.S. EPA Report EPA-909-R-11-007. https://19january2017snapshot.epa.gov/www3/region9/waste/ tribal/pdf/small-dump-landfill-closure-guidance.pdf U.S. Nuclear Regulatory Commission, 2002, Design of Erosion Protection for Long-Term Stabilization, Final Report NUREG-1623. https://www.nrc.gov/docs/ML0225/ ML022530043.pdf Weeks, B. and Salfate, E., 2017, Closure and reclamation, in Guidelines for Mine Waste Dump and Stockpile Design, Hawley, P.M. & Cunning, J. (eds.), CRC Press

New model for predicting the erosional performance of rehabilitated mine sites

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Jon D. Pelletier, Nathan Abramson, Sriram Ananthanarayan, Satya Chataut, Dave Ludwick, Brendan P. Roddy

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