Large scale rockfall experiments require time and resources not often available. While ditches are often designed based on empirically-determined criteria (Ritchie, 1963; Pierson et al., 2001), as technologies have advanced, computer-based trajectory models have become a standard tool for rockfall assessment and barrier design (Wyllie, 2015).
a)
b)
X Y Z X Y Z21
Until the early 2000s, modeling rockfall down a slope has been conducted using two dimensional (2D) models of representative slope profiles (Figure 2.11). Programs such as the Colorado Rockfall Simulation Program (CRSP), available from the Colorado Geological Survey, and RocFall from RocScience use the Newtonian laws of motion and acceleration due to gravity to predict the motion and related velocities and energies of falling rock.
Figure 2.11: 2D and 3D trajectory models.
A 2D rockfall trajectory model as part of Geobrugg's barrier design process (left, from Hess et al., 2010), and a 3-D analysis of a spherical falling rock conducted in RAMMS (right, after Arpin and Arndt, 2016).
Three dimensional (3D) rockfall models have been available since the late 1980s (Guzzetti et al. 2002; Lan et al., 2007; Turner and Duffy, 2012b). However, these are designed for and typically applied at larger scales (Guzzetti et al., 2002). Examples of these models include multiple kilometer stretches of railway in Canada (Lan et al., 2007, Lan et al., 2010) and roadway in
Malaysia (Fanos et al., 2016), a 20 km2 valley in Italy (Guzzetti et al., 2002), and large areas around
Christchurch, New Zealand (Geovert, 2012, Heron et al., 2014). These programs use geospatial elevation data, typically digital elevation models (DEMs), to model terrain (Crosta et al., 2015). Many software options exist, such as CRSP-3D from the Federal Highway Administration and
22
RAMMS from the WSL Institute, but as of 2018 no single 3D modeling software appears to be recognized as an industry standard.
In general, 3D models are considered “more rigorous” than 2D models (Arpin and Arndt, 2016). Because rocks move in 3D space, the slope profiles used in 2D modeling may not accurately capture the actual path of the falling rocks. Wyllie (2015) states that 2D modeled trajectories tend to predict higher bounce heights than are actually observed, leading to over-designed protective systems. Pierson et al. (2001) recognized that 2D modeling may over- or underestimate runout distances. However, as part of a study that included nearly 3,000 experimental rockfalls, they also concluded that 2D simulations are sufficiently comparable to experimental data to be useful as a design tool.
Arpin and Arndt (2010) concluded, in a comparison of 2D and 3D models, that benefits and limitations exist for each model type. As shown in Table 2.2, they compared rockfall velocities of two rock shapes modeled with the 2D program CRSP-2D and the 3D programs CRSP-3D and RAMMS. The average velocities from the two 3D programs are comparable for the spherical shape, while the 2D program predicts slightly faster average velocities. The maximum velocities are similar for the CRSP-2D and 3D programs and much lower than the RAMMS output. The results vary significantly for the block shape, and the CRSP-3D results for the block were excluded because the numbers were deemed unreasonable.
For modeled rockfall energy and bounce height, Arpin and Arndt (2010) found that the average energies and heights were comparable between the CRSP-2D and the 3D RAMMS programs for a spherical shape, but the maximum values were very different, and CRSP-3D results were again excluded due to unreliability. The RAMMS 3D model produced both higher energies and bounce heights than the 2D model for the block shape. The higher maximum values from the
23
RAMMs output in all of the measured parameters are due to a single modeled trajectory that launched from a 3D feature of the slope. This demonstrates the ability of 3D models to capture slope features that may be missed in a 2D slope profile. Arpin and Arndt (2010) concluded that the 2D results were no less reliable than the 3D results, despite the relative simplicity of the models, and that site-specific model calibrations and modeled rock geometries were the most significant influences on model reliability.
Table 2.2: Rockfall velocities modeled using three modeling programs (from Arpin and Arndt, 2010).
Program Rock Rocks Passing Analysis Point
Avg. Velocity Max. Velocity (ft/s) (m/s) (ft/s) (m/s) CRSP-2D Sphere 96 56.7 17.3 91.2 27.8 CRSP-3D 79 38.1 11.6 72.2 22.0 RAMMS 97 41.2 12.6 170.5 52.0 CRSP-2D Block 94 54.3 16.5 80.4 24.5 RAMMS 27 81.6 24.9 161.9 49.4
2D modeling software is readily available, relatively inexpensive or even free (CRSP-2D), and requires significantly less data and software expertise to run than GIS-based models. With calibration using site-specific model parameters, they have been found to be sufficiently accurate for structural design (Turner and Duffy, 2012b). 2D models are still used to calculate rockfall velocities and energies even when 3D modeling is performed (Geovert, 2012, Heron et al., 2014), and programs such as RocFall and CRSP are still commonly in use by state Departments of Transportation and researchers (Kemeny, 2015; Thomas, 2018; Turner and Duffy, 2012b).
Natural rockfall occurs on heterogeneous slopes with complex topography. The assumptions necessary to mathematically model a falling, bouncing, sliding object greatly simplify the system. All modeling methods should ideally be calibrated with observed and experimental data from the area of interest to best represent realistic scenarios. However, this is often not possible, due to the limited accessibility of hazardous slopes and busy transportation pathways,
24
potentially very large areas of interest, and time and funding constraints. Therefore, assumptions regarding rock and slope properties are often made based on existing experimental data from other researchers at other sites. 2D rockfall modeling requires a representative 2D elevation profile of the slope of interest, information on the slope materials and their ability to absorb energy during impact, and the mass of the rocks to be modeled.