Fig. 2 Orthophotos of the foot of mountain areas used for grain size of
fallen blocks analysis (samples of sites 2 and 5).
Rock mass strength is a very difficult characteristics to be defined in
a large area because of lack of suitable approaches and its inherent
geology uncertainty (Hoek, 1983; Gudmundsson, 2011). Some studies (Hoek,
1994; Schmidt & Montgomery,1995; Evans et al., 1997; Shipton et al.,
2002; Crosta et al., 2014) have tried to solve the problem. Various
authors tackled the subject from a geomorphological and geomechanical
point of view. Schmidt & Montgomery (1995) proposed an approach to
define rock mass strength by analyzing relief and slope angle based on
back analysis. Crosta et al. (2014) adopted an advanced geomechanical
modeling approach to characterize rock masses on Mars starting from the
distribution of landslides. Based on data of slope and relief of
historical rockfall scars and reference to previous studies
(Schmidt & Montgomery, 1995;
Burbank et al., 1996; Montgomery & Brandon,2002; Crosta et al., 2014;
DiBiase et al,2018), the rock mass strength of bedrock was
back-calculated by the Culmann method under the precondition that
bedrock relief is controlled by
rock strength in the study area. When the present relief of bedrock
areas is larger than the limit relief, the bedrock is prone to generate
rockfalls.
Using data from helicopter-based remote sensing imagery and a DEM of 10
m resolution of the complete study area, a total of 407 historical
rockfalls inventory including 284 rockfalls scars on bedrocks (Fig.1 and
Fig.3) and 123 rockfalls deposits at toe of slopes were identified (Fig.
1). 284 rockfall scars were identified based on the fresh bedrock color
left on the scars (Fig.4). 123 rockfalls deposits at the foot of slopes
were identified based on the shape of deposit (e.g. pyramid) and
identifiable rockfall blocks (e.g. meters) left on the deposits (Fig.4).
Because 284 rockfalls scars were identified on bedrocks with steep
slope, it is not easy or even impossible to track their deposits.
However, from the viewpoint of statistics rather than for a specific
rockfall concerned, we combined the 284 rockfalls scars on bedrocks and
123 rockfalls deposits together to interpolate the rockfall density map.
By the calculation of kernel density tool in ArcMap, we interpolated the
rockfall density map in a search radius of 2.5 km considering the
conditions of width of valley and slopes on site and rockfall size
(Fig.1). By ArcMap, we extracted the value of rockfall density along the
A-A profile in Fig.1, and created the value of rockfall density vs
distance from fault core in Fig.8.
We measured the relief at scar sites which were considered as limit
relief thresholds by ArcMap. We first extracted the maximum and minimum
elevation of rockfall scars by ArcMap. Then the limit relief rockfall
scar was calculated by Eq. (2). Meanwhile, we calculated mean slope of
the rockfall scar area by ArcMap. Lastly, we calculated limit relief
Hi and hillslope gradient (β) of all rockfalls scars.
\(\text{\ H}_{i}=H_{\text{imax}}-H_{\text{imin}}\) (2)
where i is the number of rockfall scar, Himax and
Himin are the maximum and minimum elevations of rockfall
scar i.
The Culmann’s two-dimensional slope stability model based on principles
of limit-equilibrium was used to back-calculate the rock mass strength
at the landscape scale, which predicts a bounding relationship between
hillslope gradient (β) and relief such that the maximum hillslope height
(Hc) is given by (Culmann, 1875).
\(H_{c}=\frac{4C}{\text{ρg}}\frac{\text{sinβcosφ}}{[1-\cos\left(\beta-\varphi\right)]}\)(3)
where c is cohesion, and φ is the internal friction angle.