Rockfall rebound: comparison of detailed field
experiments and alternative modelling approaches
Franck Bourrier,
1
* Frédéric Berger,
1
Pascal Tardif,
1
Luuk Dorren
2
and Oldrich Hungr
3
1
Cemagref, UR EMGR, 2 rue de la papeterie, BP 76, Saint Martin d’Heres, FR 38 402, France
2
Federal Office for the Environment FOEN, Hazard Prevention Division Bern, CH
3
University of British Columbia, Earth and Ocean Sciences, Vancouver, Canada
Received 15 June 2011; Revised 24 October 2011; Accepted 28 December 2011
*Correspondence to: Franck Bourrier, Cemagref, UR EMGR, 2 rue de la papeterie, BP 76, Saint Martin d’Heres, FR 38 402 France. E-mail: franck.bourrier@cemagref.fr
ABSTRACT: The accuracy of rockfall trajectory simulations mainly rests on the calculation of the rebound of fragments following
their impact on the slope. This paper is dedicated to the comparative analysis of two rebound modelling approaches currently used
in rockfall simulation using field experiments of single rebounds. The two approaches consist in either modelling the rock as a single
material point (lumped mass approach) or in explicitly accounting for the fragment shape (rigid body approach). A lumped mass
model accounting for the coupling between translational and rotational velocities and introducing a slope perturbation angle was
used. A rigid body approach modelling the rocks as rigid locally deformable (in the vicinity of the contact surface) assemblies of
spheres was chosen.
The comparative analysis of the rebound models shows that both of them are efficient with only a few parameters. The main
limitation of each approach are the calibration of the value of the slope perturbation (‘roughness’) angle, for the lumped mass
approach, and the estimation of the rock length and height from field geological and historical analyses, for the rigid body approach.
Finally, both rebound models require being improved in a pragmatic manner to better predict the rotational velocities distribution.
Copyright © 2012 John Wiley & Sons, Ltd.
Introduction
Rockfall hazard assessment is now routinely quantified using
rockfall trajectory simulation codes. Among the four basic
types of movement, flight, rebound, sliding, and rolling, most
often only the first two are considered quantitatively.
Modelling the process of impact and rebound using
physically consistent and field applicable approaches is one
of the most difficult tasks in developing these codes. One can
differentiate two general types among these approaches:
modelling the rock as a single material point or explicitly
accounting for the fragment shape. Both of these approaches
have been shown to be able to provide representative results
on different study sites (Labiouse et al., 2001; Guzzetti et al.,
2002; Dorren et al., 2006). However, in most cases, the
accuracy of the approaches is only evaluated by comparative
analysis of the stopping points of the rocks because the
kinematics of the passing rocks cannot easily be quantified
from analysis of past events. Consequently, calibration of
models does not generally include this data. Only a few
experiments have ever been done to evaluate the kinematic
parameters of falling rocks at specific locations using field
experiments (for example, Giani et al., 2004; Dorren et al.,
2006; esp3202-bib-0003Bourrier et al., 2009a). Even in the
few published detailed field studies most report only measure-
ments of the translational velocities of the rocks. Several
researchers made more complete measurements of fragment
rebound kinematics in laboratory experiments (Chau et al.,
1998, 2002; Labiouse and Heidenreich, 2009), but these are
difficult to extend to field processes due to the difficulties
encountered when defining similitude rules.
The aim of the study presented in this article is to extract from
well documented field experiments using video movies a
complete description of translational and rotational particle
kinematics before and after rebound and to use this data to
evaluate the capabilities for two different approaches to model
rockfall rebounds.
Study Site and Field Rockfall Experiments
The rockfall experimental site (Figure F1 1) is located in the ‘Forêt
Communale de Vaujany’ in France (lat. 45
12′, long. 6
3′) (Dorren
et al., 2006). The 100 m wide and 570 m long study site covers an
avalanche path denuded of trees, ranging in altitude from 1200 m
to 1400 m above sea level with a mean slope angle of 38
.
The experiments consisted of releasing rocks down the slope
using an excavator. The sizes and shapes of the rock particles
were carefully chosen. Priority was given to rocks having
nearly parallelopiped shapes and volumes approximately equal
to 1.0 m
3
. Each rock was measured along its three dominant
axes and its volume was estimated from these data. The mean
volume of the rocks was 0.8 m
3
and the standard deviation
0.15 m
3
. Five digital cameras installed along the slope were
used to record rockfall trajectories. Additional details on the
experiments can be found in Dorren et al. (2006).
EARTH SURFACE PROCESSES AND LANDFORMS
Earth Surf. Process. Landforms (2012)
Copyright © 2012 John Wiley & Sons, Ltd.
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/esp.3202
Journal Code Article ID Dispatch: 19.01.12 CE:
E S P 3 2 0 2 No. of Pages: 10 ME:
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