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 dHeres, 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 dHeres, 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 Vaujanyin 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: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140