Abstract Displacement waves (or tsunamis) generated by sub-aerial landslides cause damage along shorelines over long distances, making run-up assessment a crucial component of landslide risk analysis. Although site-specific modelling provides important insight into the behaviour of potential waves, more general approaches using limited input parameters are necessary for preliminary assessments. We use a catalogue of landslide-generated displacement waves to develop semi-empirical relationships linking displacement wave run-up ( R in metres) to distance from landslide impact ( x in kilometres) and to landslide volume ( V in millions of cubic metres). For individual events, run-up decreases with distance according to power laws. Consideration of ten events demonstrates that run-up increases with landslide volume, also according to a power law. Combining these relationships gives the SPLASH equation: R = a V b x c , with best-fitted parameters a = 18.093, b = 0.57110 and c = −0.74189. The 95% prediction interval between the calculated and measured run-up values is 2.58, meaning that 5% of the measured run-up heights exceed the predicted value by a factor of 2.58 or more. This relatively large error is explained by local amplifications of wave height and run-up. Comparisons with other displacement wave models show that the SPLASH equation is a valuable tool for the first-stage preliminary hazard and risk assessment for unstable rock slopes above water bodies.

Abstract More than 250 rock slope failures have occurred in Sogn and Fjordane County in historical times. So far, 28 sites are known where open cracks indicate that rock slope failures may occur in the future. Detailed structural and geomorphological analyses of these sites have been conducted, and form the basis for an evaluation and comparison of the unstable rock slopes. Four of these sites are described in detail herein. The main characteristics for rock slope instabilities in Sogn and Fjordane are: (1) a preferred location within relatively weak rock units, such as phyllites and weathered mafic gneisses; and (2) the development of most instabilities at convex slope breaks, which are evident as knick-points in the slope profile. Sogn and Fjordane is compared with other Norwegian regions, particularly Møre and Romsdal County, with respect to the spatial distribution of past and current rock slope instabilities. Sogn and Fjordane shows the greatest number of historical slope failures, whereas in Møre and Romsdal a larger amount of potential instabilities is observed. We propose that the larger amount of unstable rock slopes in Møre and Romsdal may be controlled by a locally high gradient of ongoing post-glacial uplift and a higher rate of neotectonic activity.

Abstract Åknes is an active complex large rockslide of approximately 30–40 Mm 3 located within the Proterozoic gneisses of western Norway. The observed surface displacements indicate that this rockslide is divided into several blocks moving in different directions at velocities of between 3 and 10 cm year −1 . Because of regional safety issues and economic interests this rockslide has been extensively monitored since 2004. The understanding of the deformation mechanism is crucial for the implementation of a viable monitoring system. Detailed field investigations and the analysis of a digital elevation model (DEM) indicate that the movements and the block geometry are controlled by the main schistosity (S 1 ) in gneisses, folds, joints and regional faults. Such complex slope deformations use pre-existing structures, but also result in new failure surfaces and deformation zones, like preferential rupture in fold-hinge zones. Our interpretation provides a consistent conceptual three-dimensional (3D) model for the movements measured by various methods that is crucial for numerical stability modelling. In addition, this reinterpretation of the morphology confirms that in the past several rockslides occurred from the Åknes slope. They may be related to scars propagating along the vertical foliation in folds hinges. Finally, a model of the evolution of the Åknes slope is presented.