A small‐scale field check on the Fisher–Lehmann and Bakker–Le Heux cliff degradation models

Abstract

The paper considers the development of initially straight, steep rock cliffs, bounded above and below by horizontal surfaces, in which basal debris removal is zero and degradation occurs by the weathering away of fine debris from the cliff face to form a scree at its foot. Of the slope degradation models available, the two earliest and simplest, namely the Fisher–Lehmann and the Bakker–Le Heux models, are regarded as most relevant and are briefly summarized. The main purpose of the paper is to check the predictions of these models, particularly with regard to the shape of the rock surface buried beneath the scree, against field data. Such data are sparse. It is concluded that the best field case currently available, despite its small scale, is that provided by the 1·75 m deep ditch which forms part of the experimental earthwork in the chalk on Overton Down, Wiltshire. The predictions of the two models are checked against field measurements made of the stage of degradation reached on each face of the ditch by July 1968, eight years after its excavation. These stages were influenced to different degrees by the presence of a surface turf layer. For the NE face, where this influence was least, the agreement of the predictions of the Fisher–Lehmann model with the actual rock profile is excellent and that of the Bakker–Le Heux model only marginally less so. For the SW face, as expected, the agreements are somewhat less close. These results may be to some extent fortuitous because of the influence of the turves and because the scree slopes tend to be concave rather than rectilinear, as assumed. Also, the free faces decline with time in a manner intermediate between those assumed in the two models. Larger scale field checks are clearly desirable before firm general conclusions can be drawn. Rates of crest recession for the Overton Down ditch are logarithmic with time after a very rapid initial phase. Extrapolation from the early phase of this logarithmic behaviour leads to a close estimate of the time needed for the slope to develop fully. The associated ultimate crest recession is also closely predicted by equations derived from both models. © 1998 John Wiley & Sons, Ltd.