Analyses of the morphological changes with time, through denudation and siltation, in ditches of trapezoidal and triangular section

Abstract

Accounts in the archaeological literature from 1898 onwards of the degradation and siltation of archaeological ditches, generally in the Chalk, are first briefly reviewed. These are often supported by a series of successive measured sections, showing a tendency for a convex outward profile to develop in the degraded rock face. This was termed as ‘trumpet-shaped’ profile by Curwen (Antiquity, 4 (1930) 97), but no theoretical models were proposed. In 1866, Fisher had put forward a theoretical, two-dimensional analysis of the degradation of a single cliff of chalk (a quarry face near Lewes, Sussex) and this work was later generalised by Lehmann (Vierteljahrsschrift der Naturforschende Gesellschaft in Zürich, 78 (1933) 83). A variant of this approach was published by Bakker and Le Heux (Koninklijke Nederlandsche Akademie van Wetenschappen, B 50 (1947) 959, 1154). These theoretical models seem first to have been referred to in an archaeological context by Jewell (A Report of the Research Committee on Archaeological Field Experiments for the British Association for the Advancement of Science, London: The British Association for the Advancement of Science, 1963) in connection with the reporting of the meticulously executed and recorded Experimental Earthwork in the Chalk of Overton Down, Wiltshire. At that time, however, no attempt was made to integrate the field measurements with the available cliff degradation theories. This initiative was taken by Hutchinson (Earth Surf. Proc. Land., 23 (1998) 913) in order to check the validity of the Fisher–Lehmann and Bakker–Le Heux models. For both these models, good agreement between the actual and predicted buried rock profiles was found for a single cliff in chalk. It is clear that in most archaeological ditches, there is mutual interference between the screes developing from the opposite faces. This alters the boundary conditions of the above-mentioned cases of cliff degradation. In this paper, new theoretical, two-dimensional models are developed to cover the main situations found. These were identified from a review of archaeological ditches in southern England and France, and are described as follows: Type I—Wide ditches, with no interference between the opposite screes. Type II—Trapezoidal ditches, with eventual interference between the opposite screes. Type III—Triangular ditches, with immediate interference between the opposite screes. For Type I, the existing models for a single cliff apply. For Types II and III, new models are presented. It should be noted that for Type II, degradation follows initially the Type I model, but switches to Type II when the toes of the opposing screes meet. This produces a point of discontinuity in the buried rock profile where a change of gradient occurs, giving rise to a ‘double trumpet’ shape. This may generally be too subtle a feature to be readily identified archaeologically. For a bulking factor of 1.67 (i.e. c=0.4), the predicted buried rock profiles for Types I, II and III are compared for two specific ditches. Dimensionless plots summarising the relationships between initial ditch face angle, ditch base width and the ultimate amount of ditch crest recession are also given for these three cases. Profiles for other geometries and bulking factors may readily be determined using the equations provided. These make no allowance for the ingress of debris from outside the ditch, for example, from the slope of a rampart, which would further steepen the profiles.