Author(s)

L. Sarno, R. Martino &M. N. Papa

Abstract

The purpose of this paper is to simulate a laminar mud flow confined in a narrow rectangular open channel. The flow bed is an erodible layer made up of the same material involved in the flow; the equilibrium condition between the moving and non-moving layer is assumed. The mud mixture under study is ruled by the Herschel–Bulkley’s (H–B) shear thickening rheological law. It is supposed that the local volumetric concentration is linearly increasing with the depth and it is constantly equal to its maximum value where the local velocity is smaller than a threshold value. Relations among rheological parameters and concentration have been obtained through laboratory rheometric tests. Turbulence effects and Coulombian stresses have been ignored. The momentum equation has to be integrated along the flow cross section for the flow velocity to be obtained. Unfortunately, it is very difficult to integrate this equation using H–B rheological law, since there are different stress functions and it is not possible to know a priori the sub-domains of them (plug, non-plug and bed regions). In the present work a modified rheological law, continuous over the whole domain of integration is employed and the momentum equation is numerically integrated. This modified law has been obtained by adding a constant correcting the denominator in the H–B stress functions. Therefore, there are no longer any dead zones or plug regions. However it is noteworthy that, using a small constant, the model produces a good simulation of plug and dead zones: i.e. the velocity gradient is very small there. The mathematical model has two parameters: maximum concentration and threshold velocity. These parameters have been adjusted by back-analysis with measurements from laboratory flume experiments in uniform flow conditions. Keywords: mud flow, Herschel–Bulkley rheological law, equilibrium, plug.

Keywords

mud flow, Herschel–Bulkley rheological law, equilibrium, plug.