An Assessment of Experimental Debris-Flow Scaling Relationships

Abstract

This research tests empirically the theoretical assumption that scaling issues make small-scale flume debris flows unrepresentative of natural debris flows. Here, results from a small-scale debris-flow flume (8 m long, 0.2 m wide) were compared with similar experiments carried out using a large-scale USGS flume (95 m long, 2 m wide) and field observations. In total, 40 experiments were carried out at different slope angles (29, 30, and 31) and different viscosities (from 0.001 Pa.s to 0.005 Pa.s) to provide a quantitative analysis of scaling relationships of debris flows of different sizes.
Dimensionless parameters, used for assessing debris-flow scaling, were typically within the range of natural debris flows: The Bagnold number was 73 – 1.9x104, the Savage number was 2x10-1 – 2.4x102, and the Friction number was 8x101 – 4.7x103. The Savage number was larger than expected based on USGS data, but this is attributed to the larger value for grain-size/flow-depth. Inherent variability of debris-flow behaviour was highlighted in the basic characteristics such as mean deposit length (150.30±44.96 cm), mean width (50.104.86 cm), and mean velocity (3.881.35 m s-1). Therefore, initial conditions are insufficient to make accurate predictions of debris-flow behaviour. There was considerable variation in flow behaviour with small changes in slope angle and viscosity. With each 1 degree change in slope, flow velocity increased by an average of 1.06 m s-1 and runout distance increased by an average of 16.35 cm. Small changes in viscosity (±0.002 Pa.s) altered the debris-flow rheology to such an extent that no lateral levees formed. Such effects can only be investigated in small-scale flumes which are free from the constraints of large flume models where initial conditions are difficult to vary.
Compared to natural and USGS flume debris flows, the reduced-scale debris-flow model used here provides results which broadly reproduce the behaviour of natural debris flows.