Skip to main content

Table 2 Scaling parameters and dimensionless scaling criteria (an example when the debris mass is 60 kg and the maximum substrate thickness is 19 cm)

From: An analysis of the entrainment effect of dry debris avalanches on loose bed materials

Variables

Model value

Scale ratio

Prototype value

ρ d (g/cm3)

2.00–2.25

1/1

2.00–2.25

θ (°)

41, 25

1/1

41, 25

g (m/s2)

9.8

1/1

9.8

M d (kg)

60

λ M  = (λ L )3 = (1/50)3

7.5 × 106

V d (m3)

0.027–0.030

λ V  = (λ L )3 = (1/50)3

(3.33–3.75) × 103

L (m)

5.1

λ L  = 1/50

255

H (m)

3.5

λ L  = 1/50

175

U (m/s)

1.5–3.5

λ U  = (λ L )1/2 = (1/50)1/2

10.6–24.7

H 0 (m)

0.19

λ L  = 1/50

9.5

H e (m)

0.075

λ L  = 1/50

3.75

D d (m)

0.04–0.08

λ D  = 1/20

0.8–1.6

D s (m)

0.002–0.005

λ D  = 1/20

0.04–0.10

  1. λ L is the length scale ratio, respectively; λ M and λ V are the scale ratio of landslide mass and volume; λ D is the scale ratio of debris avalanche’s particle diameter; λ U is the scale ratio of flow velocity; ρ d is the density of debris avalanche; θ is the terrain slope, which includes movement section (the former value) and accumulation section (the latter value); g is the gravity acceleration; M d and V d are the mass and volume of debris avalanche, respectively; L and H are the length and height in geometry dimension, respectively; U is the flow velocity; H 0 and H e are the initial thickness substrate and entrainment depth, respectively; D d and D s are the diameters of debris materials and substrate materials, respectively