SpaceMika

For debris flows, the Voellmy model typically produces better simulations, particularly regarding velocities along the path. Based on back-analyses of debris flows worldwide using DAN, calibrated values of f typically range between 0.07 and 0.2, while values of ξ range between 100 and 600 m/s2 (Hungr et al. 1998; Ayotte and Hungr 2000; Jakob et al. 2000; Hürlimann et al. 2003; Revellino et al. 2004; Bertolo and Wieczorek 2005). In the cases presented here, debris flows can be simulated well using the Voellmy rheology, although the parameters are less constrained than avalanches with an f ranging from 0.08 to 0.1 and ξ ranging from 200 to 1,000 m/s².

From Geohazards IV paper:

The frictional rheology can be used for dry friction in the source area, with a transition to the Voellmy model where significant entrainment of saturated soil begins. A similar scheme was used for the coal waste flow slides. A switch from frictional to Voellmy models is often required to produce satisfactory simulation when events initiate on open slopes and then become channelized (Ayotte and Hungr 2000, Hungr and Evans 2004).

From Geohazards IV paper:

For rock avalanches, the frictional resistance model typically produces reasonable simulations of the observed runout distance. Hungr and Evans (1996) and Pirulli (2005) used DAN-W to back-analyze 34 different rock avalanches using the frictional resistance model. The calibrated φb values ranged between 8º and 23º with a mean of 16º. For the Canadian cases, the best result with the frictional rheology falls within this range with and φb of 20º.

Hungr and Evans (1996) also noted that the Voellmy rheology produced consistently good debris distribution, velocity profile, and runout distance for f values between 0.03 and 0.24 and ξ between 100 and 1000 m/s2. Only events involving runout across a glacier or substantial entrainment combined with channelization had calibrated coefficients less than 0.1. For the Canadian cases, the best results were obtained with Voellmy as the dominant rheology, with f between 0.02-0.15 and ξ between 250-500 m/s².

Taken from Geohazards IV paper, requires re-write & expansion for thesis

Rheology

Both DAN models use simple homogeneous hypothetical materials that simulate the bulk behaviour of complex heterogeneous real landslide materials (Hungr 1995). The properties of the hypothetical materials must be assessed through back-analyses of real cases. For our back-analyses of rapid landslides we use frictional, Voellmy, and Bingham rheologies.

The Frictional rheology

In the frictional rheology, the basal shear stress τzx opposing motion is expressed as:

τzx = – σz tanφb [1]

where σz is the total bed-normal stress at the base of the flow and φb is the bulk basal friction angle (with tan φb = (1-ru) tan φ, where ru is the pore pressure ratio and φ is the dynamic basal friction angle). Overestimation of velocities and often unrealistic forward-tapering deposits are characteristics of the frictional model. (McDougall 2006)

The Voellmy rheology

The Voellmy rheology combines frictional and turbulent models such that

τzx = σz f + ρgν²/ξ [2]

where f is the frictional coefficient, ρ is the material density, g is gravitational acceleration, ν is the depth-averaged flow velocity, and ξ is the turbulence term. In comparison to the frictional model, the Voellmy model typically produces better simulations of velocity and deposit distribution.

The Bingham rheology

The Bingham resistance model combines plastic and viscous behaviour. The shear resistance is determined by solving the following cubic equation:

τzx³ + 3 (τyeild/2 + μBingham νxh) τzx² – τyeild³/2 = 0 [3]

where τyeild is the Bingham yield stress and μBingham is the Bingham viscosity. The Bingham model may produce better simulations of events involving clayey or highly plasticity materials.

The volume of this landslide is a bit strange to work with. The published volume does not match the figures in the same paper — even at the most conservative usage of the figures paired with bulking the volume, the volume differs by at least a factor of two. I know, x2 is pretty much negligible in most physics (it’s within an order of magnitude!), but it’s pretty important when calibrating a numerical model.

My current theory is that two different volumes are being used. This event had a large amount of material slump just a short distance, and a smaller volume run out a longer distance. In the figures, the two sets of material are differentiated. I think that if I treat the large slump as part of the path (exclude it from the volume) and just run the smaller volume on top of it, I should get the correct volume.

But this is exactly why papers should list exactly how it is they’re getting the volumes they’re using! Is it from field investigations? Air photos? Measuring what, exactly? It’s important!

The material for this event is unusual: it’s a loess slide. If I use the volumes from the figures and calibrate to the correct debris distribution (including the large pile-up at the base of the main scarp), it seems like a slightly runnier material than rock avalanches. Tentatively, I’m placing it as a Voellmy fluid with the parameters 0.15, 500.