Path topography

As discussed in Section 3.2.2.1, the energy dissipation and subsequent run-out of rock avalanches is strongly influenced by topography, leading to a range of depositional plan forms and surface morphologies (Okura et al., 2003). In most cases the model is able to simulate the mobility of the rock avalanches (as quantified by the apparent coefficient of friction, H/L) well, and residuals taken from the RMA fit are randomly distributed (Fig. 6.11b). However, the mobility of events 3, 6 and 15 is considerably overestimated (i.e. the modelled H/L underestimates the observed H/L; Fig. 6.14b). These events are characterised by relatively short run-out distances (ca. 1500-2100 m) and stall above topographic benches or on an alluvial fan below, having travelled over deformable and erodible substrates (Fig. 6.1; Table 6.1). In these cases, the model is not simulating the processes involved in and effects of rock avalanche emplacement across different substrates (Section 3.3). In reality, the energy required to mobilise the substrate may

Figure 6.13) Scatter plot matrix of the normalised index, , of the bulk external characteristics (run-out, apparent

coefficient of friction, surface area and lateral extent) against a series of geometric characteristics (failure volume, drop height, drop zone angle and concavity). A number of relationships are apparent, particularly the influence of volume on run-out and of slope concavity on run-out, surface area and lateral extent.

Figure 6.14) Case order plots of the normalised index of a) rock avalanche run-out, b) apparent coefficient of friction, H/L, c) lateral extent at toe, and d) surface area, for all 20 cases. The events are ordered 1-20, E-W across the site. Supporting

data may be found in Appendix J.

have been too great and caused the avalanche mass to ‘sink’ into the alluvial fan or it may have been bulldozed into mounds (Dufresne et al., 2010). In both cases, this would have impeded avalanche momentum/motion and caused a decrease in mobility.

The concavity of the path topography also influences the ability of the model to simulate spreading, with events emplaced across more concave surfaces (concavity index 0.7) tending to spread to a greater extent than observed (Fig. 6.13). For those events emplaced across fully 3D terrain, the simulated depth distributions demonstrate evidence of topographically steered flow as well as upslope thinning, hole filling and pinching out at topographic highs (Figs. 6.9 and 6.10). This suggests that the model can plausibly account for the observed morphology of a series of deposits emplaced by a range of event types and is sensitive to the local topography.

Difficulties are encountered when simulating the spreading of relatively short run-out events at topographic benches and onto alluvial fans, where the model considerably underestimates the lateral extent of a number of deposits (events 2, 3, 5, 6, 7, and 17; Fig. 6.14c). Conversely, lateral spreading is overestimated where, in reality, the flow has been laterally confined somewhere along its run-out path (events 11, 12 and 20). In these cases the rock avalanches were simulated across contour-parallel 3D terrain, which does not impose the 3D confinement effects of topography on the rock avalanche. This is also the case when considering areas of deposition, which are most poorly simulated when the event in question was emplaced across contour-parallel 3D terrain and for events that were partially confined, such as events 19 and 20 ( = +56% and +83%, respectively; Fig. 6.14d; Table 6.3). These results attest to the importance of using realistic terrain models, as the dissipation of mechanical energy from the rock avalanche, and thereby its mobility and spreading behaviour, is more accurately simulated (Section 3.2.2.1; Nicoletti and Sorriso-Valvo, 1991; McDougall and Hungr, 2004).

6.5 Summary

assuming either a constant dynamic friction or a Voellmy rheology fail to reproduce the observed event characteristics and deposit distribution at Paatuut (e.g. McEwan and Malin, 1989; Evans et al., 2001; Crosta et al., 2004; Sheridan et al., 2005; Pirulli, 2009; Kelfoun, 2011; Sosio et al., 2012; see Section 6.2). Although these models can account crudely for the observed run-out, the basal friction angles necessary to generate this run-out result in a long duration of simulated failure with deposition concentrated in the proximal reaches of the run-out path. The best-fit simulation of the Paatuut event instead assumes a plastic rheology with a velocity-dependent law (T0 = 250

kPa, ξ = 0.01). This simulates the run-out of the rock avalanche to within ±0.3% of the observed run-out, which is well within the margin of measurement error (±2%; Table 5.2, p 42). This rheology is therefore successful in reproducing the event kinematics, deposit mass distribution and morphology to justify the assumption that it constitutes a first order representation of the dominant features of the emplacement dynamics.

19 other events are simulated using the best-fit rheological calibration obtained by back- analysis of the Paatuut event (Section 6.3). For those simulated across fully 3D terrain, the model is able to replicate the morphology and distribution of mass in the resultant deposits very well (Section 6.3.1). Depositional features observed in the observed and modelled deposits developed in response to the underlying topography, suggesting that the model can plausibly account for the observed morphology of a series of deposits emplaced by a range of event types. The bulk external characteristics of the 20 cases are simulated with varying degrees of success. The run-out of 80% of the cases was simulated within an error of ±14%.

The performance of the model is sensitive to a range of topographic and geometric factors (Section 6.4). In particular, difficulties in correctly simulating the observed run-out and other bulk external characteristics of the rock avalanches are encountered when:

1) The failure volume of the simulated event is small, as the constant retarding stress acting at the base of the avalanche is applied to a greater proportion of its total surface area. This means that a greater proportion of the source mass remains stalled in the source area and therefore that the rock avalanche is simulated to run out over a shorter distance. 2) The event in question is emplaced across contour-parallel terrain, which cannot fully account for longitudinal and transverse confinement of the rock avalanche mass or topographic junctions that act to block, confine or diverge flow.

3) The rock avalanche encounters a change in substrate along its run-out path and the model is unable to simulate the associated changes in avalanche mobility.

These exercises show encouraging results in the ability of the model to simulate a series of events using a single set of parameters obtained by back-analysis of the Paatuut event alone. The results demonstrate that a plastic rheology with a velocity-dependent law describes the emplacement of these events and the resultant deposit more accurately than any other simple rheological law. The implications of this for our process understanding and the subsequent modelling of such events will be discussed in Chapter 7.

Chapter 7

Discussion

As discussed in Chapter 4, accurately simulating the emplacement dynamics of rock avalanches is complicated by the anisotropic nature of the materials involved, as well as the complex interactions that occur during their propagation across steep and irregular terrain (Manzella and Labiouse, 2013). Depth-averaging in continuum dynamic models such as VolcFlow (Kelfoun and Druitt, 2005) assumes that the rheology of the flow can be represented as a single term that expresses the frictional forces interacting between the flow and basal path (Section 4.2; Luna et al., 2013). However, the common lack of pre-, syn- and post-failure observations of rock avalanches has meant that the majority of numerical modelling studies have focussed on replicating the dynamics of a single, well-constrained event, and fail to consider the wider utility and sensitivity of the rheological calibration obtained. A series of 20 large rock avalanche deposits in Vaigat, West Greenland, has presented the unique opportunity to undertake a case-specific calibration and investigate the validity of applying the same parameters to other events emplaced in similar conditions (Chapter 5). The results presented in Chapter 6 are now discussed with regards to the use of simple rheological laws in numerical run-out models (Section 7.1) and their implications for model requirements (Section 7.2). The implications of these results for forward modelling and for the incorporation of numerical run-out models into a risk assessment framework is then discussed (Sections 7.3 and 7.4), placing particular emphasis on their implications for tsunami hazard and risk assessments (Section 7.5).

7.1 The suitability of simple rheological laws for simulating rock