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Description computational model
The applied model for the turbidity current HMBreach is a 1DH 2-layer model for stationary non-uniform depth averaged flow. It was developed at WL | Delft Hydraulics for dredging applications and validated with flume tests. The slope development and stability during sand suction (“breaching”) in specific sand layers from a bore hole is predicted. The model was applied to turbidity currents in submarine canyons (Scripps Canyon) in collaboration with University of Utrecht. Ref. [Mastbergen & Van Den Berg, 2003] The model describes the supercritical erosive 2-layer turbidity flow over a sand bed with prescribed properties from bore holes for example, for densiometric Froude numbers between 1 and 2.8. Subcritical steady uniform turbidity flow may occur on flat downslope areas with no more erosion and entrainment, but is not described with the model. An indermediate mixing layer is defined generating internal friction and entrainment of ambient water. On extremely steep slopes Froude numbers will be too high and the intermediate layer will become unstable, complete mixing of the sublayer will result. The required upper boundary is defined by a slowly retrograding “breach”: a local small and steep slope irregularity, gradually retrograding upslope generating a small but steady sandflow that may transform into an erosive and turbulent sand-water density flow. Actually the model is quasi-stationary taking into account the regression velocity that is defined by the sand properties. The erosion is described as a sediment flux at the bed with a semi-empirical model as a function of bed shear stress, slope and sand properties. This model was calibrated with experiments in a tilting flume with fine 120 mu sand resulting in erosion velocities measured perpendicular to the bed up to 5 mm/s with flow velocities up to 2.5 m/s, Ref. [Winterwerp et al, 1992]. The model is derived for high volumetric sediment concentrations taking into accoutn the effect of density differences on the momentum equation (no Boussinnesq approximation applied). Non-steady effects such as TC head and tail development are not described, nor vertical development or development in width, curves etc. For the input for the initial conditions is taken a breach of 1 m height with retrogression velocity 1 mm/s and an intial Froude number = 2 and sand volumetric concentraion = 12%. With these numbers the initial velocity, flow depth and sand transport rate per unit width are defined. The influence of the upper boundary condition is minimal as long as it is sufficient to produce an initial supercritical suspended sand flow. If the flow is capable of erosion, given sediment properties, slope and height, flow acceleration will result and erosion will increase. If not the flow will extinct, so a threshold value for TC initiation is required. A semi – empirical Erosion model / formula is applied see [Winterwerp et al, 1992] and the improved and more general version see [Mastbergen and Van den Berg, 2003] with permeability / d15 that defines the net bed erosion velocity v erosion . This expression includes hindered erosion and hindered settling effects and are validated with flume measurements in Oeverstabiliteit bij verdieping waterbodems DC 04 43 11 september 2009 Rekenmodel HMBreach Deltares 1 9 anti-dunes and in dredging experiments for sand grain size 100 – 200 ?m occuring only during short time. The maximum erosion rate is restricted due to high volumetric concentration with a supplemental empirical formula see [Winterwerp et al, 1992]. The critical value for erosion and the power are different, so computations were performed with both erosion model options.
Approval criterion for breaching
If the calculated "Decisive critical initialization height h_0" is higher than or (equal to) the used-defined "Expected maximum initialization height h_expected (h_0 >= h_expected) the judgment is "disapproved".
If h_0 < h_expected, the judgment is "approved"
