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 Deltares (former 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 intermediate 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.
A full description of equations and manual is given in Delft Cluster report Oeverstabiliteit bij verdieping Waterbodems, chapter 3 and in article Breaching in fine sand and turbidity currents.
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 account 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 initial Froude number = 2 and sand volumetric concentration = 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 anti-dunes and in dredging experiments for sand grain size 100 – 200 mu 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.
Recently it has been recognized that initiated by the dredger under certain conditions an erosive sand-water mixture density flow can be generated, finally resulting in a gradually developing slope failure. The slope failure initiation, which we call the breach, retrogrades upslope with a velocity that is related to the permeability of the sand. This explains the relatively long time of at least several hours in which the subaqueous slope failure manifests itself.
Het verschijnsel oeverval
Het Gat van Betlehem. Rond het zandgat staan overal borden met GEVAARLIJK TERREIN – OEVERVAL MOGELIJK. Op één zo’n paal zit een beul van een kraai, een gemeen monster dat klinkt als een oude schuurdeur. Oeverval is wat er twee jaar geleden gebeurde, op een nacht in de herfst, toen de weg naar het veer opeens weg was. Gewoon verdwenen. Bleek dat de zandzuigers van Betlehem Asfalt veel te lang op één plaats hadden gezogen, waardoor dat gat zichzelf was gaan vullen met het zand rondom. Dat gebeurt nu eenmaal als je een diep gat graaft, dan begint het zand rondom te rollen als het ware, naar het diepste punt toe. Zandhonger heet dat. Maar het Gat van Betlehem was zo diep dat het te weinig zand had om zichzelf te vullen, waardoor alles in de omgeving aan het schuiven raakte, want het moest ergens vandaan komen. Een heel stuk van de oever en de Lange Nek is zo het water in gegleden, en een stel bomen erachteraan. Dan sta je raar te kijken, als je daar ’s morgens langskomt en er is geen weg meer. De gas- en electriciteitsleidingen lagen los, lantaarnpalen lagen omver. Maar nu is het veilig zeggen ze, ze zuigen niet meer zo lang op één plek. Voor wie het gelooft.
Uit: Joe Speedboot (2005) van Tommy Wieringa.
Approval criterion for breach flow slide
- The advanced model for breach flow slide is only valid for silt, sand and gravel. If thin clay, loam or peat layers are present (< 0.5 m) they can be neglected and regarded as sand layers with low permeability (d50 and d15). The user has to evaluate the soil layers for input in this sense. In the case of thick clay layers the computation is only applied on the "sand clusters" in between the clay layers.
- If the calculated "critical initialization height h_0" is higher than (or equal to) the user-defined "Maximum allowable initialization height" (h_0, critical ≥ h_allowable) the slope stability assessment is "approved" or "succeeded".
- If h_0, critical < h_allowable, the assessment is "disapproved" or "failed" which means that the probability that a breach flow slide will occur is high. The maximum allowable initialization height on a certain location is a measure for the probability of a relatively small slope disturbance that could occur and trigger a breach flow slide, f.i. failure of a thin clay layer, liquefaction of a loose sand layer, effect of waves or man induced activities such as dredging.
