W. Brian Dade

LONG-RUNOUT ROCKFALLS

Large rockfalls and debris avalanches constitute spectacular geologic hazards. A physical basis for the prediction of the extent of runout of such transport events has remained elusive. We consider the simplest case in which a mass M of debris and loose rock, having fallen from a height H , is subjected to a constant, overall resisting shear stress τ during runout. A prediction for such behavior is that the area overrun by an avalanche is proportional to ( gMH /τ) 2/3 , where the coefficient of proportionality is near unity and a function of the geometry of the “footprint” of the avalanche deposit. This scaling results in a good collapse of the data for a wide range of terrestrial and extraterrestrial phenomena and implies a value of τ in the range 10–100 kPa. Such shear stress values are comparable to measures of the yield strength of unconfined, dry debris obtained by other means. The approach developed here does not give a detailed description of rockfall motion, but provides new insight for attempts to delineate the mechanisms that contribute to the mobility of rockfalls and other densely concentrated flows of geophysical interest.

Fine-Sediment Deposition from Gravity Surges on Uniform Slopes

ABSTRACT The propagation of and the deposition from a noneroding, turbulent gravity surge are described by a simple model for a two-dimensional, well-mixed buoyant cloud of suspended particles moving down an inclined surface. The model includes the effects of entrainment of ambient seawater, deposition of suspended sediment, seafloor friction, and slope. Our results are applicable to large, decelerating turbidity currents and their distal deposits on uniform slopes in lakes and the sea. The scaling arguments that emerge from our analysis, moreover, have important ramifications for the design and interpretation of laboratory analogs of these phenomena. General solutions are obtained to the coupled equations that describe the evolution of momentum, total mass, and particulate mass of a surge. The solutions vary on two horizontal length scales: xo, beyond which the behavior of the surge is independent of the initial momentum and shape; and xr, beyond which the driving negative buoyancy of the surge is lost due to particle settling. For fine particles whose settling velocity is much less than the forward propagation speed of the surge, the suspension is well mixed and xo << xr, The deposit thickness diminishes as the inverse square root of the downstream distance x when xo << x << xr, and then diminishes exponentially with downstream distance as x approaches and exceeds xr. The length of a surge deposit scales with xr = kbosin/aws(cos)2, where k is the assumed constant aspect ratio of the surge, bo is the initial buoyancy per unit width at the point of issue onto a slope of constant angle ,a is the ambient density, ws is the average settling velocity of the suspended particles, and = 6 + 8CD/ incorporates the ratio of the constant coefficients of drag CD and fluid entrainment . Extension of our model to the case of two particle sizes indicates that, even for very poorly sorted suspensions, the estimate for the length of a surge deposit xr is valid if ws is defined as the volume-averaged settling velocity of the initial suspension at xo. The ratio of coarse to fine material in model deposits generated from initially poorly sorted suspensions can diminish dramatically in the downstream direction, however, due to differential rates of gravitational settling.

Predicting the geometry of channelized deep-sea turbidites

Analytical relationships between the dynamic properties of a deposit-forming turbidity current propagating across a sea floor with small slope and the geometry of the resulting deposit have been confirmed experimentally for a wide range of particle sizes, initial concentrations, and volumes of the driving suspension. These simple expressions provide a basis for inferring the dynamics of natural flows from their deposits. We surmise that the turbidity current responsible for depositing the Black Shell turbidite in the northwestern Atlantic Ocean had an initial sediment concentration on the order of 100 g of silt per litre and a volume on the order of 1000 km 3 .

Runout and fine-sediment deposits of axisymmetric turbidity currents

We develop a model that describes the runout behavior and resulting deposit of a radially spreading, suspension-driven gravity current on a surface of negligible slope. Our analysis considers the separate cases of constant-volume and constant-flux sources. It incorporates expressions for the conservation of volume, a Froude number condition at the current front, and the evolution of the driving suspension due to settling of particles to the underlying bed. The model captures the key features of a range of experimental observations. The analysis also provides important scaling relationships between the geometry of a deposit and the source conditions for the deposit-forming flow, as well as explicit expressions for flow speed and deposit thickness as functions of radial distance from the source. Among the results of our study we find that, in the absence of information regarding flow history, the geometries of relatively well-sorted deposits generated by flows with source conditions of constant volume or constant flux are virtually indistinguishable. The results of our analysis can be used by geologists in the interpretation of some geologically important gravity-surge deposits. Using our analytical results, we consider three previously studied, radially symmetric turbidites of the Hispaniola-Caicos basin in the western Atlantic Ocean. From gross geometry and grain size of the turbidites alone we estimate for the respective deposit-forming events that upon entry into the basin the initial sediment concentrations were approximately 3% by volume and the total volumes were roughly between 30 km 3 and 100 kn1 3 . Each of the suspension-driven flows is inferred to have spread into the basin with a characteristic speed of 3-5 m s -1 , and reached its ultimate runout length of about 60-75 km while laying down a deposit over a period of about 10-12 hours.