Mark W. Schmeeckle

Rain splash of dry sand revealed by high‐speed imaging and sticky paper splash targets

[1] Rain splash transport of sediment on a sloping surface arises from a downslope drift of grains displaced ballistically by raindrop impacts. We use high-speed imaging of drop impacts on dry sand to describe the drop-to-grain momentum transfer as this varies with drop size and grain size and to clarify ingredients of downslope grain drift. The ‘‘splash’’ of many grains involves ejection of surface grains accelerated by grain-to-grain collisions ahead of the radially spreading front of a drop as it deforms into a saucer shape during impact. For a given sand size, splash distances are similar for different drop sizes, but the number of displaced grains increases with drop size in proportion to the momentum of the drop not infiltrated within the first millisecond of impact. We present a theoretical formulation for grain ejection which assumes that the proportion of ejected grains within any small azimuthal angular interval dq about the center of impact is proportional to the momentum density of the spreading drop within dq and that the momentum of ejected grains at angle q is, on average, proportional to the momentum of the spreading drop at q. This formulation, consistent with observed splash distances, suggests that downslope grain transport involves an asymmetry in both quantity and distance: more grains move downslope than upslope with increasing surface slope, and, on average, grains move farther downslope. This latter effect is primarily due to the radial variation in the surface-parallel momentum of the spreading drop. Surface-parallel transport increases approximately linearly with slope.

Numerical simulation of turbulence and sediment transport of medium sand

A model of sand transport in water is produced by combining a turbulence-resolving large eddy simulation (LES) with a discrete element model (DEM) prescribing the motion of individual grains of medium sand. The momentum effect of each particle on the fluid is calculated at the LES cell containing the particle, and the fluid velocity and pressure, interpolated to each particle center, is used to derive fluid force on each particle in the DEM. Eleven numerical experiments are conducted of an initially flat bed of particles. The experiments span a range of motion, from essentially no motion to vigorous suspension. Hydraulic roughness is found to increase abruptly at the transition from bed load to suspended load transport. Suspended sediment extracts momentum from the flow and decreases the rate of shear. Whereas, slightly higher in the flow, vertical drag by suspended grains damps turbulence and increases the rate of shear. Vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models. The bed load experiments suggest that saltation by itself is a poor model of bed load sand transport. In contrast to expectations from saltation models, the peak bed load flux occurs at essentially the same level as the bed, and grains move slowly in frequent contact with other grains. Higher- and faster-moving bed load grains that can be considered to be in saltation represent a smaller portion of the total flux. Entrainment of bed load grains occurs in response to fluid penetration of the bed by high-vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high-speed wedges.

Interparticle collision of natural sediment grains in water

Elastohydrodynamic theory and measurements of particle impacts on an inclined glass plane in water are used to investigate the mechanics of interparticle collisions in sediment-transporting flows. A collision Stokes number is proposed as a measure of the momentum of an interparticle collision versus the viscous pressure force in the interstitial gap between colliding particles. The viscous pressure force opposes motion of the particles on approach and rebound. A Stokes number of between 39 and 105 is estimated as the critical range below which particle impacts are completely viscously damped and above which impacts are partially elastic. The critical Stokes number is shown to roughly coincide with the Bagnold number transition between macroviscous and grain inertial debris flows and the transition between damped and partially elastic bed load transport saltation impacts. The nonspherical nature of natural particles significantly alters the motion of the center of mass after a partially elastic collision. The normal to the point of contact between the particles does not necessarily go through the center of mass. Thus normal rebound of the center of mass may not occur. A model of particle motion after rebound for particles of arbitrary shape, conserving both linear and angular momentum, is proposed.

Tidally induced groundwater circulation in an unconfined coastal aquifer modeled with a Hele-Shaw cell

We use a scaled Hele-Shaw cell to mimic tidally induced nearshore groundwater motion in an unconfined aquifer. The low slope angle of sandy beaches contributes to a strongly asymmetric pattern of fluid exchange across the water-sediment interface during tidal cycles. This asymmetry leads to a time-averaged groundwater circulation centered beneath the low-tide level; horizontal and vertical components of motion are of the same order. Horizontal seaward flow extends a significant depth beneath the interface, consonant with a time-averaged water table that is elevated above mean sea level, providing the hydraulic gradient necessary to drive this deeper export of mass equal to the time-averaged inflow by infiltration. This tidally forced flow behavior likely contributes to observed fluctuations in submarine seepage rates. Moreover, the circulation largely involves a subsurface cycling of seawater that infiltrates during the rising tide. Measurements of submarine seepage near the tidal zone therefore likely involve this cycled seawater as well as freshwater flows.

Experimental evidence of statistical ensemble behavior in bed load sediment transport

A high-resolution data set obtained from high-speed imaging of coarse sand particles transported as bed load allows us to confidently describe the forms and qualities of the ensemble distributions of particle velocities, accelerations, hop distances and travel times. Autocorrelation functions of frame-averaged values (and the decay of these functions) support the idea that the forms of these distributions become time-invariant within the five second imaging interval. Distributions of streamwise and cross-stream particle velocities are exponential, consistent with previous experiments and theory. Importantly, streamwise particle velocities possess a “light” tail, where the largest velocities are limited by near-bed fluid velocities. Distributions of streamwise and cross-stream particle accelerations are Laplace in form and are centered on zero, consistent with equilibrium transport conditions. The majority of particle hops, measured start-to-stop, involve short displacements, and streamwise hop distances possess a Weibull distribution. In contrast to previous work, the distribution of travel times is exponential, consistent with a fixed temporal disentrainment rate. The Weibull distribution of hop distances is consistent with a decreasing spatial disentrainment rate, and is related to the exponential distribution of travel times. By taking into account the effects of experimental censorship associated with a finite sampling window, the relationship between streamwise hop distances and travel times, Lx∼Tpα, likely involves an exponent of α ∼ 2. These experimental results — an exponential distribution of travel times Tp and a Weibull distribution of hop distances Lx with shape parameter k 1.

A criteria-based methodology for determining the mechanism of transverse drainage development, with application to the southwestern United States

The study of how rivers cross obstructing mountains, once popular in the early twenti- eth century, has seen a dramatic resurgence in the last decade. Since Huttons scholarly introduction to a possible cause for trans- verse drainage, however, no single study has compiled all of the various criteria that can be used to discriminate among the four pos- sible mechanisms of antecedence, superimpo- sition, overfl ow, and piracy. This paper pres- ents the fi rst such compilation and related methodology to apply these criteria both in tabular and graphical formats, as well as an online interactive tool in the data repository. Combining nominal and ordinal data sources, this methodology generates an objective, reproducible assessment for the mechanism most likely to have established the trans- verse drainage at fi ordinal levels of con- fi dence. When applied to southwestern U.S. sites, randomly selected through an objec- tive spatial procedure, four general observa- tions emerged on the relationship between the development of transverse drainage and landscape evolution. (1) Streams persisting through lengthy periods of extension develop antecedent canyons. (2) In order to reestab- lish through-fl owing channels, streams over- fl ow closed basins as active extension wanes. (3) Following a drop in base level related to the newly developed trunk channels, streams tributary to the trunk channels incise into basin-fi ll deposits—sometimes leading to the development of superimposed drainages. (4) Tributaries eroding headward, in response to the integration of two or more closed basins, can capture and redirect drainage; this permits transverse drainage through both piracy and superimposition upstream of the capture event. Because extant criteria use nominal and ordinal data almost entirely, considerable potential exists to refi ne this approach through future strategies that incorporate interval data. Future use of a criteria-based method has the potential to inform on prior geomorphic studies by pro- viding a new perspective with which to study how basins evolve in active tectonic regions, the analysis of related basin sedimentation, the hydrological and biological aspects of drainage evolution, and transverse drainage found in Martian crater fi elds.

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.

Sediment Entrainment and Transport in Complex Flows

Predicting the entrainment and transport rates of sediment grains making up an erodible bed underlying an arbitrary flow field requires a mechanistic understanding of the coupling between the flow and the forces on sediment grains. To help develop such an understanding, a suite of flow and sediment-transport experiments are described; these may be loosely divided into two categories. First, measurements of near-bed flow structure and sediment motion in a variety of spatially or temporally accelerating flows are used to show the manner in which changes in flow structure can impact sediment entrainment and transport. Second, direct high-frequency measurements of lift and drag on sediment particles in various turbulent flows are used to make a more direct connection between nearbed flow structure and sediment dynamics. Taken together, these experiments show how even changes in turbulence structure due to spatial and/or temporal accelerations can have a significant effect on the sediment-transport field. Finally, a method is briefly outlined for predicting sediment motion under arbitrary flows using either measured nearbed velocity time series or flow information predicted from direct numerical simulations or large-eddy simulations.

Meta-Analysis of 301 Slope Failure Calculations. I: Database Description

Since the early part of the twentieth century, two-dimensional limit equilibrium (2DLE) analysis has been the scientific community’s primary means of slope stability calculation. However, it is well established that the input parameters to 2DLE, namely, soil strength and anisotropy, slope geometry, pore water pressures, failure surface geometry, applicable correction factors, and loading conditions are all inherently uncertain. Effective modeling must account for these uncertainties statistically. Unfortunately, most of the key statistical parameters, such as the safety factor statistical distribution and standard deviation (sd), are unknown and must be estimated by the analyst. In response to this growing need for statistical information, a database was established from the literature of 157 different failed slopes and the corresponding published 301 safety factor (SF) calculations. The database, which covered more than five decades of slope stability research, also included a number of the slope stabili...

The elements and richness of particle diffusion during sediment transport at small timescales

The ideas of advection and diffusion of sediment particles are probabilistic constructs that emerge when the Master equation, a precise, probabilistic description of particle conservation, is approximated as a Fokker-Planck equation. The diffusive term approximates nonlocal transport. It “looks” upstream and downstream for variations in particle activity and velocities, whose effects modify the advective term. High-resolution measurements of bed load particle motions indicate that the mean squared displacement of tracer particles, when treated as a virtual plume, primarily reflects a nonlinear increase in the variance in hop distances with increasing travel time, manifest as apparent anomalous diffusion. In contrast, an ensemble calculation of the mean squared displacement involving paired coordinate positions independent of starting time indicates a transition from correlated random walks to normal (Fickian) diffusion. This normal behavior also is reflected in the particle velocity autocorrelation function. Spatial variations in particle entrainment produce a flux from sites of high entrainment toward sites of low entrainment. In the case of rain splash transport, this leads to topographic roughening, where differential rain splash beneath the canopy of a desert shrub contributes to the growth of a soil mound beneath the shrub. With uniform entrainment, rain splash transport, often described as a diffusive process, actually represents an advective particle flux that is proportional to the land-surface slope. Particle diffusion during both bed load and rain splash transport involves motions that mostly are patchy, intermittent and rarefied. The probabilistic framework of the Master equation reveals that continuous formulations of the flux and its divergence (the Exner equation) represent statistically expected behavior, analogous to Reynolds-averaged conditions. Key topics meriting clarification include the mechanical basis of particle diffusion, effects of rarefied conditions involving patchy, intermittent motions, and effects of rest times on diffusion of tracer particles and particle-borne substances. This article is protected by copyright. All rights reserved.