[1] Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t* rm ) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t* rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of t* rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock-Crowe equation for determining t* rm and the hiding function used to scale t* rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.
If liquid, initially saturating the pores of a soil, is allowed to drain from that soil, no such complete drainage as occurs in a simple capillary tube is observed; large quantities of liquid are retained. The quantity of liquid held by the soil immediately after drainage gradually alters; it decreases to a stationary value and the liquid so held finally arranges itself in a stable distribution. Whatever be the distribution, the bounding liquid surfaces are capillary ones and subject to the laws of thermodynamics and capillarity; the Kelvin relation, in general determines the curvatures. The problem is considered for an ideal soil, that is an assemblage of spheres, of a single size, packed at random. There are in the ideal soil three types of distribution. First, there is a pendular region where the liquid is retained in the form of single rings of liquid wrapped around the axis of each pair of adjacent grains in contact. Second, there is a funicular region, which may be considered to arise by coalescence of the rings; we have two or more grain contacts imbedded in a single liquid mass, that is, webs of liquid enmeshing two or more grain contacts and which may involve many grains of the packing. There is, finally, a saturation region in which all pores are completely filled. The limits of each of these zones are determined. The funicular zone is a zone of hysteresis and all values between a normal minimum and complete saturation are usually possible. To calculate the normal minimum distribution the actual packing is replaced by an average packing of grains in hexagonal array and equally spaced to give the required porosity. The funicular distribution is now in the form of single rings wrapped around the axis of each pair of grains of the packing. The volume of each type of ring is determined in terms of (σ/ρghr), where σ is the surface tension of the liquid and ρ its density, r the grain radius, and h the height of the ring above a free liquid reference plane. The average volume of each type of ring is obtained for all rings confined between two given planes. From the average ring volume and the number of such in each cc of packed space, the total retention in each zone above saturation is found. The distribution, that is, the liquid retained in any lamina at a height h above the free liquid, is also given. The results are compared with the data of King.
Uniform spheres packed in regular array form a non-cylindrical cyclic capillary, characterized by a maximum and minimum capillary rise with intermediate positions of possible equilibrium. In practice spheres may be packed to a variety of porosities P thus requiring a mixture of regular and irregular pilings arranged in a very distorted pattern. However the meniscus is also distorted to conform in a general way with the distortions of the lattice. Accordingly positions of maximum and minimum rise may be expected. The meniscus for maximum rise tends to pass through the plane of centers of neighboring spheres. Slight deviations from this condition due to the rise at sphere contacts are shown to be of minor importance. Any piling may be treated statistically as a hexagonal array with a spacing 2r+d where d is computed to give the observed porosity. In such a system three types of cell occur with a definite frequency, and these cell types are assumed present in the meniscus with the same frequency distribution. Hence it is possible to evaluate pr/a = ρghr/σ where p = perimeter, r = grain radius, a = area of pore opening, g = acceleration of gravity, σ = surface tension, ρ = density and h = capillary rise. The final formula so derived reduces to pra=ρghrσ=2[0.9590/(1−P)2/3]−1.This agreed with experiments made with several sizes of grains, porosities, and liquids. The minimum rises were also determined but a satisfactory interpretation in terms of a model has not been effected.
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