The Transportation of Debris by Running Water

Abstract

Scope.-The finer debris transported by a stream is borne in suspension. The coarser is swept along the channel bed. The suspended load is readily sampled and estimated, and much is known as to its quantity. The bed load is inaccessible and we are without definite information as to its amount. The primary purpose of the investigation was to learn the laws which control the movement of bed load, and especially to determine how the quantity of load is related to the stream's slope and discharge and to the degree of comminution of the debris. Method.-To this end a laboratory was equipped at Berkeley, Cal., and experiments were performed in which each of the three conditions mentioned was separately varied and the resulting variations of load were observed and measured. Sand and gravel were sorted by sieves into grades of uniform size. Determinate discharges were used. In each experiment a specific load was fed to a stream of specific width and discharge, and measurement was made of the slope to which the stream automatically adjusted its bed so as to enable the current to transport the load. The slope factor.-For each combination of discharge, width, and grade of debris there is a slope, called competent slope, which limits transportation. With lower slopes there is no load, or the stream has no capacity for load. With higher slopes capacity exists; and increase of slope gives increase of capacity. The value of capacity is approximately proportional to a power of the excess of slope above competent slope. If S equal the stream's slope and sigma equal competent slope, then the stream's capacity varies as (S - sigma)n. This is not a deductive, but an empiric law. The exponent n has not a fixed value, but an indefinite series of values depending on conditions. Its range of values in the experience of the laboratory is from 0.93 to 2.37, the values being greater as the discharges are smaller or the debris is coarser. The discharge factor.-For each combination of width, slope, and grade of debris there is a competent discharge, k. Calling the stream's discharge Q, the stream's capacity varies as (Q - k)o. The observed range of values for o is from 0.81 to 1.24, the values being greater as the slopes are smaller or the debris is coarser. Under like conditions o is less than n; or, in other words, capacity is less sensitive to change3 of discharge than to changes of slope. The fineness factor.-For each combination of width, slope, and discharge there is a limiting fineness of debris below which no transportation takes place. Calling fineness (or degree of comminution) F and competent fineness o, the stream's capacity varies with (F - o)p. The observed range of values for p is from 0.50 to 0.62, the values being greater as slopes and discharges are smaller. Capacity is less sensitive to changes in fineness of debris than to changes in discharge or slope. The form factor.-Most of the experiments were with straight channels. A few with crooked channels yielded nearly the same estimates of capacity. The ratio of depth to width is a more important factor. For any combination of slope, discharge, and fineness it is possible to reduce capacity to zero by making the stream very wide and shallow or very narrow and deep. Between these extremes is a particular ratio of depth to width, p, corresponding to a maximum capacity. The values of p range, under laboratory conditions, from 0.5 to 0.04, being greater as slope, discharge, and fineness are less. Velocity.-The velocity which determines capacity for bed load is that near the stream's bed, but attempts to measure bed velocity were not successful. Mean velocity was measured instead. To make a definite comparison between capacity and mean velocity it is necessary to postulate constancy in some accessory condition. If slope be the constant, in which case velocity changes with discharge, capacity varies on the average with the 3.2 power of velocity. If discharge be the constant, in w