h                         2
then P = h x ----- (tan. [beta]) x W x --- h =
2                          3
1
—–­ h^{3} W tan. [beta].
3

When the angle of repose, [phi], is less than 45 deg., this result must be reduced by dividing by tan. [phi]; that is,

1
h = —–­ h^{3} tan. [beta] / tan. [phi].
3

Figs. 1 and 2, Plate XXV, show recently excavated banks of gravel and sand, which, standing at a general angle of 45 deg., were in process of “working,” that is, there was continual slipping down of particles of the sand, and it may be well to note that in time, under exposure to weather conditions, these banks would finally assume a slope of about 33 degrees.  They are typical, however, as showing the normal slope of freshly excavated sandy material, and a slope which may be used in ordinary calculations.  The steps seen in Plate XXV show the different characteristics of ground in close proximity.  In Fig. 2, Plate XXVI,[D] may be seen a typical bank of gravel and sand; it shows the well-defined slope of sand adjacent to and in connection with the cohesive properties of gravel.

The next points to be considered are the more difficult problems concerning subaqueous or saturated earths.  The writer has made some experiments which appear to be conclusive, showing that, except in pure quicksand or wholly aqueous material, as described later, the earth and water pressures act independently of each other.

For a better understanding of the scope and purpose of this paper, the writer divides supersaturated or subaqueous materials into three classes: 

Class A.—­Firm materials, such as coarse and fine gravels, gravel and sands mixed, coarse sands, and fine sands in which there is not a large proportion of fine material, such as loam, clay, or pure quicksand.

Class B.—­Semi-aqueous materials, such as fine sands in which there is a large proportion of clay, etc., pure clays, silts, peats, etc.

Class C.—­Aqueous materials, such as pure quicksands, in which the solid matter is so finely divided that it is amorphous and virtually held in suspension, oils, quicksilver, etc.

Here it may be stated that the term, “quicksand,” is so illusive that a true definition of it is badly needed.  Many engineers call quicksand any sand which flows under the influence of water in motion.  The writer believes the term should be applied only to material so “soupy” that its properties are practically the same as water under static conditions, it being understood that any material may be unstable under the influence of water at sufficiently high velocities, and that it is with a static condition, or one approximately so, that this paper deals.

A clear understanding of the firm materials noted in Class A will lead to a better solution of problems dealing with those under Class B, as it is to this Class A that the experiments largely relate.