Pressure, Resistance, and Stability of Earth | Page 5

erected, there is no reason to believe that with properly adjusted weights at W or _W_{2}_, an exact equilibrium of forces and conditions cannot be obtained. Or, again, if, as in Fig. 5, the face, P Q, is sheeted and rodded back to the surface, keying the rods taut, there is undoubtedly a stable condition and one which could not fail in theory or practice, nor can anyone, looking at Fig. 5, doubt that the top timbers are stressed more heavily than those at the bottom. The assumption is that the tendency of the material to slide toward the toe causes it to wedge itself between the face of the sheeting on the one hand and some plane between the sheeting and the plane of repose on the other, and that the resistance to this tendency will cause an arching thrust to be developed along or parallel to the lines, A N, B M, etc., Fig. 2, which are assumed to be the lines of repose, or curves approximating thereto. As the thrust is greatest in that material directly at the face, A O, Fig. 6, and is nothing at the plane of repose, C O, it may be assumed arbitrarily that the line, B O, bisecting this angle divides this area into two, in one of which the weight resolves itself wholly into thrust, the other being an area of no thrust, or wholly of weight bearing on the plane of repose. Calling this line, B O, the haunch line, the thrust in the area, A O B, is measured by its weight divided by the tangent of the angle, P Q R = [phi], which is the angle of repose; that is, the thrust at any given point, R = R Q �� tan. [phi].
The writer suggests that, in those materials which have steeper angles of repose than 45��, the area of pressure may be calculated as above, the thrust being computed, however, as for an angle of 45 degrees.
In calculating the bending moment against a wall or bracing, there is the weight of the mass multiplied by the distance of its center of gravity vertically above the toe, or, approximately:
2 Area, A O B �� weight per unit �� --- height, 3
where h = height,
W = weight per cubic foot of material = 90 lb.,
90�� - [phi] and [beta] = ------------- 2
P = pressure per linear foot (vertically),
h 2 then P = h �� ----- (tan. [beta]) �� W �� --- h = 2 3 1 --- _h^{3}_ W tan. [beta]. 3
When the angle of repose, [phi], is less than 45��, 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��, 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