A Treatise On The Principles And Practice Of Dock Engineering

THF, THEORY OF CONJUGATE PRESSURES. 159 Quite apart, however, from the question of humidity, there is another difficulty in the way of estimating the angle of repose for cases in practice. The earth behind a dock wall is often anything but homogeneous. With the most moderate foundation depths, a series of totally different strata will generally be passed through, each having its own particular angle of repose. And even supposing the most favourable case—that of filling of a fairly uniform texture—it is manifest that the increased pressure upon the lower layers will confer upon them a greater density, and so modify their conditions of stability that the line of rupture, instead of being straight, will become more and more inclined. Further, the absence of pressure upon the topmost layers will enable these to stand at a steeper inclination, so that the natural outline of the mass would present the form of an ogee curve (fig. 80). Altogether, it must be frankly confessed that it is practically impossible to arrive at any thoroughly reliable data for dealing with each case in situ, and, in the absence of definite information, the only course open is to make certain assumptions, approximately accurate, and to allow a sufficient margin of safety to cover attendant errors. Fig. 80. Several theories, accordingly, have been put forward in regard to the magnitude and direction of the resultant pressure of earthwork on a retaining wall. It would be impossible, within the limits of this work, to investigate all these theories exhaustively, but it will be noticed that, however distinct in development, they contain a common elemental factor. Considering the wall as of unit length, calling the height h (A B 01 C I), fig. 77), and the angle of rupture 6, the sectional area of the earth tan 0wÄ2 tanö wedge may be stated as $ , and its weigbt as g > W being the weight per unit volume. The various theories may then be covered by the following general expression: — P=^x C, . (11) in which P stands for resultant pressure, and C is a variable coefficient dependent upon several considéra- tions, such as the angle of repose, <p, the surface slope, a, of the earth behind the wall, the batter, ß, of the back of the wall, and the direction, 7, of the Fig. 81. resultant. In the ensuing examination of some of these theories, the foregoing symbols will retain their respective significations throughout. The Theory of Conjugate Pressures.—Professor Rankine, in his work on Civil Engineering (pp. 167 and 318), has developed a theory of earth pressure which ignores the existence of any cohesion between the particles. It is based on the following principle, primarily enunciated in a paper on