Once a proper selection has been made of feasible wall types that satisfy the necessary constraints, design consists of determining the earth pressure against the back of the wall and then proportioning the wall so that it will be structurally sufficient to satisfy a number of traditional checks. These checks include stability against sliding and overturning, and foundation bearing pressure limits. Clearly, satisfying the traditional checks would be of no value if the entire structure were to move because of some condition not related to any of these three checks. Therefore, it is also important that the designer be assured that the wall is globally stable—i. e., that no deep-seated slide or slip surface exists.
An important and essential part of the design of retaining walls consists of determining the earth pressure on the back of the wall. The earliest theory of earth pressure traces back to Charles-Augustin de Coulomb, who published his work in 1773. Coulomb’s theory presented a method by which a designer could determine the pressure that dry, granular, cohesionless material would exert upon the back of a wall constructed to restrain the material. His work was based on the theory that failure is characterized by a wedge-shaped mass of the supported sand material that slides down along a sloping plane such as is shown in Fig. 8.6.
The Coulomb theory assumes a hydrostatic distribution of pressure such that the resultant forces R (reaction needed to hold wedge in equilibrium) and P (summation of normal pressure times area) act at the lower third point of the planes upon which they act, planes ab and ac, respectively. The force R acts at an angle of friction of soil on concrete, ordinarily 25°, while P acts at an angle of friction of soil on soil, generally assumed to be 34°. This latter angle will vary significantly from 34° to 40° or more. Because of the different angles of friction, the theory produces an error in the result;
however, the error is generally accepted as negligible. In essence, if it is assumed that no friction exists between the earth and the wall, the pressure determined from the Coulomb theory is the same as that determined from the Rankine theory. Thus, because of its simplicity, the tendency is to use the Rankine theory. See Art. 8.2.3 for an example of active pressure calculation.
It is evident that the theory as expressed in Fig. 8.6 does not suggest a particular plane of failure. Thus, the pressure determination of the Coulomb theory is traditionally left to graphical methods, in particular those first developed by J.-V. Poncelet, and later by a German engineer, Culmann. These constructions, which allow for the complete determination of lateral pressure acting on the wall (i. e., magnitude, direction, and point of application), are not further discussed herein. However, several failure planes are usually assumed, pressure from each assumption is graphically determined, and an envelope line of pressure is developed from these pressure points from which the maximum pressure can be determined. The methods are laborious but straightforward and may again gain in popularity with the increasing use of computers.
At approximately the same time as Culmann’s construction was developed, a Scottish physicist, W. J. M. Rankine, presented his theory in a work called On the Stability of Loose Earth, a theory that remains in active use. Rankine assumed a mass of loose earth of infinite extent, and a planar top surface subjected to its nonweight. The theory assumed granular backfill material without cohesion, but was adapted in 1915 by a British engineer to allow for cohesion.
