CHAPTER V. 

 RETAINING WALLS. 



Introduction. A retaining wall is a structure which sustains the lateral pressure of earth or 

 some other granular mass which possesses some frictional stability. The pressure of the material 

 supported will depend upon the material, the manner of depositing in place, and upon the amount 

 of moisture, and will vary from zero to the full hydraulic pressure. If dry clay is loosely deposited 

 behind the wall it will exert full pressure, due to this condition. In time the earth may become 

 consolidated and cohesion and moisture make a solid clay, which may cause the bank to shrink 

 away from the wall and there will be no pressure exerted. On the other hand all cohesion may 

 be destroyed by the vibration of moving loads or by saturation, and the maximum theoretical 

 pressures may occur. The pressures due to a dry granular mass, a semi-fluid, without cohesion, 

 of indefinite extent, the particles held in place by friction on each other, will be considered. The 

 effect of cohesion and of limiting the extent of the mass is considered in the author's "The Design 

 of Walls, Bins and Grain Elevators." 



Nomenclature. The following nomenclature will be used: 

 ^ = the angle of repose of the filling. 



<t>' = the angle of friction of the filling on the back of the wall. 

 6 = the angle between the back of the wall and a horizontal line passing through the heel of the 



wall and extending from the back into the fill. 

 8 = angle of surcharge, the angle between the surface of the filling and the horizontal; & is 



positive when measured above and negative when measured below the horizontal. 

 2 = the angle which the resultant earth-pressure makes with a normal to the back of the wall. 

 X = the angle between the resultant thrust, P, and a horizontal line. 

 h = the vertical height of the wall in feet. 

 d = the width of the base of the wall in feet. 

 t> = the distance from the center of the base to the point where the resultant pressure, E, cuts 



the base. - 



P = the resultant earth-pressure per foot of length of wall. 

 = the resultant of the earth-pressure and the weight of the wall. 

 w = the weight of the filling per cubic foot. 

 W = the total weight of the wall per foot of length of wall. 

 PI = the pressure on the foundation due to direct pressure. 

 fa = the pressure on the foundation due to bending moments. 

 P = the resultant pressure on the foundation due to direct and bending forces. 

 y = the depth of foundation below the earth surface. 



Calculation of the Pressure on Retaining Walls. To fully .determine the pressure of the 

 filling on a retaining wall it is necessary that the resultant of the pressure be known (a) in amount, 

 (b) in line of action, and (c) in point of application. Many theories have been proposed for 

 finding the pressure, each differing somewhat as to the assumptions and results. All theories 

 for the design of retaining walls that have any theoretical basis come in two classes: (i) the Theory 

 of Conjugate Pressures, due to Rankine, and commonly known as Rankine's Theory, and (2) 

 the Theory of the Maximum Wedge, probably first proposed by Coulomb, and commonly known 

 as Coulomb's Theory. Rankine's Theory determines the thrust in amount, in line of action, and 

 in point of application. In Coulomb's Theory, with the exception of Weyrauch's solution, the 

 line of action and point of application must be assumed, thus leading to numerous solutions of 

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