78 



Earth Thrust: Many complex theories have been de- 

 vised to calculate the earth thrust, but the assumptions 

 on which these theories are based are so variable and hard 

 to determine with accuracy that they give far from prac- 

 tical results. However, they are the best at hand, and 

 serve to obtain results much better than by direct assump- 

 tions. Rankine's is one of the standard formulas, and 

 can be expressed as 



iv 

 2 



Where T equals earth thrust, H equals height of wall, w 

 equals weight per cu. ft. of backing x H aiid <}> equals 

 the angle of repose. What few experiments have been 

 made to verify tnese formulas indicate that the actual 

 earth thrust under a backing of certain weight and angle 

 of repose is about one- half of the calculated value. The 

 angle of repose is taken as the smallest angle at which 

 the given earth will repose, and is seldom less than 1% 

 on 1. This will give the maximum normal earth thrust. 

 However, in actual cases the earth will probably repose 

 at a steeper angle, due to the cohesion in the earth, and 

 the earth thrust will be less. This maximum normal 

 thrust can now be multiplied by a factor of safety to get 

 the ultimate value. We use a factor of safety of 3 or 4 

 for external stresses and 6 to 8 for internal stresses. 

 These factors are large, the factors for gravity walls 

 seldom being taken over 3. With a more v economical 

 structure we can afford to use a larger factor of safety. 



A reinforced wall may fail (1> internally, or (2) ex- 

 ternally. It may fail externally (a) by overturning, or 

 (b) by sliding forward on the base. 



Sliding: To produce sufficient friction between the base 

 and the foundation to prevent sliding the heel must be 

 made of such a length as to get a sufficient weight of 

 earth upon it. This length of heel is expressed by the 

 formula 



Tt W 

 T=f(W+wA)or A= 



Where f equals the coefficient of friction, W equals weight 

 of wall and w equals weight of one cubic foot of backing, 

 multiplied l>y the height. 

 Overturning: The resultant earth thrust is assumed to 



