FOUNDATIONS AND RETAINING WALLS 



197 



In the case of wet or moist soils the same effect is obtained by 

 drainage, as indicated in the tables on the preceding page. 



A more marked increase in the bearing power may be obtained by 

 excavating the soil and replacing it by a layer of moist sand ; or by 

 driving short piles and then either removing them and filling the 

 hole immediately with moist sand, or else leaving the piles in the 

 earth and covering them with a platform of timber or concrete. 



When none of these methods will suffice, the soil must be exca- 

 vated until a subsoil with an adequate bearing power is reached. 



159. Angle of repose and coefficient of friction. When a mass of 

 granular material, such as sand, gravel, or loose earth, is poured upon 

 a level surface, the sides of the pile will assume a definite slope, 

 called the natural slope. This maximum angle which the sides of 

 the pile can be made to assume with the horizontal is called the 

 angle of repose, and is a constant for any given material. Since the 

 size of this angle is dependent upon the amount of friction between 

 the particles of the 

 material, it may be 

 taken as a measure 

 of the friction, or 

 vice versa. 



The laws of fric- 

 tion as determined 

 by experiment are 

 that the force of 

 friction is independent of the areas in contact, is dependent on the 

 nature of the material, and is directly proportional to the normal 

 pressure between the surfaces in contact. Let P F denote the force 

 of friction and P N the normal pressure. Then the above laws may 

 be expressed by the formula 



FIG. 139 



where k is the constant of proportionality, and is called the coefficient 

 of friction. 



In Fig. 139 let DE represent the natural slope and a) the angle 

 of repose, and consider a particle of the material of weight P at any 

 point A in the natural slope. Let P be resolved into two components 



