156 philbrick. FOUNDATION PROBLEMS [Ch. 8 



obtained from the direct shear tests. When the formula is used with values of 

 c and cj>, a factor of safety F of 4 is usually applied ; then 



s 3 = c + p tan <f> 

 From Equation 4 



V 



s s = - 



IT 



Then bearing capacity p becomes 



P F -7rtan<£ ' 



(2) Theory of Plasticity: 

 Using a factor of safety, F = 4 



7T 



-so = 1.81s (6) 



V3 



where so = the yield strength of the rock in tension. 



In the above formula, the ultimate tensile strength of the rock is used for s - 

 This is an allowable approximation since for brittle materials the yield strength 

 in tension is only slightly less than the ultimate tensile strength. 



The application of the preceding equations to test samples of shales 

 indicated that allowable loads could exceed 40 tons per square foot. 

 Existing building codes would probably rate similar shales in bearing 

 capacities at 8 to 10 tons per square foot, indicating an apparent 

 ultimate safety factor on the order of 16 to 20. 



In analyzing the foundation reaction under masonry dams, Creager, 

 Justin, and Hinds (1945, pp. 295-304) and Houk and Keener (1941, 

 p. 1126) have placed emphasis on the shear-friction factor of safety. 

 In these calculations, 'shear strength of the rock at the base of the dam, 

 based on average shearing strength of that material, is included. The 

 determination of the coefficient of friction is not usually subject to test 

 but is assumed to be between 0.6 and 0.8. 



In order to obtain the desired critical data it may be necessary to 

 take the test to the sample and conduct a field test on the rock in place. 

 Should the field test indicate values in the same order as the laboratory 

 tests, it may be assumed that the laboratory tests are yielding reliable 

 data. In actual practice, before field tests are resorted to, one of the 

 following conditions must arise: preliminary calculations of loadings 

 must indicate that the estimated strength of the foundation rock will 

 be approached closely by the loadings to be produced by the proposed 

 structure ; or the strength of the foundation rock must be unknown and 

 questioned, as in the case of certain shales upon which no comparable 



