Ch. 8] SAFE BEARING CAPACITY 155 



By Mohr's Theory of Rupture: 



, . fc —ft 



= arc sin (1) 



Jc -rjt 



(l + sin</>) (2) 



2 cos (f> 



where f c = unit compressive strength, f t = unit tensile strength, 4> = angle of 

 internal friction, c = cohesion. 



Using the results from equation (1) and (2) the shearing strength s s for any 

 given normal load P can be computed by Coulomb's equation: 



s s = c + P tan <f> (3) 



The elastic properties of the rock are determined by the standard 

 tests of modulus of elasticity and are pertinent to the determination 

 of the question whether or not consolidation and settlement will occur. 

 It is common to find in sedimentary rocks greatly varying elastic 

 properties between different rock types. At the site where a structure 

 is to be constructed upon rocks of different elastic properties, allowance 

 for this condition may be required in the design. This would be perti- 

 nent at a site where steeply dipping rocks strike diagonally across the 

 site so that sections of the individual foundations would be located on 

 different rock types. Elastic properties of the rock are also to be 

 considered when repeated loading and unloading of the foundation oc- 

 curs or when marked decrease in the loading may result from the 

 execution of the proposed plan of construction, as, for instance, in the 

 excavation of a spillway cut in which several hundred feet of rock may 

 be removed and a relatively large area of concrete pavement may be 

 constructed upon the rock thus exposed. 



Safe Beaeing Capacity 



Philippe (1941, p. 7) has summarized the computation of bearing 

 capacity as follows: 



In computing bearing capacities from the shearing strength of a foundation 

 material, the following formulas based on the theories of elasticity and plasticity 

 are recommended: 



(1) Theory of Elasticity: 



V = irss (4) 



where 



p = the bearing capacity 



s s = shearing strength of the material 



The above formula is to be used with minimum or average shear strengths 



