Appendix B 

 BEARING-CAPACITY ANALOGY 



One of the classic problems considered in soil mechanics is the 

 determination of the bearing capacity of a shallow footing on an infinite 

 half-space. The bearing capacity is defined as the maximum downward load 

 which may be applied to the footing before the underlying soil is ruptured 

 along continuous failure surfaces in such a way as to create a failure mechanism. 

 This condition is also often referred to as a general shear failure or a state of 

 plastic equilibrium. The usual procedure used to analyze this situation has 

 been to construct a series of hypothetical failure surfaces, assign to each soil 

 element along the surfaces a shear stress equal to the soil strength, and solve 

 the resulting structure by statics to obtain the footing load. Theoretically, 

 if this were done for every imaginable series of surfaces, the bearing capacity 

 would correspond to the lowest footing load obtained. A substantial effort 

 has been directed toward finding appropriate failure surfaces and has led to 

 the development of several bearing-capacity equations. One of the most com- 

 mon of these is that developed by Prandtl for an infinitely long footing of 

 finite width; this equation is based on the failure pattern shown in Figure B-1 .^^ 



P = bearing capacity of footing per unit length 

 <p = friction angle of soil (in degrees) 

 B = width of footing 



The log spiral is given by the equation 



r, rQ, and 8 are defined in the diagram {d is measured in radians) 

 r^j is the length of one of the sides of the isosceles triangle 



Figure B-1 . Cross section illustrating Prandtl's plastic equilibrium theory. 



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