It can be seen from Figure B-1 that the characteristics of Prandtl's 

 failure surfaces are strongly related to the soil friction angle. For short-term 

 loadings on fine-grained, low-permeability (cohesive) soils such as those usually 

 found on the seafloor, the assumption is often made that the apparent friction 

 angle is equal to zero. This is because the low soil permeability prevents signi- 

 ficant drainage and soil volume change during a short-term loading. Because 

 soil strength is primarily a function of relative volume (void ratio), there will 

 be little strength variation, and the soil friction angle, which is basically a mea- 

 sure of the change in strength corresponding to a change in stress, will appear 

 to be zero.''^ For a soil with zero friction angle, Prandtl's failure surfaces 

 reduce to those shown in Figure B-2. 



Figure B-2. Prandtl's failure surfaces with = 0. 



If it is assumed that the shear stresses along all of the failure surfaces 

 are identically equal to the undrained soil strength, S, this problem can be 

 solved by balancing moments to yield the equation 



P = 2B!| + 1)5 = 5. MBS 



(B-1) 



At this point, it should be noted that the failure surfaces of Figure B-2 

 are symmetric about the footing edges. Because the statics problem is solved 

 by balancing moments about these edges, it can be seen that the solution to 

 the problem shown in Figure B-3 is identical to that given for Figure B-2. 



p 



^ shearing resistance, S 



Figure B-3. Prandtl's failure surfaces with upward loading. 



39 



