Short Pile Analysis . Czerniak's (1957) procedure for analyzing 

 short, rigid piles was used. The procedure is based on the principle 

 of static equilibrium. The pile is assumed to be infinitely rigid. It 

 rotates about a point below the soil surface when an external lateral 

 force is applied at the top of the pile (Figure 18). Soil resistance at 

 each point along the pile is assumed to be proportional to pile deflec- 

 tion at that point. 



P = Ky/D (3) 



where p = soil pressure (Pa) 



K = modulus of horizontal subgrade reaction (Pa) 



y = lateral deflection (m) 



D = outside diameter of the pile (m) 



Assuming a linear increase of unit soil resistance with depth, the length 

 of pile necessary to maintain equilibrium under an applied load can be 

 calculated. 



For a horizontal load Rl, and moment Mo, applied at the surface, the 

 appropriate equation of equilibrium is: 



Z3., 4 .14 V - 13 - 86 M ■» < 4 > 



Dn n h 



where Z = pile length (m) 



R. = lateral force at the surface (n) 



n. = coefficient of horizontal subgrade modulus (Pa/m) 



Mo = moment at the surface (N.m) 



for the special case of no external moment, equation (4) becomes: 



R = z2pn h 

 L 14.14 (5) 



Similarly, the equation for bending moment at any point is: 



M x = R L Z f*) - 3 (f) 3 + 2 £)> 4 (6) 



42 



