where x = distance along pile below the surface (m) 



M = moment at point x (N-m) 



For R|_ applied at the surface, the maximum bending moment occurs at 

 approximately 0.42Z. Substituting this for x in equation (6), the 

 maximum bending moment becomes: 



M max = °- 260 R L Z < 7 > 



Equation (5) was used to find the lateral load capacity for pile diameters 

 of 1.2, 2.4, 4.9, and 7.6 m (4, 8, 16, and 25 ft) for pile lengths up to 

 the limit of validity of the C^rniak relationship, i.e., 10 x diameter. 

 The coefficient of horizontal subgrade modulus, n n , was selected based on 

 the recommendations in Czerniak (1957) and Anon (1967). Those values for 

 Soil Categories A, B, and C were based on the developed shear strength 

 profiles, and the value for Soil Category D based exclusively on Anon 

 (1976). The assumed values are listed in Table 11. Using these n n values 

 in equation (5) the lateral load versus pile length relationships shown as 

 solid lines in Figures 19, 20, 21, and 22 were developed. Soil pressures 

 were assumed to be sufficient to maintain equilibrium and resulting 

 deflections were assumed to be acceptable. 



Long Pile Analysis . A long pile analysis was done for two reasons: 



(1) To find out if pile capacity could be increased using longer 

 piles. 



(2) To check the short pile results at the transition length 

 (Z = 10D). 



A subgrade reaction method (Gill and Demars, 1970) was used to find 

 lateral capacity for selected pile lengths and diameters. The method is 

 similar to a commonly used method developed by Matlock and Reese (1960). 

 The non-linear soil load-deformation characteristics (p-y curves) are 

 represented by a rectangular hyperbola. Hyperbola shape is defined by 

 measurement of the undrained shear strength for clay; and effective 

 overburden and friction angle for sand. The procedure employs a finite 

 difference solution of the equation of bending to obtain deflections. 

 Soil properties, pile characteristics, and pile loading are input to the 

 computer program. Pile stiffnesses were selected on the basis of maxi- 

 mum bending moments calculated from the Czernfak rigid-pile analysis for 

 Soil Category C. The pile sections required to obtain these stiffnesses 

 appear reasonable and practical for fabrication. The long-pile analysis 

 program returns pile deflection, bending moment and soil modulus as a 

 function of depth. The external loading boundary condition was adjusted 

 until pile failure (bending moment exceeded) occurred. 



44 



