Shear resistance on skin

The shear resistance on pile skin is in the analysis represented by stiffness of springs supporting individual beams of a pile. This stiffness is associated with material parameters of the Winkler-Pasternak model C₁ and C₂. The values of C₁ and C₂ are determined from parameter E_def. They depend on the depth of influence zone, which varies with the pile deformation (settlement). The variability of influence zone is in the analysis determined such that for zero deformation it receives the value of 1x the pile diameter and for deformation at the onset of skin failure equals 2,5x the pile diameter.

The decisive parameter for the determination of magnitudes of C₁ and C₂ is the deformation modulus. Caution must be taken when estimating the value of E_def from deformational characteristics of soil using standards. In particular, in case of long piles we are essentially dealing with deep seated foundations and the soil at the pile heel will certainly experiences higher stiffness than that proposed by the standard for spread footings. This holds particularly for cohesive soils. The most reliable estimates are of course those obtained directly from experimental measurements.     

Formulas given below serve to determine the stiffness of springs representing the shear resistance of pile skin as a function of computed parameters of the elastic subsoil. They depend on the shape of cross-section and for the implemented cross-sections they receive the following forms:

Circle:

where:	r	-	radius of pile cross-section
	C1, C2	-	subsoil parameters
	K1(α r), K2(α r)	-	values of the modified Bessel functions

Parameter α  attains the value:

.

Rectangle:

,

where a,b are lengths of rectangle edges and C₁, C₂ are subsoil parameters and k_red is the reduction coefficient, which reduces the stiffness with respect to slenderness of the rectangle.

It receives the following values

                        for: ,

                for: ,

where a is the length of a shorter edge of the rectangle and H is the depth of influence zone.

Croos, "I-section":

For these cross-sections the stiffness is derived from the stiffness of rectangular cross-section reduced by subtracting the stiffness corresponding to four "removed" parts of the cross-section.

,

a₁, b₁ - evident from the following figure