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Spring’s stiffness is corr   

 

 

   

’s skin,

 

’s

 

   

   

well known “p 

y” method    

   

   

   

 

 

 

   

 

 

 

 

 

 

Vesic’s 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

  

“z”   

 

“y      ”   

 

     

 

 

   

  

 

 

 

  

     

  

  

  

  

  

    

  

 

 

   

  

 

   

 

  

=Soil layer’s thickness = pile embedded  

 

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“      

” are  

  “F    ” 

 

  “y” 

    

  

 

  

 

 

 

 

 

  

 

 

   

“  

”  

”Y(0)” 

stiffness “    

”  

“A” to “D” are derived by applying free head conditions on pile top and fixed conditions on pile tip.    

 

a finite length “H”

  

 

 

  

 

 

 

 

  

 

 

   

 

  

   

 

 

 

  

  

  

    

 

  

  

 

 

 

 

 

 

   

 

 

“K  

 ”   

   

 

cantilever, i.e. “ 

        

”.  

“K  

  ”   

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

   

 

 

 

 

    

     

 

 

3. METHODOLOGY

   

   

   

   

    

 

   

    

   

 

   

 

“z”   

 

 

 

 

    

 

 

 

 

   

 

   

typical Young’s modulus of elasticity of 25000 MPa

 

     

 A horizontal force in “y” direction

   

  

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range of Poisson’s ratio from 0 to 0.48 and a range of modulus ratio      

      

 

diameters 100, 400, 600, 800, 1500 and 2000 millimetres. Poisson’s ratio for each model    

 

 

 

   

 

 

 

                  

 

“k  

 ” 

 

“  

” which is then  

Poisson’s ratio, flexural rigidity “

 

  ” and shaft diameter. The “reference stiffness” is the spring stiffnessderived for a pile with 1m shaft diameter and for zero Poisson’s ratio.

  

   

  

  

 

  

 

 

 

 

= Reference stiffness for the shaft diameter “    

” and zero Poisson’s ratio 

= Poisson’s ratio scale factor.

   

 

 

Figure 3a includes curves of “k   ” for a fully connected model as well as that  

 

 

  

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Where “  

”  

“  

=25000MPa”

“  

” is the  

“ ” is a power that varies from 0.15 for very stiff soils to 0.036

      

   

     

 

 

 

 

                       

 

   

 

 

 

 

  

 

  

    

  

 

   

 

 

 

 

 

   

 

 

 

 

 

 

     

“   

” is Young modulus of elasticity  

soil and “ 

” is       

    

using pile’s diameter in place of beam’s

 

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expressions for deflection and rotation at pile’s top under the action of a lateral force and a bendingmoment. Using Randolph’s expression

 

head stiffness “K   ” ca  

 

 

 

 

   

     

 

 

 

    

  

 

 

 

 

 

 

 

 

 

 

 

 

 

  

   

 

 

 

 

 

 

  

 

   

 

 

  

 

 

 

 

 

 

 

 

  

 

 

 

  

 

  

  

  

 

  

  

    

 

  

 

 

 

 

  

 

 

  

 

 

  

 

  

 

 

  

 

  

 

        

 

   

 

 

 

 

   

     

 

 

 

 

 

  

   

 

 

 

 

 

   

 

 

 

 

 

  

 

Where “  

” is the ratio of bending moment to shear force on pile top. Substituting equation (19) inequation (7) results in spring’s stiffness.

  

 

  

 

 

     

 

  

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

  

 

 

 

 

 

 

 

 

 

  

 

     

 

 

 

Where “H” is the pile length and “E   ” is the soil elastic modulus. Values for “   

  ”  

 

“     ” 

 

 

 

 

 

 

 

  

 

   

 

 

 

 

    

 

 

 

 

     

 

 

ak and El Sharnouby’s solution together with Randolph’s value    

 

    

ry of Novak and El Sharnouby’s solution is based on aplane strain soil. Randolph also used triangular linear strain elements in his study. Poulos and Davis’s  

     

   

 

 

from the Poulos and Davis’s solution, keeping in mind that their pile had a thin rectangular cross

 

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6. CONCLUSION

 

 

. Dependence of spring’s stiffness with pile diameter is  

    

 

     

7. REFERENCES