Individual Pile and Group Pile Stiffness 1

[KOKONIS36]

I have to design a 3-span bridge.The piers are resting on pile foundations.I need to calculate the stiffness terms of individual piles and the stiffness terms of the pile group (7 piles X 5 piles ,total 35 ).
Any ideas how to calculate the stiffness terms ?Or any references ?

 

[Qshake]

For ordinary design of pile footings, we don't use the pile stiffness but rather the simplified method of P/A+-My/I. For this I suggest that you check out Peck, Hanson and Thornburn's Foundation Engineering.

If you really need the pile stiffness, say for seismic design (for use in the dynamic analysis), I suggest seeing one or both of Foundation Engineering by Joseph Bowles or Seismic Design of Bridge Foundations (?) by Earthtech. The latter was an FHWA publication. At any rate, Bowles is pretty comprehensive.

The reason we don't use a matrix approach to the foundation design is lack of soil stiffness information or that the soil stiffness information is vague and highly variable. This could unconservatively impact the results of the pile analysis via matrix methods. Thus for many years the above method has been used day in day out.

 

[yakpol]

Well, I did it a few times...

If individual pile stiffness matrix coefficients are:
k11 - axial (along X-axis) [k/ft]
k22 - translation along Y-axis [kip/ft]
k33 - translation along Z-Axis [kip/ft]
k44 - torsional [kip-ft/rad]
k55 - bending about Y-axis [klp-ft/rad]
k66 - bending about Z-axis [klp-ft/rad]
k26, k62, k35, k53 - off diagonal terms [kip] (or neglect)

Center of pilecap coordinates Y=0, Z=0
and y, z - individual pile coordinates,

Then equivalent matrix stiffness of Pile foundation:

K11 = Sum(k11)
K22 = Sum(k22)
K33 = Sum(k33)
K44 = Sum(k44)+Sum(k11*(y^2+z^2))
K55 = Sum(k55)+Sum(k11*z^2)
K66 = Sum(k66)+Sum(k11*y^2)
K26=K62=Sum(k26) (NEGATIVE!)
K35=K53=Sum(k35) (POSITIVE!)

The trouble comes when you will find out that each of your piles has different stiffness due to pile group effect and stiffer outside piles are overloaded. But it's a whole different issue...

Yakov

 

[yakpol]

This reply is addition to my previous posting. Axial spring k11 for individual pile will be different depending if pile is in compression or in tension under particular load. In compression stiffness equals to combined bearing and friction, in tension - uplift friction only. For simplicity you can use an average of two values.