Finding Characteristic Depth of Strip Foundation

[Zouatine]

Homework Statement

vibration of soil , get the sttifness of soil

Relevant Equations

Boussinesq solution k=4GR/1-v

hello everyone!
i have some problem in solution of this problem should i transfert the vertical stree to the horizontal stress and solve it ?

problem :

The equivalent static stiffness of the soil as an infinite elastic half-space under an infinite strip foundation is given in the vertical direction for a unit length of the foundation as:
static vertical stiffness K=1.6*G/1-v where
G: is the shear modulus of the soil ,
v : is the poisson ration of the soil

question:
Assuming an exponential increasing width ,
find the characteristic depth of the equivalent soil strip for the analysis of the horizontal vibration of the foundation.

thank you

 

[Nate810]

Yes, you should transfer the vertical stress to the horizontal stress in order to solve the problem. You can use the following equation to calculate the characteristic depth of the equivalent soil strip for the analysis of the horizontal vibration of the foundation: Khorizontal = Kvertical * (1 + v) / (1 - v) where Kvertical is the vertical stiffness of the soil, and v is the Poisson's ratio. Once you have calculated the horizontal stiffness, you can then use it to calculate the characteristic depth of the equivalent soil strip.