PSI - Issue 62

Stefano Stacul et al. / Procedia Structural Integrity 62 (2024) 617–624 Stefano Stacul and Nunziante Squeglia / Structural Integrity Procedia 00 (2019) 000 – 000

619

3

2. Pile-soil kinematic interaction mechanism and filtering effect During an earthquake soil deforms, because of seismic waves passage, and tries to impose its displacement profile to the pile foundation. The latter is unable to follow the soil deformations due to the high flexural stiffness of the piles. Therefore, the pile foundation modifies the soil motion compared to that in the free-field ( u ff ) and originates via the pile-soil kinematic interaction the so-called FIM (Figure 2).

Fig. 2. Foundation Input Motion

The modification of the free-field motion is generally quantified via kinematic response factors, I u (Equation 1) and I  (Equation 2), which represent the Fourier spectrum ratios between the pile-head motion (displacement u p and rotation  p ) and the free-field motion ( u ff ) (Blaney et al., 1976; Fan et al., 1991; Kaynia and Kausel, 1991; Nikolaou et al., 2001; Anoyatis et al., 2013; Iovino et al., 2019; Stacul et al., 2022; Stacul and Squeglia, 2023). These coefficients describe the ability of the piles to act as a filter (filtering effect) and are mainly influenced by the pile ( E p ) and soil ( E s ) stiffness and by the pile diameter ( d ).

( ) ( )  

u

( ) 

p

I

=

(1)

u

u

ff

( )   p

d

( )  

( ) 

I

=

(2)



u

ff

As an example, for an infinitely long fixed-head single pile embedded in a continuously inhomogeneous linear viscoelastic soil with the shear modulus ( G s ) varying with depth according to the Equation 3, Di Laora and Rovithis (2015) derived the Equation 4 for I u in which a eff,La is a dimensionless effective frequency (Equation 5) governing the dynamic pile-soil kinematic interaction.

n

z

(  =  + −      sd d 

( ) ) 1 G z G a a

(3)

s