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

620

4

(

) 1 −

   

   

, eff L if ⎯⎯→  a

1 0.02 +

5.0

a

, eff L

I

=

(4)

a

a

u

0.29

5.0

, eff L ⎯⎯→  if a

a

L



a

=

a

(5)

, eff L

V

a

, s a

In Equation 5,  is the cyclic frequency of the excitation, L a is the pile active length and V s,a is an average shear wave velocity within one-half of L a , respectively (Di Laora and Rovithis 2015; Iovino et al., 2019; Stacul et al., 2022). In order to highlight the importance of the filtering effect in Figure 3 we present a pile-soil system consisting of a fixed-head single pile embedded in three different soil profiles, with G s distribution with depth according to the Equation 3. The seismic loading (vertically propagating SH waves) is applied at the base of the model. In these three pile-soil systems the following parameters were kept constant: H = 30 m, E p = 30 GPa,  s (soil Poisson’s ratio) = 0.4,  r (bedrock unit weight) = 23 kN/m 3 ,  p (pile unit weight) = 24 kN/m 3 . The remaining properties are summarized in Table 1. The real length L of the pile was dimensioned to guarantee approximately the same factor of safety for axial bearing capacity. Nevertheless, L is not a relevant parameter for quantifying the kinematic response when it is larger than L a . (infinitely long pile condition).

Fig. 3. Fixed-head single pile and the three soil profiles under examination

Table 1. Soil profiles properties.

Soil profile Soil type d [m] L [m]

 s [ton/m

3 ] G sd [MPa] a [-] n [-] L a [m] V s,a [m/s] V s,30 [m/s] Ground Type

1 2 3

Sand

0.80

19 22 29

1.62

41.87

0.0 0.0 0.0

0.5 0.0 1.0

4.10

152.6 120.0

310 120 110

C D D

OC Clay 1.2 NC Clay 1.2

2.0 2.0

28.8 2.88

7.4 9.7

38.2

As shown in Figure 4a the filtering effect is relevant in the case of piles embedded in soft soils (even if not clearly shown in Figure 4a, also increasing the pile diameter results in a reduction of I u , which means an increase of the filtering effect, i.e. a reduction of the seismic demand). The same results in Figure 4a are presented in Figure 4b, with the only difference that along the x -axis the frequency ( f ) have been replaced with the dimensionless effective frequency ( a eff,La ) governing the kinematic response.