GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 2.2 300 is the equivalent shear wave velocity of the deposit calculated at the basin center. The dimensionless wavelength-normalized basin width at the surface is introduced as where λ s,eq = V Ss , eq / f is the equivalent wavelength of the vertically propagating SV-waves, V Ss , eq = ( V Ss 1 ∙ H 1 + V Ss 2 ∙ H 2 ) / H is the equivalent shear wave velocity of the deposit calculated at the basin cen dime i le s wav length-normalized basin width at th surface is introduced as k Lλ = L 0 + L i λ s 1 where it is assumed that the wavelength of the surface waves propagating horizontally i layer can be taken as being equal to the shear wave velocity in the same layer, i.e., λ s 1 = V S Two further parameters were defined as the ratio of damping ratio values and Poisson c values of the top and bottom soil layer: k Ds = D s 1 D s 2 k νs = ν s 1 ν s 2 (11) where it is assumed that the wavelength of the surface waves propagating horizontally in the top layer can be taken as being equal to the shear wave velocity in the same layer, i.e., λ s1 =V Ss1 /f . Two further parameters were defined as the ratio of damping ratio values and Poisson coefficient values of the top and bottom soil layer: s,eq Ss , eq V Ss , eq = ( V Ss 1 ∙ H 1 + V Ss 2 ∙ H 2 ) / H is the equivalent shear wave velocity of the deposit calculated at the basin cen d mensionless wavelength-normalized basin width at the surf ce is introduced as k Lλ = L 0 + L i λ s 1 where it is assumed that the wavelength of the surface waves propagating horizontally i layer can be taken as being equal to the shear wave velocity in the same layer, i.e., λ s 1 = V S Two further parameters were defined as the ratio of damping ratio values and Poisson c values of the top and b ttom s il layer: k Ds = D s 1 D s 2 k νs = ν s 1 ν s 2 (12) V Ss , eq = ( V Ss 1 ∙ H 1 + V Ss 2 ∙ H 2 ) / H is th equivalent shear wave velocity of the deposit calculated at the basin cen dimensionless wavelength-normalized basin width at the surface is introduced as k Lλ = L 0 + L i λ s 1 where it is assumed that the wavelength of the surface waves propagating horizontally i lay can be taken as being qual to the s ar wave velocity in the same layer, i.e., λ s 1 = V S Two further parameters were defined as the ratio of damping ratio values and Poisson c values of the top and bottom soil layer: k Ds = D s 1 s 2 k νs = ν s 1 2 (13) Furthermore, to assess the effect of model size and geometry, models were classified into 8 section shapes based on combinations of L 0 , L i , and H as given in Tab. 2. Section shape L o [m] L i [m] H [m] k HL k Hint 1 (2) 250 150 50 0.125 0.25 (0.50) 3 (4) 250 300 100 0.182 0.25 (0.50) 5 (6) 500 300 100 0.125 0.25 (0.50) 7 (8) 500 600 200 0.182 0.25 (0.50) Tab. 2 - Definition of basin geometries ( L o : outer-width at each edge of the basin; L i : half-width of the inner part of the basin; H : maximum thickness of soil deposit; H 1 : depth of interface soil layers) Results Peak values of spectral aggravation AGF max were retrieved for each control point in each of the 192 models, along with the corresponding spectral period, termed fundamental aggravation period T f . Peak spectral aggravation ranges from 0.65 to 1.95, with T f covering the full range of spectral periods considered in the analysis as shown in Fig. 2, where AGF max is plotted versus by section shape as defined in Tab. 2. Higher values of peak spectral aggravation ( AGF max ≥1.5) correspond to T f =0÷0.8 s, while intermediate values (1.1≤ AGF max <1.5) are associated with fundamental aggravation periods in the range 0÷2.4 s. No cases of AGF max >1.1 are observed for T f >2.4 s. 2D deaggravation (i.e., AGF max <1) is observed for the full range of spectral periods; however, the lowest values of AGF max pertain to section shapes 7 and 8, i.e., to larger basins. The quantitative analysis of aggravation outputs relies on the assessment of statistical dependence of AGF max from each of the dimensionless parameters defined above. Such assessment is conducted through Kendall’s tau test (Daniel 1990), a non-parametric statistical test which has been frequently used for geotechnical applications (Uzielli et al. 2019). It provides more objective criteria for evaluating the influence of each of the dimensionless parameters on 2D aggravation parameters. Kendall’s test involves the calculation of the test statistic, τ k , whose values range from -1 to +1, indicating, respectively, perfect negative and positive correlation. A value close to zero indicates low correlation. The p-value, which can be calculated from τ k , is the probability that the null hypothesis of statistical independence can be rejected. If the calculated p-value is below a user- defined significance level, then statistical dependence can be established.