GNGTS 2021 - Atti del 39° Convegno Nazionale

299 GNGTS 2021 S essione 2.2 All materials were assumed to be homogeneous and linear visco-elastic (with shear modulus G=G 0 and damping ratio D=D 0 ). The boundaries of the 2D models were fixed by extending the bedrock by a length x e =y e =H both in the horizontal (both sides of the basin) and vertical direction (Fig. 1). Viscous dampers were assumed at boundary nodes to avoid wave reflection from the side boundaries within the analysis domain. Outputs of 2D numerical analysis were retrieved at several control points established on ground surface at constant horizontal spacing of 50m. The number of control points on the half-basin varies from 9 to 23 depending on the width of the cross-section scheme. 1D numerical analyses were performed on associated soil columns located at the control points defined in the 2D model. Input motion was assumed as vertically incident shear SH-waves and consisted of single Ricker wavelets with varying predominant frequencies ( f P =0.6 Hz, 2 Hz, and 10 Hz) and peak acceleration PGA =0.79g. It was applied simultaneously to all nodes at the base boundary of the analysis domain. Results of 1D and 2D ground response were processed in terms of pseudo-acceleration elastic response spectrum (5% damping ratio) for periods ranging from 0 to 4s with step 0.01s. To allow the generalization of results of the aggravation analysis, a set of dimensionless parameters was defined as follows to adequately parameterize the geometric, geotechnical, and seismic properties of the models. The width-normalized distance (e.g., Bard & Bouchon 1985) describes the spatial location of control points with respect to basin width: (3) The shape ratio (e.g., Bard & Bouchon 1980, 1985; Bouckovalas & Papadimitriou 2005) is the ratio of maximum thickness of the basin to its half-width: (4) The normalized depth of the interface, with respect to the maximum thickness of the basin, is: To allow the generalization of results of the aggravation analysis, a set of dimensionless para was defined a follows to adequ ely parameterize the geometric, geotechnical, and s properties of the models. The width-normalized distance (e.g., Bard & Bouchon 1985) describes the spatial locat control points with respect to basin width: k xL = x Li + Lo The shape ratio (e.g., Bard & Bouchon 1980, 1985; Bouckovalas & Papadimitriou 2005) is t of maximum thickness of the basin to its half-width: k HL = H Li + Lo The normalized epth f interface, with r spec to the maximum thickn ss of the basin, is k Hint = H 1 H The seismic impedance ratios between the bedrock and the soil layers and between the two c soil layers, k Is 2 s 1 , were considered: k Ibs 1 = V Sb V Ss 1 ⋅ ρ b ρ s 1 k Ibs 2 = V Sb V Ss 2 ⋅ ρ b ρ s 2 k Is 2 s 1 = V Ss 2 V Ss 1 ⋅ ρ s 2 ρ s 1 where the subscripts " b ", " s 1 ", and " s 2 " refer here and hereinafter to bedrock, soil 1, and respectively. The dimensionless wavelength-normalized height (modified from the single-lay proposed by Bouckovalas & Papadimitriou 2005) combines basin geometry, dynamic geote properties of the deposit, and seismic input characteristics: k Hλ = H λ s, eq where λ s,eq = V Ss , eq / f is the equivalent wavelength of the vertically propagating SV-waves, an (5) The seismic impedance ratios between the bedrock and the soil layers and between the two covering soil layers, , were considered: To allow the generalization of results of the aggravation analysis, a set of dimensionless para was defined s follows to adeq ately parameterize the geometric, geot chnical, and s properties of the models. The width-normalized distance (e.g., Bard & Bouchon 1985) describes the spatial locat control points with respect to basin width: k xL = x Li + Lo The shape ratio (e.g., Bard & Bouchon 1980, 1985; Bouckovalas & Papadimitriou 2005) is t of maximum thickness of the basin to its half-width: k HL = H Li + Lo The normalized depth of the interface, with respect to the maximum thickness of the basin, is k Hint = H 1 H The seismic impedance ratios between the bedrock and the soil layers and between the two c soil layers, k Is 2 s 1 , were considered: k Ibs 1 = V Sb V Ss 1 ⋅ ρ b ρ s 1 2 V Sb 2 b s 2 s 2 s 1 V Ss 2 V Ss 1 ⋅ ρ s 2 ρ s 1 where the subscripts " b ", " s 1 ", and " s 2 " refer here and hereinafter to bedrock, soil 1, and respectively. The dimensionless wavelength-normalized height (modified from the single-lay proposed by Bouckovalas & Papadimitriou 2005) combines basin geometry, dynamic geote properties of the deposit, and seismic input characteristics: k Hλ = H λ s, eq where λ s,eq = V Ss , eq / f is the equivalent wavelength of the vertically propagating SV-waves, an 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 cente (6) ll t r li ti f r lt f t r ti l i , t f i i l r fi a f ll t t l r t ri t tri , t i l, properties of the models. The width- ormalized distance (e.g., Bard & Bouchon 1985) describes the spatial locat co tr l i t it r t t i i t : k xL = x i The sha e ratio (e. ., r , ; l i itri ) i t of m im t i of t i t it lf- i t : k HL H Li + Lo r li t f t i t rf , it r t t t i t i f t i , i Hint = 1 The seismic impedance ratios between the bedrock and the soil layers and betwee t t il la r , Is 2 s 1 , r i er : k Ibs 1 = Sb V Ss 1 ⋅ ρ b ρ s 1 k Ibs 2 V Sb Ss 2 ⋅ ρ b ρ s 2 k Is 2 s 1 = Ss 2 V Ss 1 ⋅ ρ s 2 ρ s 1 where the subscripts " b , s 1 ", s 2 r f r r r i ft r t r , il , respecti l . i i l l t - r li d i t ( ifi fr t i l -l proposed by Bouckovalas & Papa imitri ) i i tr , i t r rti f t it, i i i t r t ri ti : Hλ = H λ s, eq wher λ s,eq = V Ss , eq / f i t i l nt l t f t rti ll r ti - , V Ss , eq ( Ss 1 ∙ 1 Ss 2 ∙ 2 ) / i t i l t r l it f t it l l t t t i t (7) To allow the generalization of results of the aggravation analysis, a set of dimensionless para was defined as follows to adequately parameterize the geometric, geotechnical, and s properties of the models. he idth-nor alized distance (e.g., ard ouchon 1985) describes the sp tial locat control poin s with respect to basin width: k xL = x Li + Lo he shape ratio (e.g., Bard & Bouchon 1980, 1985; Bouckovalas & Papadimitriou 2005) is t of axi um thickness of the basin to its half-width: k HL = H Li Lo The normalized depth of the interface, with respect to the maximum thickness of the basin, is k Hint = H 1 H he seis ic i pedance ratios bet een the bedrock and the soil layers and bet een the two c soil layers, k Is 2 s 1 , were considered: k Ibs 1 = V Sb V Ss 1 ⋅ ρ b ρ s 1 k Ibs 2 = Sb V Ss 2 ⋅ ρ b ρ s 2 k Is 2 s 1 = V Ss 2 Ss 1 ⋅ ρ s 2 ρ s 1 here the subscripts " b ", " s 1 ", and " s 2 " refer here and hereinafter to bedrock, soil 1, and respectively. The dimensionless wavelength-normalized height (modified from the single-lay proposed by ouckovalas Papadimitriou 2005) combin s basin ge m try, dynamic geote properties of the deposit, a d eismic inpu characteristics: k Hλ = λ s, eq where λ s,eq Ss , eq / f is the equivalent wavelength of the vertically propagating SV-waves, an 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 cente (8) where the subscripts “ b ”, “ s 1 ”, and “ s 2 ” refer here and hereinafter to bedrock, soil 1, and soil 2, respectively. The dimensionless wavelength-normalized height (modified from the single- layer cas proposed by Bouckovalas & Papadimitriou 2005) combines basin geometry, dynamic geotechnical properties of the deposit, and seismic input characteristics: To allow the generalization of results of the aggravation analysis, a set of dimensionless para was defined as follows to adequately parameterize the geometric, geotechnical, and s properties of the models. The width-normalized distance (e.g., Bard & Bouchon 1985) escribes the spatial locat control points with respect to basin width: k xL = x Li + Lo The sha e ratio (e.g., Bard & Bouchon 1980, 1985; Bouckovalas & Papadimitriou 2005) is t of maximum thickness of the basin to its half-width: k HL = H Li + Lo The norm lized depth of the interface, with respect to the maximum thickness of t e basin, is Hint H 1 The seismic impedance ratios between the bedrock and the soil layers and between the two c soil layers, k Is 2 s 1 , were considered: k Ibs 1 = V Sb V Ss 1 ⋅ ρ b ρ s 1 k Ibs 2 = V Sb V Ss 2 ⋅ ρ b ρ s 2 k Is 2 s 1 = V Ss 2 V Ss 1 ⋅ ρ s 2 s 1 where the subscripts " b ", " s 1 ", and " s 2 " refer here and hereinafter to bedrock, soil 1, and respectively. The dimensionless wavelength-normalized height (modified from the single-lay proposed by Bouckovalas & Papadimitriou 2005) combines basin geometry, dynamic geote properties of the deposit, and seismic input characteristics: k Hλ = H λ s, eq where λ s,eq = V Ss , eq / f i the equivalent wavelength of the vertically propagating SV-waves, an 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 cente dimensionless wavelength-normalized basin width at the surface is introduced as (9) where λ s,eq =V Ss,eq /f is the equivalent wavelength of the vertically propagating SH-waves, and To allow the generalization of resu t of th aggravati analysis, a set of di ensionless para was defined as follows to adequately parameterize the geometric, geotechnical, and s properties of the models. The width-normalized distance (e.g., Bard Bouchon 1985) describes the spatial locat control points with respect t basin width: k xL = x Li + Lo The shape ratio (e.g., Bard Bouchon 1980, 1985; Bouckovalas Papadi itriou 2005) is t of axi u thickness of the basin to its half-width: k HL = H Li + Lo The nor alized depth of the interface, with respect to the axi u thickness of the basin, is k Hint = H 1 H Th seismic impe ance ratios b tw en t e bedrock and the soil layer and between the two c soil layers, k Is 2 s 1 , were considered: k Ibs 1 V Sb V Ss 1 ⋅ ρ b ρ s 1 k Ibs 2 = V Sb V Ss 2 ⋅ ρ b ρ s 2 k Is 2 s 1 V Ss 2 V Ss 1 ⋅ ρ s 2 ρ s 1 where the subscripts " b ", " s 1 ", and " s 2 " refer here and hereinafter to bedrock, soil 1, and respectiv ly. The di ensionless wav l ngth-nor alized height ( dified fro the single-lay proposed by Bouckovalas & Papadimitriou 2005) combines basin geometry, dynamic geote pro er es of the deposit, and seismic input characteristics: k Hλ H λ s, eq wher λ ,eq V Ss , eq / f is the equiv lent wavelength of the vertically propagating SV-waves, an 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 cente di ensionless wavelength-nor alized basin width at the surface is introduced as L 0 + L (10)