GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 2.2 GNGTS 2023 exclusively dependent on the inter-site distance hjk for the simulation of the spatial correlation, requires the following assumptions: - intra-event residuals for a set of spatially distributed sites must follow a multivariate Gaussian distribution; - Gaussian random field must be second-order stationary; - GRF must be isotropic. Under these assumptions, a decomposition approach can be adopted for the simulation of spatially correlated ground motion fields. A random field of residuals Y following a multivariate Gaussian distribution, can be defined by a set of y1, y2, … yN residual values for N sites, generated as follows: (3) = μ + where Z is a vector of z1, z2, … zN values following a Gaussian standardized distribution, μ is a vector representing the mean value of the residuals (herein assumed μ = 0) and L is a lower triangular matrix obtained by the Cholesky factorization, such that LLT = C, where C is the correlation matrix defined positive as follows: = 1 ρ(ℎ 12 ) ρ(ℎ 21 ) 1 ⋮ ρ(ℎ 1 ) ⋮ ρ(ℎ 2 ) ··· ρ(ℎ 1 ) ··· ρ(ℎ 2 ) ⋱ ··· ⋮ 1 [ ] (4) and rjk(hjk) is the correlation coefficient between residual values obtained in pair of sites with a inter-site distance equal to hjk. Seismic fragility and consequence modelling. Pipelines systems can be subject to failures if located in areas prone to seismic hazard. In such cases, release is a direct consequence of structural failure pipes and other elements drift- or acceleration- sensitive. Seismic vulnerability of gas pipes is defined through fragility curves that represent exceedance probability values for a set of possible damage states as a function of the intensity measure value to which an element is subject during an earthquake. Focusing on the loss of hazardous material, structural damage states are converted in terms of release states (RS). For pipelines three different RSs are taken into account according to Lanzano et al. (2003) namely: RS0 (no damage), in which damage do not cause any loss of containment;