PSI - Issue 62

Fabio Parisi et al. / Procedia Structural Integrity 62 (2024) 701–709 F. Parisi et al. / Structural Integrity Procedia -- (2024) _ – _

704

4

Parameter Values Characteristic (design) compressive strength of concrete ( ) Uniform (Discrete) 25-30-35 Characteristic (design) tensile strength of steel ( ) Uniform (Discrete) 375-440 Factor for the mean concrete compressive strength Normal Distribution

MPa MPa

µ = 1, σ = 0.18 µ = 1, σ = 0.09

- -

Factor for the mean steel tensile strength Volumetric ratio of transverse reinforcements ( )

Normal

Uniform (Discrete)

~ 0.05-0.08

%

The record-to-record variability is considered in fragility analysis through a suite of 100 ground-motion records selected from the SIMBAD database (Smerzini et al., 2014). For each ground-motion record, a dataset of intensity measures (IM) is derived. Those are subsequently used as features to train the RF models to predict the EDP of a given bridge pier. The seismic IM feature dataset is explained in Table 2, including several IM features which are generally used as representative of ground-motion acceleration or displacement demand intensity in the related literature. The dataset includes, also, some structure-dependent IM features which consider the spectral accelerations demand for selected vibration periods representative of the structural elastic or inelastic response (Nettis et al., 2023, 2021b).

Table 2. Intensity measure parameters adopted for machine-learning training and prediction.

IM [ ] [ / ] [ ] (1.00 ) [ ] [ ] ( ) [ ] ( ) [ ] ( ) [ ]

Name/definition

Peak ground acceleration Peak ground velocity Peak ground displacement Spectral acceleration at 1.00 s

Peak velocity and acceleration ratio, = / Spectral acceleration at 1.00 s

Spectral acceleration at 1.00 s Spectral acceleration at 1.00 s

( −1.5 ) [ ] ( −2 ) [ ] ( −1.5 ) [ ] [ ∙ ] Arias intensity, = duration

Average spectral acceleration, ( 1 − 2 ) = (∏ ( ) = 1 ) 1/ with ∈ [ 1 , 2 ] Housner intensity, = ∫ ( ) 0 2 .1 .5 , Sv(T) the spectral velocity at the period T Modified cumulative absolute velocity = ∫ ( )| ( )| 0 , ( ) = { 1, | ( )| ≥ 0.005 0, ℎ 2 ∫ 2 ( ) 0 with ( ) is the recorded acceleration at time and is the total Significant duration: time duration from 5% to 95% of the AI

[ ] [ ] [ / ]

3.2. Development of the seismic demand database We considered a population of 50 bridge model realisations to collect the seismic demand database accounting for the knowledge-based uncertainties. Each realization exhibits identical deterministic parameters but varying values for uncertain parameters: the values of the uncertain parameters are obtained by randomly sampling from the related statistical distribution by using the Latin Hypercube Sampling (LHS). For each realisation, all the quantities in Table 1 are sampled and generated according to sub-section 3.1. Opensees (McKenna, 2011) was employed to model and generate the numerical models for the bridge realisation. The modelling strategy is explained in (Nettis et al., 2023). Each model is analysed by using the abovementioned record suite, for a total number of analyses equal to 5000. For each analysis, the displacements registered at the top node of the piers are extracted as EDP and, subsequently, used to train the ML models as target values y of the dataset D . Summarising, the seismic demand dataset D is defined by means of 5000 instances in which the targets y are the