# Seismic Fragility for a Masonry-Infilled RC (MIRC) Building Subjected to Liquefaction
## 3 Methodology  
The seismic vulnerability of structures has been defined with several approaches and, in the last decades, the probabilistic-based approaches have been particularly developed. Among these, developing of analytical fragility curves has been one of the most applied in order to consider several sources of uncertainties in the demand and capacity definitions. Many contributions proposed fragility curves for RC buildings [44; 45; 46], masonry buildings [47; 48] and for different typologies of structures [49] and infrastructures [50]. Fragility curves graphically represent the relationship between the probability of exceedance of a determined level of damage and the intensity of different seismic scenarios. In particular, Ref. [29] proposed to consider four limit states (slight, moderate, extensive, complete). It is worth noting that the development of fragility curves helps to account for several sources of variabilities, such as the dispersion due to the record-to-record and the intra-model variability and that relative to the definition of the damage states. In addition, most recent developments in probabilistic approaches of the seismic assessment have been proposed, such as [51; 52]. In the present paper, PGA is selected as Intensity Measure (IM), scaled to multiple levels from zero to 1.0 g, with steps of 0.1 g, by applying the approach called Incremental Dynamic Analysis (IDA), by [53]. The seismic vulnerability was assessed herein by considering (1) the potential of liquefaction at foundation level in terms of settlement and (2) the structural performance in terms of top-floor drift. Ten input motions (Figure 8) from the PEER NGA database ([[http://peer.berkeley.edu/nga/](http://peer.berkeley.edu/nga/)]([http://peer.berkeley.edu/nga/](http://peer.berkeley.edu/nga/)), accessed on 25 June 2021) were selected by following the Eurocode 8, Part 1 prescriptions [54] in order to be compatible with the code-specified spectrum for the life-safety limit state (corresponding to an earthquake with a return period of 475 years, lat. : 42.333 N, 14.246 E., S = 1.50714, Tb = 0.257 s, Tc = 0.770 s, Td = 2.538, Cc = 2.02847 [54]). Figure 8 shows the selected elastic response spectra (5% damping) and the mean spectral ordinates. Note that the mean spectrum (calculated among the selected ones) is included between the \(-\)10% and +30% of the code-based spectral shape, as prescribed in [54]. Table 8 shows the characteristics of the selected input motions in terms of Magnitude (Mw), closest distance, peak-to-peak velocity (PPV), pulse period, peak ground acceleration (PGA), peak ground velocity (PGV) and peak ground displacement (PGD). The inputs are divided into 5 Near-Field (NF) and 5 Far-Field (FF) motions, in order to explore the importance of source distance in earthquake scenarios. In addition, the set was selected to have significant dispersion of intensities to significantly affect the dynamic characteristics of the system. Figure 8: Selected input motions. Therefore, IDA nonlinear analyses were performed and since they were particularly challenging and time-consuming, it was necessary to apply four subsequent substeps [19; 20]. In step 1, the soil alone was loaded and linear properties (weight, shear and bulk modulus) were considered. The presence of the water (0.00 m depth) was introduced in step 2. In step 3, the structure was added and structural loads were applied. The soil properties were changed from elastic to plastic (in 25 load steps). Finally, in the last steps, the dynamic analyses were performed and Newton Line Search algorithm was used to increase the speed of the solution [38]. In order to save computational time, the longitudinal components of the input motions were considered only and applied at the base of the model. The study assumes that the probabilistic quantities were defined in terms of lognormal standard deviation (\(\beta\)), the median (\(\mu\)) of the lognormal seismic intensity measure (PGA).