Various past studies have carried out multiple parameter sensitivity analyses on different structural systems. The impact of input variable uncertainties on sensitivity in seismic response parameters have been studied for steel frames (Vamvatsikos and Fragiadakis 2010, Zona et al. 2012), masonry buildings (Rota et al. 2010), RC frames, wood frames (Aslani et al. 2012), gravity dams (Alembagheri and Seyedkazemi 2015), bridges (Padgett and DesRoches 2007), and steel jacket offshore platform (Eldin and Kim 2016).
Mehanny and Ayoub (2008) considered different systems with the idealized single degree of freedom, and observed that the record-to-record variability is more considerable than the effect of uncertainty in the system parameters. Idealized systems for fourteen first mode-dominant structures with equal nominal relative lateral strength were considered in the study. Dolšek (2009) extended the incremental dynamic analysis with Latin
5.2 Need of the Study
hypercube sampling to a set of reinforced concrete (RC) structures and showed that epistemic uncertainty does not have a significant influence on the seismic response parameters in the range far from collapse, but could have a significant influence on collapse capacity. It was also shown by means of Spearman correlation coefficient that of all the sources of epistemic uncertainty, damping and the ultimate and yield rotation in the columns have the greatest influence on the response of the RC structure. The uncertainties that influence the beams were not found to be so important for structures governed by the failure of columns. Kim et al. (2011) studied the sensitivity of design parameters, such as yield strength of beams, columns, and braces, live load, elastic modulus, and damping ratio of steel buildings subjected to progressive collapse. It was observed that the sensitivity of response depends on the collapse mechanism of the system. Limited studies (Celarec et al. 2012, Uva et al. 2012) on infilled RC frames were carried out in the past for examining the sensitivity of seismic response parameters to the uncertain modelling variables. However, only pushover analysis was carried out in these studies, because the use of nonlinear time-history analysis was computationally highly demanding. They observed that the parameters related to masonry infill have major influence on the response sensitivity of masonry infilled RC frames.
The sensitivity of a single input variable in the seismic response parameters is the simplest approach that can be used to study the influence of modelling uncertainty (e.g., Porter et al. 2002, Vamvatsikos and Fragiadakis 2010, Celik and Ellingwood 2010).
Sensitivity analyses have been carried out in the past using different methods, such as tornado diagram analysis (TDA), first-order second moment (FOSM), Plackett-Burman design (Seo 2013) and Latin hypercube sampling (LHS) as discussed by Eldin and Kim (2016). TDA is a common tool for decision analysis, where the difference in the lower and the upper bound fractiles (known as swing) is evaluated to estimate the impact of a random input parameter on the output response. Porter et al. (2002) studied the sensitivity of seismic response of a high-rise non-ductile RC frame building to several parameters, and represented damage factors for the building using tornado diagrams.
More recently, Seo and Linzell (2013) investigated on sensitivity of response of curved steel bridge to different parameters using tornado diagram analysis and provided insight into the seismic behavior of curved bridges. FOSM method uses a first-order Taylor series, and the first and second moments of the input variables to determine the random probability distribution of the response (Lee and Mosalam 2005, Baker and Cornell 2008,
Vamvatsikos and Fragiadakis 2010, and Celarec and Dolšek 2013). In both TDA and FOSM methods, the mean and standard deviation of the input parameter is predetermined, and based on that, the mean and standard deviation of the structural response is obtained. However, FOSM has been observed to lose accuracy when the relationship between input and response variables is nonlinear, which is a concern when modelling collapse (Gokkaya et al. 2016). LHS method uses stratification of the probability distribution function of a random variable. However, it gives only the relative importance of the input uncertain variables, and therefore, swing values cannot be obtained. Also, in case a large number of variables are involved, the number of simulations would be large and computationally intensive. Recently, Crozet et al. (2017) used Sobol′ indices (Sobol′ 1993) or variance-based sensitivity indices, given by Eq. (5.1), for sensitivity analysis of pounding between adjacent structures.
Var[E( | )]
Var( )
i i
S Y X
= Y (5.1)
where, Si represents the first order Sobol′ index, Xi is the random input variable, Y is any output variable, Var is the variance, and
[E( | )] Y X
i represents the expectance of Y conditioned on Xi. The Sobol′ index can be determined up to any order based on the number of independent random variables. For considering qualitative variables in contrast to numerical variables, Soleimani et al. (2017) considered categorical regression model and carried out Lasso regression to evaluate the influential set of parameters out of a large number of covariates.Review of past literature clearly shows that several methods, each having its own merits and demerits, have been adopted for sensitivity analysis of variety of structures without any consensus. Further, as discussed not many studies have been conducted on sensitivity analysis of masonry infilled RC frames. The choice of a proper engineering demand parameter (EDP) is important in seismic performance assessment of structures (Choudhury and Kaushik 2018b). The present study estimates the sensitivity of global seismic response (i.e., top or roof displacement) to uncertainty in various basic structural modelling parameters, such as those related to material (strength of concrete, steel, and masonry) and geometry (column dimensions). Three different types of structural frames are analyzed using nonlinear dynamic analysis: bare frame (BF - with no infills in any storey), open ground storey (OGS) frame (i.e., vertically irregular frame with infills only