*1.1. A Brief Review of Sensitivity Analysis in Civil Engineering*

SA is a multidisciplinary science and, therefore, review articles focused purely on SA have a multidisciplinary character [14–19]. Only approximately 2.5% of all articles on SA are focused on civil engineering. In civil engineering, publications related to SA have a growing trend, but are not as progressive as traditional engineering topics, such as buckling; see Figure 1.

ling; see Figure 1.

growing trend, but are not as progressive as traditional engineering topics, such as buck-

In civil engineering, SA is focused on the stability of steel frames [20], deflection of concrete beams with correlated inputs [21], multiple-criteria decision-making (MCDM) [22], structural response to stochastic dynamic loads [23], rheological properties of asphalt [24], thermal performance of facades [25], strength of reinforced concrete beams [26], use of machines during the construction of tunnels [27], stress-based topology of structural frames [28], seismic response of steel plate shear walls [29], deformation of retaining walls [30], multiple-attribute decision making (MADM) [31], efficiency of the operations of transportation companies [32], unbalanced bidding prices in construction projects [33], shear buckling strength [34], reliability index *β* of steel girders [35], system reliability [36], seismic response and fragility of transmission toners [37], shear strength of corrugated web panels [38], inelastic response of conical shells [39], fatigue limit state [40], corrosion depth [41], building-specific seismic loss [42], vibration response of train–bridge coupled systems [43], shear strength of reinforced concrete beam–column joints [44], forecasts of groundwater levels [45], equivalent rock strength [46], vertical displacement and maximum axial force of piles [47], regional-scale subsurface flow [48], ultimate limit state of cross-beam structures [49], serviceability limit state of structures [50], deflection of steel frames [51], stability of observatory central detectors [52], bearing deformation and pylon ductility of bridges [53], load-carrying capacity of masonry arch bridges [54], free torsional vibration frequencies of thin-walled beams [55], stress and displacement of pipelines [56], fatigue dynamic reliability of structural members [57], deflection of roof truss structures [58], etc. Studies are performed using very different SA methods, which are not always chosen solely for purpose, but are subject to different paradigms that define what and how it should be investigated. Many studies apply only one type of SA, although more than one suitable SA method can be used. Some of the applied methods are traditional, In civil engineering, SA is focused on the stability of steel frames [20], deflection of concrete beams with correlated inputs [21], multiple-criteria decision-making (MCDM) [22], structural response to stochastic dynamic loads [23], rheological properties of asphalt [24], thermal performance of facades [25], strength of reinforced concrete beams [26], use of machines during the construction of tunnels [27], stress-based topology of structural frames [28], seismic response of steel plate shear walls [29], deformation of retaining walls [30], multiple-attribute decision making (MADM) [31], efficiency of the operations of transportation companies [32], unbalanced bidding prices in construction projects [33], shear buckling strength [34], reliability index *β* of steel girders [35], system reliability [36], seismic response and fragility of transmission toners [37], shear strength of corrugated web panels [38], inelastic response of conical shells [39], fatigue limit state [40], corrosion depth [41], building-specific seismic loss [42], vibration response of train–bridge coupled systems [43], shear strength of reinforced concrete beam–column joints [44], forecasts of groundwater levels [45], equivalent rock strength [46], vertical displacement and maximum axial force of piles [47], regional-scale subsurface flow [48], ultimate limit state of cross-beam structures [49], serviceability limit state of structures [50], deflection of steel frames [51], stability of observatory central detectors [52], bearing deformation and pylon ductility of bridges [53], load-carrying capacity of masonry arch bridges [54], free torsional vibration frequencies of thin-walled beams [55], stress and displacement of pipelines [56], fatigue dynamic reliability of structural members [57], deflection of roof truss structures [58], etc. Studies are performed using very different SA methods, which are not always chosen solely for purpose, but are subject to different paradigms that define what and how it should be investigated. Many studies apply only one type of SA, although more than one suitable SA method can be used. Some of the applied methods are traditional, e.g., applications of derivations [25,28], applications of Sobol SA [42,46] or application of the Borgonovo method [30], but highly specific and original SA methods [23,54], which are difficult or even impossible to compare with conventional methods [1], are also being developed.

e.g., applications of derivations [25,28], applications of Sobol SA [42,46] or application of the Borgonovo method [30], but highly specific and original SA methods [23,54], which are difficult or even impossible to compare with conventional methods [1], are also being In civil engineering, SA objectives are usually focused on the optimization of the properties of structures, design characteristics of structures or processes associated with construction activities. One of the important features of any structure is its reliability.

#### developed. *1.2. Reliability-Oriented Sensitivity Analysis*

In civil engineering, SA objectives are usually focused on the optimization of the properties of structures, design characteristics of structures or processes associated with construction activities. One of the important features of any structure is its reliability. In civil engineering, structural reliability is assessed using the well-developed concept of limit states [59,60], which clearly defines the design quantiles of resistance and the effect of load action. Regarding the ultimate limit state, a load-bearing structure is considered reliable if the high quantile of load action is smaller than the low quantile of resistance [61].

cept of limit states [59,60], which clearly defines the design quantiles of resistance and the

*1.2. Reliability-Oriented Sensitivity Analysis* 

A comparative study [61] showed large differences between four reliability-oriented sensitivity analyses (ROSA) and additional four SA used in reliability analysis. The conclusions [61] showed that a common platform that clearly translates the correlation between indices and their information value is absent in ROSA methods.

A reliability-oriented SA concept based on design quantiles was introduced in [62]. SA was performed using the total indices of the design quantiles of resistance and load without having to evaluate the SA of failure probability. This saves the computational costs of numerically demanding models. Mirroring the concept of limit states into the principles of SA brings the results of sensitivity studies closer to the engineering practice, reduces computational costs and expands the possibilities of modelers.

This article builds on [62] by introducing more general quadratic forms of quantileoriented sensitivity indices, which are compared with quantile-oriented sensitivity indices subordinated to contrasts [63]. Two SAs are compared with the classical Sobol SA in a case study using a non-linear function of the elastic static resistance of a compressed steel structural member. The advantages and disadvantages of all three methods are described and discussed.
