Shear design equation and updated fragility functions for partially grouted reinforced masonry shear walls

This paper proposes specific ultimate shear strength expressions for partially-grouted reinforced masonry (PG-RM) shear walls that are bed-joint reinforced (BJR) and made with either multi-perforated clay bricks (MPCLBs) or hollow concrete blocks (HCBs). For each unit type, a set of constant coefficients of an arbitrary mathematical expression is optimized to minimize the error against experimental databases of walls made with the same unit types. Additionally, the assembled databases are employed to calculate lognormal empirical fragility functions, following performance-based earthquake engineering (PBEE) methodologies. For this, two different engineering demand parameters (EDPs) (story drift ratio, SDR, and normalized diagonal shear demand, NDSD) are proposed, and two damage states (DS) (named DS4 for moderate damage and DS5 for severe damage) are investigated. The proposed shear formulae are used in the normalization of calculated NDSD values. Moreover, databases are sorted by a selected design parameter (aspect ratio) to calculate design parameter-sensitive fragility functions. Overall, the results indicate that the proposed expressions are more accurate than the corresponding expressions proposed by the American and Canadian codes when assessing BJR-PG-RM shear walls in terms of the average error and dispersion of relative prediction error. All the fragility curves adjusted to the whole database pass the Lilliefors goodness of fit test (α=5%). Comparing SDR-based curves of walls of a different unit type, DS4 curves present a smaller difference in the median value (θ) than DS5 curves. Additionally, the variations in the θ of NDSD-based curves of walls of different units are smaller than those observed in SDR-based fragility functions, indicating that NDSD represents a less variant EDP to describe the probability of shear damage at DS5 when a proper expression is employed for the normalization. Regarding design parameter-sensitive fragility functions, sorting databases reduces the number of data points used to calculate the functions, which produced two SDR-based and one NDSD-based function to fail the Lilliefors test (α=5%). In general, the θ value of SDR-based curves increases in proportion to the aspect ratio. Additionally, classifying the databases by a design parameter (aspect ratio) corroborated that the proposed expression has acceptable accuracy based on the adjusted NDSD-based DS5 fragility functions. It is highlighted that calculating design parameter-sensitive functions might increase the accuracy of PBEE assessments (e.g., loss estimations) when an EDP insensitive to design parameters normalization (e.g., SDR) is employed.