PSI - Issue 44

Ylenia Di Lallo et al. / Procedia Structural Integrity 44 (2023) 488–495 Y. Di Lallo et al./ Structural Integrity Procedia 00 (2022) 000–000

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angle ( Φ ). Subsequently, a data-driven mathematical model was developed through the Evolutionary Polynomial Regression (EPR) formulated by Giustolisi and Savic (2006), implemented in the Evolutionary Polynomial Regression EPR MOGA-XL-Office Excel Add-in (1.0). This regression model implements a Multi-Objective Genetic Algorithm (MOGA) strategy, which ultimately provides a set of Pareto optimal solutions that can be considered as a good compromise between structural complexity and accuracy of the model. Outcome of this regression was a set of transformation relationships describing each of the three afore-mentioned parameters ( σ tra , c, Φ ) as a function of one or more parametric variables of the wall population analysed in Step 1 which are mortar tensile stress ( σ t ), mortar friction angle ( Φ ), pre-compression vertical load ( p ) and wall aspect ratio ( B/H ). It is worth noting that all the resulting relationships presented a CoD (Coefficient of Determination) higher than 96%, meaning that the reliability and goodness of fit of all Pareto solutions were considerable. The last step consisted in performing a series of numerical analyses on well-known benchmark walls in order to determine the final set of optimal, hence most efficient, transformation relationships among the proposed ones. Detailed information about this process can be found in Di Lallo et al. (2022) and Brando et al. (2022). The final closed-form equations, chosen according to these criteria, are summarized in Table 1. Table 1. Final transformation relationships obtained from the EPR-MOGA. Optimal models CoD Average Error = +0.035 0 . 33 0 . 5 + 0.986 99.93% 2.01% = +0.049 0 . 33 0 . 5 + 1.38 99.93% 2.03% Φ = +6.206 1 0 . 33 + 0.428 1 � 0 . 33 + 0.015 2 96.80% 2.05% 3. Nonlinear pushover analysis of full-scale URM façade 3.1. Generality As mentioned in the Introduction, the proposed model was validated by the Authors in a previous study through the numerical reproduction of benchmark masonry walls. The numerical investigation was carried out using the MIDAS FEA software. The obtained results appeared very promising as the MUDis approach enabled to reproduce very well the experimental behaviour of the analysed walls under vertical and horizontal loads, and to satisfactory catch their load-displacement capacity and resistance values while reliably replicating their final crack patterns. Interested readers can refer to Brando et al. (2022) for details. To further evaluate the reliability of the proposed approach and generalize its applicability, it is important to extend its validation to more complex structures. The present work is intended for this purpose. 3.2. Experimental test With the aim of demonstrating the wide applicability of the modelling approach described in the previous Section, the MUDis procedure is here employed for simulating the in-plane behaviour of a full-scale URM façade, part of a three dimensional building tested at the University of Pavia (Magenes et al. (1995)). The original specimen consisted of a single cell with plan sizes of 6.0 × 4.4 m and four clay brick walls, 0.25 m thick and 6.4 m high, arranged following an English bond pattern. Fig. 2(a) shows the planimetric configuration of the original specimen. The floors, loaded with concrete blocks to simulate gravity loads – for a total of 248.4 kN at the first floor and 236.8kN at the second floor (i.e. about 10 kN/m 2 pe floor), were made of isolated I-section steel beams to form flexible diaphragms. The peculiarity of this test consisted in disconnecting the front façade, called the “door wall” or “wall D”, from the orthogonal walls A and C (see Fig. 2(a)), allowing to study this part as an independent structure from the rest of the building. The configuration and geometric dimensions of the analysed façade are detailed in Fig. 2(b). Considering the type of structure and the dependency of its response on the loading rate, four quasi-static cyclic forces were applied at each floor level through displacement-controlled screw jacks to simulate its in-plane response under lateral loads. As described in the following section, the testing campaign of the “door wall”, including its experimental