Issue 50

M. Godio et alii, Frattura ed Integrità Strutturale, 50 (2019) 194-208; DOI: 10.3221/IGF-ESIS.50.17 204 (16) Cases of structural resurrection, i.e. cases where the wall can sustain levels of PGA higher than those leading to collapse for the first time along the IDA [42], have already been observed in rocking masonry structures [43], but are here neglected. As observed in [32], they may occur occasionally but it would be unsafe to consider them in the evaluation of the wall collapse, since from a practical point of view the first onset of failure is of interest. The figure shows both real distributions, in dotted line, and fitted log-normal distributions, using the line type indicated in the legend. Comparing the curves obtained for all the studied configurations and for a given value of β, it can be noticed that increasing the wall thickness, which for a fixed wall height comes to decreasing the height-to-thickness ratio (C5-C8), the effective wall thickness over the nominal thickness (C9-C12) and the overburden ratio (C13-C16) increases the acceleration capacity of the wall. On the contrary, changes in the elastic modulus (C1-C4) have almost no effect on the acceleration capacity. An analogous outcome was obtained in [32] for walls subjected to identical support motion. Comparing the wall capacity for a given configuration and for all values of β, it appears that increasing β from 0 to 1, i.e. increasing the phase-shift between the top and the bottom wall supports, the fragility curves shift to the left, leading to a decrease of limit PGA for almost all probability levels and configurations. To better quantify the effect of a phase shift in the support motion, the median values PGA lim (50) are plotted in Fig. 6 for all configurations and all values of β. For the configurations C1 to C12, a phase-shift between the top and the bottom wall supports engenders a decrease of acceleration capacity of about 10% with respect to the in-phase case for β=0.5, which goes up to 20% when the phase-shift is maximum, i.e. for β=1. No significant difference between the configurations C1-C4 and C5-C12 is observed. For the configurations C13 to C16, the increase of overburden ratio at the wall top leads to a further reduction of the wall capacity. For the configuration C16, where O/W=6, the wall capacity is reduced to less than 40% of its initial value. The phase-shift of the support motions has therefore a detrimental effect on the wall acceleration capacity. This conclusion is supported by the observation of the wall failure mechanisms: even though the majority of the failure mechanisms is given by the formation of two macro-blocks spanning as illustrated in Fig. 1, for the 34% and 31% of the studied configurations and records, deformation patterns corresponding to higher rocking ‘modes’, i.e. deformation patterns characterized by the formation of more than two macro-blocks, are activated for β=0.5 and β=1, respectively. Unfavorable patterns as those discussed in [9], characterized by two macro-blocks rocking in the same direction, are observed for about the 0% and 3% of the cases, respectively. It appears, nonetheless, that the P-Δ effect engendered by the relative support motion due to the phase-shift combined with a relatively high axial load creates the worst-case scenario for the wall. Results for support motions with relative amplitude Fig. 7 shows the fragility curves for each of the configurations analysed in the parametric study and for support motions with relative amplitude, i.e. generated for different values of α, namely 0, 0.5 and 1. The fragility curves are built as for Fig. 5, as cumulative distributions of the limit PGA obtained from the IDA. Fig. 8 sums up the results, by showing the median values of the obtained limit PGA for all configurations and all values of α. Overall, the figures show how introducing relative amplitudes in the wall support motions has a detrimental effect on the wall acceleration capacity. More specifically, for the configurations C1 to C12, the relative amplitude between the top and the bottom wall supports engenders a decrease in acceleration capacity with respect to the equal amplitude case of about 10% for α=0.5, and of about 20% for α=1. For the configurations C13 to C16, the decrease in acceleration is much more important and peaks at 85% for configuration C16 for α=1. From the comparison of these results with those obtained from the first two sets of simulations (Fig. 6), it can be concluded that introducing relative amplitudes in the wall support motions has a detrimental effect on the wall acceleration capacity, which is comparable to the effect of introducing a phase-shift. It appears that the P-Δ effect engendered by support motions of relative amplitudes combined a relatively high axial load creates the worst-case scenario for the wall. The failure mechanisms activated on the walls are for 16% and 19% of the cases, respectively for α=0.5 and =1, higher ‘rocking modes’ and for 1% and 15% of the cases unfavorable patterns. O(O W) O ξ W   