Effect of Buoyancy Loads on the Tsunami Fragility of Reinforced Concrete Frames Including Consideration of Blow-out Slabs

11 Currently available performance-based methodologies for assessing the fragility of structures subjected to tsunami neglect 12 the effects of tsunami-induced vertical loads due to internal buoyancy. This paper adopts a generalized methodology for 13 the performance assessment of structures that integrates the effects of buoyancy loads on slabs during a tsunami 14 inundation. The methodology is applied in the fragility assessment of three case-study frames (low, mid and high-rise), 15 representative of existing masonry-infilled reinforced concrete (RC) buildings typical of Mediterranean region. The paper 16 shows the effect of modelling buoyancy loads on damage evolution, structural performance and fragility curves associated 17 with different structural damage mechanisms for RC frames with breakaway infill walls including consideration of blow- 18 out slabs. The outcomes attest that the predominant failure mechanism of selected case-study is the brittle shear failure 19 of seaward columns, which is slightly affected by buoyancy loads. When brittle failure is avoided, buoyancy loads 20 significantly affect the damage evolution during a tsunami, especially in the case of structures with blow-out slabs. The 21 rate of occurrence of slabs uplift failure increases with the number of stories of the building but only slightly affects the 22 fragility curves of investigated structures. However, it can significantly increase their vulnerability, affecting both direct 23 and indirect costs deriving from the repair of the damaged interior slabs.


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Far-fault tsunami events have a low frequency but can induce high human and economic losses on coastal communities 28 (Ghobarah et

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(2017), among few others, have looked at buoyancy loads on structures with main focus on buoyancy acting at foundation 38 level to assess the resistance against global overturning of buildings. The latter is a typical collapse mechanism for 39 watertight buildings, buildings with strong slabs-on-grade or buildings with small opening ratios, as observed after the 40 2011 Tohoku tsunami (Chock et al. 2013). In buildings with breakaway infill walls (i.e., walls that fail out of their plane 41 during a tsunami inundation), the magnitude of buoyancy loads acting at foundation level after the failure of exterior 42 cladding is relatively low due to the limited enclosed space inside the structure, and global overturning is unlikely to 43 happen 1 . However, internal buoyancy induces uplift loads on elevated slabs due to enclosed spaces inside the structure, 44 air trapped below floors (i.e., air pockets) and submerged structural members 4 that have been largely ignored in tsunami  The performance of existing RC buildings to tsunami loads is herein investigated by means of refined FEM analyses 116 performed through the generalised VDPO-BI. In the following, the models selected to simulate lateral and vertical tsunami 117 on-shore flows on structures are first illustrated; then, the VDPO-BI procedure is briefly presented to assess the 118 performance of RC frames with breakaway infill walls and blow-out slabs.  Tsunami-induced lateral loads on structures mainly consist of unbalanced hydrostatic pressure, hydrodynamic or drag 121 pressure, bore forces and debris impact loads, while vertical loads are mainly related to hydrostatic buoyancy and 122 hydrodynamic surge (ASCE 7-16 2017). Many of these loads are impulsive and highly transient in nature, and hence are 123 neglected in the VDPO-BI. Indeed, in the VDPO-BI analysis the tsunami is simulated as a steady state flow (hydrostatic and hydrodynamic loads), and the initial bore phase is ignored 7 . Impact loads are extremely short duration impulsive loads 125 and cannot be represented by pushover analysis. In the context of ASCE 7, the hydrodynamic and hydrostatic loads need 126 not be combined with the debris impact loads because of the low probability of simultaneous occurrence of the maximum 127 of each type of loading (Robertson 2020). Soil erosion and scour induced by the tsunami flow are also neglected in this 128 study. Lateral and buoyancy induced loads on structures considered in the VDPO-BI are further discussed in next sections.

subcritical regime if Fr < Fr_c
(1)  where hbeam is the net height of the beams with respect to the slab, ρ is the sea water density, g is the gravitational 169 acceleration.

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 Buoyancy due to submerged slabs: a reduction of weight due to buoyancy is expected in submerged slabs during 171 the inflow. This uplift pressure due to submerged slabs can be computed as function of the volume of water 172 displaced by the slab (height of the slab hslab, see Figure 1b   Step 1 : Hw< HOOP Step 2 : HOOP ≤ Hw< h-hbeam Step 3 : h-hbeam ≤ Hw< h+HOOP Step 4 : h+HOOP ≤ Hw< 2h-hbeam

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According to ASCE 7-16, hydrodynamic loads acting on single structural components should be amplified by a drag 265 coefficient, Cd, that depends on the geometry of the components and the closure ratio. Following the ASCE 7-16 (2017),

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Cd is assumed equal to 2 for rectangular columns in buildings with a closure ratio less than 0.2. Higher drag coefficients 267 need to be used for structures with greater closure ratios to account for the increase in flow velocity inside the building.

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Hence, after the failure of breakaway infill walls, the impacting surface width b will be equal to the column width 269 amplified by the drag coefficient for both exterior and interior columns. It is assumed that partitions, given their lower Air pocketing -Eq. 3 Submerged slab -Eq. 4 Enclosed spaces -Eq. 5 Overall        The mechanical behaviour of concrete in compression is modelled with the Concrete04 material, representing the uniaxial 339 Popovics (1973) material with degraded linear unloading/reloading stiffness according to the work of Jirsa and Karsan 340 (1969). Given the lack of transverse reinforcement and the low axial load in columns, the confinement effect of the core 341 concrete is herein neglected. A bilinear stress-strain envelope, Steel02 in OpenSees (Filippou 1983), is adopted for the 342 steel longitudinal reinforcement.

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A fixed restraint is adopted for the base of first story columns. The RC slab usually plays the role of diaphragm for      for the tsunami fragility assessment, for the present study, a negligible damming debris accumulation at the site of the 489 structure is assumed (i.e., Cc = 0). This is deemed acceptable as the focus of this paper is to assess the influence of vertical 490 loads on structural performance, and significant lateral loads are already considered to be attracted to the structure due to 491 the presence of infill walls. Given this assumption, the case study buildings can be considered as representative of 492 buildings directly facing the shoreline (i.e., first row), and away from significant sources of damming debris. It should be 493 noted that such structures are also exposed to the impact loads from floating debris (i.e., boats)   Figure 8 shows the damage mechanisms evolution for the three case-study frames with indicated the occurrence of the 513 different EDPs used to define the damage scale in Table 3

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Conversely, for the low-rise case-study frame, the ductile complete damage mechanism is predominant. The brittle 525 mechanism is not achieved for the low-rise case-study frame under Fr = 0.7, see Figure 8a. However, it is worth noting 526 that the assumption about the Froude number affects significantly the damage mechanisms evolution, as further discussed 527 in Section 5.2. The extensive damage associated with blow-out slabs is achieved at almost same inundation depth values 528 of the extensive damage for ductile mechanisms.

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The ductile performance of the mid and high-rise case-study frames is computed assuming that the premature brittle 530 failure mechanism is avoided. This is useful to show the inclusion of buoyancy loads in the structural analysis and their 531 influence on the structural response, without consideration of precipitation of structural failure through brittle 532 mechanisms. Figure 8 shows that the effect of uplift loads is visible for slight to extensive ductile damage states, whilst 533 it is negligible at complete damage for the three case-study frames. More specifically, uplift loads anticipate the  The curves also show that buoyancy loads lead to a slight reduction of the overall lateral capacity for the case-study 571 frames in the case of non blow-out slabs (scenario ii). This is because, in the case of non blow-out slabs, the uplift loads 572 acting on the slabs significantly increases during the incremental analysis (see Figure 3a) up to the out-of-plane failure of 573 infill walls. For the low-rise frames, the maximum lateral capacity for scenario ii is achieved before the out-of-plane 574 failure of second story infill walls. Conversely, in the mid and high-rise frame, the failure of second story infill walls is 575 reached for scenario ii, causing a significant reduction of uplift loads on first story slab, see Figure 3b.

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The axial load (P) variation in first story exterior and interior columns due to buoyancy loads during the VDPO-BI is 582 illustrated in Figure 11a and b for low and high-rise frames, respectively. The plots show there is a significant reduction 583 of axial loads caused by the uplift loads on first story slab for increasing inundation depth. When failure of blow-out slabs 584 occurs, this induces a sudden relief for the columns, reducing the effect of internal buoyancy. Overall, the reduction in 585 axial load due to buoyancy is obviously more significant for low-rise frame rather than high-rise frames due to the lower 586 dead loads, leading to a consequent reduction of flexural capacity recognized on performance curves in Figure 10 587 (scenario ii). reported for the case-study buildings in Figure 12 as a function of the building height (e.g., Figure 12a for the low rise 593 frame, Figure 12b for the mid rise frame, Figure 12c for the high rise frame  For the three case-study frames, the predominant complete damage mechanism is associated with the brittle shear failure 623 of columns. Indeed, this is the first complete damage mechanism reached for almost all building realizations in the sample.

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In 30 low-rise realizations, 41 mid-rise realizations and 137 high-rise realizations (rate of occurrence 3.0%, 4.1% and 625 13.7%, respectively) the failure of the slabs is achieved before the brittle mechanism, as previously found during the 626 single-building performance assessment in Figure 8b,c. It is also observed for the low-rise case-study frames that the 627 brittle mechanism is not achieved for 23 realizations of the sample (rate of occurrence 2.3%), characterized by a Froude 628 number lower than 0.77, as found in the performance assessment shown in Figure 8a for Fr=0.7.

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The uplift failure of slabs is not reached for all the building realizations in the samples used to derive the fragility curves.  Table 1 and are compared in Figure 15.

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Fragility curves associated with brittle damage mechanism for the three scenarios are first investigated for the high-rise 673 case-study frame, for which a higher effect of uplift loads on such failure mechanism with respect to the low and mid-674 rise frames has been observed (see Figure 8). However, fragility curves in Figure 17 shows that the effect of uplift loads 675 on fragility for the brittle mechanism is almost negligible for the investigated case-study frame. This because the brittle 676 mechanism is usually reached for inundation depths lower than the first story slab soffit, when null or negligible buoyancy capacity. For the case study buildings, such an intervention alone would more than triple the tsunami inundation depth 690 that the case study buildings can sustain before failing (i.e., comparing collapse fragilities in Figure 13). It is also observed 691 that the structures with blow-out slabs are less fragile than those ones without blow-out slabs. Thus, the adoption of

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The authors have no relevant financial or non-financial interests to disclose.

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were 826 performed by Marta Del Zoppo. The first draft of the manuscript was written by Marta Del Zoppo and all authors 827 commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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The datasets generated during the current study are available from the corresponding author on reasonable request.