Seismic Retrofit of Pilotis Buildings by Novel Aluminium Buckling-Restrained Braces (Al-BRBs). Application to a Modernist Architecture Building in Lisbon

ABSTRACT

The worldwide dissemination of the pilotis multi-storey RC buildings, generally attributed to the architect Le Corbusier, was contemporary with a structural engineering line of thought that advocated a soft first storey as a means of filtering down the seismic inertia forces in the upper storeys. These two architectural and structural international trends, combined with outdated detailing and low-code seismic design, greatly increase the risks of developing a soft storey sidesway mechanism at the first storey, as shown in past earthquake occurrences and other studies. The article explores the possibility of strengthening a representative 1955 pilotis building in Lisbon by the inclusion of novel aluminium buckling-restrained braces (Al-BRBs) at the first soft storey. This should reduce the extreme deformation concentration at that level without fully eliminating it, and thus take advantage of the additional damping provided by the stable hysteretic behaviour of the Al-BRBs. These Al-BRBs have some distinctive features that take advantage of the unique properties of the aluminium alloys, such as the formability (allowing for an extruded casing component) and the possibility of improving the low-cycle fatigue and deformation characteristics of the core component by means of thermal treatments.

KEYWORDS:

• aluminium
• multi-storey buildings
• nonlinear static analysis
• nonlinear time-history analysis
• pilotis
• soft storey

1. Introduction

There is a growing interest in the seismic assessment and retrofit of modern heritage or listed buildings with reinforced concrete (RC) structures, as exemplified by the works of Sorace and Terenzi (2013), De Luca, Verderame, and Manfredi (2014) and Terenzi et al. (2020), among many others. Within that broader research field, the so-called Pilotis buildings, examples of modernist architecture, present very specific features related to the potential soft storey sidesway mechanism at the first storey and therefore deserve particular attention.

The first half of the 20th century witnessed the inception of the Pilotis reinforced concrete (RC) frame buildings, generally attributed to the influential reflections and insights of the architect Le Corbusier. This multi-storey building type can be characterised by a relatively stiff upper body (all storeys above the first with abundant, supposedly non-structural, block masonry partition and external walls, providing unaccounted restraint to the RC structural elements) resting over unrestrained columns in the first storey, termed ‘pilotis’. This architectural building concept found great acceptance within the modernist architecture movement. Contemporary with the inception and dissemination of that architectural building type, an international structural design trend advocated resorting to a soft first storey in multi-storey buildings as a means of filtering the inertia forces developed at the upper storeys under an earthquake event. These two (architectural and structural) concurrent international trends led to extensive dissemination of the building concept with numerous important buildings in many earthquake vulnerable cities worldwide. Several earthquakes that occurred after 1970 evidenced the potential shortcomings of the building concept under discussion, with the formation of soft storey sidesway mechanisms at the first storey, generally followed by the partial or total collapse of the buildings. These observations are in line with some shaking table tests focused on the effects of irregular distribution of masonry infills in RC frame buildings. This soft (or weak) storey concept is further discussed in Section 2.

The article concentrates on one of the most promising applications of a novel aluminium buckling-restrained brace (Al-BRB), which is to strengthen pilotis buildings by including these dissipative braces at the first storey. The Al-BRB under development presents some distinctive features, such as an extruded aluminium external casing with radial stiffeners (instead of the more common mortar-filled tube) and the reliance upon the hysteretic dissipative core made with a dedicated specific heat-treated aluminium alloy, for example. Section 3 contains an overview of other Al-BRBs and a more detailed presentation of the Al-BRB under development.

The case study building is one of a set of five identical buildings known as the housing complex of Avenida Infante Santo (Infante Santo Avenue) in Lisbon. It is a multi-storey (nine floors) frame building erected in the 1950s with a particularly high (approximately 5 m) first storey almost entirely devoid of masonry walls. In addition to the pilotis building configuration, the markedly low earthquake loads considered in the design, the outdated detailing, and the sparse transversal links/hoops in the pilotis columns raised concerns about the seismic safety of the building. These concerns led to the assessment of the building’s safety in light of the requirements set by different versions of Part 3 of Eurocode 8, and subsequently to the design of an Al-BRB strengthening solution. The seismic assessment of the original building, exemplified by nonlinear static analyses, and the subsequent design and assessment of the building, strengthened by the inclusion of Al-BRBs at the first storey, exemplified by nonlinear static and time-history analyses are presented in Section 4.

Section 5 summarizes the main conclusions of the study.

2. Discussion on the soft (or weak) storey concept

The origin of the soft first storey building type, exemplified by the case study building, can be traced back to structural and architectural design trends that started in the early 1900s, coincidentally during the initial applications of reinforced concrete (RC) construction.

As for the structural design origin, one of the early concepts in the earthquake-resistant design of multi-storey buildings was that a soft first storey could act as a filter, limiting the demands in the higher storeys, similar in some ways to the ground floor level base isolation concept. Slender columns and the absence of other stiffening components at the first storey level could provide this soft first storey. One of the first known discussions on this early concept is the work of Martel (Martel 1929). Taking steel frame buildings as an example the author tried to set the simplified conditions in which the accelerations in the upper portions of the building were effectively reduced because of the deliberately created soft first storey. Those conditions were based on the linear behaviour assumption and expressed in terms of the periods of the earthquake and the fundamental mode of the building. Green (1935) and Jacobsen (1938) further discussed this linear elastic planned soft first storey concept. Later on, Fintel and Khan (1969) devised an alternative structural solution exploring the nonlinear behaviour, concentrated at the soft storey, by controlling the yielding at this level and dissipating energy in a purposeful and localized manner. This revised concept took advantage of the soft storey filtering effect, limiting the transmission of shear forces to the upper levels, supposedly truncated to the yielding force of the soft first storey. The reduction of the demands on the upper storeys was such that these upper levels were believed to remain elastic and undamaged, and have their design to lateral forces controlled only by the wind action. Chopra, Clough, and Clough (1973) subsequently studied the nonlinear behaviour of the soft first storey for two representative 8-storey building models, one considered stiff and the other flexible (fundamental periods of 0.5 s and 2 s, respectively), varying the yield shear force and post-yield stiffness at the soft storey for a collection of artificially generated accelerograms. The final outlook of those simulations was unclear as to the effectiveness of the underlying assumption that a bilinear soft first storey would limit the demands in the upper storeys, particularly for non-negligible post-yield stiffness models. That study also led to the predictable conclusion that very large displacements may occur at the first storey, especially for more flexible buildings. To the authors’ knowledge, the assumption that a deliberately soft first storey would prove beneficial for the earthquake-resistant design of multi-storey buildings has been gradually abandoned since the early 1970s.

Coincidentally, the same period (late 1910s to late 1970s) witnessed the inception, development, and dissemination in many earthquake-vulnerable urban areas worldwide of the so-called ‘Pilotis’ buildings architectural concept. The origin of this building type can be traced back to the famous architect Charles-Édouard Jeanneret, known as Le Corbusier, starting in his 1914–1915 Dom-Ino house. This was an open floor plan modular structural model in which the reinforced concrete skeleton structure (columns, flat slabs, stairs, and footings) allowing for free placement of sheeting/screening non-structural walls (or for simple suppression of these at a given storey). Later on, in Le Corbusier’s book Vers une architecture (Corbusier 1923) there are references to buildings over ‘Pilotis’, tall unobstructed columns on the ground floor that permit free circulation and simple maintenance of building utilities. In 1927, the manifesto Les cinq points d’une architecture nouvelle (‘The five points of a new architecture’), authored by Le Corbusier and Pierre Jeanneret, advocated the use of pilotis, raising the enclosed spaces of the building to a height of 3 to 6 m above ground level (1^st point) and the free plan (3^rd point), allowing for free placement of the partition and external walls, regarded as non-structural membranes. Along with other advantages, Le Corbusier argued that raising the enclosed spaces to the first floor presented benefits in terms of health and natural lighting. Some of the first implementations by Le Corbusier of this building type are the Villa Savoye, a single-family home built in 1928–1931 in Poissy, France, and the Unité d’Habitation in Marseille, France, initiated in 1939 and built in 1947–1952, a multipurpose (predominantly residential) group of multi-storey buildings with pilotis at the first storey. The latter representation is considered to have had a seminal effect on the modernist architecture movement worldwide, greatly influencing multi-storey building construction until the early 1970s, of which the case study building is an example. Langenbach (2007) in an overview of the construction techniques and materials over time, particularly in terms of the earthquake resistance consequences, drew attention to the potential design misconceptions and weaknesses resulting from the ‘dematerialization’ of the walls and the resort to pilotis at the ground floor in the influential works of Le Corbusier. Guevara-Perez (2012) further discussed the soft (first) storey (also termed as ‘weak storey’) structural concept resulting from the architectural currents (such as the one initiated by Le Corbusier) or from other architectural or urban planning considerations.

The weaknesses of the deliberate soft first storey structural design approach became increasingly evident as earthquakes struck areas with these types of buildings. The 1971, 9 February San Fernando (also known as the 1971 Sylmar) earthquake that struck the Southern California region led to damage to the Olive View Hospital buildings, completed in December 1970, to the extent that those buildings had to be demolished. Mahin et al. (1976) significantly attributed the abnormal damage to the hospital to the interruption of the structural (shear) walls below the second floor, concentrating damage in the bottom two storeys (with storey drifts over 30 in, 760 mm, at some points), leading to a partial sidesway mechanism (Figure 1a). The 1979, 15 October Imperial Valley earthquake, South of the Mexico-US border, led to the partial collapse of the Imperial County Services building in El Centro, US. According to Zeris, Mahin, and Bertero (1986) and Zeris and Scodeggio (2016), the intended pilotis structural system at the first storey was the main cause of such damage, leading to catastrophic failure of a row of peripheral columns at the first storey (Figure 1b). This occurrence and ensuing discussion raised the issue of the contribution of superstructure rocking to the lateral seismic response of pilotis RC structures. Later on, in the 19 September 1985 Mexico City earthquake (also known as the Michoacan earthquake), 8% of the damaged buildings presented a weak first storey, according to Rosenblueth and Meli (1986). Ruiz and Diederich (1989) studied the effects of the lateral strength discontinuity of the first (weak) first storey in the ductility demand of that storey for that earthquake. The study considered a narrow-band, high period, ground motion accelerogram of that event (predominant period of approximately 2 s), and concluded that the effect of the weak first storey greatly depends on the dominant periods of the excitation and response. If the nonlinear natural period of the building is clearly below that of the excitation, the soft storey effects are limited. If, on the other hand, those two periods are close, excessively high first-storey displacements are to be expected. The pattern exemplified in the previous earthquake occurrences in terms of the aggravated damage in soft first storey buildings (including pilotis buildings) continued in subsequent occurrences.

Figure 1. Examples of soft first storey building collapses: (a) Olive View Hospital, Sylmar, US; and (b) Imperial County Services building, El Centro, US (Zeris and Scodeggio 2016).

Further confirmation of the fragilities inherent to the soft first storey concept is provided by shaking table tests. Santhi, Knight, and Muthumani (2005) tested two 1:3 scaled three-storey, single-bay, RC building models, one with brick masonry infill walls in the second and third storeys only and the other without infill walls. The initial fundamental mode shapes of these two models were substantially different; the soft storey frame was shear-dominated whereas the bare frame was flexure-dominated. These models were tested for simulated earthquakes of intensities (PGA) from 0.1 g to 0.96 g (6 levels). The damage was concentrated in the first storey for both models, leading to an impending failure mechanism for the 0.96 g PGA test with hinges forming at the top and bottom of the ground floor columns. The bare frame exhibited a more ductile behaviour (ductility ratio increased by 150%, based on numerical simulations). Kabir and Shadan (2011 and Kabir, Shadan, and Kabir 2018) tested a 1:2.35 scaled three-storey, single bay, RC building model in which the first storey presented a bare moment-resisting frame structural system, whereas the others were constructed with a 3D precast wall panel system. The irregular distribution of lateral stiffness along the height led to the concentration of damage and drift in the soft first storey (at the ends of columns and beam-column connections), with limited damage in the remaining storeys. Gong et al. (2019) performed shaking table tests on two three-storey, two-bay, 1:4 scaled RC frame models designed according to the Chinese code, one with infill walls with the exception of the first storey (pilotis frame) and the other without infill walls (bare frame). These physical models were subjected to a sequence of scaled earthquake ground motions of increasing intensity (PGA of 0.1 g to 0.6 g, six levels with 0.1 g interval) and the observation focused on damage (and failure) and acceleration amplification factor and interstorey drift ratio distributions along the height. It is interesting to note that for the pilotis frame the acceleration amplification factor at all floors decreases to values close to unity for higher PGA values, at the cost of significant damage in the first storey. The interstorey drift ratio in the pilotis frame model was increasingly concentrated at the first storey as the PGA values were increased. The interstorey drift ratio of the pilotis frame is up to 50% larger than that of the bare frame for the same earthquake intensity. The damage in the pilotis frame is concentrated in the columns of the first storey.

As a preliminary conclusion, there is significant evidence, provided either by the observation of damage in past earthquakes or by scientific studies (exemplified by shaking table tests), that the vertical irregularity in pilotis buildings increases the risks of developing a soft storey sidesway mechanism at the first storey.

3. Aluminium buckling-restrained braces (Al-BRBs)

3.1. Overview

One of the most effective ways of strengthening existing building structures is that of adding, locally (at a given storey) or globally (uniformly along the height of the building), buckling-restrained braces (BRBs) to the lateral load-resisting system. These braces provide additional lateral stiffness and strength to the existing structure, unaffected by the sign of the axial force (tension or compression) since the braces are prevented from buckling. The BRBs also provide additional damping through the hysteretic dissipative behaviour of the core component. These braces are typically composed of an internal core brace (through which the axial force of the brace is transmitted), an external casing/restraining unit (providing for the flexural strength and stiffness to prevent global buckling of the BRBs and also indirectly providing for buckling restraint of the core brace), and, sometimes, an infill material between the former components.

Since the 1980s, initially in Japan, and afterwards in many other earthquake-prone countries or regions (e.g., the US, China, Italy), there has been a continuous development of numerous and diversified BRB solutions. Zhou et al. (2021) provides a comprehensive overview of existing BRBs, classified in terms of: (i) core materials (carbon steel, low-yield-point steel, aluminium alloys); (ii) cross-section of the core brace (e.g., rectangular, cruciform, H-shaped, hollow pipe); (iii) core brace longitudinal configurations (e.g., dog-bone, perforated, fish-bone); (iv) restraining units (e.g., reinforced concrete, concrete-filled steel tube, FRP, all-steel, with self-centring device).

In addition to the high corrosion resistance, aluminium alloys offer a wide range of useful properties, such as lightness (one-third the density of steel) and strength-to-weight ratio, formability (allowing for extrusion), and recyclability. These properties have led to the development of numerous aluminium core BRBs (Al-BRBs) configurations and studies.

Usami, Wang, and Funayama (2012) performed a series of tests on Al-BRBs varying the alloy composition (A5083P‐O and A6061S‐T6), end details for the core brace (welded or bolted rib stiffeners), loading history (constant or variable strain amplitude) and presence/absence of shop-welded stoppers. The low-cycle fatigue strength of the A6061S‐T6 specimens with bolted rib stiffeners without stoppers was found to conform to HPBRBs (high-performance BRBs) requirements, namely in terms of the maximum strain and cumulative inelastic strain, over 3% and 70%, respectively. Wang et al. (2013) continued that study, further testing extruded core braces with cruciform end cross-sections and new aluminium alloy (HS63S-T5, based on the A6063). The test results showed that extruded BRBs exhibit stable and repeated hysteretic performance, leading to the proposal of a formula for low-cycle fatigue damage evaluation in strain-based damage assessment. Moreover, the authors express their opinion that the fracture of extruded Al-BRBs is brittle, in contrast to steel BRBs.

Avci-Karatas and Celik (2013) presented the experimental tests of two Al-BRBs, both with A5083-H111 alloy plate for the core brace, square tube as the external casings and high-strength, non-shrink, grout infill material. These two specimens differed only in terms of the end connection details, one of which welded and the other bolted. The experimental tests showed that the welded end connection detail proved detrimental to the low-cycle fatigue performance, leading to early fracture in the heat-affected zone. In contrast, the bolted end connection detail led to satisfactory performance, with stable, repeatable, hysteretic behaviour and significant cumulative energy dissipation. Later on, Avci-Karatas, Celik, and Yalcin (2018) compared the former test results with those of two equivalent steel core brace BRBs, one with S235JR and the other with S355JR steel core brace. The bolted end connection detail Al-BRB hysteresis loops were found acceptable when compared with those of the steel BRBs, albeit with reduced dissipated energy because of lower cyclic ductility. Nevertheless, the authors recommend weld-free Al-BRBs in buildings or bridges in which severe corrosion effects are expected.

Dusicka and Tinker (2013)presented a configuration for an ultra-lightweight Al-BRB with pultruded GFRP casing wrapped with GFRP fabric. The core is composed of four, back-to-back, equal angles of the 6061-T6511 alloy, chosen (and confirmed by material testing) because of the low monotonic strain hardening and negligible cyclic strain hardening. The analytical and numerical studies pointed in the direction that global buckling could be effectively restrained by the proposed configuration.

Singh and Rai (2014) present a new Al-BRB with aluminium core brace with steel casing. The core brace is of the 6063-T5 alloy, annealed to reduce the strength and indirectly prevent buckling. This Al-BRB was subjected to 1:6 scale tests and used for the increased damping as a knee-brace in a truss frame model (with the same scale) subjected to pseudo-dynamic tests.

Liu, Zhou, and Wang (2016) experimentally studied a novel Al-BRB configuration, characterized by a bamboo-shaped core brace element and circular tube casing. The core brace element of the A6061-T6 alloy had a sequence of reduced section segments (designed to concentrate yielding) separated by enlarged section slubs. The tested specimens varied in terms of the cross-sectional sizes of the slubs and of the length of segments and these were subjected to constant or variable strain amplitude cyclic alternate tests. The experimental results showed stable and repeated hysteresis loops, without local or global buckling.

3.2. Novel Al-BRB

This article comprises the numerical simulation of the seismic retrofit of a pilotis case study building by novel Al-BRBs. The development stages of that novel Al-BRB (material alloy selection, numerical studies of alternative dissipative device internal configurations and numerical simulation of the brace as a whole) lie outside the scope of the article. The aspects pertaining to the adopted dissipative alloy are presented and discussed in Ferreira et al. (2021). It suffices to state that after an initial screening of possible compositions and heat tempers, followed by material tests, the choice fell upon the 6082 alloy, with T6 temper, annealed at 350 ºC for 120 min (6082-AN350/120), which showed superior deformation capacity and low-cycle fatigue life. The brace configuration is defined by the following characteristics:

• The connections of the brace to the structure to be retrofitted are pinned.

• Only a fraction of the brace length is dissipative, the remaining part is deemed to remain elastic. This characteristic corresponds to a derivation of the concept of the Buckling-Restrained Axial Dampers (BRADs) developed in Italy by Fip Industriale (Antonucci et al. 2006; Fip Industriale 2006), making it possible to match the strain range of the brace (dependent on the dissipative length) to the deformation capacity of the structure to be retrofitted. The brace components are identified in Figure 2.

  Figure 2. Brace components.

  

• The external casing is an extruded bicylindrical tube (with radial stiffeners), illustrated in Figure 3, such that the dissipative core brace (solid cylinder) fits within the inner tube of the casing with reduced tolerances;

  Figure 3. Extruded casing with radial stiffeners.

  

• The dissipative core brace is bolted in both extremities, precluding reduced fatigue life as a consequence of welding details.

• In one of the extremities, the bicylindrical extruded casing is embraced by an external tube (identified as ‘collar’) that slides over the casing with minimal tolerances, providing a rotational restraint. Figure 4 provides a simplified exploded view of the dissipative segment, alongside the whole bracing.

  Figure 4. Simplified exploded view of the dissipative segment and whole bracing.

  

4. Seismic assessment and retrofit of the case study building

4.1. Case study building

The case study building is one of a group of five identical buildings known as the housing complex of Avenida Infante Santo (Infante Santo Avenue) in Lisbon. That avenue was drawn in the late 1940s following a natural valley at an approximate 45º angle in plan to the river Tagus. The architectural design of the buildings was initially (1949) authored by Alberto Pessoa, from the City Hall of Lisbon, later on joined by Hernâni Gandra and João Abel Manta (also with the co-operation of the civil engineer Jordão Vieira Dias). The first four buildings (farthest away from the river, depicted in Figure 5) were constructed in the period 1954–1956 and the fifth building was erected in the early 1960s, with some variations with respect to the first four.

Figure 5. View of the first four blocks.

Each building is nine storeys high (eight elevated floors plus a reduced enclosed plan and terrace on the ninth floor), with an external rectangular plan envelope of 11.1 m × 47.20 m. The first storey is particularly high (clear height of 5 m) and almost devoid of walls (except three entrances to the building, enclosed by masonry walls) so that the first storey columns can be regarded as pilotis. The remaining storeys are 3 m high between axes (2.8 m clear height) and are fully enclosed by masonry walls (and interior masonry wall partitions), considered non-structural components. These buildings are for residential use only, with 30 three- or four-room duplex apartments (six at every couple of floors). The ninth floor is destined for communal services (e.g., clotheslines and storerooms) and for the apartment of the janitor.

The structural system is composed of 12 reinforced concrete (RC) transversal frames spaced at 3.80 m in the longitudinal direction, with two columns (here termed main columns) spaced at 7.3 m and three-span beams (a central span of 7.3 m and two cantilever spans projecting 1.9 m), as shown in Figure 6. The main columns present varying rectangular cross-sections along their height, starting at 0.40 × 0.75 m at the first storey, ending at 0.30 × 0.50 m at the top and decreasing every two floors. In the longitudinal direction, the building has 2.7 m overhangs with additional columns at the tip from the first floor upwards. These additional columns, with a 0.20 × 0.50 m rectangular cross-section, are aligned with the main columns and rest over longitudinal cantilever beams that run through the first two transversal frames. The slab is generally 0.11 m thick, but slightly thicker at specific locations (e.g., in the balconies). The main columns rest on footings, without foundation beams. The cross-sections of a typical frame column along the height with the reinforcing bars is shown in Figure 7.

Figure 6. Plan of the ceiling of the ground floor (over an original drawing, dimensions in m).

Figure 7. Cross-sections of a typical frame column along the height (over an original drawing, dimensions in m).

The frame beams’ cross-sections (and negative moments reinforcing bars) vary from 0.4 × 0.8 m² (1^st Floor, 9 Φ19 mm + 2 Φ10 mm), to 0.3 × 0.8 m² (2^nd floor, 7 Φ19 mm + 2 Φ10 mm) to 0.3 × 0.7 m² (remaining floors, 6–4 Φ19 mm + 2 Φ10 mm). The positive bending moments reinforcing bars at the supports are always 2 19 mm. The stirrups are Φ10 mm spaced at 0.2 m over the length of the beams, with additional shear reinforcement provided by the reinforcing gradually passing from top to bottom over 1.7 m distance from column faces.

The structural design process was not straightforward and involved successive versions, until the final version, dated 1955, was authored by civil engineer Mário Ramos da Cruz. The structural design was created in accordance with the Portuguese reinforced concrete design code of 1935, revised and updated in 1943. As the first earthquake-resistant Portuguese design code was released only in 1958, the structural design did not account for earthquake loads. Nevertheless, most likely following questions raised by Lisbon City Hall, this final designer performed some relatively detailed calculations based on the seismic coefficient method (i.e., lateral forces applied at floor levels, computed as a percentage of the weight of each floor), but only for the transverse direction. The reason for disregarding the detailed calculation of the earthquake loads in the longitudinal direction is unclear, attributed by the designer to the shape of the building. The seismic coefficient considered in the transverse direction was 2%, based on alleged recommendations by an ASCE committee. The calculations showed that the earthquake action effects in the transverse direction are slightly more relevant than the wind action effects, but only in the lower storeys, and that this slight increase is not enough to modify the previous cross-sections and detailing (controlled by the wind). The designer also performed some simplified calculations in the longitudinal direction, concluding that the wind action governs the design for lateral forces applied in that direction.

Given the former characterization of the case study building, the same building can be classified as a pilotis building, with the anticipated weaknesses at the soft first storey, thus exemplifying a potentially dangerous combination of an architecturally dictated trend with misconceptions from the structural design point of view. In addition to the former suspected soft first storey weakness, the structural design and detailing are outdated, as demonstrated by the use of smooth steel reinforcing bars, excessive spacing and detailing of stirrups/ties in the critical regions of the columns and beams, and insufficient anchorage and lapping length, etc.

4.2. Seismic assessment

4.2.1. Former studies

The case study building, from the housing complex of Avenida Infante Santo, is representative of a building type prevalent in urban areas of Portugal in the period between the mid-1950s and the end of the 1970s. This is why it has been the subject of successive studies, summarized below.

Rodrigues et al. (2005) present a first study on the predicted seismic behaviour of the case study building, making use of a proprietary nonlinear analysis program for RC structures, PORANL, modified by the addition of a macro-model accounting for the effect of the masonry infill walls. This modified version of PORANL was used to model the building, calibrating the same model with experimentally determined fundamental frequencies and performing time-history analyses for an artificial accelerogram in both horizontal directions for increasing PGA values (and return periods, varying from 73 to 5000 years). As expected, the interstorey drifts were found to be largely concentrated at the first storey. Despite the extreme concentration of interstorey drift at the first storey, particularly in the softest direction (the longitudinal), these drift levels conformed to the safety limits of the ATC-40 (ATC 1996). This conclusion is overshadowed by the fact that the second-order effects were not accounted for in those analyses, as explicitly stated by the authors.

Fonseca et al. (2008), considering the same building as Rodrigues et al. (2005), discussed different retrofitting and strengthening interventions, specifically through the addition of RC shear walls, steel bracings (possibly dissipative), base isolation and tuned liquid dampers, particularly in terms of their suitability in light of the architectural significance of the building. The revision of the former seismic assessment studies of Rodrigues et al. (2005), resorting again to the modified version of PORANL, this time for an extended collection of artificial accelerograms, highlighted that in some cases the building fails to comply with ATC-40 requirements in the longitudinal direction. In the wake of that conclusion, the authors studied different strengthening configurations using hysteretic dissipative eccentric bracings installed in the first storey in the longitudinal direction and concluded that the extreme concentration of the interstorey drift demands can be effectively solved. Rodrigues, Varum, and Costa (2008), give a more detailed description of the masonry infill macro-model as well as of the simulations by Fonseca et al. (2008), further corroborating the former conclusions.

Furtado et al. (2016) pursued the former studies, focusing on the comparison of the behaviour of a bare frame model (BFM) with a masonry infill model (IMM), developed with the 2004 version of SeismoStruct (Seismosoft 2004) and considering different pushover analyses (uniform, triangular and adaptive) in both horizontal directions. In addition, the authors performed nonlinear dynamic analyses, concluding that the maximum interstorey drift in some cases exceeds the limits set by international standards and recommendations, as a consequence of the concentration of the interstorey drift demands in the first storey of the IMM model. It then becomes mandatory to strengthen the building, by fixing/eliminating the soft storey mechanism. The authors went on to discuss different strengthening interventions, divided into overall intervention techniques (addition of RC shear walls, of steel braces, with or without dissipative links, base isolation, and others) or member intervention techniques (RC jacketing, steel jacketing, CFRP jacketing, and others). The study continued with the design and simulation of four strengthening techniques: RC jacketing of the ground floor columns (i); addition of RC shear walls (ii); and addition of steel braces, with (iii) and without (iv) shear links. These four alternatives were compared in terms of the increase of the base shear and of the higher storeys’ interstorey drift. Finally, a cost-benefit analysis is presented, concluding that the addition of steel braces is the most effective strengthening solution.

4.2.2. Numerical model of the building

The numerical model of the case study building in the present study was developed from scratch in SeismoStruct (Seismosoft 2021) and the subsequent analyses were also conducted with that FEM computed program. The seismic assessment was performed in accordance with Part 3 of Eurocode 8 (CEN 2005), considering the national Portuguese standards of that part, NP EN 1998–3 (CEN/CT 115, 2017) and of Eurocode 8, Part 1 (undefined).

The structural model of the building is composed of RC frame elements (e.g., columns and beams) with masonry infill panel elements, where justifiable. The geometry, dimensions of the cross-sections and reinforcing bars detailing followed the complete collection of structural drawings, accessible in the archives of Lisbon City Hall. Special attention was paid to details that could decisively influence the seismic behaviour by introducing irregularities, as exemplified by the consideration of the longitudinal beam segments that support the additional columns located at the overhangs (a critical feature apparently disregarded in some previous studies).

A preliminary model accounting for the possible rotational flexibility of the columns at their supports over the footings (considering this flexibility by means of rotational springs computed based on the footing dimensions in plan and estimates of the soil elastic modulus) led to the conclusion that these supports prevented the rotation over the horizontal axes. The subsequent, final, model considered that no deformation (either translation or rotation) was allowed by the footings.

The reinforced concrete elements were modelled with the infrmFB (‘Inelastic Force-Based Frame element type’), with the discretization of the cross-sections into fibres, assuming material models for the concrete and steel fibres. A total of 150 fibres were generally considered for each discretized cross-section. The material model for the reinforcing bars was that of Menegotto and Pinto (1973), based on a previous model by Giuffrè and Pinto (1970), accounting for the Bauschinger effect and kinematic hardening. The concrete model was the uniaxial constant confinement monotonic model proposed by Mander, Priestley, and Park (1988), adapted with the cyclic rules proposed by Martínez-Rueda and Elnashai (1997).

In the 1935 Portuguese reinforced concrete design code the safety checks consisted of comparing the stress values for the design loads with the allowable stress values, then known as ‘fatigue limits’ of the concrete. The allowable stress values were calculated by dividing the resistant stresses by relatively high safety factors, which ensured the safety margin sought. The calculation of the stresses due to loading was based on the hypothesis of elastic behaviour of the concrete and steel (calculated in the elastic phase).

At the time of the design, there were no concrete or steel strength classes, since these were introduced only in the 1967 revision of the Portuguese reinforced concrete design code, leading to some considerations to reach the mean strength properties to be adopted in the numerical model.

As for the concrete properties, the 1935 code gave indications in terms of the composition, further supplemented in the 1943 revision. That revision also prescribed a minimum compressive strength of 225 kg/cm² (approximately 22.5 MPa) for cube specimens at 28 days for structures such as the one of the case study, thereby meeting special design and construction quality control requirements. That latter condition of the minimum compressive strength places the original concrete strength somewhere between the current C16/20 and C20/25 concrete classes, leading to an assumed original characteristic cube concrete strength (f_ck,cube) of 22.5 MPa. Given the correlations between f_ck,cube and f_ck,cyl (cylinder), as well as those between f_ck,cyl and f_cm,cyl, both at 28 days, and also the ageing (hardening) effects over 67 years, a current mean concrete cylinder strength f_cm of 30 MPa was considered in this study. The previous studies – Rodrigues et al. (2005, 2008), Fonseca et al. (2008) and Furtado et al. (2016) – had considered a slightly lower concrete strength, conforming to C20/25 concrete class (f_cm = 28 MPa).

Regarding the steel reinforcing bars, the 1935 code specified an ultimate strength and strain of no less than 3.700 kg/cm² (approximately 370 MPa) and 24%, respectively, also stating that the yield strength should be no less than 60% of the ultimate strength (leading to f_yk≥222 MPa). The ‘fatigue limit’ considered in the design for the reinforcing bars was 140 MPa, consistent with the common steel specifications and special design and construction quality control requirements (in the 1943 revision of the concrete code, the allowable steel stress could be increased from 120 MPa to 140 MPa under those circumstances). The subsequent 1967 Portuguese reinforced concrete design code explicitly introduced the steel strength classes, namely the A24 class, corresponding to a characteristic yield and ultimate strengths of 240 MPa and 370 MPa respectively, with an ultimate strain of no less than 22%, values similar to those resulting from the 1935 code specifications. In the absence of tensile test data, the A24 reinforcing bars steel class was adopted. The mean yield strength considered in the model was 287 MPa, computed assuming a 10% coefficient of variation for the equivalent-A24 steel class.

The masonry infill wall panels are 0.15 m or 0.30 m thick (single or double wythe) and were modelled with the inelastic infill panel element type (Seismosoft 2021). This element type, originally developed by Crisafulli (Crisafulli 1997) and implemented and verified by Smyrou et al. (2011), simulates the in-plane nonlinear behaviour of brick masonry infill panels integrated in reinforced concrete frames. The behaviour of an infill masonry wall panel is modelled by a single macro element where the compressive/tensile behaviour and the shear behaviour of the wall are considered independently and modelled respectively by a set of four diagonal struts and by two nonlinear shear springs. The numerical model considered only the wall panels that are completely enclosed by frame elements (columns and beams) and without openings. This led to taking into account just two masonry infill wall panel alignments in the longitudinal direction (most of the walls in that direction are either located eccentrically to the columns or have openings) and of the masonry infill wall panels separating the adjoining apartments (and part of the end façades) in the transversal direction. The dimensions (clear length × clear height) of the individual longitudinal infill panels were 3.5 × 2.6 m² and 2.5 × 2.6 m², single wythe, whereas the dimensions of the transversal infill panels were 6.8 × 2.6 m² and 1.55 × 2.6 m², single or double wythe. Figure 8 shows the infill panel elements on a typical residential floor. The inelastic infill panel element properties were computed, considering the wall thickness, the geometry of the panel and typical Portuguese brick masonry wall properties, that is a compressive strength of f_m’ = 1.1 MPa (Pires 1990). The other most relevant mechanical properties for the compression/tension strut were: tensile strength f_t’ = 0 MPa; (initial) Young Modulus E_m = 1000×f_mθ; strain at maximum stress ε_m = 0.0012; ultimate strain ε_ult = 0.024; closing strain ε_cl = 0.003; strut area reduction strain ε₁ = 0.0006; and residual strut area strain ε₂ = 0.001. The shear springs mechanical properties were: shear bond strength ε₀ = 0.3 MPa; coefficient of friction μ = 0.7; maximum shear strength τ_max = 0.6 MPa; and reduction shear factor α_s = 1.5.

Figure 8. Layout of the masonry infill panels.

The numerical model weights and masses are those of the permanent loads plus a fraction of the imposed loads. The program automatically computed the self-weight/mass of the RC structural elements with the exception of the slab, whereas the other permanent weights/masses and fraction of the imposed weights/masses were computed externally and assigned to the floor beams along their length based on the tributary width. The floor slabs were considered rigid in their plane (rigid diaphragm constraint).

The Infill Masonry Numerical model (here identified by IMM) was validated by comparing the numerical modal properties (i.e., the fundamental periods in both horizontal directions) with the experimentally determined modal properties, presented in Rodrigues et al. (2005), and repeated in the subsequent studies (Fonseca et al. 2008; Furtado et al. 2016; Rodrigues, Varum, and Costa 2008). The significance of that comparison, presented in Table 1, was improved by including the numerical effective modal mass percentages, enabling confirmation of the modal typologies. Besides allowing validation of the numerical model, the contribution of the masonry infills is also portrayed in that table with the inclusion of the numerical results corresponding to a bare frame model (BFM), derived from the IMM model by simple deletion of the inelastic infill panel elements.

Table 1. Validation of numerical model and effects of the infill masonry in the numerical models.

		Period [s]		Effective modal mass percentages (numerical)
Mode	Model	Experimental (Rodrigues et al. 2005)	Numerical	MXn [%]	Myn [%]	RX [%]	RY [%]	RZ [%]	Configuration
Mode 1	IMM	0.93	1.03	98.5%	0.0%	0.0%	0.7%	0.0%	1 X (long.)
	BFM		2.77	76.0%	0.0%	0.0%	7.0%	0.0%
Mode 2	IMM		0.62	0.0%	0.0%	0.0%	0.0%	95.4%	1 R (torsion)
	BFM		1.08	0.0%	0.0%	0.0%	0.0%	81.0%
Mode 3	IMM	0.57	0.59	0.0%	95.9%	4.7%	0.0%	0.0%	1 Y (transv.)
	BFM		1.02	0.0%	81.0%	18.0%	0.0%	0.0%

The numerical model (IMM) fundamental frequencies in the X (longitudinal) and Y (transversal) directions closely match the experimental counterparts. It is interesting to note that the first mode is that of the translation in the X direction (out-of-plane flexure of the transversal frames), that the second mode is of pure torsion and that the third mode is the fundamental translational mode in the direction of the frames. The fact that the fundamental torsional mode precedes that of the translation in the Y direction is somewhat undesired, providing an indication of torsional flexibility (nonetheless mitigated by the absence of coupling with the horizontal translation directions). In the same model, the three fundamental modes engage nearly all the building mass, with an extreme concentration of deformation at the first storey. The bare frame model (BFM) is significantly more flexible, with much more evenly distributed lateral modal deformation along the height and also with reduced engagement of the building mass for the first set of fundamental modes.

4.2.3. Seismic action

The seismic action was defined in accordance with the Portuguese national standard for Eurocode 8, Part 1 (undefined).

The superficial ground layer is classified in the 1:50.000 geological chart as weathered limestone with rudist fossils (Cenomanian stage, late Cretaceous epoch). A relatively recent geotechnical survey conducted near the building, points to N_SPT values over 60, with deformability modulus in the range of 2 GPa to 3 GPa, Cu higher than 250 kPa, allowing the classification of the ground type as A.

The Portuguese version of Eurocode 8 considers two earthquake scenarios, seismic action type 1 (distant, high magnitude, interplate earthquake) and type 2 (near, moderate magnitude, intraplate earthquake). Given the relatively high periods of the fundamental modes, seismic action type 1 should control the design, for which reason seismic action type 2 was discarded in the subsequent stages of the study.

The seismic assessment investigations were conducted with nonlinear static analyses, in which the seismic action demands are represented by the horizontal elastic response spectrum. These analyses were further corroborated by time-history analyses, with artificial accelerograms compatible with the former spectrum. A suite of three pairs of sets of accelerograms (in the X and Y horizontal directions) was selected, conforming to the original elastic response spectrum, as shown in Figure 9. S_{e, EC8} is the original elastic response spectrum (return period of 475 years, Lisbon, ground type A, 5% damping, importance class II, PGA of 1.5 m/s²), S_{e, 90% EC8} is 90% of the previous spectrum, S_e1 to S_e6 are the spectra for the six artificially generated accelerograms and S_em the mean of those six spectra.

Figure 9. Elastic acceleration response spectra.

The duration of the artificial accelerograms was approximately 40 s, to comply with the provision of the Portuguese national standard for Eurocode 8 which specifies that the minimum duration of the stationary part should be 30 s for the seismic action type 1. The consistency between the suite of artificial accelerograms and the original spectrum stipulates that the mean value of spectral acceleration for null periods, S_em(0 s), should be no less than the PGA. Furthermore, in the 0.2 T₁ to 2 T₁ period range, no value of the mean response spectrum should be less than 90% of the corresponding value of the original response spectrum. Both these conditions are generally met, since S_em(0 s) = 1.66 m/s² and the second condition can be visually checked in Figure 9 for the more conservative 0.2 T1_Y to 2 T1_X range (shaded range).

4.2.4. Nonlinear static (pushover) assessment

The seismic assessment of the original structure was conducted with adaptive, nonlinear static (pushover), analyses, leaving the time-history analyses for the assessment of the retrofitted structure (and for other comparative purposes). These pushover analyses were preceded by the application of the vertical loads (permanent and a fraction of the imposed loads).

The levels of protection of the original building were checked for seismic action type 1 and for the following three limit states (LS): DL1 (Damage Limitation, as stipulated by NP EN 1998–3, 2017); SD1 (Significant Damage, as stipulated by undefined; and SD2 (Significant Damage, as suggested by EN 1998–3, 2005). Eurocode 8, Part 3 (CEN 2005) suggests return period (T_R) values of 2.475, 475 and 225 years, respectively for limit states of Near Collapse (NC), Significant Damage (SD) and Damage Limitation, leaving it to the national authorities (via the National Annexes) to make the final decision on which limit states should be checked and for which return periods. The consideration of different return periods can be expressed either by the factor multiplying the reference seismic action for the no-collapse requirement in new buildings or by the values of the probability of exceedance in 50 years, as shown for the three limit states in Table 2.

Table 2. Limit States considered in the seismic assessment of the original building.

LS (Limit State)	TR [yrs]	Factor []	Probability of Exceedance in 50 yrs []	Comments
DL1 (Damage Limitation)	73	0.29	50%	DL undefined (CEN/CT 115, 2017)
SD1 (Significant Damage)	308	0.75	15%	SD NP EN 1998–3:2017 (CEN/CT 115, 2017)
SD2 (Significant Damage)	475	1	10%	SD EN 1998–1:2004 (CEN, 2004) and default EN 1998–3:2005 (CEN 2005)

In addition to the limit states stipulated by the Portuguese national authorities, DL1 and SD1, the level of protection was also checked for the Significant Damage limit state SD2 for a return period of 475 years, as suggested in Part 3 of Eurocode 8 (EN 1998–3, 2005).

The capacity curves were those produced by SeismoStruct (Seismosoft 2021), with the assumption (option) that the structural elements keep a residual strength when reaching their ultimate deformation, therefore artificially delaying global collapse mechanisms. A brittle mechanism develops in the longitudinal direction in the main columns supporting the cantilever beams created as a part of the structural system supporting the overhangs. In fact, those columns, four in each longitudinal extremity, are significantly stiffer than the other main columns since the projecting beams that run on the first floor provide additional constraints to those columns. The columns engaged in that brittle mechanism fail by shear, as a result of outdated detailing and excessive spacing of the transversal links/hoops (5/16 in,≈ 8 mm, at 20 cm). This shear-induced failure mechanism in (relatively) early reinforced concreted structures is widely recognized (e.g., Foti 2014). A similar mechanism also occurs in the transversal direction, this time involving more columns and with a slightly less extreme concentration of deformation in the soft first storey. The onset of the brittle mechanism involving shear of the columns at the first storey in each direction is marked on the corresponding capacity curve and the rest of that capacity curve is dotted, meaning that the structure had already collapsed and that the capacity curve was extended solely to allow the computation of the target displacements for the different limit states.

SeismoStruct automatically computed these target displacements following the procedure recommended in Annex B or Eurocode 8 (initially proposed by Fajfar 2000). Figures 10 and 11 graphically summarize the results of the verifications for the three limit states, respectively for the X and Y directions. The limit displacements (DL, Damage Limitation, and SD, Significant Damage) indicated on the capacity curves are the control displacements (displacement at the ninth floor), for which somewhere the structure (always at the first storey) is on the verge of not complying with the deformation capacities allowable for that limit state.

Figure 10. Seismic assessment in the longitudinal direction.

Figure 11. Seismic assessment in the transversal direction.

The structural model is significantly stiffer and stronger in the transversal direction, as expected.

Despite the substantial concentration of drift in the soft first storey, the structure complies with the Damage Limitation limit state in both directions. Conversely, brittle mechanisms develop in both directions before the SD1 (Significant Damage) limit state, meaning that the structure is unable to comply with that limit state in both horizontal directions. The deformation and damage concentration at the onset of those brittle mechanisms can be inferred from Figures 12(a), (b).

Figure 12. Deformation and damage concentration at the onset of the brittle mechanism in the longitudinal (a) and transversal (b) directions.

Disregarding the occurrence of the brittle collapse mechanisms, the structure complies with the SD1 limit state in the longitudinal direction and with both SD1 and SD2 limit states in the transversal direction, but fails to comply with the SD2 limit state in the longitudinal direction. Table 3 summarizes the comparison between the demand and capacity for the different limit states. Due to the extreme concentration of deformations at the first storey, the compliance checks for the different limit states could disregard the rest of the storeys. Nevertheless, the table contains some information about the demands at the ninth storey, to allow a direct comparison with the results presented in Figures 10 and 11.

Table 3. Demand vs. Capacity for DL, SD1 and SD2 limit states in the original building.

Direction	Storey	DL Limit State		SD1 Limit State (TR=308 yrs)		SD2 Limit State (TR=475 yrs)
		Demand [m]	Capacity [m]	Demand [m]	Capacity [m]	Demand [m]	Capacity [m]
X (long.)	1^st storey	0.013	0.039	0.049	0.058	0.071	0.058
	9^th storey	0.023		0.061		0.080
Y (transv.)	1^st storey	0.007	0.025	0.027	0.040	0.032	0.040
	9^th storey	0.015		0.036		0.048

The former results show that the existing (original) structure does not comply with the levels of protection stipulated in Eurocode 8 for the Significant Damage limit state. The non-compliances are twofold: (in both directions) brittle collapse mechanisms develop long before SD1 limit states, involving the shear of columns P1 at the first storey; and (only in the longitudinal direction) the structure does not conform to the SD2 limit state. Moreover, the excessive deformability of the first storey, combined with the irregularity in elevation induced by the absence of masonry infills at that storey (and their presence in all the storeys above), are among the main causes of the same lack of compliance and should therefore be addressed in retrofitting studies.

4.3. Structural strengthening solution

4.3.1. General considerations

The retrofitting solution should address the formerly identified non-compliances. The brittle mechanism by shear of the first storey columns could be tackled by relatively conventional and unobtrusive interventions (e.g., by CFRP wrapping of those columns, improving shear strength and confinement), but this intervention could not, per se, solve the non-compliance in terms of the DL2 limit state in the longitudinal direction. On the other hand, the number of Al-BRBs to be installed to prevent the brittle shear mechanism without CFRP wrapping of the columns would be disproportionate. Given the former considerations, it was decided to consider a hybrid intervention, combining CFRP wrapping of the columns with the installation of a limited number of Al-BRBs, mainly in the longitudinal direction. The main objective of the retrofitting solution is to control the first storey drift within reasonable limits (also to prevent the shear mechanism of the columns) but not fully eliminating the same drift inasmuch as significant (displacement-dependent) hysteretic energy dissipation occurred at that storey, while the deformation demands on the upper storeys were prevented from increasing disproportionately (which might have resulted from excessive stiffening of the first storey).

SeismoStruct (Seismosoft 2021) permits the design and consideration of CFRP wrapping so that the shear strength of the strengthened columns (all columns in the first storey) can be significantly increased. In this case, the first storey columns were wrapped with a single sheet of bidirectional glass fibre fabric, applied with laminating resin. The glass fibre fabric fibre is 0.065 mm thick with tensile strength and elastic modulus in excess of 2850 MPa and 65 GPa, respectively. The capacity curves corresponding to that isolated intervention, here omitted for the sake of brevity, show that the brittle shear mechanism is delayed in both directions, but the non-compliance with the DL2 limit state in the longitudinal direction is kept.

4.3.2. Design of the strengthening solution (Al-BRBs)

The design of the strengthening solution — number and characteristics of the Al-BRBs — followed the methodology initially developed by Kasai, Fu, and Watanabe (1998) for the response reduction of multi-storey buildings by adding elastoplastic dampers (e.g., steel BRBs). The application of that methodology considered the modifications introduced by Almeida et al. (2017) to optimize the dimensions of the (steel) dampers at different storeys. The same methodology is based on the following approximations and steps: i) idealizing multi-storey building systems as equivalent single-degree-of-freedom (SDOF) systems with the same fundamental periods; ii) computing the response reduction factors (R_d and R_pa, respectively the displacement and pseudo acceleration reduction factors) relating the responses (spectral values) of two SDOF systems, one corresponding to the original structure (with period and damping T_fs and ξ_fs) and the other corresponding to the modified structure (period and damping T_eq and ξ_eq). The response reduction factors depend on the equivalent stiffness (K_d) and ductility (μ_d) of the dissipative part of the bracing system (these variables refer to the inclined direction of the bracing and can be converted to their horizontal equivalents K_d^H and μ_d^H).

The design of the strengthening solution was performed for the longitudinal direction, adding the Al-BRB bracings in the first (soft) storey only and considering the spectral values for the seismic action type 1, return period of 475 years (and the other characteristics of the seismic action as defined in 4.2.3). The main objective was to comply with the SD2 limit state in such a way that an initial value of 0.76 for the spectral displacement reduction factor R_d was considered. In the original structure, the capacity-demand ratio for the first storey displacement and SD2 limit state was 0.82, so the former response reduction factor should prove sufficient. The application of the methodology initially developed by Kasai, Fu, and Watanabe (1998) led to a K_d^H value of 125 MN/m, roughly of the same order of magnitude of the pre-existing first storey stiffness in that direction.

4.3.3. Strengthening solution

The detailed strengthening solution is composed of eight concentric, single, diagonal, equal Al-BRBs, symmetrically placed in the longitudinal direction. These braces are installed in some of the longitudinal spans between successive columns so that the total length of each brace is 6.28 m. The 6082-AN350/120 alloy dissipative segment is 3.33 m long with a circular cross-section of 65 mm diameter. The elastic segment cross-section area is 40% larger and is made of the 6082-T6 alloy. In spite of complying with the SD2 limit state in the transversal direction, two equivalent inverted V (chevron) concentric braces were also considered in that direction, placed between the columns of the two more peripheral transversal frames, mainly to improve the torsional stiffness.

The placement of the braces in the two directions and the plan layout of the same braces and 3D view of the strengthened structure are illustrated in Figures 13 and 14.

Figure 13. Placement of the braces in the longitudinal and transversal directions.

Figure 14. Plan of the first storey (a) and 3D view (b) with the location and identification of the Al-BRBs.

Some of the former seismic assessment investigations conducted for the same (or a similar) building also addressed the discussion of different strengthening interventions, namely the works by Fonseca et al. (2008) and, especially, by Furtado et al. (2016). The latter work discussed the efficiency of different strengthening solutions in terms of (i) the reduction of the first-storey drift; (ii) the (potentially detrimental) increase of the base shear; (iii) the energy dissipation; and (iv) the increase in the drift of the upper storeys. In the end, weighing the different efficiency aspects with the relative costs (cost of the intervention divided by the property value), varying from 0.12% to 0.5%, the solution of additional steel braces (four in the longitudinal direction and two in the transversal direction) was preferred. The strengthening solution studied in this work bears some similarities with that other solution, differing in that the increase in strength is not so significant and that it also considers the CFRP wrapping of the first storey columns.

4.3.4. Modelling issues

Each Al-BRB was modelled as a frame finite element with a bilinear axial constitutive law similar to those proposed by Zsarnóczay et al. (2013) and Vigh, Zsarnóczay, and Balogh (2017) for the purpose of designing structures strengthened with nonlinear displacement dependent devices (NLDs, e.g., BRBs) in accordance with EN 15,129 (CEN 2010). The backbone monotonic envelope curve is depicted in Figure 15. The yield stress σ_y is replaced by the 0.2% strain proof stress σ_0.2% for the 6082-AN350/120 alloy (considered as 60 MPa) whereas the (equivalent) yield strain ε_y is 0.08%. In that bilinear model the strain hardening slope depends on the maximum strain, so that the strain d_db corresponding to the design displacement of the device, d_db, considered as 2%, leads to the definition of the strain hardening adjustment factor ω(1.9 in this case). The compression strength adjustment factor β relating the compression to tension strength, was taken as 1.1. These two adjustment factors, ω and β, are also defined in ANSI/AISC 341–16, AISC (2016). The former characteristics were calibrated based on the results of the material experimental program described in Ferreira et al. (2021).

Figure 15. Monotonic envelope curve for Al-BRBs.

4.4. Seismic assessment of the retrofitted building

The stiffening consequences of the strengthening solution can be exemplified by the modification of the fundamental periods from 1.03 s to 0.81 s, 0.62 s to 0.59 s and 0.59 s to 0.58 s, respectively for the fundamental modes of translation along X, torsion and translation along Y. The effective modal masses engaged by these three mode shapes are only slightly reduced (these are kept over 90%) and translation-torsion decoupling is also kept. The major differences are those of the 12.7% decrease for the X-direction fundamental mode period and of the shortening of the gap between the torsional and Y-translation mode periods (to an extent that these periods roughly overlap).

The seismic assessment of the strengthened structure was performed by means of the nonlinear static and dynamic analyses presented in the following subsections.

4.4.1. Nonlinear static (pushover) assessment

The capacity curves for the strengthened structure are presented in Figures 16 and 17, respectively for the X (longitudinal) and Y (transversal) directions (the capacity curves for the original structure are also represented with grey shading). The target displacements for the return periods of 73, 308 and 475 years (filled circles) and the limit displacement for the DL and SD limit states are indicated on those capacity curves.

Figure 16. Seismic assessment of the strengthened structure in the longitudinal direction.

Figure 17. Seismic assessment of the strengthened structure in the transversal direction.

Like the original structure, the strengthened structure complies with the DL limit state in both directions. The brittle collapse mechanisms are precluded in the strengthened structure in both directions for the displacement ranges corresponding to the most stringent SD limit state (475 years return period). Finally, the strengthened structure presents a deformation capacity in excess of the demand required by that most stringent limit state, thereby complying with all the levels of protection stipulated in Eurocode 8.

Table 4 summarizes the comparison between the demand and capacity for the different limit states at the first and ninth storey (directly corresponding to Figures 16 and 17).

Table 4. Demand vs. Capacity for DL, SD1 and SD2 limit states in the strengthened building.

Direction	Storey	DL Limit State		SD1 Limit State (TR=308 yrs)		SD2 Limit State (TR=475 yrs)
		Demand [m]	Capacity [m]	Demand [m]	Capacity [m]	Demand [m]	Capacity [m]
X (long.)	1^st storey	0.011	0.039	0.036	0.058	0.054	0.058
	9^th storey	0.023		0.048		0.066
Y (transv.)	1^st storey	0.007	0.025	0.024	0.040	0.034	0.040
	9^th storey	0.015		0.037		0.050

4.4.2. Time-history analyses

The former general conclusions derived using nonlinear static analyses were validated by time history analyses, as exemplified by Figure 18. This shows the time-history traces of the base shear forces in the X direction for the original and strengthened structures (columns only) for the same compatible artificial accelerogram, chosen as the most stringent for the present effect. The base shear force for the strengthened structure is divided into the components withstood by the RC structure (columns), the one shown in Figure 18, and the Al-BRBs.

Figure 18. Time-history traces of the base shear forces for the original and strengthened structures (RC columns only).

The maximum values for the base shear force withstood by the RC columns, indicated on Figure 18, show a small reduction (in the order of 5%). For the same artificial accelerogram, the maximum total base shear for the strengthened structure (also accounting for the Al-BRBs contribution), of 4408.4 kN, is 28% greater than that of the original structure thanks to the increased stiffness, while the maximum contribution of the Al-BRBs to the base shear is 1136.7 kN.

The time-history traces of the first-floor displacements for the same artificial accelerogram, depicted in Figure 19, show a significant reduction in the strengthened structure, as expressed by the maximum values indicated on the figure.

Figure 19. Time-history traces of the first-floor displacement for the original and strengthened structures.

The former figures corroborate the pushover assessment analyses, showing that the strengthened structure is stiffer so that, notwithstanding the increase in base shear force, the displacement demands in the RC structure are reduced such that they do not exceed the existing capacity (improved by GFRP column wrapping), thereby complying with DL2 limit state.

5. Conclusions

The pilotis buildings, extensively dispersed worldwide since the 1950s, present some features that could precipitate soft first storey sidesway mechanisms when subjected to strong-motion earthquakes. That possibility is further increased in buildings which, due to the limited knowledge at the time of construction, observed outdated detailing rules and/or were subjected to structural design misconceptions (e.g., the soft first storey regarded as a means of filtering and truncating the inertia forces in the upper floors). One particularly adapted strengthening solution is that of adding buckling-restrained braces (BRBs) to the first storey, thus reducing the extreme deformation concentration without fully eliminating it, since these are displacement-dependent devices.

Considering the previous panorama, this article explored the possibility of strengthening a typical pilotis building, a landmark in Lisbon, by including novel aluminium buckling-restrained braces (Al-BRBs) under development. This novel Al-BRB offers some distinctive features that take advantage of the unique properties of the aluminium alloys, such as the formability (allowing for an extruded casing component) and the possibility of improving the low-cycle fatigue and deformation characteristics of the core component by means of thermal treatments.

The seismic assessment of the case study building, conducted in accordance with Part 3 of Eurocode 8, showed that brittle shear mechanisms involving the first storey columns develop markedly before the significant damage (SD) limit state demands. Even if those brittle shear mechanisms are omitted, the original structure fails to comply with the SD limit state demands in the longitudinal direction for the 475 years return period seismic action. The resulting strengthening intervention addresses the brittle shear mechanism by means of GFRP wrapping of the first storey columns, combined with the inclusion of Al-BRBs, mostly in the longitudinal direction. The nonlinear static and time history analysis show that the former non-compliance is eliminated by the relatively unobtrusive strengthening intervention. Retrospectively, even though the strengthened solution was found to comply with the most stringent SD limit state, the strengthening in the longitudinal direction could have been more significant, so that the fundamental period for the translation mode in that direction would surpass that of the torsional mode. This way, the possibility of torsional instability for unforeseen strong motions or as a consequence of unpredictable translation-torsion coupling resulting from differential nonlinear effects would have been further discarded.

As a final conclusion, the novel Al-BRB under development seems to be particularly suited to the strengthening of pilotis buildings; it offers an unobtrusive, light and sustainable strengthening intervention, and tackles the major weaknesses of those buildings, related to the extreme deformation concentration and susceptibility to brittle shear mechanism at the soft first storey.

Acknowledgments

The authors gratefully acknowledge the support provided by FCT-Fundação para a Ciência e Tecnologia (FCT), under of the InfraRisk Doctoral Program, through the PD/BD/135212/2017 PhD Grant to the second author. This work is part of the research activity carried out at Civil Engineering Research and Innovation for Sustainability (CERIS) and has been funded by FCT in the framework of project UIDB/04625/2020.

Some final words of acknowledgement go to Vasco Ribeiro for his crucial contribution to the development and analysis of the numerical model of the original building, performed as part of his MSc thesis in the IST-ULisboa (Ribeiro, 2021).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Fundação para a Ciência e a Tecnologia [PD/BD/135212/2017].