## 1 Introduction  
Reinforced concrete framed structures with a soft first story and infill walls in top stories are very common, even in areas of substantial seismic hazard. Despite their merit from a functional and an architectural perspective, they constitute a poor solution from a mechanical point of view. When subjected to earthquake loads, the discontinuity in lateral strength and stiffness at the first (ground) story causes a concentration of the energy dissipation demand (i.e., damage) in this story. This amount of energy--very large in the case of a severe earthquake--must be dissipated by the columns of the first story in the form of cumulative plastic deformations. If the columns have an insufficient energy dissipation capacity (true of many existing reinforced concrete (RC) frames), the building eventually collapses. The plastic mechanism developed by the frame, called in the literature soft first story, is one of the most undesirable forms of collapse. Observations after major earthquakes in the 1990s, such as Northridge (1994) in the U.S. [1] or Hyogoken-Nanbu (1995) in Japan [2], proved that catastrophic damage could be attributed to a soft first story. The performance of this structural typology has been investigated by many researchers in the past [3]. Several retrofitting techniques are available nowadays to mitigate this issue. The most common one is increasing the section area of the first-story columns with concrete jackets [4], which also allows for increasing the flexural and shear reinforcement. However, it implies an increase in the lateral stiffness of the structure as well, which in most cases means a greater seismic force demand upon the structure. On the other hand, increasing the strength and stiffness of the first-story columns does not change the failure mode and does not alleviate the problem of the high-energy dissipation demands on the columns of the first story--it just increases the base shear strength. Increasing the strength so that the retrofitted columns can absorb in elastic conditions (i.e., within the elastic range) the large amount of energy input by a severe earthquake can be impossible to achieve at a reasonable cost. Alternatively, using state-of-the-art solutions, e.g., confining with fibre-reinforced polymer (FRP) [5] textiles, would greatly increase the ultimate rotation of the columns, hence increasing the lateral deformation capacity at the first story, but again it will not avoid damage concentration in the first story and the collapse of the structure, as has been proven experimentally in full-scale tests [6]. Still, designers can positively exploit such damage concentration by using a retrofitting strategy similar to that used in base-isolated systems with energy dissipation devices. Under this approach, the existing columns (strengthened, if needed) could be considered as bearings that take in the gravity loads and second-order effects due to lateral deformation. In turn, the energy dissipation devices added in the first story concentrate most of the energy input by the earthquake. There are few references in the literature analysing this strategy. [PERSON] et al. and [PERSON] [7,8] compared different retrofitting strategies, concluding that the most economical solution was a combination of dampers and partial strengthening. [PERSON] and [PERSON] [9] proposed an energy-based procedure for the seismic retrofitting of RC frames with a soft first story using hysteretic dampers. In this study, the authors designed dampers for a general seismic hazard scenario and evaluated it against far-field records. However, the severe demands imposed by near-field earthquakes were not considered [10, 11, 12, 13]. Other authors have investigated the effect of near-fault earthquakes on framed structures equipped with friction and viscous dampers [14, 15, 16], concluding that the use of energy dissipation devices improved the behaviour of the structures studied.