Seismic performance of a full‐scale five‐story masonry‐infilled RC building subjected to substructured pseudodynamic tests

This paper discusses the results of a series of hybrid earthquake tests on a full‐scale reinforced concrete (RC) building with masonry infills. The prototype was a five‐story structure representing the vulnerable part of a typical RC building in Southern Europe, with beams stronger than the columns and masonry infill walls weaker than the surrounding frame elements. The specimen was subjected to a sequence of unidirectional earthquake simulations of increasing intensity up to conditions of significant damage to the infills, using the pseudodynamic (PsD) testing method with substructuring. The input ground motion was a real earthquake recording, slightly modified in amplitude and frequency to match the elastic design code spectrum. The physical substructure of the hybrid model consisted of the first story of a two‐story mock‐up structure built in the European Laboratory for Structural Assessment (ELSA); the second story ensured realistic boundary conditions at the top of the first one. The characteristics of stories two to five were simulated by a numerical finite‐element model developed in OpenSEES and updated throughout the test sequence using data obtained from preceding tests. The experiments were terminated with the onset of a soft‐story mechanism at the first story of the physical substructure for an earthquake with a peak ground acceleration of 0.3 g. The paper summarizes the key characteristics of the specimen and the major observations from the hybrid tests, illustrating the evolution of structural/nonstructural damage and the cyclic hysteretic building response. The attainment of significant damage limit states is correlated with experimentally defined engineering demand parameters and ground‐motion intensity measures for the performance‐based seismic assessment of buildings. Data and observations from these experiments add substantially to our understanding of the effects of masonry infills on the seismic behavior of RC‐framed structures.


NOVELTY
The following bullet points briefly describe the new contributions of this paper to the field: • First ever substructured pseudodynamic tests on a full-scale multistory RC building with masonry infills.
• A full-scale RC building non-compliant with modern capacity design principles (columns weaker than the beams) and infills weaker than the frame was investigated experimentally for the first time. • Qualitative definition of damage states for clay-brick masonry infills based on experimental observations. • Thresholds between the damage states were identified and related to local engineering demand parameters.
• Detailed information about the adopted experimental setup and pseudodynamic testing procedure.
• Thorough description of the building's geometric and mechanical properties that help develop numerical models.
structure was subjected to a sequence of unidirectional earthquake simulations of increasing intensity to conditions of significant damage to the masonry infills, using the PsD testing method with substructuring. 31 The physical part of the building (i.e., physical substructure) consisted of the first story of a two-story mock-up structure built in the laboratory, while the responses of stories two to five were simulated by a numerical model (i.e., analytical substructure). The physical specimen was densely instrumented with sensors that monitored the three-dimensional response of various structural elements. This paper discusses the first substructured PsD tests performed on a full-scale multistory RC building with masonry infills, adopting two structural partition approaches for substructuring. Moreover, this was the first-ever experimental assessment of the effects of strong-beam-weak-column mechanisms and the in-plane behavior of weak infills on the overall seismic response of a full-scale RC-framed structure. The paper begins with a brief overview of the geometric and mechanical characteristics of the test building. Next, it presents the selected input ground motion, the instrumentation plan, and the adopted PsD testing procedure. Subsequent sections discuss the major observations from the tests, including damage evolution, hysteretic responses, peak displacement demands, and frame-infill interaction effects. Finally, the performance of the building specimen is assessed by linking engineering demand parameters, damage limit states, and points of the global force-displacement relationship. Overall, the article provides information about the conduct of stateof-the-art hybrid earthquake tests with substructuring and experimental results that might help understand the effects of seismic actions on masonry infill walls in existing RC structures.

Geometry and construction details
The prototype building was a generic five-story cast-in-situ RC-framed structure with weak masonry infills compared to the bounding frame: the infill-to-frame stiffness ratio (K inf /K c ) was about 30, according to the infilled RC frame classification by ASCE 41-17 (2017), 32 which defines weak infills those with K inf /K c < 125. The building represented the critical part of a typical South European residential building with plan dimensions of 24.25 × 8.35 m 2 . The examined part of the building featured two 4.0 m wide bays in the longitudinal direction (i.e., the weak direction of the original building) and a single 4.0 m wide bay in the transverse direction (i.e., the strong direction of the original building), and was characterized by a 3.0 m inter-story height (measured to the top of the floor slabs). The physical specimen in these experiments consisted of the bottom two stories of the prototype building ( Figure 1). The frames were built in a rectangular layout (Figure 2A,B): the overall footprint dimensions were 8.35 m in the longitudinal direction (i.e., East-West) and 4.25 m in the transverse one (i.e., South-North). Throughout this paper, letters X and Y will refer to the longitudinal and transverse building directions, respectively. The infill walls were constructed at full contact with the RC frame elements, employing hollow 301 × 139 × 60 mm 3 and 303 × 137 × 75 mm 3 clay bricks and 5 mm thick, fully mortared head-and bed-joints made of hydraulic cement mortar. The powder was composed of cement, lime, and sand mixed in a ratio of 1:1:4; water was added to the mortar mix until achieving the desired consistency. Three of the four perimeter walls, that is, the South, East, and West walls, consisted of a  single 75 mm wide wythe built with the standard stretcher bond. The North frame was infilled with two 60 mm thick walls, including a 130 mm wide gap in-between, to simulate typical perimeter cavity walls. This resulted in varying infill wall thicknesses in the X direction (Figure 2A,B). The intention was to investigate the effect of different wall thicknesses on the type and extent of damage to the masonry infill walls. Standard symmetric openings were present at the two longitudinal façades: the first story included a 0.90 m wide, 1.80 m high door, while the second included a 0.90 m wide, 1.20 m high window ( Figure 2C). The different infill layouts were introduced to assess the influence of the opening ratio on the lateral stiffness and resistance of the infilled frames. Lintels were placed above all openings: they were 110 mm deep reinforced mortar beams, extending into the masonry 100 mm on each side of the openings for support. The inner face of the firststory infill walls was covered with plaster to facilitate detecting the cracks during the post-test damage surveys and assess the earthquake effects on nonstructural damage.
The floors consisted of 150 mm thick RC slabs, providing rigid diaphragm action. The RC frame elements were designed to promote a strong-beam, weak-column mechanism: columns and beams had cross-section dimensions of 250 × 350 mm 2 and 250 × 500 mm 2 , respectively. All RC frame members were reinforced using modern ribbed steel bars. Stirrups were placed at close spacing and were well-anchored in the concrete core providing sufficient confinement to beams, columns, and joints. The structure was deliberately over-reinforced to secure that damage to the masonry infills would occur before damage to the surrounding frame. This also allowed for future testing of the effectiveness of various retrofit interventions at full scale using the same structure. Over-reinforcing the RC frame was more cost and time effective than strengthening it between the tests, as done in other past experimental studies. 33 The geometry and steel reinforcement detailing of the RC frame elements (i.e., columns and beams) are illustrated in Figure 2E.
The construction works took place off the strong laboratory floor. The total mass of the two-story building specimen was 156.0 t (i.e., 82.2 t of the foundation beam plus 73.8 t of the infilled frame). Transportation into the structural testing facilities of the ELSA was done using nylon roller-bearing wheels. The operation was performed after a maturation period of about two months following the construction. The building was constructed on a rigid grid of 0.8 m deep RC foundation beams; consequently, the structure did not suffer damage during the lifting operation.

Mechanical properties of materials
A series of small-scale tests were carried out to determine the mechanical properties of the materials employed to construct the building specimen. The tests comprised standard strength tests on concrete and mortar samples ( Figure 3A), as well as normal and diagonal compression tests on small masonry wallette's ( Figure 3B-D).
The concrete used to cast the RC frame was of strength class C25/30 as specified by Eurocode 2 (EN-1992-1-1, 2004). 34 The compression tests on 12 standard 150-mm-size concrete cubes provided an average compression strength of 38.3 MPa (EN 12390-3, 2019). 35 The reinforcing steel bars and stirrups were of class B500C (characteristic yield strength of 500 MPa and minimum elongation at maximum tensile stress equal to 7.5%), with a measured average yield strength of 530 MPa. The 60 mm and 75 mm thick hollow clay bricks had 49% and 51% void ratios and densities of 875 kg/m 3 and 855 kg/m 3 , respectively. The average compressive strengths in the direction parallel to the perforations, f b,par , were equal to 9.1 MPa and 8.2 MPa, respectively, as provided by the manufacturer (Fornace Eugenio Casetta S.r.l.). Three-point bending tests were performed on six 160 × 40 × 40 mm 3 mortar prisms to evaluate the flexural-tensile strength of the mortar, f t = 5.7 MPa (EN 1015-11, 2019). 36 The two resulting parts were subjected to compression up to the ultimate failure of the prisms, providing compressive strength f c = 26.2 MPa (EN 1015-11, 2019). 36 Four single-wythe masonry wallettes of dimensions 620 × 590 × 75 mm 3 were subjected to uniaxial compression tests to estimate the masonry compressive strength and the elastic modulus in two orthogonal directions (EN 1052-1, 2001). 37 Two wallettes were subjected to loading perpendicular to the horizontal bed-joints (i.e., perpendicular to the brick TA B L E 1 Summary of mechanical properties for the concrete frame and masonry infill walls.  38 The masonry assemblies were fabricated from the batches of bricks and mortar employed to construct the building; all tests were performed on specimens of an age exceeding 28 days. Table 1 summarizes the estimated mechanical properties of concrete and masonry (i.e., average values and dispersions) for the building specimen.

HYBRID EARTHQUAKE SIMULATIONS
A series of full-scale experiments were carried out at the ELSA testing facilities employing the reaction wall and the continuous PsD testing method with substructuring. 32 The experiments comprised six incremental hybrid earthquake tests to assess the seismic performance of the prototype building under simulated ground motions of increasing intensity. The term hybrid reflects that part of the structure was analytically modeled while the remainder was physically tested ( Figure 1A). Cyclic quasistatic pushover tests were performed between the earthquake simulations to characterize the stiffness and hysteretic properties of the physical model. Data acquired in these tests were used to update the analytical substructure throughout the earthquake sequence. The following paragraphs provide details about the utilized PsD testing method, assumptions made for the structural partition of the hybrid model and the development of the analytical substructure, the input ground motion characteristics, and the adopted experimental setup and instrumentation plan.

Pseudodynamic substructure testing
The response of the five-story prototype building under earthquake ground motion was simulated in a quasistatic fashion through the PsD testing method with substructuring. The method is called pseudodynamic because the actual (experimental) time is much longer than the prototype (accelerogram) time applied in the equation of motion describing the dynamic response of the structure-see Equation (1) below. Inertia forces appearing in the equation are exclusively represented by an analytical model, while restoring forces are obtained in a hybrid manner by combining forces numerically computed by the analytical model with forces physically measured in the laboratory.
The prototype structure was idealized as a discrete system of five degrees of freedom (DoFs) in the X (longitudinal) building direction, where the overall translational mass was considered lumped at the floor levels while the rotational inertia was neglected. The pseudodynamic response of the hybrid building model to the time-varying input ground acceleration a g (t) was obtained through the step-by-step integration of the discrete-DoF equation of motion: In Equation (1), vectors d(t) and r(t) represent the unknown longitudinal displacements (relative to the foundation) and restoring forces at each of the five considered DoFs. Matrix M is the theoretically lumped mass matrix with elements where superscript A indicates quantities of the analytical model. The right-hand side of the equation represents the effective earthquake force, meaning the part of the inertial forces due to the ground acceleration. It is obtained by multiplying a g (t) with the incidence vector of the ground motion I g (i.e., the direction of earthquake loading) and the mass matrix M. Instead, the part of inertial forces due to the relative accelerations of the DoFs appears on the left-hand side of the equation. Both terms are numerically computed since they cannot be measured in the (quasistatic) experiment.
The heart of the substructure testing technique is the separation of the structure into two parts: the physical model of the component of interest (in this case, the first story of the prototype building) and an analytical model of the remainder of the structure (i.e., the upper building stories). This testing technique combines the efficiency of numerical simulation with the realism of physical testing of a portion of the structure that is difficult to model computationally due to its complicated nonlinear behavior. As a result of this structural partitioning, the global restoring force vector r(t) appearing in Equation (1) derives from combining the restoring forces of the analytical and physical substructures, represented by r A (t) and r B (t), respectively. The first are computed analytically by appropriately defined constitutive laws and numerical structural element models, whereas the latter are measured by the load cell of the hydraulic actuators controlling the physical DoFs. In symbols: These experiments were carried out with the continuous PsD testing method developed at the ELSA about twenty years ago-the method was initially introduced by Magonette 39 and further developed by Molina et al. 40 Equation (1) was solved step by step for the pseudodynamic relative displacements, d(t), using a monolithic time-integration algorithm, where analytical and physical DoFs were handled by a unique simulation process. 41 At each integration step, the restoring forces of Equation (2) were plugged into Equation (1) to determine the target displacements of the DoFs at the following step, d(t+Δt). Every time increment in the input accelerogram (i.e., Δt = 0.005 s) was subdivided into multiple substeps, N (in this case, N = 2000), and each substep was executed in one sampling period of the real-time controller equal to δT = 0.001 s. Thus, the time-scale expansion (or time dilation) factor of the continuous PsD test was λ = N•δT/Δt = 400, meaning that 1 s of the real earthquake lasted 400 s in the laboratory. Time delays in the control system can negatively affect the accuracy and stability of the hybrid tests; nevertheless, the performance of these PsD experiments was deemed satisfactory according to the reliability assessment methodology detailed in Molina et al.: 42,43 the error energy and apparent damping distortion were found to be negligible.
Two different approaches were adopted for the structural partition of the hybrid model into analytical and physical substructures. In the initial approach, termed 2+3 partition, the physical substructure consisted of both stories of the mock-up building constructed in the laboratory, while the analytical substructure simulated stories three to five. Some disadvantages of this partitioning approach became evident during the first hybrid tests at low to moderate seismic intensity. Specifically, the boundary conditions at the top of the second-story columns of the physical substructure were not accurately simulated. The joints were free to rotate in the absence of a third physical story, rendering the second story more flexible than one would have expected in a five-story building. Due to this increased flexibility of the physical second story, the analytically computed displacements in the second story were higher than in the first one. Consequently, deformations and damage started being concentrated in the second story of the prototype structure, resulting in the unrealistic development of a soft-story mechanism at that level. Before proceeding with the tests at higher intensities (i.e., tests at PGAs above 0.20 g), this problem was resolved by adopting an alternative partition approach to the hybrid model, termed 1+4 partition. The new physical substructure consisted of the first story of the physical model only; the second story was now there just to ensure realistic boundary conditions at the top of the first story. Accordingly, the analytical TA B L E 2 Parameters defining the nonlinear moment-curvature relationship of the RC frame elements. Unloading stiffness parameter, β 0.5 0.5 substructure simulated the stiffness of stories two to five. In this structural partitioning approach, the second story constituted the overlapping domain between the two substructures, reducing errors in the substructuring assumptions significantly. 44 APPENDIX B demonstrates the contribution of the forces measured by the actuators to the definition of the restoring force vector in the case of the 1+4 partition approach.

Analytical (or numerical) substructure
For the execution of the PsD tests, the prototype structure was simplified through a discrete five-DoF system with linearelastic behavior. The stiffness and damping matrices introduced in the equation expressing the dynamic response of the system-Equation (1)-were derived from post-processing the results from nonlinear response-history analyses on a multiple-DoF finite-element model. Specifically, at every step of the incremental testing sequence, data from numerical simulations on the nonlinear multiple-DoF model were employed to calibrate the properties of the equivalent linearelastic five-DoF system so that the peak dynamic responses of the two fit well within the significant duration of the input ground motion. The analytical substructure of the hybrid model consisted of the upper four DoFs of the linear equivalent five-DoF system; the methodology followed to derive the stiffness and damping matrices is detailed in APPENDIX A.
The multiple-DoF model was developed within the OpenSEES environment. 45,46 This software was selected for its flexibility in generating material models with multiparameter constitutive laws. First, the numerically predicted lateral force-displacement response, stiffness, and overall energy dissipation by the prototype building model were determined based on data from past experiments on similar masonry-infilled RC structures. 33,47 Then, while proceeding with increasing intensity hybrid earthquake simulations, the nonlinear force-displacement rules governing the response of the numerical model were fine-tuned using data from the preceding earthquake and cyclic pushover tests of the sequence. The calibration of the hysteretic models was carried out through displacement-controlled cyclic pushover analysis on a numerical model simulating only the physical part of the building model. It was performed by fitting the force-displacement curves predicted numerically with those obtained experimentally through varying the mechanical properties of masonry (i.e., E w , G, f w , τ cr ). APPENDIX C provides the comparison between the experimental PsD response of the five-story building and the response predicted by the calibrated numerical OpenSEES model for tests at target PGAs of 0.20, 0.25, and 0.30 g.
The RC beams and columns were modeled through force-based elements of distributed plasticity with ten integration points. The cyclic hysteretic behavior of the RC elements was described by predefined moment-curvature (M-φ) relationships: hysteretic materials with appropriate parameter values for the moment at yielding, ultimate moment, curvature at yield, and ultimate curvature were determined in accordance with the provisions of Eurocode 8 (EN 1998-1 and -3, 2005). 48,49 Table 2 lists the parameters defining the nonlinear M-φ response of the RC beams and columns. All column base nodes were fixed to the ground (since the physical specimen was supported by a rigid deep foundation beam), and rigid diaphragms were used to simulate the presence of the RC slabs. Gravity loads and story masses were distributed at the beam-column connections based on tributary floor areas.
The numerical model simulated the masonry infill walls macroscopically through simplified single-strut elements with a multilinear degrading constitutive model in compression and zero capacity in tension. The cyclic hysteretic in-plane response of the infills was reproduced by the model proposed by Fardis and Panagiotakos 17 and simplified by Koutas et al., 47 who proposed tuning only some of the parameters controlling the cyclic strength and stiffness degradation and pinching effect. Nonlinear strut elements were employed to simulate the hysteretic force-displacement response of typical weak masonry infill walls prone to corner crushing (which was the prevailing damage mechanism observed in these TA B L E 3 Properties of the strut elements simulating the masonry infill walls. 519.0 † The masonry compressive strength and elastic modulus were taken as equal to the quantities experimentally determined for loading parallel to the perforations (see Table 1). ‡ The masonry shear modulus adopted for defining the properties of the masonry infill strut elements was determined through calibration with data from the testing sequence. As such, it was higher than the one determined from diagonal compression tests (see Table 1).

Mechanical property [units] / modelling parameter
tests) rather than to explicitly reproduce all possible underlying damage mechanisms, such as shear failure of columns or bed-joint mortar failure.
The effect of the openings on the lateral strength (V cr and V u ) and stiffness (K) of the infills was accounted for through the reduction factors proposed by Decanini et al. 50 After calibration using data from the first PsD tests, reduction factors of 0.63 and 0.67 were adopted for the infill walls with door and window, respectively. The parameters governing the nonlinear response of the diagonal strut elements simulating the masonry infill walls are provided in Table 3. Some of these parameters directly come from experimental data (and were further refined throughout the testing sequence), while others were derived from analytical formulations found in the existing literature. For a detailed description of the hysteretic model, the reader is referred to the analytical study by Koutas et al. 47

Seismic input motion and test sequence
A ground motion recording from the earthquake sequence of 2016 in Central Italy was adopted as the seismic input motion for the hybrid earthquake simulations. Specifically, the accelerogram was recorded near the causative fault of the October 30 event with a magnitude M W 6.5 nearby Norcia. 52 The E-W component of the motion registered at the station of Castelluccio di Norcia, termed IT-CLO-HGE, was preferred due to its higher intensity compared to the NS component (the ground motion records are available from the ESM database by Luzi et al. 53 ). This ground motion was preferred among several other investigated earthquake records representing moderate-to-high seismicity areas in Southern Europe, as it was found to maximize the displacement demands on the numerical model of the five-story prototype building. The motion was slightly modified in amplitude and frequency content to match the EC8 Type 1 spectrum for soil type B (EN 1998-1, 2004). 48 Figure 4A shows the acceleration time series of the selected accelerogram as recorded at the site and after modification using the software SeismoMatch (SeismoSoft 2021). 54 Figure 4B and C shows the elastic pseudoacceleration and displacement response spectra for a 5% viscous damping ratio of the selected motion and the codified elastic response spectrum. In the plots, amplitudes are normalized with the PGA. The PGA of the original signal was 0.42 g, while that of the modified one was 0.33 g. The geometric mean of the pseudo-acceleration spectral ordinates, PSa avg , was equal to 0.84 g and 0.65 g for the original and modified ground motion, respectively. PSa avg was calculated in the period window from 0.2T 1,und to 3T 1,und at spacing 0.01 s, 55 where T 1,und is the fundamental vibration period of the undamaged five-story prototype building (equal to 0.30 s). The 5%-75% significant duration of the modified ground motion was D s,5-75 = 4.43 s; it was calculated as the time interval between the development of 5% and 75% of the Arias intensity. 56,57 The seismic input signal was scaled in amplitude progressively to achieve the desired seismic intensities up to severe damage conditions of the building. The nominal test protocol consisted of six main earthquake simulations. The modified motion IT-CLO-HGE (i.e., Norcia, Italy 2016) was scaled at PGAs of 0.10, 0.15, 0.20, 0.25, and 0.30 g, with testing at 0.20 F I G U R E 4 Selected seismic input motion: (A) normalized acceleration time series of the original and modified ground motion; (B,C) elastic pseudo-acceleration response spectra for 5% viscous damping ratio; comparison with the EC8 Type 1 spectrum for soil type B.

TA B L E 4
Summary of main hybrid earthquake simulations (PsD substructure tests) and cyclic pushover tests.

Cyclic pushover tests
PsD substructure tests  g being performed twice. Tests at a PGA of 0.10, 0.15, and 0.20 g were performed adopting the 2+3 structural partitioning approach; instead, the repetition of the test at a PGA of 0.20 g, and tests at 0.25 and 0.30 g were performed using a single-DoF physical substructure, representing only the first story (1+4 partition), as detailed in the previous section. In between the hybrid earthquake simulations, the building was subjected to cyclic pushover tests to obtain data on the hysteretic force-displacement behavior of the specimen; those tests are highlighted in grey in Table 4. Table 4 provides the applied test sequence, specifying: the loading pattern and target second-floor displacement in the cyclic pushover tests and the intensity of the input ground motion and structural partitioning approach adopted in the PsD tests. All PsD tests were performed by applying the horizontal acceleration component in the W-E (X) building direction; the peak acceleration was always directed toward the West (i.e., −X).

Test setup and instrumentation plan
A total of 112 sensors were installed on the mock-up building to capture its structural response during the seismic experiments: 4 linear optical encoders, 12 inclinometers, 72 linear displacement transducers, and 24 string potentiometers ( Figure 5). Linear encoders monitored the displacements at each floor level of the South and North frames; they were aligned with the axis of the four hydraulic actuators applying lateral loads to the physical specimen. Inclinometers were employed to monitor rotations at the top and bottom ends of each RC column on the South building façade. Linear position transducers (i.e., 20 on each of the South/North façades) recorded the longitudinal deformations of the RC columns at the first story and the bottom of the second story. Such sensors were also used to monitor possible separation between the masonry infills and the RC frame members at the first story. Finally, string potentiometers recorded the in-plane deformation along the diagonal of the masonry infill panels at both stories of the North and South building façades. Four 500 kN capacity actuators with stroke ±0.5 m imposed horizontal displacements: one actuator was mounted at each floor level of the two parallel South and North frames ( Figure 5). The PsD testing method solved the equation of motion for the average horizontal displacements of each floor in the longitudinal building direction, considering the restoring forces equal to the sum of forces by both frames and ensuring zero plan rotations. Despite the different masonry infill thicknesses at the longitudinal frames and the presence of rigid floor diaphragms, torsional deformation was prevented in the tests to simplify the analysis of the results. The possibility to separate forces resisted by each frame in every story was excluded since the rigid floor diaphragms and the infills in the transverse building direction (i.e., Y) resulted in a box-type behavior of the structure. Thanks to the low testing speed of the continuous PsD and cyclic quasistatic tests, each actuator was controlled with high accuracy using as feedback the displacement readings by the optical encoder displacement transducers.
No additional gravity loads were applied to the physical specimen to simulate the presence of the upper stories or other superimposed dead and live loads. The axial compressive load ratios at the base of the first-story columns of the as-tested physical specimen were N/A c f c = 0.027 for the corner columns and 0.054 for the central ones. If the additional masses had been physically applied, the corresponding axial load ratios would have been 0.092 and 0.184, respectively. This limitation was placed for safety reasons but did not compromise the PsD experiments since inertia forces were exclusively simulated by the analytical model. Even though greater axial column loads would have possibly altered the response of the bounding RC frame elements, they might have affected only slightly the seismic response and damage to the masonry infill walls, which are the main investigation subject of this study. Also, although higher axial column loads would have improved confinement (and ductility), the same effect has been accomplished through over-reinforcement of the columns.

TEST RESULTS
This section discusses the major observations from the hybrid earthquake simulations and the cyclic pushover tests performed on the building specimen. The following paragraphs briefly describe the damage evolution and the developed failure mechanisms and illustrate the hysteretic force-displacement responses, the overall displacement demands, and the performance of individual building elements.

Hysteretic force-displacement response
The plots in Figures 6 and 7 show the hysteretic responses of the first and second stories of the physical building specimen individually. Hysteretic responses for each level are provided in story-shear forces versus inter-story drift ratios (IDRs), V b,i − θ i . Eastward displacements (i.e., +X) and, consequently, drift ratios are positive. Although seismic V b,i and θ i have a phase difference of π rad, the sign of forces in the plots has been reversed so that the responses fall in the first and third quadrants, as per a traditional force-deformation relationship. IDRs θ 1 and θ 2 were defined as: where Δ 1 and Δ 2 are the average displacements measured at the two floor levels with respect to the foundation, and h 1 = h 2 = 3 m are the inter-story heights. The displacements were taken as the arithmetic mean of the measurements by two linear optical encoders mounted at the South and North edges of each floor slab (see Figure 5). The seismic responses of the two frames in the longitudinal building direction were examined by considering the two systems as being coupled. Despite the different masonry infill thicknesses, the resistances of the two frames were combined due to the rigid floor diaphragms, which provided a sufficient connection between them. In the plots, the drift-ratio demands include cumulative residual deformations from previous tests. Figure 6 shows the hysteretic responses at both stories of the physical substructure during hybrid simulations of lowintensity earthquakes, that is, for PGAs of 0.1 g, 0.15 g, and 0.2 g. These PsD tests were performed employing the 2+3 F I G U R E 7 Hysteretic response of the building specimen during the earthquake simulations at PGAs of 0.20 g (R), 0.25 g, and 0.30 g. Tests performed using the 1+4 structural partitioning scheme: the physical substructure consisted of the first story of the physical model only; the second story was part of the analytical substructure. structural partitioning approach. During the earthquake simulation at a PGA of 0.10 g, the displacement profile along the elevation of the building was linear, and the peak IDRs were only θ 1,max = 0.05% and θ 2,max = 0.06%. IDRs were rapidly increased to 0.19% and 0.38%, respectively, under testing for the first time at a PGA of 0.20 g. The response of the first story was still elastic, as indicated by the thin hysteresis loops, the minor stiffness reduction, and the negligible permanent drifts. A soft-story mechanism in the first story did not occur as predicted by the numerical model at this stage; instead, slight damage to the infills and deformations were mainly concentrated in the second story. This was due to the free boundary conditions at the top end of the second-story columns, which resulted in considerably lower lateral stiffness at the second story compared to the first one. Consequently, θ 2 appeared significantly higher than would have been observed if rotations at the top of the second story were constrained by the presence of a third story in the physical specimen.
Notable inelastic response of the first story was observed when the improved 1+4 substructuring approach was adopted, that is, when the physical substructure of the hybrid model was reduced by one story. During the test repetition at PGA = 0.20 g, θ 1,max was raised to 0.23%, approximately twice as much as θ 2,max , which was equal to 0.13%. In the following tests, nonlinearities became rapidly pronounced due to the enlargement of pre-existing cracks and the opening of new ones on the masonry infill panels. For testing under the motion with a PGA of 0.25 g, the first story attained peak IDRs of 0.39% and nearly developed its full lateral load resistance, which was about V b = 1100 kN. Subsequently, during the strong earthquake simulation at PGA = 0.30 g, the peak IDRs were 0.75% and 0.31% at the first and second stories, respectively. The almost bilinear nonlinear behavior exhibited by the first story was indicative of the attainment of the maximum lateral load resistance (V b = 1175 kN) of the infill walls and the flexure-dominated response of the RC frame. At this stage, some of the first-story columns had nearly yielded since the rotations recorded at the bottom ends reached the drift limits expected at yielding of the longitudinal reinforcement at the base of the columns (equal to 0.0097 rad). The hysteretic response of the second story was predominantly linear, as inter-story drift ratios did not exceed the peaks reached in previous tests.   Figure 8 illustrates the base-shear force and drift-ratio response histories of the first story of the physical substructure during the hybrid simulations of medium-to high-intensity earthquakes (i.e., for PGAs of 0.2 g, 0.25 g, and 0.3 g). The plots also show the significant part of the seismic input motion shaded in gray; it indicates the 5-75% significant duration of the earthquake (D s,5-75 = 4.43 s), during which most ground motion energy was imparted to the building. Some differences in the shape of both force and displacement waveforms are noticed between tests at 0.2 and 0.25 g and the final test at 0.3 g after the arrival of the PGA (i.e., at t PGA = 2.4 s). In particular, during testing under the earthquake with PGA = 0.3 g, the building exhibited longer oscillations indicative of its nonlinear behavior and the onset of a soft-story mechanism. The experiment was terminated shortly after attaining the peak first IDR (i.e., at t end = 5.6 s of the input accelerogram). Table 5 summarizes global response quantities directly measured (or derived through post-processing) from the physical two-story building specimen throughout the applied earthquake sequence. Specifically, for every PsD test, the table lists from left to right the structural partition approach, the target PGA and PSa avg of the input ground motion, the maximum attained base-shear force, the peak recorded IDRs and the effective stiffness of the two physical building stories. The effective stiffness, K i,eff , is defined here as the slope of the secant line through the point of maximum base-shear force and corresponding displacement response (i.e., white dots in Figures 6 and 7). One can readily observe the drastic reduction in the peak recorded second IDRs (i.e., θ 2,max ) and the remarkable alteration in the apparent second-story stiffness (i.e., K 2,eff ) once the structural partition changed from 2+3 to 1+4. Figure 9A illustrates the backbone curve of the first building story, consisting of the peak responses recorded in the cumulative incremental earthquake tests. In particular, the curve is constructed by the points of maximum attained forces (empty dots) at every test and the point of peak displacement demand under the earthquake with an intensity of PGA = 0.30 g (solid dot), considering the response both in the positive and in the negative direction (towards East and West, respectively). The force-displacement backbone curve can be further idealized by an elastoplastic relationship (i.e., dashed line in Figure 9A): the idealized elastic stiffness was first established as the secant at 70% of the maximum base shear; then, the idealized yield shear force and drift ratio were calculated by equating the areas below the two curves between the origin and the point at which the lateral resistance drops by 20% (NTC18; MIT 2018). 58 Vertical colored lines on the figure denote the damage limits for the first story expressed in terms of drift ratio thresholds that account for residual deformations cumulated from previous tests (see definitions in the following sections).
Cyclic quasistatic pushover tests were carried out between the earthquake simulations to characterize the stiffness and hysteretic properties of the physical model (see Table 4). Figure 9B shows the force-displacement loops obtained during three cyclic pushover tests at target second-floor displacements (Δ 2,tar ) of 7.0, 4.5, and 18.0 mm. An inverse triangular lateral load pattern was adopted for tests at Δ 2,tar = 7.0 and 18.0 mm. The test at Δ 2,tar = 4.5 mm was performed by imposing Δ 1 = Δ 2,tar , resulting in zero force at the second-floor level, F 2 = 0. In all cases, the target displacements did not exceed peak displacement demands attained in previous earthquake simulations; as such, the pushover tests did not cause further structural damage to the building specimen.

Observed damage mechanisms
At the end of every earthquake simulation, structural damage was surveyed in detail, and cracks were accurately mapped. Figure 10 shows the damage inflicted on the masonry infills of the North and South building façades under the applied earthquake sequence. Cracks marked in red were observed at the end of the annotated test; cracks shown in black were already detected in previous stages. Under the earthquake simulations at PGAs of 0.1 and 0.15 g, the structure suffered only slight to moderate damage, manifested through cracks along the infill-frame interfaces and hairline diagonal tensile cracks on the masonry infills of a width less than 1 mm. No evidence of bed-and head-joint sliding or crushing of the units was observed, as the two IDRs remained below 0.15%. Overall, the structure suffered only slight damage and was deemed fully operational with just minor repairs.
The extent of damage to the infill walls of the first story did not evolve significantly in tests at PGA = 0.2 g. During the first of those tests, deformations and consequent damage were primarily concentrated in the second story, which appeared F I G U R E 1 0 Evolution of the specimen crack pattern. Cracks marked in red were observed at the end of the annotated hybrid earthquake test. Cracks shown in black were already detected in previous tests. significantly more flexible than the first story (θ 1,max = 0.19% and θ 2,max = 0.38%). Specifically, as lateral deformations increased, the second-story frame elements tended to deform in a flexural mode, while the infill panels exhibited a shear deformation mode. The result was the frame-panel separation at the corners on the tension diagonals and the development of diagonal compression struts on the compression diagonals. The latter caused crushing of bricks at the corners of the windows. Repetition of the test at PGA = 0.2 g, that is, after modifying the structural partition of the hybrid model, did not put extra stain on the second story but caused crushing of bricks at the corners of the first-story windows. Residual crack widths on the first-story masonry infill walls did not exceed 2 mm. Due to the out-of-plane response of the transverse façades, new cracks were formed at the infill-frame interfaces of both East and West masonry walls.
The first story nearly developed its full lateral load resistance during testing under the earthquake with a PGA of 0.25 g when θ 1,max reached 0.23%. This was reflected in the progressive corner crushing failure of the 'blind' (i.e., without openings) infill panels due to high compressive stresses developed in the diagonal struts. In addition, significant diagonal cracks of residual width greater than 2 mm were formed and propagated through both mortar joints and masonry blocks at or close to the midheight of the walls. Instead, the walls with doors exhibited mostly diagonal cracks around the corners of the openings and only limited crushing of bricks due to compression. The inner wythe of the (North) double-wythe masonry infill panels underwent out-of-plane deflections that exceeded 10 mm; such behavior was not exhibited by the (South) single-wythe walls.
Testing at a PGA of 0.30 g caused more significant damage to the masonry infills of the first story ( Figure 11): wide diagonal cracks (of residual width generally larger than 4 mm) due to shear sliding along the mortar joints, and crushing and spalling of masonry units were observed. In some cases, splitting and dislocation of masonry units caused local crack widths of 10-15 mm. The masonry infills were brought to a severe structural damage condition, requiring extensive restoration works and possible disruption of the building functionality. Flexural horizontal cracks were also seen along the height of RC columns and around the column-beam joints ( Figure 12). No damage was noticed on the beams; they all exhibited elastic response since their flexural strength was greater than the columns. The building could survive further testing at higher intensities; nevertheless, the experiment was stopped to prevent damage to the RC frame, which had developed its maximum lateral load resistance.

F I G U R E 1 2
Observed damage to the RC frame members and the second-story masonry infills after the earthquake at a PGA of 0.3 g.
TA B L E 6 Summary of damage limit states for the building specimen. • First cracks along the infill-frame interface (< 1 mm).

DL1
• Corner crushing and/or sliding along head-and bed-joints with residual crack width of 2-4 mm.
• Crushing and spalling of bricks; local crack width often reached 10-15 mm; • Hairline flexural cracks on the RC columns and column-beam joints.

Identification of global damage limit states
This section proposes the definition of damage states (DS) for the masonry-infilled RC building, with reference to the damage observations from the hybrid earthquake simulations. Thresholds between the damage states, termed damage limits (DL), are subsequently identified and related to quantitative engineering demand parameters. The focus is placed on in-plane damage mechanisms of the infill walls, which appear to be weaker than the surrounding frame. Specifically, damage to the infill panels always preceded any significant damage to the RC frame elements. Five damage states were considered: DS1, no structural or nonstructural damage; DS2, minor structural damage (or moderate nonstructural damage); DS3, moderate structural damage (or heavy nonstructural damage); DS4, heavy structural damage (or very heavy nonstructural damage); and DS5: very heavy structural damage with partial or total collapse. Four damage limits were consequently defined where DL1 constitutes the limit condition at which no damage was visible, F I G U R E 1 3 Summary of the global seismic performance of the physical building specimen throughout the sequence of hybrid earthquake simulations.
DL4 is the limit condition at which heavy structural (or very heavy nonstructural) damage is reported before entering the near-collapse conditions, while DL2 and DL3 denote the attainment of intermediate levels of damage. Near-collapse conditions mean that the building is so gravely damaged that re-occupancy is not an option in any case; the level of damage sustained by structural elements is such that the building is beyond repair and most probably would be demolished in practice, as posing a threat to life and limb due to falling hazards. Such severe damage was never witnessed in these tests, as the PsD experiment was stopped to prevent damage to the RC frame.
Each DL was associated with an earthquake input: specifically, DLi was associated with the last test that caused building damage classified as DSi. Table 6 lists the earthquake tests when the structure reached each damage limit, DLi. The maximum first IDR (θ 1,max ) induced to the structure by each of those test runs was taken as the reference engineering demand parameter corresponding to DLi. 59,60 Overall, slight structural damage to the masonry infills was first observed in both stories after testing under earthquake with PGA intensity of 0.15 g (PSa avg = 0.30 g). It was associated with crack opening and separation of the infill walls from the RC frame. Damage to the masonry panels of the first story appeared only in later stages of the testing when the physical substructure was reduced to the first story of the specimen only. Specifically, such damage occurred under testing at PgA = 0.25 g (PSa avg = 0.49 g) when corner crushing and sliding along head-and bed-joints of the first-story masonry infill walls were observed. During testing under the earthquake scaled at PGA = 0.30 g (PSa avg = 0.59 g), the masonry infills at the first story exhibited significant degradation in stiffness and strength, signaling the attainment of DL3. This observation seems to agree with other experimental studies that did not report failures in the RC frame before the infills reach damage state DS3 (see studies summarized in Chiozzi and Miranda). 61 The limits DL1 through DL3, defined in this section for the entire building, are associated with points of the force-displacement backbone curve in Figure 9 in previous sections.

Summary of building seismic performance
An overall summary of the seismic performance of the building specimen is provided in Figure 13, where peak and residual displacement demands, the variation in the lateral stiffness of the physical substructure, and the first-mode period evolution are plotted for testing under the sequence of simulated earthquakes. Peak and residual displacements are provided in absolute values; however, all peaks were measured for building side sway to the negative direction (i.e., −X). The interstory stiffness degradation was computed as the ratio of the effective stiffness at the current earthquake simulation test, K i,eff , to the initial lateral stiffness of the story, K i,in (see discussion in previous sections for the definition of the effective stiffness). The second-story stiffness degradation is provided only for tests at PGAs up to 0.2 g since, for higher-intensity tests, the response of the story was simulated numerically. The first-mode period of the undamaged five-story building was T 1,und = 0.31 s, while at its ultimate condition, it shifted to T 1,dam = 0.73 s. Initially, the response was dominated by the formation of a soft-story mechanism in the second story. Changes in the modal shapes were not seen before testing at 0.20 g (R) (PSa avg = 0.39 g) when the fundamental period increased to 0.51 s. Further significant elongation was observed for testing at PGA = 0.25 g (PSa avg = 0.49 g) when the period reached 0.57 s; overall, the building specimen exhibited a period shift of 135% at severe damage conditions of the infill walls (i.e., DL3). Figure 14 reports the evolution of other significant engineering demand parameters representing the damage inflicted to the masonry infill walls and the RC columns during the applied earthquake sequence. Specifically, the figure provides measurements of column rotations, column crack widths, the shear sliding of the masonry infills, and the infill-frame separation.
Column rotations (r i ) were recorded by the inclinometers mounted at the top and bottom ends of the RC columns in both stories of the South building façade. In Figure 14, one can readily observe the effect of the free boundary conditions at the top of the second-story columns on the high values of r 2,S,t recorded during testing up to a seismic intensity of PGA = 0.20 g (PSa avg = 0.39 g). The effect was moderated once the structural partitioning approach changed from 2+3 to 1+4. Position transducers monitored the elongation (w i ) of the RC columns at the top and bottom of the first story and the bottom of the second story. Figure 14 shows that crack widths increased considerably during testing at PGAs of 0.25 and 0.30 g (PSa avg of 0.49 g and 0.59 g, respectively), and deformations were mainly concentrated within critical bottom zones of the first-story columns. Possible shear sliding of the masonry infill walls (s i ) was monitored by horizontal displacement transducers mounted at the interface between RC beams and infill panels. Accordingly, the separation of the masonry infill walls from the RC frame (d i ) was monitored by displacement transducers installed along the interface between the walls and the columns of the first story only. The bottom two plots in Figure 14 provide maximum readings among sensors installed on both bays in each of the South and North building façades. In the figure, subscripts S and N identify quantities related to elements found on the South and North building façades, while subscripts t and b denote quantities recorded at the top and bottom ends, respectively, of the various building components.

CONCLUSIONS
This paper discusses an experimental study on the seismic performance of a full-scale RC building carried out at the ELSA testing facilities of the European Commission's Joint Research Centre in Ispra, Italy. The prototype structure was a generic, five-story RC building with beams stronger than the columns and nonstructural masonry infill walls weaker than the surrounding frame. It was subjected to a sequence of six hybrid earthquake simulations of increasing intensity using the PsD testing method. The term hybrid reflects that part of the structure was analytically modeled while the remainder was physically tested. Cyclic quasistatic pushover tests were also performed between the earthquake tests to characterize the stiffness and hysteretic properties of the physical model and fine-tune the analytical component of the hybrid model. Two different approaches were adopted for the structural partition of the hybrid model. Initially, the physical substructure consisted of both stories of a two-story mock-up structure built in the laboratory, while the responses of stories three to five were simulated by a simplified analytical model with a linear-elastic response (i.e., 2+3 structural partitioning scheme). The analytical substructure was calibrated using a numerical multiple-DoF model developed on OpenSEES. Weaknesses of this partitioning approach became quickly evident during the first tests at low to moderate seismic intensity (PGA ≤ 0.20 g). Specifically, without a third physical story, the joints at the second-floor level were free to rotate, rendering the second story more flexible than one would have expected in a five-story building. Before proceeding with testing at PGA intensities over 0.20 g, this problem was resolved by adopting a new partition approach to the hybrid model: the new physical substructure consisted of the first story of the two-story physical model only. Accordingly, the analytical substructure simulated the response of stories two to five (i.e., 1+4 partitioning scheme).
In the 1+4 structural partition scheme, the presence of the second physical story ensured realistic boundary conditions (i.e., rotations) at the top of the first story. In any other case, the first story would appear more flexible than it would have been in a real multistory building. This would have resulted in larger displacement demands and increased damage for relatively lower earthquake intensities, like the second story in the 2+3 partition approach. Therefore, including the second physical story in the experimental setup significantly improved the accuracy of reproducing the seismic behavior of the first story. Contrasting the observations from tests carried out with the two structural partition approaches highlighted the importance of accurately simulating the boundary conditions between the physical and analytical parts in hybrid structural testing with substructuring of multistory buildings.
Earthquake simulations were performed up to conditions of severe structural damage to the masonry infills of the physical substructure. The experiments were terminated with the onset of a soft-story mechanism at the first story for an earthquake with a nominal PGA of 0.30 g (PSa avg = 0.59 g). The masonry infills of the building specimen displayed significant degradation in stiffness and strength, signaling the attainment of near-collapse conditions. Wide diagonal cracks (larger than 4 mm) due to shear sliding along the head-and bed-joints, as well as crushing and spalling of masonry units, were observed. The first-story RC columns suffered some flexural damage at the top and bottom ends, while cracks were also seen at the column-beam joints. The building specimen could survive further testing at higher intensities; nevertheless, the experiment was stopped to prevent further damage to the RC frame. The tests demonstrated that masonry infills significantly increase the lateral in-plane stiffness and resistance of RC-framed structures; the test structure could retain just 64% of the peak base shear at a first inter-story drift ratio of 0.75%.
Among other aspects, the experiments allowed the definition of damage states for the masonry-infilled RC building, with reference to the damage observations from the hybrid earthquake simulations. The focus was placed solely on inplane damage mechanisms of the infill walls, which were designed to be weaker than the bounding RC frame. Thresholds between the damage states were identified and related to local engineering demand parameters and points of the global force-displacement building response. For instance, the clay-brick masonry infill walls of this prototype building seem to attain limit conditions of DS1, DS2, and DS3 for first IDRs approximately equal to 0.10%, 0.40%, and 0.75%, respectively. Undoubtedly, local out-of-plane damage mechanisms of infill panels are generally more critical and expected to govern the attainment of significant damage limits. However, no such mechanisms were observed in these tests since they are activated under dynamic excitations and are primarily expected in upper stories.
Data and observations from these tests substantially improved our understanding of the effects of masonry infills on the cyclic response of RC structures and provided an experimental reference for numerical modeling. The experiment was part of a wider ongoing testing campaign investigating the effectiveness of novel construction materials and technologies in realizing the concurrent seismic and energy upgrade of existing RC buildings. The building specimen presented in this paper is the reference (i.e., control) specimen of a series of experiments and will be employed to test various hybrid retrofit configurations in later stages of the experimental campaign.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.

APPENDIX A: DEFINITION OF THE EQUIVALENT LINEAR MODEL FOR THE ANALYTICAL SUBSTRUCTURE BASED ON CONSTANT MATRICES
The analytical (or numerical) substructure was introduced in the PsD equation of motion through constant stiffness and damping matrices. For every test, these matrices were computed as follows: 1. First, a nonlinear finite-element model with multiple DoFs developed in OpenSEES was employed to numerically predict the global response of the prototype five-story building under the specified earthquake ground motion. Before every hybrid earthquake test, the model was updated by employing experimental data from preceding earthquake simulations and cyclic pushover tests of the sequence. 2. The dynamic global response numerically computed by the multiple-DoF model was post-processed to derive global stiffness and viscus damping matrices for an equivalent five-DoF system. The identification of the matrices was performed within a time window containing the peak earthquake-induced displacement demand to the building employing the spatial model method proposed by Molina et al. 42,43 3. The identified stiffness and damping matrices were forced to be symmetric by taking the mean between each matrix and its transpose. 4. Modal shapes, frequencies, and damping ratios were computed. In the case of negative damping ratios, low positive values were set, and the damping matrix was recomputed based on the new damping values. 5. The stiffness and damping matrices of the analytical substructure (i.e., the building part including the upper four stories) were extracted from the global structure matrices defined above based on the following assumptions: (i) for any given displacement vector of the five-DoF system, the internal forces in stories two to five were not affected when the elements of the first DoF (i.e., first story) were imaginarily removed; (ii) when imaginarily removing the elements of the first DoF, the corresponding first-DoF forces change so that they balance forces from the upper floors; (iii) the principle of reciprocity is applied to impose symmetry on the obtained matrices. Thus, if K represents the global stiffness matrix and K A is the stiffness matrix associated with stories two to five (superscript A indicates part of the matrix related to the analytical substructure), then according to assumption (i): and, by applying assumption (ii): Applying the principle of reciprocity, i.e., assumption (iii), we obtain: where () T is the transpose of the matrix. Finally, by applying assumption (ii) again, we obtain the stiffness matrix of the analytical substructure. In symbols: The relative damping matrix was derived following step by step the same procedure.

APPENDIX B: DERIVATION OF THE RESTORING FORCE VECTOR FROM THE PHYSICAL MEASUREMENTS FOR THE 1+4 PARTITION case
In the case of the 1+4 partition approach adopted in these experiments, the physical forces measured by the actuators at the second-floor level were considered in the PsD equation of motion at the first DoF only (not at the second). In contrast, the analytical substructure representing the upper floors (i.e., stories two to five) provided restoring forces to all DoFs. Said this, a doubt arose about what to consider as the physical restoring force for the first DoF. Two options were examined, specifically: (i) option 1001, considering only the forces measured at the first-floor level of the physical specimen, or (ii) option 1111, taking the sum of forces measured at both floor levels. This appendix demonstrates why option 1111 is the right one and was adopted in these experiments. Let us assume for simplicity the example of a three-DoF linear-elastic system where only the elements linking the first two DoFs are physically present in the laboratory. Then, the overall linear force-displacement relationship of the system is: The (physical) stiffness matrices of the first-and second-story elements (K 1 and K 2 , respectively) are given by: where, as in the case of this five-story test building, the first story happens to exhibit: Regarding the five-story prototype building of these experiments, the physical substructure initially consisted of two stories, meaning both stories of the mock-up building in the laboratory. However, in the progress of the testing sequence, the physical substructure was limited to the first story of the mock-up building (for reasons detailed in Section 3 of this paper), thus contributing to the restoring forces only of one DoF instead of two. Then, for the three-DoF linear example model, the numerical structure will include three DoFs (instead of two) in the PsD scheme, and the numerical stiffness matrix of the numerical (uniform) structure is given by: where: For a given displacement vector u of the overall structure, if its reduction on the 2 first DoFs is applied to the physical structure, the resulting force would be: and the analytical (numerical) one is: Then, what is the most appropriate overall force r to feed to the PsD algorithm? Obviously, it is not r = r p + r n since if the second DoF would also be substructured, the so-called 1001 option, obtained by reducing r p to the first DoF, is the following: But, it also in principle has to be rejected since it corresponds to an overall stiffness matrix that involves k 2 and is not symmetrical: The so-called 1111 option, obtained by combining the force r p to the first DoF is the following: It corresponds to an overall symmetrical stiffness matrix where k 2 is no longer involved: Note first that if k 2 is much lower than k 1 , K 1001 and K 1111 would be almost identical, which is the case for the PsD tests at PGA = 0.20 g (R) and PGA = 0.25 g. Note also that it could have been possible to apply only the first displacement component to the physical structure and let the force at the second floor be zero. In this simplified linear model case, the second component of the displacement would have been equal to the first since (-k 2 u 1 + k 2 u 2 ) = 0, and the first component of the restoring force k 1 u 1 . Summing up this force to r n would lead to the same stiffness matrix K 1 + K n as in the 1111 option. However, the 1111 option is preferred since the second floor is still 'tested', but the question may arise at this point to understand if it is the best option in the nonlinear case.
Secondly, in order to know what physical restoring force vector should be taken from our measured forces in the nonlinear case, we may just rethink two hypotheses that we are already adopting in our PsD model. The first hypothesis is the reduction to a discrete number of DoFs for the final prototype structure (5 DoFs) and the physical one (2 DoFs). The second hypothesis is that, at least for the physical structure, the decomposition by element stories is possible and the substructured restoring force vector for the i th story: is only determined by its level of deformation (u i -u i-1 ) and is self-balanced: , = − , −1 and , = 0 ( ≠ , ≠ − 1) (B13) In particular, for the two stories of our physical substructure, the associated restoring forces are: when, for example, they would have been assembled in the 5-DoF system. The measured forces on the physical structure are then the addition of both vectors. In symbols: The story stresses s 1 and s 2 are the shear forces in the first and second stories, respectively, whereas r 1+2 are the restoring forces measured from the physical substructure. This second hypothesis can be justified when the floor slabs are rigid and the overturning moment effect on the axial load in the columns is ignored. Then, if we want to use only the first one of the two physical levels (r 1 ) for our PsD model, we need to separate r 1,1 from the measured forces by computing the first shear force (i.e., base-shear force) back as: 1+2,1 + 1+2,2 = 1 − 2 + 2 = 1 , and this is what we are calling option 1111 because it represents the addition of the measured forces at levels 1 and 2.
Regarding the question of how to move the second floor during our PsD test, in principle, it should be better to deform it to induce some damage but also to have better boundary conditions for what concerns the rotation of the floor-column joints, the constraint of the floor by the upper-floor bricks and a small amount of overturning moment induced by the upper actuators. Note that these effects escape from the two previous hypotheses.

APPENDIX C: COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL PsD RESPONSE
The OpenSEES models were validated through a calibration exercise performed throughout the testing sequence. Specifically, the nonlinear force-displacement rules governing the response of the various elements in the FE model were updated (consequently, also validated) before every earthquake simulation using data obtained from preceding steps of the testing sequence. Tables C1 and C2 list the parameters of the numerical multiple-DoF model calibrated using data from all those TA B L E C 1 Parameters defining the nonlinear moment-curvature relationship of the calibrated RC frame elements. PsD tests preceding the test at a PGA of 0.30 g. Figure C1 compares the experimental PsD response of the five-story building with the response predicted by the numerical OpenSEES model for tests at PGAs of 0.20, 0.25, and 0.30 g. The numerical simulations also account for cumulative damage throughout the testing sequence. Although the accuracy of the numerical multiple-DoF model was satisfactory when the building responded elastically, it could not capture well enough the nonlinear force-displacement behavior associated with heavy non-structural damage to the masonry infills unless calibrated to experimental data. Therefore, testing the physical substructure was necessary to improve the predictive accuracy of the numerical model in the inelastic response regime.