Damage Estimation of Full-Scale Infilled RC Frames under Pseudo-Dynamic Excitation by Means of Output-Only Modal Identification

Abstract

To assess the health condition of structures and infrastructure during their service lives, continuous vibration-based monitoring represents a viable and cost-effective solution. Model updating and digital twins are increasingly adopted for damage detection. However, significant gaps and uncertainties in damage quantification still arise. This work presents original data from output-only modal identification tests on full-scale, two-storey reinforced concrete (RC) frames subjected to pseudo-dynamic loading to simulate seismic damage. The frames are tested with two masonry infill wall configurations with three-sided and four-sided boundary conditions, and the observed seismic damage is correlated to a damage scale. Output-only modal identification tests are performed before and after testing to catch variations in modal properties due to observed damage. Experimental data are used to build a refined finite element model able to reliably simulate the static and dynamic performance of the infilled RC frames before and after damage. The model allowed for the further assessment of the variation in natural frequencies of tested specimens at different earthquake intensities, the correlation of such variations to damage levels, and identification of the contribution of structural and non-structural components to the overall frequency variation.

1. Introduction

Structures and infrastructure experience damage over their service lives due to natural ageing or extreme events, such as earthquakes, explosions, floods, etc. A rapid identification of the structural health condition of physical assets is crucial for timely decision-making about interventions, minimising service disruptions and avoiding economic and societal loss. Traditional techniques for assessing current and post-event conditions rely on visual surveys and other more comprehensive and detailed procedures for life-cycle assessments of structures [1,2,3,4].

Due to technical advances in sensor technology, computational methods and communication systems, as well as developments in sophisticated signal processing and system identification algorithms, structural health monitoring (SHM) has emerged as a promising technology-driven solution for the rapid damage assessment of civil infrastructure. Output-only modal identification, also known as Operational Modal Analysis (OMA) [5], has attracted attention among researchers as a valid approach for measuring modal parameters for updating finite element (FE) models and digital twins [6,7], providing acceptable accuracy in structural analysis results.

Several studies in the literature adopted OMA and FE models, which were updated for analysing different structures, including bridges, churches and towers [8,9,10,11,12,13,14]. Although there are several studies that prove the applicability of output-only modal identification to update FEM models and analyse existing/initial conditions, only a few studies compare the results before and after seismic damage. Altunişik et al. [15] and Günaydin et al. [16] adopted OMA on 2D and 3D two-storey two-bay reinforced concrete (RC) bare frames in undamaged, damaged and repaired and strengthened conditions.

However, the seismic loading and displacements were not controlled during the tests. Inci et al. [17] presented OMA results for a 3D three-storey RC bare frame for the undamaged condition and for a set of damaged levels achieved by quasi-static load reversal. The frame was defined by the authors as non-ductile, which is the failure mode governed by the brittle shear failure of structural components. The authors found a variation of approximately 15% in the first modal frequency due to an imposed drift ratio of 1.0% and the shear cracking of two columns.

Conversely, Goksu et al. [18] tested full-scale substandard RC bare 3D frames governed by a ductile behaviour. After quasi-static testing, the authors observed a frequency variation greater than 17% for an imposed drift ratio of 0.5% and greater than 25% for a drift ratio of 1.0%. Durmazgezer et al. [19] also performed vibration tests and model updating for a small-scale one-storey 2D RC frame under quasi-static lateral loading.

All previous studies were performed on bare frames and did not consider the effect of non-structural components (i.e., masonry infill walls) on the variation of modal properties due to damage. This significantly reduces the applicability of tests results for the damage identification and quantification in infilled RC frames. Furthermore, in previous studies, the seismic loading was mainly simulated through quasi-static testing instead of more realistic methods.

This study presents results from output-only modal identification tests on full-scale RC frames with masonry infill walls subjected to pseudo-dynamic testing to simulate the seismic damage, bringing a novel and original contribution to the area of knowledge. Experimental results from output-only modal identification tests and validated numerical tools can support the fast damage assessment of buildings through vibration-based SHM.

In detail, the present paper investigates the effect of seismic damage experienced by structural and non-structural components on the modal properties (i.e., fundamental frequencies) of full-scale 2D two-storey reinforced concrete (RC) frames through experimental pseudo-dynamic tests and validated numerical analyses. In detail, the study presents experimental data from output-only modal identification tests performed on full-scale two-storey 2D RC frames with masonry infill walls tested under pseudo-dynamic tests.

Two frame configurations are considered, with different infill wall boundary conditions (i.e., three-sided and four-sided). Output-only modal identification tests are performed before and after the pseudo-dynamic tests to catch variations in modal properties due to damage. Experimental data are herein presented and adopted to validate a refined FEM model simulating the seismic performance of tested infilled frames.

The model is able to predict the performance and modal properties of infilled RC frames in both undamaged and damaged conditions without any intermediate updating. Nonlinear time-history analyses are then performed on the validated FEM model at different PGA levels to assess the variation in fundamental frequencies as a function of the damage experienced by the infilled frames during the ground shaking. The contribution of structural and non-structural damage to the overall frequency variation is also pointed out in the output of the FE models.

2. Output-Only Modal Identification and Pseudo-Dynamic Loading

Output-only modal identification tests were performed before and after pseudo-dynamic sequences on full-scale, one-bay, two-storey RC frames with masonry infill walls, as shown in Figure 1. Details about the experimental program and the modal identification are reported in the following paragraphs.

2.1. Specimens and Setup

The specimens adopted for the modal identification are presented in Del Vecchio et al. [20] as F2_3S_M and F2_4S_M. The geometrical and mechanical properties of the specimens are briefly reported herein. The specimens are 6.86 m high and 4.50 m long. The interstorey height is 3.10 m and the foundation block height is 0.56 m. The square columns, 400 × 400 mm², are reinforced with 8 ϕ16 mm longitudinal bars and ϕ8 mm transverse reinforcement 250 mm spaced. The beam’s cross-section has a 500 mm height and 400 mm width, and is reinforced with 6 ϕ16 mm and 4 ϕ16 mm bars at top and bottom, respectively.

The beam-column joint panels have no transverse reinforcements as commonly observed in existing buildings in the Mediterranean area. For the beam-column joints in contact with the actuators (left side of the frame), cross-section enlargement and steel profiles reinforcement are locally adopted to avoid punching failure due to the concentrated loads, as is visible in Figure 1.

The frame F2 has been casted and cured in laboratory conditions and it has been tested twice with different infill wall configurations, as discussed in detail in the following. The main characteristics of the frame are summarised in

Table 1. Test description for specimen F2.

Test ID	Infill Walls	Notes
F2_3S_M	Connected to the frame with a mortar on three sides, with a gap between the upper beam and the wall	After a pseudo-dynamic test, the infill walls are demolished and re-built
F2_4S_M	Connected to the frame on four sides with mortar	The frame is the same as those of previous test, with new infill walls

.

The frame was built with a medium quality concrete. Results from compressive tests revealed an average concrete compressive strength of about 19 MPa at the first storey and 14 MPa at the second storey [20]. Hollow clay brick infill walls are used at both floors. Square bricks with a 250 mm length edge and 200 mm in thickness are adopted. Ten millimetre joints of M10 class mortar are used to build the infill walls simulating a three-sided boundary condition with a 5 mm gap between the wall and the upper beam.

In the original experimental program, the test was named F2_3S_M, where F2 is the name of the frame, 3S stands for three-sided boundary condition, M stands for mortar (i.e., the label includes the connection system since different infill-to-frame connections were investigated in [13]). In test F2_3S_M, the specimen was tested up to a ground motion intensity of 125%. At the end of the test, the masonry infill walls were demolished and re-built with a four-sided boundary condition. Another pseudo-dynamic test sequence, named F2_4S_M, was then performed on the frame up to a ground motion intensity of 150%.

The steel adopted for longitudinal and transverse reinforcement has an average yielding strength of 535 MPa. Mechanical characterisation tests on the infill wall samples showed a shear strength of about 0.35 MPa and a shear modulus of 1063 MPa, a compressive strength of 2.59 MPa in the direction parallel to the holes and a compressive strength of 1.91 MPa in the orthogonal direction to the holes [16].

2.2. Loading Sequence and Dynamic Identification

The pseudo-dynamic tests are performed adopting the setup shown in Figure 1. A strong RC reaction wall is adopted to contrast two actuators for the application of storey displacement histories. Two hydraulic jacks are installed at the top of the frame to simulate the axial load on columns. Further details of the pseudo-dynamic tests can be found in the reference paper and are not reported herein for the sake of brevity.

The AQG record in the Est direction (peak ground acceleration PGA = 0.45 g) of the 2009 L’Aquila earthquake is used as input acceleration. The loading sequence consists of pseudo-dynamic tests of increasing intensities (i.e., 10%, 25%, 50%, 60%, 75%, 100%, 125%, 150%), as reported in

Table 2. Loading sequences.

Intensity [%]	PGA [g]	F2_3S_M	F2_4S_M
0	-	OMA	OMA
10	0.045	-	-
25	0.112	-	-
50	0.223	-	-
75	0.335	-	-
100	0.446	-	-
125	0.558	OMA + OMA without infill walls	-
150	0.669	-	OMA

.

Output-only modal identification tests are performed at the beginning of the loading sequence, representing the undamaged condition, and at the end of the loading sequence, representing the damaged condition. It is worth noting that the output-only modal identification tests are performed on the specimen without actuators and jacks to avoid undesired constrain effects. This makes the monitoring of dynamic properties variation at different earthquake intensities impossible. For test F2_3S_M, an additional modal identification test is performed after the demolition of the infill walls to record the dynamic properties of the bare frame.

Output-only modal identification tests are performed by using unidirectional piezoelectric accelerometers having a sensitivity of 10 V/g and a full scale of ±0.5 g. The modal shapes derived with the software SAP2000 of the specimen are shown in Figure 2, along with the associated fundamental frequencies. In detail, the first three modal shapes for the 2D specimen are related to out-of-plane mechanisms, while the fourth mode is in-plane. Based on this preliminary analysis, both in-plane and out-of-plane modes are monitored.

The sensors layout adopted for the tests is depicted in Figure 3 along with the recording direction. A total of 6 six accelerometers are used, three for the in-plane direction and three for the out-of-plane direction, respectively, to catch the primary response of the frame in both directions. Sensors are located at the two storey levels and the mid-height of the second storey column to further catch the experimental modal shapes.

3. Experimental Results

The damage experienced by the specimens at the end of the two loading sequences is shown in Figure 4. A detailed description of the damage occurred during the loading sequences is also reported in

Table 3. Pseudo-dynamic test results and damage description for F2_3S_M [20].

Earthquake Intensity [%]	PGA [g]	${\mathit{\zeta }}_{\mathit{e}\mathit{q}}$ [-]	Test Description
10	0.045	-	Intensity 10%. Peak Interstorey Drift 0.01%. No Damage (DL0)
25	0.112	-	Intensity 25%. Peak Interstorey Drift 0.01%. No Damage (DL0)
50	0.223	0.143	Intensity 50%. Peak Interstorey Drift 0.11%. Infill-frame separation and light diagonal cracking of infill (DL0/DL1)
75	0.335	0.175	Intensity 75%. Peak Interstorey Drift 0.19%. Light diagonal cracking of infill (DL1)
100	0.446	0.125	Intensity 100%. Peak Interstorey Drift 0.31%. Significant diagonal cracking of infill and crushing of corners (DL2)
125	0.558	0.135	Intensity 125%. Peak Interstorey Drift 0.41%. Crushing of some bricks (DL2)

for F2_3S_M and in

Table 4. Pseudo-dynamic test results and damage description for F2_4S_M [20].

Earthquake Intensity [%]	PGA [g]	${\mathit{\zeta }}_{\mathit{e}\mathit{q}}$ [-]	Test Description
10	0.045	-	Intensity 10%. Peak Interstorey Drift 0.01%. No Damage (DL0)
25	0.112	-	Intensity 25%. Peak Interstorey Drift 0.01%. No Damage (DL0)
50	0.223	0.206	Intensity 50%. Peak Interstorey Drift 0.05%. Infill-frame separation (DL0/DL1)
75	0.335	0.166	Intensity 75%. Peak Interstorey Drift 0.10%. Light diagonal cracking of infill (DL1)
100	0.446	0.178	Intensity 100%. Peak Interstorey Drift 0.16%. Significant diagonal cracking of infill (DL2)
125	0.558	0.153	Intensity 125%. Peak Interstorey Drift 0.40%. Significant diagonal cracking of infill and column cracking due to infill action (DL2)
150	0.669	0.100	Intensity 150%. Peak Interstorey Drift 0.62%. Wide diagonal cracking of infill and crushing of some bricks (DL2/DL3)

for F2_4S_M, along with the peak drift ratio reached at each storey level in the positive and negative loading directions, respectively, and the damping ζ_eq [21].The damage observations have been also correlated by Del Vecchio et al. [20] to the damage scale proposed by Cardone and Perrone for non-structural components [22].

In test F2_3S_M only damage to non-structural components is achieved. The infill walls cracking started at a ground motion intensity of 50% (DL1), and the crushing of corner bricks was observed at 125% AQG (DL2), when the test was stopped, and the infill wall was demolished and rebuilt. Similarly, in test F2_4S_M, the major damage was concentrated on non-structural components. The infill walls diagonal cracking started at a 75% intensity (DL1) and reached the crushing of almost all bricks in contact with the upper beam at a 150% intensity (DL2/DL3). At 125% AQG, a minor sub-horizontal cracking at the top of first storey right column was also observed, probably due to the full development of the infill action in the four-sided boundary condition [20].

Data acquired through output-only modal identification tests before and after damage were processed using the singular value decomposition of the PSD matrix according to the frequency domain decomposition method [23]. As an example, tests recorded in terms of frequency are plotted in Figure 5 for test F2_4S_M for the in-plane direction before Figure 5a and after damage Figure 5b.

In the plots, the experimental fundamental frequency is highlighted for the two configurations (i.e., 28.03 Hz and 10.25 Hz, for the undamaged and damaged configurations, respectively). The experimental modal shape derived from the processing of modal identification tests data are also plotted for the two configurations. The figure points out the effect of damage experienced by the specimen both in terms of fundamental frequency and modal shape. The same observations can be made for the other records, that are not reported herein for the sake of brevity.

Results from modal identification tests are summarised in

Table 5. Summary of modal identification results via OMA for the first in-plane mode.

ID	Configuration	IP 1st Frequency [Hz]	Frequency Variation [%]	Mode Shape	Peak Drift [%]	Observed Damage	Damage Level
F2_3S_M	Undamaged	25.4	-	1.00;0.78;0.59	0.41	Significant diagonal cracking of infill and crushing of corners	DL2
	Damaged	9.5	−63	1.00;0.82;0.53
	Bare	6.5	−74	1.00;0.83;0.50
F2_4S_M	Undamaged	28.0	-	-	0.62	Diagonal cracking of infills and crushing of some bricks	DL2/DL3
	Damaged	10.2	−63	1.00;0.81;0.56

and

Table 6. Summary of modal identification results via OMA for the first out-of-plane mode.

ID	Configuration	OOP 1st Frequency [Hz]	Frequency Variation [%]	Mode Shape	Peak Drift [%]	Observed Damage	Damage Level
F2_3S_M	Undamaged	3.4	-	1.00;0.10;0.03	0.41	Significant diagonal cracking of infill and crushing of corners	DL2
	Damaged	2.6	−23	1.00;0.70;0.11
	Bare	2.6	−23	-
F2_4S_M	Undamaged	2.8	-	-	0.62	Diagonal cracking of infills and crushing of some bricks	DL2/DL3
	Damaged	2.3	−19	1.00;0.69;0.12

for the in-plane (IP) and out-of-plane (OOP) directions, respectively. In detail, fundamental frequency, frequency variation and modal shape parameters are reported in the Tables.

Test records for tests F2_3S_M and F2_4S_M allow us to effectively identify the effect of seismic damage on the dynamic properties in relation to the damage level. For test F2_3S_M, the in-plane mode is significantly affected by damage. The fundamental frequency in the undamaged configuration, equal to 25.4 Hz, is reduced after the loading sequence, reaching a value of 9.5 Hz. This means that the damage occurred in infill walls, classified as DL2, induces a variation in fundamental frequency of 63%. The test performed on the frame after the demolition of damaged infill walls allows us to assess the frequency of the structural components only. From test records, the fundamental frequency of the bare frame is 6.5 Hz. Given the absence of observed damage to the structural components in F2_3S_M, this frequency can be considered as the frequency of the undamaged bare frame which is 25% of the frequency of the undamaged infilled frame.

For test F2_4S_M, the fundamental frequencies for the in-plane mode are 28.0 Hz and 10.2 Hz, respectively for the undamaged and damaged configuration. Hence, the damage of infill walls, classified as DL2/DL3, reduces the frequency by 63%, as previously observed for test F2_3S_M.

For the first out-of-plane mode, test records from the two tests show that a DL2 damage to infill walls causes a reduction in the fundamental frequency ranging from 19% to 23%. For test F2_3S_M, the bare frame frequency, equal to 2.6 Hz, is 77% of the overall frequency of undamaged infilled frame for the out-of-plane mode.

4. Model Development

A refined non-linear FE model with distributed plasticity is developed in OpenSees [24] to simulate the seismic performance of tested frames. A schematic summary of the numerical model is reported in Figure 6 where the blue dots represent the nodes created for the model development and the red dots indicate the storey masses, m₁ and m₂. Figure also reports the adopted constitutive models of each element and material, including the rotational springs for the beam-column joint and the compression-only truss elements for the infill walls. It should be noted that Figure 6 refers to the four-sided configuration. The BeamWithHinges command is used to build forceBeamColumn elements, which allow distributed plasticity to also be spread beyond the plastic hinge region. The solid cross-section of RC elements is uniformly discretised into fibres to closely represent small stress–strain variations. The effect of confinement of concrete mechanical behaviour is neglected due to the low axial load ratio and high transverse reinforcement spacing. The concrete nonlinear behaviour is simulated with the Concrete01 material, while the longitudinal steel reinforcement is modelled with the OpenSees uniaxial Hysteretic material. The parameters adopted for both stress–strain models are calibrated against the experimental data reported in Del Vecchio et al. [20].

The beam-column joints are modelled as rotational springs with a Pinching4 material, adopting the model proposed by De Risi et al. [25]. According to the model, the backbone of the beam-column capacity curve is represented as a curve with four linear branches defined by the critical points reported in

Table 7. Beam-column joint backbone critical points.

Backbone Point	${\mathit{\tau }}_{\mathit{j}}\left[{M}{P}{a}\right]$	$\mathit{\gamma }\left[\mathit{\%}\right]$
Cracking	${\tau }_{j,cr}=0.29\sqrt{f_c}\sqrt{1+0.29\frac{P}{A_j} }$	0.04
Pre-peak	$0.85 {\tau }_{j,max}$	0.17
Peak	${\tau }_{j,max}=$$0.5\sqrt{f_c}$	0.49
Residual	$0.43{\tau }_{j,max}$	4.41

where f_c = concrete compressive strength, P = axial load, A_j = beam-column joint panel area.

in terms of shear stress (${\tau }_j$) and rotation ($\gamma$).

Equivalent moments for the rotational spring characterisation are then computed adopting the following expression:

$$M_j={\tau }_j{A}_j\frac{1}{\frac{1-h_c/2L_b}{j{d}_b}-\frac{1}{2L_c}}$$

where $h_c$ is the column cross-section height, $L_b$ is the beam length, $j{d}_b$ is the beam internal level arm, $L_c$ is the column height. For the beam-column nodes in contact with the actuators, an indefinitely elastic law is used to account for the cross-section enlargement and steel profiles reinforcement locally adopted in the test specimens to avoid local punching failure due to the concentrated loads.

The FE model neglects the shear behaviour of RC beams and columns given the negligible damage occurred during the tests due to shear.

The nonlinear behaviour of the infill panels is reproduced by adopting the three-strut model suggested by Chrysostomou et al. [26] in both directions, with struts acting in compression only. Truss elements with Pinching4 material are used both for central and off-struts. The overall lateral performance of the infill wall is assessed following the multilinear model proposed by Panagiotakos and Fardis [27], as reported in

Table 8. Infill’s backbone critical points.

Backbone of Infills	K [MPa]	F [kN]
Cracking	K1 = GLt/H	Fcr = τcrLt
Peak	K2 = 0.03K1	Fpeak = 1.3Lt
Post-Peak	K3 = -0.01K1	Fu = 0.1Fpeak

* with L, H and t, respectively, being the length, height and thickness of the infill panel and G and ${\tau }_{cr}$, respectively, being the shear modulus and cracking stress measured experimentally.

. The unloading branch has a slope $K_1$ up to force equal to $0.1F_u$, while the shape and the width of full unloading-reloading loops is controlled by parameters $\gamma =0.8$ and $\alpha =0.15$.

The overall lateral capacity is provided by three struts as proposed by Chrysostomou et al. [26] and Verderame at al. [28]. For F2_3S_M specimen, the upper off-strut is removed from the model to take into account the 5 mm gap between the infill wall and the upper beam, as suggested by Del Vecchio et al. [20].

Nonlinear time-history analyses (NLTH) are carried out imposing as input data the displacements recorded at the two storey levels during the pseudo-dynamic tests. A mass of 5 tons is applied at the first storey level of the model, whereas a mass of 2.5 tons is applied on second storey to simulate the mass distribution of test specimens.

5. Numerical vs. Experimental Results

5.1. Performance Curves and Damage

Hysteretic capacity-curves for the two frames are plotted in Figure 7 in terms of base shear and first storey interstorey drift ratio (IDR). In the Figure, numerically derived curves (red line) are compared with the experimental results from pseudo-dynamic tests (black line). The comparison shows a very good agreement between numerical and experimental curves in terms of lateral stiffness, lateral strength, and pinching.

Markers are also reported in Figure 7, representing the achievement of selected damage mechanisms for the infill walls, namely, the infill cracking and crushing. In F2_3S_M, the diagonal cracking and crushing of the first storey infill panel are achieved in the numerical model for IDR = 0.06% and IDR = 0.26%, respectively. These results are in agreement with the experimental damage observed during the 50% and 125% AQG sequences, respectively. No damage to the RC frame is recorded in the FE model, in agreement with the experimental observations.

Similarly, in test F2_4S_M, the infill walls’ cracking and crushing are recorded, respectively, at IDR = 0.07% and IDR = 0.40%, which are compatible with the observed damage in 75% AQG and 125% AQG experimental sequences.

The comparison attests the reliability of the FE models in catching the experimental damage experienced by both structural and non-structural components, other than the lateral stiffness degradation due to the occurred damage.

5.2. Modal Properties

In terms of fundamental frequencies, numerical and experimental results are compared in

Table 9. Comparison of numerical and experimental frequencies for the in-plane vibration mode.

ID	Configuration	Experimental Frequency [Hz]	Numerical Frequency [Hz]	Δ [%]
F2_3S_M	Undamaged	25.4	24.9	−2
	Damaged	9.5	8.5	−10
	Bare	6.5	6.3	−4
F2_4S_M	Undamaged	27.8	27.4	−1
	Damaged	10.2	9.7	−5

for all the configurations where output-only modal identification tests were performed. Data are reported for the first in-plane mode, which is more sensitive to the imposed loading condition. Table 9 also reports the error between numerical and experimental records. For the undamaged infilled configuration, the numerical model provided fundamental frequencies that underestimate the experimental data by 1–2%. In the damaged configuration, the model underpredicts the experimental data by 5–10%. For the bare frame configuration (F2_3S_M), the numerical model slightly underestimates the fundamental frequency by 4%. Hence, the FE model is also able to capture the variation in fundamental frequency due to damage occurring during the shaking sequences.

5.3. Frequency Variation for Increasing Damage Level

The validated FE model is used to assess the variation of fundamental frequencies due to structural and non-structural damage in the tested specimens for increasing ground shaking intensity. Indeed, output-only modal identification tests only provide information for the damaged configuration at the end of all the pseudo-dynamic sequences. Numerical analyses are adopted to complete the missing information from experimental tests in terms of frequency variation for each earthquake intensity. In detail, the frequency at the damaged condition is extrapolated from the numerical model after each NLTH analysis. Furthermore, the NLTH analyses are performed both on the infilled and bare frame models to assess the contribution of the structural damage to the frequency variation. Indeed, results on the bare frame model provide information on the frequency variation due to structural damage during the pseudo-dynamic sequence. Conversely, results of the infilled frames model incorporate both structural and non-structural damage.

Table 10. Frequency variation as a function of earthquake intensity for bare and infilled frames.

Configuration	Earthquake Intensity [%]	PGA [g]	IDR [%]	Numerical Frequency [Hz]	Frequency Variation [%]	Numerical Damage	Experimental DL
Bare frame	0	0.000	-	6.90	-	-	-
	50	0.223	0.05	6.33	−8.3	-	DL0
	75	0.335	0.10	6.30	−8.7	-	DL0
	100	0.446	0.16	6.26	−9.3	-	DL0
	125	0.558	0.40	6.25	−9.3	-	DL0
	150	0.669	0.62	6.20	−10.1	-	DL0
Infilled frame F2_3S_M	0	0.000	-	24.9	-	-	-
	50	0.223	0.11	23.6	−5.2	Infills first cracking	DL0/DL1
	75	0.335	0.19	14.3	−42.5	-	DL1
	100	0.446	0.31	11.8	−52.6	Infill crushing	DL2
	125	0.558	0.41	8.5	−65.9	-	DL2
Infilled Frame F2_4S_M	0	0.000	-	27.4	-	-	-
	50	0.223	0.05	27.2	−0.7	Infill first cracking	DL0/DL1
	75	0.335	0.10	20.2	−26.3	-	DL1
	100	0.446	0.16	20.1	−26.6	-	DL2
	125	0.558	0.40	19.3	−29.6	Infill crushing	DL2
	150	0.669	0.62	9.7	−64.6	-	DL2/DL3

summarises the results achieved for test F2_3S_M and F2_3S_M for the first in-plane mode, which has been demonstrated to be more sensitive to the imposed loading condition. In the Table, the numerical results are associated with the experimentally observed damage level for that earthquake intensity. Figure 8 also depicts the comparison of variation in the fundamental frequency for bare and infilled frames as a function of the PGA and of the IDR.

The analysis on the bare frame attests that ground shaking up to an intensity of 150% (PGA = 0.669 g, IDR = 0.62%) induces in the frame a variation in fundamental frequency of less than 10% (i.e., 0.7 Hz) with respect to the undamaged frequency of the bare frame, attesting that no damage occurred to the structure (DL0), in agreement with the experimental observations. Indeed, a variation of 8.3% in fundamental frequency is already observed for an earthquake intensity of 50% (PGA = 0.223 g).

Conversely, in terms of non-structural damage, significant variations in fundamental frequencies are observed for both specimens for an earthquake intensity of 75% (PGA = 0.335 g), which corresponds to an experimentally observed DL1. However, in terms of frequency variation, a significant difference is observed between tests F2_3S_M and F2_4S_M for the same PGA, as shown in Figure 9. Indeed, test F2_3S_M globally shows a greater variation in natural frequency with respect to test F2_4S_M due to the higher flexibility caused by the 5 mm gap between the infill walls and the frame. Indeed, for the same PGA, specimen F2_3S_M reached higher drift ratios when compared to F2_4S_M. Based on the available data, it can be observed that a frequency variation for the first in-plane mode ranging between 0.7% and 5.2% is associated with a DL0/DL1 for non-structural components of both specimens (PGA < 0.223 g, IDR < 0.11%). At intermediate earthquake intensities, the two specimens behaved slightly differently in terms of frequency variation. Indeed, specimen F2_3S_M experienced a frequency variation of 42.5% at DL1 (PGA = 0.335%, IDR = 0.19%) and a variation of 52.6–65.9% at DL2 (PGA = 0.446–0.558 g, IDR = 0.31–0.41%). Conversely, specimen F2_4S_M, having experienced a lower drift demand with respect to F2_3S_M, showed less significant variation in fundamental frequencies. The frequency variation for the PGA ranging between 0.335 g and 0.558 g is about 26.3–29.6% (IDR = 0.1–0.4%), corresponding to the observed DL1 and DL2 in infill walls. A higher frequency variation, equal to 64.6%, is reached with the full cracking of the infill strut classified as DL2/DL3 (PGA = 0.669 g, IDR = 0.62%). Hence, the different boundary condition of the infill walls affected both the drift demand and the natural frequency variation in RC frames subjected to the same earthquake intensity.

6. Conclusions

The paper investigated the capabilities of output-only modal identification tests in the estimation of seismic damage levels. Combined laboratory pseudo-dynamic and output-only modal identification tests were performed on full-scale two-storey RC frames to perform a quantitative analysis of the influence of seismic damage on the dynamic properties of RC frames. The test frame was tested by adopting masonry infill walls with three-sided and four-sided boundary conditions. Test results were used to validate a refined FE model able to capture the influence of structural and non-structural damage on the fundamental frequencies of RC frames at different earthquake intensities.

The main outcomes of the study are summarised as follows:

• The fundamental frequency of the bare frame (i.e., structural component) is in the ratio 1 to 4 (25%) with respect to the fundamental frequency of the infilled frame in the undamaged configuration for the first in-plane mode and 4 to 5 (about 80%) in the first out-of-plane mode;
• Output-only modal identification tests that were output for the first in-plane mode attested that the experimental damage occurred in infill walls at the end of the loading sequences for a PGA = 0.558–0.669 g (IDR = 0.41–0.62%), consisting of the crushing of bricks and classified as DL2-DL2/DL3, produced a variation in the fundamental frequency of the infilled RC frames of about 60% with respect to the undamaged configuration;
• For the first out-of-plane mode, modal identification test records from the two tests show that a DL2 damage to infill walls caused a reduction of fundamental frequency of about 20%;
• The FE model has shown to predict the experimental static and dynamic performance of tested specimens before and after damage with a good degree of accuracy, slightly underestimating the experimental fundamental frequencies ranging between 2% and 10%;
• The numerical nonlinear analyses allowed the assessment of the contribution of structural and non-structural damage to the overall frequency variations. The analysis results confirmed that the different boundary conditions of infill walls affected the frequency variation in RC frames subjected to the same ground shaking. In detail, greater frequency variations are associated with the three-sided boundary condition with respect to the four-sided one. However, in both cases, a significant variation of frequency due to seismic damage is observed for a PGA = 0.335 g (IDR = 0.10–0.19%);
• For the tested specimens, the maximum frequency variation due to structural damage is 10% of the bare frame undamaged frequency for a PGA = 0.669 g.

Future studies will further address the effect of infill wall boundary conditions on the overall frequency variation, extend the analysis to 3D infilled RC frames and include the effect of openings that significantly affect the overall contribution of infill walls to the variation in modal properties of structures. This study validated a method for the damage evaluation of RC frames through output-only modal identification tests and numerical simulations that can be extended to different structural typologies for seismic damage evaluation by means of a proper validation over a good number of empirical data or of simulations with empirically validated models.