Alternative retrofitting strategies to prevent the failure of an under-designed reinforced concrete frame

Engineering Failure Analysis 89 (2018) 271–285

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Alternative retrofitting strategies to prevent the failure of an underdesigned reinforced concrete frame Marco Valente, Gabriele Milani

T

⁎

Department of Architecture, Built Environment & Construction Engineering ABC, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy

A R T IC LE I N F O

ABS TRA CT

Keywords: Seismic assessment Retrofitting FRP composites RC jacketing Steel bracing Infill wall

In Southern European countries several existing reinforced concrete (RC) buildings were designed before the introduction of modern seismic codes and thus they may be potentially vulnerable to horizontal loads. Recent seismic events have also shown that RC buildings designed without specific seismic provisions can be subjected to meaningful damages or even collapse during moderate-to-strong earthquakes. In this framework, straightforward methodologies for a preliminary and suitable seismic assessment and retrofitting of existing RC buildings are required, along with reliable and effective seismic rehabilitation techniques. In this study, a simplified displacement based procedure using non-linear static analyses is applied to obtain a preliminary estimation of the overall inadequacy of an under-designed four-storey RC frame and to propose suitable retrofitting interventions based on different rehabilitation strategies. To this aim, accurate numerical models are developed to simulate the seismic response of the RC frame in the original and retrofitted configurations. The effectiveness of three different retrofitting solutions countering the main structural deficiencies of the RC frame is evaluated through the displacement based approach. Then, non-linear dynamic analyses are carried out to assess and compare the seismic performance of the RC frame in the original and retrofitted configurations. A combined use of different approaches may represent a valuable tool to accurately address the retrofitting interventions and to assess their effectiveness in order to reduce the seismic vulnerability of poorly designed RC buildings.

1. Introduction A huge amount of existing Reinforced Concrete (RC) buildings in European seismic prone areas were designed without any specific attention to horizontal loads, consistently with prescriptions given by old Codes of Practice. These structures are very likely to experience severe damage or even collapse during moderate-to-strong earthquakes, as shown by recent seismic events [1–10]. Therefore, simplified procedures to evaluate the seismic performance of existing and retrofitted buildings are needed, along with reliable and effective seismic upgrading techniques [11–14]. The present paper discusses the results obtained with advanced numerical techniques applied for the seismic assessment and retrofitting of a benchmark RC frame, designed mainly for gravity loads without specific earthquake-resistant provisions, that was pseudo-dynamically tested at the JRC ELSA laboratory in Italy. First, detailed non-linear dynamic analyses are performed to reproduce the seismic behavior of the RC frame without retrofitting (original configuration). A comparison with existing experimental data is provided. Then, a displacement based approach (pushover) is adopted to evaluate the seismic performance of the original frame and the most relevant results are critically reviewed. In a more ⁎

Corresponding author. E-mail address: [email protected] (G. Milani).

https://doi.org/10.1016/j.engfailanal.2018.02.001 Received 8 January 2017; Received in revised form 30 December 2017; Accepted 2 February 2018 Available online 03 February 2018 1350-6307/ © 2018 Elsevier Ltd. All rights reserved.

Engineering Failure Analysis 89 (2018) 271–285

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general research framework, it is worth mentioning that the the effectiveness of a variety of different numerical approaches for the seismic assessment of other typologies of existing structures has been already presented by the authors in [15–18]. The displacement based procedure is also used for a preliminary design and evaluation of the most effective retrofitting strategies implementable. The aim is to provide a simplified procedure able to drive the process of retrofitting design by comparing the main structural deficiencies with the different rehabilitation strategies. In particular, three alternative retrofitting solutions for the RC frame are proposed and verified through a displacement based approach. The first intervention scheme is defined basing on the results obtained on the bare frame, adopting two conceptually different strategies, namely strength-only and ductility only solutions [19–22]. Such selective interventions are applied to different members of the frame in order to improve its global and local seismic behavior. A strength-only intervention using RC jacketing is also introduced in the in the strong column at the third and fourth storeys of the frame to reduce the large difference in terms of flexural capacity. Moreover, a ductility-only intervention is implemented at the first three storeys of the frame, where a large inelastic deformation demand is present. Such strengthening needs the application of fiber reinforced polymer (FRP) strips, and results into an increase of the confinement of the RC columns. The second retrofitting intervention is based on the implementation of steel bracing, which can be considered as a very effective method for global strengthening of structures [23–26]. In particular, the use of eccentric steel bracings in the rehabilitation of existing RC structures is efficient in limiting inter-storey drifts and can provide a stable energy dissipation capacity. The third intervention is carried out by casting a concrete shear wall into the full width of the frame short bay [27]. This solution leads to significant increases in overall strength and stiffness of the retrofitted frame, when compared to those of the initial frame configuration. This intervention is efficient in controlling global lateral drift and thus reducing damage in structural members. Then, the effectiveness of the three retrofitting solutions adopted for improving the seismic performance of the RC frame is estimated by performing non-linear dynamic analyses. The different seismic responses of the RC frame in the original and retrofitted configurations are critically compared and the most important results are discussed in detail. 2. Seismic upgrading with different retrofitting strategies A displacement based procedure is used to evaluate the seismic performance of the existing and retrofitted RC frames. The procedure is based on a simplified approach using non-linear static pushover analyses and allows comparing alternative retrofitting strategies adopted to overcome existing structural deficiencies. The base shear-top displacement relationships obtained from pushover analyses were transformed into capacity curves in the acceleration-displacement (AD) format. Several target displacements and capacity curves were estimated assuming that different strategies could be used to retrofit the structure. In fact, different types of structural interventions on existing structures can be classified according to their effect on the behavior of the structure and can be represented by the capacity curves presented in Fig. 1. The first group (group 1) includes all those strengthening interventions aimed at improving the overall ductility of the structure; the second group (group 2) collects interventions resulting into an increase of strength and stiffness; finally, the intermediate group 3 comprises solutions increasing both ductility and strength. The range of available retrofitting solutions is bounded by assuming the two alternative structural intervention techniques corresponding to groups 1 and 2. The bilinear red curve depicted in Fig. 1 shows the equivalent Single Degree of Freedom SDOF capacity of the bare frame. Say and Sdy are the spectral acceleration and the spectral displacement, respectively, at the yield point of the unretrofitted equivalent system. Sdm is the spectral displacement corresponding to the point at the end of the capacity spectrum before retrofitting and Sdt is the target spectral displacement after retrofitting according to the strategies of group 1. The extension of the horizontal (red) line represents the spectral displacement required to achieve the target spectral displacement. The green curve is the elastic demand spectrum and the

Fig. 1. Capacity curves, demand spectra and different retrofitting strategies in the acceleration-displacement (AD) format. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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C3.3&C4.3

500 mm stirr. 6//15

C4.1

C2

C3

C4.2

stirr. 5 //15

C4.3

C4

400 mm

250 mm

C1 stirr. 6 //15

2 16

2 16 2 12

C3.2 & C4.2

6 12

200 mm

C4.4

C2.1

C3.2

C3.3

C2.2

C2.3

C3.4

300 mm

C3.1

6 16

6 12

Ci.4

C2.4 200 mm

200 mm

C1.1

Ci.1

C1.2&C2.2 250 m m

4 16

C1.2

C1.3

stirr. 6 //15 600 mm 2 12

C1.4

C1.3&C2.3

stirr. 8 //15

400 mm

400 mm

stirr. 6 //15

8 12

4 16 200 mm

Fig. 2. Geometric characteristics and reinforcement details of the columns of the test frame.

blue curve is the inelastic spectrum corresponding to the ductility demand for the strategies of group 1. The bilinear curve (black line) shows the capacity spectrum for the retrofitted equivalent system according to the strategies of group 2. The velvet curve is the inelastic spectrum corresponding to the ductility demand for the strategies of group 2. Say,ret is the spectral acceleration at the yield point of the retrofitted equivalent system and Sdm is the target spectral displacement corresponding to the performance point after retrofitting. The line joining the two points with coordinates (Say,ret, Sdm) and coordinates (Say, Sdt) bounds the region of the target spectral displacements for group 3 retrofitting solutions. The procedure may be used: 1) to have an insight into the reasons of inadequacy of an existing structure subjected to horizontal loads and 2) to define effective strategies of reinforcement aimed at an increase of the seismic performance. 3. Reinforced Concrete RC frame analyzed as benchmark A four-storey RC frame, designed only for gravity loads, that was subjected to real-scale pseudo-dynamic tests at the JRC ELSA laboratory at Ispra (the frame was braced with lateral steel pinned bars in order to avoid out-of-plane deformation during the experimental tests) is analyzed in this Section as benchmark structure for the approaches proposed. The frame was intended to be representative of the typical design and construction practice in many Southern European countries in the 1960's. It On the other hand, it may be considered as a typical example of more recent RC structures conceived without both a displacement based design and up-to date detailing. Fig. 2 shows the elevation of the structure and the beam/column sections used with the corresponding reinforcement. The longitudinal reinforcement consisted of smooth round bars, which is typical for old builidings in Europe. The reinforcement of the two internal columns (C2 and C3) was reduced in the upper two storeys and only C2 worked along its strong axis, as a result of the adopted non-seismic design philosophy. C2 had a rectangular cross-section with dimensions of 0.60 m × 0.25 m in the first and second storeys, and 0.50 m × 0.25 m in the third and fourth storeys. The other columns (C1 and C4) had cross-sections of 0.20 m × 0.40 m and 0.20 m × 0.30 m, the same in all floors. The longitudinal reinforcement of all the columns had a lapped splice (70 cm) at the base of the first storey and another at the base of the third storey. All the beams were 0.25 m wide and 0.50 m deep and the thickness of the slab was equal to 0.15 m. Concrete is a C16/20 according to EC2 [28] and bars steel is a FeB22k according to 1980 Italian Standards. Experimental tests on both concrete and steel samples were also performed to provide more reliable input data for the numerical analyses. The actual values of concrete strength in compression and steel strength at yielding were approximately equal to 16 MPa and 344 MPa, respectively. Readers interested in a more detailed description of the benchmark frame are referred to [19]. Experimentation conducted at JRC ELSA consisted of several pseudo-dynamic tests on the base RC frame for different earthquakeintensity levels. The seismic motions used as input in the tests represented a moderate/high European seismic hazard scenario. A set of hazard-consistent acceleration time-histories (15 s duration) was artificially generated and three time-histories with different return periods (475, 975 and 2000 years) were chosen for the tests, as reported in [19]: Acc-475 (peak acceleration equal to 0.23 g), Acc-975 (peak acceleration equal to 0.3 g) and Acc-2000 (peak acceleration equal to 0.38 g). The acceleration time-history corresponding to a 475-year return period is shown in Fig. 3. The RC benchmark frame was modelled by means of two different commercial FE codes, namely SeismoStruct [29], which is based on a fiber-modelling approach, and Ruaumoko [30], which is based on a lumped plasticity approach. 273

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Acceleration [m/s 2]

M. Valente, G. Milani

2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 0

3

6

Time [s]

9

12

15

Fig. 3. Acceleration time-history and acceleration response spectrum (5% damping) of the input ground motion (Acc-475).

In Seismostruct, concrete was modelled by using a uniaxial constant-confinement model based on the constitutive relationship proposed by Mander et al. [31] and modified by Martinez-Rueda and Elnashai [32]. The confinement effects, provided by the transverse reinforcement, were taken into account as proposed by Mander, whereby a constant confining pressure was assumed in the entire stress-strain range. The steel behavior of the longitudinal reinforcement was simulated through the Menegotto–Pinto model, [33]. In Ruaumoko, beams and columns were modelled by one-dimensional elastic elements with inelastic behavior concentrated at the edges in plastic hinge regions (Giberson model). The Modified Takeda hysteresis model [34], widely used for RC sections, was adopted to represent the moment-curvature behavior in the hinge region of the member. Material properties obtained experimentally were used in the numerical simulations. The comparison of the numerical predictions with the experimental test results allowed calibrating the main parameters of the numerical models developed in this study. Pseudo-dynamic tests carried out experimentally on the bare frame were numerically simulated through non-linear dynamic analyses. The same artificial accelerograms with increasing intensities adopted in the pseudo-dynamic tests were used in the numerical analyses, which were performed sequentially, according to the various steps of the experimental campaign, in order to better reproduce the laboratory tests. The comparison with the test results was crucial to calibrate the typology of retrofitting and to check the accuracy of the numerical models, also in terms of the analytical relationships adopted for the materials. 3.1. Non-linear dynamic analysis with Acc-475 record The numerical results obtained from the non-linear dynamic analysis with Acc-475 artificial motion are reported in terms of top storey displacement time-history, maximum inter-storey drift and storey shear profiles. Comparisons are made between the model based on a fiber-modelling approach and the experimental results. In Fig. 4 the top storey displacement time-history shows that the numerical model accurately fits the tests in terms of phase and peak values (5.8 cm vs 6 cm). As for the drift profiles, the model is able to identify the maximum drift at the third level, Fig. 5. Furthermore, Fig. 6 shows that the maximum base shear is close to 210 kN and that the agreement between the experimental and numerical storey shear profiles is very satisfactory. 3.2. Non-linear dynamic analysis with Acc-975 record The numerical predictions and comparisons with the experimental results obtained from the non-linear dynamic analysis with Acc-975 record are reported in Figs. 7 to 9. The experimental test was stopped after 7.5 s, due to the incipient collapse of the third storey, in order to allow for a repair and subsequent strengthening of the frame. Therefore, the results of the numerical analysis are reported only for the first 7.5 s of the original Acc-975 record. The numerical model of the bare frame was able to quite well reproduce the experimental results in terms of both top storey displacement time-history and peak values, 10.7 cm vs 11.6 cm, see Fig. 7. The soft-storey drift at the third floor was fully captured by the numerical model, even if some differences were observed in the

Top displacement [cm]

6

Numerical Experimental

4 2 0.0 -2 -4 -6 -8

0

5

10

15

Time [s] Fig. 4. Top displacement time-history under Acc-475 record.

274

19

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storey level

Inter-storey drift [%] 4

storey 4 C1

3

C2

C3

C4 storey 4

4

storey 3

storey 3

3

2

storey 2

storey 2

2

1

storey 1

storey 1

0 -1.0

-0.8

-0.6

-0.4

-0.2

0

1

0.2

0

Numerical Experimental 0 0.6 0.8 1.0

0.4

Fig. 5. Maximum inter-storey drift profile under Acc-475 record.

storey level

Shear [kN] 4

storey 4 C1

3 2 1 0 -250

-200

-150

C2

C3

C4 storey 4

4

storey 3

storey 3

3

storey 2

storey 2

2

storey 1

storey 1

1

Numerical Experimental -100 -50 0

50

0

100

150

200

0 250

Top displacement [cm]

Fig. 6. Maximum storey shear profile under Acc-475 record.

12 9 6 3 0 -3 -6 -9 -12

Numerical Experimental

1

0

2

4 3 Time [s]

5

6

7

Fig. 7. Top displacement time-history under Acc-975 record.

storey level

Inter-storey drift [%] 4

storey 4 C1

3

C2

C3

C4 storey 4

4

storey 3

storey 3

3

2

storey 2

storey 2

2

1

storey 1

storey 1

0

-3.0 -2.5

-2.0

-1.5

-1.0

-0.5

0

0

0.5

1

1.0

1.5

Numerical Experimental 0 2.5 3.0 2.0

Fig. 8. Maximum inter-storey drift profile under Acc-975 record.

prediction of the peak drift value at the soft-storey, Fig. 8. Moreover, Fig. 9 shows a close agreement between the experimental and numerical storey shear profiles. The high vulnerability of the frame experienced experimentally was confirmed by numerical simulations. As a matter of fact, it was shown that in spite of the limited inter-storey drifts under Acc-475 record, the demands for a slightly higher seismic intensity 275

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storey level

Shear [kN] 4

storey 4 C1

3 2 1 0 -300

-200

C2

C3

C4 storey 4

4

storey 3

storey 3

3

storey 2

storey 2

2

storey 1

storey 1

1

Numerical Experimental -100 0

0

100

200

0 300

Fig. 9. Maximum storey shear profile under Acc-975 record.

level (1.3 times the Acc-475 record in terms of peak acceleration) led to much larger inter-storey drifts. Such a result was due to the excessive strength difference between the second and third storeys caused by the abrupt changes in dimension and reinforcement detailing of the strong column, leading to the formation of an undesirable soft-storey failure mechanism. 4. Seismic performance assessment of the bare frame Pushover analyses were performed with the aim of estimating the capacity of the structure through the global force-displacement curve. Base shear and roof displacement were converted respectively into spectral accelerations and displacements of an equivalent SDOF system. Such spectral values typically define the capacity spectrum. The bilinear (elastic-perfectly plastic) idealization of the pushover curve was defined on the basis of the “equal-energy” concept (the areas underneath the actual and bilinear curves are approximately the same, within the range of interest). In Fig. 10 the seismic demand for the equivalent SDOF system was determined for the Limit State of Significant Damage (LSSD). The elastic acceleration and the corresponding elastic displacement demand were computed by intersecting the radial line corresponding to the elastic period of the idealized bilinear system with the elastic demand spectrum. As commonly done in the N2 method, the inelastic demand in terms of accelerations and displacements was provided by the intersection point of the capacity curve with the demand spectrum corresponding to the ductility demand. In this study, the seismic demand was computed with reference to the general Eurocode 8 response spectrum (Type 1, soil type A), (Eurocode 8-Part 1 [35]). Theoretical predictions were estimated for a PGA equal to 0.3 g. The value of the total ultimate chord rotation capacity, ϑu, of concrete members under cyclic loading may be calculated from the following expression, according to Eurocode 8-Part 3 [36]: 0.225

θu =

max(0.01; ω′) ⎤ 1 ⋅0.016⋅(0.3ν )⋅⎡ ⋅fc ⎢ γel ⎣ max(0.01; ω) ⎥ ⎦

⎛

L 0.35 ⎜α ⋅ ρsx ⋅ ⋅⎛ V ⎞ ⋅25⎝ ⎝h⎠

f yw ⎞ fc

⎟

⎠ ⋅(1.25100 ⋅ ρd )

(1)

where:

• γ is equal to 1.5 for primary seismic elements, , where N is the axial force (positive for compression), b is the width of compression zone and h is the depth of the cross•ν= el

N b ⋅ h ⋅ fc

section,

• ω′ =

As′ f y bhfc

, ω=

respectively,

As f y bhfc

are the mechanical reinforcement ratios of the longitudinal reinforcement in compression and in tension,

Fig. 10. Demand spectra and capacity curve in AD format at the LSSD for the bare frame.

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• L is the shear span, i.e. the moment/shear ratio at the end section, ⎞ is the confinement effectiveness factor (b • α = (1 − )⋅(1 − )⋅⎛⎝1 − ⎠ V

sh 2 ⋅ b0

sh 2 ⋅ h0

∑ bi2

i

6 ⋅ b0 ⋅ h 0

is the spacing of longitudinal bars laterally

restrained by a stirrup corner or a cross-tie along the perimeter of the cross-section, b0 and h0 are the width and the depth of confined core, sh is the stirrup spacing), A ρsx = b sxs is the ratio of the transverse reinforcement parallel to the direction x of loading,

• • ρ is the steel ratio of diagonal reinforcement (if any), in each diagonal direction, • f (or f ) and f are the mean values of the steel yield strength and the concrete compression strength, respectively, both in MPa, w h

d

y

yw

c

as obtained from in-situ tests and from any additional sources of information, appropriately divided by the confidence factors, accounting for the knowledge level attained. A knowledge level equal to 3 (according to Eurocode 8-Part 3 [36]) was assumed corresponding to a confidence factor of 1 on the assumption that the original construction drawings were available, together with full information on the material properties. As a consequence, the mean values were adopted for the materials.

It is worth mentioning that total chord rotation capacity given by Eq. (1) should be multiplied by 0.825 in those members that have not been designed according to any seismic provisions and multiplied by 0.575 in those members that are reinforced with smooth (plain) longitudinal bars not lapping in the vicinity of the end regions, where steel yielding is expected. The Limit State of Significant Damage (usually condensed into LSSD) corresponds to the attainment of 0.75·θu. Fig. 10 shows that the bare frame lacked the appropriate capacity to resist seismic actions corresponding to PGA = 0.3 g at the LSSD. The displacement demands in Fig. 10 refer to the equivalent SDOF system. The displacement demands of the MDOF system were obtained by multiplying the SDOF system demand by the transformation factor Γ = ∑ miϕi/ ∑ miϕi2, where mi is the mass in the ith storey and ϕi is the component of the normalized displacement shape. A gap in terms of maximum top displacement was observed at the LSSD; the difference between the seismic demand and the displacement capacity was equal to 0.036 m (0.098 m vs 0.062 m). From an analysis of the results obtained through the simplified procedure, the attainment of LSSD occurred at C2 of the third storey, where the most significant damage was observed in the laboratory tests and the highest value of the Demand-to-Capacity Ratio was registered during non-linear dynamic analyses, see Fig. 11. The developed numerical models provided reliable predictions of the behavior of the test specimen, identifying the main structural deficiencies. Seven artificial accelerograms with PGA = 0.3 g were considered in carrying out non-linear dynamic analyses. Artificial accelerograms were generated using the software code SIMQKE [37] to match the general Type 1 response spectrum for soil class A, according to Eurocode 8. The seismic assessment of the RC frame was carried out on the basis of the ratio of the chord rotation demand (at member ends) to the corresponding capacity. The member chord rotation Demand-to-Capacity Ratio was considered as a damage index against the loss of the member lateral load capacity and was investigated to assess the structural capacity. The chord rotation demand may be taken equal to the element drift ratio, which is the deflection at the end of the shear span with respect to the tangent to the axis at the yielding end, divided by the shear span. In the columns belonging to a frame under seismic action, the lateral drifts at shear span ends are generally much larger than the nodal rotations at columns ends. The nodal rotations of the Demand/Capacity C1

2

1

0

C2

2

1

0

C3

2

1

0

C4

2

1

Fig. 11. Non-linear dynamic analyses: Demand-to-Capacity Ratio for the bare frame.

277

0

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columns can be neglected in structures designed without capacity design procedures, where the flexural stiffness of the beams is much larger than that of the columns. For the Limit State of Significant Damage (LSSD), which corresponds to the attainment of 0.75·θu according to Eurocode 8, the Demand-to-Capacity Ratio (DCR) is expressed as:

DCR =

θdemand 3 ⋅θ 4 u

(2)

For each dynamic analysis, the ratio between maximum demand and capacity was evaluated for each structural member at each time step. It is worth mentioning that the chord rotation capacity depends on both geometrical and mechanical properties of the member, but it is also a function of the demand and, in particular, of the axial load and the shear span, which is defined as the ratio of bending moment to shear demand, according to Eurocode 8-Part 3 [36]. Simplified expressions can be used for the computation of the shear span, as investigated in [38]: in this study the rigorous approach is adopted, computing the shear span as a function of the seismic demand. Fig. 11 depicts the Demand-to-Capacity Ratios for all the columns. Values found of the Demand-to-Capacity Ratio quite well reproduced the behavior observed during the experimental tests. The maximum value of the Demand-to-Capacity Ratio was registered in correspondence with C2, as confirmed by the experimental evidence. In fact, the 975-yrp test was stopped at 7.5 s because of both the impending collapse of the third storey and the severe damage detected at the strong column of the third storey. High deformation demands were observed at the base and at the top of the strong column of the third storey. C2 had significantly higher stiffness and strength than the other columns, since it was the only one with the strong axis in the loading direction. Large deformation demands were expected at the third storey and high values of the Demand-to-Capacity Ratio were registered due to the lack of ductility detailing. Finally, large values of the ratio between maximum demand and capacity were numerically found in correspondence of the strong column, second storey. 5. Retrofitting with FRP and RC jacketing A first retrofitting intervention constituted both by the application of glass fibers (FRP) and a RC jacketing was considered to allow the frame to withstand seismic actions corresponding to PGA = 0.3 g. The retrofitting intervention was intended to achieve a more ductile global performance of the frame by increasing the ductility of the columns and by preventing brittle failure modes. The aims of this retrofitting solution were: 1) to prevent the soft-storey mechanism at the third floor by mitigating the strength difference due to the section change of the strong column between the second and the third floor; 2) to improve the global deformation capacity of the frame by increasing the ductile resources of the columns, preventing brittle failure modes. According to a selective retrofitting scheme, a ductility-only intervention was applied to the first three storeys and a strength-ductility intervention was applied to the strong column at the upper two storeys, Fig. 12. A mixed intervention was carried out using both FRP composites and RC jacketing. FRP was a 3-layer wrapping applied to the columns of the first three storeys. The main characteristics of GFRP used for the retrofitting intervention were: Young modulus = 65 MPa, ultimate tensile stress = 1700 MPa, ultimate tensile deformation = 0.026, layer thickness = 0.23 mm. The RC jacketing consisted of 4 + 4 steel bars (Φ12) on two opposite sides of the strong column at the upper two storeys: the cross-section of the strong column became uniform (25 × 60 cm) along the whole height of the frame. A numerical model of the frame retrofitted with FRP wrapping and RC jacketing was implemented in the software SeismoStruct. The non-linear variable confinement model, which includes the constitutive relationship and cyclic rules proposed by Mander et al.

Fig. 12. Selective retrofitting intervention using FRP composites and RC jacketing.

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[31] in compression and those suggested by Yankelevsky and Reinhardt [39] in tension, was adopted for RC sections retrofitted by FRP. The confinement effect introduced by the FRP wrapping was modelled by means of the rules proposed by Spoelstra and Monti [40]. The model is a modified Mander's [31] one, where confined concrete maximum strength and its corresponding strain are defined as a function of confinement pressure. A constant lateral pressure, depending on steel yielding stress, is considered for steel confinement, whereas confinement pressure is linearly varying with concrete lateral dilation in the case of external FRP wrapping. An iterative procedure is adopted to obtain the axial stress corresponding to a given value of axial strain, taking into account the effect of confinement, according to Spoelstra and Monti [40]. The RC jacketed rectangular section available in Seismostruct libraries was used for the modelling of rectangular columns retrofitted by means of RC jacketing. Different confinement levels for the internal (preexisting) and the external (new) concrete materials were defined. To evaluate the properties of the retrofitted elements, the following assumptions were adopted according to Eurocode 8: 1) the jacketed column behaves monolithically with full composite action between old and new concrete; 2) the concrete properties of the jacket apply over the full section of the element; 3) the axial load is considered acting on the full composite section. The enhancement of the deformation capacity of the member, ϑu, was determined by adding a term due to FRP to the term describing the confinement provided by the transverse reinforcement. The total chord rotation capacity was computed using Eq. (1) with the exponent of the term due to confinement increased by (α ∗ ρf ff,e / fc), where: is the confinement effectiveness factor, where R = 20 mm is the radius of the rounded corner of the •α =1− section and b, h are the full cross-section dimensions; • ρ = is the FRP ratio parallel to the loading direction; • f = min (f ; ε E ) (1 − 0.7⋅min (f ; ε E ) ) is an effective stress, where f and E are the strength and the elastic modulus of (b − 2R)2 + (h − 2R)2 3bh

∗

2t f

f

b

ρf

f ,e

u, f

u, f

f

u, f

the FRP and εu,f is the ultimate strain.

u, f

f

u,f

fc

f

In Fig. 13, the capacity curve and the demand spectra for the SDOF equivalent system are depicted. As can be noted, the retrofitted frame was able to satisfy LSSD requirement (the bilinear curve intersects the inelastic demand spectrum). The seismic demand in terms of displacement, transformed to the actual MDOF system, was equal to 0.094 m, while the capacity of the frame was increased up to 0.104 m (0.062 m for the bare frame). The retrofitted frame fully complied with the LSSD requirements, in contrast with the response of the original frame that lacked the required ductility. The soft-storey failure mechanism was prevented, allowing the LSSD performance target to be met. The column confinement generated by the application of FRP provided the frame with significantly enhanced ductility and allowed it to achieve the seismic demand by increasing the plastic branch of the base shear - top displacement curve. The retrofitting intervention slightly increased the stiffness and strength of the frame and considerably enhanced its global deformation capacity. The adopted selective scheme proved to be effective for the seismic upgrading of the RC frame. Seven different spectrum-compatible artificial accelerograms with PGA = 0.3 g were used to carry out non-linear dynamic analyses in order to verify the validity of the simplified procedure and the effectiveness of the retrofitting intervention. The storey drift profile of the retrofitted model exhibited a slight increase of the drift values at the first two storeys, while a significant reduction occurred at the third storey, as shown in Fig. 14. The increase of the flexural strength of C2 and the confinement effect generated by FRP prevented the development of a soft-storey behavior at the third floor. Fig. 15 provides the values of the Demand-to-Capacity Ratio in terms of chord rotation obtained from the dynamic analyses for the columns of the bare and retrofitted models. A clear reduction of the Demand-to-Capacity Ratio can be observed for all the columns of the first three storeys, above all at the third storey. Numerical analyses showed high values of deformation demand in the strong column, but in the retrofitted case the column was detailed for ductility due to the high level of confinement provided by FRP. A considerable improvement in deformation capacity was obtained and a significant decrease of the Demand-to-Capacity Ratio was observed for the retrofitted model.

Fig. 13. Demand spectra and capacity curve in AD format at the LSSD for the frame retrofitted with FRP composites and RC jacketing.

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4

storey 4

3

storey 3

2

storey 2

1 0

0

0.5

C1

C2

C3

C4

storey 1 Bare frame Retrofitted frame 1.0 1.5 2.0 2.5 Inter-storey drift [%]

Fig. 14. Non-linear dynamic analyses: inter-storey drift profiles for the bare frame and the frame retrofitted with FRP composites and RC jacketing.

Demand/Capacity C2

C1

2

1

0

2

1

0

C3

2

1

0

C4

2

Bare frame

1

0

Retrofitted frame

Fig. 15. Non-linear dynamic analyses: Demand-to-Capacity Ratio for the bare frame and the frame retrofitted with FRP composites and RC jacketing.

6. Retrofitting with eccentric steel bracing The second retrofitting investigated consisted of an eccentric steel bracing (a so called chevron bracing with vertical shear link) inserted in the middle bay of all the frame storeys. The vertical shear link was located at the mid-span underneath the floor beams and connected to a chevron bracing. For the link specimen a European HE120A section was adopted; the diagonal elements consisted of 2U100. Vertical steel straps were connected to the adjacent columns and horizontal steel beams (HEA200) were anchored to the floor beams. The steel grade used for all the elements of the bracing system was S235. Fig. 16 shows a schematic view of the proposed eccentric bracing system inserted in the middle bay of all the storeys of the RC frame. For the numerical analyses, a so called link model was used, which bases on the approach proposed by Ricles and Popov [41] for horizontal shear link elements. Steel links are subjected to high levels of shear forces and bending moments in the active link regions and elastic and inelastic deformations of both the shear and flexural behaviors have to be taken into account. The link was modelled as a linear beam element with non-linear rotational and translational springs at the ends. The need to use a rotational spring was to represent the flexural inelastic behavior, whereas the translational springs were used to properly reproduce the inelastic shear behavior. Multilinear relationships were assumed for the shear force-deformation and bending moment-rotation curves. Isotropic hardening was used in shear yielding, while kinematic hardening was assumed for moment yielding, as suggested by experimental evidences, see for instance [41,42]. An upper bound of the shear force after complete hardening was considered. The shear link model 280

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Fig. 16. Elevation view of the RC frame retrofitted with eccentric steel bracing.

was implemented in the numerical model built within Ruaumoko. The accuracy and reliability of the shear link model utilized were verified by comparing the numerical shear force – displacement curve with experimental tests performed at the JRC ELSA laboratory, as reported in [43]. With the aim of evaluating the effectiveness of the proposed retrofitting technique, pushover analyses were performed on the retrofitted frame. Results in terms of maximum top displacement needed for seismic actions corresponding to a PGA equal to 0.3 g are depicted in the AD format in Fig. 17. The retrofitting intervention considerably increased the stiffness and strength of the frame: in fact, the retrofitted frame was able to satisfy the LSSD and the capacity exceeded the demand. The seismic demand in terms of displacement, transformed to the actual MDOF system, was equal to 0.06 m (0.098 m for the bare frame), while the capacity of the frame was increased up to 0.071 m (0.062 m for the bare frame). The procedure confirmed the effectiveness of the retrofitting intervention in both reducing the displacement demand and increasing the global deformation capacity of the bare frame. It is worth mentioning that the retrofitting intervention eliminated the irregularities of the frame and the global response of regular structures may be more accurately captured by pushover analyses. As done previously, seven artificial accelerograms were considered to perform non-linear dynamic analyses. Significant decreases of the values of both the inter-storey drift and the Demand-to-Capacity Ratio were registered in the strengthened frame, in particular at the third storey, as shown in Figs. 18 and 19. Such a result confirms the effectiveness of the retrofitting intervention in both increasing the strength and stiffness of the frame and preventing the formation of the soft-storey mechanism at the third floor. The maximum value of the Demand-to-Capacity Ratio for the bare frame was registered in the strong column (C2) at the third storey; on the contrary, for the strengthened frame the highest values of the Demand-to-Capacity Ratio were found in the columns of the first two storeys.

Fig. 17. Demand spectra and capacity curve in AD format at the LSSD for the frame retrofitted with eccentric steel bracing.

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4

storey 4

3

storey 3

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storey 2

1 0

0

C1

C2

C3

C4

storey 1 Bare frame Retrofitted frame 1.0 1.5 2.0 2.5 Inter-storey drift [%]

0.5

Fig. 18. Non-linear dynamic analyses: inter-storey drift profiles for the bare frame and the frame retrofitted with eccentric steel bracing.

Demand/Capacity C1

2

1

0

C2

2

1

0

C3

2

1

0

C4

2

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1

0

Retrofitted frame

Fig. 19. Non-linear dynamic analyses: Demand-to-Capacity Ratio for the bare frame and the frame retrofitted with eccentric steel bracing.

7. Retrofitting with infill wall The third (and last) retrofitting intervention considered represents one the most common methods used to strengthen existing RC frames and relies into the construction of a concrete shear wall in correspondence of the short bay of the frame, incorporating existing columns C3 and C4. It is worth mentioning that the existing columns were not adequate to act as boundary elements and therefore additional boundary elements were created with a 30 × 30 cm cross-section and eight Φ16 vertical longitudinal bars. As regards the connection between the existing members and the infill wall, dowels should be placed between the wall and the columns in order to assure a monolithic connection. Fig. 20 shows the elevation of the retrofitted frame and the cross-section of the wall, with a detail of the reinforcement used. The height of the critical region was set equal to the height of the first storey. Two structural systems were identified in the building: the wall and the other vertical elements. It is evident that the behavior of the retrofitted frame was significantly influenced by the presence of the wall. Non-linear static analyses were performed on the retrofitted frame and the base shear – top displacement curve was obtained. The response of the frame with the infill wall introduced into the short bay is compared with the response of the original frame in Fig. 21. It can be noted that the insertion of the infill wall substantially increases the stiffness and strength of the original frame. The base shear of the retrofitted frame using infill wall is about four times greater than that of the bare frame and 1.65 times greater than that of the frame retrofitted with steel bracing. In agreement with simulations performed in the previous Sections, the effectiveness of the present retrofitting solution was 282

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Fig. 20. Elevation view of the frame retrofitted using infill wall and cross-section detailing of the infill wall (dimensions in cm). Boundary elements: vertical bars ϕ16, transversal reinforcement ϕ12/10. Web reinforcement: vertical bars ϕ16/17, horizontal bars ϕ14/20.

Fig. 21. Demand spectra and capacity curve in AD format at the LSSD for the frame retrofitted with infill wall.

storey level

assessed through non-linear dynamic analyses, using the same records as for the previous structural configurations. The inter-storey drift profile imposed by artificial accelerograms with PGA = 0.3 g is presented and compared with the inter-storey drift profile of the bare frame in Fig. 22. A considerable reduction of the inter-storey drifts was registered for all the levels of the frame. The wall acts as

4

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1 0

0

0.5

C1

C2

C3

C4

storey 1 Bare frame Retrofitted frame 1.0 1.5 2.0 2.5 Inter-storey drift [%]

Fig. 22. Non-linear dynamic analyses: inter-storey drift profiles for the bare frame and the retrofitted frame using infill wall.

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Demand/Capacity C1

2

1

0

C2

2

1 Bare frame

0

Wall

1

0.5

0

Retrofitted frame

Fig. 23. Non-linear dynamic analyses: Demand-to-Capacity Ratio for the bare frame and the retrofitted frame using infill wall.

a stiff vertical spine preventing the formation of a soft-storey mechanism and the maximum drift was smaller than that of the retrofitting solution using steel bracing. The maximum value of the Demand-to-Capacity Ratio for the retrofitted frame was registered for the wall, see Fig. 23. Due to the large cross-section dimensions of the wall, the deformation capacity in terms of chord rotation was smaller than that of slender columns. Moreover, a drastic reduction of deformation demands was observed for all the other columns. 8. Conclusions This study has presented the results of numerical investigations performed according to a simplified displacement based procedure for the seismic assessment and retrofitting of a four-storey RC frame, designed mainly for gravity loads without specific earthquake-resistant provisions and tested at the JRC ELSA laboratory. The effectiveness of three alternative retrofitting interventions based on different rehabilitation strategies was assessed to prevent possible failures of the RC frame. Detailed numerical models of the RC frame in the bare and retrofitted configurations were developed to perform non-linear static and dynamic analyses. The numerical findings obtained from the simplified displacement based procedure were verified and complemented by the results of non-linear dynamic analyses. From an overall analysis of the results obtained in this study, the following observations can be made. − The theoretical predictions of the simplified procedure in terms of global performance showed that the bare frame was unable to satisfy the seismic demand corresponding to PGA = 0.3 g at the Limit State of Significant Damage. The simplified procedure provided useful information about both the overall inadequacy and the possible different strategies countering the main structural deficiencies of the original frame. − A selective retrofitting intervention based on FRP composites and RC jacketing was first proposed and investigated for the seismic performance enhancement of the RC frame. The FRP wrapping increased the deformation capacity of the columns and the RC jacketing was found to be effective in mitigating the abrupt change in the flexural capacity of the strong column at the third storey and then avoiding the soft-storey failure mechanism. It is worth mentioning that in the case of RC jacketing an accurate preparation of the surface of existing members is required and some uncertainties may arise about the durability and bond of FRP composites over time. − The second retrofitting intervention proposed in this study was based on the introduction of eccentric steel bracings in the middle bay of all the storeys of the frame. It reduced the displacement demand and increased the global deformation and energy dissipation capacities of the RC frame. However, it has to be noticed that high stress concentrations may occur at connections between brace members and existing structure, and the lateral strength of the existing members may be adversely affected by high axial force levels induced by the steel bracings. Consequently, the strengthening of columns, beams and beam-to-column joints of braced bays is needed for a satisfactory performance of the bracing system. − The third retrofitting solution based on the addition of a concrete shear wall was extremely efficient in controlling global lateral drift and thus reducing damage in frame members. However, the main drawback of this method is related to the strengthening of the existing foundation system to resist the increased overturning moment and the larger weight of the structure. Moreover, full interaction should be ensured between the existing structural system and the infill wall, and long execution times with high disruption are required. The drawbacks and economic losses related to the addition of walls may render the local retrofitting solution carried out by using RC jacketing and FRP wrapping more appealing. − It is important to highlight that the proposed retrofitting interventions can be effectively used also in the case of real structures with irregularities in plan. A proper use of RC jacketing on selected columns can relocate the center of stiffness, mitigating unfavorable torsional effects. Moreover, the insertion of steel bracings or shear walls, arranged symmetrically and along the perimeter of the buildings, can increase the torsional stiffness of torsionally unbalanced structures, reducing the displacement demand on the perimeter structural elements. − The results of the numerical analyses showed that the simplified procedure based on non-linear static analyses can be considered a valuable tool for a preliminary evaluation of the retrofitting interventions applicable to existing RC buildings. The simplified procedure allows for the identification of the main structural deficiencies that should be properly countered through suitable 284

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retrofitting solutions, leading to an easy evaluation of their effectiveness. The consistency of the simplified procedure was confirmed by the results of non-linear dynamic analyses. A careful combined use of different approaches may provide a valuable insight to accurately address the retrofitting interventions and then to improve the seismic performance of under-designed RC buildings. References [1] CEB-FIB (Comité Européen du Béton - Fédération Internationale du Béton), Seismic assessment and retrofit of reinforced concrete buildings, CEB-FIB Bulletin No. 24. International Federation for Structural Concrete, Task Group 7.1, 2003. [2] J.G. Ruiz-Pinilla, J.M. Adam, R. Pérez-Cárcel, J. Yuste, J.J. Moragues, Learning from RC building structures damaged by the earthquake in Lorca, Spain, in 2011, Eng. Fail. Anal. 68 (2016) 76–86. [3] M.G. Mulas, F. Perotti, D. Coronelli, L. Martinelli, R. Paolucci, The partial collapse of “Casa dello Studente” during L'Aquila 2009 earthquake, Eng. Fail. 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