# Advanced Composite Retrofit of RC Columns and Frames with Prior Damages—Pseudodynamic Finite Element Analyses and Design Approaches

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Explicit Dynamics Finite Element Modelling

#### 2.1. Concrete

_{eq}is the uniaxial compressive strength, Y

_{TXC(P)}is the fracture surface and F

_{CAP(P)}is a dimensionless cap function that activates the elastic strength surface within the RHT material model at high pressures. R

_{3(θ)}is the third invariant dependence term, and (F)

_{RATE(ε)}is the strain rate effect represented through fracture strength with plastic strain rate.

#### 2.2. Longitudinal Steel Bars and Steel Stirrups

_{1}, σ

_{2}and σ

_{3}are the first, second and third principal stresses, and Y is the yield stress of steel reinforcement under tension.

_{p}(Equation (3)):

_{0}is the yield strength and A is the tangent modulus.

#### 2.3. Brick Infill

#### 2.4. Carbon Fiber Reinforced Polymers (CFRP)

_{f}= 0.13 mm, the elastic modulus was E

_{f}= 230 Gpa, and the failure strain was ε

_{uf}= 0.015. FRP jacket was modelled as an orthotropic elastic material. The elastic modulus along the direction of carbon fibers used for the analyses was equal to 59.16 GPa, when also including the effects of the impregnation epoxy resin. Therefore, the thickness of the jacket was suitably increased so that the elastic modulus multiplied by the thickness of the jacket, in both cases, gives the same axial rigidity value. This approach enables more accurate reproduction of global behavior and local failure effects in the FRP jacket [38].

#### 2.5. Polyurethane Flexible Joints (PUFJ)

#### 2.6. Element Types

## 3. FE Models of Published RC Columns and Frames Tests

#### 3.1. RC Columns with Lap Splices

_{c}) varied among different columns from 26.9 MPa to 32.9 MPa, while their steel yield stress (f

_{yL}) was 514 MPa. The normalized axial load (v) of the column was 0.26–0.30. The columns differed in lap-splice length, which was 15 times the diameter of the longitudinal bar (15 d

_{bL}), 30 d

_{bL}or 45 d

_{bL}. The thickness of one layer of CFRP jacket was t

_{f}= 0.13 mm, the elastic modulus was E

_{f}= 230 GPa, and the failure strain was ε

_{uf}= 0.015. The corners of the section were rounded with a radius of r = 30 mm. The FRP confinement was applied at a height of h

_{f}= 600 mm at the base of the column. Herein, the columns R-P2L0, R-P2L1 and R-P2L3 with no lap splices, 15 d

_{bL}lap length and 30 d

_{bL}lap length and externally confined with 2 layers of CFRP are presented.

_{bL}lap length and 30 d

_{bL}lap length, respectively. The experimental values for push (+) and push (−) direction and the analytical values are indicated as “experimental push (+)”, “experimental push (−)” and “analytical”, respectively. Figure 2d presents the analytical curves comparatively. The dashed lines mark the 20% drop in the maximum values of the analytical and experimental base shear (for both directions, push + and −), considered as the lowest acceptable threshold of base shear at failure according to several seismic codes. In particular (see Table 1), for column R-P2L0 without lap splices, these experimental limit values for push (+) and (−) are 0.8 × 240 = 192 kN (black dashed line) and 0.8 × 194 = 155.2 kN (grey dashed line), respectively. The analytical prediction is 0.8 × 217.7 = 174.2 kN (red dashed line), being around the average of experimental values per cycle.

_{bL}and 30 d

_{bL}, externally confined with CFRP jackets. It presents and compares the maximum and ultimate lateral force (P

_{max}, P

_{u}= 0.80 P

_{max}) and the corresponding displacements (δ

_{Pmax}, δ

_{Pu}). The parameter used to compare the analytical with the experimental values in this study is absolute divergence (AD), also known as absolute error (AE), and it is defined in Equation (4).

_{exp}.) to be subtracted from the analytical ones (α

_{anal}.) and then take the absolute values and divide it by the experimental ones (α

_{exp}.).

_{max}, P

_{u}) suggest that the analytical predictions are very close to the experiments both qualitatively and based on the AD (%) values (Figure 2 and Table 1). This allows for extensive analytical elaborations of the global performance of the bars at the lap-splice region, their local slip and stress development, and other characteristics.

_{bL}lap splices (R-P2L1) shows a significantly reduced base shear (a mean reduction of about 20%) and reduced deformation capacity compared with the column without lap splices (R-P2L0). The column with 30 d

_{bL}(R-P2L3) achieves ultimate displacement similar to that of R-P2L0 but at marginally lower base shear (around 4%).

_{bL}(R-P2L1), while Figure 3b,c presents the slippage of the bars of columns R-P2L1 and R-P2L3 at ultimate displacement.

#### 3.2. RC Columns with Corroded Steel Reinforcement

_{bL}) and Φ8/100 mm closed stirrups (peripheral). They had concrete strength and steel yield stress of f

_{c}= 25.5 MPa and f

_{yL}= 460 MPa, respectively. The normalized axial load on the column was v = 0.18. Four different degrees of corrosion, 9%, 16%, 22% and 54% corresponding to the columns NS-X9, NS-X16, NS-X22 and NS-X54, were investigated experimentally (NS-X0 being the non-corroded column).

_{c}= 18.1–20.4 MPa, f

_{yL}= 560 MPa and v = 0.34–0.38. They were reinforced with 4Φ18 longitudinal continuous rebars and Φ8/200 mm closed stirrups (peripheral). For one layer of CFRP, t

_{f}= 0.13 mm, E

_{f}= 230 GPa and ε

_{uf}= 0.015, while r = 30 mm and h

_{f}= 600 mm. The cross-sectional area loss of corroded bars was estimated at about 10%. For a low corrosion degree, FRP confinement could reverse the negative effects of corrosion. For the 10% corroded specimen CS-C2 externally confined with FRPs, the base shear force increased by 6% compared to the unretrofitted specimen CS-0.

_{max}, P

_{u}) and the corresponding displacements (δ

_{Pmax}, δ

_{Pu}) are presented in Table 2. Column NS-X16 has the lowest AD of maximum base shear in s(+) and (−) directions, which are 2.64% and 0.88%, respectively. The lowest AD of ultimate displacement is 2.08% for column CS-0. All comparisons of analytical loads and displacements at characteristic states against the experimental ones suggest that the analytical predictions are satisfactory in most of the cases.

#### 3.3. RC Frames

## 4. Parametric FE Analytical Investigation of Damaged RC Frames

#### 4.1. RC Frames with Lap-Spliced Longitudinal Bars

_{bL}. However, this lap length is further reduced to 11 d

_{bL}, as the concrete strength of the frames is higher (C30 quality) and corresponds to higher bond strength of the bars inside concrete than in the columns used by [1] (C20 quality). Figure 11a presents the analytical base shear force–displacement curve of frame A1F with 11 d

_{bL}, 22.5 d

_{bL}or 30 d

_{bL}lap length, while Figure 11b presents the corresponding curves for frame B2.

_{bL}or 30 d

_{bL}lap lengths provides P-δ response better than for the frame without lap splices in terms of maximum base shear (similar to the upper-bound experimental one). The ultimate base shear is similar to the frame without lap splices. Analysis of A1F with 11 d

_{bL}lap length reveals a maximum base shear of 139.67 kN, which is only 5.63% lower than the analytical value at maximum for the frame without lap splices (148 kN). The corresponding ultimate base shear is 131 kN (only 11.4% lower than 148 kN, correspondingly). The ultimate base shear in A1F with lap splices is higher than all limit values at the 20% drop (experimental or analytical), being sufficient globally, despite insufficient bottom lap splices. It seems that the base shear degradation at ultimate because of insufficient lap splices is higher in half-column specimens of rectangular cross-section with only four longitudinal bars and deficient stirrup detailing (e.g., too sparse). Indeed, the shear force is only 141.49 kN in R-P2L1, while the corresponding maximum base shear in half-column without lap splices is 217.13 kN (in R-P2L0), denoting a drop of 34.8% (three times higher in half-column specimens than in the RC frame). Besides the difference in steel detailing, the main reason for this divergence in performance may be the engagement of the sections on the top of the columns of the frame to a higher extent to compensate for the insufficiency of the bottom sections and potential redistribution effects. In half-column specimens, only the lap-spliced critical region is available and fully engaged up to column collapse (no redistribution potential).

_{bL}or 30 d

_{bL}lap lengths provides P-δ response similar to the frame without lap splices in terms of maximum base shear and ultimate base shear. Analysis of B2 with 11 d

_{bL}lap length reveals a maximum base shear of 165.04 kN, which is 14.4% lower than the analytical value at maximum for frame B2 without lap splices. The ultimate base shear in B2 with lap splices is 147.76 kN (22.3% lower, correspondingly). This value is around the analytical limit value at the 20% drop for frame B2 without lap splices (152.2 kN), being only marginally insufficient globally, despite heavily insufficient lap splices. The 3D FE analyses suggest there is a higher effect on the lap-spliced bars’ performance, as the infill interacts both horizontally and vertically with the RC frame through the seismic joint. Further, if the B2 frame is considered in the retrofitting scenario for the A1F bare frame with lap splices, then the analytical behavior of lap-spliced A1F retrofitted with orthoblock infills and PUFJ (lap-spliced B2) is far better than the analytical behavior of A1F without lap splices. Indeed, the maximum base shear of B2 with lap splices is 165.04 kN (higher than 148 kN in A1F without lap splices). Moreover, the ultimate base shear is 147.76 kN, compared with 139.14 kN in A1F without lap splices. In this case, orthoblock-PUFJ emergency retrofit [26,27,28] could enable the lap-spliced frame to sustain P-δ demands higher than the A1F frame without lap splices.

_{bL}while Figure 12b,c reveal the slippage of the bars of frames A1F and B2 at ultimate. In both cases, the analyses suggest that the lap-spliced bars reach the yielding force under tension (96.5 kN) despite the slip.

_{bL}lap splices present similar damage accumulation at the final step (at ultimate) of the analytical procedure. Damage occurs mostly at the bottom and the top of the columns (critical regions) and inside the joints. Specimen B2 with 11 d

_{bL}lap splices presents damage of higher severity than in A1F, observed at the upper left beam-column joint region and at the bottom of the right column. However, the maximum shear force does not drop below 80% of the maximum experimental and analytical values.

#### 4.2. Corrosion of Steel Reinforcement

#### 4.3. Performance of the Seismic Joint

_{bL}). At 81.4 mm top horizontal displacement, the stresses are 23% lower in B2 frames with or without corrosion and 13% lower in B2 frames with inadequate lap splices. Figure 17 presents the variation of stresses within the seismic joint (red color for the highest stresses) at different top horizontal displacements of the frame B2 with inadequate lap splices. For 0.5 mm frame top displacement, the upper left boundary with the top beam and the middle height boundary with the right column are highly activated (however, at only 1% of the maximum stress). For 23 mm frame top displacement, the joint starts to accumulate damage at the top of the left column (at around 67% of maximum stress). For 42 mm displacement, the damage is extended over a greater region at the top of the left column, while high stresses are developed at the nearby boundary with the top beam (at around 67% of the maximum). For 53.7 mm displacement (at maximum stress value), the damage is extended over the left corner with the top beam. For 81.4 mm displacement, the variation in the stresses over the boundary interface seems unchanged but for 13% lower peak stresses. These values seem to be in agreement with the base shear load drops in the frame. The performance of the remaining B2 frames with or without corrosion is similar.

## 5. Proposed Modifications of Existing Design Relations

_{s}) is the shear ratio, (α) is the confinement effectiveness factor, (ρ

_{s}) is the geometric ratio of transverse reinforcement parallel to the direction of loading, (f

_{yw}) is the yield strength of transverse reinforcement and (ρ

_{d}) is the geometric ratio of any crosswise diagonal reinforcement. It is applied for columns with deformed longitudinal bars and designed and constructed based on modern seismic codes (after 1985). For columns designed and constructed before 1985 using deformed longitudinal bars, (Equation (5)) needs to be multiplied by 1/1.2.

_{R}> V

_{Mu}), according to EC8.3 and KANEPE. Therefore, the value of the shear force during flexural yielding could be calculated as the ratio of yield moment to shear span (V

_{Mu}= M

_{y}/L

_{s}). The following Equation (6) (KANEPE) is used to calculate the yield moment (M

_{y}), in which (b) is the height of compression zone, (d) is the effective depth of member section, (E

_{c}) is the modulus of elasticity of concrete, (ξ

_{y}) is the height of compression zone at yield, (d’) is the distance from the center of the compression reinforcement up to the extreme compression fiber, (δ’) is equal to d’/d, (ρ) is the ratio of the tension reinforcement, (ρ’) is the ratio of the compression reinforcement, (ρ

_{v}) is the ratio of the intermediate reinforcement and (E

_{s}) is the modulus of elasticity of steel.

#### 5.1. Lap-Spliced Longitudinal Bars

_{b}< l

_{b,min}):

_{b}is the lap length, l

_{b,min}is the minimum necessary lap-splice length for the development of ultimate bending moment equal to 0.3·d

_{bL}·f

_{y}/√fc and α is the term ${25}^{\left(\mathsf{\alpha}\xb7{\mathsf{\rho}}_{\mathrm{w}}\xb7\frac{{\mathrm{f}}_{\mathrm{yw}}}{{\mathrm{f}}_{\mathrm{c}}}{+\mathsf{\alpha}}_{\mathrm{j}}\xb7{\mathsf{\rho}}_{\mathrm{j}}\xb7\frac{{\mathrm{f}}_{\mathrm{fe}}}{{\mathrm{f}}_{\mathrm{c}}}\right)}$ of Equation (5) to take into account confinement effects.

_{s}is multiplied by 1.25 (f

_{s}= f

_{y}·c·1.25) in order to take into account the stress at hardening of the internal steel bars (see also [45]).

_{u}and V

_{R}for the examined column specimens with lap splices as well as the divergence of their values are gathered in Table 3. The design approach provides fairly accurate predictions and can be used in RC frames as well.

_{bL}is the lower-limit acceptable one.

- the thickness t of the diagonal strut;
- the width b of the diagonal strut ($\mathrm{b}\approx 0.15\mathrm{L}$); and
- the mean compressive strength of the infill wall along the direction of the diagonal $\overline{{\mathrm{f}}_{\mathrm{wc},\mathrm{s}}}$.$$\mathrm{N}=\left(\mathrm{t}\ast \mathrm{b}\right)\ast \overline{{\mathrm{f}}_{\mathrm{wc},\mathrm{s}}}$$$$\mathrm{V}=\mathrm{N}\ast \mathrm{cos}\mathrm{a}$$

_{Pu}for the frame B2 with 11 d

_{bL}lap length equal to 71.3 mm, which is close to the one provided by ANSYS analyses 80 mm (AD of 10.1%). The corresponding base shear strength is 193.9 kN, which is close to the analytical value of 165 kN by FE analysis (AD of 17.5%).

#### 5.2. Corrosion of Steel Reinforcement

_{u}) and base shear strength (V

_{R}) according to the equations of EC8.3, taking into account the reduced cross-section of the corroded bars. The corresponding AD (%) against the experimental results is also tabulated. The design approach provides fairly accurate predictions, especially for corrosion degrees of 16% and 22%, which are characteristic limit cases. This approach can be used in RC frames as well.

## 6. Discussion

_{bL}length is only 57% of the tensile force at yielding of the bars in columns without laps. Therefore, the bars do not yield, and relative slip is recorded during analysis despite CFRP jacketing. The column shows a significantly reduced ultimate base shear (reduction of 34.8%) when compared with the maximum base shear of the column without lap splices (R-P2L0) as well as reduced deformation capacity. For 30 d

_{bL}lap length, the P-δ response of the FRP jacketed columns is very close to the one without laps, and bars’ yielding is recorded.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Bousias, S.N.; Fardis, M.N.; Spathis, A.L.; Biskinis, D. Concrete or FRP jacketing of concrete columns for seismic retrofitting. In NATO Science Series: IV: Earth and Environmental Sciences; Wasti, S.T., Ozcebe, G., Eds.; Springer: Dordrecht, The Netherlands, 2006; Volume 66, pp. 33–46. [Google Scholar]
- Kalogeropoulos, G.I.; Tsonos, A.-D.G. Cyclic performance of RC Columns with inadequate lap splices strengthened with CFRP jackets. Fibers
**2020**, 8, 39. [Google Scholar] [CrossRef] - Goksu, C.; Ilki, A. Seismic Behavior of Reinforced Concrete Columns with Corroded Deformed Reinforcing Bars. ACI Struct. J.
**2016**, 113, 1053–1064. [Google Scholar] [CrossRef] - Rousakis, T.C.; Panagiotakis, G.D.; Archontaki, E.E.; Kostopoulos, A.K. Prismatic RC columns externally confined with FRP sheets and pre-tensioned basalt fiber ropes under cyclic axial load. Compos. Part B Eng.
**2019**, 163, 96–106. [Google Scholar] [CrossRef] - Karantzikis, M.; Papanicolaou, C.G.; Antonopoulos, C.P.; Triantafillou, T.C. Experimental investigation of nonconventional confinement for concrete using FRP. J. Compos. Constr.
**2005**, 9, 480–487. [Google Scholar] [CrossRef] - Triantafillou, T.C.; Papanicolaou, C.G.; Zissimopoulos, P.; Laourdekis, T. Concrete confinement with textile-reinforced mortar jackets. ACI Struct. J.
**2006**, 103, 28–37. [Google Scholar] [CrossRef] - Ilki, A.; Peker, O.; Karamuk, E.; Demir, C.; Kumbasar, N. FRP retrofit of low and medium strength circular and rectangular reinforced concrete columns. J. Mater. Civ. Eng.
**2008**, 20, 169–188. [Google Scholar] [CrossRef] - Yu, T.T.; Teng, J.G.; Wong, Y.L.; Dong, S.L. Finite element modeling of confined concrete-I: Drucker–Prager type plasticity model. Eng. Struct.
**2010**, 32, 665–679. [Google Scholar] [CrossRef] - Ilki, A.; Kumbasar, N. Compressive behaviour of carbon fibre composite jacketed concrete with circular and non-circular cross-sections. J. Earthq. Eng.
**2003**, 7, 381–406. [Google Scholar] [CrossRef] - Nistico, N.R.C. Square Sections Confined by FRP: A numerical procedure for predicting stress strain relationship. Compos. Part B
**2014**, 59, 238–247. [Google Scholar] [CrossRef] - Wang, Z.Y.; Wang, D.Y.; Smith, S.T.; Lu, D.G. CFRP-confined square RC columns. I: Experimental investigation. J. Compos. Constr.
**2012**, 16, 150–160. [Google Scholar] [CrossRef] - Wu, Y.F.; Wei, Y.Y. Effect of cross-sectional aspect ratio on the strength of CFRP-confined rectangular concrete columns. Eng. Struct.
**2010**, 32, 32–45. [Google Scholar] [CrossRef] - Triantafyllou, G.G.; Rousakis, T.C.; Karabinis, A.I. Corroded RC beams patch repaired and strengthened in flexure with fiber-reinforced polymer laminates. Compos. Part B Eng.
**2017**, 112, 125–136. [Google Scholar] [CrossRef] - Triantafyllou, G.G.; Rousakis, T.C.; Karabinis, A.I. Analytical assessment of the bearing capacity of RC beams with corroded steel bars beyond concrete cover cracking. Compos. Part B Eng.
**2017**, 119, 132–140. [Google Scholar] [CrossRef] - Triantafyllou, G.; Rousakis, T.; Karabinis, A. Corroded RC beams at service load before and after patch repair and strengthening with NSM CFRP strips. Buildings
**2019**, 9, 67. [Google Scholar] [CrossRef] [Green Version] - Jiang, C.; Wu, Y.F.; Wu, G. Plastic hinge length of FRP-confined square RC columns. J. Compos. Constr.
**2014**, 18, 04014003. [Google Scholar] [CrossRef] - Rousakis, T.C. Inherent seismic resilience of RC columns externally confined with nonbonded composite ropes. Compos. Part B Eng.
**2018**, 135, 142–148. [Google Scholar] [CrossRef] - Belardi, V.G.; Fanelli, P.; Vivio, F. Structural analysis and optimization of anisogrid composite lattice cylindrical shells. Compos. Part B Eng.
**2018**, 139, 203–215. [Google Scholar] [CrossRef] - Ye, G.; Bi, H.; Hu, Y. Compression behaviors of 3D printed pyramidal lattice truss composite structures. Compos. Struct.
**2020**, 233, 111706. [Google Scholar] [CrossRef] - Chalioris, C.E.; Kytinou, V.K.; Voutetaki, M.E.; Karayannis, C.G. Flexural Damage Diagnosis in Reinforced Concrete Beams Using a Wireless Admittance Monitoring System—Tests and Finite Element Analysis. Sensors
**2021**, 21, 679. [Google Scholar] [CrossRef] [PubMed] - Karayannis, C.G.; Golias, E. Full scale tests of RC joints with minor to moderate seismic damage repaired using C-FRP sheets. Earthq. Struct.
**2018**, 15, 617–627. [Google Scholar] [CrossRef] - Katakalos, K.; Manos, G.; Papakonstantinou, C. Seismic retrofit of R/C T-beams with steel fiber polymers under cyclic loading conditions. Buildings
**2019**, 9, 101. [Google Scholar] [CrossRef] [Green Version] - Triantafyllou, G.G.; Rousakis, T.C.; Karabinis, A.I. Effect of patch repair and strengthening with EBR and NSM CFRP laminates for RC beams with low, medium and heavy corrosion. Compos. Part B Eng.
**2018**, 133, 101–111. [Google Scholar] [CrossRef] - Anagnostou, E.; Rousakis, T.C.; Karabinis, A.I. Seismic retrofitting of damaged RC columns with lap-spliced bars using FRP sheets. Compos. Part B Eng.
**2019**, 166, 598–612. [Google Scholar] [CrossRef] - Kwiecień, A. Highly deformable polymers for repair and strengthening of cracked masonry structures. GSTF Int. J. Eng. Technol. (JET)
**2013**, 2, 182–196. [Google Scholar] [CrossRef] - Akyildiz, A.; Kwiecień, A.; Zając, B.; Triller, P.; Bohinc, U.; Rousakis, T.; Viskovic, A. Preliminary in-plane shear test of infills protected by PUFJ interfaces. In Proceedings of the 17th International Brick and Block Masonry Conference from Historical to Sustainable Masonry (IB2MaC 2020), Krakow, Poland, 5–7 July 2020. [Google Scholar]
- Triller, P.; Kwiecien, A.; Bohinc, U.; Zajac, B.; Rousakis, T.; Viskovic, A. Preliminary in-plane shear test of damaged infill strengthened by FRPU. In Proceedings of the 10th International Conference on FRP Composites in Civil Engineering (CICE 2020/2021), Istanbul, Turkey, 8–10 December 2021. [Google Scholar]
- Rousakis, T.; Ilki, A.; Kwiecień, A.; Viskovic, A.; Triller, P.; Ghiassi, B.; Benedetti, A.; Gams, M.; Rakicevic, Z.; Halici, O.F.; et al. Quick Reparation of RC Infilled Frames after Seismic Damages—Experimental Tests on Shaking Table. In Proceedings of the 10th International Conference on FRP Composites in Civil Engineering (CICE 2020/2021), Istanbul, Turkey, 8–10 December 2021. [Google Scholar]
- Rousakis, T. Brick walls Interventions with FRPU or PUFJ and of RC columns with FR in Brick-Infilled RC Structures with the use of Pushover Beam-Column Element Analysis and Pseudo-Dynamic 3D Finite Element Analysis. In Proceedings of the 17th International Brick and Block Masonry Conference from Historical to Sustainable Masonry (IB2MaC 2020), Krakow, Poland, 5–7 July 2020. [Google Scholar]
- Rousakis, T.; Ilki, A.; Kwiecień, A.; Viskovic, A.; Gams, M.; Triller, P.; Ghiassi, B.; Benedetti, A.; Rakicevic, Z.; Colla, C.; et al. Deformable Polyurethane Joints and Fibre Grids for Resilient Seismic Performance of Reinforced Concrete Frames with Orthoblock Brick Infills. Polymers
**2020**, 12, 2869. [Google Scholar] [CrossRef] [PubMed] - Rousakis, T.; Vanian, V.; Fanaradelli, T.; Anagnostou, E. 3D FEA of Infilled RC Framed Structures Protected by Seismic Joints and FRP Jackets. Appl. Sci.
**2021**, 11, 6403. [Google Scholar] [CrossRef] - Zając, B.; Kwiecień, A. Thermal stress generated in masonries by stiff and flexible bonding materials. In Proceedings of the 9th International Masonry Conference (9th IMC), Guimarães, Portugal, 7–9 July 2014; Lourenço, P.B., Haseltine, B.A., Vasconcelos, G., Eds.; ISBN 978-972-8692-85-8. [Google Scholar]
- Koutas, L.; Triantafillou, T.C.; Bousias, S.N. Analytical modeling of masonry-infilled RC frames retrofitted with textile-reinforced mortar. J. Compos. Constr.
**2014**, 19, 04014082. [Google Scholar] [CrossRef] - Rouka, D.; Kaloudaki, A.; Rousakis, T.; Fanaradelli, T.; Anagnostou, E.; Kwiecien, A.; Gams, M.; Viskovic, A.; Zajac, B. Response of RC buildings with Low-strength Infill Walls Retrofitted with FRP sheets with Highly Deformable Polymer—Effects of Infill Wall Strength. In Proceedings of the 25th International Conference on Composites/Nano Engineering (ICCE-25), Rome, Italy, 13–15 June 2012. [Google Scholar]
- Hany, N.F.; Hantouche, E.G.; Harajli, M.H. Finite element modeling of FRP-confined concrete using modified concrete damaged plasticity. Eng. Struct.
**2016**, 125, 1–14. [Google Scholar] [CrossRef] - Youssf, O.; ElGawady, M.A.; Mills, J.E. Displacement and plastic hinge length of FRP confined circular reinforced concrete columns. Eng. Struct.
**2015**, 101, 465–476. [Google Scholar] [CrossRef] - Yuan, F.; Wu, Y.F.; Li, C.Q. Modelling plastic hinge of FRP-confined RC columns. Eng. Struct.
**2017**, 131, 651–668. [Google Scholar] [CrossRef] - Fanaradelli, T.D.; Rousakis, T.C. 3D Finite Element Pseudodynamic Analysis of Deficient RC Rectangular Columns Confined with Fiber Reinforced Polymers under Axial Compression. Polymers
**2020**, 12, 2546. [Google Scholar] [CrossRef] [PubMed] - Anagnostou, E.; Rousakis, T.; Georgiadis, N. Finite element analysis of deficient RC columns with square and rectangular section under pseudoseismic load and comparison with retrofit code predictions. In Proceedings of the ICCE-26 Conference, Paris, France, 15–21 July 2018. [Google Scholar]
- Riedel, W. Beton unter Dynamischen Lasten: Meso- und makromechanische Modelle und ihre Parameter; Fraunhofer-Institut für Kurzzeitdynamik, Ernst-Mach-Institut EMI, Freiburg/Brsg., Eds.; Fraunhofer IRB Verlag: Stuttgart, Germany, 2004; ISBN 3-8167-6340-5. [Google Scholar]
- Riedel, W.; Thoma, K.; Hiermaier, S.; Schmolinske, E. Penetration of Reinforced Concrete by BETA-B-500, Numerical Analysis using a New Macroscopic Concrete Model for Hydrocodes. In Proceedings of the (CD-ROM) 9th Internationales Symposium, Interaction of the Effects of Munitions with Structures, Berlin Germany, 3–7 May 1999; pp. 315–322. [Google Scholar]
- Riedel, W.; Kawai, N.; Kondo, K. Numerical Assessment for Impact Strength Measurements in Concrete Materials. Int. J. Impact Eng.
**2009**, 36, 283–293. [Google Scholar] [CrossRef] [Green Version] - ANSYS. Academic Research, Release 15.0; SAS IP, Inc.: Canonsburg, PA, USA, 2003. [Google Scholar]
- Bousias, S.N.; Triantafillou, T.C.; Fardis, M.N.; Spathis, L.; O’Regan, B.A. Fiber-reinforced polymer retrofitting of rectangular reinforced concrete columns with or without corrosion. Struct. J.
**2004**, 101, 512–520. [Google Scholar] [CrossRef] - Meda, A.; Mostosi, S.; Rinaldi, Z.; Riva, P. Experimental evaluation of the corrosion influence on the cyclic behaviour of RC columns. Eng. Struct.
**2014**, 76, 112–123. [Google Scholar] [CrossRef] - Code, P. Eurocode 8: Design of Structures for Earthquake Resistance—Part 3: Assessment and Retrofitting of Buildings; Incorporating corrigendum March 2010; European Committee for Standardization: Brussels, Belgium, 2005. [Google Scholar]
- Greek Retrofit Code (KANEPE), 2nd Revision. 2017. Available online: https://oasp.gr/node/92 (accessed on 25 May 2021).

**Figure 2.**Comparative experimental (the envelope P-δ curves of the original experimental response) and analytical base shear force–displacement curve for specimens (

**a**) R-P2L0, (

**b**) R-P2L1, (

**c**) R-P2L3; (

**d**) Comparison of the analytical P-δ curves.

**Figure 3.**(

**a**) Specimen R-P2L1 with 15 d

_{bL}lap length, undeformed; (

**b**) Slippage of longitudinal steel bars of specimen R-P2L1 at ultimate displacement 58.46 mm; (

**c**) Specimen R-P2L3 at ultimate displacement of 66.85 mm (magnification factor 5).

**Figure 5.**Comparative experimental (the envelope P-δ curve of the original experimental response) and analytical base shear force–displacement curve for specimens (

**a**) NS-X0, (

**b**) NS-X16; (

**c**) The comparison of their analytical P-δ curves.

**Figure 7.**Comparative experimental (the envelope P-δ curve of the original experimental response) and analytical base shear force–displacement curve for specimens (

**a**) CS-0; (

**b**) CS-C2; (

**c**) The comparison of their analytical P-δ curves.

**Figure 9.**(

**a**) Dimensions of the RC frame; (

**b**) Specimen B2 with polymer joint applied on the 3 interfaces of the existing infill with the 2 concrete columns and the top beam.

**Figure 10.**Analytical base shear force–displacement curve for (

**a**) A1F and (

**b**) B2, compared against the experimental ones.

**Figure 11.**Analytical base shear force–displacement curve for (

**a**) A1F (without infill) and (

**b**) B2 (with infill), with different lap lengths, compared against the experimental ones.

**Figure 12.**(

**a**) Specimen A1F with 11 d

_{bL}lap length undeformed; (

**b**) Slippage of longitudinal steel bars of specimen A1F at ultimate displacement 101.5 mm; (

**c**) Specimen B2 at ultimate displacement 81.4 mm (magnification factor 5).

**Figure 14.**Analytical base shear force–displacement curve for (

**a**) A1F and (

**b**) B2 with different corrosion levels, compared against the experimental ones.

**Figure 15.**Concrete damage of (

**a**) specimen A1F with 29% corrosion at total displacement 101.50 mm and specimen B2 with (

**b**) 29% corrosion at total displacement 81.40 mm.

**Figure 16.**Concrete damage of (

**a**) specimen A1F with no corrosion/no lap splices and (

**b**) specimen B2 with no corrosion/no lap splices.

**Figure 17.**Stress concentration on the seismic joint for different levels of horizontal displacement for B2 frame with 11 dbL lap-splice length: (

**a**) 0.5 mm, (

**b**) 23 mm, (

**c**) 42 mm, (

**d**) 53.7 mm, (

**e**) 81.4 mm.

R-P2L0 | R-P2L1 | R-P2L3 | Average AD (%) | ||||
---|---|---|---|---|---|---|---|

Exp | Anal | Exp | Anal | Exp | Anal | ||

P_{max} (+) (kN) | 240.00 | 217.73 | 175.00 | 176.86 | 215.00 | 209.11 | 4.36 |

δ_{Pmax} (+) (mm) | 48.50 | 34.84 | 19.50 | 27.77 | 48.50 | 38.13 | 30.65 |

P_{max} (−) (kN) | 194.00 | 217.73 | 168.00 | 176.86 | 208.00 | 209.11 | 6.01 |

δ_{Pmax} (−) (mm) | 38.50 | 34.84 | 19.00 | 27.77 | 34.50 | 38.13 | 22.06 |

P_{u} (+) (kN) | 192.00 | 174.18 | 140.00 | 141.49 | 172.00 | 167.29 | 4.36 |

δ_{Pu} (+) (mm) | 70.40 | 75.37 | 54.40 | 58.46 | 75.20 | 66.85 | 8.54 |

P_{u} (−) (kN) | 155.20 | 174.18 | 134.40 | 141.49 | 166.40 | 167.29 | 6.01 |

δ_{Pu} (−) (mm) | 64.00 | 75.37 | 50.00 | 58.46 | 65.00 | 66.85 | 12.51 |

**Table 2.**Comparative results for specimens NS-X0, NS-X16, CS-0 and CS-C2 with different corrosion levels.

NS-X0 (without Corrosion) | NS-X16 (16% Corrosion) | CS-0 (10% Corrosion) | CS-C2 (10% Corrosion and FRP Jacket) | Average AD (%) | |||||
---|---|---|---|---|---|---|---|---|---|

Exp | Anal | Exp | Anal | Exp | Anal | Exp | Anal | ||

P_{max} (+) (kN) | 60.70 | 54.56 | 50.90 | 49.56 | 187.00 | 169.35 | 192.00 | 180.08 | 7.10 |

δ_{Pmax} (+) (mm) | 20.00 | 20.87 | 18.00 | 42.12 | 24.00 | 30.39 | 54.00 | 27.69 | 53.43 |

P_{max} (−) (kN) | 52.00 | 54.56 | 50.00 | 49.56 | 187.00 | 169.35 | 183.00 | 180.08 | 4.21 |

δ_{Pmax} (−) (mm) | 15.00 | 20.87 | 30.00 | 42.12 | 24.00 | 30.39 | 45.00 | 27.69 | 36.16 |

P_{u} (+) (kN) | 51.60 | 46.38 | 43.27 | 42.13 | 149.60 | 135.48 | 153.60 | 161.89 | 6.90 |

δ_{Pu} (+) (mm) | 81.10 | 73.75 | 55.10 | 52.86 | 44.80 | 45.73 | 80.00 | 86.21 | 5.74 |

P_{u} (−) (kN) | 44.20 | 46.38 | 42.50 | 42.13 | 149.60 | 135.48 | 146.40 | 161.89 | 6.46 |

δ_{Pu} (−) (mm) | 70.00 | 73.75 | 55.00 | 52.86 | 44.80 | 45.73 | 75.00 | 86.21 | 6.57 |

Column Specimen | Lap Length (d _{bL}) | Layers CFRP | θ_{u,exp} | θ_{u,anal}(Proposed) | AD (%) | V_{R,exp}(kN) | V_{R,anal} (kN)(Proposed) | AD(%) |
---|---|---|---|---|---|---|---|---|

R-P2L0 | 0 | 2 | 0.044 | 0.0419 | 4.8 | 217.0 | 200.9 | 7.4 |

R-P2L1 | 15 | 2 | 0.034 | 0.0352 | 3.5 | 171.5 | 154.6 | 9.8 |

R-P2L3 | 30 | 2 | 0.047 | 0.0442 | 5.9 | 211.5 | 205.2 | 3.0 |

Average AD (%) | 4.73 | 6.73 |

Column Specimen | Corrosion Degree (%) | θ_{u,exp} | θ_{u,anal}(Proposed) | AD (%) | V_{R,exp}(kN) | V_{R,anal} (kN)(Proposed) | AD (%) |
---|---|---|---|---|---|---|---|

NS-X0 | 0 | 0.0676 | 0.0455 | 32.6 | 60.7 | 55.3 | 8.8 |

NS-X9 | 9 | 0.0804 | 0.0438 | 45.5 | 59.1 | 53.1 | 10.2 |

NS-X16 | 16 | 0.0459 | 0.0425 | 7.4 | 50.9 | 51.2 | 0.6 |

NS-X22 | 22 | 0.0462 | 0.0414 | 10.3 | 51.9 | 49.7 | 4.3 |

NS-X54 | 54 | 0.0273 | 0.0355 | 29.9 | 44.3 | 41.2 | 7.0 |

Average AD (%) | 25.14 | 6.18 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rousakis, T.; Anagnostou, E.; Fanaradelli, T.
Advanced Composite Retrofit of RC Columns and Frames with Prior Damages—Pseudodynamic Finite Element Analyses and Design Approaches. *Fibers* **2021**, *9*, 56.
https://doi.org/10.3390/fib9090056

**AMA Style**

Rousakis T, Anagnostou E, Fanaradelli T.
Advanced Composite Retrofit of RC Columns and Frames with Prior Damages—Pseudodynamic Finite Element Analyses and Design Approaches. *Fibers*. 2021; 9(9):56.
https://doi.org/10.3390/fib9090056

**Chicago/Turabian Style**

Rousakis, Theodoros, Evgenia Anagnostou, and Theodora Fanaradelli.
2021. "Advanced Composite Retrofit of RC Columns and Frames with Prior Damages—Pseudodynamic Finite Element Analyses and Design Approaches" *Fibers* 9, no. 9: 56.
https://doi.org/10.3390/fib9090056