A numerical study was conducted to investigate the in-plane behavior of a masonry-infilled reinforced concrete (RC) frame retrofitted with textile-reinforced mortar (TRM). A two-dimensional finite element model was developed using DIANA finite element analysis (FEA) software to simulate the 2 : 3 scaled three-storey masonry-infilled RC frame retrofitted with TRM that was studied experimentally in the past. The three-storey structure used in the test was with a nonseismic design and detailing, and was subjected to in-plane displacement-control cyclic loading. The current study evaluates the capabilities of a representative numerical model to simulate the results of the experimental test, and after the calibration of the numerical model sensitivity analysis and parametric study were performed. In order to create an accurate numerical model, suitable constitutive models, based on the smeared crack approach, were used to characterize the nonlinear response of concrete, masonry infill, and TRM. The calibration of the models was based on the experimental results or inverse fitting based on optimizing the simulation of the response. The numerical model proved capable of simulating the in-plane behavior of the retrofitted masonry-infilled RC frame with good accuracy in terms of initial stiffness, and its deterioration, shear capacity, and cracking patterns. The calibrated model was then used to perform sensitivity analysis in order to examine the influence of infill-frame interface properties (tangential and normal stiffness) on the behavior of the retrofitted infilled frame. The numerical results showed that the gap opening is influenced significantly by the stiffness of the interface. In addition, a parametric study was performed in order to evaluate the importance of the full-bond condition between the TRM and the masonry-infilled RC frame. The numerical results indicate that the composite action between the TRM and the masonry-infilled RC frame improves the global stiffness and lateral resistance of the infilled frame, and it reduces the gap opening between the masonry infill and the RC frame.

Masonry-infilled RC frame structures are widely dispersed around the world, and most of them are located in the seismic region while they were built before the development of new seismic design codes. Therefore, seismic retrofitting of existing masonry structures is nowadays a challenging engineering problem, since the most significant seismic risk in the world today is associated with existing buildings. Several rehabilitation techniques have been developed over the years [

Retrofit or repair structures built before any provision for an earthquake is one of the most serious problems faced by the engineers today. Several rehabilitation techniques have been developed over the years so that the masonry-infilled frame structures can be enhanced to satisfy modern seismic design codes [

Numerical studies aiming for predicting the behavior of retrofitted masonry infill wall are limited and most of them used the macromodelling approach and focused on the simulation of the behaviour of TRM-retrofitted masonry infill wall under monotonic loading. Koutas et al. [

Focusing on the numerical modelling of masonry-infilled frame structures retrofitted with TRM, initially, an efficient technique for modelling the behavior of masonry infill is chosen, followed by the determination of adequate constitutive models for each component of the structural system. In the literature, different modelling techniques that simulate the behavior of the infill wall can be found and can divided into three categories [

This paper presents a numerical model that represents the in-plane behavior of a three-storey TRM-retrofitted masonry-infilled RC frame under cyclic loading, following the mesomodelling approach to simulate the masonry infill wall. A two-dimensional FE model was developed in the DIANA FEA software, and a eigenvalue analysis, followed by a nonlinear displacement-based cyclic analysis was performed to simulate the experimental test conducted by Koutas et al. [

Koutas et al. [

Figure

(a) Geometry of the masonry-infilled RC frame and (b) the strengthening scheme: textile anchors of the first and the second storeys and the TRM layer on the faces of masonry infill at the first, second, and third storeys. (c) Test setup. [

In order to provide full clamping between the foundation beam and the laboratory floor, prestressing rods were placed, as shown in Figure

Geometry and mesh details of the FE model.

A two-dimensional numerical model was developed to simulate the nonlinear behavior of the TRM-retrofitted masonry-infilled RC frame described above. The DIANA FEA software Version 10.2 was used for the purpose of this study. The following sections describe the element type, size of meshing, boundary conditions, and loading sequence that were used in this numerical model. In addition, the appropriate constitutive material models which were selected to characterize the nonlinear response of concrete, masonry infill, and TRM are also presented. DIANA FEA was selected for modelling this structural system since it provides the elements and constitutive models needed for the TRM composite material, concrete, reinforcement, and masonry infill [

The geometry of the TRM-retrofitted masonry-infilled RC frame model was similar as possible to the experimental one, as shown in Figure

The interaction between masonry infill and bounding frame was modelled using the line interface element in order to take into account the gap opening and the sliding along the interface which was observed in the experiment. In addition, in this numerical model, the glass and carbon TRM were perfectly bonded to the masonry infill wall and to concrete elements, respectively, since in the experimental test, no debonding of the TRM surface from the masonry and the RC frame was observed. The bond condition provided by the existence of anchors at the top and bottom sides of the first and the second floor beams (Figure

In addition, the strong foundation RC-beam plate that was used at the bottom of the frame in the experiment was simulated by restraining all nodes at the base of the first floor of the masonry infill by preventing any translation in the

Two types of loads, representing the vertical compression and horizontal cyclic load, have been applied on the model. The dead load of the structure was simulated with a constant axial load equal to 0.174 kN/mm on the top of each column. In addition, for the horizontal cyclic loading, prescribed deformation load at the top of each floor was applied to simulate as closely as possible the experimental loading as shown in Figure

Four constitutive models are considered in this numerical model to reproduce the nonlinear behaviour of (1) concrete, (2) steel reinforcement, (3) masonry infill, and (4) TRM composite material. In addition, the interface between the masonry infill and the RC frame is modelled as described below. In this study, most of the material properties are taken from the experimental case study as described in Section

The Total Strain Crack model was adopted for the concrete since this model can simulate in detail the nonlinear response of concrete with a limited number of parameters. Nevertheless, concrete members are expected to undergo low nonlinear deformations and the use of a more complicated model was not deemed necessary. Figure

Typical uniaxial stress-strain curve as defined by the Total Strain Crack model with Maekawa–Fukuura compressive behavior.

The Menegotto–Pinto model was selected for simulating the nonlinear behaviour of steel bar reinforcement since this model is available for embedded reinforcements including the cyclic behavior of steel bar reinforcement [

The infill wall material was modelled using the Engineering Masonry model to simulate the nonlinear behavior of the masonry infill at mesolevel [

Engineering masonry model (a) behavior in traction, (b) behavior in compression, and (c) shear behavior [

Material properties of the engineering masonry model.

Modulus of elasticity— | 7 |

Modulus of elasticity— | 3.37 |

Shear modulus (GPa) | 1.38 |

Mass density (kg/m³) | 800 |

Cracking: head joint failure | |

Tensile strength normal to the bed joint (MPa) | 0.5 |

Residual tensile strength (MPa) | 0.2 |

Fracture energy in tension (N/mm) | 0.05 |

Crushing parameters | |

Compressive strength (MPa) | 5.1 |

Fracture energy (N/mm) | 40 |

Compressive unloading factor | 0.2 |

Shear failure parameters | |

Cohesion (MPa) | 0.71 |

Friction angle (degree) | 20 |

The gap opening and sliding occured due to interaction between the frame and the masonry infill significantly influence the overall behavior of the masonry-infilled RC frame as described by Filippou et al. [

Coulomb friction interface model [

Material properties of the interface Coulomb friction model.

Normal stiffness (kN) | 6000 N/mm³ | 3000 N/mm³ |

Shear stiffness (ks) | 60 N/mm³ | 30 N/mm³ |

Friction angle ( | 30 degree | 30 degree |

Dilatancy ( | 0 | 0 |

Model for gap appearance | Brittle | Brittle |

Tensile strength | 1^{2} | 1^{2} |

For the simulation of the TRM composite material, the Total Strain Crack model with the Fiber-Reinforced Concrete model for tensile behavior [

Material properties of total strain crack model for glass and carbon TRM.

Glass TRM | Carbon TRM | |
---|---|---|

Elastic modulus (GPa) | 30.00 | 34.00 |

Poison ratio | 0.2 | 0.2 |

Mass density (kg/m³) | 2400 | 2400 |

Total crack strain model | Crack orientation rotating | |

Tensile behavior | ||

Tensile strength (MPa) | 2.72 | 5.57 |

Tensile stress point I (MPa) | 2.72 | 5.57 |

Strain at point I (%) | 0.009 | 0.017 |

Tensile stress point | 2.72 | 5.57 |

Tensile strain point | 0.21 | 0.1 |

Tensile stress point | 12 | 15 |

Tensile strain point | 1.5 | 0.7 |

Ultimate strain (%) | 1.5 | 0.7 |

Crack band width | Rotating | |

Compressive behavior | ||

Compressive strength (MPa) | 18 | 18 |

Strain at maximum stress (%) | 0.21 | 0.21 |

Strain at ultimate stress (%) | 0.35 | 0.35 |

Numerical monotonic and cyclic tensile tests were performed in order to validate the nonlinear response of the TRM composite material. The validation was performed by comparing the numerical results with those obtained from monotonic tensile TRM-coupon tests conducted by Koutas et al. [

(a) Comparison of the results between the numerical model using the total strain crack model with the fiber-reinforced concrete model

The numerical results show good agreement with the experiment data in terms of peak and ultimate stress and strain, stiffness, and postcracking behavior. Previous studies concluded that the TRM nonlinear stress-strain curve is divided into three states: State I (the uncracked matrix), State II (the crack formation), and State III (the crack stabilization and failure) [

In this section, the calibration of the numerical model is presented, by comparing the numerical results of the eigenvalue and nonlinear cyclic analysis with experimental ones. Nonlinear cyclic analysis was performed (displacement control analysis) with the secant iteration scheme and the automatic incrementation procedure, in which both the number of steps and the corresponding step size are automatically computed. The energy-based convergence criterion was applied with the standard tolerance value (0.0001).

The fundamental period of the bare frame and for the masonry-infilled RC frame with and without TRM is presented in Table

Comparison of experimental and numerical fundamental periods.

Fundamental period (seconds) | Bare frame | Masonry-infilled RC frame | TRM strengthened masonry-infilled RC frame |
---|---|---|---|

Experiment | 0.24 | 0.06 | 0.047 |

Model | 0.23 | 0.062 | 0.049 |

The comparison between the experimental (black line) and numerical (red line) results concerning the global performance of the TRM-retrofitted masonry-infilled RC frame subjected to cyclic loading is presented in Figures

Comparison between experimental and numerical model results in terms of (a) base shear and top floor displacement hysteric curves, (b) base shear in relation to the load step, and (c) and top floor displacement in relation to the load step.

Comparison between the numerical model and the experimental results for the TRM masonry-infilled frame in terms of the (a) global lateral stiffness per cycle and (b) cumulative global hysteretic energy per half cycle.

Figures _{max,i}| is the absolute value of the positive and negative peak base shear values of the _{max,i}| is the absolute value of the displacement corresponding to the positive and negative peak base shear values of the

The energy dissipated at each cycle of loading is obtained by calculating the area enclosed by the loop in the base shear versus the top floor displacement diagram. The dissipated energy is associated with the propagation of damage through the wall (crack opening) and with the increase of the lateral capacity which leads to a higher area inside the hysteric loop. For easy calculations, the evolution of the dissipated energy is expressed by the following equation:

Numerical results and experimental data of the TRM-masonry-infilled RC frame have been compared (Figures

In addition, the comparison between the experimental and numerical results in terms of crack patterns is presented in Figure

(a) Damage at the first storey on the east column in the experimental study, (b) cracking of the masonry at the first storey in the experimental study, and (c) crack patterns in the numerical model in the masonry infill in the first floor at the end of the test.

In the TRM-retrofitted masonry-infilled RC frame model, flexural and tensile cracks occurred on external face of TRM both in the diagonal and horizontal directions at the first floor where these cracks have the same location as observed in the experiment. In addition, in the numerical model, shear and tensile cracks appear at the top of the first storey east column, which resembles the rupture of the TRM at the experimental study. It can be concluded that the crack pattern is well reproduced by a numerical model since the same damage is observed in the experiment upon test completion. It is observed that the proposed numerical model is capable of detecting the major features of the real behavior of the TRM-retrofitted masonry-infilled RC frame. The crack propagation and the global performance of retrofitted masonry-infilled RC frame in terms of base shear, stiffness, and energy are well reproduced by the numerical model. The discrepancy between numerical and experimental results is due to the nonlinearities that are introduced in the last cycle during the experiment (soft-storey failure of the ground floor wall).

After the calibration of the numerical model, sensitivity analysis is performed in order to examine how the stiffness properties (tangential and normal) of the infill-frame interface element affect the behavior of the retrofitted infilled frame. In addition, numerical experiments through a parametric study are performed to evaluate how important is the full-bond condition between the TRM and the masonry-infilled RC frame.

As mentioned in Section

Number of trials for normal and tangential stiffness of the interface.

Name of analysis | ||||
---|---|---|---|---|

Interface between masonry infill and column ( | Interface between masonry infill and beam ( | |||

Case 0 (calibrated model) | 3.03 | 0.030 | 6.167 | 0.06167 |

Case 1 | 3.03 | 0.30 | 6.167 | 0.6167 |

Case 2 | 30.03 | 0.30 | 61.67 | 0.617 |

Case 3 | 30.03 | 3.03 | 61.67 | 6.67 |

The comparison between the numerical results from the three analyses concerning the global and local performance of the TRM-retrofitted masonry-infilled RC frame subjected to cyclic loading is presented in Figures

Comparison between numerical model results using different values in the stiffness of the interface for the TRM masonry-infilled frame in terms of the (a) global lateral stiffness per cycle and (b) cumulative global hysteretic energy per half cycle.

Comparison between numerical model results using different values in the stiffness of the interface for the TRM masonry-infilled frame in terms of gap opening between the masonry infill and (a) the beam and (b) the column.

From Figures

From the sensitivity analysis, it is concluded that the nonlinear response of the masonry-infilled RC frame retrofitted with TRM is sensitive to the normal and shear stiffness of the infill-frame interface because the interaction between the frame and the infilled panel is considered as the major cause of the nonlinear behaviour of this type of structure [

In this section, numerical experiments are performed using the calibrated model in order to evaluate the importance of full-bond condition between the TRM and the masonry-infilled RC frame on global and local response of the retrofitted infilled frame under cyclic loading. A parametric investigation of the response of the calibrated model is undertaken in order to assess the effectiveness of considering full bond condition between the retrofitted wall and the surrounding frame. Two different configurations of connection were examined in order to evaluate the importance of the full-bond condition between the TRM and the masonry-infilled RC frame that the anchors provide: (1) full bond, where the glass TRM layer of the wall is fully bonded (Section

The numerical results of the two different configurations (full bond and no bond) are compared with the results obtained from the calibrated model in terms of stiffness and energy dissipation as shown in Figures

Comparison of the results in terms of (a) stiffness and (b) hysteric energy between the numerical model results considering full bond, no bond, and calibrated model bond conditions.

In order to investigate the effect of bond condition between the TRM and the masonry-infilled RC frame on the behaviour of the retrofitted infilled frame structure, the local results are presented in terms of gap opening between the infill wall and the beam (Figure

Comparison of the results in terms of gap opening between the numerical model results considering full bond, no bond, and calibrated model conditions.

From the experimental study performed by Koutas et al. [

A numerical model that simulates the in-plane nonlinear behavior of a masonry-infilled RC frame retrofitted with TRM under cyclic loading using the DIANA FEA software is presented in this paper. The test was conducted on a 2 : 3 scale three-storey infilled frame structure with nonseismic design and detailing, subjected to in-plane cyclic loading through the displacement control load. In this study, constitutive models based on the smeared crack approach for each component of the structural system were selected and calibrated based on the experimental results or inverse fitting with clear identification and justification. It is important to note that the anchors are not modelled in this numerical study so their failure is not predicted. The bond condition that the anchors provide between the masonry infill and the frame is taken into account in the model.

The numerical model was capable of simulating the in-plane nonlinear behavior of the TRM-retrofitted masonry-infilled RC frame with good accuracy in terms of initial stiffness and its deterioration, and shear capacity. In particular, the energy absorption and maximum shear force capacity in the last cycle of loading are overestimated compared to experimental results, due to high nonlinearities that are introduced in the last cycle of loading in the experiment (soft-storey failure of the ground floor wall). The crack patterns observed numerically show good agreement with the ones observed at the end of the experiment, concerning the location and propagation of the cracks.

After the calibration of the numerical model, sensitivity analysis was performed in order to examine the influence of infill-frame interface properties (tangential and normal stiffness) on the behaviour of the retrofitted infilled frame under cyclic loading. In addition, a parametric study was performed in order to evaluate the importance of the full-bond condition between the TRM and the masonry-infilled RC frame. From the sensitivity analysis, it can be concluded that the nonlinear response of the masonry-infilled RC frame retrofitted with TRM is sensitive to the normal and shear stiffness of the infill-frame interface, and these parameters are essential for simulating the infill-frame interface since they are able to control the gap opening and the sliding of adjacent elements in the model. The results from the parametric study showed that the composite action of the TRM jacket at the beam-infill interface (full bond) contributes to increase the load capacity and the hysteric energy of the TRM masonry-infilled RC frame, and to reduce the gap opening between the masonry infill and the RC frame. The numerical results show that improving the bond condition between the TRM and the interface between the masonry infill and the RC frame the performance of this structural system is improved. Further numerical and experimental studies are needed to find the optimal retrofitting strategies using the TRM composite material in a large-scale structure and to find an adequate configuration of textile-based anchors. This will expand the results’ database and will allow the development of design guidelines for a new strengthening technique on masonry-infilled RC frames using TRM.

All data related to the numerical work included in the submission can be made available upon request.

The authors declare that they have no conflicts of interest.