# Numerical simulation of the experimental results of the seismic strengthening of existing structures

Elpida Georgiou, Nicholas Kyriakides, Christis Chrysostomou, Panagiotis Kotronis, Christiana Filippou

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Elpida Georgiou, Nicholas Kyriakides, Christis Chrysostomou, Panagiotis Kotronis, Christiana Filippou. Numerical simulation of the experimental results of the seismic strengthening of existing structures. 16th European Conference on Earthquake Engineering, Jun 2018, Thessalokini, Greece. hal-05481578

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# NUMERICAL SIMULATION OF THE EXPERIMENTAL RESULTS OF THE SEISMIC STRENGTHENING OF EXISTING STRUCTURES

Elpida GEORGIOU<fnref n="1" />, Nicholas KYRIAKIDES<fnref n="2" />, Christis CHRYSOSTOMOU<fnref n="3" />, Panagiotis KOTRONIS<fnref n="4" />, Christiana FILIPPOU<fnref n="5" />

## ABSTRACT

An experimental campaign that studied the effectiveness of seismic retrofitting of existing structures was simulated and analyzed in DIANA finite element analysis (FEA) software. The retrofitting method that was studied is the conversion of selected bays into new infilled RC walls for the retrofitting of a multi-storey multi-bay RC frame building. The building was tested at the ELSA facility of the Joint Research Centre (JRC) in Ispra (Italy). It was a full-scale four-storey model tested with the pseudo-dynamic (PsD) method. The frames were designed and detailed for gravity loads only using different connection details between the walls and the bounding frame. The purpose of the experiments was the study of the effectiveness of the proposed retrofitting method, including the design of new infill walls and the contribution of dowels that connect the new infill wall to the existing RC frame. In DIANA FEA, 2D frames were modeled and nonlinear transient analyses were performed in order to simulate the experimental results. In this paper, the finite element models of the test specimen are described and presented along with a comparison of the numerical results to the experimental ones. The capabilities of the finite element models that simulated the experimental nonlinear cyclic behavior of the tested RC building are illustrated. Finally, conclusions are drawn regarding the effectiveness of the numerical models to capture the behavior of the proposed structural system.

Keywords: Retrofitting of RC buildings; RC Infill Walls; Connection Details; Dowels; Finite Element Analysis

## 1. INTRODUCTION

In recent decades, the aim of building rehabilitation and strengthening gained research attention, and numerous techniques have been developed to achieve this. Most of the strengthening techniques disturb the occupants, who must vacate the building during the intervention. Nowadays, most of the strengthening strategies are based on global strengthening schemes (Kaplan et al. 2011, Moehle 2000) and the structures are usually strengthened for limiting lateral displacements in order to compensate the low ductility (Kaplan et al. 2011, Sonuvar et al. 2004). Increasing the global stiffness and reducing the seismic deformation expectations of a building for seismic retrofitting purposes may be more cost-effective in comparison with the local intervention of the existing components in order to strengthen their capacities (Fardis 2009).

The addition of RC infilled walls in selected bays within existing RC frames, especially on the perimeter, is a popular method for seismic retrofitting and a simple and cost-effective method (Fardis et al. 2013, Kaplan et al. 2011). According to Chrysostomou et al. (2013) this is the most effective and

<footnote n="1">¹PhD Candidate, Cyprus University of Technology, Limassol, Cyprus, es.georgiou@edu.cut.ac.cy</footnote>

<footnote n="2">²Lecturer, Civil Engineering and Geomatics, Cyprus University of Technology, Limassol, Cyprus, nicholas.kyriakides@cut.ac.cy</footnote>

<footnote n="3">³Professor, Civil Engineering and Geomatics, Cyprus University of Technology, Limassol, Cyprus, c.chrysostomou@cut.ac.cy</footnote>

<footnote n="4">⁴Professor, Institut de Recherche en Génie Civil et Mécanique, University of Nantes, Nantes, France, Panagiotis.Kotronis@ec-nantes.fr</footnote>

<footnote n="5">⁵PhD Candidate, Civil Engineering and Geomatics, Cyprus University of Technology, Limassol, Cyprus, ca.filippou@edu.cut.ac.cy</footnote>
economic method for retrofitting multi-storey RC building, especially those with pilotis (soft-storey). With the full infill of selected bays of an existing RC frame, the effectiveness of the retrofitting is increased and the construction cost is reduced. The use of RC infill walls with the same thickness as the frame members that bound the wall for retrofitting RC buildings with openings is a relatively new retrofit method, which can be used to increase the strength, stiffness and ductility of the building. However, the RC infills as a retrofitting method is commonly applied to guarantee monolithic behavior between the old and new members in order to design the new RC walls according to EC8-3. This is achieved by the construction of new thicker web than the beams and the columns of the existing frame panel with the location of the new reinforcement outside the existing members and the details of reinforcement as in a new wall (Fardis et al. 2013). In this way, the new walls are much stronger than what is actually needed for the strengthening of the structure, and this ‘over-strength’ causes additional issues like the weakening of the foundations of the existing buildings (Fardis et al. 2013). Hence, a significant rotation is expected at the foundation (KANEPE 2012).

Even though the RC infills is a common retrofitting method and it is extensively applied, it is not addressed quantitatively by the codes, not even by Eurocode 8 – Part 3 (EC8-3). On the other hand, KANEPE (2012) refers to the introduction of RC infills within a frame, only in terms of forces, providing tools for calculating their deformations (at yield and failure) and stiffness only if they are integral with the bounding frame. Although for other strengthening methods of existing structures there are guidelines regarding the retrofit design and certain aspects of the seismic response of the retrofitted structure, there are still open issues about the studied retrofit method. For example, their interaction with the bounding frame, their design and detailing between the new web and the surrounding frame members need to be regulated (CEN 2010, Fardis et al. 2013). The inadequacy of design codes in this respect is due to our poor knowledge of the behavior of walls created by infilling with RC a bay of an existing frame. It is apparent that the codes or standards for seismic retrofitting do not provide proper guidance for the design and detailing of the attachment of new walls to existing frames. Furthermore, regulations do not exist for modeling or evaluation of frame bays converted into RC walls depending on the type and details of the connection.

Regarding the experimental research work that has been performed in the last decades, most of the experiments cover sufficiently the other frequently used types of retrofitting, in particular the use of fibre-reinforced polymers (FRP) and the concrete jackets despite the common field practice of new walls which encapsulate the frame members (Chrysostomou et al. 2016). There is no adequate experimental research work on the use of RC infill walls and most research has mainly targeted what is feasible: testing of one- to two-storey specimens due to the practical difficulties of testing large specimens with high resistance (Chrysostomou et al. 2016). The tests have been limited to small-scale specimens with new webs thinner than the surrounding beams or columns (possibly owing to the technical limitations of testing walls of very large shear force resistance) (Chrysostomou et al. 2013, Fardis et al. 2013). Another drawback of past investigations, is that they did not propose or even follow a quantitative procedure for the design of the connection between the RC infilling and the surrounding frame members. Furthermore, they have not led to, or supported, any procedure for the quantification of the engineering properties of the RC infilled frame which is essential for its analysis and design in the context of modern performance based seismic design, that is the effective stiffness, the moment and shear resistances, the deformation at yielding and the cyclic deformation capacity (Strepelias et al. 2012). Subsequently, data is lacking for taller full-scale specimens that reflect real applications (Chrysostomou et al. 2016).

In order to start filling the gap of knowledge regarding infilling of existing RC frames with RC walls, the effectiveness of seismic retrofitting of multi-storey multi-bay RC-frame buildings by converting selected bays into new walls through infilling with RC was studied experimentally through a full-scale pseudo dynamic (PsD) test within the project named SERFIN at the Elsa Laboratory of Structural Assessment (ELSA) facility at JRC, in Ispra. The research was under the project "Seismic Engineering Research Infrastructures for European Synergies" (SERIES). Further details can be found in Chrysostomou et al. (2013) and Chrysostomou et al. (2014) and Poljansek et al. (2014). This prototype model reflects correctly the real situation and its results and data are very useful. The results from the full-scale experiment that took place within the project SERFIN were studied and data from this test was used for the simulation of RC walls in finite element software in order to study the behavior of the RC infills within RC frames.
In this paper the numerical simulation of the frame that was tested in Ispra and the comparison of the
results with the experimental ones are presented. The DIANA FEA tool was used to simulate this
experiment and to validate the experimental results, taking into account the hysteretic behavior of
materials in order to capture and evaluate the behavior of RC infills. The results of the numerical
model are compared with the experimental results of the experimental model. In this way, with the
validated model, numerical experiments and various parametric studies can be developed and the
reliable investigation of shear connectors (dowels) contribution can be done. The aim of this finite
element simulation is the numerical parametric study by varying the number of dowels that connects
the existing frame with the new infill wall and the web reinforcement of the wall.

## 2. DESCRIPTION OF THE EXPERIMENTAL CASE STUDY

The subject of the project SERFIN was the conversion of selected bays into new infilled RC walls for retrofitting of multi-storey multi-bay for RC frame buildings. The purpose of the SERFIN experiment was to study the efficiency of the retrofitting method, and to examine the amount of the web reinforcement in the walls and the connection details between the wall and the bounding frame. The two parallel planar frames which were infilled with RC infills, were unidirectional pseudo-dynamically tested.

### 2.1 The specimen geometry

The specimen was a four-storey prototype building structure that was designed at full-scale to represent the two exterior three-bay frames of the prototype structure, which were spaced at 6 meters and linked by 0.15m thick RC slab and four 0.25m by 0.50m beams perpendicular to the plane of the two three-bay frames. The center-line length dimension of the specimen was 8.5m (central bay 2.5m and the two exterior bays 3m), the storey height 3m, and the total height of the specimen (excluding the foundation) 12m as it is shown in Figure 1. The dimensions of the columns were 0.25m by 0.4m with the long dimension along the plane of the three-bay frames, while those of the beams 0.25m by 0.5m. The walls in the two frames, had a thickness of 0.25m equal to the width of the beams and columns of the bounding frame. The RC infill walls were in the central bays of the specimen and they had the same thickness of 0.25m as the columns and beams framing them. These frames were named North and South as it is defined in Figure 2. Hence, the direction towards the reaction wall (front-side of Figure 2) is East and the one in the opposite direction (backside of Figure 2) is West. For this paper, the South wall simulation in DIANA FEA will be presented.

<figure><img src="image_4.png" /><figcaption>Figure 1. Dimensions of the full-scale specimen without the RC infill</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 2. Elevation of the specimen in the lab. The wall shown on the left is the South wall (frame) and the one on the right is the North wall (frame)</figcaption></figure>

## 2.2 The specimen design

The proposed structure represents a typical construction of the late '70s and beginning of the '80s in Cyprus. At that time, there were no provisions for earthquake loading, so the structures were designed for gravity loads only. There was no specific design standard and the authorities used to accept any standard that was acceptable to other countries. For the mock-up design, it was decided to use the provisions of BS8110, which were very close to those of CP110 with minor differences.

The material properties used in the mock-up were constrained by the availability of materials in the Italian and European market. It was decided to use concrete C20/25 for both the frame and the walls, of unit weight 25kN/m³ and modulus of elasticity, E=30GPa. The yield strength of the ribbed bar reinforcing steel was fyk=400MPa for both bending and shear reinforcement of the frame members and the slab, while for the RC infill and the dowels to be used for connecting the wall to the bounding frame members, the yield strength steel represents the one used in Cyprus construction practice in the 1970s and '80s, while the 450MPa was the closest available in the Italian market to substitute for the 500MPa steel that would have been used in the walls for retrofitting such a structure.

The self-weight was calculated using the unit weight of concrete specified above. The imposed dead load including the load of masonry infill walls was 3kN/m², and the live load was 1.5kN/m². These loads were combined using partial factors of safety of 1.4 for self-weight and imposed dead-load, and 1.6 for the live load. The material partial factors used were 1.5 for concrete and 1.15 for steel.

The reinforcement details of the beams, the columns and the slabs are given in Chrysostomou et al. (2013) and Chrysostomou et al. (2014) and Poljansek et al. (2014). Herein, it is important to emphasize the fact that a compression lap was used for columns, in line with a design for gravity loads only, and was expected to fail when subjected to tension.

In order to facilitate the study of the effect of as many parameters as possible, the two frames of the specimen were reinforced with different amount and arrangement of reinforcements, with the North wall being the strongest of the two. More specifically, an elaborate and varying system of dowels and starter bars was used to join the walls with the frame. The differences are about the diameter and the length of reinforcements mainly in the ground and first floor, and less in the third floor. In the fourth floor the reinforcements were exactly the same.

Moreover, it is important to mention that the tested model was designed using two different connection details between the new walls and the surrounding frame in order to evaluate the contribution of dowels that connect the new infill wall to the existing RC frame. In the first detail, two reinforcement bars were used; the starter bars and the short dowels. The web bars were used to connect the web bars of the wall to the surrounding frame through lap splicing with the same diameter starter bars that were epoxy grouted into the frame members. Then, short dowels were used in order to transfer the shear at the interface between the wall and the right column on the ground floor and 1st floor of the North frame, while for the South frame it was used to connect the wall at the bottom beam of the ground floor and first floor, and the west and east columns of the ground floor and first floor, respectively.
In the second detail, longer dowels were used to act both as dowels and as starter bars of the web
reinforcement, which are placed at the two faces of the wall. Thus, these dowels are considered as lap-
spliced with the nearest – smaller diameter – web bars. However, in this case, the clear distance
between the dowel and the nearest web bar, violated the maximum clear distance of 50mm or 4Φ
between lapped bars, specified in Eurocode 2 (CEN 2004). This detail was used to connect the wall at
the top beam and west column at the ground floor and 1st floor of the North frame, while for the South
frame it was used to connect the wall at the top beam of the 1st and 2nd floors, and the east and west
columns of the ground floor and 1st floor, respectively. In the 3rd floor of both the North and South
frames, only the second detail was used, while for the 4th floor only two dowels per wall interface were
used to provide safety against the falling of the wall out of plane. The completed wall reinforcement
(including web, starter bars and dowels) is shown in Figure 3. In all cases, the dowels were positioned
along the centerline of the elements (i.e. at 0.125m from the face of the wall). Detailed guidelines for
the design of such walls can be found in Fardis et al. (2013).

<figure><img src="image_6.png" /><figcaption>Figure 3. (a) Short dowels, (b) Dowels and starter bars, (c) Long dowels, (d) Dowels, starter bars and web reinforcement</figcaption></figure>

Since the lapping of the column reinforcement could take only compression, it was obvious that there would be lap splice failure at the ground floor columns next to the RC infill wall, which could be detrimental to the whole experiment. Therefore, in order to safeguard against this type of failure and allow the experiment to be performed without any premature failure, it was decided to reinforce the edges of the wall at the ground floor with three-sided CFRP for the height of 0.6m (lapping stopped at 0.55m) from the base of the column. Based on the performance of the ground floor RC infill wall during the experiments, this additional retrofit of the lap length region is crucial and constitutes part of the proposed retrofit strategy.

**2.3 Experiment campaign**

The specimen was pseudo-dynamically (PsD) tested and within the testing campaign two PsD tests and one cyclic test were run. The accelerogram was scaled to a maximum acceleration of: 0.1g-first PsD test and 0.25g-second PsD test. For the final cyclic test, a history of displacements was imposed on the fourth floor, while maintaining a triangular distribution of loads along the height of the north frame and zero rotation at each of the four floors.

In each storey a pair of servo hydraulic actuators applied horizontal loads as derived from the PsD test method. To connect an actuator to the structure a system of steel beams was installed. One beam was passing above and the other under the slab. The beams were then clamped together with prestressed bars. On the actuators' side, they were welded together to a sheen plate to which the actuators were bolted. Spacers were designed to allow the bottom beam passing without leaning against the beams of the structure. All actuator generated load was thus transmitted to the structure by friction minimizing stress concentrations. This ensured smooth transmission of forces also when the direction of loading was changed.

The accelerogram was scaled to a maximum acceleration of 0.1g and 0.25g for the first and second
PsD tests, respectively. The 0.1g test was performed initially to include minimum damage on the
structure. Then, the 0.25g test performed to study the performance of the specimen at its ultimate
capacity. For the final cyclic test, a history of displacements was imposed on the fourth floor, while
maintaining a triangular distribution of loads along the height of the North frame and zero rotation at
each of the four floors (unidirectional test). The aim of this final test was to explore the final capacity
of the specimen up to a 20% drop of peak strength of the structure.
The test structure was instrumented with 108 potentiometric displacement transducers, 22 inclinometers, 8 Heidenhain linear encoders and 8 load cells built in the actuators. Displacement transducers were installed to measure load displacements in critical areas. In particular transducers were placed to monitor slip and crack opening between all walls and their bounding beams and columns, the displacements between the ground floor walls and the foundation beams, and the shear deformations of the two ground floor walls. Displacement transducers were also installed to measure all the storeys vertical elongation of the bounding columns. Inclinometers were used to measure the rotation of beams and columns at the first floor. They were placed at the center joints and on beams and columns 30cm away from the joints. Inclinometers were also placed at selected columns 30cm above the foundation beam. Heidenhain linear encoders were installed to measure the horizontal displacement of the two frames at each of the four floors in the direction of testing. They served as reference displacement instruments for control in all tests.

### 3. EXPERIMENTAL RESULTS AND SHORT DISCUSSION

The main parameters that were examined in this experiment were the connection between the RC infill, the surrounding RC frame, and the percentage of the reinforcement in the RC infill. The effect of these parameters was studied during the experiment too, by using different connection details and reinforcement percentages for the two infilled frames. The findings regarding the behavior of the structure were that the structure managed to sustain an earthquake of 0.25g without significant damage. Although some column lap-splices failed with concrete spalling, the structure continued to carry load. It is noteworthy to mention that the three-sided CFRPs protected the wall bounding columns on the ground floor and prevented lap-splice failure. In addition, the “weak” south frame behaved equally well as the “strong” north frame. There was no visible movement at the interface between the wall and the bounding frame.

Overall, the behavior of the wall was mainly flexural, although on the south-frame wall some diagonal cracks appeared. Moreover, some vertical cracks appeared on the connection of the beams to both the exterior and the wall columns and horizontal crack appeared on the ground-beam of the walls, which was the main cause for the loss of strength of the south frame. From the experimental outcomes that will be discussed in this section it can be concluded that this is a viable method for retrofitting and it can be used to validate the analytical model that was developed to simulate the behavior of similar frames.

In this paper, the second 0.25g acceleration test results will be compared with the ones from the finite element model that was created, so the second PsD test results of the experiment will be presented in more detail.

#### 3.1 PsD test results

The 0.1g test was designed to induce minimum damage on the structure. For the low-level acceleration, the structure behaved very well. After a visual inspection of the specimen, no visible cracks on either the columns or the walls could be noticed. Some hairline cracks that appeared on the surface of the wall at maximum displacement closed down at the end of the experiment. The maximum top storey displacement was 24mm and the displacement in the opposite direction was 26mm. These displacements were the same for both the north and south frames, since the forces in the south frame were imposed in such a way so as to keep the displacements of the two frames equal, and hence avoid any torsional effects on the specimen. Based on the results of the test and the observed damage, it can be considered that both walls have reached their cracking moment, and this was the purpose of this experiment.

The 0.25g test was designed to study the performance of the specimen at its ultimate capacity. The south frame had suffered larger levels of damage than the north frame, which was confirmed by a crack that opened at the ground beam of the foundation at the base of the wall and by a lap-splice failure that appeared in the outer column at the east side of the south frame (Figure 4 (c)). The percentage of the Carbon fiber reinforced polymer (CFRP) on the bounding columns of the wall prevented a similar failure, thus allowing the completion of the experiment. From the graph of the base shear versus the top storey displacement of 0.25g test in Figure 5 (b) we can see that the hysteresis
loops are stable and provide some energy dissipation. The maximum top storey displacement was 109mm and the displacement in the opposite direction was -93mm (Figure 5 (a)). Some difference was observed in the base shear between the two frames. The maximum base shear in the positive direction (specimen was moving towards the East, i.e. towards the reaction wall) was 1074kN for the south frame and 1036kN for the north, which are about the same, while a negative base shear of -843kN was recorded for the south frame and -1011kN for the north one in the negative direction (specimen was moving towards the West, i.e. away from the reaction wall). This was an indication that the south frame has suffered some damage and it could not take further load. The only visual indication of this was a crack that opened in the ground beam at the base of the wall and the lap-splice failure due to tensile forces of the outer column on the east side of the south frame (Figure 4 (a) and (b)). It should be noted that the presence of the CFRP on the bounding columns of the wall, have prevented a similar failure and it allowed the completion of the experiment.

<figure><img src="image_7.png" /><figcaption>Figure 4. (a) Crack opened at the bottom of the west column of the south wall, (b) Crack opens at the bottom of the east column of the south wall, (c) Tensile lap-splice failure of the ground floor column at the east side of the frame</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 5. (a) Storey displacements for 0.25g acceleration test, (b) Top storey displacement versus base shear force for 0.25g acceleration test</figcaption></figure>

The general behavior of the specimen during the two PsD tests showed that its performance was in accordance with the damage expected from the retrofit design corresponding to a life-safety limit-state for the 0.25g earthquake (475 years return period). No visible diagonal cracks on the walls were observed, confirming that the wall responded in flexure. In nearly all the corner columns and on floors, a horizontal crack appeared at a height of 0.55m, corresponding to the limit of the lap-splice; in some cases spalling of the concrete cover was observed. Some vertical cracks appeared in the beams close to the beam/column interface, but no severe damage was observed, despite the fact that there were no ductile connections in the structure. In general, the stronger north frame had an overall better behavior compared to the south frame; nevertheless the differences between the two frames were minor.

## 4. 2D FINITE ELEMENT MODEL SIMULATION

The results and data, from the full-scale test that was tested in Ispra in Italy within the context of the project named SERFIN, were used to calibrate the numerical model. This prototype model reflects correctly the real situation and its results and data are very useful. The DIANA FEA (10.1 version) was used to simulate the SERFIN experiment and to validate the model using the experimental results, taking into account the nonlinear hysteretic behavior of materials in order to capture the behavior of RC infills. Having a validated model, numerical experiments and various parametric studies can be
developed and a reliable investigation of the proposed system that will complement the experimental
results can be performed.

In DIANA FEA the nonlinear transient analysis with base excitation was used. Suitable elements for the simulation of the RC infills, reinforcement and frame members were chosen along with material models for concrete and reinforcement, which included hysteretic behavior with strength and stiffness degradation.

The model of the south frame of the SERFIN specimen was simulated in DIANA FEA with the same geometry like the prototype specimen, with a 2D continuum finite element model. A rigid foundation was assumed for the simulation, with pin supports at the base of the frame. Moreover, the additional weight of the half of the specimen slab and transverse beams was added to the 16 joints of the model through mass point elements. Rayleigh damping coefficients were used with a damping ratio of 0.25%. The CFRP's were not included in the model.

Two distinct models were developed in DIANA FEA and will be presented in this paper. In the first model, the infills were monolithic with the bounding frame and all the reinforcing bars were modeled to curry axial forces only. In the second model, the interaction between the existing bounding frame and the new RC wall was modeled through interface elements, in order to allow for the separation of the bounding framing members and the RC wall at their interface when they are in tension. In this case, the dowels were modeled to take both shear forces and moments as it is the case in the real structure.

The dead and live loads were applied on the beams as edge pressure load with the same values like the prototype model and the earthquake signal with 0.25g peak acceleration was added as body force for base excitation with the earthquake time history function. Then, the nonlinear transient analysis was executed in DIANA FEA. The secant Newton method (quasi-newton), which is an implicit algorithm iterative method, was applied, together with the line search method. For the first model, the convergence tolerance was applied for force and displacement, whereas for the second model the convergence tolerance was applied for force, displacement, and energy.

## 4.1 Elements and mesh

For the 2D concrete frame simulation, the regular plane stress quadrilateral elements (CQ16M, quadrilateral, 8 nodes) were applied. The size of these elements in the model was 100mm by 100mm and their thickness was 250mm. The basic variables of the regular plane stress elements are the translations of the nodes: $u_x$ and $u_y$. The displacement field yields the deformations of an infinitesimal part of the element. The plane stress elements may be loaded with distributed load on one or more edges or over the entire element face.

For the first model, where the infills were monolithic with the bounding frame, all the reinforcements and dowels were modeled as reinforcement steel bars and for their mesh embedded bar reinforcements inside the plane stress elements were used, which can carry only axial loads (Figure 6). In this way, perfect bonding was assumed between the concrete and steel bars, the existing structure and the RC infilling. The strains in the reinforcement are computed from the displacement field of the mother elements by default. The reinforcements are defined by their location in the model, their material properties, their physical properties (cross-section) and their integration point schemes. DIANA FEA performs a numerical integration of each particle of a reinforcement bar. In each integration point it determines a vector tangential to the bar axis. The variables for a bar reinforcement are the strains $\epsilon_{xx}$ and the stresses $\sigma_{xx}$ oriented along the longitudinal axis of the bar.

In the second model, for the reinforcement elements of the frame and the web reinforcement of the infill, the same 1D embedded bar reinforcements inside the plane stress elements as the ones for the first model, were used. For the south wall that will be examined, four cross-section-areas of bars were used like in the prototype model. For the dowels, in order to capture the shear stress that they take in the model, the bond-slip reinforcements with beam elements (BAR LINE, INTERF BEAM) of DIANA FEA were selected to model their behavior. Three diameters were used for the dowels, as in the prototype model. For the interface between the frame and the walls the 2D line interface elements (CL12I) with the same thickness of plane stress elements of 0.25m were used. The second finite element model is shown in Figure 7.
<figure><img src="image_9.png" /><figcaption>Figure 6. (a) RC frame monolithic with infills with plane stress elements, (b) Embedded reinforcement bars which can take only axial loads, (c) Complete first model</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 7. (a) RC frame with 2D line interface elements at the interfaces and plane stress elements, (b) Embedded reinforcement bars for the existing frame and web reinforcements and dowel special elements which can take shear forces and moments, (c) Complete second model</figcaption></figure>

The mass of the half weight (312 Tons) of the prototype building was added in the model by using the point mass elements (PT3T) on the 16 joints of the frame.

## 4.2 Constitutive laws

The material models should describe the hysteretic behavior under cyclic loading. More specifically, the models should model the stiffness and strength degradation and the material softening behavior which causes localization and redistribution of strains in the structure (plasticity).

For concrete, the material model that was used was the Total strain based crack model, with rotating orientation with Maekawa cracked concrete curves for the behavior of concrete in compression with 33MPa for compression strength. The Young's modulus of concrete was calibrated in the model in order to get the real behavior of the building that was already cracked. Hence, the Young's modulus was reduced from 30GPa to 15GPa. For the tensile behavior of concrete, the fib Model Code 2010 for Concrete Structures was used with tensile strength 2.6MPa. In the table below, the concrete material properties are shown.

<table><caption>Table 1. Concrete material model in DIANA FEA.</caption><thead><tr><td>Linear material properties</td><td>Total strain based cracked model</td><td>Tensile behavior</td><td>Compressive behavior</td></tr></thead><tbody><tr><td>Young's modulus (E) – 15GPa</td><td>Rotating crack orientation</td><td>Fib Model Code for Concrete Structures 2010</td><td>Maekawa cracked concrete curves</td></tr></tbody></table>
Poisson's ratio – 0.2

Mass density –
2500kg/m³

Rots crack bandwidth
specification

Tensile strength –
2.6MPa
Mode-I tensile fracture
energy – 136.98N/m

Compressive strength – 33MPa
No stress confinement

Regarding the reinforcement, the Menegotto-Pinto model was chosen for the reinforcement bar elements of the existing frame and for the dowels and web reinforcements for the first monolithic model. For the second model, where the dowels were modeled to capture the shear stress, the Menegotto-Pinto model was replaced with the von Mises plasticity model because Menegotto-Pinto is appropriate for the reinforcement elements that can solely take axial loads. As a result, it can only control the tensile and compressive stresses, whereas von Mises plasticity model can be applied to control shear stresses for cyclic loading of the reinforcement as well. In both cases, the yield stress of existing frame reinforcement was 400MPa and the yield stress of the infill wall web reinforcement and dowels was 450MPa. The material properties of reinforcement bars in DIANA FEA are shown in Table 2.

<table><caption>Table 2. Menegotto-Pinto and von Mises plasticity models in DIANA FEA.</caption><thead><tr><th>Linear elasticity</th><th>Menegotto-Pinto</th><th>Von Mises</th><th>Bond-slip interface</th></tr></thead><tbody><tr><td>Young's modulus<br>(E) – 200GPa</td><td>Yield stress for frame members – 400MPa</td><td>Yield stress for frame members – 400MPa</td><td>Normal stiffness modulus</td></tr><tr><td>Mass density –<br>7800kg/m³</td><td>Yield stress for walls –<br>450MPa</td><td>Yield stress for walls –<br>450MPa</td><td>Shear stiffness modulus</td></tr><tr><td></td><td></td><td>No hardening function</td><td>Shear bondslip function</td></tr></tbody></table>

For the interface behavior between the new infill wall and the surrounding frame members of the second model, the Coulomb friction material model was applied to represent the cohesion and the friction between the interfaces, and at the same time it provides the option of the gap criterion in the case of tensile stress between the two interfaces. For this aim, the brittle gapping model was applied with minor tensile strength, in order to let the dowels carry the shear stresses in the model. The linear material properties of Coulomb friction model, were set through trials in order to achieve the outcomes that were the closest to the results of the test specimen.

## 5. 2D FINITE ELEMENT MODEL RESULTS

The global results of the experiment of the South wall are compared with the first monolithic model outcomes of DIANA FEA in Figures 8(a) and 8(b), where the fourth-floor displacements through the time history of the analysis are illustrated. The base shear in relation to the top storey displacement graph is presented so as to check the energy absorption and the stiffness degradation of the finite element model. From these results, it is obvious that the finite element model matches the real structure very well. The peak values are captured in both forces and displacements and the stiffness degradation is captured as well. Moreover, it is clearly shown that the model captures the period of the actual structure.

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>
(a)

(b)

<caption>Figure 8. First model global results: (a) Fourth floor displacements versus time, (b) Base shear force versus top storey displacement</caption>

The global results of the South wall are also compared to the second finite element model, with the interface line elements between the bounding frame and the infill wall and where the dowels are modeled as circular beam bond-slip reinforcements so they can take shear forces and moments. As it is shown in the graphs in Figures 9(a) and 9(b), both finite element models capture the real structure well. If we compare the two finite element models, we can see that in the second finite element model, the peak displacement of the frame is not captured exactly like in the first monolithic frame. However, the second model is very close to the real values as well.

<figure><img src="image_13.png" /><figcaption>Figure 9. Second model global results: (a) Fourth floor displacements versus time, (b) Base shear force versus top storey displacement</figcaption></figure>

The main failures that occurred were the diagonal cracks starting at the bottom of the column-wall for both sides of the wall and the tensile failure of the east column at the bottom of the south frame. From the stress distribution in the numerical model, it is shown that the specific failures were captured. From the shear stress distribution in Figure 10(a) and 10(b) the diagonal strut that was captured in the finite element model that lead to the diagonal cracks is shown in both sides of the simulated wall. In Figure 10(c), the tensile yield stress that was reached at the left-hand-side of the east column, where the failure of the column occurred in the experiment, was also captured.

<figure><img src="image_14.png" /><figcaption>Figure 10. Second model local results: (a) Shear stress distribution; diagonal strut in the west side of the wall at 5.8seconds, (b) Shear stress distribution; diagonal strut in the east side of the wall at 6.4seconds, (c) Tensile stress of 2.6MPa at 6.4seconds at the east column (right-hand-side column in the figure)</figcaption></figure>

## 6. CONCLUSIONS

The numerical results of the 2D finite element model capture the behavior of the test specimen. It is clearly seen that there is an agreement between the real case-study and the numerical model results,
despite the large number of influencing factors affecting the analysis. Calibration of the model was
necessary regarding the methods and nonlinear analysis parameters used, the normal and shear
stiffness modulus of the interface model, and the bond-slip material models, in order to be able to
capture the response of the test specimen. This is because there are no clear values defined for these
mechanisms, since their behavior is difficult to measure in actual tests.

At this point, it can be concluded that the aim to have a reliable model of RC infills walls, and their
interaction with the surrounding frame through the dowel action and starter bars contribution at the
interface, was achieved. This model simulates very closely the experimental results and it can be
therefore used to perform numerical experiments. A parametric study is under way that will cover a
range between monolithic behavior and infilled frame, by varying the number of dowels connecting
the wall to the bounding frame. This will allow to complement the experimental results and to study
the interaction between RC infills and bounding frame both in the local and global level. These results
will contribute to the investigation of a general model for the application and the design of RC infills
in existing RC frames.

7. ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Community's 7th Framework Program [FP7/2007-2012] for access to the EUROPEAN LABORATORY FOR STRUCTURAL ASSESSMENT of the EUROPEAN COMMISSION – JOINT RESEARCH CENTRE under grant agreement no. 227887.

8. REFERENCES

CEN (2004). Eurocode 2: Design of concrete structures - Part 1: General rules and rules for buildings, (EN-1992-1-1), Comité Européen De Normalisation.

CEN (2010). Assessment and retrofitting of buildings: Eurocode 8: design of structures for earthquake resistance: Part 3: Assessment and retrofitting of buildings / European Committee for Standardization, editor Cyprus Organisation of Standardisation, Brussels: European Committee for Standardization.

Chrysostomou C. Z, Kyriakides N, Kotronis P, Georgiou E (2016). Derivation of Fragility Curves for RC Frames Retrofitted with RC Infill Walls based on Full-Scale Pseudodynamic Testing Results, *Proceedings ECCOMAS Congress 2016*, Paper 16727, June 5-10, Crete, Greece.

Chrysostomou C. Z, Kyriakides N, Poljansek M, Taucer F, Molina F. J (2014). RC infilling of existing RC structures for seismic retrofitting, *Geotechnical, Geological and Earthquake Engineering*, 303–328.

Chrysostomou C. Z, Poljansek M, Kyriakides, N, Taucer F, Molina F. J (2013). Pseudo-dynamic tests on a full-scale four-storey reinforced concrete frame seismically retrofitted with reinforced concrete infilling, *Structural Engineering International: Journal of the International Association for Bridge and Structural Engineering (IABSE)*, 23(2), 159–166.

Fardis M. N (2009). Seismic design, assessment and retrofitting of concrete buildings: based on EN-Eurocode 8, *Geotechnical, geological, and earthquake engineering*, Springer, Dordrecht; New York.

Fardis M. N, Schetakis A, Strepelias E (2013). RC buildings retrofitted by converting frame bays into RC walls, *Bulletin of Earthquake Engineering*, Department of Civil Engineering, University of Patras, Patra, Greece, 1–21.

KANEPE (2012). Code for Intervention in Reinforced Concrete Buildings, Earthquake Planning and Protection Organization (OASP).

Kaplan H, Yilmaz S, Cetinkaya N, Atimtay E (2011). Seismic strengthening of RC structures with exterior shear walls, *Sadhana*, Springer, 36(1), 17–34.

Moehle J. P (2000). State of research on seismic retrofit of concrete building structures in the US, *US-Japan symposium and workshop on seismic retrofit of concrete structures*.

Poljansek M, Taucer F, Molina J, Chrysostomou C. Z, Kyriakides N, Onoufriou T, Roussis P, Kotronis P, Kosmopoulos A (2014). Seismic Retrofitting of RC Frames with RC Infilling (SERFIN Project), *JRC Scientific and Policy Report*, Publications Office of the European Union, Luxembourg, doi: 10.2788/630.

Sonuvar M. O, Ozcebe G, Ersoy U (2004). Rehabilitation of reinforced concrete frames with reinforced concrete
infills, *ACI Structural Journal*, ACI, 101(4).

Strepelias I, Fardis M, Bousias S, Palios X, Biskinis D (2012). RC Frames Infilled Ino RC Walls for Seismic Retrofitting: Design, Experimental Behaviour and Modelling, *Report No. SEE 2012-02*, Department of Civil Engineering, University of Patras, Patra, Greece.