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51 st ASC Annual International Conference Proceedings Copyright 2015 by the Associated Schools of Construction 345 Optimizing the Structural Performance of Concrete Elements against Seismic Excitation by Placing Crack-like Joints: Infill Wall Mohammad Saied Andalib, PhDc and Mehdi Tavakolan, Prof. University of Tehran Tehran, Iran Armin Aziminejad, Prof. Islamic Azad University, Science & Research Branch Tehran, Iran Fayaz Rahimzadeh Rofooei, Prof. Sharif University of Technology Tehran, Iran A new constructible and low-cost method is introduced in the present study for optimizing the structural behavior of concrete elements against seismic excitation. The method is based on placing specific cracks named “Crack-like Joints” (CLJ) in the concrete components and evaluating its effect on the member’s performance. The method is applied on infill walls against earthquake excitation. The infill wall considered in this study is a concrete wall embedded in a reinforced concrete frame. Infill walls can have significant positive effect on the structure’s resistance, hardness and overall performance against earthquake, if used properly. The finite element models used in this study have been modeled finely with the ABAQUS software. The results of the verification model matches appropriately with the previous experimental study. The results show that by placing CLJs suitably in the middle of an infill wall, the sudden diagonal failure during earthquake excitation would diminish. In the presence of a suitable CLJ in the infill wall, the force transition is spread through the wall and the stiffness and strength deterioration during lateral loading on the frame is extremely reduced. Keywords: Concrete Infill Wall, Crack-like Joints, Weakening Technique, Seismic Excitation Introduction Most techniques for protecting concrete structures against earthquake excitations are able to theoretically achieve a targeted structural performance; however excessive costs, invasiveness and constructability are still main issues for a wider implementation. The most common procedures to improve the seismic performance of existing buildings are the following: - Strengthening produced by adding (or by reinforcing) lateral elements, which lead to a reduction of deformations and displacements but lead to an increase in accelerations in the yielding structures. - Base isolations change the dynamic properties of structures, reducing the seismic acceleration and drift but increasing the total displacement. - Supplemental Damping devices reduce lateral displacements, but do not change substantially the amount of seismic acceleration in the inelastic structures. In the recent decade, researchers have proposed a counter-intuitive but rational seismic retrofit strategy of selectively weakening a structural system (Reinhorn, Viti et al. 2005; Ireland, Pampanin et al. 2006; Kam and Pampanin 2009). Although, weakening reinforced concrete walls by segmenting it vertically has been done by Ireland, Pampanin et al. 2006 to improve its ductility, but the literature has a gap in weakening infill walls in order to prevent its brittle failure during earthquake excitation. Also, the literature has not comprehensively studied different possible methods of weakening the structures in order to enhance their behavior against earthquake excitations. This study proposes placing crack-like joints in infill walls to enhance the infill wall’s behavior under cyclic earthquake excitations. It should be noted that the application of the proposed method is not only limited to infill walls. One of the main problems of using infill walls in reinforced concrete frames is its brittle failure during sweeping earthquake excitation. Usually, when the use of infill walls becomes necessary, it is isolated from the surrounding frame in order to prevent its influence on the structure’s behavior. This is while infill walls can have a significant

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Page 1: Optimizing the Structural Performance of Concrete … the Structural Performance of Concrete ... wall embedded in a reinforced concrete ... type of concrete panels which is usually

51st ASC Annual International Conference Proceedings Copyright 2015 by the Associated Schools of Construction

345

Optimizing the Structural Performance of Concrete

Elements against Seismic Excitation by Placing Crack-like

Joints: Infill Wall

Mohammad Saied Andalib, PhDc and Mehdi Tavakolan, Prof.

University of Tehran

Tehran, Iran

Armin Aziminejad, Prof.

Islamic Azad University, Science & Research Branch

Tehran, Iran

Fayaz Rahimzadeh Rofooei, Prof.

Sharif University of Technology

Tehran, Iran

A new constructible and low-cost method is introduced in the present study for optimizing the

structural behavior of concrete elements against seismic excitation. The method is based on placing

specific cracks named “Crack-like Joints” (CLJ) in the concrete components and evaluating its effect

on the member’s performance. The method is applied on infill walls against earthquake excitation.

The infill wall considered in this study is a concrete wall embedded in a reinforced concrete frame.

Infill walls can have significant positive effect on the structure’s resistance, hardness and overall

performance against earthquake, if used properly. The finite element models used in this study have

been modeled finely with the ABAQUS software. The results of the verification model matches

appropriately with the previous experimental study. The results show that by placing CLJs suitably

in the middle of an infill wall, the sudden diagonal failure during earthquake excitation would

diminish. In the presence of a suitable CLJ in the infill wall, the force transition is spread through

the wall and the stiffness and strength deterioration during lateral loading on the frame is extremely

reduced.

Keywords: Concrete Infill Wall, Crack-like Joints, Weakening Technique, Seismic Excitation

Introduction

Most techniques for protecting concrete structures against earthquake excitations are able to theoretically achieve a

targeted structural performance; however excessive costs, invasiveness and constructability are still main issues for a

wider implementation. The most common procedures to improve the seismic performance of existing buildings are

the following:

- Strengthening produced by adding (or by reinforcing) lateral elements, which lead to a reduction of deformations

and displacements but lead to an increase in accelerations in the yielding structures.

- Base isolations change the dynamic properties of structures, reducing the seismic acceleration and drift but

increasing the total displacement.

- Supplemental Damping devices reduce lateral displacements, but do not change substantially the amount of

seismic acceleration in the inelastic structures.

In the recent decade, researchers have proposed a counter-intuitive but rational seismic retrofit strategy of

selectively weakening a structural system (Reinhorn, Viti et al. 2005; Ireland, Pampanin et al. 2006; Kam and

Pampanin 2009). Although, weakening reinforced concrete walls by segmenting it vertically has been done by

Ireland, Pampanin et al. 2006 to improve its ductility, but the literature has a gap in weakening infill walls in order

to prevent its brittle failure during earthquake excitation. Also, the literature has not comprehensively studied

different possible methods of weakening the structures in order to enhance their behavior against earthquake

excitations. This study proposes placing crack-like joints in infill walls to enhance the infill wall’s behavior under

cyclic earthquake excitations. It should be noted that the application of the proposed method is not only limited to

infill walls.

One of the main problems of using infill walls in reinforced concrete frames is its brittle failure during sweeping

earthquake excitation. Usually, when the use of infill walls becomes necessary, it is isolated from the surrounding

frame in order to prevent its influence on the structure’s behavior. This is while infill walls can have a significant

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and positive effect on the structure’s resistance, hardness and overall performance if used properly. Currently,

specific infill walls are introduced to enhance the structure’s performance, but they often use expensive materials

and construction methods, which often makes them economically unfeasible in wide application.

Different techniques can be developed for strategic weakening of a structure. A typical method with this regard is

“weakened plane joints” which is a plane through a section of a concrete element without any cohesive bind

between the two sides of the concrete. A crack-like joint could be like a thin elliptic void through a wall’s thickness.

This void could be constructed by placing a piece of foam similar to the designed crack, in the desired location prior

to shotcrete or concrete work. The geometry of the crack is such that, it shall be closed under the ultimate

compressive strength without causing failure in the element. This method would reduce the stiffness of the element

before the closure of crack and add compressive strength to the element after its closure. Additionally, this crack

would change the force distribution through continuous massive elements such as walls. This method of weakening

is easily constructible whether the concrete work is in-situ or precast and also does not charge considerable costs to

the construction.

Background

Preliminary suggestions regarding the use of strategic weakening to improve the performance of a structure can be

found in FEMA-273 (FEMA, 1997), FEMA-356 (FEMA, 2000). The concept for an alternative seismic retrofit

strategy referred to as a “selective weakening” approach which focuses on protecting undesirable seismic response

mechanisms by first strategically weakening specific elements within a structure was discussed by Pampanin in

2006(Pampanin 2006). Also Reinhorn, 2005 offered a new procedure to retrofit existing structures subjected to

seismic excitation by weakening the structure and using supplemental damping devices(Reinhorn, Viti et al. 2005).

Weakening a structure will reduce the seismic demand while at the same time changing the inelastic mechanism

according to capacity design principles in order to achieve an overall higher performance level. In a second phase, to

achieve a complete retrofit solution other currently available and applicable retrofit techniques can be used in

combination with the selective weakening strategy to upgrade the weakened structure to the desired and controlled

level of capacity. Comprehensive experimental and numerical study is done on “selective weakening” (SW) retrofit

strategy for earthquake vulnerable existing RC frames with particular focus on the exterior beam-column (b-c)

joints(Kam and Pampanin 2009; Kam, Pampanin et al. 2010).

Infill Walls

Walls are inseparable parts of buildings which their capacity can be used in the structural design. However, the

seismic behavior of building systems with infill walls has not yet been well known (Pavese and Bournas 2011).

Implementation of infill walls in buildings, without considering them in the design process changes the mechanism

of failure and generally the structural behavior against earthquakes. For a structure which has been designed

according to the regulations and its performance is guaranteed to a certain extent, changing the force transmission

paths by using influential walls is often undesirable. For example, a comprehensive report by PEER (Pacific

Earthquake Engineering Research Center) was released in 2007 that explained the effect of brick walls in concrete

frame buildings. The results from this research indicate that the existence of brick walls in the structure, increases its

stiffness, reduces the time period and increases the seismic attenuation. These changes generally increase the level

of resistance and displacement demand in the structure’s seismic design. Brick walls also change the force

transmission path and the strength demand between the peripheral frame elements. It is worth mentioning that the

walls act as lateral bearing members and absorb greater amount of inertia in the earthquake. Finally, the new force

transmission path increases the strength demand in the ceiling diaphragm and therefore it must be designed stronger

(Hashemi and Mosalam 2006). Most of the above-mentioned phenomena are considered undesirable for a flexural

frame building that has been designed according to seismic codes.

As mentioned previously, extensive research is done for rehabilitating structures using infill walls, or designing infill

walls as one of the structure’s lateral bearing system. For example, Billington et al. (2004) did laboratory and

analytical study on an innovative infill wall system for retrofitting building frames against earthquake loads. The

infill walls in this study consist of prefabricated panels with a new ECC concrete material. The results showed a

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dominant flexural failure mode for the walls and also the material used in the walls increased the systems resistance

compared to normal concrete, more than 45% (Billington and Yoon 2004).

The failure mode of concrete panels under gradually increasing axial load experiments has shown to be crushing at

the foot instead of buckling(Pavese and Bournas 2011). Also laboratory studies on reinforced concrete walls under

pure axial load has shown negligible effect of reinforcement on the wall’s final strength and only walls with a height

to thickness ratio bigger than 20 were reported to fail of buckling (Pillai and Parthasarathy 1977). Therefore, as the

height to thickness ratio in this study’s modeling is approximately 18, and as the software results also approve, the

buckling of panels is not a matter of concern.

Concrete Sandwich Panels

This study uses a specific type of concrete panels which is usually known as 3D, prefabricated, precast or sandwich

concrete panels(Rezaifar, Kabir et al. 2008; Pavese and Bournas 2011). However, the prefabricated characteristic of

these panels is not a matter of concern in this study; therefore we shall name it concrete sandwich panel (CSP).

CSP’s consist of a double reinforced concrete layer and a polystyrene insulating core with variable thicknesses. The

polystyrene foam layer acts as the concrete mold and an acoustic-thermal insulation. The steel texture of the panel is

woven automatically in the factory. The connection of the two concrete layer reinforcements which look like truss

members is named “shear connectors” as seen in Figure 1. If there is enough shear connectors in terms of resistance

and stiffness for transmitting the shear strength caused by the panels bending, the behavior of these composite

panels is named “Fully Composite”. The thickness of the polystyrene layer varies from 4 to 20 cm. Technically the

minimum thickness of the concrete layers should be 4 cm with at least 200 kg/cm2 strength (Kabir and

Hasheminasab 2002).

Figure 1: Schema of a concrete sandwich panel

Methodology

The finite element (FE) “Abaqus/CAE 6.11-PR3” modeling software is used in this study due to its robustness and

special capabilities in modeling the material’s nonlinear behavior in comparison to similar software. For example

some of the main modeling specifications used in this study is stated in Table 1.

Table 1

Specifications used in the modeling by ABAQUS

Modeling Item Selected value or option

Analysis method Explicit. Although using the implicit method is easier but the current method is

useful and comes in handy for the upcoming dynamic modeling.

Concrete element type

C3D8R: This is a 3D element with 8 nodes and reduced integration. The use of

three-dimensional elements instead of shell elements gives the ability to model

the concrete layer’s peripheral contact behavior.

Reinforcement modeling element B31: This is a 3D element in the space consisting of two nodes with elasto-

plastic behavior and embedded in the whole solid parts.

Concrete material model Damaged Concrete Plasticity

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Is the polystyrene insulation layer

modeled? Yes

Friction coefficient between

concrete contacts 0.8 according to (Mansur, Vinayagam et al. 2008)

Number of elements through the 4

cm concrete layer 2

Interaction of rebar and concrete Concrete is modeled independently from the rebar and for considering their

interaction a software’s option named “Tension Stiffening” has been defined

Compressive behavior of concrete Kent & Park’s Model (Park and Harik 1987)

Contact surface formulation Kinematic contact method

Concrete Plasticity

Specifications

Dilation

Angle A 45 degree caused the model to validate with the relevant experimental results

Eccentricity 0.1

Fb0/fc0 1.12

K 0.67

Viscosity

parameter 0

Loading method Displacement Control Pushover

The “standard cubic sample’s strength” used for this modeling is calculated by dividing the “standard cylindrical

sample strength” to 1.25(Park and Gamble 1999). Concrete reaches its ultimate tensile strength in the tensile strain

10-4, and it has a linear behavior up to 70% of this strain which is shown in Figure 2(a) (Park and Harik 1987). In

Figure 2(b) the brittle behavior of the steel mesh is shown in tension. This brittle behavior is due to pretensioning

and carbonizing the steel meshes in order to increase its strength.

(a) (b)

Figure 2: The force-deflection curve in tension, (a) Concrete (Park and Harik 1987); (b) Panel’s

steel mesh (Kabir and Hasheminasab 2002).

Regarding the fact that intensive cyclic loading of a concrete segment will damage it and decrease its stiffness, the

two indicators dc & dt are defined as the fraction of concrete’s destruction respectively in pressure & tension. These

indicators can have values from 0 to 1, which the bigger values show more destruction. For example, when the

concrete firstly reaches its maximum strength, dc is equal to zero and thereafter its value is computed by the formula

1-σ/σCmax. FE modeling practitioners suggest selecting 80% and 99% respectively for the maximum damage in

compression and tension of concrete. If these values are exceeded in some location of the model, the location will be

colored in red as shown in Figure 3.

Figure 3: Guide to the colors used in the modeling outputs.

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The gravity load is imposed within the first seconds in the modeling and afterwards the lateral load is applied. At the

instant of applying the lateral load, the structure endures acceleration due to change in the speed of loading and that

the method of analysis is explicit. An option named “smooth step” is applied through the loading amplitude of the

ABAQUS software, to resolve such undesirable effect.

Model Validation

In order to validate the FE modeling, a reliable experiment chosen through the literature is modeled with the highest

details possible by ABAQUS. Validating CSP’s FE model under flexural loading is more challenging than other

types of loading due to the composite behavior of these panels. Figure 4 shows the experiment setup and further

details on the experiment can be found in Benayoune and Samad’s paper in 2008. Due to the lack of experiments on

CSPs as infill walls under lateral loading, the experiment setup shown in Figure 4 is chosen as the sample for this

study’s modeling validation. Figure 5 shows the comparison between the force-deflection results of the experiment

and FE modeling in this study. Both of the compared curves show the initiation of crack and final strength in

approximately 11 kN and 21 kN, respectively and their corresponding displacements also match commensurately.

However, the FE result shows a sudden drop in the force after the initial cracking which is due to a phenomenon

called “snap back”. This incident is not shown in the experimental results due to the limited number of test output

points.

Figure 4: The experiment setup for model validation (Benayoune, Samad et al. 2008).

Figure 5: Comparing the force-deflection curves of the FE modeling & the experimental outputs.

The study’s modeling

Figure 6 represents the embedment of the panel in the Reinforced Concrete (RC) frame and also Table 2 expresses

the modeling properties of the panel. A 5 cm gap is considered in Figure 6(b) for the spacing between the infill wall

and the frame columns. A frame in the base elevation of a conventional four-story building design is chosen for the

modeling in this study. Usually the frames in the lowest building story are more vulnerable to earthquake

excitations. Such frame has a rigid footing connection and a uniform surface lateral load is applied at the top of the

upper beam.

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Table 2

Alternative material properties in the model

Component Poisson

Ratio

Elasticity

Module (kg/cm2)

Yield

Strength (kg/cm2)

Tensile

Strength (kg/cm2)

Compressive

Strength (kg/cm2)

Rebar 0.3 2,000,000 4,500 - -

Frame Concrete 0.2 200,000 - 20 200

Panel Concrete 0.15 150,000 - 10 180

(a) (b)

Figure 6: (a) Panel sections (units in mm); (b) Panel scheme in the RC frame.

Loading of the Bare Frame

The bare frame chosen for the placement of the infill wall in this study is analyzed under a pushover loading and its

force-deflection behavior is shown in Figure 7. A flexural failure with a maximum strength of approximately 16 tonf

occurs according to the analytical results and also the deterioration of the system’s strength is fairly low.

Figure 7: Bare frame force-displacement curve

Loading of the Composite Frame (CF)

The phrase “composite frame” is used for the companion system of the frame and infill wall together. According to

Figure 8(b), after 0.18 cm displacement, the two corners of the panel partially fail and the system exits the linear-

elastic mode. After the system reaches its maximum strength, the diagonal failure initiates and then a sudden

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resistance drop occur after the peak strength. When the diagonal failure of the infill wall is completed, suddenly

acceleration is imposed to the system and then a residual strength of approximately 25 tonf is preserved.

(a) (b)

Figure 8: (a) The contour of dt in the CF at the peak load; (b) Force-displacement curve of CF.

Loading of the Composite Frame with Crack-Like Joints (CF-CLJ)

Many placements and geometrical configurations were tested in this study for the crack, in order to achieve a

general perception of the composite frame’s behavior plus the crack. According to Figure 9(a)&(b) a cross crack at

the middle of the wall was chosen. The void due to the crack is only applied on the concrete and the steel mesh is

left intact. The opening of the crack is equal to sqrt(2)/2 cm and is closed after approximately 1 cm lateral

displacement of the frame. This closure is observed in Figure 9(b) and results in an additional compressive strength

according to Figure 9(d). Figure 9(c) shows the spreading of force distribution at the peak lateral strength in

comparison to Figure 8(a). The sudden strength deterioration occurred in the previous systems no longer happens,

but rather a smooth degradation in the lateral stiffness is observed. Also, after a small drop in the strength at a lateral

displacement of 1 cm, the CLJ increases the strength and the system uses its reserved strength capacity.

(a) (b)

(c) (d)

Figure 9: (a) Cross crack placement; (b) Closure of the CLJ; (c) The contour of dt in the CF-CLJ

at the peak load; (b) Force-displacement of the CF-CLJ.

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Conclusion

In the recent decade, researchers have proposed a seismic retrofit strategy of selectively weakening a structural

system. However, the literature has a gap in weakening infill walls in order to prevent its brittle failure during

earthquake excitation. Also, the literature has not comprehensively studied different possible methods of weakening

the structures in order to enhance their behavior against earthquake excitations. This study offers a new constructible

and low-cost method for optimizing the structural behavior of concrete elements against seismic excitation. The

method is based on placing specific cracks named “Crack-like Joints” (CLJ) in concrete components and evaluating

its effect on the member’s performance. The method is applied on infill walls against earthquake excitation. The

force-deflection results and the amount of destruction in the concrete show that by placing CLJs suitably in the

middle of an infill wall, the brittle failure during earthquake excitation will diminish. In the presence of a suitable

CLJ in the infill wall, the force transition is spread through the wall and the stiffness and strength deterioration

during lateral loading on the frame is extremely reduced. Future works can consider other arrangements of CLJs in

structural components and evaluate the structures behavior against seismic loads. Furthermore, the general strategy

of weakening the structure in order to enhance its behavior against seismic loads is not limited to using weakened

plane joints or CLJs; others methods can also be developed.

References

Benayoune, A., A. Samad, et al. (2008). "Flexural behaviour of pre-cast concrete sandwich composite panel

Experimental and theoretical investigations." Construction and Building Materials 22(4): 580-592.

Billington, S. L. and J. Yoon (2004). "Cyclic response of unbonded posttensioned precast columns with ductile

fiber-reinforced concrete." Journal of Bridge Engineering 9(4): 353-363.

Hashemi, A. and K. M. Mosalam (2006). "Shake‐table experiment on reinforced concrete structure containing

masonry infill wall." Earthquake engineering & structural dynamics 35(14): 1827-1852.

Ireland, M., S. Pampanin, et al. (2006). "Concept and Implementation of a selective Weakening Approach for the

Seismic Retrofit of RC buildings."

Kabir, M. Z. and M. Hasheminasab (2002). Mechanical properties of 3D wall panels under shear and flexural

loading. CSCE Conference.

Kam, W. and S. Pampanin (2009). Experimental and numerical validation of selective weakening retrofit for

existing non-ductile RC frames. Proc. of ATC-SEI Conf on Improving the Seismic Performance of Existing

Buildings and Other Structures.

Kam, W., S. Pampanin, et al. (2010). "A summary of test results for selective weakening and post-tensioning for

retrofit of non-ductile RC exterior beam-column joints."

Mansur, M., T. Vinayagam, et al. (2008). "Shear transfer across a crack in reinforced high-strength concrete."

Journal of Materials in Civil Engineering 20(4): 294-302.

Pampanin, S. (2006). "Controversial aspects in seismic assessment and retrofit of structures in modern times:

Understanding and implementing lessons from ancient heritage."

Park, M. H. and I. E. Harik (1987). Optimum design of horizontally curved R/C slabs. Journal of Structural

Engineering, ASCE. 113: 2195-2211.

Park, R. and W. L. Gamble (1999). Reinforced concrete slabs, Wiley.

Pavese, A. and D. A. Bournas (2011). "Experimental assessment of the seismic performance of a prefabricated

concrete structural wall system." Engineering Structures 33(6): 2049-2062.

Page 9: Optimizing the Structural Performance of Concrete … the Structural Performance of Concrete ... wall embedded in a reinforced concrete ... type of concrete panels which is usually

51st ASC Annual International Conference Proceedings Copyright 2015 by the Associated Schools of Construction

353

Pillai, S. U. and C. Parthasarathy (1977). "Ultimate strength and design of concrete walls." Building and

Environment 12(1): 25-29.

Reinhorn, A. M., S. Viti, et al. (2005). Retrofit of structures: Strength reduction with damping enhancement.

Proceedings of the 37th UJNR panel meeting on wind and seismic effects.

Rezaifar, O., M. Kabir, et al. (2008). "Dynamic behaviour of 3D-panel single-storey system using shaking table

testing." Engineering Structures 30(2): 318-337.