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Procedía Engineering 114 (2015) 298 - 305

Procedía Engineering

www.elsevier.com/locate/procedia

1st International Conference on Structural Integrity

Comparative study on the behavior of slender RC walls with two

methods of reinforcement

Ourdia Belaidia Madjid Almansbaa, Djamila Amrania, Fatma Taouche-Khelouia, Aghiles Nekmouchea, Neceur Eddine Hannachia

aLaboratory of LAMOMS, University Mouloud Mammeri of Tizi Ouzou, 15000, Algeria

Abstract

RC walls (reinforced concrete) may be subdivided into three categories from the point of view of mechanical behavior which are mainly dependent on the geometric relationship of the height to the width (h/l). Also, the RC walls are defined as slender when this relationship is higher than 1.5, and considered short if it is less than 1.0. When the relationship is in between these two values, the element is called current or moderately slender RC wall. The use of RC walls in seismic regions is becoming more frequent. The reason is that RC walls, in addition to their enabling role in line to-screws of vertical loads, are particularly effective concerning resistance to horizontal forces, thus withstanding the greater part of the seismic action. The RC walls are shaping the behavior of structures, and play a critical role for security on several typologies of structures.

This paper focuses on the analysis of the behavior of slender RC walls according to two different methods of reinforcement; the method of bands, and the classical method. A local approach is used by modeling the RC walls solicited under horizontal loading. The numerical model used for concrete is the model "Concrete Damage Plasticity" (CDP) and for steels, the elastic-plastic model serves to work the hardening isotropic. The models allow the visualization of the damage and determination of the failure mode. The numerical aspects are particularly detailed.

© 2015Published byElsevierLtd.This isanopenaccess article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of INEGI - Institute of Science and Innovation in Mechanical and Industrial Engineering Keywords: Simulation, RC walls, reinforcement, damage, method of bands, classical method.

1. Introduction

The reinforced concrete walls (RC walls) are vertical structures of two dimensions. They are generally strong and

* Corresponding author. Tel.: +213-559-415-905. E-mail address: bel_ouar@yahoo.fr, belle_ouar@yahoo.fr

1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of INEGI - Institute of Science and Innovation in Mechanical and Industrial Engineering doi:10.1016/j.proeng.2015.08.072

resist to horizontal forces in their plan. They are present in buildings and play an important role for the safety even if they are under the seismic loads [1-2].

From the mechanical behavior point of view, RC walls can be subdivided into three categories which are mainly dependent on the geometric relationship of the height to the width (h/l). ). Thus, the RC wall is defined as slender when this relationship is higher than 1.5, and is considered short if it's less than 1.0. When the ratio is in between these two values, the element is called current or moderately slender RC wall. The breaking mode of the slenders RC walls is governed by bending, but the breaking of the short RC walls is occurs by shearing. For moderately slender RC walls, the breakage is produced by the coupling bending-shear [3-4-5].

In this work, we are interested in the behavior of the RC walls rushed in reinforced concrete scrap according to two different methods, the method of bands (MDB) [6], and the classical method (MC) [7]. We used a local approach by modeling the RC walls solicited under horizontal loading. The numerical model used for concrete is the model 'Concrete Damage Plasticity'(CDP) [8] and for steels the model used is the model 'elastic-plastic to work hardening isotropic' [8].

The geometry and dimensions of the studied RC wall are represented in Fig. 1.a. The slenderness is given by: h/1 = 1.6. The RC wall is solicited by a bending moment M and a normal effort N which are respectively: M =

48 t.m, N = 18 t.

2. Modeling of steels behavior

The steel is modeled using anelastoplastic behavior law with the isotropic hardening based on the three-dimensional criterion of von Mises stresses. This model is incorporated into the code of finite elements ABAQUS [8].

3. Modeling of concrete behavior

The coupling between plasticity (representation of irreversible deformations) and damage (cracks representation) is used to describe the mechanical behavior of concrete. This model is integrated into the code of finite elements ABAQUS (Concrete damage plasticity, (CDP)) [8]. The characteristics of concrete, steel and the model parameters are listed in Table 1.

Table 1. Materials mechanical characteristics

Mechanical properties of concrete Young's modulus E (MPa) Poisson's ratio V Density P Tensile damage threshold Dt (MPa) Compressive damage threshold Dc (MPa) Compressive strength (MPa) Tensile strength (MPa)

32000 0,18 2,4-E006 0,00628 0,00818 25 2,1

Mechanical properties of steel Young's modulus E (MPa) Poisson's ratio L> Density P Yield strength (MPa)

210000 0,3 7,85E-006 400

4. Study of slender RC wall by the method of bands (MDB) [6]

The method of bands (MDB) is a materials resistance method, which does not take into account the dynamic amplification phenomena due to earthquakes. The efforts are summarized in a vertical resultant, equivalent to the most unfavorable position (N, M) which is supposed to be taken over vertical armatures. The calculation will be done for the bands of width d. The width of the band must satisfy the following condition:

with he : height of RC wall.

lc : length of the compressed area.

The final reinforcement for the RC wall studied by the method of bands and respecting the recommendations of the Algerian earthquake regulations [9] is:

• 20 vertical bars of O 6 divided into two layers, spaced of 20cm,

• 8 vertical bars of O 10 which form the bollards of the ends,

• 42 horizontal bars of O 6 divided into two sheets with a spacing of 20 cm,

• 42 frames of O 6 distributed along the bollards spaced of 20cm. The corresponding reinforcement diagram is shown in Fig. 1.b.

5. Study of slender RC wall by the classical method (MC) [7]

The same RC wall is studied with the classical method of reinforced concrete [7]. It's solicited with the same efforts (M, N). So, taking into account the recommendations of RPA [9], the final reinforcement becomes:

• 20 vertical bars of O 8 divided into two layers, spaced of 20cm,

• 8 vertical bars of O 16 which form the bollards of the ends,

• 42 horizontal bars of O 8 divided into two layers with a spacing of 20 cm,

• 42 frames of O 8 distributed along the bollards spaced of 20cm. The corresponding reinforcement diagram is shown in Fig. 1.c.

(a) (b) (MDB) (c) (MC)

Fig. 1. (a) Dimensions and geometry of RC wall, (b) reinforcement of RC wall by the method of bands (MDB), (c) reinforcement of RC wall by the classical method of reinforced concrete (MC).

6. Numerical simulation

The RC wall is solicited by a load at the top and a constraint embedding at the base. The load and constraint at the limits of the RC wall are represented in Fig. 2. For the simulation, a local approach was used to model the RC wall solicited with horizontal load. The models used permit to visualize the damage and determine the failure mode.

Fig. 2. Load and conditions at the limits of the RC wall. 6.1. Representation of results in the concrete

6.1.1. Displacements in the RC walls: Evolution of displacements in the RC wall is represented in Fig. 3.

U, Magnitude - i «./&;:• U--8.®+0 J- +B.0S9e+0

, flagoitude -+6.8№t01 +6.24ee+01 +5.67M1 üiÄ I4.SM1 +3.97M1 +3.40iet01 +2.TOÜ1 +2.271eföl +1.7GM1 +1.13M Ï5.67M' -O.OODefOC

Fig. 3. Evolution of displacements in the RC wall.

From Fig. 3, it's observed that the displacement in the RC wall with the method of bands is 97.19 mm but a lower displacement (68.14 mm) is obtained with the classical method.

6.1.2. Vertical displacement in RC walls (U2): The evolution of vertical displacement (U2) in the RC wall is represented on Fig. 4.

Fig. 4. Vertical displacement in RC wall.

According to the second direction U2 (Fig. 4), the RC wall with the method of bands has moved of 47.26mm and with the classical method, it has reached 17.14mm.

6.1.3. Stresses in RC walls: The evolution of stresses in the concrete is shown in Fig. 5.

Fig. 5. Evolution of stresses in the concrete.

The maximum stress reached in the RC wall reinforced with the method of bands is 66.03MPa, which is lower than the maximum stress of the classical method which equal to 73.22MPa. This is due to the breaking mode of a slender RC wall heavily armed that crushes the concrete at its base.

6.1.4. Real deformations in RC walls: The evolution of strains in the RC wall is shown in Fig. 6.

Fig. 6. Evolution of strains in the RC wall.

The RC wall reinforced with the method of bands was deformed of 0.48 and with the classical method; it was distorted with a lower value equal to 0.37. This difference has no meaning because the concentration of stresses in the concrete of the RC wall using the classical method is important.

6.1.5. Visualization of damage in tensile: the spread of damages in tensile, in the RC wall, is represented in Fig. 7.

DAHAGET (tog: 75*1

i+S.288e-DL +5.J64e-01 +5.240e-0l +4.Ä-01 _ +4.192e 01 I-+3.M86-01 I - +3.144e-GL l-+2.S20e-01 I-+2.0966-01 I-+1.5726-01 l-+l.M8e-01 ---52406-02

L-L +0,0№+00

Fig. 7. Propagation of damages in tensile in the RC wall. In two RC walls, the damage value reached is the same, even if the spread is different.

6.1.6. Visualization of a damage in compression: The spread of damages in compression, in the RC wall, is shown in Fig. 8.

' ' ' MMGEC

(Aig: m)

S+8.18M1 H.5'»-01 +6 .№-01 +S.13M1 +5.45M1 +4.7] Ml +4.®e-01 M.41ie-01 HJ2M1

— MMe-Ol

- tl.354e-01 _ +S.82M2 ■- rt.OOOeWO

Fig. 8. Propagation of damages in compression in the RC wall.

In both RC walls, the maximum value of damage reached is the same. The RC wall using the method of bands reached the maximum value at 0.4 seconds, but that of the classical method has reached it at 0.6 second.

6.2. Representation of results in steel bars

6.2.1. Stresses in the RC wall: the stresses in steel bars are given in Fig. 9.

5,511 (Aig: JM)

■REM MM

Fig. 9. Development of the stresses in the RC wall.

The steels of RC wall with the method of bands plasticize first at tenth increment, of 0.50 seconds, while steels of the classical method enter in plasticization after a time equal to 0.75 second, at fifteenth increment.

6.3. Local study and comparison of results

From observations and comments on the various results, and for a better validation, two elements located in critical areas were chosen:

6.3.1. Interpretation of results in a compressed concrete element: the selected item in the compressed area is shown in Fig. 10.

Fig. 10. Selected item in the compression area.

The stresses-strains curve is given in Fig. 11. The capacity curve is given in Fig. 12.

Fig. 11. Stresses-strains curve. Fig. 12. Strengths-displacements curve.

Fig. 11 shows that the concrete has an elastic behavior with a compressive stress that turns around 62 MPa for both reinforcement models, and a deformation of 0.0018. Beyond these values, the stress drops for the two cases of reinforcement. In the classical case, the stress is kept at a value of 5.5 MPa with a deformation of 0.041, then decreases again to a value of 1.31MPa with a deformation of 0.112. This is due to a better containment that prevents the fragmentation of the concrete.

Fig. 13 show that the RC wall of the classical method (MC) has a higher bearing capacity than of the method of bands (MDB). The RC wall of the classical method resumes a force of 40 kN causing a displacement of 60.33 mm and that of the method of bands resumes 33.27 kN and generates a displacement of 84.93 mm.

6.3.2. Interpretation of results in a stretched concrete element: the selected item is represented in Fig. 13. The stresses-strains curve in the concrete is shown in Fig. 14.

In Fig. 14, the concrete of the two RC walls touches simultaneously the drop point of the stress (peak) and within a very short time, about 0.05 seconds. This explains and confirms that whatever the method of reinforcement, the concrete remains a very brittle material in tension. It has an almost similar resistance with 1.23 MPa in concrete (the stresses of the breaking with tensile). Therefore, the forces are supported by the steels.

6.3.3. Interpretation of results in steels for a tense element: the selected item is shown in Fig. 15. The stressesstrains curve in the steel is given in Fig. 16.

To similar stresses, the plasticity is reached in the case of the method of bands to a strain of 0.016, and in the case of the conventional reinforcement, the plasticity is achieved at a strain of 0.014. Because of similar characteristics of used steels in simulated models in this paper, Fig. 16 is here to testify the elastic limit stress and the importance of plastic level of the steels, through which is spread all abilities in terms of ductility and dissipation.

Fig. 15. Representation of studied item. Fig. 16. Stresses-strains curve in steels.

7. Conclusion

This study focuses on two types of slender RC walls designed and reinforced according to two methods: MDB and MC. The simulation was done with ABAQUS Software.

The results obtained have permitted to compare the reinforced model with MDB and MC concerning the stresses, strains, displacements and damages. The failure criterion of slender RC walls was checked (bending) [1]. The different results obtained are:

> For concrete

* In terms of stresses, there is an increase of 9.81% in the classical RC wall.

* In terms of strains, it's registered a decrease of 25.72% in the RC wall of MC due to the reinforcement.

* It's noted that a decrease of 9.81% of displacements in the RC wall that reflects the stability provided by the reinforcement.

> For steels

* A decrease of 26.14% of plastic strains in steels using the MC.

* Steels of MDB reach their limits of plasticity before those of MC.

* In terms of carrying capacity, the RC wall of MC can support more charges.

At the end, it was verified that MC offers best resistance for RC walls (high load capacity, less of strains), leading to a higher stability. The method of bands, having a smaller steel section, shows superiority in terms of deformation, displacement, and a lower bearing capacity. This increases their vulnerability during earthquakes.

However, the boundaries of RC walls are "solicited by the seism". It's required to reinforce these boundaries, by increasing the diameter of reinforcement [10], or by the vertical reinforcement of lattice in double faces [5]. Based on these results, the reinforcement using the MC greatly improves the RC wall.

References

[1] V. Davidovici & al., Génie parasismique, Ed. Ecole Nationale des ponts et chaussées (1985).

[2] V. Davidovici, Séisme de BOUMERDES - 21 mai 2003, Preliminary report. Ministry of habitat. République algérienne démocratique et populaire. June 8, (2003).

[3] B. Faure, Prise en compte du comportement du béton en cas particulier des voiles plans en béton armé, en génie parasismique, Ed. ENPC, (1985).

[4] T. Paulay, M .J.N. Priestley, Seismic design of reinforced concrete and masonry buildings, New York: Willy & Sons, (1992).

[5] Eurocode 8, Design of structures for earthquake resistance — Part 1: General rules, seismic actions and rules for buildings. European standard. NF EN 1998-1, 2005.

[6] DTU 23-1-, Parois et murs en béton banché, CSTB. February, (1990).

[7] BAEL 91 révisé 99, Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états limites (1999).

[8] ABAQUS, Version 6.12.

[9] RPA 2003, Règlement parasismique algérien, (1999) ; Reprinted (2003).

[10] Règles PS-92, Règles de construction parasismique, Règles PS applicables aux bâtiments, dites Règles PS 92, french standard, AFNOR 1995.