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Procedía Engineering 144 (2016) 1332 - 1339

Procedía Engineering

www.elsevier.com/locate/procedia

12th International Conference on Vibration Problems, ICOVP 2015

Seismic Damage in Shear Wall-Slab Junction in RC Buildings

Snehal Kaushika* , Kaustubh Dasguptab

aResearch Scholar, Indian Institute of Technology Guwahati, Guwahati, India, 781039 bAssistant Professor, Indian Institute of Technology Guwahati, Guwahati, India, 781039

Abstract

Nonlinear time history analyses, under different levels of recorded earthquake ground motion, are carried out using the computer program ABAQUS to study the seismic damage in shear wall - slab junction of an RC wall-frame building. The beams, columns, shear walls and slabs are discretized with eight-noded solid elements. The incurred cumulative damage is determined at various locations for all the three models. It is observed that the damage gets primarily concentrated at the wall - slab junction region with increasing levels of ground motion.

© 2016 The Authors. Published by ElsevierLtd. 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 the organizing committee of ICOVP 2015 Keywords: RC wall building, wall- slab junction, seismic damage, time history analysis

1. Introduction

Most of the high-rise apartment buildings consist of spatial assemblies of shear walls and floor slabs. Due to strong earthquake shaking, the dynamic force may lead to high stress concentration at the shear wall-slab junction and subsequent localized failure. In the past, both experimental and analytical research have been carried out to simulate the nonlinear behaviour of concrete shear wall and steel/composite members [4, 11]. In the previous study the distribution of shear stresses at the slab wall junction was determined and concluded that the junction between the floor slab and structural wall is subjected to severe stress concentration [1]. It was also proposed that the design of slab-wall connection must be done considering the stress concentration to avoid redistribution of forces from walls to other elements not necessarily designed for lateral load resistance [10]. The floor slab - shear wall connection has also been investigated experimentally by considering different reinforcement detailing under combined gravity and lateral

* Corresponding author. Tel.: +91 9435746736; fax: +91 361 258 2440. E-mail address: k.snehal@iitg.ernet.in; snehalhk@gmail.com

1877-7058 © 2016 The Authors. 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 the organizing committee of ICOVP 2015

doi: 10.1016/j.proeng.2016.05.162

cyclic loading. It was observed that the wall - slab j oint with slab shear reinforcement and bent 90° at the j oint can be effective in moderate to high seismic risk region [2].

Considering the limited research carried out on seismic behaviour of wall-slab junctions, the purpose of this study is to investigate the damage caused at the shear wall slab junction due to earthquake shaking. Time history analysis of the RC shear wall- slab junction is carried out to observe the behaviour of wall-slab junction under the action of earthquake loading. To investigate the seismic behavior of the structure under earthquake action, a refined finite element model is developed using the computer program ABAQUS [5]. Nonlinear time history analyses are conducted using implicit integration method to study the tensile damage at the shear wall-slab junction.

Model 2

Roller Support

Base Acceleration along x direction Fixed Support

Fixed Support

Base Acceleration along Z direction

(a) (b) (c)

Fig.1. Geometry and boundary conditions used for time history analysis.

2. Methodology

A hypothetical plan of an RC wall-frame building is selected [6]. Three different models are created from a single lateral frame of the building, namely (a) frame model along one bay, (b) wall-slab model and (c) wall sub-assembly model (Figures 1a, 1b and 1c). The beams, columns, slabs and walls are modelled using 8-noded solid element with reduced integration (C3D8R) in the program ABAQUS [5]. A realistic nonlinear stress-strain curve is used for concrete [9] along with the Concrete Damaged Plasticity (CDP) model. As the seismic damage is primarily governed by the concrete behavior, the reinforcement is not modelled in the current study. All the Degrees of Freedom (DOFs) are restrained at the base of the wall for all the models. The out-of-plane bending of the shear wall and the vertical bending of slab are also restrained.

2.1. Concrete damage plasticity model

The Concrete Damaged Plasticity (CDP) model in ABAQUS uses the concepts of isotropic damaged elasticity and hardening plasticity to represent the behavior of plain and reinforced concrete [6]. The model uses the yield function of Lubliner et al. [8] with the modifications proposed by Lee and Fenves [7] to account for the multiple damage states (compression and tension damage). The flow potential is defined using a Drucker-Prager function of the hyperbolic type. The model is a continuum, plasticity-based, damage model for concrete with the two principal failure

mechanisms as tensile cracking and compressive crushing of concrete. The evolution of the yield (or failure) surface is controlled by two hardening variables, tensile and compressive equivalent plastic strains, linked to failure mechanisms under tension and compression loading.

Among the input parameters for CDP, the modulus of elasticity, Poisson's ratio, yield stresses in compression and tension are considered as 25,000 MPa, 0.2, 25 MPa and 3.5 MPa respectively. The dilation angle, eccentricity, viscosity parameter, shape factor (Kc) and stress ratio 0j,o/°co are assumed as 55°, 0.1 [3], 0.01, 0.667 and 1.16 respectively. Under uniaxial tension, the stress-strain response follows a linear elastic relationship until the onset of micro-cracking in concrete (failure stress) (Figure 2). Beyond this limit, the micro-cracked concrete is characterized by a softening stress-strain response. Under uniaxial compression, the response is linear till the value of initial yield. In the plastic regime, the response is typically characterized by stress hardening followed by strain softening beyond the ultimate stress. When the concrete specimen is unloaded from any point on the strain softening branch of the stress-strain curve, the unloading response is weakened and the elastic stiffness of the material is damaged. The degradation of the elastic stiffness is characterized by two damage variables, dt and dc as given in Eqs. 1 and 2 respectively [11].

dt = l~ L , \17 x>l, x = -, at = 0.312A2 (1)

r (x-l)17+x] et v JZ w

dc = l- I , n x>l, x = -, at = 0.157/,0-785 - 0.9 0 5 (2)

c y][ad(x-l)2+x] e/ f Jc w

where, ft is the average value of axial tensile strength, fc the average value of axial compressive strength (taken

as 25 MPa in the study), s the compressive or tensile damaged plasticity strain, ec the compressive strain corresponding to fc (taken as 0.002 in the study), and et the tensile strain corresponding to ft.

2.2. Tensile behavior of concrete

As discussed, concrete behaves as a linear elastic material till the uniaxial cracking strength, ft, after which softening behavior is assumed. The softening rate depends on the size of the elements in the crack region. The post-failure behavior for direct straining across cracks is modeled with a TENSION STIFFENING option, which is specified by either post-failure stress-strain relation or by applying a fracture energy based cracking criterion. In this study, tension stiffening is defined with an assumed post-failure stress-strain relation (Figure 3).

Fig. 3. Uniaxial tensile stress-strain relationship for concrete

2.3. Compressive behavior of concrete

In the current study, the uniaxial stress-strain curve is linearly elastic up to 30% of the maximum compressive strength (Figure 4). Beyond this point, the curvilinear nature extends till the maximum compressive strength, fc. The post-peak softening behavior of the stress-strain curve, till the crushing failure at an ultimate strain eu, is given by the parabolic expression of Eq. (3) as,

^NK1-^)] (3)

where, Eq is the strain related to the peak stress.

Fig. 4. Uniaxial tensile stress-strain relationship for concrete

3. Ground motion

A ground motion, recorded during 1997 Indo-Burma earthquake at station Jellapur with a Peak Ground Acceleration (PGA) of 0.14g (Figures 5a and 5b), is selected for dynamic analysis. During the analysis, no damage is observed in the models with PGA of 0.14g. Thus, the same motion is scaled up twice to generate another two ground motions with PGA of 0.56g and 1.12g. All the three ground motions are applied at the base of the model in the in-plane direction to carry out nonlinear time-history analyses of the three models.

(a) (b)

Fig. 5. (a) Recorded horizontal ground motion at Jellapur station during 1997 Indo-Burma earthquake and (b) Fourier spectrum of the ground motion

4. Finite element analysis result

While carrying out the nonlinear time history analyses, damage is introduced in CDP model in tension and compression as per Eqs. (1) and (2) respectively. Concrete damage is assumed to occur in the softening range in both tension and compression. In compression, the damage is introduced after reaching the strain level Eg. Figure 6 represents the tensile damage pattern for Model 1 (Figures 6a, 6b and 6c). It is observed that the damage started at the base of the shear wall first and then shifts to the beam column joint of the frame (Figures 6d, 6e and 6f).

Fig. 6. Tensile damage pattern in Model 1: damage pattern in the frame for PGA values of (a) 0.14g, (b) 0.56g (c) 1.12g; detailed damage pattern in wall and wall-slab junction for PGA values of (d) 0.14g, (e) 0.5 6g and (f) 1.12g.

As the acceleration is applied in the plane of the shear wall, maximum principal stresses are developed at the base of the wall leading to cracking of concrete. The damage also depends on the magnitude of acceleration with the maximum damage incurred for PGA of 1.12g. The damage increases till the attainment of PGA of the ground motion, thereafter it remains constant. The cumulative tensile damage patterns are shown in Table 1. On carrying out nonlinear time-history analyses for Model 2, the damage is observed to initiate at the base of the shear wall, and then propagate to shear wall - slab junction for every floor of the building (Figures 7a, 7b and 7c) under the different PGA values. The cumulative damage is determined and is observed to increase at the wall-slab junctions from the lower level. The cumulative damage shows that the damage starts earlier at the base of the shear wall and propagates to the upper stories (Table 1). The maximum damage level is observed around the time of occurrence of PGA in the ground motion. It is also observed that average tensile damages of the first story slab are more severe than other stories. As floor slab is not expected to get damaged during earthquake shaking, the earthquake-resistant design philosophy for floor slabs needs to be prescribed. The comparative tensile damage patterns for Models 1 and 2 are illustrated in Table 1.

(a) (b) (c)

Fig. 7. Tensile damage pattern in Model 2 for PGA values of (a) 0.14g, (b) 0.56g and (c) 1.12g

Figures 8a, 8b and 8c represent the tensile damage pattern for Model 3. In this case, no significant damage is observed at the slab-wall junction. Most of the damage occurs at the bottom of the wall with the dominance of squat wall effect. The cumulative tensile damage at the base of the shear wall is shown in Figure 9.

(a) (b) (c)

Fig. 8. Tensile damage pattern in Model 3 for PGA values of (a) 0.14g, (b) 0.56g and (c) 1.12g

Table 1. Comparison of average tensile damage parameter for Models 1 and 2 under different PGAs

Model 1

Model 2

5. Discussion and Conclusion

To predict the behavior of shear wall - floor slab junction, the finite element analysis with the concrete damaged plasticity model is used. In particular, (a) frame model along one bay, (b) wall-slab model and (c) wall sub-assembly model are simulated and analyzed under scaled ground motions with different PGA values. The salient conclusions of the study are as follows:

(a) The maximum stress concentration initially develops at the base of the shear wall and then propagates to the wall-slab junction in the first floor. The level of damage depends on the PGA level of applied ground motion.

(b) In case of wall sub-assembly model, the aspect ratio of the model causes the squat wall behavior to dominate its response. Thus, no significant damage is observed at the slab-wall junction.

(c) The observed damages in floor slab highlight the requirement of prescription of a revised earthquake-resistant design philosophy for floor slabs. Currently, this guideline is absent in the earthquake-resistant design guidelines of different countries.

0.8 0.7

-PGA= •••• PGA=C ■12g -56g

— — PGA=C -14g

r /----------------

6 S 10

Time (sec)

Fig. 9. Cumulative tensile damage pattern in Model 3 for PGA values of 0.14g, 0.56g and 1.12g

Acknowledgments

The support and resources provided by Department of Civil Engineering, Indian Institute of Technology Guwahati and Ministry of Human Resources and Development, are gratefully acknowledged by the authors.

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