Seismic Damage Index Based on Fractal Dimension ...

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title No. 114-S134

Seismic Damage Index Based on Fractal Dimension of Cracking on Thin Reinforced Concrete Walls by Julian Carrillo, Dario Dominguez, and Nestor Prado This paper proposes an empirical damage index for rapid estimation of damage level of thin and lightly reinforced concrete walls for housing subjected to seismic demands. The proposed damage index is based on the fractal dimension of the cracking observed during seismic tests of 39 wall specimens constructed with typical characteristics of this type of housing. Variables of the experimental program were the type of concrete, aspect ratio of walls, web steel ratio and type of web shear reinforcement, and the testing method. The effect of these factors on the cracking pattern of walls was assessed by using an advanced statistical analysis method—namely, factorial design. Expected damage index at defined limit states and performance levels are proposed for computing the residual capacity of walls for code-based seismic design and rehabilitation. Keywords: concrete walls; cracking; factorial design; fractal dimension; housing; lightly reinforced; seismic damage index; thin walls.

INTRODUCTION Crack width is one of the main indicators of damage severity experienced by reinforced concrete (RC) structural components during an earthquake. Moreover, the cracking pattern on wall surface is associated to the experienced seismic demands—that is, to the variation of shear stresses in relation to the height of the wall. Therefore, several studies have focused efforts on estimating the seismic performance level in terms of damage. For instance, Carrillo and Alcocer1 have applied a damage index based on the relation between the damaged area (area of cracks) and the area of the façade of the RC wall. Carrillo2 has proposed a damage index based on the stiffness degradation of walls. Such index depends on the story-drift ratio and the number of cycles experienced by the wall during a particular seismic event. The structural engineering community has applied the approach of fractal theory for proposing alternative and innovative methodologies of damage and performance evaluation. Chiaia et al.3 carried out fracture tests of concrete for assessing the failure modes using the fractal dimension of cracking patterns. Tzu-Kang et al.4 proposed a novel bridge health monitoring system and a safety index based on the fractal dimension of the correlation between the scour depth and the fundamental period of the bridge superstructure. Similarly, Hadjileontiadis and Douka5 proposed a cracking detection model based on the fractal dimension of the vibration mode shapes and the fundamental period of plate elements. Li et al.6 used the fractal theory for describing numerically the shape and distribution of aggregates for concrete. Erdem7 considered the fractal analysis and digital images from three-dimensional (3-D) X-ray tomography for numerically evaluating the segregation resistance and cracking induced by accelerated corrosion of self-consolidating lightweight concrete. ACI Structural Journal/November-December 2017

Miao et al.8 studied fractal and multifractal characteristics of 3-D asphalt pavement macro-structures in terms of its depth and friction coefficient. Werner et al.9 used a fractal-based approach for assessing numerically the parameters related to fractured surface of concrete using laser scanning techniques. Mistakidis and Panagouli10 evaluated the ultimate strength of retrofitted shear wall elements involving the connection between rough interfaces and fractal geometry. Farhidzadeh et al.11 pioneered the approach of fractal analysis for studying the cracking of concrete walls. They implemented a theoretical model based on a damage index that depends on the fractal dimension of the cracking propagation recorded in concrete walls. Such damage index was intended to remove the subjectivity and the variability associated with damage assessment based on visual inspection. Farhidzadeh et al. highlighted the simplicity and effectiveness of such approach for evaluating the damage related to a natural hazard. A literature review carried out by authors also reveals lacking of a guideline for seismic damage evaluation of concrete walls for low-rise housing. Low-rise concrete housing in Latin America embraces particular characteristics such as thin concrete walls, low concrete strength, low axial loads, low steel reinforcement ratios, and web shear reinforcement made of deformed bars and welded-wire reinforcement. Current guidelines for estimating seismic damage are based mainly on the qualitative judgment of engineering and are more directed to medium- or high-rise buildings. Damage quantification based on visual inspection of cracking pattern is a subjective estimate because the damage criterion depends on the expertise of the inspector engineer. Although characteristics of cracks (length, maximum width, and residual width) are key indicators of structural damage, pattern and distribution of cracks of the damaged structural component should be also considered. In addition, most of current earthquake-resistant building codes do not include explicit recommendations of tolerable damage and thus they do not evaluate explicitly the performance of the building after the onset of damage.12 This paper proposes a damage index for rapid estimation of the damage level and the residual performance of thin and lightly reinforced concrete walls subjected to seismic demands. The proposed damage index is based on the fractal dimension of the cracking observed during tests of 39 thin RC wall specimens constructed with typical characteristics of this type of housing. Variables of the experimental ACI Structural Journal, V. 114, No. 6, November-December 2017. MS No. S-2017-025.R1, doi: 10.14359/51700919, received February 14, 2017, and reviewed under Institute publication policies. Copyright © 2017, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

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