MARS and Neural Network Models for Shear Strength Prediction of Squat Reinforced Concrete Walls: Shear Strength of Squat Reinforced Concrete Walls

Introduction

Reinforced concrete (RC) walls with a ratio of height to length of less than or equal to two, commonly described as squat or short walls, are widely used structural components in many commercial buildings and nearly all safety-related nuclear structures. Squat walls are generally grouped by plan geometry, namely, rectangular, barbell, and flanged. The performance of these short (squat) walls is most important because they are designed to provide most of the lateral stiffness and strength to resist earthquake shaking or wind loadings. Accurate modelling of the response of squat walls is essential considering that the conventional buildings are likely to experience multiple deformation cycles at or beyond yield in maximum earthquake shaking. Current design provisions in codes and standards for reinforced concrete walls, such as the ACI 318-08 (ACI, 2008) and ASCE 41-06 (ASCE, 2007), focus on tall (slender) walls and pay less attention to squat walls, although the latter is far more common in practice.

A desirable earthquake resistant design philosophy for RC walls is to prevent shear failure in earthquake shaking. Experimental studies have shown that well designed and detailed slender walls will yield in flexure and not fail in shear. In contrast, squat walls are prone to shear failure that is generally associated with rapid loss of strength and stiffness under cyclic loading. Three types of shear failure are commonly observed in squat walls, namely, diagonal tension, diagonal compression, and sliding shear (Paulay & Priestley, 1992). If a shear failure occurs after the wall achieves its flexural strength, the failure mode is considered mixed and termed a flexure-shear failure (e.g., flexure-diagonal tension). It is generally recognized that the design parameters such as horizontal and vertical web reinforcement ratios, wall geometry, and axial force also affect the behaviour of squat reinforced concrete walls.

A significant number of experiments on squat reinforced concrete walls have been completed in the past 60 years. The first experimental programs on squat walls were conducted at Massachusetts Institute of Technology and Stanford University (Galletly, 1952; Benjamin & Williams, 1956) on bar bell cross-section. These tests were performed using monotonic loading and focused mainly on evaluation of peak shear strength. In the United States, the first cyclic tests on squat walls were performed by Barda (1972). Almost in the same period, a substantial number of cyclic loading experiments on squat walls were conducted in Japan (Hirosawa, 1975).

Although there is substantial experimental data in the literature on squat walls, current design procedures have been essentially unchanged for more than 40 years. One such example is the prediction of peak shear strength, which is the key parameter in the design of squat walls. The empirical equations and procedures available to calculate the peakshear strength of squat walls do not correlate well with the experimental results with substantial scatter in the predictions. In addition, one limitation of using the commonly used five sets of predictive equations, i.e., Section 11.9 of ACI318-08 (ACI, 2008), Section 21.9 of ACI 318-08 (ACI, 2008), Barda et al. (1977), ASCE 43-05 (ASCE, 2007) and Wood (1990), is the reliance on the use of many assumed intermediate parameters and generally these intermediate parameters are functions of other introduced parameters. Some use of Artificial Neural Networks in structural engineering includes Soleimanbeigi and Hataf (2005, 2006), and Padmini et al. (2008). Recently, other soft computing techniques including the Support Vector Machine (e.g., Samui, 2012) and Relevant Vector Machine (e.g., Samui 2012), the Genetic Programming (e.g., Shahnazari & Tutunchian, 2012), and Fuzzy models (e.g., Padmini et al. 2008) have been applied to foundation engineering for estimation of the ultimate bearing capacity of footings on cohesionless soils. Despite reasonable accuracy obtained by these soft computing methods, the developed models are generally difficult to interpret.