Advances in Materials Science and Engineering

Volume 2016 (2016), Article ID 6475161, 9 pages

http://dx.doi.org/10.1155/2016/6475161

## Shear Stress-Relative Slip Relationship at Concrete Interfaces

Department of Plant & Architectural Engineering, Kyonggi University, Suwon, Republic of Korea

Received 1 May 2016; Revised 29 May 2016; Accepted 28 June 2016

Academic Editor: Pavel Lejcek

Copyright © 2016 Keun-Hyeok Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study develops a simple and rational shear stress-relative slip model of concrete interfaces with monolithic castings or smooth construction joints. In developing the model, the initial shear cracking stress and relative slip amount at peak stress were formulated from a nonlinear regression analysis using test data for push-off specimens. The shear friction strength was determined from the generalized equations on the basis of the upper-bound theorem of concrete plasticity. Then, a parametric fitting analysis was performed to derive equations for the key parameters determining the shapes of the ascending and descending branches of the shear stress-relative slip curve. The comparisons of predictions and measurements obtained from push-off tests confirmed that the proposed model provides superior accuracy in predicting the shear stress-relative slip relationship of interfacial shear planes. This was evidenced by the lower normalized root mean square error than those in Xu et al.’s model and the CEB-FIB model, which have many limitations in terms of the roughness of the substrate surface along an interface and the magnitude of equivalent normal stress.

#### 1. Introduction

The direct shear transfer mechanism has been examined significantly in highly stressed concrete interfaces such as those found in the details between columns and corbels, squat shear walls, and foundations, in dapped end beams, and in precast concrete assemblies [1]. Load transfer along concrete interfaces subjected to simultaneous shear and lateral forces applied normally to the interfaces is commonly explained using the shear friction mechanism [2, 3]. Many empirical models [4–7] have been proposed to estimate the shear friction strength of the interfacial shear planes on the basis of different experimental programs, the shear friction theorem associated with the truss model, and/or the Mohr-Coulomb failure envelope. Yang [8] derived an integrated model for the shear friction strength of concrete interfaces based on the upper-bound theorem of concrete plasticity. The proposed models successfully demonstrated that the shear friction strength of concrete interfaces is significantly governed by concrete cohesion and equivalent normal stresses generated from the tensile resistance of transverse reinforcements crossing the interface and external forces applied normally to the interface. However, such models dealt insignificantly with shear displacement along the interface; as a result, very few equations are available to generalize the function of shear stress for shear slip assessment.

Knowledge of the shear stress-relative slip relationship at concrete interfaces is essential for ensuring serviceability and ductility of concrete structures. Xu et al. [9] attempted to assess the shear stress and slip characteristics of an initially uncracked concrete interface using a total of 36 sets of simulated data obtained from finite element analysis. In their nonlinear equations, the shear stress-relative slip relationship was characterized using a trigonometric function and reference values such as shear friction strength and different slip amounts. However, the roughness of the substrate surface along the interface was not considered in the shear stress-relative slip relationship proposed by Xu et al. Moreover, the reliability of the model needs to be further examined because the curve fitting is fundamentally followed by finite element analysis using the LS-DYNA software because of a lack of available test data. The CEB-FIP model code [3] determines the relative slip amount as a function of the dowel action of transverse reinforcements crossing the interfaces. The dowel action of transverse reinforcements for construction joints is explained simply as the product of the friction coefficient and the equivalent normal stress applied to the interface. However, the code does not specify the nonlinear behavior of the shear stress-relative slip curve, including the slope at the ascending and descending branches. Hence, a more sophisticated model needs to be developed in order to rationally understand the relative slip characteristics at concrete interfaces and ensure a design perspective of serviceability and strength in terms of shear friction resistance.

The present study proposes a relatively simple and rational model for the shear stress-relative slip curves of concrete interfaces with monolithic castings or smooth construction joints with no special treatment. For this model, a key parameter determining the slopes of the ascending and descending branches is formulated from a parametric fitting approach to the test data. The initial shear cracking stress, shear friction strength, and relative slip amount at the peak shear stress are selected as reference indices for the shear stress-relative slip curve. The initial shear cracking stress and relative slip amount corresponding to the shear friction strength are formulated from a nonlinear regression analysis using test data for push-off specimens. The shear friction strength is determined from the generalized equations on the basis of the upper-bound theorem of concrete plasticity [8]. The reliability of the developed model is verified using a normalized root mean square error obtained from a comparison of model estimates with the experimental data. The comparisons also examine the reliability of Xu et al.’s model for monolithic joints and the CEB-FIP model code for smooth construction joints.

#### 2. Mathematical Equation for Shear Stress-Relative Slip Curves

According to Yang [8] and Xu et al. [9], the shear stress-relative slip relationship at concrete interfaces can be characterized as follows (see Figure 1): with compatibility along the interface, slip displacement along the interfacial shear plane begins with the occurrence of a shear crack; nonreinforced interfaces fail immediately with the occurrence of the initial shear crack, indicating that the shear stress-relative slip curve is insignificant for nonreinforced interfaces; reinforced construction joints commonly exhibit a typical stress flow phenomenon, showing that the relative slip after the peak stress increases rapidly without a noticeable drop of the applied shear stress; reinforced monolithic joints have greater slopes at the descending branch as compared to construction joints; and after the peak stress, shear stresses applied to reinforced monolithic joints drop sharply up to a certain level and then remain constant, showing a stress flow phenomenon after the sharp stress drop. Hence, the shape of the shear stress-relative slip curve of concrete interfaces can be similarly generalized as a parabola with its vertex at the peak stress, as plotted in Figure 1. In this study, the following nonlinear equation is applied in generating a complete curve:where (=) is the normalized shear stress, (=) is the normalized relative slip, is the shear stress along the interfacial failure plane corresponding to relative slip , is the shear friction strength, and is relative slip at peak shear stress. The physical meaning of the equation gives the following boundary conditions (see Figure 1): for , representing that the slip displacement along the interfacial shear plane begins with the occurrence of cracks, where is the initial shear cracking stress; for , representing the peak stress; and for at the peak point. From the first condition, as the -intercept of the curve can be set to . Substituting the second condition into (1), can be written as . The tangential modulus at a point, , is written as follows:The third condition for (2) is that is equal to . Therefore, the shear stress-relative slip curve of concrete interfaces can be expressed in the following basic form with the key parameter :Note that the slopes of the ascending and descending branches of the curve depend on the value of ; however, the value of differs for each branch.