Finite Element Fracture Analysis of Steel-Concrete Bond

The effect of deformation pattern on bond strength is studied using a finite element model of a beam-end specimen. The model includes concrete, steel, and transverse reinforcement substructures. A splitting crack is assumed to occur along the specimen center line, and only onehalf of the specimen is modeled. Splitting concrete is modeled using the nonlinear fracture mechanics approach known as the "fictitious crack model" (Hillerborg et al. 1976). The steelconcrete interface is modeled using special link elements that follow a Mohr-Coulomb failure law. Bond strength is studied as a function of rib height, rib shape, concrete cover, lead length, embedded length, and transverse reinforcement. A 1 in. square bar with ribs heights of 0.06 in. or 0.09 in. is used. Models with 1, 2, and 3 in. covers and one-half in. and 2 in. lead lengths are studied. Embedded lengths range from 0.82 to 7.86 in. The study shows that steel-concrete interaction can be accurately represented by placing interface elements only on the compression faces of the ribs. Under conditions of low cover and no transverse reinforcement, bond force is not dependent on rib height or rib shape; however, an increase in rib height produces an increase in the initial stiffness of the load-slip curves. Under conditions of increased concrete cover, bond force and the initial stiffness of the load-slip curves mcrease. Under conditions of increased bar confinement provided by additional lead length, bond strengths increase compared to bars with lower lead lengths. Bond force increases with an increase in embedded length. However, the amount of concrete that is split at failure is not proportional to the embedded length. The degree of splitting Qateral displacement at the front face of the specimen) up to the peak load is not dependent on rib height or shape but is dependent on concrete cover. Lateral displacements after the peak load increase with an increase in rib height Under conditions of increased confinement provided by transverse reinforcement, bond strength increases compared to models without transverse reinforcement. A statical model of steel in contact with concrete provides a means of relating the clamping force provided by the concrete to the pull-out force of the reinforcing bar