Theoretical Analysis Of Bond Behavior For Reinforced Concrete Based On Stress Intensity Factor(SIF) Crack Propagation Criterion

The bond performance between reinforcement and concrete is not only the most fundamental guarantee of the behaviour of reinforced concrete structures（safety and durability）,but its intrinsic relationship facilitates theoretical analysis and numerical simulations.Structural strength,crack width,deflection and ductility under static loads as well as energy absorption and dissipation capacity under cyclic loads are all directly or indirectly related to bonding.In fact,the main critical factor leading to the failure of reinforced concrete structures in service is the inadequate anchorage strength of the reinforcement,particularly in the area of plastic hinge connections,where concrete cracking of the reinforcement due to inadequate concrete restraint results,which in turn leads to a rapid reduction in the bond（stiffness and strength）of the member and ultimately to the collapse of the structure.Although empirical models have been developed for unconfined,cracked and confined bond performance,the bond mechanisms involving cracks,lateral stresses and passive confinement are not yet clear,and in addition the theoretical analysis is made more difficult by the properties of the concrete section（cross-sectional shape and contact interface）.Based on the above problems,the bond model and bond-slip intrinsic relations for deformed reinforcement under various conditions are developed based on the stress intensity factor（SIF）crack propagation criterion,and then analyzes the mechanism of the influence of the contact interface on the bond performance with stirrup confinement.To follow are the main findings and conclusions of the paper:1.Based on the SIF crack propagation criterion,the analytical expressions for the internal pressure at the interface are derived using the weight function theory and the finite element model.Comparing the friction coefficient and recommended rib angle of existing failure planes,a virtual angleα₀related to the rib height-rib spacing ratio h_r/S_r is introduced to correct the recommended rib angle for splitting failure planes,and thus an unconfined bond strength prediction model applicable to different failure modes is proposed.The results of the sensitivity analysis indicate that the compressive strength of the concrete and the relative cover thickness have a greater influence on the internal pressure required to crack the concrete cover,in addition to the failure plane characteristics which cannot be ignored.2.The influence mechanism of section defects on the internal pressure is analysed in conjunction with the elastic mechanics complex function,and an analytical expression for the internal pressure concerning surface defects is proposed.The weakening mechanism of crack width on the failure plane properties is analysed,and the superiority of the proposed model in predicting the failure modes and concrete cracked cases is verified.In addition,the expression for the bond-slip intrinsic relationship in the form of a power function can be applied to a range of allowable crack widths（w_c≤0.4 mm）.Combining a simplified model of bond strength to assess critical bond lengths in relation to cracks.3.Validation of the measured internal pressure shows that the accuracy of the prediction model depends to some extent on the crack number.The effect of active stress confinement on the virtual angle is considered to develop prediction models applicable to uniaxial,multiaxial and multiple active stresses.Different from active restraint,a bond slip model is introduced at the stirrup/FRP-concrete interface to analyse the mechanism of the effect of passive confinement under concrete cracked cases and to verify the accuracy of the single passive confinement model.In addition,the effect of bond length on splitting bond strength decreases as the confinement level increases.4.The bond failure mechanism of multiple confinement such as concrete cover,stirrup and FRP is further explored in conjunction with the mechanism of the effect of concrete crack depth on single confinement,a theoretical calculation model and simplified expression for bond strength highly correlated with failure mode is developed,and the power function form of the bond-slip model accurately predicts failure modes and multiple confinement cases（stirrup and FRP coupled confinement）.In addition,design recommendations for assessing the minimum thickness and bond length of FRPs for seismic strengthening are given.5.The SIF crack propagation criterion is introduced into the irregular contact interface between section steel and concrete,and the section properties of section steel and concrete are simplified by using the thick-walled cylindrical model and equivalent area.The potential relationship between concrete cover thickness and crack distribution is considered,and the expression for the weight function is modified by introducing an elliptical crack shape factor,so that an internal pressure model relating stirrup confinement and the crack number can be derived.An ultimate bond strength model incorporating chemical bond forces,mechanical bite forces and friction forces is proposed,the superiority of the proposed model in terms of bond strength is verified by the section type and stirrup confinement conditions compared to other models.