Evolutions of SIFs of Concrete under Sustained Loading by Considering the Effects of Stress Relaxations

Sustained loading has an important impact on concrete structures in service due to deteriorations of material properties and degradations of durability. Sustained loading and three-point bending (TPB) tests were carried out to study the influence of long-term loading on the fracture of concrete. The specimens were firstly tested under three load levels, i.e., 30% and 60% of the maximum load and the crack initiation load over 30 days. After that, these specimens were removed from the loading frames and immediately loaded up to failure under static TPB loading. The critical crack propagation length ($\mathrm{\Delta }{a}_{\mathrm{c}}$), the initial cracking load ($P_{\mathrm{ini}}$), the peak load ($P_{\max }$), and the fracture energy ($G_{\mathrm{f}}$) were obtained in the TPB tests. Accordingly, the initial fracture toughness ($K_{\mathrm{IC}}^{\mathrm{ini}}$), the unstable fracture toughness ($K_{\mathrm{IC}}^{\mathrm{un}}$) and the evolution of stress intensity factors (SIFs) were determined by considering the stress relaxation at the precrack tip. Furthermore, the fracture properties of concrete affected by the long-term loading can be obtained by comparing with those from the static TPB tests. The results indicated that the stress relaxation at the precrack tip caused by the viscoelasticity of concrete led to the increases in $P_{\mathrm{ini}}$ and $P_{\max }$ but had almost no effects on $\mathrm{\Delta }{a}_{\mathrm{c}}$ and $G_{\mathrm{f}}$. The formula for calculating $K_{\mathrm{IC}}^{\mathrm{ini}}$ and $K_{\mathrm{IC}}^{\mathrm{un}}$ from linear elastic fracture mechanics would no longer be appropriate for those creep specimens and would overestimate the values of $K_{\mathrm{IC}}^{\mathrm{ini}}$ and $K_{\mathrm{IC}}^{\mathrm{un}}$. By taking into account the stress relaxation, the calculated values of $K_{\mathrm{IC}}^{\mathrm{ini}}$ and $K_{\mathrm{IC}}^{\mathrm{un}}$ for the creep specimens were almost the same as those under the static loading. Therefore, the values of $K_{\mathrm{IC}}^{\mathrm{ini}}$ and $K_{\mathrm{IC}}^{\mathrm{un}}$ derived from the static TPB tests can still be used to evaluate the cracking resistance of concrete materials and the stability of concrete structures under different load levels.