21.2.2 Rough Crack Model (Gambarova & Karakoç)

An improvement to the rough crack model of Bazant & Gambarova [§21.2.1] has been proposed by Gambarova & Karakoç [33]. Figure 21.9 shows the response diagram for this model.

Figure 21.9: Rough crack model (Gambarova and Karakoç)

The authors claim that their model gives a better formulation to the relation between the normal traction and the crack displacements, because this relation is based on tests with a constant confinement stress by Daschner & Kupfer [19]. Further, this formulation takes the effect of aggregate size in account. The relations are

$$\begin{split}f_{t} &= \tau_{0} \left( 1 - \sqrt{ \frac{ 2 \De... ... \Delta u_{n}} \frac{r}{ (1+ r^{2} )^{0.25} } f_{t} \end{split}$$ (21.17)

with

$${\frac{{ 2.45 }}{{ \tau_{0} }}} \left(\vphantom{ 1 - \frac{ 4 }{ \tau_{0} } }\right. {\frac{{ 4 }}{{ \tau_{0} }}} \left.\vphantom{ 1 - \frac{ 4 }{ \tau_{0} } }\right)$$ a₁a₂

$$\tau_{{0}}^{}$$ = 0.25f_c = 0.2f_cc

For the tangential stiffness coefficients see Feenstra [26].