## 3 Material and Numerical Models
### Material Models
#### 3.2.3 Model of Contact (Interface) Elements
Characteristic breaking points of curves were defined according to [52], from the following equations:  
\[s_{1}=\frac{f_{\mathrm{t}}}{4},\ \Delta u_{1c}=0.75\frac{G_{f}^{\mathrm{II}}}{f_{ \mathrm{t}}}. \tag{20}\]  
Figure 12: The relationship of shear stress and normal stress with displacement of contact elements (**a**) at shearing, (**b**) under tension; \(1\)—default function of softening. \[\tau=\tau_{o}\sqrt{1-\frac{\left(\sigma-\sigma_{c}\right)^{2}}{\left(f_{ \text{t}}-\sigma_{c}\right)^{2}}},\,\tau_{o}=\frac{1}{\sqrt{1-\frac{\sigma_{ c}^{2}}{\left(f_{\text{t}}-\sigma_{c}\right)^{2}}}},\,\sigma_{c}=\frac{-f_{ \text{t}}^{2}\text{tg}\alpha}{f_{\text{vo}}-2f\text{tg}\alpha} \tag{14}\]0 Simplified softening laws (**a**) for normal tensile stresses, (**b**) for cohesion (initial shearing strength). Apart from fracture energy \(G_{f}^{I}\) determined under the axial tension and \(G_{f}^{II}\) at shearing, the softening laws depended on equivalent displacement, and were defined in the following way:  
\[\tau=\tau_{o}\sqrt{1-\frac{\left(\sigma-\sigma_{c}\right)^{2}}{\left(f_{ \text{t}}-\sigma_{c}\right)^{2}}},\,\tau_{o}=\frac{1}{\sqrt{1-\frac{\sigma_{ c}^{2}}{\left(f_{\text{t}}-\sigma_{c}\right)^{2}}}},\,\sigma_{c}=\frac{-f_{ \text{t}}^{2}\text{tg}\alpha}{f_{\text{vo}}-2f\text{tg}\alpha} \tag{14}\]1  
where \(\Delta u_{f}=\Delta u-\Delta u_{e}\) signifies non-elastic horizontal displacement, calculated as the difference between total \(\Delta u\) and elastic displacements \(\Delta u_{e}\), and \(\Delta v_{f}=\Delta v-\Delta v_{e}\) signifies non-elastic vertical displacement, calculated as the difference between total \(\Delta v\) and elastic displacements \(\Delta v_{e}\). That solution caused the cohesion degradation to have an impact on tensile strength, and vice versa. For example, when the bond was damaged by compression, tensile strength was also reduced. A typical behaviour of the contact elements in elastic and post-elastic phases caused by shearing and tensions is shown in \[\tau=\tau_{o}\sqrt{1-\frac{\left(\sigma-\sigma_{c}\right)^{2}}{\left(f_{ \text{t}}-\sigma_{c}\right)^{2}}},\,\tau_{o}=\frac{1}{\sqrt{1-\frac{\sigma_{ c}^{2}}{\left(f_{\text{t}}-\sigma_{c}\right)^{2}}}},\,\sigma_{c}=\frac{-f_{ \text{t}}^{2}\text{tg}\alpha}{f_{\text{vo}}-2f\text{tg}\alpha} \tag{14}\]2 The default behaviour of the contact elements was brittle (straight line) when the softening laws were not defined. In addition, default breaking of the curve and shear stress values reduced to the value of dry friction at shearing. Material parameters are presented in Tables 5 and 6. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Test Formula or Results** & **Bed Joint** & **Head Joint** \\ \hline \(1\) & 2 & 3 & 4 \\ \hline Normal stiffness \(K_{\text{nn}}\), MN/m & Calculated from the equation: \(K_{\text{nn}}=\frac{\ell}{2}10\) & \(3.92\times 10^{6}\) & \(1.02\times 10^{6}\) \\ Shear stiffness \(K_{\text{kt}}\), MN/m & Calculated from the equation: \(K_{\text{kt}}=\frac{\ell}{2}10\) & \(1.67\times 10^{5}\) & \(4.51\times 10^{5}\) \\ Tensile strength \(f_{\text{kt}}\), N/mm\({}^{2}\) & & \(1.5\) & \(1.5\) \\ \(\text{Cohesion}\,r_{\text{0}}\) & Assumed value as for the wall & \(\infty\) & \(\infty\) \\ Friction coefficient \(\text{tg}\) & & \(\infty\) & \(\infty\) \\ Normal stiffness \(K_{\text{nn,min}}\), MN/m & Calculated as 0.01 \(K_{\text{nn}}\) & \(3.92\times 10^{4}\) & \(1.02\times 10^{4}\) \\ Shear stiffness \(K_{\text{kt,min}}\), MN/m & Calculated as 0.01 \(K_{\text{kt}}\) & \(1.67\times 10^{5}\) & \(4.51\times 10^{5}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Parameters of interface elements at the interface of the wall and reinforced concrete elements.