# Predicting Behavior of Grounded Dowel Connections Using Interfacial Cohesive Elements
## 5 Model Validation
### Validation Examples  
#### 5.2.1. Grouted Ducts in Walls  
Finite element models of three monotonic pull-out tests conducted by [PERSON] and [PERSON] [3] were analyzed. The specimens consisted of concrete rectangular prisms having a cross-section of \(208\times 208\times 406.4\) mm, where the grouted ducts were placed concentrically. The specimens were constructed using No. 8 bars with a measured yield stress and strain of 418 MPa and 0.2%, respectively. The average 28-day compressive strengths of the concrete and grout were 50.6 and 40 MPa, respectively. The three specimens had embedded lengths of 6, 8, and 12 \(d_{b}\). The specimens were carefully selected to highlight several key features. Firstly, an embedded length of 6 \(d_{b}\) was chosen for a direct comparison of the bond-slip model since it represents a close rendering of the local envelope of the anchorage. At such an embedment length, the difference between the observed slip at the loaded and free ends is nominal, which explains the common assumption of uniform bond stress used in bond studies. Secondly, an embedded length of 8 \(d_{b}\) represents a departure from the uniform slip assumption as moderate non-linearity is expected. Thirdly, an embedded length of 12 \(d_{b}\) represents a highly non-linear distribution as the effective bond stresses peak closer to the loaded end and attenuate toward the unloaded end. This non-linearity introduces redundant lengths along the bar, whose ribs engage as the bond toward the loaded end experiences plastification. The choice of the embedment lengths analyzed was also based on the different failure modes experienced by the specimens. The model components, meshes, boundary conditions, and loading are shown in Figure 8a. The force versus free-end slip results, along with the results of sensitivity analyses, are displayed in Figure 9. The purpose of this analysis was to appraise convergence to the experimental solution, as well as highlight the computational efficiency of the model. The convergence criteria were both quantitative and qualitative based on evaluation of the predicted response and the relative error calculated from Equation (18) (maximum 25%). Four mesh sizes were considered, namely \(6.5\times 7\), \(6\times 4\), \(3\times 2\), and \(1\times 2\) mm, results of which are displayed in Figure 9 for 6 \(d_{b}\) embedment length. It canbe observed that the convergence rate dramatically increased when the mesh size decreased from \(6.5\times 7\) mm to \(6\times 4\) mm. The rate of convergence had a slight increase as the mesh size was reduced until a mesh size of \(3\times 2\) mm, below which no significant improvements were observed. Good agreement between the curves was observed when the mesh size was \(3\times 2\) mm. The computational effort was calculated as the time required to complete the analysis on a standard single-core processor of a desktop computer. For instance, the computational time increased by 54% when the mesh was refined from \(6.5\times 7\) (V \(\approx 0.23\)) to \(6\times 4\) (V \(\approx 0.68\)) mm. A slight increase in computational time by 15.4% was observed when the mesh size was refined from \(6\times 4\) to \(3\times 2\) (V \(\approx 0.82\)) mm but was justifiable given the significant improvements in the load versus slip response, as observed from Figure 8. The time required to complete the analysis for the \(1\times 2\) mm mesh size increased by five orders of magnitude compared to its \(6.5\times 7\) counterpart. Overall, the model exhibited computational efficiency even when the mesh size decreased. It is noteworthy that, due to the presence of some induced compression at the boundary of the specimens, the ascending branch was characterized by a stiffer response. This was further verified by comparison of the confinement parameter \(\alpha\), which was in the range of 0.16-0.19. The bond-slip law presented in Equation (3) was based on an \(\alpha\) value of 0.21-0.28.