# Investigation of Debonding Effect in Internal Replacement Pipe System Under Lateral Loading
## 2 Finite Element Analysis
### Internal Replacement Pipe (IRP) System Modelling and Validation  
#### 2.2.1 IRP System Modelling  
This section provides a detailed analysis of the nonlinear load-deformation characteristics of an IRP system. The system consists of a steel host pipe with a 12.7 mm (0.5 inch) wide circumferential discontinuity, which has been repaired using ALTRA10 supplied by Sanexen Environmental Service Incorporated. The analysis is conducted through a comprehensive investigation that includes 3D FEA simulations and experimental studies. A 0.25 mm (0.01 inch) thick layer of epoxy adhesive is utilized to bond the host pipe and the IRP. In the FEA modeling, the contact conditions between the adhesive and the host pipe, as well as between the adhesive and the IRP, were assumed to be fully bonded. The pipe cavity is assumed to be filled with water, and a point mass representing the water is attached to the internal surface of the IRP and blind flange to simulate the experimental work. The water density is specified as 1000 kg/m\({}^{3}\). A total force of 71.2 kN (16 kip) is applied in the vertical direction to the loading head of the model to simulate the traffic load [17]. Additionally, an internal pressure of 0.448 MPa (65 psi) is applied on the inertial surfaces of the system to represent the operating pressure of a gas pipeline [17]. The standard earth gravity of 9.81 m/s\({}^{2}\) is considered, acting vertically on the entire model. A nonlinear static structural FEA was conducted to capture large deformations and material plasticity in the study of the ALTRA10 internal replacement pipe (IRP) system, \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Load kN (kip)**} & **Numerical** & **Analytical** & **Deflection** & **Numerical** & **Analytical** & **Stress MPa** \\  & **Deflection mm** & **(inch)** & **Error \%** & **(psi)** & **(psi)** & **(psi)** \\ \hline
16 (4) & 0.175 (0.00689) & 0.178 (0.007) & 1.742 & 3.375 (489.5) & 3.645 (528.7) & 7.413 \\
31 (7) & 0.350 (0.01380) & 0.356 (0.014) & 1.567 & 6.764 (981.1) & 7.291 (057.4) & 7.224 \\
47 (11) & 0.526 (0.02069) & 0.534 (0.021) & 1.592 & 10.144 (1471.3) & 10.936 (1586.1) & 7.242 \\
63 (14) & 0.701 (0.02758) & 0.712 (0.028) & 1.614 & 13.522 (1961.3) & 14.581 (2114.9) & 7.263 \\
79 (18) & 0.875 (0.03447) & 0.890 (0.035) & 1.636 & 16.899 (2450.9) & 18.227 (2643.6) & 7.286 \\
94 (21) & 1.050 (0.04135) & 1.068 (0.042) & 1.657 & 20.276 (2940.8) & 21.873 (3172.3) & 7.301 \\
110 (25) & 1.225 (0.04822) & 1.246 (0.049) & 1.693 & 23.653 (3430.5) & 25.517 (3701.0) & 7.305 \\
126 (28) & 1.400 (0.05510) & 1.424 (0.056) & 1.721 & 27.029 (3920.2) & 29.163 (4229.7) & 7.317 \\
142 (32) & 1.573 (0.06194) & 1.602 (0.063) & 1.798 & 30.404 (4409.7) & 32.808 (4758.5) & 7.327 \\
157 (35) & 1.747 (0.06877) & 1.780 (0.070) & 1.860 & 33.769 (4897.7) & 36.454 (5287.2) & 7.365 \\ \hline COV (\%) & & & 5.529 & & & 0.772 \\ \hline \end{tabular}
\end{table} 
Table 2: Validation of numerical and theoretical models for four-point bending deflection. where the IRP exhibits nonlinear stress-strain behavior. This nonlinear approach captures the effects of significant deformations and material-yielding factors that are essential for accurately understanding the true performance and potential failure modes of the structure, which linear assumptions would not adequately address. The FEA model is developed using the same parameters as the CUB test setup, which was discussed in the preceding section. The positions of interest for validation are 43.345 mm (1.7065 inches) and 591.833 mm (23.3005 inches) from the midspan of the system. Figure 4 depicts the FEA setup for the IRP system, illustrating the 12.7 mm (0.5 inch) discontinuity in the middle of the host pipe. This situation represents a full circumferential line crack in the IRP system. Furthermore, Tables 3 and 4 present the dimensions and material properties of the components used in the analysis. The mechanical properties of the steel components and epoxy adhesive were modeled as linear materials.