# Investigation of Debonding Effect in Internal Replacement Pipe System Under Lateral Loading
## 2 Finite Element Analysis  
### Four-Point Bending Deflection Modelling and Validation  
#### 2.1.1 Four-Point Bending Deflection Modelling  
It is essential to account for the most severe conditions expected over a 50-year design lifespan when determining the imposed loading protocols for buried pipelines subjected to lateral loading or bending due to traffic. A worst-case scenario can be modeled by introducing a complete circumferential fracture or crack along the pipe specimens [17]. In this work, finite element analysis (FEA) simulations were conducted using ANSYS/Mechanical software 2023 R2 to investigate the behavior of pipelines under lateral loading. Three-dimensional (3D) finite element models were created to simulate the conditions specified in the experimental setup conducted at the University of Colorado Boulder, as detailed in [17]. The center-to-center dimensions of the four-point bending setup were maintained at 63.5 cm by 101.6 cm by 63.5 cm (25 inches by 40 inches by 25 inches), as shown in Figure 1. The deflection measurement was zeroed at the initial stage of the experiment before any lateral loading was applied. A single cast iron pipe with an outer diameter of 342.9 mm (13.5 inches) and a wall thickness of 17.272 mm (0.68 inches) was utilized [15; 17; 18] to calibrate and validate the numerical results. The standard A48 Class 20 gray cast iron [21], with a modulus of elasticity (MOE) of 70 GPa (10,153 ksi) and a Poisson's ratio of 0.29, is used. The chemical composition of the cast iron is listed in Table 1. The test system was subjected to a load of 157.3 kN (35.4 kip) to achieve a design displacement of approximately 1.78 mm (0.07 inches) at its midspan, corresponding to the nominal diameter and wall thickness of the pipe. The measured deflection represented the overhead traffic load experienced by a pavement and subgrade system directly above the pipeline [15; 16; 17; 18]. The load was oriented parallel to the pipeline's longitudinal axis [17; 18]. By applying this load, the stresses and deformations experienced by the specimen represent worst-case scenarios under vibrational loading, aiming to achieve a design fatigue life of 1 million cycles, which corresponds to a 50-year service life as introduced by [PERSON] et al. in 1985 [18; 19]. The 1 million cycles over a 50-year period equate to approximately 20,000 cycles per year. This fatigue life estimate was rounded up from the original value of 780,000 cycles based on the expected number of heavy truck crossings over 50 years. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Standard** & **C (\%)** & **Si (\%)** & **Mn (\%)** & **P (\%)** & **S (\%)** \\ \hline ASTM A48 & 3.2–3.5 & 1.8–2.4 & 0.5–0.9 & 0–0.12 & 0–0.12 \\ Class 20 & & & & & \\ \end{tabular}
\end{table} 
Table 1: Chemical composition of ASTM A48 Class 20 gray cast iron [21]. A linear static structural FEA was performed on a single cast iron pipe during a four-point bending assessment to validate the analytical approach using linear solution methods. Both ends of the pipe were capped with blind flanges, fully bonded to the pipe. To ensure precise simulation of the mechanical contacts within the system, specifically the pin-lug and clamp-host pipe, a standard friction coefficient of 0.13 has been employed [20]. This selected value for the friction coefficient guarantees a realistic depiction of the frictional forces that arise during the interaction of these components. To simplify the model, a quarter of the system was simulated with symmetry boundary conditions applied in the longitudinal and transverse directions. A quarter FEA model and its components for the validation of single-pipe deflection are shown in Figure 2. An element size of 10 mm is used for the clamp, the loading head, and the blind. An optimal surface mesh size of \(5\times 5\) mm was chosen, as recommended in previous studies [18; 19], to avoid redundant work in the pipe modeling.