Bending Response and Design Equations for Gravity-Flow Pipe Liners Passing across Ring Fractures or Joints

Vehicle loads and differential ground movements can induce tensile strains in close-fitting polymer liners installed within gravity flow pipes, where the liner stretches across ring fractures or joints experiencing rotation (i.e., opening of the joint at the invert if the joint is moving down relative to the other ends of the pipe segments, or at the crown if the joint is moving upward compared with the other ends). A finite-element model is established and suitable pipe length and mesh size are determined. The stress and strain distributions along hoop and axial directions are then evaluated, considering factors such as inside diameter of the host pipe, liner thickness, rotation angle, liner elastic modulus, friction coefficient between the liner and host pipe, and Poisson’s ratio of the liner. After that, curve fitting is used to develop design equations for estimating stress and strain, and their performance is evaluated against the finite-element data. Finally, the potential effects of gravity and buoyancy are investigated. For small rotations, the stress is proportional to strain, and the maximum stress of the liner occurs directly at the joint, at the point where joint opening is greatest. The friction coefficient and liner thickness have a small effect on the maximum stress, so this simplifies consideration of this limit state in design. The design equation for stress provides estimates within 8.6% of those obtained from the three-dimensional finite-element analysis (with $R^2$ between 0.992 and 0.993). Subsequent evaluation of the proposed equation using strain measurements obtained from full-scale experiments is recommended.