Mechanical response of buried and covered pipes under water hammer

The classical water hammer model omits bending and inertial effects in the pipe wall. The validity of such assumptions for buried and covered pipes is assessed by developing a one-way coupled water hammer model based on an axisymmetric thin shell pipe finite element that captures bending and inertial effects. A finite/infinite pipe element formulation is developed to capture the stiffness contribution of the surrounding soil (or pipe cover) by adopting a decay function derived from plane strain analysis of the medium surrounding the pipe. Continuous and discrete elastic longitudinal restraint effects are also incorporated into the formulation. The model is then used to investigate the effects of viscous damping, elastic longitudinal restraints, presence of intermediate longitudinal anchors, and the elastic modulus of the surrounding soil. The pipe response is found insensitive to viscous damping. The present model shows that, while classical model predictions are valid for cases where the valve end of the pipe is fully (or nearly-fully) restrained in the longitudinal direction, this is not the case where the valve end is longitudinally unrestrained. Intermediate longitudinal restraints are found to divide the pipe into two segments with distinct responses. The ability of the proposed finite/infinite element to predict the response of buried pipe subjected to water hammer is illustrated through numerical examples.