A closed-form solution for lateral indentation of pressurized pipes resting on a flexible bed

• The paper deals with the response of pressurized pipes under lateral loading.
• The obtained closed-form expression is in good agreement with numerical results.
• The surrounding soil affects the pipe response against quasi-static impact loads.
• Increase in the soil bed stiffness causes the pipe to behave stiffer.
• Increase in the embedment depth leads to stiffer response against lateral load.

The work described in this paper forms part of a closed analytical solution for the quasi-static response of flexibly supported pressurized pipes against lateral impacts. The results can be used, for example, in an analytical study of offshore oil/gas pipelines subjected to impacts from falling anchors, trawl boards or other dropped objects. The solution is based on the principles of virtual velocities. It employs a simplified three dimensional analytical model to provide a closed-form relationship for the denting force in terms of the dent depth. A rigid-perfectly plastic behavior is considered for the tube wall resistance. The flexibility of the soil, existing around and underneath the pipe, is modeled using a subgrade reaction modulus. This work can be regarded as a continuation of previous works reported by one of the authors. It is now extended to take into account the bed flexibility.Predictions from the proposed mathematical solution are also examined against those from numerical finite element simulations. Various states of end condition, internal pressure, soil stiffness and the pipe embedment into the soil are considered. The comparisons show a good agreement between the results from the analytical model and finite element analyses.