Joint Bearing Behavior of Buried Steel Pipes and Surrounding Rock

Literature Overview

Published in Water and Power Resources Science in 2021, this paper by Wang Bifei and colleagues from the Yangtze River Survey, Planning, Design and Research Co., Ltd., and Henan University of Technology, investigates the joint bearing mechanism of a buried steel pipe, backfill concrete, and surrounding rock in an underground powerhouse penstock system. The study uses three-dimensional finite element analysis to model the coupled system and examines the influence of different constitutive models for the backfill concrete and the elastic modulus of the surrounding rock on the structural response.

Technical Analysis of Constitutive Models

The study evaluates three constitutive models for the backfill concrete: elastic, elastic-plastic, and elastic-plastic-fracture. The key finding is that the backfill concrete is prone to yielding and crack formation under the combined loading conditions, and therefore the fracture characteristics of concrete must be considered in the analysis. The elastic-plastic-fracture model produces results that are in close agreement with those obtained from the standard design code calculations, confirming its reliability and safety for engineering applications.

The following table presents the comparative assessment of the three constitutive models:

Key Response Patterns

The study analyzes three critical response indicators: the hoop stress in the steel pipe, the contact stress between the steel pipe and the backfill concrete, and the load-sharing ratio of the surrounding rock. The hoop stress distribution in the steel pipe is influenced by the stiffness contrast between the pipe, the backfill, and the rock. When the surrounding rock is stiffer, it attracts a larger portion of the load, reducing the stress in the steel pipe. Conversely, a softer surrounding rock transfers more load to the pipe and backfill system.

The contact stress between the steel pipe and backfill concrete is particularly important for assessing the integrity of the interface. Excessive contact stress can lead to local buckling of the pipe or crushing of the concrete, both of which are potential failure modes. The surrounding rock load-sharing ratio provides a quantitative measure of how much of the total load is carried by the rock mass versus the pipe-backfill system. This ratio is directly affected by the elastic modulus of the surrounding rock and has significant implications for the design thickness of both the steel pipe and the backfill concrete.

Engineering Practice Implications

For underground powerhouse penstocks, this study provides clear guidance that the elastic-plastic-fracture constitutive model should be adopted in finite element analyses to obtain reliable results. The design should account for the possibility of backfill concrete cracking, which may occur even under service loads if the concrete is not adequately designed. Engineers should ensure that the backfill concrete mix has sufficient tensile strength and that reinforcement is provided in critical zones to control crack widths.

The load-sharing ratio concept is directly applicable to design optimization. By adjusting the backfill concrete thickness and the steel pipe wall thickness, the load-sharing ratio can be manipulated to achieve a desired balance between the costs of steel and concrete. However, the study does not address the long-term creep behavior of the backfill concrete or the potential for differential settlement, which are important considerations in real underground environments.

Study Insights and Reflections

This research effectively demonstrates the importance of constitutive model selection in coupled structural analyses. The finding that the elastic-plastic-fracture model yields results consistent with code calculations validates the use of advanced finite element methods for this class of problems. However, the study is limited to a specific case study and does not provide generalized design equations or charts. Future work should include parametric studies across a wider range of pipe diameters, wall thicknesses, and rock properties to develop practical design guidelines. The study also does not consider the effect of internal water pressure fluctuations or seismic loading, which are relevant for underground penstocks in seismically active regions. Overall, this paper is a valuable contribution to the understanding of pipe-rock interaction mechanics and provides a practical methodology for the analysis of buried steel pipe systems.