System Reliability-Based Overall Safety Assessment of Penstocks in Hydropower Stations

Literature Overview

This paper by Liu Jingmin, Yang Lüfeng, and Zhang Wei (2013), published in the Journal of Waterway and Port Engineering, addresses a critical gap in the structural safety evaluation of penstocks — the large-diameter exposed steel pipes used in hydropower stations to convey water from the headrace to the turbine. Traditional reliability analyses of penstocks focus on individual component reliability at basic locations, failing to capture the system-level safety performance. The authors propose a series system model composed of four basic locations and employ the second-order bounding method to evaluate the system reliability of a typical penstock engineering case.

Core Technical Content

The study is grounded in the recognition that penstocks are not merely assemblies of independent pipe segments but rather a coupled structural system where the failure probability at one location influences the overall system behavior. The four basic locations identified in the series system model are: the straight pipe section, the inclined pipe section, the support ring and its adjacent pipe wall, and the pipe joint/welding zone. The authors treat these as a series system, meaning that failure at any single location leads to system failure — a conservative but physically reasonable assumption for pressure-carrying structures.

The second-order bounding method is used to estimate the system failure probability by computing both the lower and upper bounds of the joint failure probability of the basic events. This approach is particularly suitable when the correlation coefficients between basic events are known or can be estimated from the physical interaction between locations.

Key Technical Findings

The most significant finding is that the support ring and its adjacent pipe wall consistently emerge as the controlling location for system failure in both straight and inclined pipe configurations. This is physically intuitive: the support ring creates a geometric discontinuity that produces stress concentrations, particularly under the combined action of internal water pressure, external loads, and bending moments from the pipe's own weight and seismic forces.

Engineering Practice Implications

From a steel pipe manufacturing and welding perspective, this finding has direct implications for the quality control of support ring welds. The adjacent pipe wall regions are subject to:

• High hoop stress concentration due to the ring's stiffness mismatch with the pipe shell
• Residual stress accumulation from the welding process itself
• Geometric imperfections such as weld reinforcement and undercuts that further amplify stress gradients

In practice, the following measures should be emphasized:

1. Welding procedure optimization: Use of low-heat-input processes (GTAW for root passes, followed by FCAW or SAW for fill and cap) to minimize the heat-affected zone (HAZ) width and residual stress magnitude.
2. Post-weld treatment: Consideration of local hot isothermal tempering (HOT) or post-weld heat treatment (PWHT) at support ring welds to reduce residual stresses below the yield threshold.
3. NDT stringency: Full-penetration radiographic testing (RT) or phased array ultrasonic testing (PAUT) at all support ring welds, with acceptance criteria aligned with the more stringent side of the applicable code.
4. Mean value control: The paper emphasizes that the mean values of random variables (material strength, wall thickness, internal pressure) have the most significant influence on system reliability. This translates to strict incoming material inspection, dimensional control during fabrication, and operational monitoring during service.

Study Insights and Reflections

The transition from component reliability to system reliability represents a paradigm shift in structural safety assessment. For steel pipe engineers, this means that optimizing the strength of individual pipe segments alone is insufficient — the weak links in the chain, particularly at discontinuities such as support rings, welds, and bends, must receive disproportionate design attention. The paper's conclusion that current code designs are generally adequate provides reassurance, but the emphasis on mean value control underscores the importance of manufacturing quality consistency. A single poorly fabricated support ring weld can compromise the safety of the entire penstock system, regardless of how well the remaining pipe segments perform.