An Approach Developed for Fatigue LIfe Estimation of Penstock Tie Rods


Additional inspection methodologies are now available for use in the hydroelectric industry resulting from a study on tie rod threaded connections’ fatigue life performed in penstock bifurcations at Hoover Dam.

By Jerzy Salamon

In the design of penstock branches and wyes, structural integrity is the main consideration. Because the strength of the penstock shell is reduced at the branches, additional reinforcement needs to be provided to resist the internal pressure within the pipe. Tie rods have been used on several facilities to strengthen the penstock wyes and branches. Failure of a tie rod, a critical structural component, may lead to cracking or breaching of the penstock.

During penstock inspections at Palisades Dam in the 1980s and 1990s, personnel with the U.S. Department of Interior’s Bureau of Reclamation discovered a broken 9-inch-diameter tie rod reinforcing the penstock wye branch. Inspection of the penstocks at New Melones Dam in the 1990s resulted in the detection of several cracks in the 10-inch-diameter tie rods. Although the tie rods at both facilities have been repaired and no failure has been reported since the repair, evaluation of the penstock wyes and branches reinforced by tie rods became a high priority at other Reclamation facilities.

In 2002, Reclamation initiated structural investigations on the penstock bifurcations at the Hoover Dam hydropower facility. The threaded type connections associated with the 11-inch- and 13-inch-diameter tie rods were identified as fatigue critical.

In 2012, Reclamation conducted comprehensive investigations of the Hoover Dam penstocks using a combination of field examinations and structural and fatigue analysis methodologies. Reclamation developed a method of estimating the remaining operational fatigue life and inherent probability factors that might contribute to failure of tie rods.

The investigation included structural and fatigue analyses supported by data gathered from instrumented tests of tie rods at three selected penstock junctions. Fatigue life estimations of the tie rod connections were performed using two procedures which included the crack growth approach (based on the concept of fracture mechanics) and the strain-life fatigue analysis approach (using the Smith-Watson-Topper relation).

The results of the structural and fatigue analyses, as well as the lessons learned from combining the instrumented test with the analytical computations, convey an overall confidence that failure of the tie rods over the expected 200-year operational life of the penstocks is very low.

Background

According to Reclamation penstock inspection reports from 1980 and 1997, a broken 9-inch-diameter tie rod was discovered at the wye branch within the river outlet works at Palisades Dam on the Snake River near Irvin, Idaho. The tie rod was completely sheared off along the top welded connection and was displaced by about 0.5 inch. Cracks were also discovered in the lower welded tie rod connection. In the 1990s, Reclamation personnel observed cracks in the 10-inch-diameter penstock tie rods at New Melones Dam on the Stanislaus River, near Modesto, Calif. The tie rods were repaired in both cases and no failures have occurred at this facility since that repair.

Hoover Dam penstocks

Constructed between 1931 and 1936, Hoover Dam, located along the Colorado River between Nevada and Arizona, is an engineering milestone for hydropower facilities. The first release from the powerplant was made in 1935.

Two vertical tie rods, 13 inches in diameter, are being readied for inspection in a Hoover Dam header/penstock bifurcation.

Water from the reservoir enters four intake towers, leading to a system of four 30-foot-diameter header pipes located inside rock tunnels. Each header pipe bifurcates into four smaller 13-foot-diameter penstocks that supply water to turbine-generators in the facility’s powerhouse.

Two internal steel tie rods at each of the 16 penstock bifurcations carry the unbalanced loading which results from the transition between the header pipes and penstocks. The ends of the rods are threaded and connected to the fittings welded into the header’s external stiffening plates. Two external 4-inch-thick stiffening plates, spanning between the tie rods on the outside of the header pipes, distribute the load from the tie rods uniformly into the header shell.

This graphic illustrates components of a penstock/header pipe bifurcation (blue): the header-penstock transition (brown), transition plate (gold), tie rod stiffener plates (red), header-penstock transition pipe (green) and tie rod (orange).

Analysis of the header/penstock bifurcation

Finite element (FE) analysis of the header section, header-penstock transition, penstock section, two tie rods, and two tie rod stiffener plates was initially performed by the Reclamation in 2012 (see Figure 1). Tensile forces and bending moment in the tie rods were estimated for the upper and lower penstock structures. The self-weight of the steel structure, the weight of water, and the internal pressure corresponding to various operational conditions were considered in the analysis.

Comparative data

In 2002, Reclamation conducted an instrumented test of the tie rods at the lower and upper penstock. In 2012, a similar test was performed on the lower penstock tie rods.

Since the operational conditions of the penstocks during the test in 2002 and 2012 were different, an adjustment was made to the 2002 test data to compensate for variations in reservoir water surface during testing, as well as the different locations of strain gages.

Tension recorded in the tie rods in 2002 exceeded the tension from the 2012 test by 20%. No explanation was found for the difference in the measured data.

Tension in tie rods obtained from the FE analysis matched the adjusted test data recorded in 2002 relatively well. The computed combined stress in the tie rod exceeded the stress measured in 2002 by about 12% within the upstream tie rods. Stress measured in the downstream tie rods was 4% lower than the computed combined stress. The computed forces in the upstream tie rod were used in the structural and fatigue analysis of the tie rod threaded connection (conservative assumption).

Analysis of the tie rod threaded connection

An axisymmetric FE model was used in the analysis of the tie rod/socket threaded connections to determine the local stress concentration at the tie rod threads. The side of the finite elements was about 0.03 inch at the thread roots. The socket was restrained against movement at the connection to the header shell. The nominal tie rod forces determined in the FE analysis of the header-to-penstock bifurcation were applied as an input load to the rod FE model. The contact interface between the tie rod end and the socket threads was assigned a friction of 0.5.

Estimated fatigue life for tie rods

Fatigue cracking in metals is associated with the accumulation of irreversible plastic strains. In the modern fatigue analysis of metals, two main approaches dominate the engineering investigations: total life and crack growth. Reclamation implemented both approaches in estimating the fatigue life of the penstock tie rods for three load cases defined for the power unit operations. Dr. Ted Anderson, P.E., Chief Technology Officer at the Quest Integrity Group of Boulder, Colorado, was consulted on the approach for the tie rod fatigue analysis and reviewed results of the analysis.

The three operational cyclic load conditions were identified in the fatigue analysis of the header/penstock branches at the Hoover Dam power plant: 1) header/penstock pressurization and dewatering; 2) change in penstock discharge; and 3) fluctuating operational loads due to unit pulsation and tie rod vortex shedding.

Results of fatigue analysis

The safe fatigue life of the tie rods exceeds the anticipated operation life of 200 years for the penstock structure. based on current operation conditions projected into the future.

The crack growth approach estimated duration of about 7,700 years for a crack to grow from 0.50 to 0.51 inch.

In the absence of pre-existing cracks, estimated fatigue life of tie rods would be even longer. Therefore, it can be concluded that failure of the tie rods over the assumed 200-year operational life of the penstocks is very low.

Lessons learned

The main lesson learned from examining the penstock tie rods at Hoover Dam is the importance of calibrating the analysis models and checking the results by alternative methods.

Jerzy Salamon, PhD, PE, is a technical specialist at the U.S. Department of Interior’s Bureau of Reclamation, Technical Service Center, in the Waterways and Concrete Dams Group.

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