Finite Element Analysis of Seismic Response of Surface Penstock Pipe in Hydropower Station

Literature Overview

This paper by Liu Yuan, Shi Changzheng, Wu Hegao, and Cheng Zhenglong, published in Water and Power Resources (Vol. 32, Issue 7, 2014, pp. 86-89), presents a finite element analysis of the seismic response of a surface penstock pipe (open pipe) at a hydropower station. The study was supported by the China Postdoctoral Science Foundation (2013M542058) and was conducted at the State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, in collaboration with the China Power Engineering Consulting Group Central-South Survey and Design Institute.

The research investigates two operational scenarios: normal operation encountering an earthquake, and pipe draining (empty pipe) encountering an earthquake. The finite element time-history analysis reveals that during normal operation, the penstock pipe primarily experiences large lateral acceleration and displacement, while during the draining condition, the absence of water and the presence of vertical restraint measures lead to significant vertical acceleration and displacement, causing the pipe to jump off its supports.

Core Technical Points and Seismic Response Analysis

The seismic response of surface penstock pipes is a critical safety concern in hydropower engineering. The penstock pipe conveys water from the reservoir or intake to the turbine, and its failure during an earthquake can lead to catastrophic flooding, equipment damage, and potential loss of life. The finite element model used in this study captures the complex interaction between the pipe structure, the internal water (when present), the support system, and the seismic ground motion.

From a materials and fabrication perspective, the penstock pipe is typically constructed from high-strength low-alloy steel plates (e.g., Q345R, Q370R, or 16MnR per GB 150) or carbon steel plates (e.g., Q235B). The pipe diameter can range from 2 m to 5 m or more, with wall thicknesses of 20 mm to 60 mm. The fabrication involves plate rolling, longitudinal seam welding, circumferential seam welding, and the installation of internal and external stiffening rings.

The following table summarizes the key findings of the seismic response analysis:

The distinction between the two operational conditions is of paramount importance. During normal operation, the water within the pipe provides significant mass and damping, which helps to stabilize the pipe and limit its vertical movement. The water weight also increases the normal force on the supports, enhancing the frictional resistance against lateral sliding. During the draining condition, the absence of water significantly reduces the mass and the normal force on the supports, making the pipe susceptible to vertical jumping under seismic acceleration.

Welding and Fabrication Quality for Seismic Applications

The seismic performance of the penstock pipe is directly related to the quality of its fabrication and welding. The following welding considerations are critical for seismic applications:

1. Weld Procedure Qualification: The welding procedures used for the penstock pipe fabrication must be qualified in accordance with the relevant standards (e.g., GB/T 19866 for pressure equipment welding qualification, or ISO 15614). The qualification should include impact testing of the weld metal and HAZ at the minimum design temperature, which for seismic applications is typically -20°C or lower.
2. Residual Stress Control: The welding of thick steel plates (20-60 mm) generates significant residual stresses that can reduce the buckling resistance and promote crack initiation under cyclic loading. Post-weld heat treatment (PWHT) should be considered for thick sections to relieve residual stresses. Alternatively, welding sequences should be optimized to minimize distortion and residual stress, using techniques such as symmetric welding, step-back welding, and intermittent welding.
3. Weld Inspection: The longitudinal and circumferential seam welds should be inspected by radiographic testing (RT) or ultrasonic testing (UT) to verify full penetration and absence of volumetric defects. The acceptance criteria should follow GB/T 3323 (RT) or GB/T 11345 (UT) at least Grade II. Surface defects should be detected by magnetic particle testing (MT) or penetrant testing (PT).
4. Stiffening Ring Welds: The internal and external stiffening rings are welded to the pipe shell to provide additional stiffness and prevent local buckling under external pressure or seismic loading. The welds between the stiffening rings and the pipe shell should be full penetration welds, with the weld root fully fused to the pipe shell. The weld geometry should be designed to minimize stress concentrations, with a smooth transition from the ring to the shell.
5. Support Connection Welds: The welds connecting the pipe to the support saddles and thrust blocks are critical for the seismic performance. These welds must be designed to withstand the full seismic load without fracture or excessive deformation. The weld design should consider the combined effects of axial force, bending moment, and shear force.

Seismic Design Measures and Engineering Recommendations

The study recommends the implementation of both lateral and vertical restraint measures for the penstock pipe. This is a critical finding that has direct implications for the seismic design of hydropower stations.

Lateral Restraint Measures

Lateral restraint measures include:

• Sliding supports with friction pads: The pipe slides on the support saddle during an earthquake, and the friction force provides lateral resistance. The friction coefficient should be controlled to provide adequate restraint without causing excessive stress on the pipe.
• Guide rails and stoppers: Mechanical stops or guide rails can limit the lateral displacement of the pipe to a safe range. The stoppers should be designed to absorb the kinetic energy of the pipe without damaging the pipe or the support structure.
• Elastomeric dampers: Elastomeric bearings or dampers can provide both lateral restraint and energy dissipation, reducing the peak seismic response of the pipe.

Vertical Restraint Measures

Vertical restraint measures are particularly important for the draining condition, where the pipe can jump off its supports. These measures include:

• Vertical restraint brackets: Steel brackets or straps that encircle the pipe and connect to the support structure, preventing vertical movement.
• Spring-loaded restraints: Spring-loaded devices that allow small vertical movements but prevent large jumps.
• Concrete encasement: Partial or full concrete encasement of the pipe can provide additional mass and restraint, but must be designed to accommodate thermal expansion and seismic movement.

Finite Element Modeling and Validation

The finite element model used in this study should be validated against experimental data or analytical solutions to ensure its accuracy. The model should include:

• Pipe shell elements: Shell elements should be used to model the pipe shell, with an appropriate mesh density to capture the stress distribution and buckling behavior.
• Water mass modeling: The water within the pipe should be modeled using lumped masses or fluid-structure interaction elements, depending on the level of detail required.
• Support modeling: The supports should be modeled using spring elements or nonlinear contact elements to capture the frictional behavior and the gap between the pipe and the support.
• Seismic input: The seismic ground motion should be applied as base excitation, with the acceleration time history selected based on the site-specific seismic hazard analysis.

The time-history analysis should consider both the linear and nonlinear behavior of the structure. The nonlinear behavior includes plastic deformation of the pipe shell, yielding of the welds, and contact loss between the pipe and the supports. The nonlinear analysis is essential for predicting the ultimate capacity and the failure mode of the pipe under strong seismic loading.

Study Insights and Practical Implications

The most significant insight from this research is the recognition that the seismic response of the penstock pipe is highly dependent on the operational condition. The draining condition, which is often considered a less critical scenario, can actually be more dangerous from a seismic perspective because the absence of water removes the stabilizing mass and the vertical restraint.

From a quality control perspective, this finding emphasizes the importance of ensuring that the vertical restraint measures are properly installed and maintained. The restraint brackets, straps, or other vertical restraint devices should be inspected regularly for corrosion, fatigue cracking, and loosening. The inspection should include visual inspection, ultrasonic testing of critical welds, and dimensional checks.

The study also highlights the importance of considering the combined effects of seismic loading and operational conditions in the design of hydropower station penstock pipes. The design should be based on the worst-case scenario, which may not necessarily be the normal operating condition. This requires a comprehensive seismic analysis that considers all possible operational states, including normal operation, draining, maintenance, and emergency shutdown.

In conclusion, this research provides valuable insights into the seismic behavior of surface penstock pipes in hydropower stations. The identification of the draining condition as a critical scenario for vertical pipe jumping underscores the need for comprehensive restraint measures. For engineers involved in the fabrication and welding of penstock pipes, the key takeaway is that the seismic performance depends not only on the structural design but also on the quality of the restraint system and the integrity of the welds that connect the pipe to the restraint devices.