The round robin analysis on containment performance will consist of two rounds of analyses, two workshops, and an interim review meeting. The initial workshop, to be held in April of 2010 in Mumbai, India, will include an introductory session on the NRC/NUPEC test and the ISP48 results. Additionally, one session will be devoted to technical presentations pertaining to finite element experience and lessons learned from the ISP48 exercise. Finally, sessions will be held to discuss and determine the scope of the analyses to be performed in phases one and two of the round robin analysis on Containment Performance.
Phase-One
Phase One of the round robin analysis on containment performance, whose focus is the further examination of those local effects which were observed to require more study in the previous round robin analyses, will include an examination into the effects of containment dilation on prestressing force, slippage of prestressing cables, steel-concrete interface, failure mechanisms, and the use of nominal versus in-situ conditions in the previous round robin analyses. Analysis results from this phase may also help in calibrating the model in Phase Two of the analyses.
Phase 1.1. Tendon Forces as a Function of Containment Dilation
Some important observations made in the previous round robin analyses hosted by Sandia National Laboratories (SNL) concerned the nature of hoop tendon measurements as pressure increased within the model. It was noted that when pressure overcame prestress, tendon stress distributions changed from the classical angular friction design assumption to an approximately uniform distribution; then they stayed fairly uniform at most higher pressures. Toward the end of the test, some tendon interior forces slightly exceeded the force at the anchor. The pre- and post-test analyses resulted in poor agreement in the hoop tendon stress distributions despite the good agreement with radial displacements. The overprediction of dome and overall vertical displacements and anchor forces, in addition to the underprediction of interior gage stresses warrant further examination. Participants will be asked to analytically explore tendon forces as a function of containment dilation.
Phase 1.2. Slippage of Prestressing Cables
It was also observed that the apparent strain increases in the tendons corresponding to the force/strain gage readings are significantly larger (e.g. 0.48% versus 0.35%) than the strain that corresponds purely to radial expansion. This could only be explained by force redistribution associated with sliding. Thus the position of the tendon relative to the concrete must be allowed to change after initial prestress in order to adequately simulate tendon behavior during over-pressurization.
It was seen through test measurements and analytically that tendon friction is important to the tendon behavior, but traditional friction design formulas that predict tendon stress distribution begin to break down once pressurization exceeds the pressure that overcomes prestress. The coefficient of angular friction appears to lessen, allowing sliding and force redistribution as the vessel expands, but more importantly, some parts of the tendon are forced to reverse direction of travel relative to the duct, reverse it from the direction of travel experienced during prestressing.
Cylinder hoop tendon data shows evidence that angular friction forces were overcome by differential tendon forces resulting in the tendons sliding, relative to the ducts, during pressurization. The measurements indicate that the shape of the tendon stress profile completely changes during pressurization. The increase in tendon strain, which is greater than the corresponding cylinder wall hoop strain, implies that the portions of the tendons are slipping in order for higher deformation at other azimuths to be accommodated. The participants will be asked to investigate the slippage of prestressing cables.
Phase 1.3. Steel-Concrete Interface
Separations were observed surrounding containment penetrations during testing of the PCCV structure. Many of the highest strains recorded during the limit state test (LST) were near the Mainstream (M/S) and Feedwater (F/W) penetrations. Even at locations which were designed to be identical in geometry, there was a wide variation in peak strain data. These variations were most likely due to slight variations in liner thickness (due to manufacturing and weld repair grinding), gage position relative to the collar/weld, material properties (including welding heat effects), etc. Of particular interest is the separation between the concrete and sleeves, the stress concentrations that lead to liner tearing, and the development of potential leak paths using strain information. The participants will be asked to quantify the risk associated with the formation of a gap as a function of a potential leak path.
Phase 1.4. Failure Mechanisms
During the PCCV test, tearing in the liner was observed. Of interest is the characterization of the liner tearing mechanism. The applicability of a fracture mechanics approach versus ductile failure approach needs further investigation. Ultimately, the participants need to determine how to predict tears in the liner from the finite element model strains. To this end, they need to determine if there are areas where fracture mechanics can be applied to predicting the size of liner tears or if the tears should be characterized with ductile failure.
Phase 1.5. Differences Between Nominal Design and In-Situ Construction
In the initial pre-test Round Robin Analysis (completed in 2000), participants were provided with detailed design drawings and material properties. Upon construction of the PCCV, participants were provided with the in-situ construction details (where different from design). Of interest is the use of the in-situ material properties and geometric details versus nominal design values in analysis. Many participants made little to no changes to the analytical models for the pre-test and post-test analyses. This part of the Round Robin Analysis Containment Exercise would like participants to examine the significance of variation from design in geometric and material property values in analytical results. The participants will examine scatter in data, non-uniformity of tendon forces, geometric irregularities, deviations in material properties, friction losses, and initial conditions from a probabilistic rather than deterministic framework. To this end, the participant will present containment capacity as a cumulative distribution function, incorporating the aspects mentioned in Phase 1.1 through 1.4.
Phase-Two
This phase of work has two distinct parts. Following the first phase of the round robin analyses, the participants will be asked to examine methods to estimate leakage rate as a function of pressure. These methods will be evaluated relative to the PCCV test results, and incorporate lessons learned from the first phase of the Round Robin Analysis. The second part of this phase of the analyses will consist of enumeration of methods for predicting leakage of the prestressed concrete containment vessel as a function of pressure and temperature. These methods will then be applied to characterize the performance, in terms of leakage rate under pressure and temperature loads, and transition them to probabilistic space.