The following discussion provides only a brief review of the PRAISE software. The references cited give the details. The results reported here were generated by use of the PRAISE software, which was developed with NRC support over a period of some 20 years. PRAISE is based on deterministic fracture mechanics, with some of the inputs considered as random variables. This allows the statistical distribution of lifetime to be computed, rather than a single deterministic failure time. The probability of failure (leaks of various sizes) is obtained from the computed lifetime distribution.

Several versions of PRAISE were employed, depending on the nature of the problem. The original version of PRAISE [F.1] considers fatigue crack growth from crack-like weld defects introduced during

fabrication. Semi-elliptical interior surface cracks are considered, usually circumferentially oriented.

The initial crack size and fatigue crack growth properties are the major random variables, and Monte Carlo simulation is used to generate numerical results. Stratified sampling of crack depth and aspect ratio is employed to allow very small probabilities to be obtained without excessive computer time. Figure F. 1 is a schematic representation of the probabilistic fracture mechanics procedures used in the original version of PRAISE. The cumulative probability of a flow (leak) rate exceeding a specified size is generated by PRAISE as a function of time. If the stress history is specified in reactor-years, then the

Figure F.1 Overview of PRAISE Methodology for Probabilistic Analysis of Fatigue Crack Growth

A later version of PRAISE was used the analyze initiation and growth of stress corrosion cracks [F.2]. Both the fatigue crack growth and stress corrosion initiation and growth capabilities are included in pcPRAISE [F.3] and also in WinPRAISE [F.4], which is a Windows version that is much easier to use than the earlier DOS versions. WinPRAISE gives the same results as pcPRAISE for the same problem with the same inputs.

In some cases, the cyclic stresses were such that fatigue crack initiation is the expected dominant degradation mechanism, and it was necessary to use a later version of PRAISE. This version was developed and used in Reference F.5, with additional capabilities described in Reference F.6 (such as the ability to consider detailed circumferential variations of the stresses). The fatigue crack initiation analyses employed probabilistic strain-life relations developed by Argonne National Laboratory [F.7,

F. 8]. Once a fatigue crack initiates, the original growth analysis capabilities in PRAISE are used for the crack growth portion of the lifetime. The depth of an initiated fatigue crack is taken to be 3.0 mm (0.12 inches), in accordance with the ANL correlations, with a random surface length. In some instances, modifications to the source code of PRAISE were made to provide results of particular use for the problem at hand. These instances are discussed in the specific base case problem where they were employed.

In cases where inspection was considered, the nondetection probability was represented by the expression

In this expression, є is the probability of not detecting a crack no matter how deep it is, a* is the crack depth having about a 50% chance of being detected, and v controls the slope of the PND curve. “Good” and “outstanding” detection capabilities were considered [F.9], with the parameters given in Table F.1.

Table F.1 Parameters in Non-Detection Relation

The operating and hydro pressures of Table F.2 were considered.

Table F.2 Operating and Hydro Pressures, psi

A leak detection capability of 19 lpm (5 gpm) was considered, which means that any through-wall crack with a leak rate greater than 19 lpm (5 gpm) was immediately detected and removed from service.