Discussion of “Probability and Risk of Slope Failure” by F. Silva, T. W. Lambe, and W. A. Marr

Abstract

The discussers had the opportunity to use the subject paper in an important consulting problem involving bearing stability. We thought the paper provided very useful experience-based judgments, and applying it to our consulting problem allowed us to possibly expand the potential use of the paper. Peck 1969, p. 174–176 explained the initial problem with the potential instability of NASA’s tracked transporter TR. The TR carried the Apollo, and later the shuttle rockets, several kilometers from the vertical assembly building VAB to the A and B launch pads along the A and B crawlerways CW at the Cape Kennedy Space Center in Florida. The CWs have now experienced roughly 100 loaded TR transverses to periodically stress and improve the CW foundation conditions as well as experiencing approximately 45 years of aging since construction. However, NASA’s proposed new Constellation series of rockets include the Ares V, and it will increase the TR bearing load on the CWs by approximately 35%. Our problem: to estimate the probability of success, or reliability, of the TR carrying an Ares V rocket and traversing the weakest foundation area under the existing CW without any distress that could delay a launch. We found the subject paper useful to make the first phase of this estimate, as described below. We first made a comprehensive field investigation of the most critical part of the CWs as identified by Peck 1969. Then we used the information produced to model the problem and predict pore pressure generation and settlement during a first traverse with the new loading. Settlement seemed acceptable but bearing stability remained an issue. A 2D limit equilibrium, slope stability analysis for bearing stability gave a FS= 1.25. Then a draft copy of the subject paper became available and gave us a methodology for estimating reliability. To do this we assumed that the paper applied to all slopes, including our very flat slope of only 3°. We later assumed it also applied to a 2D finite-element analysis. We also estimated from the Table 1 found in the paper under Discussion guide that our overall level of engineering for the problem fell between categories I and II. Using these at FS= 1.25 with the experience curves in Fig. 1 found in the paper under Discussion, the theoretical curves in Fig. 2 found in the paper under Discussion, and the $10 7 consequences curves in Fig. 5 found in the paper under Discussion, we estimated that the annual probability of a bearing stability failure fell between 10 �2 to 10 �4 . Because previous experience Peck 1969 showed the first traverse as the most critical, we concluded that the probability of success equaled at least 99% for the first traverse of the TR carrying the Ares V over only the critical part of the CW identified by Peck. The above methodology provided a quantitative estimate of the probability of success at 99%, based on the authors’ experience. This seemed consistent with our own subjective thinking. It appears that engineers might also use the paper to evaluate the reliability of bearing stability on a surface with a near-zero slope angle. We look forward to the authors’ comments.