ballasted to achieve full and even skirt penetration, but there are limits to the magnitudes of the forces that can be applied. It is thus essential to predict the maximum possible resistance to skirt penetration with high reliability.

Borings and CPTs performed at several platform sites reveal that layers of dense sand or hard clay may be encountered at some locations, giving rise to locally very high resistance to penetration of the skirt system. Measurements of cone penetration resistance are available only at a few points in the vicinity of the proposed platform location. Even if cone penetration resistance values were known at all points, the penetration resistance could not be predicted with certainty, since the actual location of the platform can be 20 to 30 m from the planned locations.

A probability model was used by Tang (1979) to evaluate the individual sources of uncertainties and their effect on predicted penetration resistances. The CPT data recorded at discrete locations near a site were first converted to skirt penetration resistance values at those points. These values were then analyzed to yield an average penetration resistance at a given depth; the standard deviation was also estimated, to serve as a measure of the spatial variability of penetration resistance between points at the given depth. The resistance values were expected to be similar at adjacent locations, whereas they might be practically unrelated at locations that are distant from one another. The recorded cone penetration resistance values were analyzed to estimate this correlation of penetration resistance with distance. The model was then used to calculate the expected total penetration resistance, the possible unbalanced moment, and their standard deviations as functions of depth of skirt penetration. Besides accounting for the spatial variation of penetration resistance, these standard deviations included the uncertainty in correlation of skirt resistance with cone resistance, and the uncertainty due to the limited number of CPTs that were performed at the site.

The probability model was applied to the Brent D platform, where 31 CPTs were carried out within an area of 50,000 m². To describe the uncertainty of the prediction using the probability model, a band of one standard deviation of total penetration resistance (corresponding to about 68 percent probability) and the central 50 percent band of the unbalanced moment were developed. These are shown in figures 2-5a and 2-5b. The figures show that there is good agreement between the predicted and observed values. The width of the probability bands depends on the accuracy of the correlation of skirt penetration resistance with cone penetration resistance values, the degree of spatial variation of the resistances, and the number of CPTs performed, and it would thus vary from site to site.

As an alternative to probability analysis, a commonly used empirical method to estimate the unbalanced moment assumes that one-half of the platform base will be subjected to 130 percent of the average skirt penetration resistance at a given depth whereas the other half will be subjected to only 70 percent. From this differential pressure on adjacent halves of the platform base, the unbalanced moment can be estimated as a function of penetration depth. The result is shown by the “empirical prediction” curve in Figure 2-5a. Using a 50 percent probability band provides a more realistic approach by accounting for the degree of inherent spatial variability at different depths, as shown in Figure 2-5b. The result was useful in choosing the design ballast capacity, so that a given