Gregory B. Baecher

The effect of discontinuity persistence on rock slope stability

Discontinuity persistence has a major effect on rock mass resistance (strength) but, as direct mapping of discontinuities internal to a rock mass is not possible, persistence is a difficult parameter to measure. As a result, the conservative approach of assuming full persistence is often taken. In this paper a method is developed for relating rock mass stability and hence persistence to the geometry and spatial variability of discontinuities. The method is applied to slope stability calculations in which the probability of failure is related to discontinuity data, as obtained in joint surveys. The complete method makes use of dynamic programming and simulation, but a closed form expression satisfactory for most purposes is also presented.

Statistical analysis of rock mass fracturing

Over the past 10 years considerable empirical work has been reported on the stochastic description of rock mass fracturing, and on the statistical design of joint surveys. This has led to consistent conclusions on the distributional properties of such discontinuities, and is beginning to lead to improved survey designs. Two of the strongest conclusions appear to be the exponentiality of the distribution of spacings between discontinuities when measured by their intersections with sampling lines, and the lognormality of discontinuity trace lengths as observed in outcrops. Consistent conclusions on the form of orientation distributions appear more elusive. Sampling biases in joint surveys now seem more pervasive than was earlier thought. In addition to the well-known orientation bias in sampling from two-dimensional outcrops, proportional length bias in which larger discontinuities are sampled with increased probability, and censoring biases in which larger discontinuities are often only partially observed, complicate statistical inferences. These results are reviewed against a recent study involving some 15,000 data.

Progressively censored sampling of rock joint traces

A number of sampling problems in geology and engineering geology involve geometric variables, and must deal with the almost pervasive biases that accompany geometric sampling. Among these biases is the fact that not all elements of the sampled population are fully observable. Some members, usually the largest, are censored. Inferences cannot ignore the censored members of the sample, because the censoring is often related to the variable being inferred—for example, the case of sampling for feature size. Inferences from samples are conceptually straightforward, and for the simple case of exponential parent distributions, mathematically tractible. Maximum likelihood and Bayesian results are given for the exponential case, and examples are drawn from joint surveys in rock mechanics.

DECISION ANALYSIS APPLIED TO ROCK TUNNEL EXPLORATION

Abstract Exploration planning is a process of decision making under uncertainty. The decision if and where to explore depends on construction strategies and cost; the selection of construction strategies depends on knowledge of geologic conditions which are not known with certainty before exploration is performed. The proposed application of decision analysis provides a relatively simple approach to the tunnel exploration problem. The existing knowledge of geology, the possible construction strategies and their costs, the reliability and the cost of considered exploration methods are used to establish if and where exploration is beneficial. The resulting hierarchy of locations where exploration is beneficial and the comparison of expected values of exploration for different exploration methods provides the basis for the selection of a particular site and method. Graphical and simple numerical means have been created that make the proposed approach a convenient and fast tool in the hands of the decision maker.

Simplified Geotechnical Data Analysis

The simplified procedure is a relatively straightforward technique for the analysis of data scatter and uncertainty in geotechnical exploration. This is a first-order second-moment method which imposes little computational burden and requires few special assumptions, yet which helps rationalize parameter estimation and the selection of design factors of safety.

Applied Geotechnical Reliability Analysis

This paper builds upon a companion piece, “geotechnical profile estimation,” to illustrate applications of reliability analysis to geotechnical engineering. To this end, three case studies are discussed, each illustrating a different aspect of reliability analysis in application to geotechnical problems. The case studies are actual projects for which reliability analyses have been used in reaching decisions(1).