Slope reliability analyses using the principle of maximum entropy

John Russell Lee Read, Purdue University

Abstract

Conventional deterministic, two-dimensional limiting equilibrium analyses define the reliability of slopes in terms of a factor of safety which compares the strength necessary to maintain limiting equilibrium with the available strength of the soil or rock along specified surfaces, generally the base of individual slices. In addition to the constraint of limiting equilibrium, there is the requirement that the calculated values of the factor of safety must be calibrated against those found to be tolerably safe from previous experience with like structures. Despite such precautions, slope failures continue to occur. A new approach that couples the concept of the safety margin with the principle of maximum entropy has been developed to supplement the existing methods of analysis. The principle of maximum entropy demonstrates that there is a unique measure of the uncertainty contained in a given process. The implication is that a probability distribution represents a state of knowledge and that the concept of satisfying maximum entropy provides the least biased measure of uncertainty. The developed solution incorporates two random (uncertain) variables, phi and cohesion and, utilizing their expectations, variances and covariances, provides a measure of the reliability of the overall system. This is done by balancing the forces and moments acting on the individual slices in such a way that their probabilities of failure are equated for each slice, not their factors of safety as is done conventionally. The resulting distribution maximizes the entropy of the system. The end result is that a least biased solution is obtained using only what is known about the geotechnical model and the parametric values. In turn, the computed probability of failure is a global value that provides a linearly scaled measure of the expected performance of the slope. Four examples of the use of the developed method of analysis in typical geotechnical situations are studied. These examples include the assessment of the reliability of an earthen embankment, a levee system, and slopes excavated in clay and rock materials.

Degree

Ph.D.

Advisors

Harr, Purdue University.

Subject Area

Civil engineering

COinS