Properties of rock mass vary and an exact value of one of the properties at any given location cannot be predicted. On the other hand, in applying some classical methods of structure stability analyses, only one value of certain parameter must be input to the formulas or even the computer codes. Stability of the structure is evaluated by comparing the capacity (strength or resisting force) of the structure and the demand (stress or disturbing force) and expressed in term of Factor of Safety (FoS). The FoS calculated by this deterministic approach obviously has limitation for assuring the stability of structure.

The rock mass uncertainties can be dealt with by taking into account statistical distributions of the parameters in the FoS calculation or by developing empirical design guidelines or curves based on a particular regression techniques on case histories of stable and unstable structures with particular design parameters and properties. This paper gives some examples illustrating approaches for dealing with uncertainties in the rock mass.

1. Introduction

Design and construction in rock require processes and procedures that are in many ways different from other design and construction projects, because the main construction material is the rock mass itself rather than an engineered material. The rock mass properties do not have a single fixed value but may assume any number of values at any given location. It is then obvious that the classical approach of Factor of Safety (FoS) where the calculations are based on one value of a certain parameter, is unable to fully assure that a structure with FoS greater than 1.0 will be stable.

Two approaches can be utilised in dealing with the rock mass properties uncertainties. First, the FoS calculation is conducted by taking into consideration all possible values of rock mass properties. In practice, the values can be represented by the statistical mean and the standard of deviation of the parameters which depend on their statistical distribution functions. The calculated FoS then has also mean value and standard of deviation. Probability of having a particular value of FoS can also be calculated. Secondly, stable and unstable structures case histories can be collected and for practical reasons, the main data that must be recorded for each structure are geometry, strength, stress, and stability condition. Curve separating stable and unstable case histories can be constructed by using regression techniques. In addition, iso-probability of stable (or failure) curves can also be plotted.

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