Rock mass deformability can be expressed with empirical correlations or analytical component models. The paper discusses currently used empirical correlations and analytical models and points out their limitations. A new statistically based analytical model is proposed and the relations between results of the model and current empirical correlations are discussed. The new approach improves understanding of rock mass behavior and appreciation of variance of observations.


La deformabilite des massifs rocheux peut être exprimee par des correlations empiriques et modèles analytiques. On presente et discute, dans cet article, les correlations empiriques et les modèles analytiques disponibles à l'heure actuelle. On propose ensuite un modèle analytique nouveau base sur des statistiques. On explore, enfin, les liens entre le nouveau modèle et les correlations empiriques. Le nouveau modèle permet de mieux comprendre le mecanism de la deformation des massifs rocheux et d'expliquer la variance des observations.


Die Gebirgsverformbarkeit kann mit empirischen Beziehungen oder analytischen Komponenten-Modellen ausgedrueckt werden. Gegenwartig im Gebrauch stehende empirische Beziehungen und Komponenten- Modelle werden besprochen und ihre Schwachen aufgezeigt. Der Artikel beschreibt dann ein neues analytisches Modell, das auf statistischen Prinzipien beruht. Ausserdem werden die Resultate, die mit dem Neuen Modell erzielt werden, mit den gegenwartig in Gebrauch stehenden empirischen Beziehungen und die Varianz von Beobachtungen zu erklaren.


Rock mass deformabiltiy affects the performance of essentially all structures in and on rock, from underground openings and excavations to foundations. Thus, the prediction of deformabiltiy is an important part of rock engineering. The most direct way of estimating deformability is through field testing. However, for meaningful results, field tests must subject large volumes of rock to significant stress. Therefore, the tests are expensive, time consuming, and must be limited in number. To supplement direct testing and to provide estimates of deformability when field tests are impractical, other procedures have been introduced. Broadly, these derive from empirical correlations, on the one hand, or analytical decompositions, on the other. Many such procedures have been introduced. Empirical correlations attempt to statistically relate deformability to index properties, such as RQD, or to descriptive rock mass classifications. Analytical decompositions attempt to predict deformability by summing deformations over elements of the rock mass, such as intact blocks and joints. Both approaches suffer limitations. Correlations are limited by the character of the case studies from which the baseline data come. Decompositions are limited by an inability to measure and specify parameters of the models. Improvement of these techniques is needed. To improve predictions of deformability either more and better data are required, better information is required on joint stiffness and geometries, or a tie-in is required between correlations and decompositions. A tie-in between correlations and decompositions would allow information of each type to, in part, compensate inadequacies in the other, and would allow extrapolations of correlations through decompositions. The present work indicates a connection between correlations and decompostions, which becomes increasingly apparent as the strict geometric assumptions underlying decompositions are relaxed.

2.l Empirical Correlations

Possibly the best known correlation of deformability to indices or descriptions is that of Deere (1967), using RQD. However, others have been proposed, ranging from the refined descriptions of the German-Austrian school (Muller, 1963; Terzaghi, 1946; Stini, 1950), to intricate quantitative descriptions of Barton (1977) and Bieniawski (1975). Indices or descriptions are correlated:

  1. to deformability by correction factors on material properties that are easily determined (e.g., intact modulus),

  2. directly to a rock mass deformability,

  3. to design features (e.g., structural dimensions).

Obviously, correlations are based on field studies, and are limited by the geologic richness of the calibrating cases.

2.1.1 RQD - Modulus Ratio Relations

Deere's work (1967) in conjuction with co-workers was originally based on field studies at Dworshak Dam(1964). Field plate loading tests were compared with intact modulus and RQD to arrive at the empirical correlation of Figure 1. Further data were added by Coon and Merritt (1970) from other sites. All of the data, however, were from good quality rock and the lower portion of the curve is therefore poorly defined. Although Coon and Merrit noted the inadequacy of their data base, little additional data has been publicly presented. A problem with these correlations is that they are based upon jacking tests of limited load and zone of influence. Further, some RQD's are obtained indirectly by correlation with seismic velocity ratios. Although RQD is often assumed to equal the velocity ratio, this is in fact only an approximation. Finally, only a limited number of tests and sites form the basis for the correlations.

2.1.2 Direct Correlations between Descriptors and Rock Mass Deformability.

Quantitative geologic descriptors like fracture spacing and qualitative descriptors of structural features and weathering have been related directly to the deformability observed under one or several structures. Boughton(1968), for example, produced a correlation at dam sites.

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