Residual stresses observed in rocks often result from non-compatible initial strains. These stresses can be determined when the incompatibility tensor associated with the initial strain tensor is known. The residual stresses in a cylindrical rock sample can be computed the sample is considered small enough for its incompatibility tensor to be constant.


Les contraintes residuelles, dont on observe couramment les manifestations dans les roches, resultent souvent de l'existence de deformations initiales non-compatibles. Ces contraintes peuvent être calculees lorsque le tenseur d'incompatibilite associe aux deformations initiales est connu. Les contraintes residuelles dans une eprouvette cylindrique sont donnees dans le cas où le tenseur d'incompatibilite est constant.


Eigenspannungen, die man haeufig in Steinen beobachtet, sind oft Ergebnis einer inkompatiblen Deformation des Anfangszustandes. Diese Spannungen koennen berechnet werden, wenn der Inkompatibilitaets-Tensor der Anfangsdeformation bekannt ist. Die Eigenspannungen einer zylindrischen Probe werden fuer Fall eines konstanten Inkompatibilitaets-Tensor bestimmt.


The notion of residual stresses is of constant use in Continuum Mechanics. In metals, these stresses result from quenching, molding or welding, or from a severe thermal or mechanical loading that generates plastic transformations. In other words, residual stresses result from transformations from an initial state in which no residual stress exist; these mechanical or metallurgical transformations can be described. The same cannot be said in the case of rocks. A complete description of the transformations to which a rock - whether sedimentary or metamorphic - has been submitted is, in most cases, impractical. One can only describe the actual rock state and the stresses that are trapped inside the rock - not the process that led to the actual state. However there is no doubt that residual stresses, or internal stresses, are present in rock masses or rock samples. 'Anomalous features' such as: large tunnel convergence, rock outburst, or the disking of rock cores sampled at great depths may have several distinct origins; one of them is the existence of residual stresses.

The incompatibility tensor

A precise definition is needed at this step. Cornet1 (1999) suggests the following definition: ‘Residual stresses: the stress state remaining in the rock mass after the preexisting mechanisms has ceased to operate. The stress can be considered as within an isolated body that is free of external traction.’

Let Ω be an isolated body; residual stresses exist in Ω if the constitutive behaviour of the rock is such that the state of stress satisfying:

(Equation in full paper)

Some residual stresses properties

Inspection of [6] leads to several interesting conclusions, as noted below.

1. Residual stresses are completely defined when the body shape Ω, the elastic constants E and ν, and the incompatibility tensor field E0ij are known.

(Equation in full paper)

2. The residual stresses at any given point depend on the shape Ω of the body in which the point is included. Generally, stresses will be larger when the considered body is larger. A constant or nearly constant incompatibility tensor cannot exist in a large rock mass.

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