Michel Aubertin

A multiaxial stress criterion for short- and long-term strength of isotropic rock media

Natural and induced stress states around man-made openings in rock generally have different magnitudes along the principal axes. Accordingly, appropriate stability analyses should be based on expressions that take into account the full stress tensor. Based on the main features of compressive and tensile failure of isotropic media, the authors propose a general multiaxial criterion for describing the short-term failure (STF) strength as well as the damage initiation threshold (DIT) of rocks and rock masses. Time and size effects are explicitly included in the formulation. The influence of time is described by an extension of the subcritical crack growth theory in which the DIT is introduced. This damage initiation threshold represents the stress state below which there is virtually no crack growth, and hence corresponds to the long-term rock strength. Size effects, on the other hand, are treated using a generalized version of existing power-law expressions in which limiting values have been imposed for the relative size of representative elements. Application of the criterion to rock masses is done using simultaneously the size effect function for the case where no new types of defects are introduced, and a function of the RMR geomechanical classification to take into account the influence of new types of discontinuities such as joint sets. Sample applications of the criterion, using simplified calculations for rock structures, are shown and briefly discussed.

Practical pedotransfer functions for estimating the saturated hydraulic conductivity

The saturated hydraulic conductivity k is one of the most important and widely used geotechnical parameters, commonly involved in a diversity of applications. The value of k depends on many factors, which can be divided into three classes: properties of the fluid, pore size distribution, and characteristics of the solid surfaces. Because the latter two are not necessarily constant within a given deposit, the hydraulic conductivity may vary significantly in space. Engineers and scientists need indications about how changing factors may affect the actual k value. In this paper, the authors propose some simple expressions, based on pedologic properties, to estimate the value of k. Using experimental results of their own and taken from the literature, it is shown that the proposed pedotransfer functions can be used for quickly estimating the k value for granular and plastic/cohesive soils. Such expressions can be employed, with a useful chart format, for the preliminary design phase of a project, and also for estimating the range of k values to be anticipated within a given deposit.

Evaluation of diffusive gas flux through covers with a GCL

Abstract The main purpose of geosynthetic clay liners (GCLs) used in cover systems is to limit the infiltration of water to the wastes disposed underneath. In many situations however, the cover system should also be able to limit gas flux, so that undesirable products emitted from the wastes, like radon or methane, will not escape to the atmosphere. In other situations, covers may have to prevent oxygen from the atmosphere to come into contact with reactive materials, such as sulphidic tailings that could otherwise generate acid. It is thus important for cover design to evaluate gas flux through the GCL used in the system. This gas flux is usually controlled by diffusion through the porous media, because such highly saturated fine grained materials have a very low gas permeability. In this paper, the authors briefly review the basic theory used to calculate diffusive gas flux F g , and introduce an experimental procedure to evaluate, in the laboratory, the effective diffusion coefficient D e which controls this flux. Experimental results obtained on a nonwoven needlepunched GCL are shown and compared to values ensuing from a predictive model that relates D e to porosity and degree of saturation. Sample calculations on gas flux in cover systems are finally presented and discussed.

A unified viscoplastic model for the inelastic flow of alkali halides

Abstract The present paper proposes a novel viscoplastic model to describe the inelastic behaviour of polycrystalline alkali halides. This model is of the unified type. It consists of a kinetic law and three evolution laws associated with three state variables, B, R and K. Variables B and R are internal stresses, which usually oppose the applied stress, and which induce kinematic and isotropic hardening respectively. The variable K is a scalar used to normalize the active stress, thus contributing to the isotropic hardening of the material. The proposed unified model is physically based, and allows a correct representation of both transient and steady-state flow under diverse loading conditions. It is valid for both instantaneous (plastic) and delayed (creep) components of the inelastic strains. Various phenomenological attributes of the model are discussed and compared to the theoretical and experimental behavior of polycrystalline alkali halides.

An improved analytical solution to estimate the stress state in subvertical backfilled stopes

The increasing use of backfill in underground mines requires a better understanding of the interaction between the relatively soft fill material and the surrounding rock mass. In recent years, it has been shown that stresses in backfilled stopes can be estimated using an approach based on Marston’s arching formulation developed initially for buried conduits in trenches. However, despite its advantages, this approach has some shortcomings. For instance, it postulates that both the vertical and horizontal normal stresses are uniformly distributed across the opening width. Numerical investigations conducted by the authors have shown that this assumption is not always valid. This paper presents a modification to the Marston-based solution, which leads to a nonuniform vertical stress distribution across the opening. This modification of the analytical solution involves parameters that have been calibrated against some numerical modelling results. The same equations and parameters are then shown to provide a go...

An analytical solution for the nonlinear distribution of effective and total stresses in vertical backfilled stopes

The increasing use of backfill in underground mines requires a proper evaluation of the stress state in and around the filled openings. This is, however, a relatively complex issue due, in part, to the large contrast in strength and stiffness between the backfill material and surrounding rock mass. In recent years, it has been shown that arching theory, based on limit equilibrium analysis, can be used to estimate the stress distribution in backfilled stopes. Nonetheless, many simplifications are involved in such analytical solutions and this affects the precision and significance of the calculated results. In this paper, a previously developed solution is enhanced by introducing the combined effects of non-uniform vertical stress distribution and positive pore water pressure. This leads to a more representative analytical solution, as demonstrated by successful comparisons with numerical simulations. The results indicate that the proposed solution can be used to estimate the effective and total stress state in submerged or partially submerged backfilled stopes with a simple geometry.

A damage initiation criterion for low porosity rocks

Abstract When low porosity rock samples are loaded beyond a certain threshold, microcracking occurs. This threshold can be seen as a yielding condition in an elasto-plastic model, or as a damage initiation criterion in an internal state variable constitutive model. In this paper, the authors present a simple multiaxial formulation used to describe this threshold in the conventional stress space. The criterion is applied to a hard rock (granite) and to a soft rock (rocksalt), and its significance is discussed.

Horizontal pressure on barricades for backfilled stopes. Part I: Fully drained conditions

Stope backfilling is used in underground mines to provide a safer working space for personnel and machinery. To ensure a secure application of backfill, it is critical to accurately evaluate the pressures exerted on the walls and barri- cades placed near the base of the stope to retain the fill materials. In this paper, existing solutions for evaluating the stresses on barricades are reviewed. The authors then propose a new three-dimensional analytical solution that takes into account the stress transfer from the backfill to the walls in both the stope and access drift. In particular, the solution con- siders the influence of the barricade position within the drift on the stress state. Comparisons are made between the pro- posed solution, physical model test results, and numerical simulations. The good agreement between various results indicates that the proposed formulation provides a good estimate of the pressure on a barricade. The solution presented here is applicable to fully drained backfill (without water-pore pressure); the solution for saturated backfill is given in a companion paper (see Part II, this issue).

An internal variable model for the creep of rocksalt

SummaryThe creep strain rate