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Riahi A.,Rocscience Inc. | Curran J.H.,University of Toronto
Mathematics and Mechanics of Solids | Year: 2011

In this paper we discuss the mechanics of the Cosserat continuum and its relevance to the description of structural elements and materials with microstructure. It shows how the standard beam and plate formulations can be derived as reduced forms of the generalized Cosserat continuum. Furthermore, the Cosserat description of materials with microstructure and the procedure to determine the constitutive equations for such materials are described. ©The Author(s) 2011.

Dang H.K.,Rocscience Inc. | Yacoub T.,Rocscience Inc. | Curran J.,Rocscience Inc. | Curran J.,University of Toronto | And 2 more authors.
Computers and Geotechnics | Year: 2014

Newton's method is a commonly used algorithm for elasto-plastic finite element analysis and has three common variations: the full Newton-Raphson method, the modified Newton-Raphson method and the initial stiffness method. The Newton-Raphson methods can converge to the solution in a small number of iterations when the system is stable; however, the methods can be quite computationally expensive in some types of problems, for example where the tangent stiffness matrix is unsymmetric or the plasticity is highly localized. The initial stiffness method is robust in those cases but requires a larger number of iterations. This prompted the formulation of many acceleration techniques in literature. In this paper, those techniques will be briefly discussed. This will be followed by the development of a modified acceleration technique for the initial stiffness method. The performance of the modified accelerated initial stiffness method will be examined in elasto-plastic analyses, using both direct and iterative matrix solvers. The results will be compared - in terms of the required number of iterations and the computation time - with an existing accelerated initial stiffness method, the non-accelerated initial stiffness method and the Newton-Raphson tangent stiffness method. © 2014 Elsevier Ltd.

Hammah R.E.,Rocscience Inc. | Yacoub T.E.,Rocscience Inc. | Corkum B.,Rocscience Inc. | Riahi A.,Rocscience Inc. | Curran J.H.,University of Toronto
44th US Rock Mechanics Symposium - 5th US/Canada Rock Mechanics Symposium | Year: 2010

This paper explores the application of the Finite Element Method (FEM) with discontinuity networks and Shear Strength Reduction (SSR) analysis to analyze and design large open pit slopes. It discusses the uncertainties in the input parameters for an FEM model of a blocky rock slope, and describes the attributes of the modelling tools needed for practical open pit analysis. The paper then shows how the FEM, through scenario and probabilistic analysis, can be used to design optimal pit slopes under uncertainty. Copyright 2010 ARMA, American Rock Mechanics Association.

Allan F.C.,Rocscience Inc. | Yacoub T.E.,Rocscience Inc. | Curran J.H.,University of Toronto
46th US Rock Mechanics / Geomechanics Symposium 2012 | Year: 2012

Kriging is a well-documented spatial interpolation technique used in geotechnical engineering problems where a material property is governed by an unknown spatial distribution. This paper studies the effect of kriging on slope stability analysis and compares it to other interpolation methods. Statistical distributions describing the factor of safety (FS) of a trial slope are generated. For reference, purely random Gaussian fields with increasing variance are examined first. Kriging and other spatial interpolation methods are then introduced using subdomains of the random field as input points. The number of known points is found to have a significant effect on the FS distribution, underscoring the importance of good sampling methods. Kriging has a smoothing effect on the input data and kriged predictions revert to the mean of the input points when no input points are nearby. The interpolated fields it produces tend quickly to the reference value of the FS as the number of input points becomes larger. In this respect, kriging outperforms other interpolation methods by supporting the results of homogeneous analyses while accommodating measured deviations from the mean rock properties. However, the smoothed field generated by kriging does not reproduce the statistical features of the original data. It may omit potential failure mechanisms due to localized, probabilistic weakness in the rock mass. Several representative examples of rock slopes are presented in this paper to illustrate the effects of using kriged estimates to calculate the overall FS for a slope stability problem. Copyright 2012 ARMA, American Rock Mechanics Association.

Vijayakumar S.,Rocscience Inc. | Yacoub T.,Rocscience Inc. | Ranjram M.,Rocscience Inc. | Curran J.H.,University of Toronto
46th US Rock Mechanics / Geomechanics Symposium 2012 | Year: 2012

In the lumped mass model which is used in various commercial software (eg. CRSP and Rocfall 4.0), the division of kinetic energy into translational and rotational components is done through a combination of energy balance and empirical relationships. Other than slope geometry, the required input data are the normal coefficient of restitution, the tangential coefficient of restitution and the coefficient of rolling friction. In order to accommodate shape and rotational effects in lumped mass models, two empirical factors related to size and normal impact velocity are employed. Using the lumped mass model, values of normal coefficient of restitution greater than 1 were reported in many field observations, with values as large as 2 obtained. This makes the application of the lumped mass model questionable in some situations. We have proposed a two-dimensional shape-dependent mechanistic model where only two material parameters, namely the normal coefficient of restitution and the friction coefficient, are used. The proposed model uses the shape, size and point of contact of the rock to calculate the translational and rotational components of the kinetic energy. Through this new approach which incorporates complete two-dimensional rigid body dynamics, we are able to predict an apparent normal coefficient of restitution greater than 1 while, at the same time, not violating the principle of conservation of energy. Copyright 2012 ARMA, American Rock Mechanics Association.

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