Saeed Nazari; Alireza Arab Amiri; Abolghasem Kamkar Rouhani; Fereydoun Sharifi
Abstract
In this work, we simulate the frequency-domain helicopter-borne electromagnetic (HEM) data over the two-dimensional (2D) and three-dimensional (3D) earth models. In order to achieve this aim, the vector Helmholtz equation is used to avoid the convergence problems in Maxwell’s equations, and the ...
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In this work, we simulate the frequency-domain helicopter-borne electromagnetic (HEM) data over the two-dimensional (2D) and three-dimensional (3D) earth models. In order to achieve this aim, the vector Helmholtz equation is used to avoid the convergence problems in Maxwell’s equations, and the corresponding fields are divided into primary and secondary components. We use the finite difference method on a staggered grid to discretize the equations, which can be performed in two ways including the conventional and improved finite difference methods. The former is very complex in terms of programming, which causes errors. Furthermore, it requires different programming loops over each point of the grid, which increases the program’s running time. The latter is the improved finite difference method (IFDM), in which pre-made derivative matrices can be used. These pre-made derivative matrices can be incorporated into the derivative equations and convert them directly from the derivative form to the matrix form. After having the matrix form system of linear equations, Ax = b is solved by the quasi-minimal residual (QMR). IFDM does not have the complexities of the conventional method, and requires much less execution time to form a stiffness or coefficient matrix. Moreover, its programing process is simple. Our code uses parallel computing, which gives us the ability to calculate the fields for all transmitter positions at the same time, and because we use sparse matrices thorough the code memory space, requires to store the files is less than 100 MB compared with normal matrices that require more than 15 GB space in the same grid size. We implement IFDM to simulate the earth’s responses. In order to validate, we compare our results with various models including the 3D and 2D models, and anisotropic conductivity. The results show a good fit in comparison with the FDM solution of Newman and the appropriate fit integral equations solution of Avdeev that is because of the different solution methods.
Rock Mechanics
H. Zebarjadi Dana; R. Khaloo Kakaie; R. Rafiee; A.R. Yarahmadi Bafghi
Abstract
Slope stability analysis is one of the most important problems in mining and geotechnical engineering. Ignoring the importance of these problems can lead to significant losses. Selecting an appropriate method to analyze the slope stability requires a proper understanding of how different factors influence ...
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Slope stability analysis is one of the most important problems in mining and geotechnical engineering. Ignoring the importance of these problems can lead to significant losses. Selecting an appropriate method to analyze the slope stability requires a proper understanding of how different factors influence the outputs of the analyses. This paper evaluates the effects of considering the real geometry, changes in the mesh size, and steepness of the slope, as the dimensional effects, and changes in the geomechanical parameters, as the media effects on the global slope stability of an open-pit mine using finite difference methods with a strength reduction technique. The case study is the Tectonic Block I in the old pit (steep slope) and the redesigned new pit (gentle slope) of the Choghart iron mine. In the first step, a series of 2D and 3D slope stability analyses are performed and compared in terms of safety and potential failure surface. The results obtained show that by considering the real geometry of the slope, the FOS3D/FOS2D ratio (3D-effect) is more than 1 in the all cases. The 3D-effect in the new pit is smaller than that in the old one. In the next step, sensitivity analysis of the cohesion and the friction angle is performed for the 2D and 3D analyses. The results obtained show that the sensitivity of the analyses in terms of the 3D-effect to the change in the friction angle, especially in a low-friction angle, is more significant than that to the change in the cohesion.
S. E. Mirsalari; M. Fatehi Marji; J. Gholamnejad; M. Najafi
Abstract
Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is ...
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Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each higher order element is divided into four sub-elements bearing a cubic variation in the displacement discontinuities). Then the classical finite difference formulation (i.e. the backward, central, and forward finite difference formulations) is hybridized using the boundary element formulation, enabling us to obtain the nodal tangential stresses and horizontal strains along the elements. Several example problems are solved numerically, and the results obtained are then compared with their corresponding results available in the literature. These comparisons show the effectiveness and validness of the proposed method. A classical practical problem is also used to verify the applicability of the hybridized method.
