نشریه روش های تحلیلی و عددی مهندسی معدن
پیاپی 27 (تابستان 1400)

Summary:

Normalizing data distribution, modifying outlier data, and converting datasets from the closed system to the open system are initial preprocessing using multivariate statistical methods. In this paper, PPMT, MAF, and SCT transformation methods are also introduced for this purpose in addition to the log-ratio transformation method. The analyzed data of 396 litogeochemical samples in the Hemych exploration area have been used to evaluate the performance of the transformation methods. The presence of hydrothermal alterations and Cu, Zn, Pb and Fe mineralization on the surface of the study area indicate the susceptibility of this area to porphyry and hydrothermal mineralization. The results of factor analysis on the transformed data by the four mentioned methods show when the distribution function of the transformed data is closer to the multivariate normal distribution, the values of the variance and loading factors are lower. This is due to the decreased correlation of the variables. The results of factor analysis also show that the contour maps of the factor scores obtained from the SCT transformation method can identify the internal and external zones of the porphyry mineralization system of the study area well.

The use of statistical methods, especially multivariate statistical methods, is among the basic principles of geochemical data analysis. However, data with non-normal distribution function, the existence of outlier data, and the closed system of the geochemical data are challenges on the way of using these methods. These problems can cause bias in the results of multivariate statistical analysis such as regression, discriminant analysis, principal component analysis, and factor analysis. The solution to this problem is to use nonlinear transformations to transfer data from one coordinate system to another.

Methodology and Approaches:

In addition to the conventional log-ratio transformation method (ilr-clr), projection pursuit multivariate transform (PPMT), Min/Max autocorrelation factors (MAF), and step-wise conditional transformation (SCT) were used to convert data distribution to a multivariate normal distribution. Then, the factor analysis method was used on the transformed data to identify the factors related to mineralization and the internal and external zones of the porphyry and hydrothermal systems of the study area.

The results of factor analysis on the transformed data by the four mentioned methods show that the closer the distribution of the transformed data to the multivariate normal distribution is, the lower values of the variance and loading factors are. This is due to the decreased correlation of the variables. The results of factor analysis also showed that the contour maps of the factor scores obtained from the SCT transformation method can identify the internal and external zones of the porphyry mineralization system of the study area well. Also, the contour maps of the factor scores obtained from the data transform by the ilr-clr method have been able to show the external zone of mineralization well and the internal zone of mineralization to some extent. Therefore, this paper suggests using the introduced transformation methods along with the log-ratio transformation method for all preprocessing of the statistical and data mining on the exploration data.

Summary:

It is demonstrated that the mechanical behavior of rocks is a function of the 3D stress state. But the limitations in the true-triaxial compression test have resulted in more use of the two-dimensional failure criteria in rock mechanics. Mohr-Coulomb criterion is the most applicable theoretical criterion in rock mechanics but the calculation of the equation of the failure envelope is still the main matter in this regard.

The failure criterion of intact rocks is a matter of fundamental importance in rock engineering design and a substantial amount of research on the failure criteria of intact rock has been developed during the past years. Among them all, one of the most significant suggestions was made by Mohr and Coulomb. The major limitation of the Coulomb criterion is that it is a linear criterion and expresses the strength of the rock as a linear function of confining pressure or normal stress. On the other hand, a large amount of experimental observation suggests that Mohr failure envelopes of most of the intact rocks and soils are not linear, particularly under relatively low or extremely high amounts of confining stresses. In addition, difficulties involved in developing a theoretical model which satisfactorily predicts non-linear behavior of intact rocks under different stress conditions led engineers to propose some empirical relationships between principal stresses or between shear and normal stresses at failure. But for practical applications, it is more important, how easily the parameters of a strength criterion can be obtained in the field and whether corresponds to the applied field situation by the specific field conditions which empirical criterion was developed. Then, this article aims to present a simple and accurate analytical procedure for calculating Mohr failure envelop based on at least three triaxial experiment data obtained from core samples.
 

Methodology and Approaches:

Finding the equation of the tangent of the general equation of a curve set is a solved problem in mathematic. Then, in rock mechanics, if we consider the system equations of Mohr’s circles as a general differential equation, the unusual answer of this differential equation is the equation of cover curve (or failure envelop) of Mohr circles which is known as failure criterion. In mathematics, the abnormal (or unusual) answer (or solution) of the first-order differential equation is a curve that is tangent to all curves generated from the general equation. Then, by finding a correlation between centers and radius of circles, substituting the parameters and few mathematical calculations the new non-linear Mohr’s failure envelope can be expressed by a parabolic equation.

The proposed theoretical failure criterion in this paper follows Mohr’s hypothesis and is expressed in functional form τ = f (σ). in order to compare the new proposed model by Hoek-Brown and Coulomb linear model a computer code was developed to plot all of these criteria in a same τ-σ coordinate system. The results obtained from the new parabolic Mohr failure envelope have good accordance with the data points presented by the Hoek-Brown failure criterion. It should be noted that the new technic directly results from the failure equation while the Hoek-Brown model only represents the locus of data points of the normal and shear stresses on the failure plane.

The paper introduces the 3D Cross-Correlation for modeling of total magnetic intensity and its vertical gradient which is the fast way to model data, detect anomalies and estimate their depths and locations. In this approach first, we divide the subsurface space into a 3D regular grid, after computing the correlation value for each node of the grid, these values are plotted. It is noted that the results fall in the range [-1, +1] that represents the mass excess or mass deficit of magnetization (or susceptibility) relative to the magnetization (or susceptibility) of the host volume. This approach is applied to 2 synthetic models. The results show acceptable accuracy of this method in depth estimation and expansion of buried masses. After this method is verified and validated, it will be applied to the Shavvaz mine's total magnetic intensity (TMI) data of Yazd and its vertical gradient, and the results will be discussed.

There are two major approaches for 3D inversion of magnetic data: (i) direct inversion of the density contrast using a linear or nonlinear algorithm, and (ii) modeling of the source distribution in a purely probabilistic sense, in which the results are equivalent physical parameters between +1 and -1. Direct inversion has an inherent problem called Non-uniqueness of solutions and requires a lot of computer memory because of the number of model parameters and data.
In this paper, we introduce and evaluate the 3D Cross-Correlation (CC) method for 3D modeling of magnetic data (or its vertical gradient). This method was applied to 2 different synthetic models and its strengths in modeling of total magnetic field anomaly and vertical magnetic gradient data are discussed and finally, the method was applied to the Shavvaz mine's TMI data and its vertical gradient.
 

Methodology and Approaches:

The 3D cross-correlation approach is a method for modeling the magnetic data (or its vertical gradient) without any external constraints and any linearization.

The results of synthetic examples showed the high accuracy of the CC method in determining the shape and depth of the buried mass. This method is simple and easy to run and there is no need for prior information. In the end, this method was applied to the Shavvaz mine's TMI data and its vertical gradient. These results showed that orebody continues deeper than 40m (estimated from the previous modelling).

Summary:

Hydrodynamic components play an important role in the process performance of column flotation. CFD as a numerical method can help analyze and predict flow components. In this paper, the single-bubble rising velocity profile in the flotation column is studied in two-phase with CFD. Simulations have been performed in Fluent software using a two-phase VOF model. A computational column with a square cross-section of 10 cm and a height of 100 cm has been considered. The air is taken in by a single bubble from the bottom of the column by an internal sparger. To validate the simulation results, a series of experiments were performed exactly according to the mentioned conditions, while imaging was used to record hydrodynamic components such as inlet airflow, bubble diameter, and bubble rise velocity, etc. The experimental results are consistent with previous observations that studies by others. Also, the results of the simulations performed are qualitatively and quantitatively consistent with the experimental results. The results show that CFD simulation can well predict the rise of the bubble and its related parameters in the flotation column, including the bubble rise rate with a difference of less than 5% compared to the experimental values. In this paper, the single-bubble rising velocity profile in the flotation column is studied in two-phase with CFD.

This article consisted of two parts: the experimental tests and the CFD simulations. The authors tried to present a set of setting to simulate the bubble rising velocity as well as possible by their facilities.

Methodology and Approaches:

Simulations have been performed in Fluent software using a two-phase VOF model. A computational column with a square cross-section of 10 cm and a height of 100 cm has been considered. The air is taken in by a single bubble from the bottom of the column by an internal sparger. To validate the simulation results, a series of experiments were performed exactly according to the mentioned conditions, while imaging was used to record hydrodynamic components.

The results showed that CFD simulation can well predict the rise of the bubble and its related parameters in the flotation column, including the bubble rise rate with a difference of less than 5% compared to the experimental values.

Summary:

One of the important geometric features of rock mass discontinuities is its surface roughness. The discontinuity level has different heights that differentiate each level from the other. In practice, it is not possible to assign a roughness value to each of these levels, so to levels that are similar in height; The same amount of roughness is assigned. In analyzing the problems of stone mechanics related to coercion, it is necessary to choose one of the many levels of discontinuities that have the same amount of roughness. Discontinuity Roughness Simulation (DRS) is a random selection of different levels of surface roughness for a certain amount of surface roughness. In this method, the level of discontinuity is simplified by connecting several pieces together; So that each piece has an unevenness. By simplifying and using different layouts of components that make up the discontinuity surface, the DRS method can produce different levels, the JRC value of which is almost the same.

Several methods have been proposed to measure the roughness feature of rock mass, all of them work based on the elevation of its fracture's measurement. Precise measurements and illustration of roughness values were the subjects of the previous studies.

Methodology and Approaches:

Barton's field method and determination of the maximum distance, a, between fracture and the field survey profile, L, is the foundation of the proposed method here. So fracture's length would be divided into n pieces in which its length is less than L and there exist an asperity with the height of a. By considering a number between 0 and an as the flange's height and a random number in the [0,l] interval as the distance between two adjacent flanges, locus of the fracture's flange points would be determined. The locus of the fracture's atrio points would be determined by measuring the distance between two adjacent flange and atrio points of a fracture which is a number between 0 and two adjacent flanges.

In order to validate and ensure the accuracy of the results obtained from the application of the DRS method, the validity, and reliability of the method have been checked for all possible JRCs. The results of the validity test for different JRCs indicated that the value of the mean percentage of absolute error (MAPE) for different parts of a simulated fracture is always less than 10 percent and this means that if a fracture needs to be simulated using the DRS method in order to produce a roughness value of JRC = 10, the JRC value for all parts of the simulated fractures would a number be between 9 and 11. The reliability of the DRS method for different JRCs has also been investigated. Outcomes showed that the value of MAPE in 100 of repetition of DRS method implementation for a part of the simulated fracture that is randomly determined is less than 6 percent, which is an acceptable value and a confirmation of the accuracy of the DRS method to simulate and produce fracture’s roughness.

The characteristics of fire clay soil mines are their High Geologic Variable Reserves. This article presents a model for scheduling such mines. The objective function is defined by minimizing costs. For the first time, constraints were added to the model to explore new minerals. Slope constraints were also defined by cost. To execute the model, one of the working face in the mine was considered. Standard scheduling model was used to evaluate the validity of the obtained results and the material layers were considered as hypothetical blocks. These models were solved for 8 time periods (weeks) by CPLEX software. The results showed that the assumed model was able to reduce costs by 4% compared to the standard model. Extract rate increased by 18.5% and transferring to stockpile by 17% compared to standard model. But the rate of material reclaiming from the stockpile was 90% lower than the standard model. The results of the sensitivity analysis of the parameters also showed that the extraction cost per ton of minerals is currently at a turning point in the graph. The cost of transporting each ton of minerals to the stockpiles has two minimum points, which is currently at the local minimum. Mining costs were not sensitive to the cost of reclaiming. Slope creating costs are not optimal in the second bench of the mine, and with a bit of optimization these costs can reduce overall mine costs. The costs of developing slopes in the third and fourth levels also follow a rational procedure, and as these costs increase, overall mine costs also increase.

Summary:

Recent developments in eXtended Finite Element Method (XFEM) opened new avenues through crack propagation problems. However, in most researches, exact porosities are not considered or are just replaced with some circular pores. This means the effects of the shape, location, and arrangement of the porosities are less evaluated. In this study, by considering the porosity as an elliptical pore, parameters such as elliptical shape, relative location, and arrangement of pores are studied. The results revealed that this kind of considerations can improve the accuracy of crack growth modeling through porous media.

The shape and location of a pore have a significant effect on the cracks' growth and propagation in porous media. Due to the concentration of stress around these discontinuities, tensile cracks are created and coalesced leading to the final failure in the sample. Since these kinds of tests in pore-scale are practically hard to implement in the laboratory, numerical computation of these behaviors is of great importance to correctly understand this phenomenon. In recent years, the use of XFEM, which eliminates the need for remeshing along the crack path, has been extensively developed and used by many researchers. However, due to the complex shape of the porous structure, even in numerical modeling, they either are not considered or their shape is assumed to be circular. We, in this study, will go a step forward in this limitation by assuming an elliptic shape for porosities.

Methodology and Approaches:

In this article, the effect of shape, location, and arrangement of elliptical porosity on crack growth is numerically modeled. By placing these porosities beside and in front of the crack, the stress distribution, stress intensity factor variation, and maximum resistance of the sample are investigated.

The results showed that for the equal size of pores if the vertical elliptical pore is located in front of the crack, its destructive effect is about 20% more than the horizontal elliptical pore. Also, when the porosity is located beside the crack, by increasing the angle between the horizontal axis with the direction of the large ellipse diameter (here we call it α), the stress intensity factor decreases from 1 to 0.94 and reduces the crack propagation in the porous sample. In addition, we defined the angle between the horizontal axis and the line joining the centers of the two porosities as β and evaluated the effect of the porosity shape and its location on crack growth in more complex models (i.e., models containing two elliptical porosities). By increasing the α and β from 0o to 90o, the maximum strength of the sample decreases by 18.12%, and the von Mises stress value increases from 0.154 to 0.922 MPa. However, the results revealed that the effect of β on crack growth is greater than α.