linear regression

Blasting operation is one of the most important and costly operations in the mining process. Blasting is the beginning of the rock comminution system in the mine. The dimensions of the blasted product will play a significant role in the ability of stone crushing and grinding, for this reason, to produce a product with suitable dimensions, it is first necessary to obtain sufficient knowledge of the physical, mechanical, and chemical conditions of mineral blocks. In this research, by studying 26 iron ore blocks of the Chogharat mine, after the blasting operation, the physical, mechanical, and chemical characteristics of the ore blocks were taken. In the following, after blasting operation, by taking pictures from surface of the exploded block, an image analysis of the dimensions of blasting product was carried out. In the next step, stone samples were taken from the surface of the fired block to conduct geomechanical and chemical tests. After conducting the tests, the relationship between the physical, chemical, and mechanical characteristics of the tested stones with the dimensions of the Blast products (D50) was investigated. The characteristics examined in this study include uniaxial compressive strength, modulus of elasticity, Poisson's ratio, indirect tensile strength, cohesion, internal friction angle, and percentage of silica, iron, and iron oxide in the Blasted block. Finally, using univariate and multivariate linear regression statistical analysis, equations to estimate the dimensions of the product (D50) resulting from the blasting using the physical, mechanical, and chemical characteristics of the rock masses of the explosive product. With coefficients of determination (R2) 92.48% for D50 were predicted...

In this paper, the effect of the intermediate principal stress on the failure of different rocks and the accuracy of several 3D criteria in estimating failure of the true tri-axial tests results was investigated. Then, applying linear and nonlinear regression, a new 3D criterion was proposed that the criterion can successfully predict failure behavior of deep rocks with accuracy higher than other existing criteria.Failure criteria are relations between the strength properties of rock and applied stresses and used to describe the behavior and failure of rocks. This function is determined based on analytical and empirical methods. Some researchers neglect the effect of intermediate principal stress σ2 in the failure mechanism of rocks (2D failure criteria). However, there are experimental documents showing that the intermediate principal stress affects the failure behavior for at least some of the rocks (3D failure criteria. The intermediate principal stress has considerable effect on failure mechanism of very deep underground rock masses (such as hydraulic fracturing, wellbore and reservoir stability, underground storage in petroleum engineering). In this paper, the effect of the intermediate principal stress on the failure of five different rock types in 175 true tri-axial tests was studied. Also, the accuracy of several 3D criteria (such as Von Mises, Drucker-Prager and Pan & Hudson) in estimating failure of the tests results was investigated. Applying nonlinear regression, a new 3D criterion was proposed based on the true tri-axial tests results. Maximum, minimum, and intermediate principal stresses, along with uniaxial compressive strength and internal friction angle are used in the new criterion. In order to validation of the proposed criteria for other rocks, results of the true tri-axial tests for 190 specimens of seven different rock types were studied.The results of studies showed that the effect of intermediate principal stress is more significant in competent rocks than weak rocks and Pan & Hudson criterion gives the most accuracy with an MRAE equal to 0.24. Von Mises and Drucker-Prager criteria gave the next best results by MRAE respectively equal to 0.28 and 0.44. Also, RSQ and MRAE of the proposed criterion for all type of rocks are equal to 0.94 and 0.06 respectively that the criterion can successfully predict failure behavior of deep rocks with accuracy higher than other existing criteria.

There have been some efforts to investigate shear mode of fracture using rock specimens by different methods in the recent years. Most of the fractures occurring in nature are of the shear, tensile or the combination of both. The determination of Mode II fracture toughness is important for understanding and analyses of the failure process in rock masses. The comprehensive investigations in the methods of determination of Mode II fracture toughness of rocks indicated that punch and shear box tests are reasonable, although there may be still some illusions. Artificial neural networks are capable to establish logical relationship between different variable parameters in order to predict the value of Mode II fracture toughness. In an effort, the test results obtained from punch and shear box tests along with some affective parameters are considered to predict Mode II fracture toughness through neural network models. Thus an optimum network was established and the precision was evaluated. A comparison of the neural network results is made with the linear regression. The details of the investigation are presented in this paper.