Spherical data validation of rock discontinuities orientation from Drone-derived 3D Point Clouds

This work presents a methodology for the statistical validation of discontinuity surfaces obtained from point clouds using digital photogrammetry from drones. Our methodology allows you to review the quality of the data obtained with photogrammetry and decide whether these measurements are representative of the discontinuity surfaces that they analyze. It consists of three steps, the first one being a shape analysis that allows defining which statistical model should be used: Fisher for circularly symmetric clusters or Bingham fits better for axially symmetric clusters. This step also makes the most significant difference to other works since our methodology starts from the premise that not all discontinuity surfaces are flat. Therefore, Fisher parameters do not allow validating data that do not correspond to a plane. In the second step of the methodology, we calculate the consistency parameters that depend on the statistical model defined in step 1. The parameters are similar for both models; both estimate κ which indicates how much the sample is concentrated around the mean orientation and validates the existence of this and which is the value of the generating angle of a cone with a 95 % confidence limit that it contains within the mean orientation. Finally, step 3 is used when there are control measurements to compare the point cloud data and define if both samples characterize the same discontinuity surface in the rock mass. The results obtained on a rock outcrop allowed us to observe that the measurements obtained from the drone faithfully represent the discontinuity surface analyzed when these were compared with the measurements made manually with the compass. Furthermore, the dispersion parameters (

Compatibility of strong discontinuities in micropolar thermoelastic media. A pseudotensor formulation

В статье рассматривается процедура вывода условий совместности на поверхностях сильных разрывов в микрополярных термоупругих средах. Условия совместности сильных разрывов 4-тензора Пиолы-Кирхгофа и 4-тензора энергии-импульса выводятся из принципа наименьшего действия. Приведена определяющая форма микрополярного термоупругого потенциала для изотропных и гемитропных сред. Развиваемая псевдотензорная формулировка условий совместности сильных разрывов может быть применена при моделировании динамики изотропных и гемитропных микрополярных термоупругих сред. The paper deals with the regular procedures for deriving compatibility conditions on the surfaces of strong discontinuities in thermoelastic micropolar media. The jump conditions of the Piola-Kirchhoff 4-pseudotensor and the energy-momentum 4-pseudotensor are derived from the principle of least action. The compatibility conditions on the propagating strong discontinuity surface are explicitly formulated for a micropolar thermoelastic continuum. The developed pseudotensor formulation of the compatibility conditions for strong discontinuities can be applied to the dynamic problems for isotropic and hemitropic micropolar thermoelastic media.

A study of a quasilinear model of the particles of a suspension that are aggregated and settled in an inhomogeneous field

The mathematical model of the sedimentation process of suspension particles is usually a quasilinear hyperbolic system of partial differential equations, supplemented by initial and boundary conditions. In this work, we study a complex model that takes into account the aggregation of particles and the inhomogeneity of the field of external mass forces. The case of homogeneous initial conditions is considered, when all the parameters of the arising motion depend on only one spatial Cartesian coordinate x and on time t. In contrast to the known formulations for quasilinear systems of equations (for example, as in gas dynamics), the solutions of which contain discontinuities, in the studied formulation the basic system of equations occurs only on one side of the discontinuity line in the plane of variables (t; x). On the opposite side of the discontinuity surface, the equations have a different form in general. We will restrict ourselves to considering the case when there is no motion in a compact zone occupied by settled particles, i.e. all velocities are equal to zero and the volumetric contents of all phases do not change over time. The problem of erythrocyte sedimentation in the field of centrifugal forces in a centrifuge, with its uniform rotation with angular velocity ω = const is considered. We have studied the conditions for the existence of various types of solutions. One of the main problems is the evolution (stability) problem of the emerging discontinuities. The solution of this problem is related to the analysis of the relationships for the characteristic velocities and the velocity of the discontinuity surface. The answer depends on the number of characteristics that come to the jump, and the number of additional conditions set on the interface. The discontinuity at the lower boundary of the area occupied by pure plasma is always stable. But for the surface separating the zones of settled and of moving particles, the condition of evolution may be violated. In this case, it is necessary to adjust the original mathematical model.

NUMERICAL STUDY OF THE FRACTURING MECHANISM AROUND A BLASTHOLE AND INVESTIGATING THE EFFECT OF DISCONTINUITIES ON THE FRACTURE PATTERN

The mechanism of rock fragmentation around blastholes is of prior importance in the evaluation of drilling and blasting performance in open pit and underground mines. This paper aims to numerically investigate the crack propagation mechanism around a single blasthole using the distinct element method (DEM). In this study, two specimens with different borehole diameters were considered and the effects of the stress waves on their cracking mechanism were simulated. To validate the numerical model, the length of the radial cracks around each blasthole was measured and compared against an analytical fracture mechanics model. The fractured zones around the blasthole were also compared against previous experimental tests and good agreement was observed. The effect of a single discontinuity on the crack propagation mechanism was also studied and it was found that the discontinuity normal stiffness plays a significant role in the fractured zones around the blasthole. For low values of normal stiffness, the discontinuity surface acted as a free surface, and the shock wave was significantly reflected, while at high values of normal stiffness, cracks propagate across the discontinuity surface.

On spontaneously radiating shock waves

A solution representing the structure of a spontaneously radiating shock wave is constructed and its stability in the linear approximation is investigated. Linear waves of perturbations that can propagate through the structure and waves radiating into the flow region behind the structure are found, i.e. there are waves corresponding to the spontaneous radiation of perturbations by a shock wave considered as a discontinuity surface.