Modeling of falling rock

Introduction. At present, the study of the movement of falling rock (collapses of rocks), the causes of their occurrence, as well as their influence on other slope processes is an important field of research. These studies are based on both theoretical knowledge and experimental observations. Separately, it is necessary to highlight the methods of mathematical and computer modeling, which are widely used in cases where experimental data are not enough. The study of the influence of the slope angle and the slope height (on which the falling rock mass was located at the initial moment of time) on the affected area was made using the methods of mathematical and computer modeling. Materials and methods. Two-fluid model based on the continuum approach and the kinetic theory of granular gas was used for a theoretical study of the movement of falling rock along the slope. The model takes into account the fluidization of the falling mass flow, and its implementation does not require the use of powerful computing resources. The modeling results obtained using the two-fluid model were compared with the results of an experimental study on the collapse of dolomite particles (average diameter 5 mm) carried out in the laboratory. The values of the slope height varied from 35 cm to 86 cm, the values of the slope angle varied from 35 degrees to 53 degrees in accordance with the experimental data. The results and discussion. The graphs of the distance of the rock run after its collapse in the dependence of the slope height and the slope angle were plotted. It is found that the calculation results are in good agreement with the experimental data (the relative error does not exceed 11%) for relatively large values of the slope angle. The results of calculations of the distance of the rock run are somewhat overestimated relative to the experimental data for small values of the slope angle. It is found that the affected area of dolomite particles increases with increasing slope angle and slope height. It should be noted that the affected area depends more on the values of the slope angle than on the height of the slope. If the slope is steeper (the value of the slope angle is greater), than the affected area is greater. Conclusion. The calculation results obtained using the two-fluid model describe the experimental data of the rock collapse satisfactorily. The results of calculations of the distance of the rock run are in good agreement with the experimental data (the relative error does not exceed 11%) for relatively large values of the slope angle. It is found that the distance of the rock run after its collapse depends more on the values of the slope angle than on the height of the slope. Resume. The research results can be useful in estimating the distance of the rock run after its collapse, as well as in developing a methodology for assessing affected areas during rock falls. The direction of future research is to improve the two-fluid model based on the continuum approach and the kinetic theory of granular gas for describing of real rock falls.