Моделирование движения обвальной массы горной породы с использованием двухжидкостной математической модели

Abstract

Introduction. Rock falls are considered to be very dangerous slope processes that can lead to serious consequences. In addition to real observations, numerical (mathematical) or experimental (physical) modeling methods are used to study slope processes. Mathematical modeling is used in the cases where experimental data is insufficient. There are quite a lot of models to describe slope processes. The choice of model to describe a particular slope process lies in the approach on which the model is based. In this work, the debris flow taking into account the fluidization of the collapse mass during its movement along the hillside was described. We used a two-fluid model based on the continuum approach and the kinetic theory of granular gas. The model takes into account the fluidization of the collapse mass, and its implementation does not require the use of powerful computing resources. Purpose of the study. Investigation of the collapse mass motion along a hillside using a two-fluid model based on continuum approach and kinetic theory of granular gas. Estimation of the maximum height of the collapse mass flow layer and the average flow velocity. Materials and methods. The two-fluid model based on the continuum approach and the kinetic theory of granular gas was used for theoretical study of the collapse mass flow. The motion of the collapse mass flow consisting of rock granules (average diameter 7.5 cm) along the hillside (slope angle of 30 degrees) was considered. The 3D simulation results obtained using the two-fluid model were compared with experimental data and calculated data obtained using the discrete element method. The results and discussion. Three-dimensional modeling was applied to study the motion of the collapse mass flow along the hillside using the two-fluid model. The obtained calculations of the maximum height of the flow layer and the average flow velocity are compared with experimental data and calculated data using the discrete element method. The comparison showed that the averaged value (obtained as the arithmetic mean) of the experimental data of the average flow velocity coincides with the result of calculations using the two-fluid model. And the average value of the calculated data using the discrete element method differs slightly from the calculated value using the two-fluid model. The paper proposes a method for calculating the maximum height of the flow layer using graphs of the distribution of the particles volume fraction along the normal to the inclined surface. Using this technique, the maximum value of the layer height was obtained. This value coincides with the maximum value obtained using the discrete element method and differs only slightly from the maximum value obtained in the experiments. Using the two-fluid model, additional calculations were carried out at different values of the slope angle in the range from 20 to 60 degrees. The calculation results of the maximum height of the flow layer and average flow velocity were compared with the calculated data obtained using a model based on the discrete element method. It was found that the calculation results obtained using two different models agree better with each other when the dependence of the average flow velocity on the slope angle is studied. Conclusion. In general, it can be concluded that the results of calculations of the maximum layer height and average flow velocity obtained using the two-fluid model are in fairly good agreement with experimental data and calculated data obtained using the discrete element method. It can also be concluded that the two-fluid model can be used to describe the motion of the flows of the collapse mass with a relatively low liquid content (up to 18 %) and fine inclusions (up to 27 %). Resume. The research results can be useful in estimating the maximum height of the flow layer of the collapse mass and the average flow velocity. 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 slope processes.