Modeling the hydraulic washing-out process of amber-bearing rocks during amber extraction

Purpose. The study focuses on the hydromechanical extraction of amber from sandy amber-bearing deposits in the Volyn Polissia region to identify conditions for efficient washing-out and optimize the technological parameters of extraction. Methods. The research employs a modeling approach for hydraulic washing-out based on the conditions of the Klesiv deposit. A mathematical model was developed to simulate the motion of solid particles in a turbulent flow, considering the stochastic nature of flow velocity and particle size distribution. The model integrates a system of differential equations describing particle movement and a block diagram of a statistical algorithm for evaluating the probability of amber particle detachment. Laboratory experiments were conducted using samples collected from productive sand horizons of the deposit. Findings. It was established that the probability of amber particle detachment increases significantly with higher near-bed velocity dispersion and granulometric heterogeneity of the rocks. Numerical simulations demonstrated that fine particles (d ≤ 1.4 mm) detach without rolling, while larger ones predominantly roll along the surface. A quantitative relationship was obtained between detachment probability and environmental parameters, allowing for a predictive assessment of hydraulic washing-out efficiency. Originality. A novel mathematical model was proposed, which accounts for the interaction between turbulent stochastic factors and the physical properties of particles. A statistical approach was applied for the first time to determine the critical conditions for amber particle detachment from the rock matrix. Practical implications. The results can be used to improve existing and develop new hydromechanical technologies for amber extraction, particularly in challenging sandy-clayey formations with high heterogeneity. Determining the critical flow parameters that ensure the highest probability of amber particle detachment enables the optimization of hydraulic mining giant operation modes and the designing of efficient slurry transport systems.