Attenuation of hole wall pressure and the prediction model for crack length in the scenario of blasting with water-coupled medium

For fixing the parametric design problem of blasting with water-coupled medium and improving the rock breaking quality, efforts should be made to quantify and examine the blasthole pressure and the explosive crack growth length in the scenario of blasting with water-coupled medium. The water medium was treated as an ideal fluid on the precondition that its flow velocity and internal energy would change continuously with time. Under the elastic wave theory and combining the propagation law of shock wave in water and rock or rock-like medium, the pressure, velocity, and other parameters in relation to shock wave at the interface between explosive and water, in the water medium, and in the peripheral medium after the occurrence of transmission and reflection at the interface between water and hole wall, were subject to theoretical calculations. As a result, the equation for the peak blasthole pressure in the scenarios of explosive and hole wall medium parameters was derived. Further considering the weakening effect of sparse wave on shock wave and the effect of multiple reflections superimposed on shock wave by the hole wall medium, the equation for the attenuation of blasthole pressure as a function of the time constant T was obtained. Next, the prediction model for crack length in the scenario of blasting with water-coupled medium was constructed by the aforementioned equation for calculation of blasthole pressure in the scenario of blasting and according to the model for explosive gas-driven one-dimensional crack growth. Finally, the blasthole pressure and one-dimensional crack length applicable to the explosive and hole wall medium parameter with decoupled coefficients of 1.33, 1.67, 2.00, 2.67, and 3.33 at a given time point were examined by combining the derived equations for theoretical calculations and numerical simulations. Results showed that in the scenario of blasting with water-coupled medium, the blasthole pressure would reduce as the decoupled coefficient η increases, and it is significantly influenced by η, up to 25% even above 50%. Similarly, the crack length would reduce as the decoupled coefficient η increases, but it is slightly influenced by η, only at 15% or so in general.