Construction of a mathematical model of rock strength under compression taking into account contact friction

Abstract

Research of the strength of rocks under various types of compression is presented, tak-ing into account contact friction.
In this work, mathematical models of the influence of friction characteristics under three-component compression and under a load of the "uniaxial sliding compression" type are developed. They correspond to the available experimental data and take into account the "scale effect" and the effect of the high sensitivity of the strength of the samples to a change in the type of load - from uniaxial compression to compression with sliding.
The simplicity of the constructed models does not require the use of specialized computer programming tools. To calculate the ultimate loads, it is enough to enter one of the formulas in the cell of the office spreadsheet (EXCEL).
The main factors of the influence of external friction are the redistribution of normal stresses on the contact surface and the formation of horizontal stresses inside the sample even under the action of only a vertical load.
The degree of influence of external friction on the strength of the samples is estimated. The presence of external friction increases the strength of the specimens by 17% in uniaxial compression and decreases by 32% in sliding compression. The relative difference between uniaxial compression and sliding compression reaches 50% with an external friction coeffi-cient of 0.2. This shows that the most energy efficient disintegration method is slip compres-sion.
An algorithm has been developed for calculating the strength of rocks in compression using mathematical models of the influence of friction characteristics. This type of stress distribution in the rock is typical for the destruction of hard materials in the contact zone with armor plates in jaw crushers with a complex jaw movement and with cones in cone crushers. Thus, it has been shown that it is possible to control the loading modes to reduce the energy consumption of the crushing process.