Accurate prediction of damage depth of multi-story structural footings with Matlab implementation

The bottom slab disturbance in the working face of coal rock mining will induce the upper part of the bottom slab water barrier to be damaged, and the calculation of the bottom slab damage depth is the basic premise to determine the bottom slab damage depth scientifically. In the past, the theoretical calculation of the plastic slip line field of the bottom slab of a single rock stratum often deviated greatly from the actual one, because the structure within the damage range of the bottom slab mainly consisted of multi-layer structures. Firstly, we construct a mechanical model of plastic slip line field of multilayer structure base plate, derive the analytical solution of base plate damage depth under multiple working conditions, and optimize five working conditions for calculating the damage depth of multilayer structure base plate; secondly, we analyze the shortage and error causes of manual calculation method of damage depth of multilayer structure base plate; we propose a logical flow for calculating the damage depth of multilayer structure base plate, and develop a system for calculating the damage depth of multilayer structure base plate with the help of Matlab language. The system was developed with the help of Matlab language, and the reliability and stability of the system were analyzed with the actual working conditions. The results show that ① most of the working conditions in the calculation of the damage depth of multilayer structure base plate need to be solved by Taylor expansion and quadratic equation several times, and the manual calculation process is long and complicated, which is very likely to lead to deviations in the calculation results; ② by comparing the maximum damage depth of the base plate under the same working condition with the same parameters by manual calculation and machine calculation (Matlab built-in function), it can be seen that with the increase of the number of layers of the base plate, the manual solution process leads to the maximum damage depth of the base plate due to the repeated application of Taylor expansion. ③ The main interface of the software contains the number of layers, layer thickness, mechanical parameters, input boxes, calculation buttons, etc., which can quickly and intelligently identify the working conditions and calculate the maximum depth of damage of the bottom slab and the maximum depth of damage from the mining face to the bottom slab. ④ will be a mine of flat coal related lithological mechanical parameters into the software solution, by comparing and analyzing the five-layer structure of the maximum depth of destruction of the base plate theoretical value, fitting value, measured value and software value can be seen, the theoretical value and measured results deviation of 0.57 m, software value and measured value of the difference of 0.14 m, the results of multi-layer calculations under the software calculations are more in line with the actual needs, can be for the bottom of the board of the prevention and control of water hazards and safety of mining to provide a reliable technology parameter.