An uniaxial compression mechanical model for the roof rock-coal (RRC) composite sample was established in order to study the effects of height ratio of roof rock to coal on the structural strength of composite sample. The composite sample strengths under different height ratios were established through stress and strain analysis of the sample extracted from the interface. The coal strength near the interface is enhanced and rock strength near the interface weakened. The structural strength of composite sample is synthetically determined by the strengths of rock and coal near and far away from the interface. The area with a low strength in composite sample is destroyed firstly. An analytical model was proposed and discussed by conducting uniaxial compression tests for sandstone-coal composite samples with different height ratios, and it was found that the structural strength and elastic modulus decrease with a decrease in height ratio. The coal strengths far away from the interface determine the structural strengths of composite sample under different height ratios, which are the main control factor for the structural strength in this test. Due to its lowest strength, the rock near the interface first experienced a tensile spalling failure at the height ratio of 9:1, without causing the structural failure of composite sample. The coal failure induces the final failure of composite sample.
The normal modes cannot be extracted even in the Pekeris waveguide when the source-receiver distance is very close. This paper introduces a normal mode extraction method based on a dedispersion transform (DDT) to solve this problem. The method presented here takes advantage of DDT, which is based on the waveguide invariant such that the dispersion associated with all of the normal modes is removed at the same time. After performing DDT on a signal received in the Pekeris waveguide, the waveform of resulting normal modes is very close to the source signal, each with different position and amplitude. Each normal mode can be extracted by determining its position and amplitude parameters by applying particle swarm optimization (PSO). The waveform of the extracted normal mode is simply the waveform of the source signal; the real waveform of the received normal mode can then be recovered by applying dispersion compensation to the source signal. The method presented needs only one receiver and is verified with experimental data