**1. Introduction**

The sedimentary process and the arrangement of mineral particles during the formation of coal measure rock mass give an obvious bedding structure and show layered structure macroscopically [1–3]. This layered rock mass widely exists in mining, construction, transportation and water conservancy projects [4–6], and is prone to vibration, damage and even failure under the action of external dynamic disturbances, such as blasting, roof and floor breaking, rock instability and so on [7,8]. For example, the roof strata of working face in mines, especially in the early stage of mining, is subjected to the loading/unloading action of dynamic disturbance and the appearance of mineral pressure is violent, which

**Citation:** Li, F.; Wang, G.; Xiang, G.; Tang, J.; Ren, B.; Chen, Z. Vibration Response of the Interfaces in Multi-Layer Combined Coal and Rock Mass under Impact Load. *Processes* **2023**, *11*, 306. https:// doi.org/10.3390/pr11020306

Academic Editor: Yidong Cai

Received: 6 November 2022 Revised: 29 December 2022 Accepted: 5 January 2023 Published: 17 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

leads to obvious mine earthquakes and even roof collapse. Therefore, in the process of underground engineering excavation, the dynamic damage of a series of layered rock masses is one of the most important factors causing geological disasters.

At present, scholars in China and other countries have mainly studied the static mechanical properties of single, two-layer or three-layer combined coal and rock mass. Zuo et al. demonstrated that both the breaking strength and elastic modulus of the coal– rock assemblage increased to some extent compared with the single coal sample, with the rock–coal–rock assemblage having the largest breaking strength and elastic modulus [9]. Li et al. demonstrated that more than one peak was observed in the spectrum of green sandstone with repeated impact loads, and the relative weight of peak frequencies increased in the low frequency range [10]. Mu et al. demonstrated that the damage state of coal rock specimens was determined by the post peak stiffness of the coal in relation to the rock stiffness [11]. Liu et al. demonstrated that the dynamic strength and fragmentation dimension of the combined coal rock specimens increased with increasing stress wave energy and showed a trend of first increasing and then decreasing with static load [12]. However, the research on dynamic response, the vibration characteristics and dynamic damage of coal and rock mass, especially multi-layer combined coal and rock mass, are still in the stage of experimental exploration. The stress wave generated by impact or dynamic load has significant reflection and transmission at the rock–coal or rock–rock interfaces in the process of propagation, resulting in dynamic effects such as dynamic tensile, stress superposition and mutation. These dynamic effects lead to obvious vibration at the interfaces, which is a key factor leading to dynamic damage and failure of coal and rock mass [13–16]. Meanwhile, Li et al. demonstrated that the initial location of damage and failure can be determined by the lowest frequency effective vibration mode [17]. These articles illustrate that the study of coal rock vibration signals can help to initially reveal the vibration response characteristics of the coal rock interface under impact loading. Unlike previous studies on the static response characteristics of combined coal and rock mass below three layers, this paper conducts a study on the dynamic response characteristics of five-layer combined coal and rock mass.

Based on the two-dimensional similar material simulation experiment, the coal and rock mass combined by five layers of fine sandstone, medium sandstone, coal, coarse sandstone and mudstone was taken as the research object, single and multi-point excitation (synchronous/step-by-step) were used to test the time–history vibration curves of rock–coal and rock–rock interfaces under impact load, and the dynamic attenuation law of amplitude was obtained. Based on Fast Fourier transform (FFT), the spectrum structures of amplitude–frequency of interfaces vibration were studied. Based on Hilbert-Huang transform and energy equation, the time–history curves were decomposed by Ensemble Empirical Mode Decomposition (EEMD) and the vibration modes were obtained. According to the distribution laws of marginal spectrum and energy proportion, the most effective and main vibration modes and the predominant frequencies were obtained. The vibration response characteristics of the interfaces between coal and rock mass under impact load were preliminarily revealed.
