## 1 Introduction  
Coal spontaneous combustion (CSC) threatens the safety and production of coal mines and it often causes great economic loss, casualties and large-scale environmental pollution [1; 2; 3]. Goaf is easily subjected to CSC, which occurs due to the autothermal reaction between broken coal masses and air [4; 5; 6]. There are many factors influencing the CSC in goat, involving internal and external factors [7]. Among various factors, air leaking from the working face is the main factor triggering fire in the goat, which depends on the permeability of the broken coal-rock mass in goat [8; 9]. Therefore, investigating the permeability characteristics of broken coal-rock mass during compaction is important when trying to prevent CSC in goat. When multiple coal seams are present in mines, the stress and permeability of goat are disturbed again during the mining of subsequent coal seams [10; 11; 12]. Repeated loading and unloading cause further breakage of broken coal-rock masses in goat, resulting in changes in porosity and permeability, therefore, the evolution of the permeability of a broken coal-rock mass in goat during the mining of coal seam groups differs from that during the mining of a single coal seam. It is necessary to explore the evolution of permeability of broken coal-rock masses under cyclic loading and unloading conditions. However, goaf is an enclosed space with complex and unknown environments and therefore it is extremely dangerous to measure directly the permeability of broken coal masses in goaf; such a task is also expensive [13; 14; 15; 16; 17; 18]. In current research, the permeability of coal masses in goaf is generally indirectly evaluated by establishing the prediction model for permeability of coal masses in goaf based on theoretical analysis, numerical simulation and laboratory trials [19; 20; 21; 22; 23]. [PERSON] [24] acquired the empirical formula for the permeability of coal masses in goaf by fitting the experimental data of permeability of rocks in the post-peak failure zone under different stresses. [PERSON] and [PERSON] [25] obtained a simple model to predict the permeability of coal masses in goaf based on Carman-Kozeny (C-K) and Happel (H) equations. Supposing that particles of broken rock masses are cuboidal, [PERSON] and [PERSON] [26] proposed a theoretical calculation model for permeability of broken rock masses based on elastic theory. [PERSON] [27] proposed a model for fractal porous media, which is used for predicting the porosity and permeability of goaf as well as the air leakage in goaf. [PERSON] et al. [28] experimentally investigated the evolution of strain, porosity and permeability of broken coal samples of different particle sizes, under different stresses and various temperatures. [PERSON] et al. [29] investigated the evolution of permeability of broken coal-rock mass and its influencing factors during the repeated mining of coal seam groups. Based on Hertzian contact deformation, the deformation of broken coal particles was evaluated. By conducting water seepage tests on broken rock masses, [PERSON] et al. [30] concluded that the water seepage from a broken rock mass is non-Darcian. After carrying out seepage tests on sandstones with different porosities, [PERSON] et al. [31] suggested that different porosities correspond to different non-Darcian coefficients. By utilising a self-designed test system for gas seepage, [PERSON] et al. [32] investigated the relationship between the porosity and permeability of broken coal mass under different gas pressures and continuously measured the gas pressures and flow velocities therein. The aforementioned research concentrates on the permeability characteristics of broken coal-rock mass during compaction while rarely reporting on the permeability characteristics of broken coal-rock masses under cyclic loading and unloading conditions.