## 5 Conclusions  
The WAW-1000D electric servo-motor testing machine and compressors with different inner diameters were used to assess the influence of specimen size on the compressive behavior of WRBM based on the particle size distribution of specimens and inner diameter of compressors. The stress-strain relationship and changes in the void ratio of specimens were analyzed, and the influencing mechanism of the specimen size on the compressive behavior of WRBM was revealed. Moreover, the test method to reduce the influence of the size effect was determined and in situ monitoring was performed for verification. The main conclusions obtained are as follows:  
(1) The particle size distribution of specimens affects their compressive deformation characteristics. Under natural crushing, waste rock specimens with continuous particle size distribution have pre-existing fine particles that can fill the voids, so their strain and initial void ratio are lower than those of specimens with uniform particle size distributions. As compression proceeds, pre-existing fine particles in specimens with continuous particle size distribution cannot slip to fill the voids due to the presence of the skeleton, while fine particles produced by broken waste rock particles are more efficiently filled in the voids. As a result, the void ratio of waste rock specimens with continuous particle size distribution is, on the contrary, slightly lower than that of specimens with uniform particle size distributions.  
(2) The inner diameter of the compressors affects the compressive behavior of the specimens. Under random distribution of waste rock particles, the larger the inner diameter of the compressor, the lower the probability of formation of stable skeleton structures by hinged hard waste rock particles, and thus the lower the strain and void ratio. The relationship between the inner diameter \(\Phi\) of compressors and strain \(\varepsilon\) is expressed by the function \(\varepsilon=y_{0}+A_{1}e^{-\phi/t_{1}}\). When the ratio of the inner diameter of compressors to the maximum particle size of waste rock is 15:1 and above, the strain \(\varepsilon\) tends to stabilize and the specimen size exerts a slight influence on the compressive behaviors of the specimens.  
(3) Taking the 1303N-1# backfill panel in Xinjulong Coal Mine as an example, the tests show that the strain of waste rock specimens with a particle size of 0-20 mm under 20 MPa is 0.183. Based on this result, it is predicted that the maximum roof subsidence is 583.77 mm. After stabilization of the backfill panel, the maximum in situ roof subsidence measurement is 568 mm, which differs slightly from the test results.  
Conceptualization, M.L. and P.H.; Data curation, X.L.; Formal analysis, Q.G.; Funding acquisition, M.L. and P.H.; Investigation, M.L. and Q.G.; Methodology, M.L.; Resources, M.L.; Supervision, M.L. and P.H.; Visualization, X.L.; Writing--original draft, S.X.; Writing--review & editing, M.L. and P.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China [52274142, 52104105], the National Key R&D Program of China [2023 YFC3904300], and the Independent research project of State Key Laboratory for Fine Exploration and Intelligent Development of Coal Resources, CUMT [SKLCRSM24X009].