LAUSR

Abstract Concerning the matrix compression and inter-particle volids, the multifractal characteristics [ f ( α ) and D q ] were revealed through LPCO 2 /N 2 GA (low temperature CO 2 /N 2 adsorption) and HPMI (high-pressure mercury intrusion) for bituminous TDCs (tectonically deformed coals). The CCs (compression coefficients) increase with the increasing tectonic deformation during brittle deformation stages and decrease for the shear- and ductile deformation coals. The singular index ( α 0 ) transformations demonstrate that the brittle- and shear deformation can promote the PSD (pore size distribution) irregularity. The lower spectral width ( α q − - α q + ) for the cataclastic- (0.54–0.58, 0.56 in average), mortar- (0.63–0.64, 0.64 in average), and granulitic coals (0.63–0.64, 0.64 in average) indicates the relatively simple multifractal structures of the PSD. While for the shear- and ductile deformed coals, the multifractal structures are complex with high heterogeneity and significant internal differences within PSD. The left-hand side width ( α q − − α 0 ) and D 0 - D 1 (the difference of information dimension to capacity dimension) increase, indicating that the shear- and ductile TDCs have a more clustered distribution in pore volume than brittle TDCs. There exist good positive linear relationships between D ap (adsorption pores’ fractal dimension by Sierpinski model) and left-side width D −10 -D 0 ( R 2  = 0.8741), as well as between D sp (seepage pores’ fractal dimension by Sierpinski model) and right-side width D 0 -D 10 ( R 2  = 0.831), indicating that the variations of multifractal parameters for q  > 0 are attributed to seepage pores’ heterogeneity and these for q D −10 -D 0 increases with the increasing deformation intensity, indicating the most complex shapes of the adsorption pores for the ductile TDCs. The D 0 - D 10 firstly decreases for the brittle- and shear TDCs then increases for the ductile TDCs.