## 3 Results and Discussion
### Law of Energy Evolution  
Figure 8 illustrates the stress-strain relationship and energy-evolution characteristics of coal-gangue concrete. The energy-evolution characteristic curve of coal-gangue concrete can be segmented into four distinct stages. (I) Primary crack closure stage: during this phase, the initial load causes the primary crack in the coal-gangue concrete to close, resulting in relatively low total strain energy. No new cracks form in the gangue concrete interior, and the dissipation energy remains low. (II) Linear elastic stage: this stage corresponds to the elastic deformation of coal-gangue concrete, with no formation of new cracks. Consequently, the dissipation energy remains low, and the total strain energy is stored in the coal-gangue concrete in the form of elastic strain energy. (III) Rapid crack expansion stage: new cracks gradually emerge in the coal-gangue concrete during this stage. A portion of the total strain energy is converted into dissipative energy, and the rate of increase in elastic strain energy decreases. (IV) Crack-penetration stage: as soon as reaching the peak stress, the cracks in  
Figure 7: The variation of compressive strength and elastic modulus of HBPRGC. (**a**) Compressive strength; (**b**) Elastic modulus. the coal-gangue concrete progressively extend, forming macroscopic cracks and leading to material failure. During this phase, as the load gradually decreases, the total strain energy increases at a slower rate. The elastic strain energy stored in the coal-gangue concrete is dissipated as a result of crack penetration, leading to a gradual reduction in elastic strain energy and a simultaneous increase in dissipative energy. Figures 9 and 10 depict the strain energy evolution of HBPRGC specimens with different matrix strength grades. When the matrix strength is identical, the total strain energy aligns closely with the dissipated energy of HBPRGC. Initially, at a fibre volume content of 0.1%, the impacts of the fibre on both the total strain energy and dissipated energy in coal-gangue concrete are minimal. However, with ongoing deformation, the addition of fibre notably accelerates the increase in both total strain and dissipative energy, which is particularly evident when blending BF and PF. Compared to standard coal-gangue concrete, BC-20-0.1 and BC-30-0.1 display increases in total strain energy of 26.12% and 27.44%, respectively, with corresponding increases in dissipative energy of 28.15% and 23.01%, respectively. Similarly, PC-20-0.1 and PC-30-0.1 exhibit amplified total strain energies of 26.34% and 31.85%, respectively, along with corresponding increases in dissipative energies of 48.61% and 52.16%. HBPRGC-20-0.1 and HBPRGC-30-0.1 have elevations of 53.66% and 51.45% in total strain energy and 54.11% and 50% in dissipative energy, respectively. When the volume content of hybrid fibres reaches 0.2%, it is relatively modest when it comes to the rates of increase in both the total strain energy and the dissipative energy in coal-gangue concrete during the initial deformation stage. However, as deformation progresses, the rates of increase in total strain energy and dissipative energy for coal-gangue concrete with 0.2% hybrid-fibre content become significantly more pronounced. In the final deformation stage, relative to standard coal-gangue concrete, HBPRGC-20-0.2 and HBPRGC-30-0.2 exhibit substantial increases of 42.16% and 44.87% in total strain energy, along with increases of 42.14% and 43.19% in dissipative energy, surpassing both the base group coal-gangue concrete and single-fibre gangue concrete. These values are second to coal-gangue concrete with a mixed fibre volume of 0.1%. By analysing the elastic strain energy variation curve, it is evident that prior to reaching the peak elastic strain energy, the influences of the fibre type and content on the elastic strain energy of coal-gangue concrete closely mirror those of the total strain energy and dissipated energy.