The second invariant of deviatoric stress of the coal and rock mass is closely related to the distortion energy driving the deformation and failure of the surrounding rock. Based on the second invariant of deviatoric stress, this study built a global model of gob-side entry with different widths of the coal pillar through numerical analysis, and compared and analyzed the evolution law of the surrounding rock distortion energy, plastic location state, and roadway deformation with the width of the coal pillar. This study concluded that the peak distortion energy in the virgin coal rib and the roof and floor of the gob-side entry gradually increases with the reduction in the coal pillar width. When the coal pillar width is 5 m, the second invariant peak value of deviatoric stress in the virgin coal rib reaches the maximum of 294.8 MPa². When the width of the coal pillar is reduced from 30 m to 5 m, the second invariant of the deviatoric stress in the side of the coal pillar and the roof and floor of the side presents the law of first increasing and then decreasing. The greater the damage degree of the coal pillar, the smaller the distortion energy it contains. The distortion energy is the key factor in driving the deformation and failure of the surrounding rock. The greater the distortion energy, the greater the deformation degree of the surrounding rock, the more vulnerable it is to external mining stress disturbance, and the greater the difficulty in controlling the stability of the roadway-surrounding rock.

Hydrophobic silica aerogel was synthesized from a water-glass precursor via CO₂-mediated carbonation. A water-based dispersion strategy was adopted to incorporate silica aerogel and hollow glass microspheres (HGMs) as dual insulating fillers into styrene–acrylic emulsion, yielding composite architectural coatings with hierarchically porous architecture. The impacts of filler loading and mass ratio on thermal-insulation performance were systematically explored. The optimized composite coating delivers a low thermal conductivity of 0.035 W/(m·K) and retains good thermal stability up to 350 °C. The outstanding thermal-insulating capability originates from the synergistic effect between macropores of hollow glass microspheres and nanopores of silica aerogel. Aerogel nanoparticles fill inter-particle voids among stacked hollow glass microspheres, break thermal-bridge conduction pathways, and suppress heat transfer by virtue of the intrinsically ultralow thermal conductivity of aerogel. Such structural features effectively mitigate both solid heat conduction and internal convective heat transfer within the coating matrix. This work establishes a facile, scalable route to fabricate gel-derived hierarchically porous thermal-insulating materials, showing promising applicability for functional decorative coatings in building energy-saving scenarios.