Abstract: This study conducted time-dependent compression tests on asperities with different height-to-radius ratios using ultra-hard gypsum. According to Hertz contact theory, the attenuation laws of the elastic modulus of different asperities over time were fitted. Time-dependent closure tests were performed on fresh fracture surfaces of red sandstone and limestone under varying normal stresses. By integrating wavelet analysis, region growth algorithms, and the reference surface method, a novel approach was developed for identifying the mesoscale asperity morphology of rock fractures, and compared the differences in the number, height, and height-to-radius ratio of asperities before and after the experiment. Utilizing Boussinesq's solution, an influence matrix was constructed to account for interactions between asperities. Based on the law of the elastic modulus decaying over time, enabling time-dependent closure calculations for different rock fractures under variable stress conditions. This approach precisely analyzes the temporal evolution of strain, contact area, and contact stress for individual asperity, with simulation results matching experimental data in terms of damage area and creep deformation. The study reveals the pivotal role of asperities with distinct mesoscale morphological features in the time-dependent closure process of rock fractures under compression.