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Understanding the mechanical properties plays pivotal roles in rock engineering. This work aims to establish novel relations linking the porosity, ultrasonic wave and fluid saturation to estimate the uniaxial compressive strength (UCS) fast and simply. The uniaxial compressive coupled with ultrasonic wave tests on sandstone samples are carried out to obtain the datasets of the UCS, P-wave and S-wave velocities. X-ray CT imaging technique is employed to capture the microstructure information. The color difference phase separation approach to segment the pore, water and solid phases is proposed, and pore-scale variables to describe the microstructure characteristics are defined. Novel relations to determine the micro velocities of P-wave and S-wave are established, and the modulus of deformation and the physical properties of rocks are evaluated. Novel relation to determine the UCS is established and validated by the real and virtual experiment datasets. Results show that the UCS, P-wave and S-wave velocities computed by the proposed method decrease with increasing fluid saturation. The errors between the calculated and experimental UCS, P-wave and S-wave velocities are all < 5%, showing excellent consistency with each other. The proposed method is effective to estimate the mechanical properties fast and accurately, simplifying the estimation of the UCS in rock engineering.
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