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In recent years, significant research has been conducted to explore the use of 3D triply periodic minimal surface (TPMS) structures for their exceptional vibrational damping properties and their ability to provide a continuous, smooth surface. The emergence of 3D printing has enabled the application of TPMS structures in fields such as medicine and aviation. In civil engineering, the compressive capacity of structures is a fundamental parameter in structural design. To evaluate the potential of porous TPMS structures in civil engineering, we have designed and manufactured four types of Skeletal-TPMS units using Stereolithography (SLA) technology. Axially loaded tests and nonlinear finite element method (NFEM) simulations have been performed to investigate the compressive strength and stiffness of the units. Our findings indicate that compared to solid blocks, the compressive strength of Skeletal-TPMS units decreases by 71.3% to 82.6%, and the stiffness decreases by 64.9% to 79.2%. The Skeletal-SP units show better compressive resistance than Skeletal-IWP units. This study provides new valuable insights for structural design and applications using TPMS structures in civil engineering. [ABSTRACT FROM AUTHOR]