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This paper presents a new approach for quantifying the effect of porosity, at meso and macro-scales, on the strength behaviour of cementitious materials at a macro-scale. The proposed approach combines a cohesive-strength homogenisation model with second-order cone programming through establishing the analytical upper bound solution of cohesive-strength behaviour using inverse analysis. The derived formulation presents a nonlinear relationship between the uniaxial compressive strength-to-porosity ratio and the material parameters of the developed homogenisation model. The results show that the curing ages increase the friction coefficient, cohesion and the mesoporosity of the hydration products, while the macroporosity decreases. The results also show that the volume fraction of the solid hydration products decreases with curing ages but the increase in the mesoporosity causes the expansion of the porous hydration products at mesoscales This outcome provides a compelling new evidence that the development of the hydration products of cementitious materials affects the volume fraction of pores in which meso and macroporosity are inversely related.
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