Cement-based materials are the most widely used and largest quantity of engineering materials. Enhancing carbon fixation efficiency and reducing carbon emissions in cement-based materials is an active method of coping with climate change, which has important environmental and social benefits. The amount of carbon dioxide transported into the cement-based material represents the maximum carbon fixation capacity. Enhancing the carbon transport performance of cement-based materials is the material guarantee and basic premise for improving their carbon fixation levels. Considering the impact of particle connections on the maximum cluster, a permeation probability calculation model of porous media system was established, providing the changing rule of the permeation probability with the mathematical expectation of the Poisson distribution, which was verified to be reasonable through experimental studies. The experimental results showed that under the same cement -based conditions, the water transport properties of biochar cement-based materials increased as the mathematical expectation increased. The carbon dioxide transport properties were influenced by the surface area of the biochar particles and exhibited a trend of first decreasing and then increasing with an increase in the mathematical expectation. When the water-cement ratio decreased, the differences in the microstructure of cement -based materials with different biochar particle size distributions increased, the change rate of permeation probability therefore was more sensitive, resulting that the differential effects of different particle size distributions on the transport properties were amplified, and the influence of the particle size distribution of biochar on the transport properties of cement-based materials was more significant.