The transport of liquids, gases, and dissolved species through cracks in quasi-brittle materials is critical in applications such as oil and gas extraction, geothermal energy, CO₂ sequestration, and concrete durability. In reinforced concrete, for instance, surface cracks allow rapid ingress of water and aggressive ions, accelerating corrosion. Accurate modelling of this crack transport is essential in multiphysics simulations. Phase-field fracture models have become popular due to their robustness and ability to capture complex crack patterns. The phase-field variable ϕ, which is linked to the damage of the material, is often used to interpolate transport properties, such as permeability or diffusivity, in order to represent enhanced transport through cracks. A common approach is to use a power function of the form D= (1-ϕ)^m D_C+ ϕ^m D_L linking the undamaged diffusivity D_C and the diffusivity in a fully cracked material D_L, typically with m=1. However, phase-field models do not directly yield crack width, and this interpolation can misrepresent the actual transport behaviour. In particular, for chloride diffusion in cracked concrete, this approach significantly overestimates flux compared to experiments. It also fails to capture the experimentally observed threshold crack width below which diffusivity remains unchanged, and the plateau above which it no longer increases. To address this, we distinguish between physical diffusivity D and numerical diffusivity D_N, proposing a new algorithm to compute a suitable D_N=f(ϕ) based on the material’s mechanical properties and the phase-field length scale. This algorithm restores the correct flux/crack width relationship for arbitrary softening. Its effectiveness is demonstrated for both chloride diffusion and water convection in cracked concrete, and it shows low sensitivity to numerical parameters, supporting its general applicability to various transport regimes, including hydraulic fracture.