We propose a two-phase damage theory in a viscoelastic medium to study the pressure and porosity diffusion in fractured near-surface porous rocks. The key ingredient in the viscoelastic theory is that the pressure difference between solid and fluid is divided into three parts, which contribute to reversible elastic potential energy, irreversible viscous entropy production and surface energy stored during deformation. The resulting continuum description of weakening and failure (distributed void generation and microcracking) in a linear Kelvin body accounts for surface energy being created by both viscous and elastic deformational work. The model shows that while non-linear permeability models leads to an enhanced diffusivity, damage makes the matrix more compressible if we assume the geometry/size of cracks remain unchanged. The net effect is that the porosity diffusivity is reduced causing fluid infiltration to accumulate closer to the injection source, leading to a slower fluid diffusion during hydraulic fracturing with a fixed porosity boundary condition. However if a constant overpressure boundary condition is applied, a weakened matrix with damage leads to greater pressure diffusivity than for porosity.