Abstract: A method for determining a column-hemispherical permeation radius with time-varying property of power-law cement grout and tortuosity of rock and soil mass is provided, including: acquiring a porosity ? of rock and soil mass and a corresponding permeation coefficient K by geotechnical tests, measuring a groundwater pressure P0 at a grouting point and determining tortuosity ? of rock and soil mass; acquiring an initial consistency coefficient c0, a rheological index n and a time-varying property coefficient k of power-law cement grout with a designed water to cement ratio by rheological tests, and determining the viscosity of water ?w; acquiring grouting parameters, including a grouting pressure P1, grouting time t, a number m of grouting holes of a side surface of a grouting pipe and a grouting hole radius r; and solving a column-hemispherical permeation grouting diffusion radius R considering coupling effect both the tortuosity of rock and soil mass and the time-varying property of power-law cement grout.