The main objective of this master's thesis is to determine a mathematical model for the estimation of the blast front advance of the blasting carried out in the "El Aljibe" quarry in Almonacid de Toledo (Toledo, Spain) within the SLIM (Sustainable Low Impact Mining) project funded by the European Commission within the Horizon 2020 research and innovation program under grant agreement No. 730294. For each of the blasts, the data obtained from recordings with a high-speed camera were transformed into coordinates referring to a plane perpendicular to the blast face, using as reference points the coordinates of bags measured in situ in the quarry. Also, an adjustment of the rock trajectories has been carried out, obtaining the initial velocities, and an approximate adjustment of the time it takes for the fragments to move from the start of the detonation of the explosive loaded in the blast hole, i.e. the response time. The initial velocities and response times have been adjusted with a mathematical model as a function of blasting parameters and the position of the targets. The correlation between parameters for each blast has also been studied. In addition, a methodology has been developed to obtain 3D trajectories using a map of the front topographed with a profilometer. All calculations and analyses have been developed using the MATLAB technical computing language.