Well completion for oil and gas, geothermal energy as well as CO2 storage sometimes require stimulation to achieve economical fluid flow rates (for both injector and producer wells). Predicting the growth of fluid-driven fractures in geological systems is essential for the sustainable and efficient engineering of those reservoirs. The quasi-brittle nature of rocks complexifies the coupling between fluid flow and fracture growth – especially in the fracture process zone. To better understand the impact of the non-linear fracture in such materials, we perform different laboratory hydraulic fracturing experiments under controlled stresses and fluid injection conditions in a cubic block of 250*250*250 millimeter in size. We choose two different rocks (marble and gabbro) with an order of difference in grain sizes (and as a result most likely different process zone size) but both with very low permeability. We report a series of experiments performed under different regimes of propagation (lag-viscosity as well as toughness dominated) in these two rocks under different levels of confining stress. We use active acoustic monitoring to reconstruct the evolution of the fracture front with time with a spatial resolution of a few millimeters every 4 seconds in time (see Liu et al. (2020) for details). We show that the fracture growth is also consistent with other measurements such as fluid injection pressure and displacement measured. Attenuation of the transmitted acoustic energy also indicates the existence of a damage zone (often denoted as a process zone) ahead of the fracture. This process zone grows differently inside these two rocks during fracture propagation. Its final size appears limited by the specimen dimensions with a decrease of the fracture apparent toughness at later time.