Geological sequestration of CO2 into depleted hydrocarbon reserviors or saline aquifers presents the enormous potential to reduce greenhouse gas emission from fossil fuels. However, it may give rise to a complicated coupling physical and chemical process. One of the processes is the hydro-mechanical impact of CO2 injection. During the injection project, the increase of pore pressures of storing formations can induce the instability, which finally results in a catastrophic failure of disposal sites. This paper focuses mainly on the role of CO2-saturated water in the fracturing behavior of rocks. To investigate how much the dissolved CO2 can influence the pore pressure change of rocks, acoustic emission (AE) experiments were performed on sandstone and granite samples under triaxial conditions. The main innovation of this paper is to propose a time dependent porosity method to simulate the abrupt failure process, which is observed in the laboratory and induced by the pore pressure change due to the volume dilatancy of rocks, using a finite element scheme associated with two-phase characteristics. The results successfully explained the phenomena obtained in the physical experiments.