Abstract: Water injection used in industry can lead to the activation of existing faults and have induced many destructive earthquakes. Therefore, it is of great significance to study the dynamic response of faults under water injection to explore the mechanism of induced earthquakes. The poroelastic spring-slider model calculates the fault stability under three kinds of classical water injection schedules（ascending, rapidly ascending, descending and intermittent）using poroelastic coupling numerical simulation. The results show that, with the continuous injection of fluid, the pore pressure inside the fault will go through three stages: slow rise, rapid rise, and stable rise. For different water injection schedules, the three stages are not fully reflected, and the forms are different; under the same water injection schedule, the smaller the reservoir permeability is, the greater the pore pressure near the wellhead is, the smaller the pore pressure at fault is, and the greater the difference of pore pressure between the two is; the larger the value is, the easier the earthquake will be induced. The value is negatively correlated with the fluid pressure of injected reservoir fluid but positively correlated with the change rate of fluid pressure; the critical stiffness increases rapidly in the early stage due to the increase of the change rate of pore pressure and decreases in the later stage due to the influence of pore pressure. The rapid rising and falling water injection schedule greatly increase the possibility of inducing earthquake in the early stage of water injection. The intermittent water injection schedule causes a large change of necessary stiffness in the late stage of water injection, which increases the possibility of inducing an earthquake. This study can provide the quantitative scientific basis for the risk assessment of water injection-induced earthquakes and reduce the possibility of water injection-induced earthquakes.