Dilatancy and fluid movements in a fault zone significantly affect the mode of the nucleation process and are one of the key factors for understanding the physical mechanisms of some short-term precursory phenomena. We investigated a model of the earthquake nucleation processes on a vertical fluid-infiltrated strike-slip fault in a three-dimensional elastic half-space using a Dieterich/Ruina rate- and state-dependent friction law and an evolution equation for plastic porosity. Because of dilatancy, porosity is thought to increase with slip velocity. We assume that plastic porosity depends logarithmically on the state variable in the friction law. The results of numerical simulations show that porosity in the fault zone increases with increasing slip velocity in the nucleation zone. Then pore fluid pressure in the fault zone drops significantly, resulting in dilatant hardening. With increasing dilatancy coefficient $varepsilon$ or with decreasing pore compressibility ¿$varphi$, larger pore fluid pressure drop is observed during the nucleation process, which in turn increases the size of the nucleation zone. We observe that when a dilatancy coefficient $varepsilon$ is large, a quasi-static nucleation zone extends widely with a low stress drop. Finally, slip velocity is accelerated in a localized area in the quasi-static nucleation zone, which is a place where a dynamic rupture originates. The size of the accelerated slip zone is significantly smaller than that of the quasi-static nucleation zone. Numerical results using a larger dilatancy coefficient can explain the extension of foreshock activity, which is occasionally observed in large earthquakes.