Understanding the failure mechanism of a tunnel excavation face under complex hydrogeological conditions is a key challenge for geotechnical engineering. In this study, we investigated the excavation face instability induced by the longitudinal slope angle of the tunnel and steady state seepage flow. First, a fiber Bragg grating (FBG) system suitable for centrifuge model tests was proposed. The test apparatus was enhanced to investigate the influence of longitudinal slope angle on the active limit support pressure. Subsequently, a series of centrifuge model tests and Abaqus numerical simulation analyses were conducted to investigate the progressive failure mechanism of the excavation face. The experimental and numerical simulation results showed that the proposed geotechnical centrifuge FBG test system is fully feasible for multi-parameter monitoring of the centrifuge model. Under the assumptions of homogeneous and isotropic soil and steady state seepage flow, the seepage force in the limit support pressure is independent of the permeability coefficient. Moreover, the active and passive limit support pressures increase and decrease, respectively, with longitudinal slope angle, and the gap between them progressively decreases. Furthermore, under isotropic permeability, the soil internal friction angle, rather than soil cohesion, is responsible for the change in excavation face stability with longitudinal slope angle.