Clay-gravel mixture has been widely used in high embankment dams and understanding its seepage characteristics is critical to dam safety. From the instrumental perspective, the realization of continuous pressurized water supply becomes a key technical challenge, significantly restricting the working conditions replicated in previous seepage apparatuses. To this end, a novel water provision system, relying on parallel-disposed sensor-based pressure devices, was introduced, so that the application of an existing large-scale stress-controlled apparatus can be expanded to long-term seepage tests regarding coarse-grained cohesive soils. Constant-head permeability tests were conducted on original-graded clay-gravel mixtures to investigate their hydraulic properties, incorporating the influence of stress relaxation. Test results show that with 35% gravel content, the clay-gravel mixture is suitable for dam construction as the core material. The stress relaxation holds a marginal effect on the hydraulic conductivity of soil. The functionality of this improved apparatus is verified, especially under long-term seepage conditions.