In order to address the inherent limitations of traditional heat storage systems with regard to heat storage efficiency and heat extraction, the effects of different heat storage media and heat conduit structures on heat storage efficiency, heat extraction efficiency and temperature distribution uniformity are analyzed through numerical analyses of three-dimensional heat transfer and flow models. The study demonstrates that sandy soil material possesses a superior final heat storage capacity, attributable to its elevated heat capacity. Conversely, concrete exhibits a higher heat storage completion rate (up to 94.9%) and approaches a closer saturation state during the heat storage process. In terms of heat conduit arrangement, the serpentine heat conduit has higher power at the beginning of heat storage, but after approximately 120 min, the U-type heat conduit shows higher heat storage efficiency and more uniform temperature distribution to ensure the stability of the system operation. During the process of heat extraction, the U-type heat pipe demonstrates continuous and stable heat extraction capacity, which is 12.5% higher than that of the serpentine heat pipe. The incorporation of graphene has been demonstrated to enhance thermal conductivity, promote uniform temperature field distribution, and mitigate low-temperature regions. The synergy between the concrete/graphene material and the U-shaped heat conduit is found to be highly effective in enhancing uniformity, stability, and efficiency. This synergistic enhancement significantly improves system efficiency (by 12.1%).