As the preferred configuration for autonomous vehicles, the steer-by-wire (SbW) system replaces the mechanical linkage with electric signals. However, the disconnection of the steering column deteriorates the origin steering feedback torque (SFT), necessitating the road sense construction. To provide the potential driver convincing steering feel, this article proposes a road sense construction scheme, including an SFT designer employing the data-driven method and an SFT controller based on the friction compensated explicit model predictive control (FEMPC). Initially, the hand wheel module and the road wheel module are introduced to analyze network features and establish controller foundations. Subsequently, the torque designer combining convolutional neural network (CNN) and gated recurrent unit (GRU) layers is proposed, which can extract the spatial and temporal information of vehicle dynamic (VD) states, respectively. To ensure precision and real-time performance, the torque controller based on the explicit model predictive control (EMPC) is then presented and the Brown friction model is also adopted for feedforward compensation. After training the designer with real vehicle data, the whole road sense construction scheme is verified subjectively and objectively. The simulation and experiment results show the authenticity of the designer on the one hand and the precision of the controller on the other hand. In addition, the results simulating the road sense construction failure show the significance of hardware redundancy.