At urban signalized intersections, pedestrian twice-crossing is usually viewed as a complex human behavior, since there are many factors influencing it. Mostly, pedestrians engage in a complicated cognitive process of perception, attention and decision-making. Therefore, it is necessary to identify the major factors affecting this behavior, and develop an effective pedestrian dynamic model, in order to increase the safety and efficiency of crossing streets. This study proposes a force-based model of pedestrian dynamics by improving the classic social force model, in order to determine the influencing factors and quantify the forces acting on pedestrians crossing in two stages at signalized intersections. Through analyzing the characteristics of pedestrian twice-crossing behavior, the social force model was enhanced by providing a new component of the green signal countdown. The improved model includes four parts of the self-driving force in the ideal state, the repulsive and attractive forces generated by surrounding pedestrians, the resistance of the crosswalk boundary line, and the force produced by the green signal countdown. Each part was considered with qualitative analysis and quantitative calculation. The results show that the proposed model can achieve high accuracy in measuring the forces acting on pedestrian twice-crossing. The findings of this study have great implications for designing pedestrian facilities and optimizing pedestrian signal timings, helping thus to increase the mobility and safety of pedestrian twice-crossing.

Pedestrian two-stage crossing, as one of the key elements of the urban roadway network, affects not only vehicle flow at signalized interactions, but also road capacities in the transport system. Therefore, it is vital to deeply understand the behavioral characteristics of pedestrian twice-crossing in order to improve the safety and efficiency of the road transport network. Based on our previous study, this study continues to improve the social force model by classifying the trajectory type of pedestrian twice crossing. In the interactive aggregation, the pedestrian trajectory line was divided into two types: straight path and curved path. The Work–Energy Principle and Impulse–Momentum Principle were used to identify the spatial and temporal characteristics of pedestrian twice-crossing behaviors. It was found that when pedestrians on the two sides are facing very close in a congested section, the maximum repulsive force appears to be a dramatic increase and remains for a period of time. This result provides us with direction for updating the social force model, focusing on the repulsive force generated by the opposite flow. The improved model can achieve high precision in predicting pedestrian twice-crossing behaviors. The findings of this study have great implications for designing pedestrian facilities and optimizing pedestrian signal timings, thus helping to increase the mobility and safety of pedestrian twice-crossing.