This study focuses on the multiphase flow properties of crowd motions. Stability is a crucial forewarning factor for the crowd. To evaluate the behaviors of newly arriving pedestrians and the stability of a crowd, a novel motion structure analysis model is established based on purposiveness, and is used to describe the continuity of pedestrians\' pursuing their own goals. We represent the crowd with self-driven particles using a destination-driven analysis method. These self-driven particles are trackable feature points detected from human bodies. Then we use trajectories to calculate these self-driven particles\' purposiveness and select trajectories with high purposiveness to estimate the common destinations and the inherent structure of the crowd. Finally, we use these common destinations and the crowd structure to evaluate the behavior of newly arriving pedestrians and crowd stability. Our studies show that the purposiveness parameter is a suitable descriptor for middle-density human crowds, and that the proposed destination-driven analysis method is capable of representing complex crowd motion behaviors. Experiments using synthetic and real data and videos of both human and animal crowds have been conducted to validate the proposed method.