Mitigating the risk of falling is an area of significant interest among clinicians due to the often profound health-related consequences of falls. Consequently, there is acute interest in characterizing the biomechanical conditions associated with increased fall risk, and in methods for quantifying gait stability under those conditions toward predicting and ultimately preventing falls. Considerable insights into the biomechanics of fall risk have been provided by examining the passive dynamic walking (PDW) model under nominal and perturbed conditions. This work aims to expand upon prior efforts and develop the PDW model as a model of tripping and slipping by simulating and analyzing the behavior of the model during transient perturbations. We show that fall risk increases with increasing perturbation magnitude, yet stable walking may be found even with fairly large perturbations. In cases where transient perturbations result in a fall, a nontrivial portion exhibit a substantial period of stumbling before the fall, indicating an opportunity for developing early fall-risk detection and intervention techniques. In such cases, we show that widely used kinematic metrics are able to predict whether or not a fall will occur with up to 82% balanced accuracy, even when a variety of gait kinematics are considered.