Applied Mathematical Modelling 40 (2016) 4380–4396 Contents lists available at ScienceDirect Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm A conceptual fatigue-motivation model to represent pedestrian movement during stair evacuation Enrico Ronchi a,∗ , Paul A. Reneke b , Richard D. Peacock b a Department of Fire Safety Engineering, Lund University, Lund, Sweden b Fire Research Division, National Institute of Standards and Technology, Gaithersburg, USA a r t i c l e i n f o Article history: Received 30 April 2015 Revised 16 November 2015 Accepted 25 November 2015 Available online 2 December 2015 Keywords: Evacuation Egress Stair Fatigue Modelling Pedestrian a b s t r a c t Evacuation models often neglect the impact of fatigue on pedestrian movement during stair evacuation. While a limited number of sub-models are available in the literature to repre- sent fatigue during evacuations, they mostly refer to simple, fixed walking speed reductions due to physical fatigue. This paper introduces a more comprehensive conceptual model for the representation of the impact of fatigue on the performance of evacuees during building stair evacuation. The model is presented considering its conceptual formulation and the is- sues associated with its implementation. First, a comprehensive conceptual representation of the factors concerning fatigue affecting human behaviour is discussed. The model takes into account (1) physical factors (i.e., physical fatigue), and (2) psychological factors (i.e., motiva- tion, intended as the variable balancing the perceived risk and the perceived fatigue). Second, the application of the proposed fatigue-motivation model to a hydraulic or Newtonian based evacuation modelling tool is discussed at various levels of sophistication. © 2015 Elsevier Inc. All rights reserved. 1. Introduction Evacuation models are often used to assess the life safety performance of a building in case of an emergency [1,2]. Cur- rent evacuation models focus mostly on representing the impact of crowding on walking speeds [1]. To date, more than sixty evacuation models (both commercial and research models) are available, each with different features or modelling methods [3]. Although those features have been categorized and analysed in different reviews and studies [1,4–7], no discussion on the impact of fatigue on occupant walking speed is included. The need for the inclusion of fatigue in evacuation modelling is a known issue in the research community. For instance, Pelechano and Malkawi [8] explicitly pointed out that fatigue should be included in evacuation models used for engineering calculations. Additional studies highlighted the same issue in various applications such as high-rise building evacuations [9] and fire-fighter intervention during evacuations [10]. The experimental studies conducted by Denny [11] implemented in the simulations performed by Koo et al. [12] show that the reduction in speed due to fatigue may reach up to 66% of the initial speed for people without disabilities and up to 41% of the initial speed for people with disabilities. In such cases, the use of walking speeds which do not consider the impact of fatigue would lead to significantly shorter estimated evacuation times. The consequence of the lack of a comprehensive model for the representation of fatigue can thus lead to overly optimistic results (i.e. the actual walking speeds of people could be slower than the simulated walking speed, with subsequent shorter simulated evacuation times) which may impact the life safety design of a building. ∗ Corresponding author. Tel.: +46 462227694; fax: +46 462224612. E-mail address: enrico.ronchi@brand.lth.se (E. Ronchi). http://dx.doi.org/10.1016/j.apm.2015.11.040 S0307-904X(15)00784-2/© 2015 Elsevier Inc. All rights reserved.