Discrete element model of the dynamic response of fresh wood stems to impact I. Olmedo a,⇑ , F. Bourrier a , D. Bertrand b , F. Berger a , A. Limam b a Irstea Grenoble, UR EMGR, 2 rue de la papeterie, 38402 St-Martin d’Hères, France b INSA Lyon, Villeurbanne, France article info Article history: Received 5 August 2015 Revised 7 March 2016 Accepted 8 March 2016 Keywords: Rockfall Wooden protective structures Fresh wood Impact Discrete element method abstract Forest stands are an efficient natural protection solution against rockfall. After windstorms or forest maintenance tasks, their protection capacity decreases. To compensate the loss of the protective function, a certain number of felled trees can be left on the slope as wooden protective structures. Studies are currently being conducted to estimate the efficiency of these devices and most particularly their resis- tance to block impacts and their energy dissipation capacity. A numerical model based on the discrete element method is developed herein to describe the fresh wood stem’s response to a dynamic loading. The fresh wood stem is modeled by a cylindrical beam composed of discrete elements. Studying the interaction between the elements makes it possible to describe the relation between bending moment and rotation accounting for the elasto-plastic response of the stem. The numerical model is validated by comparing the predictions with analytical solutions. Then the model is calibrated using experimental data from quasi-static and impact laboratory experiments. The numerical approach provides an accurate description of the quasi-static and dynamic response of fresh wood stems. The mechanical properties of fresh wood stems are assessed from the model calibration results and are coherent with the data found in the literature. Ó 2016 Published by Elsevier Ltd. 1. Introduction In mountain areas, significant investments have been made to protect inhabitants and infrastructures against natural hazards such as rockfalls. Civil engineers develop and optimize rockfall protection devices. However, the complexity of impact loadings, the interaction with projectiles, and the large displacements of the structure make the design of such devices a complex task. For this reason, numerical models based on the finite element method (FEM) have been intensively used for structure analysis and design. However, FEM simulations can become expensive in terms of computation costs when nonlinear behaviors and failure are integrated. Among the other numerical methods that can be used for structure design, the discrete element method (DEM) [1] is well adapted to easily describe large displacements, material nonlinearities, and contact interactions. The DEM has already been extensively used for modeling rock- fall protective structures: flexible metallic fences, e.g., [2–6], and embankments [7,8]. In particular, this technique can simulate the block’s impact onto the structure accounting for the different phys- ical processes involved. In the field of rockfall protection engineering, most studies have investigated protective structures such as flexible metallic fences or embankments [3]. However, forest and bio-engineering devices also have a significant capacity to dissipate rockfall energy [9,10]. This study aims to develop, calibrate, and validate a numerical model of bio engineering rockfall protection devices made of trees. The final goal is to provide a numerical model of a protection device made of a felled tree considering their mechanical proper- ties after setting up the structure and their evolution over time. In the first step, it is necessary to characterize the behavior of fresh wood stems under dynamic loading. The mechanical characteris- tics of fresh wood differ from the characteristics of dry wood given the differences in water content [11,12]. A numerical model of fresh wood stems based on the DEM is proposed to model bio engineering structures and their interaction with rockfalls. Block impacts are considered mainly orthogonal to the tree’s longitudinal axis and occurring far enough from the sup- ports, leading to reduced shear loadings. Thus, the study focuses on the characterization of the bending response of fresh wood stems under quasi-static (QS) or dynamic loadings. The numerical model http://dx.doi.org/10.1016/j.engstruct.2016.03.025 0141-0296/Ó 2016 Published by Elsevier Ltd. ⇑ Corresponding author. E-mail address: ignacio.olmedo@irstea.fr (I. Olmedo). Engineering Structures 120 (2016) 13–22 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct