Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo Research Paper Impact forces of granular flows on rigid structures: Comparison between discontinuous (DEM) and continuous (MPM) numerical approaches Francesca Ceccato a, ⁎ , Irene Redaelli b , Claudio di Prisco b , Paolo Simonini a a DICEA – University of Padua, via Ognissanti 39, 35129 Padua, Italy b DICA – Politecnico di Milano, Pz. L. da Vinci 32, 20133 Milano, Italy ARTICLE INFO Keywords: Landslide protection DEM MPM Landslide Impact forces ABSTRACT The evaluation of forces due to the impact of flow-slides against structures is essential for both risk assessment and protection structure design. However, the impact process is very complex and not fully understood yet. Peak forces are in fact commonly evaluated by simplified empirical methods whose reliability is questionable. In this paper, the impact process is numerically investigated by comparing the results obtained from software based on a discontinuous Discrete Element Method (DEM) and a continuous Material Point Method (MPM). The impact process and its key features are highlighted and the principal parameters influencing the peak force value are identified. This study focuses on the impact phase, rather than on the propagation phase. The soil mass is initially positioned in front of the wall with a prescribed uniform velocity and the evolution of the impact force is monitored. 1. Introduction Landslides of the flow type, i.e. when the material behaves like a fluid and can move with high velocities, are among the most destructive landslide events. They include a wide range of phenomena, still difficult to classify, because they present mixtures of water, air and solid grains with percentages extremely variable in space and time. Examples of flow-like landslides are rock avalanches, dry sand/debris flow, sand flowslides, debris flows, sensitive clay flowslides and mud flows [1]. To reduce the risk associated with these class of landslides, very common protection measures are earth embankments and rigid ob- stacles built with the purpose of deviating or stopping the flow. To design these sheltering structures, the maximum impact force is often estimated by means of simplified relationships which are based on theories that consider the granular material to be an incompressible fluid and evaluate the fluid force according to either the hydrostatic or hydrodynamic approaches. The former approach assumes a triangular distribution of the normal pressure, whose maximum value is the hy- drostatic pressure multiplied by an empirical factor (p max =kρgh, ρ = bulk density, h= flow thickness, g = gravity acceleration, k = empirical factor) [2,3]. The latter assumes a constant pressure distribution along depth, in which the pressure is a modified value of the dynamic pressure (p max =aρv 0 2 ,v 0 = impact velocity, a = em- pirical factor) [4,5]. The empirical factors a and k have been estimated with both small and large scale test results and are a function of the flow characteristics. These coefficients vary within a wide range, making the practical use of these approaches rather difficult. More re- cently, mixed approaches, in which the peak pressure is a function of both velocity and thickness, have also been proposed [6,7]. In the past, the maximum impact force rarely has been assessed by using numerical codes. In fact, only very recently, computational tools able to deal with large displacements and to simulate soil-structure interaction increased in popularity. The aim of this paper is to study the impact process numerically, thus contributing to a better understanding of the phenomenon. This will lead to a better estimation of the max- imum impact force and, therefore, a more efficient design of protective structures with respect to traditional methods. Numerical techniques suitable for the study of impact forces are Discrete Element Methods (DEMs), Eulerian methods, Arbitrary Lagrangian-Eulerian (ALE) methods, and Lagrangian particle-based methods. DEMs apply a discrete approach in which the granular ma- terial is represented by an assembly of particles moving independently and interacting at contact points [8]. They can simulate the granular material response, both under static and dynamic conditions [9–11], by taking into consideration the microstructural response of the material without introducing sophisticated constitutive models. They are also capable of automatically taking into account large displacements [12–15]. Nevertheless, the computational cost may become excessive https://doi.org/10.1016/j.compgeo.2018.07.014 Received 7 February 2018; Received in revised form 10 July 2018; Accepted 16 July 2018 ⁎ Corresponding author. E-mail addresses: francesca.ceccato@dicea.unipd.it (F. Ceccato), irene.redaelli@polimi.it (I. Redaelli), claudio.diprisco@polimi.it (C. di Prisco), paolo.simonini@unipd.it (P. Simonini). Computers and Geotechnics 103 (2018) 201–217 0266-352X/ © 2018 Elsevier Ltd. All rights reserved. T