Comput Geosci (2014) 18:817–830

DOI 10.1007/s10596-014-9428-9

ORIGINAL PAPER

Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures

Carter M. Mast · Pedro Arduino · Gregory R. Miller ·

Peter Mackenzie-Helnwein

Received: 11 June 2013 / Accepted: 3 June 2014 / Published online: 31 July 2014 © Springer International Publishing Switzerland 2014

Abstract In this paper, the material point method (MPM) is presented as a tool for simulating large deformation, gravity-driven landslides. The primary goal is to assess the interaction of these flow-like events with the built environment. This includes an evaluation of earthen mounds when energy dissipating devices are placed in the path of a snow avalanche. The effectiveness of the embankments is characterized using displacement, velocity, mass, and energy measures. A second example quantifies the force interaction between a landslide and a square rigid column. Multiple slide approach angles are considered, and various aspects of the impact force are discussed.

Keywords Material point method · Granular flow ·

Landslide · Debris flow · Avalanche · Reaction force ·

Impact force · Contact · Soil-structure interaction ·

Large deformation 1 Introduction

Each year, landslides and avalanches cause significant damage and loss of life around the world. In the USA alone, the annual economic costs of landslides can be estimated to be between $1 and $2 billion, with an associated 25 to 50

P. Arduino () · G. R. Miller · P. Mackenzie-Helnwein

Department of Civil & Environmental Engineering,

University of Washington, Box 352700, Seattle,

WA 98195, USA e-mail: parduino@uw.edu

C. M. Mast

Greenpoint Technologies, Kirkland, WA 98033, USA e-mail: cmast@greenpnt.com yearly casualties [7]. To help protect people, infrastructure, and lifelines against such disasters, it is critical to: (i) control the path and/or redirect flow when potential interaction with the built environment exists and (ii) have engineered structures that are capable of resisting the loads imparted by an avalanche or landslide.

Capturing the mechanical behavior and structural interaction is challenging—as these flow events are highly dynamic, unpredictable, and inherently complex in nature.

Researchers have developed both physical and numerical models in an effort to build understanding of these phenomena. Physical models typically require well-controlled, large-scale experiments (see, e.g, [5, 9, 10, 12, 21, 31]).

While these experiments provide valuable insight into the governing behavior and controlling mechanisms, their general effectiveness is limited due to scale restrictions and the inability to accurately recreate in situ conditions.

Application in general contexts requires numerical models that are capable of reproducing key aspects observed in the field and the ability to represent slides at their full scale. Such models are necessary not only for prediction and design but also for the guidance of additional experimentation as well as furthering engineering understanding and education in professional practice.

To this end, various numerical simulation methodologies and techniques have been used for predicting flow initiation, evaluating flow patterns, and analyzing the general flow dynamics of avalanche and landslides. This includes the well established depth average techniques (see e.g. [4, 8, 24]). While these methods do reasonably well in estimating global quantities such as runout patterns, there can be limitations that make fully three-dimensional (3D) analyses cumbersome or impossible or there can be difficulties obtaining the force interaction between the flowing mass 818 Comput Geosci (2014) 18:817–830 and structures. These limitations follow primarily from the two-dimensional (2D) nature of such techniques, which use depth-averaged variables. The end result is a smearing of localized 3D phenomena and an inability to accurately assess obstacle interactions with the flow. Alternately, purely Eulerian frameworks can provide a reasonable representation of granular flow and the interaction with rigid objects. This includes finite difference techniques [18] and control volume methods [6]. Different particle techniques, such as smoothed particle methods [2, 17] and the discrete element method (DEM) [30], can also be used. The primary drawback of particle methods in this context is scale—particularly for the DEM.

The current work uses the material point method (MPM) as a continuum-based tool for modeling avalanche and landslides via coupling with an appropriate constitutive framework, highlighting the method’s suitability for obtaining the dynamic reaction force interaction between the flowing material and a rigid structure(s). An example of MPM simulation is shown in Fig. 1, where a gravity-driven landslide impacts a square column. The left image shows the slide as it engulfs the column, with the colormap indicating the net velocity magnitude of the flow. The right image shows the column at the same instant in time without the landslide.

The resulting normal reaction force vector field is shown using a colormap corresponding to the normal force vector magnitude. Similar examples are evaluated in the remaining pages of this document.

This paper is organized as follows: Section 2 contains a basic overview of the material point method and presents the method as a tool for representing landslides and avalanches from the perspective of continuum-based granular media. This includes a brief discussion of the constitutive framework, and in Section 2.1, a description of a simple two-invariant, isotropic model sufficient for capturing the large deformations is provided. The remainder of the paper focuses on applications. Section 3 highlights the use of earthen mounds as energy dissipation devices for slowing a snow avalanche. Emphasis is placed on the reduction in apparent velocity and corresponding kinetic energy, as well as the effectiveness of the mounds in reducing the extent of the snow runout. In Section 4, a series of simulations investigate the approach angle of a concentrated flow impacting a square column. Reaction force time histories are presented, and the study identifies key force characteristics inherent to these types of analyses. 2 Material point method representation of landslides and debris flows