E3S Web of Conferences 415, 02005 (2023)
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https://doi.org/10.1051/e3sconf/202341502005

Impact of a dry granular flow against a rigid wall: MPM
simulations with a new constitutive approach
Claudio di Prisco1, Pietro Marveggio1, Irene Redaelli2, and Matteo Zerbi1*
1Department of Civil and Environmental Engineering, Politecnico di Milano, Milan, Italy
2Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano, Milan, Italy

Abstract. The dynamic interaction between granular flowing masses and obstacles is a very complex
phenomenon involving large displacements and high strain rates. To simulate the event in a continuumbased framework both advanced numerical tools and constitutive relationships are required. In this work,
the impact of a dry granular mass against a rigid wall is numerically simulated using the open-source
Material Point Method code ANURA3D, while the constitutive model proposed by Marveggio et al., 2021
is adopted for the granular mass. The model accounts for rate and grain packing dependence, which havebeen shown to be crucial to reproduce the propagation of compression and rarefaction waves inside the mass.
The model is capable of reproducing “solidification” and “liquefaction” phenomena observed in the DEM
impact tests results already available in the literature.

1 Introduction
Risk mitigation measures for flow-like landslides are
aimed at protecting the territory by modifying thepropagation phase, which is by deviating/arresting theflowing mass. In particular, one popular strategy consistsof protecting lifelines or buildings by installingconcrete/earth retaining walls. The design of thesemitigation works requires the definition of the force
exerted on the structure by the impacting mass. Up to now,practical design applications are based on simplified
equivalent pseudo-static approaches, which completelydisregard the evolution of the interaction mechanism withtime[1].
To improve the design technique, continuum-based
approaches can be adopted to simulate the impact, bymeans of numerical tools suitable for large displacements
analyses. In particular, Ceccato et al. [2] and Cuomo etal. [3] have shown the Material Point Method (MPM) tobe a promising approach to simulate such a dynamicinteraction. In their work, to reproduce the mechanicalbehavior of granular assemblies, the authors consider
simple constitutive laws (elastic-plastic Mohr Coulomb
non-dilatant relationships) in which strain-rate and grains
packing dependence are disregarded. Nevertheless, thesehave been demonstrated to be dominant when describing
the volumetric response and the fluidification and resolidification
mechanisms(“solid-fluidphasestransition”) occurring under dynamic conditions [4,5,6].
In this work, the impact of a dry polydisperse granularmass on a rigid wall has been numerically simulated bymeans of the open-source code ANURA3D, which isbased on a dynamic explicit MPM formulation. To thisaim, since the discussion is limited to dry conditions, asingle point formulation has been considered [7]. The
novelty of this approach consists in the use of theconstitutive model proposed by Marveggio et al. [8],which has been conceived to interpret solid-fluid phases
transitions that occur during fluidification/solidification
processes taking place during the arrest of a flow-likelandslide [1].
The reliability of the MPM results is discussed bycomparing the results with those of Redaelli et al. [9], whonumerically simulated the phenomenon adopting a
Discrete Element Method based code.
The aim of this work consists in trying to numerically
reproduce the mechanical processes taking place when a
dry granular mass impacts against a rigid wall in acontinuum-based framework. The use of the advanced
constitutive model seems to be a promising approach toreproduce (i) the temporal evolution of the impacting
force, (ii) the propagation of compression and rarefaction
waves that induce solidification and liquefaction in thegranular mass, after the impact takes place and (iii) thevolumetric behavior associated to phase solid-to-fluid(and viceversa) phase transitions.

2 The numerical model
The numerical simulations are conducted considering thesame scheme proposed by Calvetti et al [10]: the impactis
simulated by generating prismatic granular mass withvertical front of length 𝐿, height ℎ impacting on a verticalrigid wall and sliding over a horizontal rigid base. It is
assumed that, at the initial instant of time, corresponding* Corresponding author: matteo.zerbi@polimi.it© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

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to the time just before the impact, the mass ischaracterized by an initial uniform velocity 𝑢0 andporosity 𝑛0 . Plane strain conditions are imposed. The
rigid bodies, that are the wall and the base, are modelledaccording to Zambrano-Cruatty and Yerro [11].Frictionalcontacts ([12]) between both the mass and the base (𝜇𝑏)and the mass and the wall (𝜇𝑤) are introduced. Gravity isapplied to the material at the initial instant of time. To beconsistent with DEM numerical simulations of Redaelli etal. [9], adopted as a comparison, an initiallynil the state ofstress for the flowing mass is considered.

Fig. 2. Temporal evolution of the impact force 𝐹: comparison
between DEM and MPM predictions

As already observed by Calvetti et al., 2019, by analyzing thefields of particles velocities and force chains in numericalDEM results, after the impact, the propagation ofcompression and rarefaction waves occurs inside thegranular mass. These can be easily identified even in
MPM numerical results by looking at the spatial andtemporal evolution of the mean effective pressure inside
the impacting mass (Figure 3). After the impact, acompression wave propagates horizontally (Figure 3a).
This induces a significative increase in the mean effective
stress. Then, a rarefaction wave starts to propagate fromthe top to the bottom of the mass, inducing a considerable
reduction in the mean effective stress (Figures 3b and 3c).

Fig. 1. Impact scheme

The same flow height ℎ=3m, base friction coefficient𝜇𝑏 = 0.3 and obstacle friction coefficient 𝜇𝑤 = 0.6
adopted by Redaelli et al. [9], are assigned, whereas
the length L has been assigned equal to 15m.
The mechanical behavior of the flowing mass is simulated
by considering the strain hardening visco-elastic-plastic
model, based on the critical state concept and kinetic
theories of granular gases, proposed by Marveggio et al.
[8]. Model parameters have been calibrated on DEM
triaxial tests (both in compression and in extension)
performed on specimens characterized by the same
parameters employed in Redaelli et al. [9], considering
different confining pressure and relative densities.

3 Numerical results
The capability of the numerical model to reproduce DEM
impact tests has been here tested for a unique reference
configuration characterised by 𝑛0= 0.45 and 𝑢0 ranging
between 2 and 12 m/s (the reference value is 8 m/s). The
comparison between DEM and MPM numerical results interms of horizontal force exerted by the mass on the wallis quite satisfactory (Figure 2). With respect to DEM
results, MPM results present oscillations with a lower
amplitude and which decays faster. This seems to be
associated to the pathological numerical dissipation andviscosity typical of MPM approaches compared to
traditional Lagrangian methods [13].

Fig. 3. Mean effective pressure distribution inside the granularmass at a) 0.01s, b) 0.07s and c) 0.1s

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4 Conclusions
In this work, the impact of a dry granular mass against arigid wall is simulated using the MPM open-source code
ANURA3D. The comparison between MPM and DEM
results put in evidence the capability of the constitutive
model proposed by Marveggio et al. [8] to simulate ahighly dynamic process involving high strain rates andsolid-fluid (and viceversa) phases transitions associatedwith the propagation of compaction and rarefaction
waves, inside the medium. The results obtained suggestthat the proposed approach represents a promising tool for
sheltering structure design improvements, in terms ofstructure input load and prompt the authors in applying
the same approach for larger ranges of initial velocities,
porosities as well as geometries.

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