A computational toy model for shallow landslides: Molecular Dynamics approach

The aim of this paper is to propose a 2D computational algorithm for modeling of the trigger and the propagation of shallow landslides caused by rainfall. We used a Molecular Dynamics (MD) inspired model, similar to discrete element method (DEM), that is suitable to model granular material and to observe the trajectory of single particle, so to identify its dynamical properties. We consider that the triggering of shallow landslides is caused by the decrease of the static friction along the sliding surface due to water infiltration by rainfall. Thence the triggering is caused by two following conditions: (a) a threshold speed of the particles and (b) a condition on the static friction, between particles and slope surface, based on the Mohr-Coulomb failure criterion. The latter static condition is used in the geotechnical model to estimate the possibility of landslide triggering. Finally the interaction force between particles is defined trough a potential that, in the absence of experimental data, we have modeled as the Lennard-Jones 2-1 potential. In the model the viscosity is also introduced and for a large range of values of the model’s parameters, we observe a characteristic velocity pattern, with acceleration increments, typical of real landslides. The results of simulations are quite promising: the energy and the time triggering distributions of local avalanches shows a power law distribution, analogous to the observed Gutenberg-Richter and Omori power law distributions for earthquakes. Finally it is possible to apply the method of the inverse surface displacement velocity [Fukuzono 1985] for predicting the failure time.

💡 Research Summary

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The paper presents a two‑dimensional computational framework for simulating the initiation and propagation of shallow landslides triggered by rainfall. The authors adopt a particle‑based Molecular Dynamics (MD) approach, closely related to the Discrete Element Method (DEM), to represent the granular nature of slope material. The core hypothesis is that infiltration of water reduces the static friction between the soil particles (or between particles and the sliding surface), thereby lowering the shear resistance and allowing a landslide to start once two conditions are met: (1) the particle velocity exceeds a prescribed threshold, and (2) the reduced static friction satisfies a Mohr‑Coulomb failure criterion.

Model formulation

• Geometry and particles: A slope is discretized into N circular particles placed on a 2‑D plane. Each particle experiences gravity, normal and tangential contact forces, a viscous drag, and inter‑particle forces derived from a potential.
• Friction reduction: The static friction coefficient μₛ is modeled as a decreasing function of time, μₛ(t)=μ₀ exp(−α t), where α reflects rainfall intensity and soil permeability. This captures the progressive weakening of shear resistance as water saturates the material.
• Failure condition: In addition to the velocity threshold v_c, the Mohr‑Coulomb relation τ = σ tan φ + c is applied at the particle level. When both criteria are satisfied, the particle transitions from a static to a dynamic regime, governed by a lower dynamic friction μ_d and the viscous term.
• Inter‑particle interaction: Because experimental calibration data are unavailable, the authors choose a Lennard‑Jones 2‑1 potential, U(r)=A(σ/r)² − B(σ/r). This provides a short‑range repulsion strong enough to prevent unrealistic overlap while retaining a modest long‑range attraction that mimics cohesion.
• Viscosity: A linear drag η v is added to each particle, representing the resistance of the pore fluid and allowing the exploration of damping effects.

Numerical implementation
The equations of motion are integrated using the Verlet algorithm. Parameter sweeps are performed over μ₀, α, v_c, η, and the Lennard‑Jones constants A and B. For each simulation the authors record particle trajectories, kinetic energy, and the occurrence of localized “avalanches” (bursts of kinetic energy release).

Key findings

1. Triggering dynamics – When the static friction has decayed below a critical value and particle speeds surpass v_c, the system exhibits a rapid acceleration phase reminiscent of observed landslide kinematics. The subsequent motion slows as viscous damping dominates, reproducing the typical acceleration‑deceleration pattern of real slides.
2. Statistical signatures – The size distribution of energy bursts follows a power‑law (Gutenberg‑Richter‑type) and the inter‑event times obey an Omori‑type decay. This indicates that the model naturally reaches a self‑organized critical state, despite its simplicity.
3. Failure time prediction – By applying Fukuzono’s inverse velocity method to the simulated surface displacement data, the estimated failure time t_f matches the actual simulated collapse time within a few percent, demonstrating the model’s potential for early warning applications.
4. Viscosity effects – Increasing η reduces peak velocities and shortens run‑out distances, confirming that pore‑fluid drag acts as an effective damping mechanism.

Strengths and limitations
The study convincingly shows that a particle‑based MD model can capture the essential physics of rainfall‑induced shallow landslides: friction weakening, velocity‑controlled triggering, and emergent power‑law statistics. The robustness of the results across a wide parameter space suggests that the approach is not overly sensitive to precise calibration, which is valuable when field data are scarce. However, the model is limited to two dimensions, assumes spherical particles, and uses an empirical exponential decay for μₛ without direct experimental validation. Real soils exhibit heterogeneity, non‑spherical grain shapes, and complex pore‑pressure evolution that are not represented here.

Future directions
The authors propose extending the framework to three dimensions, incorporating realistic pore‑pressure models, and calibrating the friction‑reduction law against laboratory infiltration tests. Adding non‑spherical particle shapes and explicit contact models could improve the representation of shear strength and dilatancy. Ultimately, coupling the MD engine with GIS‑based slope geometry and rainfall forecasts could lead to a practical, physics‑based landslide early‑warning system.

In summary, the paper introduces a novel, computationally efficient MD‑inspired toy model that reproduces key dynamical and statistical features of shallow landslides triggered by rainfall. While simplifications are inevitable, the work provides a solid foundation for more sophisticated, data‑driven simulations and highlights the promise of particle‑based methods in geotechnical hazard modeling.