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Register a new userA rain induced landslide 3D model based on molecular dynamics with fractal and fractional water diffusion
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Added by
Gianluca Martelloni
Publication date
2016
fields
Physics
and research's language is
English
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We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the fractal diffusion partial differential equation (PDE) with particular boundary conditions to simulate a rainfall event. Then, for the PDE, we developed a numerical integration scheme that we integrate with MD (Molecular Dynamics) algorithm for the triggering and propagation of the simulated landslide. Therefore we test the numerical integration scheme of fractal diffusion equation with the analytical solution. We adopt the fractal diffusion equation in term of gravimetric water content that we use as input of triggering scheme based on Mohr-Coulomb limit-equilibrium criterion, adapted to particle level. Moreover, taking into account an interacting force Lennard-Jones inspired, we use a standard MD algorithm to update particle positions and velocities. Then we present results for homogeneous and heterogeneous systems (i.e. composed by particles with same or different radius respectively). Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally we show the parameter sensibility analysis both for triggering and propagation phase. Our simulations confirm the results of our previous two-dimensional model and therefore the feasible applicability to real cases.
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Distributed models to forecast the spatial and temporal occurrence of rainfall-induced shallow landslides are based on deterministic laws. These models extend spatially the static stability models adopted in geotechnical engineering, and adopt an infinite-slope geometry to balance the resisting and the driving forces acting on the sliding mass. An infiltration model is used to determine how rainfall changes pore-water conditions, modulating the local stability/instability conditions. A problem with the operation of the existing models lays in the difficulty in obtaining accurate values for the several variables that describe the material properties of the slopes. The problem is particularly severe when the models are applied over large areas, for which sufficient information on the geotechnical and hydrological conditions of the slopes is not generally available. To help solve the problem, we propose a probabilistic Monte Carlo approach to the distributed modeling of rainfall-induced shallow landslides. For the purpose, we have modified the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis (TRIGRS) code. The new code (TRIGRS-P) adopts a probabilistic approach to compute, on a cell-by-cell basis, transient pore-pressure changes and related changes in the factor of safety due to rainfall infiltration. Infiltration is modeled using analytical solutions of partial differential equations describing one-dimensional vertical flow in isotropic, homogeneous materials. Both saturated and unsaturated soil conditions can be considered. TRIGRS-P copes with the natural variability inherent to the mechanical and hydrological properties of the slope materials by allowing values of the TRIGRS model input parameters to be sampled randomly from a given probability distribution. [..]
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A comprehensive microscopic understanding of ambient liquid water is a major challenge for $ab$ $initio$ simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for $ab$ $initio$ approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile $ab$ $initio$ based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model---a neural-network representation of the $ab$ $initio$ PES---in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H$_2$O and D$_2$O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects.
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