An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

We propose an explicit GPU-based solver within the material point method (MPM) framework using graphics processing units (GPUs) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e. granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and non-local computational aspects (i.e. the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report (i) a maximum 200-fold performance gain between a CPU- and a single-GPU-based implementation, provided that (ii) the hardware limit (i.e. the peak memory bandwidth) of the device is reached. Furthermore, our multi-GPU implementation can resolve models with nearly a billion material points. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.</p

Resolving Wave Propagation in Anisotropic Poroelastic Media Using Graphical Processing Units (GPUs)

Biot's equations describe the physics of hydromechanically coupled systems establishing the widely recognized theory of poroelasticity. This theory has a broad range of applications in Earth and biological sciences as well as in engineering. The numerical solution of Biot's equations is challenging because wave propagation and fluid pressure diffusion processes occur simultaneously but feature very different characteristic time scales. Analogous to geophysical data acquisition, high resolution and three dimensional numerical experiments lately redefined state of the art. Tackling high spatial and temporal resolution requires a high-performance computing approach. We developed a multi- graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells. We present a comprehensive dimensional analysis reducing the number of material parameters needed for the numerical experiments from ten to four. Furthermore, the dimensional analysis emphasizes the key material parameters governing the physics of wave propagation in poroelastic media. We perform a dispersion analysis as function of dimensionless parameters leading to simple and transparent dispersion relations. We then benchmark our numerical solution against an analytical plane wave solution. Finally, we present several numerical modeling experiments, including a three-dimensional simulation of fluid injection into a poroelastic medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results. The high efficiency of our numerical implementation makes it readily usable to investigate three-dimensional and high-resolution scenarios of practical applications.ISSN:2169-9313ISSN:0148-0227ISSN:2169-935

Spontaneous formation of fluid escape pipes from subsurface reservoirs

Ubiquitous observations of channelised fluid flow in the form of pipes or chimney-like features in sedimentary sequences provide strong evidence for significant transient permeability-generation in the subsurface. Understanding the mechanisms and dynamics for spontaneous flow localisation into fluid conductive chimneys is vital for natural fluid migration and anthropogenic fluid and gas operations, and in waste sequestration. Yet no model exists that can predict how, when, or where these conduits form. Here we propose a physical mechanism and show that pipes and chimneys can form spontaneously through hydro-mechanical coupling between fluid flow and solid deformation. By resolving both fluid flow and shear deformation of the matrix in three dimensions, we predict fluid flux and matrix stress distribution over time. The pipes constitute efficient fluid pathways with permeability enhancement exceeding three orders of magnitude. We find that in essentially impermeable shale, vertical fluid migration rates in the high-permeability pipes or chimneys approach rates expected in permeable sandstones. This previously unidentified fluid focusing mechanism bridges the gap between observations and established conceptual models for overcoming and destroying assumed impermeable barriers. This mechanism therefore has a profound impact on assessing the evolution of leakage pathways in natural gas emissions, for reliable risk assessment for long-term subsurface waste storage, or CO2 sequestration

Strain localisation: Interplay between thermal and chemical softening

International audienceLocalisation of strain is a ubiquitous feature in rocks that can happen at any scale and in either brittle and ductileportions of the lithosphere. In ductile rocks, strain localisation is induced by local reduction of rock viscosity.While shear heating (thermal softening) and grain size evolution have been emphasized as potentials causes ofstrain localisation, the role of compositional variations (chemical softening) has been less explored.We establish a closed system of equations that incorporates thermo-mechanical-chemical coupling and apply dimensionalisationto identify governing dimensionless numbers. Using two-dimensional models, we investigate therelative importance of thermal and chemical softening on the development of ductile strain localisatio

Achieving complete reaction while the solid volume increases: A numerical model applied to serpentinisation

International audienceSolid volume increases during the hydration of mantle rocks. The fluid pathways necessary to feed the reaction front with water can be filled by the low density reaction products. As a result, the reaction front dries out and the reaction stops at low reaction progress. This process of porosity clogging is generally predicted to dominate in reactive transport models, even when processes such as reaction-induced fracturing are considered. These predictions are not consistent with observations at mid-ocean ridges where dense mantle rocks can be completely replaced by low density serpentine minerals. To solve this issue, we develop a numerical model coupling reaction, fluid flow and deformation. High extents of reaction can only be achieved when considering that the increase in solid volume during reaction is accommodated through deformation rather than porosity clogging. The model can generate an overpressure that depends on the extent of reaction and on the boundary conditions. This overpressure induces viscoelastic compaction that limits the extent of the reaction. The serpentinisation rate is therefore controlled by the accommodation of volume change during reaction, and thus by deformation, either induced by the reaction itself or by tectonic processes

Resolving hydro-mechanical coupling in two and three dimensions

International audienceEvidences of localised flow patterns are ubiquitous on Earth and drive a range of geo-processes across all scales.Classical Dacian models predict a diffusive behaviour leading to spreading and delocalisation, observations rathersuggest focusing of porous fluids within fingers, veins or channels.We aim to investigate numerically a physical mechanism, the de-compaction weakening, which leads to theformation and propagation of localised flow pathways in fluid saturated porous media. We use high-resolutiontwo- and three-dimensional numerical modelling to solve nonlinear Darcian porous flow in a viscously deformingmatrix using a nonlinear Stokes flow. In order to accurately capture strong localisation in space and time, westreamline matrix-free Pseudo-Transient approaches on graphical processing units. The Pseudo-Transient routinesconverge towards identical solutions compared to Direct-Iterative solving strategies.We discuss performance benefits of the matrix-free method on modern parallel hardware. We show thathigh porosity channels may be a dynamic and natural outcome of sufficiently resolved hydro-mechanical couplingand de-compaction weakening. In addition, we systematically study the channel propagation velocity as a functionof bulk and shear viscosity ratios.We conclude on the viability of buoyancy driven fluid migration at rates up to the three orders of magnitudehigher than expected by pure Darcian flow regimes. We provide both the two-dimensional MATLABbased Direct-Iterative and Pseudo-Transient routines for full reproducibility and suggest our model setup as akey benchmark case to validate implementation of hydro-mechanical coupling in two- and three-dimensionalnumerical code

Evgenii B. Burov: A co-convenor tribute

International audiencePlate tectonics is based on the assumption that the plates have behaved rigidly for long periods of geological time. While plate rigidity has allowed the kinematics of the major plates to be described and plate motion models to be constructed, we still lack a full understanding of the physical properties of the plates, their long-term strength and how they respond to geological load shifts on their surface and convective tractions on their base. Evgenii Burov (1963-2015) was a pioneer in the application of geological observations such as plate flexure to better understand the structure, rheology and stress state of continental lithosphere. By comparing observations in compressional and extensional settings to multi-layered models that incorporated realistic rheologies based on data from experimental rock mechanics he showed that the response of the lithosphere varied with thermal and load age. We review here some of Evgenii's contributions to plate mechanics and mantle dynamics and the enduring impact that his studies have had on our understanding of lithosphere behavior on short and long time-scales and the link between surface crust and deep mantle processes

2D porosity wave code with new viscoplastic rheology

This package contains the 2D matlab code for porous wave with viscoplastic rheology. It can be used to produce the 2D models result for the paper of Yarushina et al 2020