We present an efficient MATLAB-based implementation of the material point method (MPM) and its most recent variants. MPM has gained popularity over the last decade, especially for problems in solid mechanics in which large deformations are involved, such as cantilever beam problems, granular collapses and even large-scale snow avalanches. Although its numerical accuracy is lower than that of the widely accepted finite element method (FEM), MPM has proven useful for overcoming some of the limitations of FEM, such as excessive mesh distortions. We demonstrate that MATLAB is an efficient high-level language for MPM implementations that solve elasto-dynamic and elasto-plastic problems. We accelerate the MATLAB-based implementation of the MPM method by using the numerical techniques recently developed for FEM optimization in MATLAB. These techniques include vectorization, the use of native MATLAB functions and the maintenance of optimal RAM-to-cache communication, among others. We validate our in-house code with classical MPM benchmarks including (i) the elastic collapse of a column under its own weight; (ii) the elastic cantilever beam problem; and (iii) existing experimental and numerical results, i.e. granular collapses and slumping mechanics respectively. We report an improvement in performance by a factor of 28 for a vectorized code compared with a classical iterative version. The computational performance of the solver is at least 2.8 times greater than those of previously reported MPM implementations in Julia under a similar computational architecture.

Understanding the dynamics of slope instabilities is critical to mitigate the associated hazards, but their direct observation is often difficult due to their remote locations and their spontaneous nature. Seismology allows us to get unique information on these events, including on their dynamics. However, the link between the properties of these events (mass and kinematics) and the seismic signals generated is still poorly understood. We conducted a controlled rockfall experiment in the Riou Bourdoux torrent (southern French Alps) to try to better decipher those links. We deployed a dense seismic network and inferred the dynamics of the block from the reconstruction of the 3D trajectory from terrestrial and airborne high-resolution stereophotogrammetry. We propose a new approach based on machine learning to predict the mass and the velocity of each block. Our results show that we can predict those quantities with average errors of approximately 10 % for the velocity and 25 % for the mass. These accuracies are as good as or better than those obtained by other approaches, but our approach has the advantage in that it does not require the source to be localised, nor does it require a high-resolution velocity model or a strong assumption on the seismic wave attenuation model. Finally, the machine learning approach allows us to explore more widely the correlations between the features of the seismic signal generated by the rockfalls and their physical properties, and it might eventually lead to better constraints on the physical models in the future.

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.

Quantitative characterization of discontinuities is fundamental to define the mechanical behavior of discontinuous rock masses. Several techniques for the semi-automatic and automatic extraction of discontinuities and their properties from raw or processed point clouds have been introduced in the literature to overcome the limits of conventional field surveys and improve data accuracy. However, most of these techniques do not allow characterizing flat or subvertical outcrops because planar surfaces are difficult to detect within point clouds in these circumstances, with the drawback of undersampling the data and providing inappropriate results. In this case, 2D analysis on the fracture traces are more appropriate. Nevertheless, to our knowledge, few methods to perform quantitative analyses on discontinuities from orthorectified photos are publicly available and do not provide a complete characterization. We implemented scanline and window sampling methods in a digital environment to characterize rock masses affected by discontinuities perpendicular to the bedding from trace maps, thus exploiting the potentiality of remote sensing techniques for subvertical and low-relief outcrops. The routine, named QDC-2D (Quantitative Discontinuity Characterization, 2D) was compiled in MATLAB by testing a synthetic dataset and a real case study, from which a high-resolution orthophoto was obtained by means of Structure from Motion technique. Starting from a trace map, the routine semi-automatically classifies the discontinuity sets and calculates their mean spacing, frequency, trace length, and persistence. The fracture network is characterized by means of trace length, intensity, and density estimators. The block volume and shape are also estimated by adding information on the third dimension. The results of the 2D analysis agree with the input used to produce the synthetic dataset and with the data collected in the field by means of conventional geostructural and geomechanical techniques, ensuring the procedure’s reliability. The outcomes of the analysis were implemented in a Discrete Fracture Network model to evaluate their applicability for geomechanical modeling.