arXiv subjects

Roberto J. Cier

Publications and source records attributed to Roberto J. Cier.

5 recordsLinked to original sources

arXiv2022

A high-fidelity seismic intensity measure to assess dynamic liquefaction in tailings

Deformation analyses of tailings dams under dynamic conditions require using earthquake records as input loading. Moreover, these records must represent the local seismicity, expressed by ground motion power indicators denominated intensity measures (IM). The ability and accuracy to describe the characteristics of a seismic record play a fundamental role in earthquake engineering and damage assessment of geotechnical facilities. None of the existing IMs represents a robust enough predictor of a given seismic demand (e.g., residual displacements). Different signals may generate a wide spectrum of results, with diverse effects that could produce insignificant damage to global failure depending on the structure. Usual engineering procedures select a huge number of records to overcome this limitation and develop a large set of numerical simulations to bound the uncertainty of the results, which becomes a time-consuming approach. This paper presents a new high-fidelity seismic IM to perform more accurate ground motion {selection}, which captures the spectral properties of the record for the frequency content that the dam does not filter. This IM represents a way to estimate beforehand a seismic demand, expressed, for instance, in terms of displacements. The proposed IM is applied to a finite element model for an upstream tailings dam cross-section, using a constitutive model capable of capturing dynamic liquefaction. The obtained results show that our proposal gives highly reliable correlations with different selected demands. Comparisons with classical IMs are also discussed, showing that our proposal emerges as a practical solution to a large dated discussion within our community.

physics.geo-ph↗

arXiv2022

Compaction band localization in geomaterials: a mechanically consistent failure criterion

Compaction bands play a key role in the deformation processes of porous rocks and explain different aspects of physical processes in geological formations. The state-of-the-art description of the localized strains that lead to compaction banding has limitations from the mechanical point of view. Thus, we describe the phenomenon using a consistent axiomatic formulation. We build a viscoplastic model using minimal assumptions; we base our model on six principles to study compaction band localization triggered by viscous effects. We analyze different stress states to determine the conditions that trigger compaction bands. Laboratory experiments show that a material undergoes different localizations depending on the confinement pressure; thus, we perform a series of numerical experiments that reproduce these phenomena under varying triaxial compression conditions. These simulations use a simple viscoplastic constitutive model for creep based on Perzyna's viscoplasticity and show how confinement changes the localization type for different triaxial tests. Our analysis allows us to describe this transition, band periodicity and spacing, and their dependence on the material parameters.

physics.geo-ph↗

arXiv2020

An automatic-adaptivity stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems

In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and anisotropic diffusivities, as well as advection-dominated diffusion problems. The general stabilized finite element framework was described and analyzed in arXiv:1907.12605v3 for linear problems in general, and tested for pure advection problems. The method seeks for the discrete solution through a residual minimization process on a proper stable discontinuous Galerkin (dG) dual norm. This technique leads to a saddle-point problem that delivers a stable discrete solution and a robust error estimate that can drive mesh adaptivity. In this work, we demonstrate the efficiency of the method in extreme scenarios, delivering stable solutions. The quality and performance of the solutions are comparable to classical discontinuous Galerkin formulations in the respective discrete space norm on each mesh. Meanwhile, this technique allows us to solve on coarse meshes and adapt the solution to achieve a user-specified solution quality.

math.NA↗

arXiv2020

A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This method combines a nonlinear penalty formulation with a discontinuous Galerkin-based residual minimization method. We illustrate the efficiency of this scheme for both uniform and adaptive meshes through proper numerical examples.

math.NA↗

arXiv2020

Adaptive stabilized finite elements: Continuation analysis of compaction banding in geomaterials

Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the capability of the material to diffuse internal perturbations and lead to localized failure features (e.g., cracks and compaction bands). This type of solution, generally found in fluids, has strong nonlinearities and periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, effective numerical tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This method provides a residual representation to drive adaptive mesh refinement, a particularly useful feature for the problem at hand. We compare against analytical and standard finite element solutions to demonstrate the performance of our approach. We then investigate the sensitivity of the diffusivity ratio, main parameter of the problem, and identify multiple possible solutions, with multiple stress peaks. Finally, we show the evolution of the spacing between peaks for all solutions as a function of that parameter.

physics.comp-ph↗