PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

Schaa, Ralf; Gross, Lutz; Plessis, J. P. Du

doi:10.1088/1742-2132/13/2/s59

Cited by 40 publications

(26 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Material properties are updated according to the damage before the next loading step is applied. This iterative process has been implemented using esys‐escript for solving partial differential equations in python using the FEM . In this section, we describe this procedure in more details.…”

Section: Methodsmentioning

confidence: 99%

“…This was our method of choice as it provides higher geometrical flexibility and allowed for a better representation of the disk-shaped flaw and consequently for an easy variation of flaw geometry such as flaw depth, angle, and length through locally adapted meshes. For the implementation of the damage model, we used the python-based FEM software esys-escript 25,26 where for fine meshes we have deployed its parallelized version. 27 In recent works, other researchers have included plasticity and anisotropy in their models of rock failure.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Mondal

Olsen-Kettle

Gross

2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Summary Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3‐D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk‐shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti‐wing cracks, and far‐field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Mondal

Olsen-Kettle

Gross

2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…The macro-scale solution procedure has been implemented in the finite element code ESyS-Escript [32]; details on the solution algorithm are provided in Sect. 3.3.…”

Section: Dynamic Relaxationmentioning

confidence: 99%

“…, with the corresponding number of integration points as n i p = [4,8,32,128], respectively. The specimen first undergoes isotropic compression, followed by biaxial compression, as described in Sect.…”

Section: Mesh Convergence Studymentioning

confidence: 99%

Multi-scale modelling of granular materials: numerical framework and study on micro-structural features

2018

View full text Add to dashboard Cite

A multi-scale model for the analysis of granular systems is proposed, which combines the principles of a coupled FEM-DEM approach with a novel servo-control methodology for the implementation of appropriate micro-scale boundary conditions. A mesh convergence study is performed, whereby the results of a quasi-static biaxial compression test are compared with those obtained by direct numerical simulations. The comparison demonstrates the capability of the multi-scale method to realistically capture the macro-scale response, even for macroscopic domains characterized by a relatively coarse mesh; this makes it possible to accurately analyse large-scale granular systems in a computationally efficient manner. The multi-scale framework is applied to study in a systematic manner the role of individual micro-structural characteristics on the effective macro-scale response. The effect of particle contact friction, particle rotation, and initial fabric anisotropy on the overall response is considered, as measured in terms of the evolution of the effective stress, the volumetric deformation, the average coordination number and the induced anisotropy. The trends observed are in accordance with notions from physics, and observations from experiments and other DEM simulations presented in the literature. Hence, it is concluded that the present framework provides an adequate tool for exploring the effect of micro-structural characteristics on the macroscopic response of large-scale granular structures.

show abstract

“…This was our method of choice as it provides higher geometrical flexibility and allowed for a better representation of the disk-shaped flaw and consequently for an easy variation of flaw geometry such as flaw depth, angle and length through locally adapted meshes. For the implementation of the damage model we used the python-based FEM software esys-escript [157,158] where for fine meshes we have deployed its parallelized version [159].…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of damage evolution and fracture propagation in brittle materials

Mondal¹

View full text Add to dashboard Cite

The understanding of damage evolution and fracture propagation in rocks as a brittle material is important for many industrial applications; for instance to investigate mine safety, to analyze material failure in manufacturing and construction and to understand the behaviour of pre-existing fractures on hydraulic fracturing in oil and gas extractions. Currently, numerical studies for fracture propagation in brittle rock specimens with pre-existing fractures show strong mesh dependence. To address the issue of mesh independence, further numerical investigation and improvement of damage models under a fully 3-D assumption is critical.In this thesis, we develop numerical tools to investigate the effect of model parameters, including the heterogeneity of rock by allowing Young's modulus to vary spatially, and of the geometry of a pre-existing fracture on the stress-strain response and damage evolution in rocks. The fracture propagation model uses continuum damage mechanics where the elastic modulus reduces with damage as the rock is weakened through the formation of fractures. Two failure conditions are presented, a micromechanical model [1,2] using the unified strength theory [3,4] and a strain-based form of a modified von-Mises condition [5]. Various damage evolution laws are considered which can simulate a range of behaviour from brittle to quasi-brittle. Four different damage evolution laws are analyzed for a 3-D rectangular single flaw specimen to deliver the most realistic results. The quasi-static equilibrium equation is solved for various cases of brittle failure and damage evolution for specimens under loading using the Finite Element Method (FEM) with tetrahedron elements on unstructured meshes. In contrast to previous implementations based on rectangular grids, the use of unstructured meshes provides higher geometrical flexibility and allows a more accurate way of including geological features, such as flaws, through locally adapted (FEM) meshes.An important factor affecting the mechanical behaviour during the failure process is the heterogeneity of the rock. Heterogeneity is simulated by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values are then interpolated to the computational (unstructured FEM) mesh. This approach introduces an additional length scale for rock heterogeneity represented by the cell size in the sampling grid that is independent of FEM mesh size. This approach is different from previous implementations of rock heterogeneity [6][7][8] where the length scale is determined by the mesh resolution.A well-known problem which arises in "local" damage models is that they suffer from mesh dependency [2] and strain localization [9]. In this work, we apply the non-local implicit gradient damage formulation of Peerlings et al.[5] to address the issue of mesh dependency. The basic concept of the non-local implicit gradient model is that the strain at a given point depends not only on the strain at that point but also on the nearby strain field. The lo...

show abstract

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

Cited by 40 publications

References 41 publications

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Multi-scale modelling of granular materials: numerical framework and study on micro-structural features

Numerical modelling of damage evolution and fracture propagation in brittle materials

Contact Info

Product

Resources

About