scholarly journals Roughness of fracture surfaces in numerical models and laboratory experiments

Solid Earth ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 2407-2424
Author(s):  
Steffen Abe ◽  
Hagen Deckert
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Numerical Models ◽  
Stress Conditions ◽  
Roughness Coefficient ◽  
Confining Stress ◽  
Rock Samples ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Hurst Exponents

Abstract. We investigate the influence of stress conditions during fracture formation on the geometry and roughness of fracture surfaces. Rough fracture surfaces have been generated in numerical simulations of triaxial deformation experiments using the discrete element method and in a small number of laboratory experiments on limestone and sandstone samples. Digital surface models of the rock samples fractured in the laboratory experiments were produced using high-resolution photogrammetry. The roughness of the surfaces was analyzed in terms of absolute roughness measures such as an estimated joint roughness coefficient (JRC) and in terms of its scaling properties. The results show that all analyzed surfaces are self-affine but with different Hurst exponents between the numerical models and the real rock samples. Results from numerical simulations using a wide range of stress conditions to generate the fracture surfaces show a weak decrease of the Hurst exponents with increasing confining stress and a larger absolute roughness for transversely isotropic stress conditions compared to true triaxial conditions. Other than that, our results suggest that stress conditions have little influence on the surface roughness of newly formed fractures.

scholarly journals Roughness of Fracture Surfaces in Numerical Models and Laboratory Experiments

2021 ◽  
Author(s):  
Steffen Abe ◽  
Hagen Deckert
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Numerical Models ◽  
Stress Conditions ◽  
Roughness Coefficient ◽  
Confining Stress ◽  
Rock Samples ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Hurst Exponents

Abstract. We investigate the influence of stress conditions during fracture formation on the geometry and roughness of fracture surfaces. Rough fracture surfaces have been generated in numerical simulations of triaxial deformation experiments using the Discrete Element Method and in laboratory experiments on limestone and sandstone samples. Digital surface models of the rock samples fractured in the laboratory experiments were produced using high resolution photogrammetry. The roughness of the surfaces was analyzed in terms of absolute roughness measures such as an estimated joint roughness coefficient (JRC) and in terms of its scaling properties. The results show that all analyzed surfaces are self-affine, but with different Hurst exponents between the numerical models and the real rock samples. Results from numerical simulations using a wide range of stress conditions to generate the fracture surfaces show a weak decrease of the Hurst exponents with increasing confining stress and a larger absolute roughness for transversely isotropic stress conditions compared to true triaxial conditions. Other than that, our results suggest that stress conditions have little influence on the surface roughness of newly formed fractures.

scholarly journals Combined numerical and experimental study of microstructure and permeability in porous granular media

2020 ◽  
Author(s):  
Philipp Eichheimer ◽  
Marcel Thielmann ◽  
Wakana Fujita ◽  
Gregor J. Golabek ◽  
Michihiko Nakamura ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Granular Media ◽  
Large Scale ◽  
Earth Science ◽  
Numerical Models ◽  
Effective Porosity ◽  
Flow Properties ◽  
Wide Range ◽  
Flow Through

Abstract. Fluid flow on different scales is of interest for several Earth science disciplines like petrophysics, hydrogeology and volcanology. To parameterize fluid flow in large-scale numerical simulations (e.g. groundwater and volcanic systems), flow properties on the microscale need to be considered. For this purpose experimental and numerical investigations of flow through porous media over a wide range of porosities are necessary. In the present study we sinter glass bead media with various porosities. The microstructure, namely effective porosity and effective specific surface, is investigated using image processing. We determine flow properties like hydraulic tortuosity and permeability using both experimental measurements and numerical simulations. By fitting microstructural and flow properties to porosity, we obtain a modified Kozeny-Carman equation for isotropic low-porosity media, that can be used to simulate permeability in large-scale numerical models. To verify the modified Kozeny-Carman equation we compare it to the computed and measured permeability values.

scholarly journals Manning's roughness coefficient determination in laboratory experiments using 2D modeling and automatic calibration

2020 ◽  
pp. 22-33
Author(s):  
Basile Lavoie ◽  
Tew-Fik Mahdi
Keyword(s):  
Experimental Data ◽  
Laboratory Experiments ◽  
Numerical Models ◽  
Roughness Coefficient ◽  
Automatic Calibration ◽  
Test Cases ◽  
Data Sets ◽  
Step Method ◽  
Numerous Data

Reliable experimental data are essential for choosing and validating numerical models. Although numerous data sets have been presented in the literature, few have been made widely available to the scientific community. Additionally, these experimental data sets have generally given little attention to the determination of Manning's roughness coefficients. This paper addresses these two issues. Three channel configurations are studied: a flatbed channel, a channel with a triangular sill and a channel with a triangular abutment. Three increasing permanent discharges are used for each configuration, leading to nine test cases. The Manning's coefficients are determined using three methods: the traditional step method, automatic calibration, via a 2D hydrodynamic model, considering theoretical value intervals and automatic calibration ignoring these intervals. The results show that automatic calibration with theoretical value intervals is advantageous compared to the step method. Automatic calibration ignoring theoretical intervals yields low errors but unphysical values; therefore, it is not recommended.

Roughness of fracture surfaces in Discrete Element Model triaxial deformation experiments

2020 ◽  
Author(s):  
Steffen Abe ◽  
Hagen Deckert
Keyword(s):  
Standard Deviation ◽  
Power Law ◽  
Hurst Exponent ◽  
Numerical Experiments ◽  
Discrete Element ◽  
Height Distribution ◽  
Confining Stress ◽  
Triaxial Deformation ◽  
Fracture Surfaces ◽  
Hurst Exponents

<p>The roughness of fracture surfaces is important for a range of geological processes such as the mechanical behaviour of faults or the fluid flow in jointed rocks or fault zones. However, the processes and parameters controlling the details of the fracture roughness are not fully understood yet. We therefore use numerical simulations based on the Discrete Element Method (DEM) to study the formation of fractures in triaxial deformation experiments under a wide range of stress conditions and to quantify the geometric properties of the resulting fracture surfaces. In the numerical experiments a DEM-model of a box-shaped rock sample is subjected to a displacement controlled load along its x-axis while a defined confining stress is applied to the other surfaces.</p><p>Based on the data from 131 numerical simulations the roughness of 388 fracture surfaces has been analysed. For this purpose the surface point clouds extracted from the Discrete Element models have been converted to height fields relative to a "best-fit" plane and the height distributions quantified. The results show that the heights are normally distributed. We observe no dependence on the confining stress except that models with equal confining stress in y- and z-direction show a higher standard deviation of the height distribution than those with differing y- and z-confinement. An analysis of the height-height correlation functions for those surfaces shows that they follow a power-law, demonstrating that the surfaces are self-affine. The Hurst exponent H describing the scaling of the roughness can be derived from the power-law relation. Values obtained are in the range H=0.2-0.6 for the full suite of experiments, while the mean of the Hurst exponents for each group of fracture surfaces generated under the same stress conditions is H=0.3-0.45. A weak decreasing trend of the Hurst exponent with increasing confining stress can be observed, but contrary to the standard deviation of the height distribution there is no dependence on the ratio of the confining stresses. There is also no difference between fractures generated in tensile (mode 1) or compressive conditions (mode 2).</p><p>Additionally, surfaces of rock samples fractured in triaxial tests in the laboratory have been analysed using the same methods. The surfaces show similar self-affine characteristics as those in the numerical experiments, although with significantly higher Hurst exponents H=0.6-0.8.</p><p>A comparison between our numerical models and laboratory experiments and data obtained from literature shows that natural and lab-created fracture surfaces and their numerically modelled counterparts are similar regarding the normally distributed heights and the self-affine scale, but the Hurst exponents do not match exactly. While the majority of field and experimental studies find significantly higher Hurst exponents of about 0.8, there are some studies, for example on Sandstone, which find H=0.4-0.5, falling into the range observed in our numerical experiments.</p>

scholarly journals Combined numerical and experimental study of microstructure and permeability in porous granular media

2020 ◽  
Author(s):  
Philipp Eichheimer ◽  
Marcel Thielmann ◽  
Wakana Fujita ◽  
Gregor J. Golabek ◽  
Michihiko Nakamura ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Granular Media ◽  
Large Scale ◽  
Earth Science ◽  
Numerical Models ◽  
Effective Porosity ◽  
Flow Properties ◽  
Wide Range ◽  
Flow Through

<div> <div> <div> <p>Fluid flow on different scales is of interest for several Earth science disciplines like petrophysics, hydrogeology and volcanology. To parameterize fluid flow in large-scale numerical simulations (e.g. groundwater and volcanic systems), flow properties on the microscale need to be considered. For this purpose experimental and numerical investigations of flow through porous media over a wide range of porosities are necessary. In the present study we sinter glass bead media with various porosities, representing shallow depth crustal sediments. The microstructure, namely effective porosity and effective specific surface, is investigated using image processing. We furthermore determine flow properties like hydraulic tortuosity and permeability using both experimental measurements and numerical simulations. By fitting microstructural and flow properties to porosity, we obtain a modified Kozeny-Carman equation for isotropic low-porosity media, that can be used to simulate permeability in large-scale numerical models. To verify the modified Kozeny-Carman equation we compare it to the numerically computed and experimentally measured permeability values.</p> </div> </div> </div>

Laboratory observations of frictional stability and fault zone evolution under heterogeneous friction, rheology, and stress conditions

2020 ◽  
Author(s):  
Chun-Yu Ke ◽  
Sara Beth Leach Cebry ◽  
Srisharan Shreedharan ◽  
Chris Marone ◽  
David S. Kammer ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Laboratory Experiments ◽  
Patch Size ◽  
Numerical Models ◽  
Seismic Stability ◽  
Heterogeneous Environment ◽  
Normal Stresses ◽  
State Dependent ◽  
Earthquake Ruptures ◽  
Fault Gouges

<p>Natural faults experience a variety of frictional, rheological, and stress heterogeneities. To investigate the effects of these heterogeneities on seismic stability and the mode of fault slip behavior, laboratory experiments were conducted using a biaxial shearing apparatus with a 0.76 m by 0.076 m simulated fault where 2.5 to 5 mm thick gouge layers were sheared at applied normal stresses of 7 to 12 MPa for 25 mm of cumulative slip. Laboratory faults consisted of uniform layers of gouge, homogeneous mixtures, and/or heterogeneous patches of talc, quartz, and gypsum minerals. Experiments with a uniform layer of velocity weakening fault gouge revealed the development of two asperities at the highly stressed ends of the fault that could fail independently, and creep fronts that facilitated interaction between asperities. This behavior was also reproduced with simple numerical simulations that employ rate- and state-dependent friction. In other experiments, the fault consisted of patches of alternating velocity strengthening and velocity weakening fault gouges. Patch size and location were varied to understand how earthquake ruptures accelerate or decelerate in this heterogeneous environment. These experiments revealed that a velocity weakening fault patch was more likely to remain stable if located next to a velocity strengthening fault patch. However, stability was dependent on the patch sizes and location relative to where the load is applied. In certain cases, some sections of the fault slipped unstably while others slid stably. These experiments, and matching numerical models, highlight the complexity that can arise on natural faults due to frictional, rheological, and stress heterogeneities.</p>

scholarly journals Two-Dimensional Numerical Modeling of Flow in Physical Models of Rock Vane and Bendway Weir Configurations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 458
Author(s):  
Drew C. Baird ◽  
Benjamin Abban ◽  
S. Michael Scurlock ◽  
Steven B. Abt ◽  
Christopher I. Thornton
Keyword(s):  
Numerical Modeling ◽  
Physical Model ◽  
Numerical Models ◽  
Hydraulic Performance ◽  
Physical Models ◽  
Protection Measures ◽  
Design Engineers ◽  
Model Study ◽  
Study Results ◽  
Wide Range

While there are a wide range of design recommendations for using rock vanes and bendway weirs as streambank protection measures, no comprehensive, standard approach is currently available for design engineers to evaluate their hydraulic performance before construction. This study investigates using 2D numerical modeling as an option for predicting the hydraulic performance of rock vane and bendway weir structure designs for streambank protection. We used the Sedimentation and River Hydraulics (SRH)-2D depth-averaged numerical model to simulate flows around rock vane and bendway weir installations that were previously examined as part of a physical model study and that had water surface elevation and velocity observations. Overall, SRH-2D predicted the same general flow patterns as the physical model, but over- and underpredicted the flow velocity in some areas. These over- and underpredictions could be primarily attributed to the assumption of negligible vertical velocities. Nonetheless, the point differences between the predicted and observed velocities generally ranged from 15 to 25%, with some exceptions. The results showed that 2D numerical models could provide adequate insight into the hydraulic performance of rock vanes and bendway weirs. Accordingly, design guidance and implications of the study results are presented for design engineers.

scholarly journals Preliminary Results on the Dynamics of a Pile-Moored Fish Cage with Elastic Net in Currents and Waves

2020 ◽  
Vol 9 (1) ◽  
pp. 14
Author(s):  
Gianluca Zitti ◽  
Nico Novelli ◽  
Maurizio Brocchini
Keyword(s):  
Numerical Model ◽  
Laboratory Experiments ◽  
Numerical Models ◽  
Offshore Structures ◽  
Fish Farm ◽  
Maximum Displacement ◽  
Drag Forces ◽  
Real Size ◽  
Lift And Drag ◽  
Mesh Grid

Over the last decades, the aquaculture sector increased significantly and constantly, moving fish-farm plants further from the coast, and exposing them to increasingly high forces due to currents and waves. The performances of cages in currents and waves have been widely studied in literature, by means of laboratory experiments and numerical models, but virtually all the research is focused on the global performances of the system, i.e., on the maximum displacement, the volume reduction or the mooring tension. In this work we propose a numerical model, derived from the net-truss model of Kristiansen and Faltinsen (2012), to study the dynamics of fish farm cages in current and waves. In this model the net is modeled with straight trusses connecting nodes, where the mass of the net is concentrated at the nodes. The deformation of the net is evaluated solving the equation of motion of the nodes, subjected to gravity, buoyancy, lift, and drag forces. With respect to the original model, the elasticity of the net is included. In this work the real size of the net is used for the computation mesh grid, this allowing the numerical model to reproduce the exact dynamics of the cage. The numerical model is used to simulate a cage with fixed rings, based on the concept of mooring the cage to the foundation of no longer functioning offshore structures. The deformations of the system subjected to currents and waves are studied.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

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