scholarly journals A Formal Homogenization Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil

2020 ◽  
pp. 26-45
Author(s):  
Adu Sakyi ◽  
Peter Amoako-Yirenkyi ◽  
Isaac Kwame Dontwi
Keyword(s):  
Particle Concentration ◽  
Seepage Flow ◽  
Soil Mass ◽  
Cylindrical Structures ◽  
Proposed Model ◽  
Effective Coefficients ◽  
Heterogeneous Soil ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Piping Erosion

We model and simulate piping erosion phenomena with deposition in a spatially heterogeneous soil mass motivated by seepage flow. The soil is considered to be a porous media with periodic positioning of pores spread around cylindrical structures or microstructures making the heterogeneities periodic in space.The period of the heterogeneities defines a microscopic length scale ϵ of the microscopic problem and this allows the use of periodic homogenization methods.We studied the asymptotic behaviour of the solutions to the micro problem as ϵ ! 0 and obtained a homogenized model or macro problem with explicit formula for effective coefficients. Numerical simulations of the proposed model captures the expected behaviour of soil particle concentration and deposition as observed in piping flow erosion phenomena.

scholarly journals A Rigorous Homogenization for a Two-Scale Convergence Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil

2020 ◽  
pp. 9-25
Author(s):  
Adu Sakyi ◽  
Peter Amoako-Yirenkyi ◽  
Isaac Kwame Dontwi
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Behaviour ◽  
Particle Deposition ◽  
Particle Concentration ◽  
Soil Particle ◽  
Length Scale ◽  
Soil Mixture ◽  
Heterogeneous Soil ◽  
Homogenization Approach ◽  
Homogenized Model

We present a rigorous homogenization approach to modelling piping ow erosion in a spatially heterogeneous soil. The aim is to provide a justication to a formal homogenization approach to piping ow erosion with deposition in a spatially heterogeneous soil. Under the assumption that the soil domain is perforated periodically with cylindrical repeating microstructure, we begin by proving that a solution to the proposed set of microscopic equations exist. Two-scale convergence is then used to study the asymptotic behaviour of solutions to the microscopic problem as the microscopic length scale approaches zero(0). We thus derive rigorously a homogenized model or macro problem as well as explicit formula for the eective coecients. A strong observation from the numerical simulation was that, soil particle concentration in the water/soil mixture decreases but at a decreasing rate whereas soil particle deposition increases at regions with increasing amount of particle concentration in the ow causing a reduction in bare pore spaces across the soil domain.

Convergence–confinement analysis of a bolt-supported tunnel using the homogenization method

2006 ◽  
Vol 43 (5) ◽  
pp. 462-483 ◽  
Author(s):  
Henry Wong ◽  
Didier Subrin ◽  
Daniel Dias
Keyword(s):  
Input Parameter ◽  
Uniaxial Stress ◽  
Homogenization Method ◽  
External Input ◽  
Proposed Model ◽  
Homogenization Approach ◽  
Parametric Studies ◽  
Perfect Bonding ◽  
The Moment ◽  
Grouted Bolts

The behaviour of tunnels reinforced with radially disposed fully grouted bolts is investigated in this paper. Perfect bonding and ideal diffusion of bolt tension are assumed, so that the bolt tension can be assimilated to an equivalent uniaxial stress tensor. An analytical model of the convergence–confinement type is proposed that accounts for the delayed action of bolts due to ground decompression prior to bolt installation. This factor leads to nonsimultaneous yielding, and more generally, a different stress history for each constituent, requiring special treatments in the incremental elastoplasticity calculations. Nonetheless, the resulting model remains sufficiently simple, and an analytical solution is still accessible. Charts are provided to allow for parametric studies and quick preliminary designs. Comparisons with 3D numerical calculations show that the model gives precise results if the correct convergence at the moment of bolt installation is used as an "external" input parameter, validating the homogenization approach. An approximate methodology based on previous works is proposed to determine this parameter to render the proposed model "self-sufficient." Its predictions are again compared to 3D numerical computations, and the results are found to be sufficiently accurate for practical applications.Key words: reinforcement, anisotropy, analytical, lining, yield, elastoplasticity.

Simulation-based verification of homogenization approach in predicting effective thermal conductivities of wavy orthotropic fiber composite

2019 ◽  
Vol 08 (04) ◽  
pp. 1950015
Author(s):  
C. Mahesh ◽  
K. Govindarajulu ◽  
V. Balakrishna Murthy
Keyword(s):  
Volume Fraction ◽  
Fiber Composite ◽  
Micromechanical Model ◽  
Two Stage ◽  
Micromechanics Models ◽  
Simulation Based ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Good Agreement ◽  
Thermal Conductivities

In this work, applicability of homogenization approach is verified with the micromechanics approach by considering wavy orthotropic fiber composite. Thermal conductivities of [Formula: see text]-300 orthotropic wavy fiber composite are determined for micromechanical model and compared with the results obtained by two stage homogenized model over volume fraction ranging from 0.1 to 0.6. Also, a methodology is suggested for reducing percentage deviation between homogenization and micromechanical approaches. Effect of debond on the thermal conductivities of wavy orthotrophic fiber composite is studied and compared with perfectly aligned fiber composite for different volume fraction. It is observed that results obtained by the homogenization approach are in good agreement with the results obtained through micromechanics approach. Maximum percentage deviation between homogenized and micromechanics models is 2.13%.

A Novel Water-Injectivity Model and Experimental Validation With CT-Scanned Corefloods

SPE Journal ◽  
2015 ◽  
Vol 20 (06) ◽  
pp. 1200-1211 ◽  
Author(s):  
Ramesh Chandra Yerramilli ◽  
P.L.J.. L.J. Zitha ◽  
Sanjay Surya Yerramilli ◽  
Pavel Bedrikovetsky
Keyword(s):  
Ct Scan ◽  
Oil Recovery ◽  
Particle Concentration ◽  
Produced Water ◽  
Optical Microscope ◽  
Transition Time ◽  
Surface Deposition ◽  
The Core ◽  
Proposed Model ◽  
Particle Retention

Summary Injectivity decline is an issue during produced-water reinjection (PWRI) for water disposal in aquifers, waterflooding, chemical enhanced oil recovery, and geothermal-energy exploitation. A novel model for injectivity decline under flow conditions reminiscent of PWRI was developed taking into account deep-bed filtration and buildup of external filter cake. A distinct feature of the model is that it describes particle-retention kinetics responsible for internal filtration by an exponential decaying function of the retained-particle concentration. The corresponding nonlinear governing partial-differential equations were solved numerically and coupled with a known analytical model for external filtration with the concept of transition time. Coreflood experiments consisting of the injection of brine containing suspended hematite particles (volume fractions in the range of 2 to 6 ppm) were also performed. Computed-tomography (CT) scans of the core were taken to obtain deposition profiles along the core at different times. In addition, effect of various parameters (particle concentration and number of grids) on injectivity was investigated. From CT-scan and optical-microscope analyses, it was found that surface deposition in the porous medium and face plugging at the injection face of the core were responsible for decline in injectivity. The transition time from pure internal to external filtration was accurately determined from the CT-scan and pressure data. The newly proposed model and experiments were found to be in excellent agreement, indicating that the adopted retention function is a good heuristic description of particle retention.

scholarly journals Apprehending the effects of mechanical deformations in cardiac electrophysiology: A homogenization approach

2019 ◽  
Vol 29 (13) ◽  
pp. 2377-2417
Author(s):  
Annabelle Collin ◽  
Sébastien Imperiale ◽  
Philippe Moireau ◽  
Jean-Frédéric Gerbeau ◽  
Dominique Chapelle
Keyword(s):  
Cardiac Electrophysiology ◽  
Microscopic Level ◽  
Numerical Results ◽  
Specific Cell ◽  
Periodic Media ◽  
Cell Problem ◽  
Mechanical Deformations ◽  
Ionic Motion ◽  
Homogenization Approach ◽  
Homogenized Model

We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure — and associated with a specific cell problem to be solved to obtain the macroscopic conductivity tensors — in which mechanical deformations play a nontrivial role, i.e. they do not simply lead to a standard bidomain problem posed in the deformed configuration. We then present detailed numerical illustrations of the homogenized model with coupled cardiac electrical–mechanical simulations — all the way to ECG simulations — albeit without taking into account the abundantly-investigated effect of mechanical deformations in ionic models, in order to focus here on other effects. And in fact our numerical results indicate that these other effects are numerically of a comparable order, and therefore cannot be disregarded.

scholarly journals On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

2021 ◽  
Vol 39 (5) ◽  
pp. 1430-1442
Author(s):  
Roman Kulchytsky-Zhyhailo ◽  
Stanisław J. Matysiak ◽  
Dariusz M. Perkowski
Keyword(s):  
Axial Stress ◽  
Layered Composite ◽  
Functionally Graded ◽  
Thermoelastic Problem ◽  
Graded Materials ◽  
Varying Thickness ◽  
Representative Cell ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Pipe Materials

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

scholarly journals Investigation of the Models of Flow through Fractured Rock Masses Based on Borehole Data

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Long Tan ◽  
Wei Xiang ◽  
Jin Luo ◽  
Qingbing Liu ◽  
Xu Zuo
Keyword(s):  
Permeability Coefficient ◽  
Flow Model ◽  
Fractured Rock ◽  
Confining Pressure ◽  
Seepage Flow ◽  
Rock Masses ◽  
Borehole Data ◽  
Proposed Model ◽  
Flow Through ◽  
Fractured Rock Masses

When only limited borehole data are available, making optimum use of the existing data is crucial for performing a preliminary assessment of the investigated site. In this paper, the relationships between the borehole data and the permeability coefficient were first analyzed. These relationships were then used to establish a model for estimating the permeability coefficient of rock mass that takes into account the influence from the confining pressure on the seepage flow. The proposed model can reduce the number of hydraulic tests which are time consuming and very costly and allow the determination of change in the permeability coefficient throughout the borehole. The flow model could assist in providing important references for selecting an appropriate permeability coefficient in hydrogeological simulation and in evaluating the condition of large cracks developed in boreholes. In general, the seepage flow model developed in this study will contribute to the design practice of a tunnel project constructed in fractured rock masses.

scholarly journals Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach

2019 ◽  
Vol 24 (11) ◽  
pp. 3554-3574 ◽  
Author(s):  
Ariel Ramírez-Torres ◽  
Raimondo Penta ◽  
Reinaldo Rodríguez-Ramos ◽  
Alfio Grillo
Keyword(s):  
Composite Structures ◽  
Effective Properties ◽  
Elastic Solid ◽  
Asymptotic Homogenization ◽  
Linear Elastic ◽  
Homogenization Technique ◽  
Effective Coefficients ◽  
Out Of Plane ◽  
Mineralized Tissues ◽  
Homogenization Approach

The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. During the past decades, the multiscale asymptotic homogenization technique has shown its potential in the description of such composites by taking advantage of their characteristics at the smaller scales, ciphered in the so-called effective coefficients. Here, we extend previous works by studying the in-plane and out-of-plane effective properties of hierarchical linear elastic solid composites via a three-scale asymptotic homogenization technique. In particular, the approach is adjusted for a multiscale composite with a square-symmetric arrangement of uniaxially aligned cylindrical fibers, and the formulae for computing its effective properties are provided. Finally, we show the potential of the proposed asymptotic homogenization procedure by modeling the effective properties of musculoskeletal mineralized tissues, and we compare the results with theoretical and experimental data for bone and tendon tissues.

scholarly journals Investigation of Multi-Frequency SAR Data to Retrieve the Soil Moisture within a Drip Irrigation Context Using Modified Water Cloud Model

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 580
Author(s):  
Emna Ayari ◽  
Zeineb Kassouk ◽  
Zohra Lili-Chabaane ◽  
Nicolas Baghdadi ◽  
Mehrez Zribi
Keyword(s):  
Soil Moisture ◽  
Drip Irrigation ◽  
Cloud Model ◽  
Bare Soil ◽  
Vegetation Fraction ◽  
Proposed Model ◽  
Heterogeneous Soil ◽  
Water Cloud ◽  
Sar Data ◽  
Underlying Soil

The objective of this paper was to estimate soil moisture in pepper crops with drip irrigation in a semi-arid area in the center of Tunisia using synthetic aperture radar (SAR) data. Within this context, the sensitivity of L-band (ALOS-2) in horizontal-horizontal (HH) and horizontal-vertical (HV) polarizations and C-band (Sentinel-1) data in vertical-vertical (VV) and vertical-horizontal (VH) polarizations is examined as a function of soil moisture and vegetation properties using statistical correlations. SAR signals scattered by pepper-covered fields are simulated with a modified version of the water cloud model using L-HH and C-VV data. In spatially heterogeneous soil moisture cases, the total backscattering is the sum of the bare soil contribution weighted by the proportion of bare soil (one-cover fraction) and the vegetation fraction cover contribution. The vegetation fraction contribution is calculated as the volume scattering contribution of the vegetation and underlying soil components attenuated by the vegetation cover. The underlying soil is divided into irrigated and non-irrigated parts owing to the presence of drip irrigation, thus generating different levels of moisture underneath vegetation. Based on signal sensitivity results, the potential of L-HH data to retrieve soil moisture is demonstrated. L-HV data exhibit a higher potential to retrieve vegetation properties regarding a lower potential for soil moisture estimation. After calibration and validation of the proposed model, various simulations are performed to assess the model behavior patterns under different conditions of soil moisture and pepper biophysical properties. The results highlight the potential of the proposed model to simulate a radar signal over heterogeneous soil moisture fields using L-HH and C-VV data.

Sign in / Sign up

Export Citation Format

Share Document