The Role of Terzaghi Effective Stress in Linearly Elastic Deformation

1983 ◽  
Vol 105 (4) ◽  
pp. 509-511 ◽  
Author(s):  
M. M. Carroll ◽  
N. Katsube
Keyword(s):  
Elastic Deformation ◽  
Effective Stress ◽  
Linear Elasticity ◽  
Simple Form ◽  
Pore Space ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Pore Geometry ◽  
Average Strain

It has been shown that the overall strain of a fluid-filled porous elastic solid is not governed by the Terzaghi effective stress law. We show, in the context of anisotropic linear elasticity, that the overall strain may be resolved into a component which is the average strain of the solid matrix and a component due to change in relative pore geometry, and that the latter is determined by the Terzaghi effective stress. This leads to a simple form of the response laws and, in particular, to effective stress laws for overall strain (obtained previously) and for strain of the pore space.

scholarly journals N<sub>2</sub>O and N<sub>2</sub> losses from simulated injection of biogas digestate depend mainly on soil texture, moisture and temperature

2017 ◽  
Author(s):  
Sebastian Rainer Fiedler ◽  
Jürgen Augustin ◽  
Nicole Wrage-Mönnig ◽  
Gerald Jurasinski ◽  
Bertram Gusovius ◽  
...  
Keyword(s):  
Agricultural Soils ◽  
Pore Space ◽  
Inhibitory Effect ◽  
Application Rate ◽  
Organic Fertiliser ◽  
Potential Capacity ◽  
Clayey Silt ◽  
Biogas Digestate ◽  
Silty Soils

Abstract. Biogas digestate (BD) is increasingly used as organic fertiliser, but has a high potential for NH3 losses. Its proposed injection into soils as a counter-measure has been suggested to promote the generation of N2O, leading to a potential trade-off. Furthermore, the effect on N2 losses after injection of BD into soil has not yet been evaluated. We performed a simulated BD injection experiment in a helium-oxygen atmosphere to examine the influence of soil substrate (loamy sand, clayey silt), water-filled pore space (WFPS; 35, 55, 75 %), temperature (2° C, 15° C) and application rate (0, 160, 320 kg N ha−1) as a proxy for row spacing of injection on the emissions of N2O, N2, and CO2. To determine the potential capacity for these gaseous losses, we incubated under anaerobic conditions by purging with helium for the last 24 h of incubation. N2O and N2 emissions as well as the N2 / (N2O + N2) ratio depended on soil type and increased with WFPS and temperature, indicating a crucial role of soil gas diffusivity for the formation of these gases in agricultural soils. However, the emissions did not increase with the application rate of BD, i.e. a broader spacing of injection slits, probably due to an inhibitory effect of the high NH4+ content of BD. Our results suggest that the risk of N2O and N2 losses even after injection of relatively large amounts of BD seems to be small for dry to wet sandy soils and acceptable when regarding simultaneously reduced NH3 emissions for dry silty soils.

scholarly journals Stabilizing electrodeposition in elastic solid electrolytes containing immobilized anions

2016 ◽  
Vol 2 (7) ◽  
pp. e1600320 ◽  
Author(s):  
Mukul D. Tikekar ◽  
Lynden A. Archer ◽  
Donald L. Koch
Keyword(s):  
Elastic Solid ◽  
Present Theory ◽  
Metal Electrode ◽  
Mitigation Strategies ◽  
Factors Affecting ◽  
Wide Range ◽  
Current Densities ◽  
Morphological Instabilities ◽  
The Stability

Ion transport–driven instabilities in electrodeposition of metals that lead to morphological instabilities and dendrites are receiving renewed attention because mitigation strategies are needed for improving rechargeability and safety of lithium batteries. The growth rate of these morphological instabilities can be slowed by immobilizing a fraction of anions within the electrolyte to reduce the electric field at the metal electrode. We analyze the role of elastic deformation of the solid electrolyte with immobilized anions and present theory combining the roles of separator elasticity and modified transport to evaluate the factors affecting the stability of planar deposition over a wide range of current densities. We find that stable electrodeposition can be easily achieved even at relatively high current densities in electrolytes/separators with moderate polymer-like mechanical moduli, provided a small fraction of anions are immobilized in the separator.

scholarly journals On unsteady flows of pore pressure-activated granular materials

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Anna Abbatiello ◽  
Miroslav Bulíček ◽  
Tomáš Los ◽  
Josef Málek ◽  
Ondřej Souček
Keyword(s):  
Granular Materials ◽  
Plastic Material ◽  
Pore Space ◽  
Nonlinear Partial Differential Equations ◽  
Large Data ◽  
Existence Theory ◽  
Solid Matrix ◽  
Lithostatic Pressure ◽  
Generalized Newtonian Fluid ◽  
Stick Slip

AbstractWe investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

THE INFLUENCE OF COMPOSITION, DIAGENESIS AND COMPACTION ON SEAL CAPACITY IN THE MUDERONG SHALE, CARNARVON BASIN

2004 ◽  
Vol 44 (1) ◽  
pp. 201 ◽  
Author(s):  
G.E. Kovack ◽  
D.N. Dewhurst ◽  
M.D. Raven ◽  
J.G. Kaldi
Keyword(s):  
Effective Stress ◽  
Pore Geometry ◽  
Burial Depth ◽  
Threshold Pressure ◽  
Direct Influence ◽  
Different Depths ◽  
Northern Carnarvon Basin ◽  
Vertical Effective Stress ◽  
Mercury Injection Capillary Pressure ◽  
Carnarvon Basin

The Muderong Shale blankets most of the northern Carnarvon Basin and is the top seal to over 90% of all commercial discoveries. This study examines the influence that vertical effective stress, mineralogy and diagenesis have on regional variations of seal capacity. Throughout the basin, threshold pressures (determined from Mercury Injection Capillary Pressure (MICP) analyses), range from less than 1,000 psi (equivalent to ~100 m gas column) up to 10,000 psi (~1,000 m gas column). Because the Muderong Shale varies in thickness (5 m to >900 m) and burial depth (~0.5–3.5 km), effective stresses and temperatures also vary. Effective stress and temperature significantly control pore geometry at different depths through compaction and diagenesis. The data from this study show that shale grain size has no direct influence over seal threshold pressure except that finer-grained Muderong Shale (36–45% particles 2.5 km) along the Northern Alpha Arch and Rankin Platform, total illite content is only moderate.

scholarly journals Modelling surface NMR spin-echo experiments in a heterogeneous B1 field

2019 ◽  
Vol 219 (2) ◽  
pp. 1395-1404
Author(s):  
Denys Grombacher
Keyword(s):  
Pore Space ◽  
Spin Echo ◽  
Petroleum Industry ◽  
Bloch Equation ◽  
Transverse Magnetization ◽  
Subsurface Water ◽  
Great Promise ◽  
Pore Geometry ◽  
Analytic Expression ◽  
B1 Field

SUMMARY Surface nuclear magnetic resonance (NMR) measurements show great promise for characterization of subsurface water content, pore-sizes and permeability. The link between surface NMR and pore-size/permeability is founded in the connection between the NMR signal's time dependence and the geometry of the pore-space. To strengthen links between the NMR signal and pore-geometry multipulse surface NMR sequences have been developed to estimate the parameter T2, which carries a strong link to pore-geometry and has formed the basis for NMR-based permeability estimation in the petroleum industry for decades. Producing reliable subsurface characterizations from multipulse surface NMR measurements that measure T2 requires that the forward model is able to accurately predict the transverse magnetization at the time when the measurement occurs. Traditional surface NMR T2 forward models employ an analytic expression for the transverse magnetization, an expression developed in the context of laboratory NMR experiments conducted under conditions significantly different from surface NMR and which require several assumptions to simplify the underlying Bloch equation. To investigate the reliability of this analytic expression under surface NMR conditions, a synthetic comparison is performed where the analytic expression is contrasted against the transverse magnetization predicted from a solution of the full-Bloch equation without the same simplifying assumptions and which can appropriately weight heterogeneity in the applied and background magnetic fields. The comparison shows that the analytic expression breaks down in a range of conditions typical to surface NMR measurements.

LINEAR ELASTICITY AND POTENTIAL THEORY: A COMMENT ON GURTIN (1972)

2008 ◽  
Vol 22 (28) ◽  
pp. 5035-5039 ◽  
Author(s):  
FALK H. KOENEMANN
Keyword(s):  
Potential Theory ◽  
Linear Theory ◽  
Elastic Deformation ◽  
Physical Process ◽  
Linear Elasticity ◽  
Short Note ◽  
Theory Of Elasticity ◽  
Divergence Free ◽  
Fundamental Physical

In an exhaustive presentation of the linear theory of elasticity by Gurtin [The Linear Theory of Elasticity (Springer-Verlag, 1972)], the author included a chapter on the relation of the theory of elasticity to the theory of potentials. Potential theory distinguishes two fundamental physical categories: divergence-free and divergence-involving problems. From the criteria given in the source quoted by the author, it is evident that elastic deformation of solids falls into the latter category. It is documented in this short note that the author presented volume-constant elastic deformation as a divergence-free physical process, systematically ignoring all the information that was available to him that this is not so.

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