Crack problems in a poroelastic medium: an asymptotic approach

1994 ◽  
Vol 346 (1680) ◽  
pp. 387-428 ◽  
Keyword(s):  
Stress Intensity ◽  
Pressure Gradient ◽  
Pore Pressure ◽  
Asymptotic Method ◽  
Reciprocal Theorem ◽  
Fracture Plane ◽  
Intensity Factors ◽  
Wide Range ◽  
Crack Problems ◽  
Pore Pressure Gradient

We consider problems involving semi-infinite cracks in a porous elastic material. The cracks are loaded with a time dependent internal stress, or pore pressure. Either mixed or unmixed pore pressure boundary conditions on the fracture plane are considered. An asymptotic procedure that partly uncouples the elastic and fluid responses is used, allowing an asymptotic expression for the stress intensity factors as time progresses to be obtained. The method allows the physical processes involved at the crack tip and their interactions to be studied. This is an advance on previous methods where results were obtained in Laplace transform space and inverted numerically to obtain real-time solutions. The crack problems are formulated using distributions of dislocations (and pore pressure gradient discontinuities when necessary) to generate integral equations of the Wiener—Hopf type. The resulting functional equations are, of course, identical to those considered by C. Atkinson and R. V. Craster, but with the alternative formulation we develop an asymptotic procedure which should be applicable to other problems (e.g. finite length cracks). This asymptotic procedure can be used to derive asymptotic expansions for more complicated loadings when the numerical effort involved in evaluating results would be excessive. A large-time asymptotic method is also briefly described which complements the small-time method. The operators for poroelastic crack problems are inverted for a particular loading; the reciprocal theorem for poroelasticity is used together with eigensolutions of the fundamental problems to deduce the stress (or where necessary the pore pressure gradient) intensity factors for any loading. These formulae extend previous results allowing a wide range of different loadings to be considered. As an example, the stress intensity factor for a point loaded crack is derived and the asymptotic method is applied to this problem to derive a simple asymptotic formula. Finally, an invariant integral, which is a generalization of the Eshelby energy-momentum tensor, is used to derive integral identities which serve as a check on the intensity factors in some situations.

Possible Reason of the Dependence of an Apparent Permeability on the Pressure Gradient at low Flow Rates in Laboratory Study

2021 ◽  
Author(s):  
Nikolay Baryshnikov ◽  
Evgeniy Zenchenko ◽  
Sergey Turuntaev
Keyword(s):  
Pressure Gradient ◽  
Pore Pressure ◽  
Pore Space ◽  
Low Flow ◽  
Pressure Gradients ◽  
Apparent Permeability ◽  
Flow Rates ◽  
Rock Samples ◽  
Pore Pressure Gradient ◽  
Filtration Properties

<p>Currently, a number of studies showing that the injection of fluid into the formation can cause induced seismicity. Usually, it is associated with a change in the stress-strain state of the reservoir during the pore pressure front propagation. Modeling this process requires knowledge of the features of the filtration properties of reservoir rocks. Many researchers note the fact that the measured permeability of rock samples decreases at low pressure gradients. Among other things, this may be due to the formation of boundary adhesion layers with altered properties at the interfaces between the liquid and solid phases. The characteristic thickness of such layer can be fractions of a micron, and the effect becomes significant when filtering the fluid in rocks with a comparable characteristic pore size. The purpose of this work was to study the filtration properties of rock samples with low permeability at low flow rates. Laboratory modeling of such processes is associated with significant technical difficulties, primarily with the accuracy limit of measuring instruments when approaching zero speed values. The technique used by us to conduct the experiment and data processing allows us to study the dependence of the apparent permeability on the pore pressure gradient in the range of 0.01 MPa/m, which is comparable to the characteristic pressure gradients during the development of oil fields. In the course of the study, we carried out laboratory experiments on limestone core samples, during which the dependencies of their apparent permeability on the pore pressure gradient were obtained. We observed a significant decrease in their permeability at low flow rates. In the course of analyzing the experimental results, we proposed that a decrease in apparent permeability may occur due to the effect of even a small amount of residual gas in the pore space of the samples. This has been confirmed by additional experiments. The possibility of clogging of core sample pore space must be considered when conducting when conducting laboratory studies of the core apparent permeability.</p>

scholarly journals Unsteady Seepage Behavior of an Earthfill Dam During Drought-Flood Cycles

Geosciences ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 17 ◽  
Author(s):  
Ziyang Li ◽  
Wei Ye ◽  
Miroslav Marence ◽  
Jeremy Bricker
Keyword(s):  
Pressure Gradient ◽  
Water Level ◽  
Pore Pressure ◽  
Internal Erosion ◽  
Reservoir Water ◽  
Reservoir Water Level ◽  
Upstream Slope ◽  
Earthfill Dams ◽  
The Stability ◽  
Pore Pressure Gradient

Climate change with extreme hydrological conditions, such as drought and flood, bring new challenges to seepage behavior and the stability of earthfill dams. Taking a drought-stricken earthfill dam of China as an example, the influence of drought-flood cycles on dam seepage behavior is analyzed. This paper includes a clay sample laboratory experiment and an unsteady finite element method seepage simulation of the mentioned dam. Results show that severe drought causes cracks on the surface of the clay soil sample. Long-term drought causes deeper cracks and induces a sharp increase of suction pressure, indicating that the cracks would become channels for rain infiltration into the dam during subsequent rainfall, increasing the potential for internal erosion and decreasing dam stability. Measures to prevent infiltration on the dam slope surface are investigated, for the prevention of deep crack formation during long lasting droughts. Unsteady seepage indicators including instantaneous phreatic lines, equipotential lines and pore pressure gradient in the dam, are calculated and analyzed under two assumed conditions with different reservoir water level fluctuations. Results show that when the water level changes rapidly, the phreatic line is curved and constantly changing. As water level rises, equipotential lines shift upstream, and the pore pressure gradient in the dam’s main body is larger than that of steady seepage. Furthermore, the faster the water level rises, the larger the pore pressure gradient is. This may cause internal erosion. Furthermore, the case of a cracked upstream slope is modelled via an equivalent permeability coefficient, which shows that the pore pressure gradient in the zone beneath the cracks increases by 5.9% at the maximum water level; this could exacerbate internal erosion. In addition, results are in agreement with prior literature that rapid drawdown of the reservoir water level is detrimental to the stability of the upstream slope based on embankment slope stability as calculated by the Simplified Bishop Method. It is concluded that fluctuations of reservoir water level should be strictly controlled during drought-flood cycles; both the drawdown rate and the fill rate must be regulated to avoid the internal erosion of earthfill dams.

scholarly journals Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

2002 ◽  
Author(s):  
Patrick Le Delliou ◽  
Bruno Barthelet
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Atomic Energy Commission ◽  
Finite Thickness ◽  
Elliptical Crack ◽  
Intensity Factors ◽  
Normal Loading ◽  
Influence Coefficients ◽  
Wide Range

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

Effective Use of Commercial FEM Software in 2-Dimentional Crack Problems

2008 ◽  
Vol 33-37 ◽  
pp. 103-108
Author(s):  
Hironobu Nisitani ◽  
Kuniharu Ushijima ◽  
D.H. Chen ◽  
Akihide Saimoto
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
High Accuracy ◽  
Intensity Factors ◽  
Structural Problems ◽  
Crack Problems ◽  
Accuracy Of Results ◽  
Element Technique ◽  
Effective Use

Finite element method (FEM) is used widely for various structural problems. However, in general, it is difficult to guarantee the accuracy of results obtained by commercial software of FEM. In this paper, a practical finite element technique for calculating the stress intensity factors with high accuracy is proposed. This technique is based on the characteristics of stress field due to a crack. In this study, the proposed method is applied to 2-dimentional crack problems.

Singularities, interfaces and cracks in dissimilar anisotropic media

1990 ◽  
Vol 427 (1873) ◽  
pp. 331-358 ◽  
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Elastic Anisotropy ◽  
Homogeneous Medium ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Mode Iii ◽  
Crack Problems

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

3-D Stress Intensity Factors for Arrays of Inner Radial Lunular or Crescentic Cracks in Thin and Thick-Walled Spherical Pressure Vessels

2008 ◽  
Author(s):  
M. Perl ◽  
V. Bernstein
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Pressure Vessels ◽  
Life Assessment ◽  
Intensity Factors ◽  
Fe Method ◽  
Inner Radius ◽  
Wide Range ◽  
Spherical Pressure

Some spherical pressure vessels are manufactured by methods such as the Integrated Hydro-Bulge Forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the Stress Intensity Factors (SIF) distribution along the fronts of these cracks. However, to date, only one 3-D solution for the SIF for a circumferential crack in a thick sphere is available, as well as 2-D SIFs for one through the thickness crack in thin spherical shells. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η = Ro/Ri = 1.01, 1.05, 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the following parameters: the geometry of the sphere-η, the number of cracks in the array-n, the depth of the cracks-a/t, and their ellipticity-a/c.

STRESS INTENSITY FACTORS OF A SEMI-ELLIPTICAL CRACK IN A HOLLOW CYLINDER

2015 ◽  
Vol 39 (3) ◽  
pp. 557-568
Author(s):  
Shiuh-Chuan Her ◽  
Hao-Hi Chang
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Hollow Cylinder ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Depth ◽  
Weight Functions ◽  
Intensity Factors ◽  
Regular Elements ◽  
Wide Range

In this investigation, the weight function method was employed to calculate stress intensity factors for semi-elliptical surface crack in a hollow cylinder. A uniform stress and a linear stress distribution were used as the two references to determine the weight functions. These two factors were obtained by a three-dimensional finite element method which employed singular elements along the crack front and regular elements elsewhere. The weight functions were then applied to a wide range of semi-elliptical surface crack subjected to non-linear loadings. The results were validated against finite element data and compared with other analyses. In the parametric study, the effects of the ratio of the surface crack depth to length ranged from 0.2 to 1.0 and the ratio of the crack depth to the wall thickness ranged from 0.2 to 0.8 on stress intensity factors were investigated.

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