On linear-elastic cross-anisotropic rock pdf

On linear-elastic cross-anisotropic rock pdf
& Stephenson 2007).3 Plastic response of anisotropic rock The stress-strain behaviour has a nonreversible part which refers to the plastic nature of the rock material.3 Elastic isotropy For isotropic elastic rocks.3. The yield conditions for an interface in which β are the orientation of applied load with respect to state of stress. the system can described by only two elastic constants which
A cross-anisotropic rock exhibiting horizontal bedding planes (α = 0 °) and an initial isotropic stress state are considered in order to highlight the effect of material anisotropy on the development of shear bands around the gallery:
The Jointed Rock model is a cross-anisotropic, elastic, perfectly-plastic model, especially meant to simulate the behavior of stratified and jointed rock layers. In this model, two angles define the
Amandeep Singh Virk, John Summerscales, Wayne Hall. 2016. A Finite Element Analysis to Validate the Rule-of-Mixtures for the Prediction of the Young’s Modulus of Composites with Non-circular Anisotropic Fibres.
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT* Shell Development Company, New York City, Ilew York (Received May 5, 1954) The author’s previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12,
3.5 allows the Linear Elastic Solid stress-strain law.7) But the stress transformation equations. give xx 2 xy and yy 2 xy and so Eqn. 1.3).79 Table 6. It follows that normal stresses produce volume changes and shear stresses produce distortion (change in shape).3 0.
The paper examines the validity of assuming that granular material behaviour can be considered as cross-anisotropic, linear elastic, within a kinematic ‘kernel’ yield surface that is dragged through stress space with the current effective stress point.
The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid…
the rock mass and rock improvement system (rock bolts, shotcrete and wire mesh). The fundamental material parameters include; Young’s modulus, Poisons ratio, uniaxial compressive strength, shear strength (both peak and residual c and φ),
CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS 9.1 Mechanical Constitutive Equations Recall that in Chapters 2, 3 and 8 we briefly introduced the concept of a constitutive equation, which generally relates kinetic variables to kinematic variables in the application of interest. With respect to the application of the analysis of mechanical deformations in solids, the kinetic variable is the
Abstract. AbstractPrevious studies by the authors have determined pavement responses under dynamic loading considering cross-anisotropy in one layer only, either the cross-anisotropic viscoelastic asphalt concrete (AC) layer or the cross-anisotropic stress-dependent base layer, but not both.
Poisson’s ratio in orthotropic materials. AIAA Journal
https://www.youtube.com/embed/iNG4bLMyeFA

Boundary element analysis of anisotropic rock masses
FIELD VALIDATION OF THE CROSS-ANISOTROPIC BEHAVIOR OF UNBOUND AGGREGATE BASES by Erol Tutumluer Assistant Professer University of Illinois at Urbana-Champaign
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
In this equation, (a) A ij (i, j ¼ 1–6) are the elastic moduli or elasticity constants of the medium (Liao & Wang, 1998), and can be expressed in terms of the five independent elastic
Cross-anisotropic elasticity can also be considered but is not used in this study. The meaning of the swelling parameters is shown in Figure 1 and Figure 2. The maximum swelling pressure s q0 is the axial stress beyond which no swelling occurs, the swelling potential k q gives the inclination of the swelling curve in semi-logarithmic scale and the parameter h q is related to the time until the
Modeling of Pavement Response Using Nonlinear Cross-Anisotropic Approach Vol. 9, No. 4 / July 2005 331 respectively. (7) (8) From these equations, the n and m values are determined by
Anisotropic strength and deformational behavior of Himalayan schists M.H.B. Nasseria,*, K.S. Raob, T. Ramamurthyb a Department ofCivil Engineering, University of
EURO:TUN 2013 3rd International Conference on Computational Methods in Tunneling and Subsurface Engineering Ruhr University Bochum, 17-19 April 2013 397 Cross-anisotropic…

Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic
On Linear-Elastic, Cross-Anisotropic Rock (Advances in Geotechnical Engineering and Tunneling) [Anastasia Blioumi] on Amazon.com. *FREE* shipping on qualifying offers. English summary: Rocks composed of parallel layers are cross-anisotropic materials. This thesis describes a new approximate solution for the determination of the properties of
The basic criteria that are considered for the design of steel-lined pressure tunnels and shafts are (i) the working stress and deformation of the steel liner, and (ii) the load-bearing capacity of the surrounding rock mass (Schleiss, 1988).
two-dimensional microstructural models: (1) a linear elastic-perfectly plastic material with isotropic grains having random yield limits and/or elastic moduli, and (2) a ploycrystal with anisotropic grains following Hill’s yield criterion and having random orientations.
Seismology and the Earth’s Deep Interior Elasticity and Seismic Waves LinearLinear and non-linear stress and strainand non-linear stress and strain Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming linear elasticity is usually sufficient. Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming
0045-7949187 13.00 + 0.00 pergnmon journals ltd. stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace prabhat kumar…

LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory
Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
rock heterogeneity such as ripples on bedding planes or inclusions (concretion, nodule, clast, fossil, etc) in beds. Hackles are often very fine near the joint origin, while the differential relief may amplify

Tested By The Cross Download eBook PDF/EPUB
tested by the cross Download tested by the cross or read online here in PDF or EPUB. Please click button to get tested by the cross book now. All books are in clear copy here, and all files are secure so don’t worry about it.
In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the
PDF Rock nature is widely different than soil or concrete, most of failure criterions which are addressed to CHILE material (Continuous, Homogeneous, Isotropic and Linear-elastic material) are
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity isthe book of human emotions pdfA Closed-Form Solution for Tunnels with Arbitrary Cross Section Excavated in Elastic Anisotropic Ground in an infinite elastic rock mass with transverse isotropy. It is assumed that the tunnel axis is parallel to the z-axis and that axes x and z lie in the plane of isotropy. The initial state of stress is assumed to be homogeneous and aniso-tropic and is expressed in the vertical plane as
Anisotropic Elastic Parameters For an anisotropic elastic medium assuming vertical transverse isotropy (VTI), by applying linear Hook’s law expressed in Eq. (10) and taking 𝑋3 as the axis of rotational symmetry the stiffness matrix becomes Eq. (11) in the conventional two-index Nye notation [25]: 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙 𝜀𝑘𝑙 (10) where 𝜎𝑖𝑗 is the stress tensor
Download Cavity expansion theory is a simple theory that has found many applications in geotechnical engineering. In particular, it has been used widely to analyse problems relating to deep foundations, in-situ testing, underground excavation and tunnelling, and wellbore instability.
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion on material stability in Hyperelastic behavior of rubberlike materials). Stability requires that the tensor D e ⁢ l be positive definite, which leads to certain restrictions on the values of the elastic constants.
The cross-anisotropic elastic material “equivalent” to stratified rock or soil is examined, assuming the individual strata to be isotropic. It is shown that there are restrictions on the ranges of permissible variation of some of the five characteristic constants compared with those of a general cross-anisotropic material.
pdf Abstract A large database of pavement responses and corresponding material and structure properties were generated based on numerous runs of the developed geogrid-reinforced and unreinforced pavement models.
6.3 Anisotropic Elasticity There are many materials which, although well modelled using the linear elastic model, are not nearly isotropic. Examples are wood, composite materials and many biological materials. The mechanical properties of these materials differ in different directions. Materials with this direction dependence are called anisotropic (see Section 5.2.7). 6.3.1 Material Constants
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is
This result was transferred to the case of linear-elastic cross-anisotropic rock and thus, yielded the approximate solution. Measurements from large-scale cavity expansion tests (radial jack tests) were used to back calculate the material constants.
(PDF) Circular Tunnel Driven in Elastic Cross Anisotropic
Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8-1 8 Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8.1 Problem Statement This problem concerns the analysis of a lined circular tunnel in an elastic continuum. The tunnel is supported with a concrete liner that is in direct contact with the surrounding mass. The medium is subjected to an anisotropic
dent elastic parameters of the cross-anisotropic elasticity model are evaluated. The three parameters E v , ν vh , F h formulation proposed in Lings et al. (2000) offers the possibility to evaluated the five independent elastic parameters for
In this paper, closed-form solutions for the stresses and displacements around unlined circular tunnels excavated in an elastic, orthotropic (cross-anisotropic) medium are developed. The effect of both the elastic parameters characterizing the behaviour of the medium and the anisotropy of the initial stress system on the stresses and displacements induced are evaluated. An example of utilizing
form vertical circular load are directly integrated from the point load solutions in a cylindrical co-ordinate system. Elastic inho-mogeneous cross-anisotropic half-space has planes of isotropy
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts
soft rock is assumed to be cross-anisotropic. A damage function has been used to derive the A damage function has been used to derive the appropriate elastic …
dependent instead of linear elastic unbound layers, the horizontal tensile strain at the bottom of the asphalt layer increased and vertical strains on top of the base and subbase also increased. 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
cross-anisotropic half-space induced by an end-bearing (a point load), and various skin frictions (uniform, linearly varying, and non-linearly parabolic varying) of an axially loaded pile. These
In that domain, the rock sample can be modeled as a spring. If the rock If the rock is isotropic, two elastic constants can be introduced to describe its deformability: the Young’s
Tunnels in saturated elastic transversely anisotropic rock

Development of nonlinear cross-anisotropic model for the

Lined Circular Tunnels in Elastic Transversely Anisotropic Rock at Depth Antonio Bobet Received: 29 September 2009/Accepted: 4 August 2010/Published online: 1 October 2010 Springer-Verlag 2010 Abstract Closed-form solutions for displacements and stresses of both the liner and the rock are presented for a deep circular tunnel excavated in transversely anisotropic rock above or below the …
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Abstract: Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core
The equation of bit rotation in anisotropic rock allows the difference in directions of the bit axis and the borehole axis (the tangent ot the trajectory) to be determined. 2. The asymptotic approach here proposed allows the curvature and the normal to the trajectory with a specified direction of
A failure criterion for cross-anisotropic soils considering microstructure rock, are typically cross-anisotropic [2]. The material behavior within the depositional plane is found largely isotropic, while it is quite different in the direction per-pendicular to this plane (the direction is commonly called the axis of anisotropy). The cross-anisotropic structure of geomaterials affects many
Blioumi Smilauer Cross-anisotropic Rock Modelled with

STEEL-LINED PRESSURE TUNNELS AND SHAFTS IN ANISOTROPIC ROCK
So our rock sample provided the first opportu-nity to characterize the mechanical properties of the problem formation. It is widely accepted that fine-grained argillaceous rocks are anisotropic with respect to elastic moduli and compres-sive strength. Moreover, elastic moduli measured in standard triaxial compression tests are commonly found to be signif-icantly smaller than those computed
for anisotropic materials the elastic modulus given in (I) is some polycrystalline average of the elastic constants (Farthing rt c/l., 1989) or corresponds to the elastic modulus in the direction of the indentation (Cammarata et r/l., 1990 ; Doerner, 1987).
C region AB is more or less linear and corresponds to the elastic response of the rock, C region BC is associated with strain hardening and is concave downwards, C region CD …
predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K
Boundary element analysis of anisotropic rock masses where xi, Yi are values of the coordinates of node i of the element. In this paper, the following forms are adopted
Both linear and NL elastic properties of the rock must be affected by this order. The purpose of this paper is to quantify both the linear and the non linear elastic constants of rocks, considered as anisotropic, from ultrasonic velocity measurements on statically pre-stressed samples. The complete
Comparison of Isotropic and Cross-anisotropic Analysis of Pavement Structures. In most existing pavement design methods, pavements are analyzed using linear elastic multilayer theory, with the assumption that isotropic conditions are present in the structural layers of the pavement section.
Awad, A.S., Antonopoulos, I., Sadeghian, M. (2017) Case study: Geotechnical Design of Bored Piles in Rock for the Kawarau Falls Bridge 5 To account for the anisotropic behavior in …
the cross-anisotropy out of the anisotropic triaxial testing. This enables the This enables the application of a cross-anisotropic elastic constitutive law on both the undis-
Model of borehole deviation in anisotropic rock Springer
This report presents the mechanical response of an elastic cross anisotropic or transverse ly isotropic rock mass to circular excavation subjected to uniform and non-unifo rm in-situ stresses.
The integral transform techniques are used to derive the closed-form solutions of a homogeneous cross-anisotropic half space with an isothermal impervious ground surface subjected to a hot fluid injection.
Paper from proceedings of the EURO:TUN conference in year 2013. by soxodue
Room and pillar stability analysis using linear elastic exposure to water and varies in thickness from rock wall contact (<1 mm) up to 0.05 m. Consequently, the nature of structural discontinuities in the ore zone and immediate host rock has a significant influence on pillar stability. 2.1.3 Pillar condition The condition of a selection of pillars in current mining areas was visually

https://www.youtube.com/embed/ZLgAQTMgZ6g
Room and pillar stability analysis using linear elastic

https://en.wikipedia.org/wiki/Linear_elasticity
Comparison of Isotropic and Cross-anisotropic Analysis of
whiskey words and a shovel pdf free Elasticity and Seismic Waves Geophysics Homepage
Prediction of geogrid-reinforced flexible pavement

Geomechanical Modeling of an Anisotropic Formation- Bakken
https://www.youtube.com/embed/ZLgAQTMgZ6g

Anisotropic Stress-Strain Behaviour of Belgian Boom Clay

On Linear-Elastic Cross-Anisotropic Rock (Advances in
06 Linear Elasticity 01 Elastic Model Elasticity

Modeling of Pavement Response Using Nonlinear Cross-Anisotropic Approach Vol. 9, No. 4 / July 2005 331 respectively. (7) (8) From these equations, the n and m values are determined by
C region AB is more or less linear and corresponds to the elastic response of the rock, C region BC is associated with strain hardening and is concave downwards, C region CD …
In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the
Comparison of Isotropic and Cross-anisotropic Analysis of Pavement Structures. In most existing pavement design methods, pavements are analyzed using linear elastic multilayer theory, with the assumption that isotropic conditions are present in the structural layers of the pavement section.
A failure criterion for cross-anisotropic soils considering microstructure rock, are typically cross-anisotropic [2]. The material behavior within the depositional plane is found largely isotropic, while it is quite different in the direction per-pendicular to this plane (the direction is commonly called the axis of anisotropy). The cross-anisotropic structure of geomaterials affects many
dent elastic parameters of the cross-anisotropic elasticity model are evaluated. The three parameters E v , ν vh , F h formulation proposed in Lings et al. (2000) offers the possibility to evaluated the five independent elastic parameters for

10.2.1 Linear elastic behavior Engineering School Class
Modelling Swelling Rock Behaviour in Tunnelling Plaxis

A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
Amandeep Singh Virk, John Summerscales, Wayne Hall. 2016. A Finite Element Analysis to Validate the Rule-of-Mixtures for the Prediction of the Young’s Modulus of Composites with Non-circular Anisotropic Fibres.
In this paper, closed-form solutions for the stresses and displacements around unlined circular tunnels excavated in an elastic, orthotropic (cross-anisotropic) medium are developed. The effect of both the elastic parameters characterizing the behaviour of the medium and the anisotropy of the initial stress system on the stresses and displacements induced are evaluated. An example of utilizing
Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
tested by the cross Download tested by the cross or read online here in PDF or EPUB. Please click button to get tested by the cross book now. All books are in clear copy here, and all files are secure so don’t worry about it.
the cross-anisotropy out of the anisotropic triaxial testing. This enables the This enables the application of a cross-anisotropic elastic constitutive law on both the undis-
for anisotropic materials the elastic modulus given in (I) is some polycrystalline average of the elastic constants (Farthing rt c/l., 1989) or corresponds to the elastic modulus in the direction of the indentation (Cammarata et r/l., 1990 ; Doerner, 1987).
Download Cavity expansion theory is a simple theory that has found many applications in geotechnical engineering. In particular, it has been used widely to analyse problems relating to deep foundations, in-situ testing, underground excavation and tunnelling, and wellbore instability.

ebooks.iospress.nl
Anisotropic strength and deformational behavior of

PDF Rock nature is widely different than soil or concrete, most of failure criterions which are addressed to CHILE material (Continuous, Homogeneous, Isotropic and Linear-elastic material) are
pdf Abstract A large database of pavement responses and corresponding material and structure properties were generated based on numerous runs of the developed geogrid-reinforced and unreinforced pavement models.
Anisotropic Elastic Parameters For an anisotropic elastic medium assuming vertical transverse isotropy (VTI), by applying linear Hook’s law expressed in Eq. (10) and taking 𝑋3 as the axis of rotational symmetry the stiffness matrix becomes Eq. (11) in the conventional two-index Nye notation [25]: 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙 𝜀𝑘𝑙 (10) where 𝜎𝑖𝑗 is the stress tensor
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic

Surface and defect morphologies in anisotropic elastic and
On the applicability of cross-anisotropic elasticity to

The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid…
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Abstract. AbstractPrevious studies by the authors have determined pavement responses under dynamic loading considering cross-anisotropy in one layer only, either the cross-anisotropic viscoelastic asphalt concrete (AC) layer or the cross-anisotropic stress-dependent base layer, but not both.
predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K
3.5 allows the Linear Elastic Solid stress-strain law.7) But the stress transformation equations. give xx 2 xy and yy 2 xy and so Eqn. 1.3).79 Table 6. It follows that normal stresses produce volume changes and shear stresses produce distortion (change in shape).3 0.
Comparison of Isotropic and Cross-anisotropic Analysis of Pavement Structures. In most existing pavement design methods, pavements are analyzed using linear elastic multilayer theory, with the assumption that isotropic conditions are present in the structural layers of the pavement section.
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
soft rock is assumed to be cross-anisotropic. A damage function has been used to derive the A damage function has been used to derive the appropriate elastic …
On Linear-Elastic, Cross-Anisotropic Rock (Advances in Geotechnical Engineering and Tunneling) [Anastasia Blioumi] on Amazon.com. *FREE* shipping on qualifying offers. English summary: Rocks composed of parallel layers are cross-anisotropic materials. This thesis describes a new approximate solution for the determination of the properties of
The paper examines the validity of assuming that granular material behaviour can be considered as cross-anisotropic, linear elastic, within a kinematic ‘kernel’ yield surface that is dragged through stress space with the current effective stress point.

Cavity expansion in cross-anisotropic rock Kolymbas
Stress concentration due to underground excavation in

In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
So our rock sample provided the first opportu-nity to characterize the mechanical properties of the problem formation. It is widely accepted that fine-grained argillaceous rocks are anisotropic with respect to elastic moduli and compres-sive strength. Moreover, elastic moduli measured in standard triaxial compression tests are commonly found to be signif-icantly smaller than those computed

Surface and defect morphologies in anisotropic elastic and
Shear banding modelling in cross-anisotropic rocks

predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K
Seismology and the Earth’s Deep Interior Elasticity and Seismic Waves LinearLinear and non-linear stress and strainand non-linear stress and strain Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming linear elasticity is usually sufficient. Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming
In that domain, the rock sample can be modeled as a spring. If the rock If the rock is isotropic, two elastic constants can be introduced to describe its deformability: the Young’s
PDF Rock nature is widely different than soil or concrete, most of failure criterions which are addressed to CHILE material (Continuous, Homogeneous, Isotropic and Linear-elastic material) are
A failure criterion for cross-anisotropic soils considering microstructure rock, are typically cross-anisotropic [2]. The material behavior within the depositional plane is found largely isotropic, while it is quite different in the direction per-pendicular to this plane (the direction is commonly called the axis of anisotropy). The cross-anisotropic structure of geomaterials affects many
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
rock heterogeneity such as ripples on bedding planes or inclusions (concretion, nodule, clast, fossil, etc) in beds. Hackles are often very fine near the joint origin, while the differential relief may amplify
This result was transferred to the case of linear-elastic cross-anisotropic rock and thus, yielded the approximate solution. Measurements from large-scale cavity expansion tests (radial jack tests) were used to back calculate the material constants.

A Closed-Form Solution for Tunnels with Arbitrary Cross
Modelling Swelling Rock Behaviour in Tunnelling Plaxis

Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic
LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
In this paper, closed-form solutions for the stresses and displacements around unlined circular tunnels excavated in an elastic, orthotropic (cross-anisotropic) medium are developed. The effect of both the elastic parameters characterizing the behaviour of the medium and the anisotropy of the initial stress system on the stresses and displacements induced are evaluated. An example of utilizing
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion on material stability in Hyperelastic behavior of rubberlike materials). Stability requires that the tensor D e ⁢ l be positive definite, which leads to certain restrictions on the values of the elastic constants.
Anisotropic Elastic Parameters For an anisotropic elastic medium assuming vertical transverse isotropy (VTI), by applying linear Hook’s law expressed in Eq. (10) and taking 𝑋3 as the axis of rotational symmetry the stiffness matrix becomes Eq. (11) in the conventional two-index Nye notation [25]: 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙 𝜀𝑘𝑙 (10) where 𝜎𝑖𝑗 is the stress tensor
The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid…
The basic criteria that are considered for the design of steel-lined pressure tunnels and shafts are (i) the working stress and deformation of the steel liner, and (ii) the load-bearing capacity of the surrounding rock mass (Schleiss, 1988).
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
dependent instead of linear elastic unbound layers, the horizontal tensile strain at the bottom of the asphalt layer increased and vertical strains on top of the base and subbase also increased. 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is

Lateral stresses caused by uniform rectangular area loads
(PDF) E-Book Behavior of Anisotropic Rocks ResearchGate

Abstract: Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core
EURO:TUN 2013 3rd International Conference on Computational Methods in Tunneling and Subsurface Engineering Ruhr University Bochum, 17-19 April 2013 397 Cross-anisotropic…
This report presents the mechanical response of an elastic cross anisotropic or transverse ly isotropic rock mass to circular excavation subjected to uniform and non-unifo rm in-situ stresses.
This result was transferred to the case of linear-elastic cross-anisotropic rock and thus, yielded the approximate solution. Measurements from large-scale cavity expansion tests (radial jack tests) were used to back calculate the material constants.
Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic
0045-7949187 13.00 0.00 pergnmon journals ltd. stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace prabhat kumar…
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion on material stability in Hyperelastic behavior of rubberlike materials). Stability requires that the tensor D e ⁢ l be positive definite, which leads to certain restrictions on the values of the elastic constants.

Consolidation of a poroelastic half-space with anisotropic
A failure criterion for cross-anisotropic soils

two-dimensional microstructural models: (1) a linear elastic-perfectly plastic material with isotropic grains having random yield limits and/or elastic moduli, and (2) a ploycrystal with anisotropic grains following Hill’s yield criterion and having random orientations.
The basic criteria that are considered for the design of steel-lined pressure tunnels and shafts are (i) the working stress and deformation of the steel liner, and (ii) the load-bearing capacity of the surrounding rock mass (Schleiss, 1988).
for anisotropic materials the elastic modulus given in (I) is some polycrystalline average of the elastic constants (Farthing rt c/l., 1989) or corresponds to the elastic modulus in the direction of the indentation (Cammarata et r/l., 1990 ; Doerner, 1987).
pdf Abstract A large database of pavement responses and corresponding material and structure properties were generated based on numerous runs of the developed geogrid-reinforced and unreinforced pavement models.
the rock mass and rock improvement system (rock bolts, shotcrete and wire mesh). The fundamental material parameters include; Young’s modulus, Poisons ratio, uniaxial compressive strength, shear strength (both peak and residual c and φ),
0045-7949187 13.00 0.00 pergnmon journals ltd. stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace prabhat kumar…
On Linear-Elastic, Cross-Anisotropic Rock (Advances in Geotechnical Engineering and Tunneling) [Anastasia Blioumi] on Amazon.com. *FREE* shipping on qualifying offers. English summary: Rocks composed of parallel layers are cross-anisotropic materials. This thesis describes a new approximate solution for the determination of the properties of

Prediction of geogrid-reinforced flexible pavement
Modeling of Pavement Response Using Nonlinear Cross

A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
& Stephenson 2007).3 Plastic response of anisotropic rock The stress-strain behaviour has a nonreversible part which refers to the plastic nature of the rock material.3 Elastic isotropy For isotropic elastic rocks.3. The yield conditions for an interface in which β are the orientation of applied load with respect to state of stress. the system can described by only two elastic constants which
the cross-anisotropy out of the anisotropic triaxial testing. This enables the This enables the application of a cross-anisotropic elastic constitutive law on both the undis-
Anisotropic Elastic Parameters For an anisotropic elastic medium assuming vertical transverse isotropy (VTI), by applying linear Hook’s law expressed in Eq. (10) and taking 𝑋3 as the axis of rotational symmetry the stiffness matrix becomes Eq. (11) in the conventional two-index Nye notation [25]: 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙 𝜀𝑘𝑙 (10) where 𝜎𝑖𝑗 is the stress tensor
rock heterogeneity such as ripples on bedding planes or inclusions (concretion, nodule, clast, fossil, etc) in beds. Hackles are often very fine near the joint origin, while the differential relief may amplify
form vertical circular load are directly integrated from the point load solutions in a cylindrical co-ordinate system. Elastic inho-mogeneous cross-anisotropic half-space has planes of isotropy
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts
predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K

Theory of Elasticity and Consolidation for a Porous
Elastic solutions of an isothermal impervious cross

Seismology and the Earth’s Deep Interior Elasticity and Seismic Waves LinearLinear and non-linear stress and strainand non-linear stress and strain Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming linear elasticity is usually sufficient. Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the
A Closed-Form Solution for Tunnels with Arbitrary Cross Section Excavated in Elastic Anisotropic Ground in an infinite elastic rock mass with transverse isotropy. It is assumed that the tunnel axis is parallel to the z-axis and that axes x and z lie in the plane of isotropy. The initial state of stress is assumed to be homogeneous and aniso-tropic and is expressed in the vertical plane as
Awad, A.S., Antonopoulos, I., Sadeghian, M. (2017) Case study: Geotechnical Design of Bored Piles in Rock for the Kawarau Falls Bridge 5 To account for the anisotropic behavior in …
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory
The cross-anisotropic elastic material “equivalent” to stratified rock or soil is examined, assuming the individual strata to be isotropic. It is shown that there are restrictions on the ranges of permissible variation of some of the five characteristic constants compared with those of a general cross-anisotropic material.
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion on material stability in Hyperelastic behavior of rubberlike materials). Stability requires that the tensor D e ⁢ l be positive definite, which leads to certain restrictions on the values of the elastic constants.
0045-7949187 13.00 0.00 pergnmon journals ltd. stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace prabhat kumar…
FIELD VALIDATION OF THE CROSS-ANISOTROPIC BEHAVIOR OF UNBOUND AGGREGATE BASES by Erol Tutumluer Assistant Professer University of Illinois at Urbana-Champaign
Boundary element analysis of anisotropic rock masses where xi, Yi are values of the coordinates of node i of the element. In this paper, the following forms are adopted
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
C region AB is more or less linear and corresponds to the elastic response of the rock, C region BC is associated with strain hardening and is concave downwards, C region CD …

Lined Circular Tunnels in Elastic Transversely Anisotropic
A nonlinear model for soft rock and its application in

Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic
Amandeep Singh Virk, John Summerscales, Wayne Hall. 2016. A Finite Element Analysis to Validate the Rule-of-Mixtures for the Prediction of the Young’s Modulus of Composites with Non-circular Anisotropic Fibres.
two-dimensional microstructural models: (1) a linear elastic-perfectly plastic material with isotropic grains having random yield limits and/or elastic moduli, and (2) a ploycrystal with anisotropic grains following Hill’s yield criterion and having random orientations.
Abstract. AbstractPrevious studies by the authors have determined pavement responses under dynamic loading considering cross-anisotropy in one layer only, either the cross-anisotropic viscoelastic asphalt concrete (AC) layer or the cross-anisotropic stress-dependent base layer, but not both.
In this paper, closed-form solutions for the stresses and displacements around unlined circular tunnels excavated in an elastic, orthotropic (cross-anisotropic) medium are developed. The effect of both the elastic parameters characterizing the behaviour of the medium and the anisotropy of the initial stress system on the stresses and displacements induced are evaluated. An example of utilizing

NON-LINEAR ELASTIC Rock Mechanics Group
Modeling of Pavement Response Using Nonlinear Cross

Abstract. AbstractPrevious studies by the authors have determined pavement responses under dynamic loading considering cross-anisotropy in one layer only, either the cross-anisotropic viscoelastic asphalt concrete (AC) layer or the cross-anisotropic stress-dependent base layer, but not both.
Download Cavity expansion theory is a simple theory that has found many applications in geotechnical engineering. In particular, it has been used widely to analyse problems relating to deep foundations, in-situ testing, underground excavation and tunnelling, and wellbore instability.
0045-7949187 13.00 0.00 pergnmon journals ltd. stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace prabhat kumar…
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
The Jointed Rock model is a cross-anisotropic, elastic, perfectly-plastic model, especially meant to simulate the behavior of stratified and jointed rock layers. In this model, two angles define the
3.5 allows the Linear Elastic Solid stress-strain law.7) But the stress transformation equations. give xx 2 xy and yy 2 xy and so Eqn. 1.3).79 Table 6. It follows that normal stresses produce volume changes and shear stresses produce distortion (change in shape).3 0.
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT* Shell Development Company, New York City, Ilew York (Received May 5, 1954) The author’s previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12,
The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid…
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory
Awad, A.S., Antonopoulos, I., Sadeghian, M. (2017) Case study: Geotechnical Design of Bored Piles in Rock for the Kawarau Falls Bridge 5 To account for the anisotropic behavior in …
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is

A nonlinear model for soft rock and its application in
Dynamics of Transtropic Elastic Continuums with Non

Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
Abstract: Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core
soft rock is assumed to be cross-anisotropic. A damage function has been used to derive the A damage function has been used to derive the appropriate elastic …
predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is
CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS 9.1 Mechanical Constitutive Equations Recall that in Chapters 2, 3 and 8 we briefly introduced the concept of a constitutive equation, which generally relates kinetic variables to kinematic variables in the application of interest. With respect to the application of the analysis of mechanical deformations in solids, the kinetic variable is the
FIELD VALIDATION OF THE CROSS-ANISOTROPIC BEHAVIOR OF UNBOUND AGGREGATE BASES by Erol Tutumluer Assistant Professer University of Illinois at Urbana-Champaign
This result was transferred to the case of linear-elastic cross-anisotropic rock and thus, yielded the approximate solution. Measurements from large-scale cavity expansion tests (radial jack tests) were used to back calculate the material constants.
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT* Shell Development Company, New York City, Ilew York (Received May 5, 1954) The author’s previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12,
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
Download Cavity expansion theory is a simple theory that has found many applications in geotechnical engineering. In particular, it has been used widely to analyse problems relating to deep foundations, in-situ testing, underground excavation and tunnelling, and wellbore instability.

ebooks.iospress.nl
On Linear-Elastic Cross-Anisotropic Rock (Advances in

On Linear-Elastic, Cross-Anisotropic Rock (Advances in Geotechnical Engineering and Tunneling) [Anastasia Blioumi] on Amazon.com. *FREE* shipping on qualifying offers. English summary: Rocks composed of parallel layers are cross-anisotropic materials. This thesis describes a new approximate solution for the determination of the properties of
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
Abstract: Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is
EURO:TUN 2013 3rd International Conference on Computational Methods in Tunneling and Subsurface Engineering Ruhr University Bochum, 17-19 April 2013 397 Cross-anisotropic…
LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts

Field Validation of the Cross-Anisotropic Behavior of
Lateral stresses caused by uniform rectangular area loads

The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid…
soft rock is assumed to be cross-anisotropic. A damage function has been used to derive the A damage function has been used to derive the appropriate elastic …
EURO:TUN 2013 3rd International Conference on Computational Methods in Tunneling and Subsurface Engineering Ruhr University Bochum, 17-19 April 2013 397 Cross-anisotropic…
Both linear and NL elastic properties of the rock must be affected by this order. The purpose of this paper is to quantify both the linear and the non linear elastic constants of rocks, considered as anisotropic, from ultrasonic velocity measurements on statically pre-stressed samples. The complete
Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8-1 8 Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8.1 Problem Statement This problem concerns the analysis of a lined circular tunnel in an elastic continuum. The tunnel is supported with a concrete liner that is in direct contact with the surrounding mass. The medium is subjected to an anisotropic
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
two-dimensional microstructural models: (1) a linear elastic-perfectly plastic material with isotropic grains having random yield limits and/or elastic moduli, and (2) a ploycrystal with anisotropic grains following Hill’s yield criterion and having random orientations.
LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
The paper examines the validity of assuming that granular material behaviour can be considered as cross-anisotropic, linear elastic, within a kinematic ‘kernel’ yield surface that is dragged through stress space with the current effective stress point.
Abstract. Tunnel has been recognized as one of the most important underground structures and widely used for a number of infrastructures. Most of the existing analyses of tunnels were based on the assumption of homogeneous and isotropic rock.
Anisotropic strength and deformational behavior of Himalayan schists M.H.B. Nasseria,*, K.S. Raob, T. Ramamurthyb a Department ofCivil Engineering, University of
Lined Circular Tunnels in Elastic Transversely Anisotropic Rock at Depth Antonio Bobet Received: 29 September 2009/Accepted: 4 August 2010/Published online: 1 October 2010 Springer-Verlag 2010 Abstract Closed-form solutions for displacements and stresses of both the liner and the rock are presented for a deep circular tunnel excavated in transversely anisotropic rock above or below the …
predetermine the anisotropic model of rock mass. The model of transtropic (transversal isotropic) solid with an inclined plane of isotropy, simulating the folded rock layers, is really relevant to anisotropic properties of massif. Anisotropic (transtropic) model of the folded-layered massif with Dynamics of Transtropic Elastic Continuums with Non-Homogeneities Lyazzat B. Atymtayeva , Zhailau K
In that domain, the rock sample can be modeled as a spring. If the rock If the rock is isotropic, two elastic constants can be introduced to describe its deformability: the Young’s
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory

Analytical solutions for stresses and displacements around
Cavity expansion in cross-anisotropic rock Kolymbas

In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS 9.1 Mechanical Constitutive Equations Recall that in Chapters 2, 3 and 8 we briefly introduced the concept of a constitutive equation, which generally relates kinetic variables to kinematic variables in the application of interest. With respect to the application of the analysis of mechanical deformations in solids, the kinetic variable is the
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
6.3 Anisotropic Elasticity There are many materials which, although well modelled using the linear elastic model, are not nearly isotropic. Examples are wood, composite materials and many biological materials. The mechanical properties of these materials differ in different directions. Materials with this direction dependence are called anisotropic (see Section 5.2.7). 6.3.1 Material Constants
Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
form vertical circular load are directly integrated from the point load solutions in a cylindrical co-ordinate system. Elastic inho-mogeneous cross-anisotropic half-space has planes of isotropy
A cross‐anisotropic linear elastic law is adopted for the mechanical behaviour. Elements for a proper modelling of gas flow along preferential paths include an embedded fracture permeability model. Rock permeability and its retention curve depend on strains through a fracture aperture. The hydraulic and mechanical behaviours have a common anisotropic structure. Small‐scale heterogeneity is
& Stephenson 2007).3 Plastic response of anisotropic rock The stress-strain behaviour has a nonreversible part which refers to the plastic nature of the rock material.3 Elastic isotropy For isotropic elastic rocks.3. The yield conditions for an interface in which β are the orientation of applied load with respect to state of stress. the system can described by only two elastic constants which
Abstract. AbstractPrevious studies by the authors have determined pavement responses under dynamic loading considering cross-anisotropy in one layer only, either the cross-anisotropic viscoelastic asphalt concrete (AC) layer or the cross-anisotropic stress-dependent base layer, but not both.

Modeling of Pavement Response Using Nonlinear Cross
[1112.4938] Dislocation core field. I. Modeling in

Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
Amandeep Singh Virk, John Summerscales, Wayne Hall. 2016. A Finite Element Analysis to Validate the Rule-of-Mixtures for the Prediction of the Young’s Modulus of Composites with Non-circular Anisotropic Fibres.
Comparison of Isotropic and Cross-anisotropic Analysis of Pavement Structures. In most existing pavement design methods, pavements are analyzed using linear elastic multilayer theory, with the assumption that isotropic conditions are present in the structural layers of the pavement section.
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory
tested by the cross Download tested by the cross or read online here in PDF or EPUB. Please click button to get tested by the cross book now. All books are in clear copy here, and all files are secure so don’t worry about it.
two-dimensional microstructural models: (1) a linear elastic-perfectly plastic material with isotropic grains having random yield limits and/or elastic moduli, and (2) a ploycrystal with anisotropic grains following Hill’s yield criterion and having random orientations.

Displacements and Stresses Due to a Uniform Vertical
Dynamics of Transtropic Elastic Continuums with Non

dependent instead of linear elastic unbound layers, the horizontal tensile strain at the bottom of the asphalt layer increased and vertical strains on top of the base and subbase also increased. 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options
tested by the cross Download tested by the cross or read online here in PDF or EPUB. Please click button to get tested by the cross book now. All books are in clear copy here, and all files are secure so don’t worry about it.
Seismology and the Earth’s Deep Interior Elasticity and Seismic Waves LinearLinear and non-linear stress and strainand non-linear stress and strain Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming linear elasticity is usually sufficient. Stress vs. strain for a loading cycle with rock that breaks. For wave propagation problems assuming
Read “Cavity expansion in cross‐anisotropic rock, International Journal for Numerical and Analytical Methods in Geomechanics” on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS 9.1 Mechanical Constitutive Equations Recall that in Chapters 2, 3 and 8 we briefly introduced the concept of a constitutive equation, which generally relates kinetic variables to kinematic variables in the application of interest. With respect to the application of the analysis of mechanical deformations in solids, the kinetic variable is the
Abstract: Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core
Schistous rock can be considered—in a first approximation—as cross-anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory
Cross-anisotropic elasticity can also be considered but is not used in this study. The meaning of the swelling parameters is shown in Figure 1 and Figure 2. The maximum swelling pressure s q0 is the axial stress beyond which no swelling occurs, the swelling potential k q gives the inclination of the swelling curve in semi-logarithmic scale and the parameter h q is related to the time until the
soft rock is assumed to be cross-anisotropic. A damage function has been used to derive the A damage function has been used to derive the appropriate elastic …
In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the

Stresses due to vertical subsurface loading for an
Surface and defect morphologies in anisotropic elastic and

tested by the cross Download tested by the cross or read online here in PDF or EPUB. Please click button to get tested by the cross book now. All books are in clear copy here, and all files are secure so don’t worry about it.
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT Theory of Elasticity and Consolidation for a Porous Anisotropic Solid M. A. BIOT* Shell Development Company, New York City, Ilew York (Received May 5, 1954) The author’s previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12,
This report presents the mechanical response of an elastic cross anisotropic or transverse ly isotropic rock mass to circular excavation subjected to uniform and non-unifo rm in-situ stresses.
C region AB is more or less linear and corresponds to the elastic response of the rock, C region BC is associated with strain hardening and is concave downwards, C region CD …
In that domain, the rock sample can be modeled as a spring. If the rock If the rock is isotropic, two elastic constants can be introduced to describe its deformability: the Young’s
PDF Rock nature is widely different than soil or concrete, most of failure criterions which are addressed to CHILE material (Continuous, Homogeneous, Isotropic and Linear-elastic material) are

Model of borehole deviation in anisotropic rock Springer
LS-DYNA Keyword User’s Manual Volume II Material Models

the rock mass and rock improvement system (rock bolts, shotcrete and wire mesh). The fundamental material parameters include; Young’s modulus, Poisons ratio, uniaxial compressive strength, shear strength (both peak and residual c and φ),
for anisotropic materials the elastic modulus given in (I) is some polycrystalline average of the elastic constants (Farthing rt c/l., 1989) or corresponds to the elastic modulus in the direction of the indentation (Cammarata et r/l., 1990 ; Doerner, 1987).
3.5 allows the Linear Elastic Solid stress-strain law.7) But the stress transformation equations. give xx 2 xy and yy 2 xy and so Eqn. 1.3).79 Table 6. It follows that normal stresses produce volume changes and shear stresses produce distortion (change in shape).3 0.
Defining linear elastic material behavior The total stress is defined from the total elastic strain as where is the total stress (“true,” or Cauchy stress in finite-strain problems), is the fourth-order elasticity tensor, and is the total elastic strain (log strain in finite-strain problems).
Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8-1 8 Lined Circular Tunnel in an Elastic Medium with Anisotropic Stresses 8.1 Problem Statement This problem concerns the analysis of a lined circular tunnel in an elastic continuum. The tunnel is supported with a concrete liner that is in direct contact with the surrounding mass. The medium is subjected to an anisotropic
Cross-anisotropic analyzing the stress–strain response of a metal also be- elasticity has been widely used to present the defor- longs in this class. Jardine and Potts [22] proposed a mation anisotropy of soils, because it is composed of simple model that includes nonlinear bulk and shear the different YoungÕs moduli and PoissonÕs ratios in the moduli fitted by a periodic logarithmic
LS-DYNA® KEYWORD USER’S MANUAL VOLUME II Material Models August 2012 Version 971 R6.1.0 LIVERMORE SOFTWARE TECHNOLOGY CORPORATION (LSTC)
In this equation, (a) A ij (i, j ¼ 1–6) are the elastic moduli or elasticity constants of the medium (Liao & Wang, 1998), and can be expressed in terms of the five independent elastic
rock heterogeneity such as ripples on bedding planes or inclusions (concretion, nodule, clast, fossil, etc) in beds. Hackles are often very fine near the joint origin, while the differential relief may amplify
A comparative study of the anisotropic dynamic and static elastic moduli of unconventional reservoir shales: Implication for geomechanical investigations
Abstract— This paper is devoted to the research analysis of stress-strain state of anisotropic massif containing the deep located diagonal mines of arbitrary profile under the propagation of elastic longitudinal and shift waves. The special case of generalized plane deformation is considered at this paper to demonstrate possible results of the solutions for different located mines (drifts
Linear elastic materials must satisfy the conditions of material or Drucker stability (see the discussion on material stability in Hyperelastic behavior of rubberlike materials). Stability requires that the tensor D e ⁢ l be positive definite, which leads to certain restrictions on the values of the elastic constants.
models for rock and soil including Anisotropic, Mohr-Coulomb with Cap, and Softening/Hardening. Groundwater pore pressure can be determined using steady state or transient finite element seepage analyses. For consolidation analysis, Phase2 9.0 also comes with fully-coupled fluid/solid analysis based on Biot Theory. Support Design Phase2 9.0 offers a wide range of support modeling options