Approximate relation between the elastic constants of anisotropic rocks and the anisotropy parameters

Batugin, S. A.; Nirenburg, R. K.

doi:10.1007/bf02497798

Cited by 46 publications

(18 citation statements)

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“…It can be shown that condition (2) actually occurs for fractured rock foundations. A sufficient experimental confirmation of this is given in [7].…”

supporting

confidence: 54%

Comments on calculation of the stress state in an anisotropic rock foundation

Merzlyakov¹

1983

Hydrotechnical Construction

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“…It can be shown that condition (2) actually occurs for fractured rock foundations. A sufficient experimental confirmation of this is given in [7].…”

supporting

confidence: 54%

Comments on calculation of the stress state in an anisotropic rock foundation

Merzlyakov¹

1983

Hydrotechnical Construction

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“…However, despite the simplicity of the constitutive relations, the determination of these elastic properties is not simple due to the lack of standardization for the measurement methods (Gonzaga et al 2008). The cross-shear modulus G 0 is the most difficult parameter to assess (Batugin and Nirenburg 1972;Homand et al 1993). Amadei et al (1987) discuss the ranges of properties for transversely isotropic rocks which can be found in nature.…”

Section: Ranges Of Properties Of Transversely Isotropic Rocksmentioning

confidence: 98%

Stresses and Displacements in Steel-Lined Pressure Tunnels and Shafts in Anisotropic Rock Under Quasi-Static Internal Water Pressure

Pachoud

Schleiss

2015

Rock Mech Rock Eng

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Steel-lined pressure tunnels and shafts are constructed to convey water from reservoirs to hydroelectric power plants. They are multilayer structures made of a steel liner, a cracked backfill concrete layer, a cracked or loosened near-field rock zone and a sound far-field rock zone. Designers often assume isotropic behavior of the farfield rock, considering the most unfavorable rock mass elastic modulus measured in situ, and a quasi-static internal water pressure. Such a conventional model is thus axisymmetrical and has an analytical solution for stresses and displacements. However, rock masses often have an anisotropic behavior and such isotropic assumption is usually conservative in terms of quasi-static maximum stresses in the steel liner. In this work, the stresses and displacements in steel-lined pressure tunnels and shafts in anisotropic rock mass are studied by means of the finite element method. A quasi-static internal water pressure is considered. The materials are considered linear elastic, and tied contact is assumed between the layers. The constitutive models used for the rock mass and the cracked layers are presented and the practical ranges of variation of the parameters are discussed. An extensive systematic parametric study is performed and stresses and displacements in the steel liner and in the far-field rock mass are presented. Finally, correction factors are derived to be included in the axisymmetrical solution which allow a rapid estimate of the maximum stresses in the steel liners of pressure tunnels and shafts in anisotropic rock.Keywords Steel liner Á Anisotropy Á Transversely isotropic rock Á Pressure tunnels and shafts Á Finite element method Á Water pressure List of symbolsLatin characters E, E 0 Elastic moduli of a transversely isotropic rock E c , E crm , E rm , E s Elastic moduli of the backfill concrete, the near-field rock, the isotropic far-field rock and the steel liner, respectively E h Elastic modulus in the tangential direction in polar coordinates G, G 0 Shear moduli of a transversely isotropic rock G 0 SÀV Empirical cross-shear modulus of a transversely isotropic rock according to Saint-Venant G hr , G hz Shear moduli in polar coordinates p c , p c;corr , p crm , p rm Pressures transmitted at radii r c (and its correction), r crm and r rm , respectively p i Quasi-static internal water pressure r c , r crm , r i , r rm Internal radii of the backfill concrete, the near-field rock, the steel liner and the far-field rock, respectively t c , t crm , t s Thicknesses of the backfill concrete, the near-field rock and the steel liner, respectively u c r , u crm r , u rm r , u s r Radial displacements of the backfill concrete, the near-field rock, the farfield rock and the steel liner, respectively û s r ,û s r;max ,û s r;min Normalized radial displacements in the steel liner, and the maximum and minimum values, respectively u s r;iso , u s r;aniso Radial displacements in the steel liner considering isotropic and anisotropic rock, respectively Greek symbols c xy , c xz , c yz Shear st...

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“…While it is difficult to measure the shear modulus in the direction normal to the plane of isotropy of the TI material, several approximations in literature were made 17 : (15) will not be used in the examples presented in this work. It should only be used when laboratory measurements are not available.…”

Section: Materials Anisotropymentioning

confidence: 99%