Stress state of a transversely isotropic medium with a parabolic crack when linearly changing pressure is applied to its surface

1994 ◽  
Vol 30 (12) ◽  
pp. 927-932 ◽  
Author(s):  
Yu. N. Podil'chuk ◽  
V. F. Tkachenko
Keyword(s):  
Stress State ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Parabolic Crack

scholarly journals STRESSED STATE OF A SYSTEM OF THREE PARALLEL TUNNELS WITHOUT DRAWING FROM OWN WEIGHT OF AN ANOTROPHONE ROCK MASSIF

2019 ◽  
Vol 45 (4) ◽  
pp. 162-171
Author(s):  
D. T. Bautdinov ◽  
M. M. Djamaludinov ◽  
K. S. Zhukova
Keyword(s):  
Rock Mass ◽  
Stress State ◽  
Isotropic Medium ◽  
Parametric Analysis ◽  
Transversely Isotropic ◽  
Rock Massif ◽  
Transversely Isotropic Medium ◽  
Tangential Stresses ◽  
Degree Of Anisotropy ◽  
Elastic Characteristics

Objectives. The aim of the study is to carry out a parametric analysis of the stress state of an anisotropic rock massif on the contours of the workings of a system of three parallel circular tunnels without lining due to the mass of the massif, for various ratios of the elastic characteristics of the rock massif in orthogonal directions, and at different distances del transverse isotropic medium. Method. The calculation of a system of three parallel tunnels without a large extension lining, laid in a strong transversely isotropic rock massif, is reduced to the problem of plane deformation of the theory of elasticity for a transversely isotropic medium containing parallel workings. A model of a transversely isotropic medium (a special case of an anisotropic medium) is used, in which the rock massif in one plane has the characteristics of an isotropic medium (the isotropy plane), and in the perpendicular direction, characteristics different from the isotropic medium. The stress state was investigated by the finite element method using the ANSYS software package. The sizes and type of the finite element suitable for calculation on the basis of the solution in the program complex of the verification task were previously determined. The Kirsch problem was accepted as the verification problem. Result. The relative tangential stresses on the contours of three parallel tunnels were determined depending on the degree of anisotropy of the rock mass and depending on the distance between parallel tunnels. The influence of the distance between the tunnels on the stress state on the contours of three parallel tunnels was evaluated, depending on the degree of anisotropy.Conclusion. The results of a parametric analysis of the system of three parallel free-flow tunnels without lining, depending on the degree of anisotropy of the rock mass and the distance between the tunnels, show that the stress state is significantly affected by the degree of anisotropy of the elastic properties of the soil massif and the distance between the tunnels. When designing underground structures, it is necessary to take into account the anisotropy of the elastic properties of the soil mass. It is also necessary to determine in more detail the physical and mechanical properties of rocky soils and pay special attention to elastic characteristics. As studies have shown, taking into account transverse-isotropy and the distance between the tunnels leads to both an increase and a decrease in tangential stresses on the contours of parallel tunnels. At some ratios of elastic characteristics in orthogonal directions, regardless of the distance between the tunnels, there are no tensile stresses on the contours of the tunnels, which favorably affects the operation of the hydraulic tunnel. 

Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium

1984 ◽  
Vol 51 (4) ◽  
pp. 811-815 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.

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