Presentation on design of circular openings.ppt

Design of circular opening in underground mines.

2. Induced stresses
It is man-made stress component due to removal
or addition of material. The reasons for induced
stress conditions in rock are:
–Loosening of the rock mass around cavities;
–Weight of the overburden rock mass;
–Tectonic forces, and
–Volumetric expansion of the rock mass by thermal
effects, or by
swelling brought about by the action of physical or
physicochemical processes.

3. Stress Assumptions
Prior to disturbance of rock mass, it is
visualized that the rock is subjected to the
effect of the rock-forming forces as well as
the force of gravity.
Vertical stresses are equal to σ
v= ρgh
• The horizontal stresses are generated by
assuming that the strain is zero.
σ
h= (ט/1-ט) σ
v=k σ
v
For example: ט= 0.3; σ
h= 0.43 σ
v

4. Vertical and Horizontal stresses

6. Stresses around mine openings
The underground rock structures (openings) are the
excavations which are created in a pre-stressed
environment. Stress analysis provide insight into the
changes in preexisting stress equilibrium caused by an
opening. It interprets the performance of an opening in
terms of stress concentrations and associated deformations
and serves as a rational basis for establishing the
performance of requirements for design.
The properties of the rockmass are complex, and no single
theory is available to explain rockmass behaviour. However,
the theories of elasticity and plasticity provide results that
have relevance to the stress distributions induced about
openings and provide a first step to estimating the
distribution of stresses around openings.

9. Prior to excavation, the in situ stresses in
the rockmass are in equilibrium. Once the
excavation is made, the stresses in the
vicinity of the opening are redistributed
and stress concentrations develop.

17. Three types of stress Fields

19. Various cross section of
Underground openings

20. Circular Opening
Prediction of the stresses and
displacements around a circular opening in
the rock mass at great depth is an
important problem in geotechnical,
petroleum and mining engineering such as
the design of tunnels, boreholes and mine
shafts.

21. Stress concentration around mine
openings

23. Kirsch Equation (1898)
Analytical or Closed form solution
forcircular opening in 2D.
Continuous, Homogenous, Isotropic and
Linear Elastic material (CHILE).
• Circular opening of radius, a
• In Polar co-ordinate system find the
radial, tangential and shear stress as well
as radial and tangential displacement at a
point located at (r,θ).

26. Krisch’s equations for stresses around mine Openings

29. Inferences from kirsch equation
For any excavation shape, only tangential
stresses exist at the boundary of an
excavation (without internal loading), for
example: put a/r = 1
For, r = 4a, the ratio of induced to applied
stress are close to unity,means no
influence of opening beyond that.
For a hydrostatic stress field (k =1),–The
stress concentration is 2 times SV or SH
everywhere on the boundary AND no
shear stress any where within rock mass.

30. For k = 0, maximum stress concentration
is 3 (i.e. compression) and minimum
stress concentration is -1(Tensile).
Stress is independent of elastic constant
like young’s modulus and poisons ratio.
The equation is not including the radius,
but a ratio a/r (dimensionless) i.e. the
stress at boundary of an excavation are
independent of absolute value of the
radius.