Innovation in Stress Measurements II

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Innovation in Stress Measurements II

• AV Dyskin

2
Plan

• Variability of stresses in rock mass
• Average stresses at different scales
• Scales of stress measurements. Existing methods
• Modified cylindrical jack method
• Excavation as a measuring device
• Conclusions

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Variability of stresses in rock mass
Principal stresses inferred from overcoring test
measurements in a uniform rock. Apparent stress
variations along the borehole are random (Cuisiat
Haimson, 1992)
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Sources of the spatial stress variability

• Heterogeneity in properties
• Heterogeneity in the deformation moduli
• Non-elasticity and local failures
• Heterogeneity in the coefficient of thermal
  expansion
• Phase transformation
• The presence of internal boundaries (structure of
  rock mass)
• Inter-grain boundaries
• Fissures (cracks, joints, etc.)
• Pores
• Residual stresses
• Water flow

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The role of internal structure
A fragment of photoelastic representation of the
heterogeneous stress field created in a blocky
rock mass under uniform external loading (after
Ergun, 1970)
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Nominal (average) stresses

• Continuous materials do not exist
• Stress definition
• Make a cut, remove one part of the material and
  replace its action with a total force F
• Determine F/A
• Make the area representatively small

Not possible in rock mass
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Average stresses at different scales

• Example. Skin rockburst

5 m

• Rockburst mechanism
  1 m average
• Original (pre-mined) stress for computations of
  stress concentration at the excavation
  
  10 m average
• Original (pre-mined) stress for computations of
  interactions between excavations
  
  gt100 m average

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Scales of stress measurements. Some existing
methods

• Stress Relief Methods (0.1-0.3 m)
• Overcoring
• Core drilling
• Core disking
• Flat Jack Methods (1-2 m)
• Hydraulic Fracturing (10 m)
• Borehole Breakouts (few hundred meters)
• Earthquake Source Studies (thousands meters)
• X-Ray Diffraction Technique (scale of crystals)

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Flat jack
Cylindrical jack. Dean and Beatty, 1968
Result One stress component, s
s
extensometers
pins
jack
d
d0
d
s
p 0
drilling
p
Results s1, s2, q, G
pump
Small scale and inconvenient
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Modified cylindrical jack method
isotropic or orthotropic
Stress Moduli
- larger scale - stress monitoring
capability - new interpretation
method
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Determination of shear modulus
Dean and Beatty, 1968 used the Kirsh solution for
linear-elastic homogeneous rock mass
p
The difference in the radial displacements,
determines the shear modulus, while the
circumferential displacements can be used to
control the accuracy of measurements.
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Reconstruction of the in situ stresses and
Poisons ratio
Let d be a vector of readings and W(P,s,t,k) be
2N-vector of relative displacements between pins
calculated theoretically. Then solving the
problem of
Minimization
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The determination of Poissons ratio
s1 s2.
k3-4n
for plane strain
If the 2-D in situ stress field is hydrostatic,
then the Poisson's ratio does not affect the
displacements and therefore it cannot be
determined. This means that for stress fields
close to hydrostatic the accuracy of the
determination of Poisson's ratio will be low.
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Numerical experiments

• Elastic moduli and the stress state (s1-32MPa,
  s2-18MPa, j20o) have been specified.
• Readings were modeled as the ideal ones computed
  by direct solutions and distorted by adding to
  each of them an independently generated random
  error uniformly distributed within 10.
• For each number of the measuring pairs, the
  averages over 50 sets of independently generated
  readings and the variation coefficients were
  computed.
• The numbers of measuring pairs tried are N5, 6,
  7, 8.

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Isotropic rock (granite)E81.9GPa, m33.5GPa
k2.11 (n0.222).
Reconstructed stresses and moduli for isotropic
rock
k3-4n
Variation coefficients () are given in brackets
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Reconstructed stresses and moduli for anisotropic
rock
Ortotrophic rock (schist) E163.4GPa, E220GPa,
G7.9GPa, n10.067. Two values of the cylindrical
jack pressure Q0 and 10 MPa.
Variation coefficients () are given in brackets
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Excavation as a measuring device

• Stress measurements at the excavation surface
• Numerical model of the excavation
• Back analysis to determine the average pre-mined
  stresses

Large-scale stress determined by back analysis
Surface stress measurements
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Existing method. Under-excavation technique
Willes Kaiser, 1994

• Based on recording strain and displacement
  changes due to advancing of the excavation
• Strain measurements ahead of the excavation face
  - interfere with the mining operations
• Small scale strain measurements Hence a lot of
  measurements are needed
• Requires the knowledge of the large -scale rock
  mass moduli

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Advantages of the proposed method

• It does not require the prior determination of
  the rock mass moduli the method determines them
  as a byproduct
• It is based on large-scale stress measurements
  hence does not need many measurements
• It does not interfere with the mining operations

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Large scale 3D stress reconstruction
Cylindrical tunnel arbitrarily oriented with
respect to the principal directions of the
original stress s 1s2 s3
Cartesian coordinate frame Ox1x2x3
x3-axis is parallel to the generatrix of the
tunnel axes x1 and x2 coincide with
the directions of

secondary principal stresses
s22
y
x2
x
Stress tensor
x1
O
z,x3
s11
Stresses at the excavation wall
s33
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Procedure of 3D stress tensor reconstruction
Let non-zero stress components be determined at M
different locations given by qk, k1,M. The
reference angle Q is unknown, but angles, Dk,
between local measurements are known.
Minimisation
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Numerical experiments

• Ideal stresses used were s11-2MPa, s22-3MPa,
  (P-2.5MPa and D-0.5MPa), s33-1MPa, s130.5MPa,
  s23-0.2Mpa and the reference angle chosen was
  Q22o.
• The surface stresses were modeled as the ideal
  ones and distorted by adding to each of them an
  independently generated random error uniformly
  distributed within 20.
• n0.3 was supposed to be known in this
  simulation.
• For each number of surface measurements, 200
  combinations of readings were independently
  generated, and the values of P, D, s33, s13,s23,
  Q were reconstructed.
• Numbers of measurements were M3...16
• The averages and the variation coefficients, d,
  were then computed.

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Results of numerical experiments
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Effect of the presence of a fractured zone around
the excavation

• Fractured zone is modeled by an elastic ring
  possessing moduli lower than those of the rock
  mass.
• Ambient stress field satisfies the plane strain
  conditions and is purely hydrostatic (s11s22P,
  s12s13s230).

Displacements
outside the fractured zone
inside the fractured zone
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Fractured zone (cont)
Interface pressure is found from continuity of
the displacements
qdpd/P, mm/mdgt1
Non-zero stress and displacement at the
excavation wall
Using surface stress and modulus measurements
one can only recover a certain combination of
the unknown ambient stress P, the fractured zone
radius, Rd and the moduli of the rock mass (the
surface measurements can only provide the moduli
of the fractured zone). Separation of these
parameters is impossible even using measurements
of wall displacements.
The presence of fractured zone becomes a serious
obstacle for the stress reconstruction. Thus
installation of the measuring pins and the
cylindrical jack deep enough to reach the
competent rock is essential
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Conclusions

• Excavation design requires the stress
  determination at large scale
• The proposed method based on
• large-scale surface stress and modulus
  measurements at a number of points in the
  excavation and then
• the back analysis for a given excavation shape
• allows simultaneous reconstruction of the
  stress components at the scale of excavation
• An advantage of the proposed method over the
  under-excavation technique is that it does not
  require the prior determination of the rock mass
  moduli and does not interfere with the mining
  operations