Lecture3(RockTestingTechnique)

8/13/2019 Lecture3(RockTestingTechnique)

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Lecture 3

Rock Stress Measurements


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Most common method is based on determining the strains in the wall of a borehole induced by overcoring that

forms part of the hole containing the measurement devices.

The second most common method is by flat jack measurements or hydraulic fracturing, where the normal stress

component is obtained by applying pressure in a slot.

The third most common method is based on analyzing and interpreting the pattern of fractures around deep

boreholes.


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Three strain

rosettes

Triaxial Strain Cells

Drill a hole from the gallery

Drill a smaller hole at the end ofthe borehole

Insert the strain cell and glue the

strain cell to the borehole wall

(assuming there is no stress relief

at this stage)

Drill an over-sized hole (over-

coring) and measure the strain

developed in the strain cell

during the stress relief

Calculate the stress from thestrain measured


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Stress Calculations from Strain Measured (based on stress distribution around a circular hole)

Definition of hole

local axes

Field stress component

relative to hole local

axes

Cartesian Coordinate

axes on hole wall

boundaryholetheatOBOAAxesCartesiantoaxesnfromangleRotation

axeslocalholeinstressFieldPPPPPPaxesholetoparallelnaxesLocalnml

drillingtopriorstressFieldPPPPPP

axesGlobalzyx

DirectionDip

Dip

nlmnlmnnmmll

zxyzxyzzyyxx

,,

,,,,,)(,,

,,,,,

,,

=

=

Relationship between

polar coordinates andxy coordinates)


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[ ]

=

=

sin0cos

coscoscossinsin

coscossincossin

znzmzl

ynymyl

xnxmxl

RRotation Matrix between two reference axes

For Isotropic Elastic Medium

sin2cos2)2sin22cos2cos(2

2sin4)2cos21()2cos21(

0

nlmnn

lmmmllnnnn

lmmmll

rnrrr

pppppp

ppp

= ++=

++=

===

Normal components of the boundary stress in the Cartesian coordinates OA, OB are:

2sin2cos)(2

1)(

2

1

2sin2cos)(2

1)(

2

1

nnnnnB

nnnnnA

+=

+++=

Suppose the orientation of the strain cell is along direction OA, and that plane stress condition is

assumed at the hole boundary during the relief:

)(1

BAAE

=

1


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[ ]

[ ]

[ ]

[ ]

[ ][ ]

[ ][ ] [ ]bpA

or

bEpapapapapapa

or

p

p

p

p

p

pE

Anlmnlmnnmmll

nl

mn

lm

nn

mm

llA

=

==+++++

+

+

+++

+++

+=

654321

2

2

2

sin2sin)1(2

cos2sin)1(2

2sin)2cos1)(1(2

2cos)1()1(2

1

2cos)2cos1)(1(2cos)1()1(2

1

2cos)2cos1)(1(2cos)1()1(2

1Combining the above equations:

If 6 strain measurements are made independently, then 6 independent

simultaneous equations can be established to solve for the stress components

l k


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Flat Jack Measurements

Coring a slot for flat jack tests Cross sectional view

Need to assume:

Relatively undisturbed surface

Closed form solution relating far-field to boundary stressRock mass behaves elastic

Procedure:

1. The distance dobetween the pins

is measured2. Slot is cut

3. Closure measured during the slot

is cut

4. Insert flat jack and grout it5. Pressurize the flat jack to restore

to the original distance


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[ ]{ }

[ ]{ }

[ ]

sin2sin2cos2sin2

2cos)1()1(2sin2)2cos1(2

1

2cos)1()1(2cos2)2cos1(2

1

2cos)1()1(2cos2)2cos1(2

1

nlmn

lmnn

mm

llA

pp

pp

p

p

+

+++

+++

+=

[ ][ ] [ ]

=

=+++++

pC

or

pcpcpcpcpcpc

or

Anlmnlmnnmmll 654321

If 6 stress measurements are made independently, then 6 independent

simultaneous equations can be established to solve for the stress components

H d li F t i b d t d t d b h l d t di t i d i fl t j k i


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Hydraulic Fracturing can be conducted at deep borehole as opposed to direct access required in flat jack or over-coring

Major principal stress

2pppressureinShut s=

Minor principal stress

Crack re-opening pressure is the pressure

separating the fracture surface

Interpretation of results

sometimes subjective

Fracture initiates and propagates when tensilestresses are higher than the tensile strength of rock

Several cycles of pressurization and declination are

needed to establish the instantaneous shut-in

pressure ps and the crack re-opening pressure pr.


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12min 3 pp =Minimum boundary stress at the borehole wall

0p=Induced tangential stress at the borehole wall

By superposition012min 3 ppp =

sectiontesttheatpressureporetheis

3 012min

uwhere

uppp =Minimum effective stress at the borehole wall

If it is assumed that the crack re-opening pressurecorresponds to the state where the minimum

effective boundary stress is zero, then

uppp

or

uppp

or

uppp

rs

r

r

=

=

==

3

3

03

1

21

12min

Important assumptions:

1. Rock is linear elastic, homogeneous isotropic

2. Hole axes are parallel to the principal axes

3. Induced fracture plane is parallel to the hole

axes


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Mathematically, the stress tensor is a

second-order Cartesian tensor with

nine stress components.

A stereonet or the Dot product can

then be used to check that the

orientation of the three mean principal

stresses are in fact perpendicular to

each other, i.e., the Dot Product oforthogonal vectors is zero.

Variability associated with stress measurements


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Large variation of vertical stress with depth


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Large variation of horizontal stress with depth


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16Representative of conditions near

excavation walls or for rock masses at

shallow depth


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g

Disturb the in situ rock conditions, i.e. by inducing strains, deformations or crack

opening pressures

hydraulic methods, including hydraulic fracturing

hydraulic tests on pre-existing fractures (HTPF)

borehole relief methods and

surface relief methods.

Based on observation of rock behaviour without any major influence from the

measuring method

statistics of measured data (database),

core-discing,

borehole breakouts,

relief of large rock volumes (back analysis),acoustic methods (Kaiser effect),

strain recovery methods,

geological observational methods and

earthquake focal mechanisms


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Are the results

representative ofthe vertical depth

variation, the

geological

boundaries, and the

presence of major

faults?

C. Ljunggren, Yanting Chang, T. Janson, R. Christiansson. International Journal of

Rock Mechanics & Mining Sciences 40 (2003) 975989


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Hydraulic methods

Hydraulic fracturing and HTPF


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Assumptions:

Vertical or sub-vertical hole

The fracture plane is

normally parallel to theborehole axis

Fracture will develop in a

direction perpendicular to

the minimum principal stress

Orientation of initiated

fractures coincides with the

orientation of the maximum

horizontal stress

One principal stress is

parallel to the borehole

Hydraulic fracturing


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Stress estimation in rock: a brief history and review by C. Fairhurst

International Journal of Rock Mechanics & Mining Sciences 40 (2003) 957973

R ti l d t d th f l th d f t f f


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Routinely used at depths of several thousands of metres from a surface access.

A sealed-off section of a borehole in an oil or gas producing horizon is

pressurized until a fracture develops in the borehole wall.

Application of pressure to the borehole walls generates a tangential tension in thewall of the borehole.

When the tangential tension is high enough to overcome the tangential compression

induced around the hole by the in situ stress state and, further, to reach the tensilestrength of the rock, a fracture develops along the length of the packed-off interval.

Once a fracture is initiated and fluid enters, it is assumed that it will propagate

at a pressure somewhat above the normal compression acting across thefracture.

Shutting off the pump and closing the pressure system should allow the fluid to

stop flowing in the fracture, so that pressure losses due to flow are eliminated

(assuming that leaf-off of fluid into the formation can be neglected).

This static pressure is known as the Instantaneous Shut-In Pressure (ISIP).

From the classical Kirsch 1898 equations for stress concentrations


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From the classical Kirsch 1898 equations for stress concentrations

around a circular elastic hole:

isiph

bhH PPT

=

+= 03 Hole is drilled verticallyVertical stress (v) is a principal stress

Maximum horizontal principal stress H

Fluid pressure in the packed-off interval is raised

to the value Pb; at which a vertical fracture is

initiated and propagates in its own plane.

Minimum horizontal stress is designated h

T is the tensile strength of the rock

P0 is the ambient pore pressure and Pisip is the ISIP

Hydraulic methods


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Hydraulic methods

Borehole relief methods

1) overcoring of cells in pilot holes

2) overcoring of borehole-bottom cells and

3) borehole slotting

1) Overcoring of measuring

cells in pilot-holes


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2) Overcoring of borehole-bottom cells

Doorstoppers andSpherical or conical strain cells

cored boreholeboreholebottom

flattenedpolished

Installation of Doorstopper (after INTERFELS)

A difi d d t ll ll d th D D t


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A modified doorstopper cell called the Deep Doorstopper

Gauge System (DDGS) has been developed jointly by the

Rock Mechanics Laboratory at Ecole Polytechnique in

Montreal and the Atomic Energy of Canada.

Allow overcoring measurements at depths as great as

1000m in subvertical boreholes

A data logger that collects and stores strain data duringstress measurement tests

Overcoring lengths required is only some 50mm as

compared to 300mm in pilot hole method


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(1) After flattening and cleaning of the bottom, the instruments are lowered down the hole with the wire

line cables.

(2) When the DDGS is at the bottom the orientation of the measurement is noted in the orientationdevice and the strain sensor is glued.

(3) The (Intelligent Acquisition Module) IAM and Doorstopper gauge are removed from the installation

equipment.

(4) The installation assembly is retrieved with the wire line system.

(5) The monitoring and overdrilling start, the strain change in the bottom is measured by the time.

(6) When overdrilling is completed, the core is taken up and a bi-axial pressure test done to estimate the

Youngs modulus.


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A borehole is first drilled. Its

bottom surface is then reshaped

into a hemispherical or conical

shape using special drill bits.

Thereafter, the strain cell is

bonded to the rock surface at thebottom of the borehole.

After the cell has been

positioned properly at the

end of the borehole andreadings of the strain

gauges have been

performed, the instrument

is overcored.

During overcoring, the

changes in

strain/deformation are

recorded.

Installation of Spherical or conical strain cells


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3) Borehole slotting

A contact strain sensor is mounted

against the wall of a large diameter

borehole

Three slots, 1200

apart, are cut into thewall

Each slot is typically 1.0mm wide and

up to 25mm deep

Tangential strains induced by release

of tangential stresses by the slots aremeasured on the borehole surface

S f li f h d


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Surface relief methods

The method is to measures the rock response to stress relief (by cutting or

drilling) by recording the distance between gauges or pins on a rock surface

before and after the relief.

Examples of the technique are the flat jack method and the curved jack

method.The category is most suitable for measurement on tunnel surfaces

Techniques of stress measurement


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Flat-jack Method A slot is then cut into the rock

Extensometer gauge is

installed between the

points A and B

The jack is then pressurized until thedistance AB is restored to the value

measured before cutting the slot

Stress estimation in rock: a brief history and review by C. Fairhurst

International Journal of Rock Mechanics & Mining Sciences 40 (2003) 957973

Assumed pressure in the jack is equal to the average normal stress


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Assumed pressure in the jack is equal to the average normal stress

acting across the slot before the slot was cut

Assumed rock is elastic over the range of unloading and reloading

Limitation: technique needs to be conducted on the surface of an

excavation in the region of maximum stress concentration around the

excavation (which may be overstressed). Hysteresis likely in theloading and unloading path

=Equation may not be correct

Borehole-jack Method


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Stress Meters


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Circular elastic inclusion of modulus E within an elastic material of modulus E

Assumed that the circular interface between the two media is welded so that

no differential movement can occur across the interface

The ratio between the vertical stress 1 in the inclusion to the vertical stress inthe host material changes very little when the ratio of the modulus E of the

inclusion is five times or more greater than the host material

Borehole deformation strain cellCircular hole in an elastic isotropic medium subjected to normal and shear stresses at infinity


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Measurement of the radial deformation u across four different


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Measurement of the radial deformation uracross four different

diameters (i.e. four different values of the angle will allow theequation for u

rto be solved for the magnitude and orientation of the

secondary principal stresses s1,s2 and their orientation in the xyplane, and the magnitude of the axial stressz along the borehole.

These stresses have no influence on the diametral deformation of thedrill hole because a linear element experiences no change of length

due to a shearing stress that acts parallel to it or at right angles to it.

The effect of shearing stress is only to change the angle between two

linear elements, one of which is parallel to, and the otherperpendicular to, the direction of the shear.

The deformation cell contains some form of transducer designed to

measure the change in radial displacement of a borehole when the

hole is overcored by a larger concentric hole.

Overcoring removes the preexisting stress field from the annulus of

rock.

Change in displacement can then be related to the change in stress.

Borehole breakouts


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Breakouts were found to

occur along the direction

of the least principalstress.

May be used to determine

the orientation of in situ

stresses.

Shape and depth ofbreakouts in vertical holes

depend on the magnitude

of the major and the minor

horizontal in situ stresses.

Core discing


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When boreholes are core

drilled in highly stressed

regions, the rock core often

appears as an assemblage of

discs.

These discs sometimes

exhibit parallel faces but are

often shaped like a horse

saddle.

This phenomenon has beencalled core discing.


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High stresses bring about failure, not only at

the borehole wall (resulting in breakouts),but also in the base of the core, giving rise to

discing.

Core tensile fractures initiated below the

coring-bit extend toward the axis of the core

with slight downward tilt in the direction of

the least horizontal stress (h).

In the maximum horizontal stress (H)direction, the same cracks are practically

horizontal.

Discs recovered from oriented cores could be

used as indicators of the in situ Horientation.


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The H magnitude andorientation could be

estimated from the average

disc thickness


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41C. Ljunggren, Yanting Chang, T. Janson, R. Christiansson. International Journal of

Rock Mechanics & Mining Sciences 40 (2003) 975989

Determination of stress orientation and magnitude in deep wells


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Stress magnitudes at depth and frictional faulting theory

Assume that the three principal stresses at depth are the vertical stress, Sv,and two horizontal principal stresses, SHmax and Shmin

The greatest, intermediate, and least principal stresses at depths S1, S2, and S3 replaced

by the vertical stress, Sv, and two horizontal principal stresses, SHmax and Shmin

minmaxv hH SSS Gravity drives N faulting and fault slip occurswhen the least horizontal principal stress (Shmin)reaches a sufficiently low value depending on

the depth and pore pressure

vminmax SSS hH Folding and reverse faulting (RF) could occur

minvmax hH SSS Strike-slip (SS) faulting represents anintermediate stress state

M.D. Zoback, C.A. Barton, M. Brudy, D.A. Castillo, T. Finkbeiner, B.R.Grollimund, D.B. Moos, P. Peska, C.D. Ward, D.J. Wiprut. International

Journal of Rock Mechanics & Mining Sciences 40 (2003) 10491076

minmaxv hH SSS Normal Faulting


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( )

frictionofcoeff

pressureporeP

PS

PS

p

ph

p

.

1

2

2

12

min

v

3

1

=

=

++

=

vminmax SSS hH Reverse Faulting

( )2

2

12

v

Hmax

3

1 1

++

=

p

p

PS

PS

minvmax hH SSS Strike-slip (SS) faulting


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minvmax hH

( )2

2

12

hmin

Hmax

3

1 1

++

=

p

p

PSPS


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Depth =3 km

=0.6

Density=2.3 gm/cm3

Well-known Kirsch equations


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Vertical wellbore of radius R

is measured from the

azimuth of hmin

Mud weight in the wellbore is

equal to the pore pressure Pp

T Thermal stresses arising

from the difference betweenthe mud temperature and the

formation temperature (T)


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Image logs from ultrasonic borehole televiewer

M.D. Zoback, C.A. Barton, M. Brudy, D.A. Castillo, T. Finkbeiner, B.R.

Grollimund, D.B. Moos, P. Peska, C.D. Ward, D.J. Wiprut. International

Journal of Rock Mechanics & Mining Sciences 40 (2003) 10491076

At the wellbore wall


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(at the point of minimum

compression =0 degree, 180

degree parallel to hmin),

(at the point of maximum

stress concentration =90degree, 270 degree parallel to

Hmax),

P is the difference

between the wellborepressure (mud weight,

Pm) and the pore

pressure.

is Poissons ratio

Hydraulic fracturing stress measurements in Hong Kong


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(WNW-ESE)Orientation of the maximum horizontal stress =

Above 150 m depth, the vertical stress Sv due to the weight of the overburden

with given rock density = the minimum principal stress

Design optimization of underground excavations requires site-specific in-situ stress

investigations with respect to the uncertainties particularly at shallow depth

G. Klee, F. Rummel, A. Williams. International Journal of Rock

Mechanics and Mining Sciences 36 (1999) 731-741

Comment on Stress Orientation based on overcoring Technique and Stress/Strain


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Comment on Stress Orientation based on overcoring Technique and Stress/Strain

Relief Measurements:

Measurements must not be made near a free surface

Strain relief is determined over very small areas (a few square millimetres to square

centimetres).

Near surface measurements have been shown to be subject to effects of localtopography, rock anisotropy, and natural fracturing (Engelder and Sbar, 1984)

Places where topography, fracturing or nearby excavations could strongly perturb

the regional stress field.

World Stress Map gives first order estimates of the stress directions

Stress measuring programme is essential in any major underground mining or civil

engineering project.

Measurements are better carried out in deep boreholes from the surface, using

hydraulic fracturing techniques, or from underground access using overcoring

methods.

Documents

Lecture3(RockTestingTechnique)