9. Initial stress‡：このマークが付してある著作物は、第三者が有する著作物ですので、同著作物の再使用、同著作物の二次的著作物の創作等については、著作権者より直接使用許諾を得る必要があります。

Initial stressStress state in rock mass without artificial disturbances.
One of the basic data in designing rock structure.
Competence factor = Uniaxial compressive stress / initial
vertical stress is a good index for stability of an opening inrock mass

Stress state near opening is
disturbed
Disturbed zone is avoided
for measurement of initialstressDisturbed stress is alsomeasured in some cases
where investigating
deformation and failure
behavior around theopening9.1 Initial stress valuePrimitive estimationσV =γ hInitial vertical stress σV isequal to the weight ofoverburdenrock(overburden pressure)γ is unit volume weight(ex. 27 kN /m3）
h is the depth (m)Ex. Initial vertical stressat 500 m deep is 13.5
MPaσV = γ hσ h = k 2σ V
σ H = k1σ V

Initial horizontal stress σH at a shallow depth.
Horizontal stress ε H is assumed to be zero.
Eε H = σ H − ν (σ H + σ V ) = 0σ H = kσ Vk=ν1 −ν

E is Young's modulus.
ν is Poisson's ratio
k is the coefficient for horizontal stressk is assumed to be 1 at great depth.

σV = γ hσ h = k 2σ V
σ H = k1σ VMeasured initial stress values
Initial verticalstress is roughly
equal to theprimitive
estimation

著作権処理の都合で、この場所に挿入されていた『Goodman (1980), Introduction to RockMechanics, John Wiley and Sons, p. 106, Fig.
4.7a』
を省略させて頂きます。

Goodman, 1980

Initial horizontal
stress is different
from the primitive
estimation

著作権処理の都合で、この場所に挿入されていた『Goodman (1980), Introduction to RockMechanics, John Wiley and Sons, p. 106, Fig.
4.7b』
を省略させて頂きます。

Average initial horizontal stress,Goodman, 1980

Average initial horizontal stress
Lower limit of σHav (2.7 + 0.0081 h)Upper limit of σHav (40.5 + 0.0135 h)
0Depth (m)

200
400

σV

600
800
1000

0 10 20 30 40 50 60
Stress (MPa)

Average initial horizontal
stress = depth independent
value + depth proportional
value for 0.25 - 0.33 ofpoisson's ratio

Depth independent value?
Movement of the tectonic plates
Spherical shell subsidence modelTectonic plates

制限資料"Reprinted from http://pubs.usgs.gov/gip/earthq1/fig1.gifwith permission from USGS".

著作権処理の都合で、この場所に挿入されていた『Goodman (1980), Introduction to Rock Mechanics, John
Wiley and Sons, p. 107, Fig. 4.7』を省略させて頂きます。

Orientation of the maximum horizontal stress measured byhydraulic fracture method (Goodman, 1980)

Average focal
mechanism of deep
earthquakes in andaround Japan
projected on theupper hemisphere.
Arrows show
tension andcompression axes
(Kasahara, 1983)

著作権処理の都合で、この場所に挿入されていた『笠原慶一（1983） 地震の力学、鹿島出版会、p. 52, 図3.15』を省略させて頂きます。

Spherical shell subsidence model
The earth shrinks bygravity force.
Compressive strain
appears by the sphericalgeometry.

9.2 Method to measure initial stressNeed for initial stress measurement
Initial stress can roughly estimated by the primitive
methodMeasurement is required for precise values
Initial stress can be affected by such geological phenomena as fold,faults, intrusion of magma etc.

Method

Description

FeatureStress relief method

A borehole is drilled to desired depth. Aprobe is installed in the hole. Stressaround he probe is relieved by usually
overcoring.

Three dimensional stress state can be
estimated by one overcoring in mostmethods. It takes costs and time. There
are many results. The hole is drilledusually from a roadway.

Stress compensation method

Stress is relieved measuring displacement
or strain. Stress is applied until thedisplacement or strain recovers to thevalues before the stress relief. Necessarystress is regarded as initial stress.
A borehole is drilled from the groundsurface or a roadway. Initial stress isestimated from hydraulic fracturing data.

Measurement is usually carried out atrock surface. It is difficult to estimate
three dimensional stress state. Elastic
constants are not required to estimaterock stress.
Only horizontal stresses are usuallyestimated. It can be apllied up toseveral km deep. There are any results.

Methods using oriented core

Material tests in laboratory are carried out
for rock cores. Initial stress is estimatedfrom such data as stress-strain curves.

Results similar to other methods areoften
obtained
althoughthemechanisms are not well understood.

Method based
earthquake data

Orientation of initial stress is estimatedbased on the focal mechanism of fault
earthquakes.

Enormous data can be used although
the stress magnitude can't be estimated.

Hydraulic fracturing method

onfault

9.3 Stress relief methods

Stress relief method(1)

A borehole is drilled usuallyfrom a roadway. The borehole
should be longer than theroadway width to avoid areas
where stress concentrates.
A pilot hole is drilled from theborehole top.
A probe is installed in the pilothole.
Overcoring is carried out
measuring deformation and/orstrains.

(2)

(3)

(4)

Principle of stress relief method
No stress exists in the hollow cylinder formed byovercoring.
Magnitude of strain and/or deformation with overcoringare equal to that when the pilot hole is drilled under the
initial stress state with an inverted sign.
The strains and/or deformations can be obtained by analyticalmethods or numerical methods assuming an elastic medium.

Initial stress can be estimated by solving the simultaneousequations.

ExampleA rosette gage wasatacched to a rocksurface and overcoring
was carried out aroundthe gage. Representchange in strains of thegauges 1, 2 and 3 by E,
ν, σx, σy τxy.

32y1xOvercoring

σ α = σ x cos 2 α + σ y sin 2 α + 2τ xy cos α sin αExample of stress relief method
Conical bottom strainmethod (Sakaguchi et al.,1994)
著作権処理の都合で、この場所に挿入されていた『坂口清敏他、資源と素材. 110(4)[1994.04]資源素材学会、p. 332, Fig.
2』を省略させて頂きます。

著作権処理の都合で、この場所に挿入されていた『坂口 清敏 他、資源と素材. 110(4) [1994.04]資源素材学会、p. 333, Fig. 3 』を省略させて頂きます。

Sakaguchi et al., 1994

9.4 Hydraulic fracturingHydraulic fracturing method
Often used method.
Originally developed forwells for petroleum andgeothermal energy tomeasure stress and toenhance the prodcution
There are some cases inwhich hydraulic fracturing
is carried out from anexisted roadway.

FracturepPacker

Hydraulic fracturing
A borehole is drilled.
Packer and a water pipe isinstalled.
Water is injected measuring
pressure and flow rate.

FracturepPacker

Hydraulic fracturing
Water valve is closed after
breakdown which is a decrease ofwater pressure and represents that afracture appears at the borehole wall.
The pressure at the breadown iscalled pb.
Water is injected again.
Decrease of the slope of the waterpressure-time
curve
represent
reopening, namely, the fracture isopened again. The pressure at reopening is called re-openingpressure pr.
Injection is continued for a while
and then the valve is shut.Water
pressure will converge. The
converged pressure is called shut-inpressure ps.

Breakdownpbpr
Down-hole pressureps

Flow rate

TimeHydraulic fracturing
Packer etc. are removed andfracture orientation isobserved by a boreholecamera or impression packer.

Breakdownpbpr
Down-hole pressureps

Flow rateTime

Principle of hydraulic fracturing
Tangential stresses σA, σB at points A and B when internalpressure p acts to a circular hole under maximum principal
stress σH and minimum principal stress σh (pore pressure isignored for convenience).
σHA

σ A = 3σ h − σ H − p
σ B = 3σ H − σ h − pσhp
B

σ A = 3σ h − σ H − p
σ B = 3σ H − σ h − pPrinciple of hydraulic fracturing
σA is smaller than σB. A fracture

initiate and grows from point A
when the following criterion issatisfied.
T0 is tensile strength.

σHA

T0 ≤ −σ A = −3σ h + σ H + p
The following equation isderived for the breakdownpressure pb.

T0 = −3σ h + σ H + p bσhp
B

σ A = 3σ h − σ H − p
σ B = 3σ H − σ h − pPrinciple of hydraulic fracturing
Reopening occurs when thetangential stress at point A
becomes tensile.

0 ≥ 3σ h − σ H − pσHAConsequently, for reopeningpressure,

0 = 3σ h − σ H − p rσhp
B

Principle of hydraulic fracturing
It is said that shut-inpressure is roughly equal toσh.
σ h = psσHAσhpB

Procedure to estimate initial stress
Minimum principal stress is estimated from the shut-in pressure

σ h = psMaximum principal stress is estimated from the minimum principal
stress and the re-opening pressure.

0 = 3σ h − σ H − p r
Orientation of the maximum principal stress is equal to that of thefracture observed by a borehole camera or an impression packer.

Vertical fracture (left) and horizontal fracture(right)

Criterion for horizontal fracture
Vertical stress σv at borehole wall is
σv = σV − 2p

Criterion for horizontal fracture isσ v < 3σ h − σ H

Another method has to be used in he case where horizontal
fracture occurs.

More detail
Consideration on pore pressure and fracture mechanics（Nihon Kikai Gakkai, 1989)
Determination of three dimensional stress state based ondata from one borehole (Nihon Kikai Gakkai, 1989)
Statistical consideration (Shin & Okubo, 1999)
Estimation of initial stress measuring strains (Sato et al.,1999b、Itoh et al., 2001)
Detailed consideration on re-opening pressure (Ito et al.,1999b)

Example
Calculate breakdown, re-opening and shut-in pressures
for a rock mass whose tensile stress is 10 MPa.
Maximum and minimum horizontal stresses are 25 MPaand 20 MPa, respectively.

9.5 Methods using oriented cores

Estimation of initial stress from laboratory test on oriented cores (Ex.
Nihon Kikai Gakkai, 1989)
AE mehod (Lavrov, 2003)
DSCA method (Oikawa et al.,1995, Yamaguchi et al., 1991, Matsuki et al.,
1995)
DRA mehod
ASR method
Mehod utilizing P-wave velocity

Results similar to such reliable methods as stress relief method andhydraulic fracturing method are often obtained.
Principle is not well known. There are many points which should beclarified. For example, how long rock core maintain the stress memory
is not well known.

Example of DRA methodb3

Stress (MPa)40
Loading3020
10Unloading
000.1

0.2

Strain (10-2)

Stress-strain curves

Strain difference (10-6)

b360
40
2000

10203040

Stress (MPa)Strain difference function

9.6 Method based on fault earthquakes

Sign and amplitude of elastic wave from fault slip depends
on orientation to the observatory.
Compressional and dilatational wave can be observed for
P-wave, for example.

Compressional wave

Dilatational wave

Compression andtensile axes can beobtained by projecting
polarity of P-wave on
the direction ofobservatory.
Directions ofcompression andtension axes aresometimes regarded as
those of the maximum
and minimum principal
stress, respectively.

著作権処理の都合で、この場所に挿入されていた『笠原慶一（1983） 地震の力学、鹿島出版会、p. 52, 図3.15』を省略させて頂きます。

Compression and tension axes represents stress change due
to fault slip and their directions should not be always
coincides to those of initial stress. However, similar results
to stress relief method and hydraulic fracturing method areoften obtained.
The directions of initial stress can be easily estimated fromenormous fault earthquake data although the magnitude of
initial stress can't be estimated.

9.7 Other methods

Borehole breakout
Failure phenomena which areobserved at sidewall of
petroleum and geothermal wells
Failure zones of dog ear-shape
grow in the direction of theminimum principal stressInitial stress magntude can be
estimated from the shape of thefailure zone.
For detail, refer Brudy &Zoback (1999), Cuss et al.
(2003), Haimson & Lee (2004)

σHσhCore discing
Rock core breaks in amany discs when aborehole is drilled to ahigh pressure zone.
Relationship between
stress state and discshape is investigated(ex. Obara et al., 1998).
Initial stress state canbe roughly estimated.

Core discing which wasobserved at Kamaishi Mine

Other other otherCalcite twins （Kang et al., 1999）
Sub-crater of volcano (Karino and Murata, 1998）
Electric resistivity (Ito et al., 1999a）
etc.........................

9.8 Example result of initials stressmeasurement

Example of results at Ikeshima Coal Mine. Depth is 416 m.