8. Rock mass‡：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。

Rock mass?
原典不明

Rock or stone (diamondore)

Rock mass (Suburb of Mudgee,Australia)

Numerous discontinuities!

Rock mass (Suburb of Mudgee, Australia)

Tuff breccia slope at Oshoro

8.1 Classification of discontinuities

Rock mass contains
discontinuities(fractures)
No slip: joints
Slip: faults

Fault and unconformity at
Sunago Coal Mine inMikasa and Bibai,
Hokkaido, Japan（May 11,1998, Prof. Emeritus
Ishijima is standing right
low part)

Discontinuity is not so small that it can be seen by nakedeye.
Roughly speaking, there are many discontinuities in hardrock mass and less discontinuities in soft rock mass.
Behavior of rock mass consisted of hard rocks often
significantly ruled by physical properties of discontinuities.

Classification of faults

Right lateral

Sectional view of a normal fault (it is called a lag if the dip is less than 45o)

Left lateral
Sectional view of a reverse fault (it is called a thrust if the dip is less than 45o)Plan view of a strike-slip fault

8.2 Quantity and orientation of discontinuities

Scan line method (Priest and Hudson, 1981)
A scan line is written on the surface of a rock mass.
Number of discontinuities which cross the scan line per 1 m of scanline
is calculated to represent density of dicontinuities.
Results depend on the orientation of the scanline.

Length and orientation are measured for a more precise analysis.

Discontinuities

Scan lineOther representations
Number of discontinuities per unit area (m-2)
Total length of discontinuities per unit area (m/m2)

Example
5B

4y (m)Calculate density of
discontinuity （m-1）
along the scan lines Aand B, respectively,by using the scan line
method.
Calculatediscontinuity density
as number of
discontinuities per 1m2.

A

32
100

123x (m)45

RQD（Rock Quality Designation）
Total length of rock cores whose lengths are more than
twice the diameter (ex. 5 cm) is calculated. RQD is
obtained as percentage of the total length (ex. 1 m) to a
specified length.
RQD is originally defined as percentage of the total length of rockcores whose lengths are more than 4 in. to a 60 in. part.

Example of rock core from Kushiro Coal MineExample
Calculate RQDfrom the photoshown rightwhich are rockcores from apilot boring at Atunnel

著作権処理の都合で、この場所に挿入されていた『Deere, D. U., (1967), AIME, pp.
237-302、 p.252, Fig. 6一部修正』を省略させて頂きます。

RQD = 110.4 − 3.68λ
RQD = 115 − 3.3λRelationship between RQD
and discontinuity density.
Upper:(1981).

Priest&Hudson

Lower: ISRM (1978)

Discontinuity density (ft-1)
Relationship between discontinuity density
and RQD （Deere et al., 1967）

where λ is discontinuity
density (m-1) or an inverse ofaverage
spacingofdiscontinuities (m).

Utilization of RQD
Rock mass clasification
A close relathionshp between RQD and roadway
deformationEx. Bolted roadway in Taiheiyo Coal Mine

Related to Young's modulus of rock mass （Zhang &Einstein, 2004）

Fracture coefficient (Ikeda, 1967）⎛V ⎞K = ⎜⎜ F ⎟⎟⎝ VL ⎠2

VF is P-wave velocity of rock mass, VL is that of an intact
rock specimen.
A small K represents high discontinuity density.

Application of the fracture coefficient
Young's modulus of rock mass used in a numericalanalysis for tunnel design is sometimes assumed as follows
E ′ = KEE ′ : Young' s modulus of rock mass
E : Young' s modulus of intact rock specimen

Orientation of discontinuity
NStrikeEx.
Strike: N30W（=S30E）

EW

Dip: 45SW(a) Plan view

Strike and dip:
N30W45SW

S

Horizontal plane
Dip
Discontinuity(b) Sectional view

Stereo projection
Orientation of a normal of a plane can be
represented by a point on Wulff net by the lower
hemisphere stereo projection technique
Ex. N50E45NWN

θ/2WESθPoint denoting normal
Normal

NN

θ/2EW

WES

θ

Point denoting normal
NormalSThe hatched plane is draw as the right figure

Example for the case where strike is NS
Strike: NS
Dip: 0Zenith

W

Strike: NS
Dip: 30W

E

ZenithW

E

Sectional view
Downward
Plane
normalBottom

BottomNN

W

Lower hemisphere
stereo projection

ES

W

E

S

Vector isrepresented
by a point

A plane isrepresented bya great circle

When we want to represent an upward direction.
ZenithWESectional view

BottomNW

Lower hemisphere
stereo projection

ESCoordinate of the point
representing a point
Strike φ, dip θ、radius r.
x 、y toward E, N,
respectively.

x = r tan

2y = r tan

NStrikeθN

θ/2EW

cos φθ
2S

θPoint denoting normal
Normalsin φNE
W(a) Plan view

WS

E

Horizontal plane
Dip
Discontinuity(b) Sectional view

SApplication of stereo projection
Analysis of joint sets, joints
which orientations are similar
with each other.
Orientation of principalstresses
Analysis of rock slope failureNGroup 2Group 1WE

θ = 30oθ = 60oGroup 2S

θ = 90o8.3 Strength of discontinuityτ ≤ C + σ tan φσ ≥ −T0τ and σ is shear and normal stress acting on discontinuity,
respectively, C is cohesion, φ is friction angle, T0 is tensile
strength.
Cohesion and friction angle is said to be 0～7 MPa and 27～35°, respectively (Yamaguchi and Nishimatsu, 1991)
Tensile strength of discontinuity is considered nearly zero
without detailed research.

Plane shear test
Normal loadDiscontinuity

Shear load

Plane shear test is often carried out to investigate shear strength ofdiscontinuity
It is difficult to use a natural discontinuity
Rapture plane by splitting is regarded as discontinuity in most cases.

Plane shear test
Load-shear
displacement curve
A strain-softening
behavior due tolocking between
discontinuities

著作権処理の都合で、この場所に挿入されていた図表を省略させて頂きます。

Normaldisplacement
Similar to dilatancy

Shear test for a rapture plane bysplitting

8.4 Deformation and strength of rock mass

Deformation behavior of rock mass is significantly
affected by discontinuities
The behavior is clearer for rock mass consisted of hard rock.

Young's modulus for in-situ rock massis smaller than that for an intact rock specimen.
is estimated based on
The product of the Young's modulus of an intact specimen and thefracture coefficient is sometimes used as Young's modulus of rockmass (Ex. Nihon Tetsudo Kensetsu Kodan, 1996)
Young's modulus of rock mass is estimated based on RMR which will
be described later (Okabe et al., 2000 in Japanese)
Borehole jack test
Jack test

Borehole jack test
Borehole wall

Young's modulus isevaluated from loadand displacement ofborehole wall whensteel platens arepressed against theborehole wall.

PlatenJack test
Young's modulus of rockmass is evaluated fromload and displacement
when a pair of surfaces
are pressed.

MortarPlatenRoadway
Hydraulic Jack

PlatenExample of strength of rock mass having a
discontinuity
Cohesion of discontinuity is zero.
It is assumed for convenience that friction angle ofdiscontinuity and intact rock mass is equal.
Intact rockmass (1)
⏐τ⏐

σ1

φ

Intact rockmass (2)θσ3Discontinuity

C12θ 2
Discontinuity

C2

σσ32θ 1

σ1

When cohesion is C1
Rock mass itself does
not failure
Discontinuity slips
when θ 1 ≤ θ ≤ θ 2
In a special case, itslips when σ3 = 0 andθ≥φ

Intact rockmass (1)⏐τ⏐φIntact rockmass (2)When cohesion is C2
Rock mass failures
C1
Discontinuity does not
slip when θ ≤ θ 1 or θ ≥θ 2, namely, rock mass C2
failures but
discontinuity does not
slip.

2θ 2
Discontinuity

σσ3

2θ 1

σ1

In-situ shear test
A rock block whose height
and area is 30 cm and 0.36 1.5 m2, respectively, is shapedfrom the rock floor.
Horizontal load is increased
under a constant normal load
until the specimen shows
shear failure
Stress is not uniform
Strength of in-situ rock masscan be roughly obtained

In-situ tension test (Takada etal, 2000)
In-situ triaxial test (Tani,2005)

Vertical load
Specimen
Horizontal load

8.5 Rock mass classification

Material tests of rock is important as basic data indesigning rock structures.
However, mechanical behavior of rock mass is affected bydiscontinuities.

Rock mass classification
Classification of rock mass from engineering view points.
There are several methods
Rock mass classification is carried out at an designing stage.
Data for classification should be obtained through surface
investigation and borehole measurement

Rock massclassification fortunnels (JSCE,1996)

著作権処理の都合で、この場所に挿入されていた図表を省略させて頂きます。

RMR (Rock Mass Rating, Goodman, 1980 )Rock mass classification for underground mining
Score for compressive strength
Score for RQD
Score for joint spacing in the most influencing orientation
Score for condition of the joint
Score for water
Score for joint orientation
Rock mass is classified according to the total score

Compressive strengthUCS (MPa)> 200
100 - 200
50 - 100
25 - 50
10 - 25
3 - 10<3Rating
151274210RQD
RQD (%)

Rating91 - 100

2076 - 90

1751 - 75

1325 - 50

8< 253

Joint spacing in the most influencing
orientation
Joint spacing (m)Rating>330

1-3

250.3 - 1

200.005 - 0.3

10< 0.005

5

Condition of joint
Description

RatingVery rough surfaces of limited extent; hard wall rock25

Slightly rough surfaces; aperture less than 1 mm; hard wall rock20

Slightly rough surfaces; aperture less than 1 mm; soft wall rock

12Smooth surfaces, OR gouge filling 1 - 5 mm thick, OR aperture of 1 5 mm thick; joints extend more than several times

6Open joints filled with more than 5 mm of gouge, OR open more than
5 mm; joints extend more than several meters0Water inflow
Inflow per 10 mtunnel length (l/ min) OR

Joint water pressure divided
by major principal stress ORGeneral condition

RatingNone0

Completely dry10< 250.0 - 0.2Moist

725 - 1250.2 - 0.5

Water undermoderate pressure4> 1250.5

Severe water
problems0Joint orientation
Assessment of influence of orientationon the work

Ratingtunnels

incrementfor

Ratingincrements
foundations

Very favorable

00Favorable-2-2

Fair-5-7

Unfavorable-10-15

Very unfavorable-12-25forClassification
RMR (sum of rating increments from theabove tables)

Class

Description of rock mass

81 - 100

I

Very good rock61 - 80

IIGood rock41 - 60

III

Fair rock21 - 40

IV

Poor rock0 - 20V

Very poor rock

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 Mechancs,
John Wiley and Sons, p. 239, Fig. 7.13』を省略させて頂きます。

Application of RMR for estimation of unsupported span (Goodman, 1980)

Example
Classify a moist rock mass whose uuniaxial compressive
strength is 60 MPa, RQD is 52%, joint spacing is 50 cm,
jint orientation is very favorable, joint aperture is 2 mm.
Answer: III、Fair rock

8.6 Permeability of rock massPermeability （m2）

RockPorosity

Laboratory

In-situ

Sandstone*
Navajo sandstone*
Berrea sandstone*
Graywacke*
Rodessa sandstone**
Wilcox sandstone**
Shale*
Pierre shale*

3 × 10−12 to 8 × 10−17
2 × 10−124 × 10−14
3.2 × 10−17
3.3 × 10−13
1.9 × 10−13
10−18 to 5 × 10−22
5 × 10−21

1 × 10−12 to 3 × 10−17

Limestone, dolomite*
Salem limestone*
Indiana limestone***Elenberger dolomite**
Hugoton dolomite**
Basalt*10−14 to 10−22
2 × 10−15
4 × 10−15
1.3 × 10−12
1.4 × 10−14
10−21

10−12 to 10−16

Granite*10−16 to 10−20

10−13 to 10−18

Schist*10−17

2 × 10−16

Fissured schist*

1 × 10−13 to 3 × 10−13

Hyaloclastite
Toyohama hyaloclastite****1.1 × 10−13 to 1.3 × 10−13

10−17 to 10−20
2 × 10−18 to 5 × 10−20

30.2%
17.5%

12.2%
5.4%
13.5%
10−11 to 10−1622%

Permeability of rock mass is significantly affected by discontinuities.
Permeability of an intact rock specimen and that of rock mass are different
with each other in most cases

Measurement of permeability of rock mass
Lugeon test
Vacuum air test (Yamada et al., 1999)

Lugeon test
A part of drill hole isshielded by a pair ofpackers
Water pressure is applied
to the part
Water pressure and water
inflow are recorded

Bourdon gage
Water pumpflow meter

PackerPressurized partEvaluation of hydraulic conductivity
Lugeon value

Lu =10 QPl

Q：Water inflow (l / min)
P：Water pressure (kgf / cm2, 10 kgf / cm2 is standard)l：Length of the pressurized part (m, 5 m is standard）

Hydraulic conductivity (cm/s)lR
k=1000 × 60 × 2π
Lu ln

R：Radius of drill hole (m)8.7 Failure of rock mass

Conventional concept:
conjugate shear planes
Recent concept: fractures which
are parallel to the free surface
Sheeting joint at V-shaped valley ofPonbetsu River in Ikushunbetu, Mikasa.

Yield zone