1

Estimation of regional stress state and

Young’s Modulus of ground at Torigatayama

limestone mine in Japan

J. Kodama Hokkaido University, Sapporo, Japan

T. Sasaki Sapporo City hall, Sapporo, Japan

D. Fukuda Hokkaido University, Sapporo, Japan

K. Kaneko Horonobe research institute for the subsurface environment,

Horonobe, Japan

Y. Fujii Hokkaido University, Sapporo, Japan

R. Kudo Nittetsu Mining Co., Ltd., Tokyo, Japan

2

Limestone deposits in Japan

• More than 150 limestone mines in operation in 2013

Shikagoe

Hachi-nohe

Garo

Shiriya

Kitagami

Bukoh-zan, Okutama

Abukuma

Kochi Tsukumi

Kumamoto

Hiraodai, Tagawa

Akiyoshi Kuzuu

Atetsu, Taishaku

Akasaka, Ibuki,

Fujiwara

Ome, Tomi

Motobu

Geological age ◆ Mesozoic

● Paleozoic

■ Mesozoic - Paleozoic

Okinawa

Sapporo

Tokyo Kyoto

Fukuoka

3

Domestic production and export

• 150Mt between 1980 and 2013 (Exported to Australia)

• Continue for the next 100 years

1980 1985 1990 1995 2000 2005 20100

50

100

150

200

250

Production Export

Year

An

nu

al

pro

du

cti

on

an

d e

xp

ort

(M

illi

on

to

n)

4

Rock slopes at mine closure

• Height of some will exceed 400 m (Highest is more than 550 m)

• The stability assessment of rock slopes is one of important issues

0 100 200 300 400 500 6000

30

60

90

Slope height (m)

120 slopes in 60 mines

Av

era

ge s

lop

e a

ng

le (

deg

ree)

5

Bukoh mine

6

Concept of slope stability assessment

Slope failure must be prevented

Early detection of unstable state is important

for effective countermeasure

Rock slope is deformed elastically due to mining

Health checkup of a rock slope

Monitoring of slope behavior

Elastic deformation (behavior)

Monitoring

Stable

7

Estimation of elastic deformation

Elastic deformation strongly depends on Young’s modulus and Poisson’s ratio Regional stress

We have proposed a estimation method of them By a back analysis for displacement measurement

Reliability of the proposed method has not

sufficiently cleared.

8

Objectives

The proposed method is applied to Torigatayama limestone mine, Japan

Surface displacement measured with GPS was analyzed

Regional stress and Young’s modulus of the ground are estimated

Reliability of the estimation is discussed

9

Excavation

Mining induced deformation

Due to excavation

GPS station

GPS station

10

GPS station

GPS station

Dumping site

Mining induced deformation

Waste hauling

11

Due to dumping

Mining induced deformation

Dumping site

GPS station

GPS station

12

Mining induced deformation

GPS station

GPS station

Change in regional strain

Change in regional strain

Due to change in regional strain and rigid rotation

Due to excavation

Due to dumping

GPS measurement

Back analysis

Regional s stress state Young’s modulus

13

GPS measurement Estimated by

numerical analysis

Estimated by

numerical analysis

Estimated by

numerical analysis

Estimated by regional

displacement measurement

by GPS

),,;(),,;( 00000

00 EgtEgttE

E

G xuxu ⊿

),;(),;(

),;(),;(

),;(),;(

00

000

00

000

00

000

xyxy

xy

Gxy

yyyy

yy

Gyy

xxxx

xx

Gxx

ttt

ttt

ttt

XYXY

YY

XX

xuxu

xuxu

xuxu

⊿

⊿

⊿

　

　

　

)(xuDue to gravity

release

Due to horizontal

stress release

Unit value

最小二乗法

Estimation of Young’s modulus of ground and regional strain state

Due to excavation

Due to dumping

Due to change in regional strain state

Due to rigid rotation

Depend on

Young’s modulus Independent of

Young’s modulus

　ω　

　

　

　

⊿

⊿⊿

⊿⊿

⊿⊿

)~,~(

);(

);(

);(

0

0

0

xyt

ttt

ttt

ttt

G

xy

G

xy

G

yy

G

xx

XY

Y

X

,

,

,

xu

xu

x u

),',;(),',;( 000

00 EgtEgttE

E DD

G xuxu ⊿

Ground displacement at when

gravity is applied to a model for

after excavation state at

is unit Young’s modulus

tt ⊿0

g

0E

x

),,;(),,;( 000000 EgtEgtt xuxu ⊿

Displacement obtained from gravity field analysis

0t

Ground displacement at when

gravity is applied to a model for

before excavation state at

is unit Young’s modulus 0E

gx

14

Estimation of change in distance

• Change in distance (expansion or contraction) between two points of m and n

• Displacement due to rigid rotation can be canceled

)(mnr : Unit vector of the line m-n

)()(),( )()()()()( nmmnnm rxxs xuxu

m

n

r (mn)

u(x(m))

u(x(n))

15

Estimation of regional stress

G

xy

G

xy

G

yy

GG

xx

GG

yy

G

yy

GG

xx

GG

xx

c

c

c

2

1

1

])1([

])1[(

)21)(1(1 GG

GEc

)1(22 G

GEc

16

Torigatayama mine

• One of the largest limestone mine in Japan

• Annual production rate is approximately 10 million ton

3km

1km

17

Rock slope in Torigatayama mine

・1ベンチ高さ15m

・最終残壁予想高さ400m

鳥形山最終残壁予想図

400m

Slope height will reach in excess of 400 m for another 100 years

At present At mine closure

150m

18

Displacement measurement by GPS

6 stations were set up in 1999 Differential positioning method Data were recorded twice a day over 3 hours at a rate of 30 s Stations 1 and 2 were relocated to 1’ and 2’ in 2003 Station 5 was removed in 2006 for mining Data at same time on June 30th every year were used

to eliminate affects of the annual variation

19

Relative displacements of GPS stations

• Reference point is GPS3

• Direction was nearly unchanged

x

y

TN

(c) GPS6

GPS5

-10 0 100

10

20

x (mm)

y (

mm

)

GPS5

1999

2001

2003

2006

GPS4

0 10 20 30 40 50

0

10

x (mm)

y (

mm

)

GPS4

19992001

20032006

2008

2011

0 10 20 30 40-30

-20

-10

0

x (mm)

y (

mm

)

GPS61999

2001

2003

2006

2008 2011

GPS6

20

The change in distance

Unit: mm

From 1999 to 2003

GPS1

GPS2

GPS3

GPS4

GPS5

GPS6

8.4

0.4 14.6

3.4

1.1

-2.9

-8.2

-10.9 -2.5 -0.4

-17.9

-16.4

-11.4 -12.9

-0.8

Unit: mm

From 2003 to 2006

GPS1’

GPS2’

GPS3

GPS4

GPS5

GPS6 11.6

-25.9

10.5

-4.8

-11.9 -14.6

-10.9 8.8

3.4 -16.6

-14.5

-8.5 -12.1

-3.9

-1.7

Unit: mm

From 2006 to 2011 GPS1’

GPS2’

GPS3

GPS4

GPS6

7.8

-9.6

-8.9 -3.5

10.0

1.7

-3.5 -2.5

-8.5

9.9

21

GPS measurement

),,;(),,;( 00000

00 EgtEgttE

E

G xuxu ⊿

),;(),;(

),;(),;(

),;(),;(

00

000

00

000

00

000

xyxy

xy

Gxy

yyyy

yy

Gyy

xxxx

xx

Gxx

ttt

ttt

ttt

XYXY

YY

XX

xuxu

xuxu

xuxu

⊿

⊿

⊿

　

　

　

)(xuDue to gravity

release

Due to horizontal

stress release

Unit value

Estimation of Young’s modulus of ground and regional strain state

Due to excavation

Due to dumping

Due to change in regional strain state

Due to rigid rotation

　ω　

　

　

　

⊿

⊿⊿

⊿⊿

⊿⊿

)~,~(

);(

);(

);(

0

0

0

xyt

ttt

ttt

ttt

G

xy

G

xy

G

yy

G

xx

XY

Y

X

,

,

,

xu

xu

x u

),',;(),',;( 000

00 EgtEgttE

E DD

G xuxu ⊿

22

Estimation of regional strain rate

• GPS data from the earth observation network system(GEONET) • Average strain rate between 1999-2011 was analyzed

-2.36×10-7

+0.30×10-7

48.9°

Region I

-3.37×10-7

+0.58×10-7

49.3°

Region II

8

7

7

19

1078.1

1063.1

1008.2

)(1010.2

xy

xy

yy

xx y

ω

γ

ε

　　ε

8

7

7

18

1071.7

1046.2

1094.2

)(1051.1

xy

xy

yy

xx y

ω

γ

ε

　　ε

Analytical region

RegionⅡ

RegionⅠ X

Y

23

GPS measurement

),,;(),,;( 00000

00 EgtEgttE

E

G xuxu ⊿

),;(),;(

),;(),;(

),;(),;(

00

000

00

000

00

000

xyxy

xy

Gxy

yyyy

yy

Gyy

xxxx

xx

Gxx

ttt

ttt

ttt

XYXY

YY

XX

xuxu

xuxu

xuxu

⊿

⊿

⊿

　

　

　

)(xuDue to gravity

release

Due to horizontal

stress release

Unit value

Estimation of Young’s modulus of ground and regional strain state

Due to excavation

Due to dumping

Due to change in regional strain state

Due to rigid rotation

　ω　

　

　

　

⊿

⊿⊿

⊿⊿

⊿⊿

)~,~(

);(

);(

);(

0

0

0

xyt

ttt

ttt

ttt

G

xy

G

xy

G

yy

G

xx

XY

Y

X

,

,

,

xu

xu

x u

),',;(),',;( 000

00 EgtEgttE

E DD

G xuxu ⊿

24

3-D finite element model

Magnified view of

the mining area

X

Z

Y

11.5 km

2.6 km

4.3 km

Homogeneous, isotropic and elastic Poisson’s ratio is varied between 0.00 and 0.35

Node：1,273,561

Element：1,580,955

Model for 1999

25

Models for mining area

(a) June 1999

(b) June 2003

(c) June 2006

(d) June 2011

L22

0

L190

L220

(b) June 30th,

2003 L330

X

Y

(b)

2003.6

.30

L2

35

L2

05

(a) June 30th,

1999

L330

L2

50

L265

L2

20 L2

50 X

Y

L22

0

L175 L250

L190

L330

L205

L265

(c) June

30th, 2006

2006.6.30

X

Y

L17

5

L19

0 L22

0

L25

0

X

Y

(d) June

30th, 2008

2006.6.30

26

Change in estimation

Little significant change was observed from 2008 Reliability of estimation increases as mining progresses

Contraction

Extension

2000 2004 2008 2012-20

-10

0

10

20

-10

0

10

20

30S

train

(x10

-4)

Year

EG

εGxx

εGyy

γGxy

Young's

modulu

s (G

Pa)ν = 0.10

27

Estimated Young’s modulus and regional strain

Poisson’s ratios less than 0.10 are reasonable Estimated Young’s modulus is between 5 and 10 GPa

Contraction

Extension

0 0.1 0.2 0.3 0.4-20

-10

0

10

0

5

10

15

Str

ain

(x

10

-4)

Poisson's ratio

EG

εGxx

εGyy

γG

xy

Yo

ung

's m

od

ulu

s (G

Pa)

1999 - 2011

28

Estimated regional stress

= 0.00

E = 6.1 GPa

ν=0.10

E = 2.6 GPa

= 0. 05

E = 4.6 GPa

-6.39

-2.30

16.9°

-5.24

-0.42

30.8°

-4.40

+0.62

33.2°

Unit: MPa

29

Estimation of regional strain rate

• GPS data from the earth observation network system(GEONET) • Average strain rate between 1999-2011 was analyzed

-2.36×10-7

+0.30×10-7

48.9°

Region I

-3.37×10-7

+0.58×10-7

49.3°

Region II

8

7

7

19

1078.1

1063.1

1008.2

)(1010.2

xy

xy

yy

xx y

ω

γ

ε

　　ε

8

7

7

18

1071.7

1046.2

1094.2

)(1051.1

xy

xy

yy

xx y

ω

γ

ε

　　ε

Analytical region

RegionⅡ

RegionⅠ X

Y

30

Discussion • Estimation by seismological

technique (Kochi Earthquake Observatory, Japan 1986).

• Maximum compressive direction in 23km depth was between E-W and ENE-WSW

Maximum compressive direction of strain rate was between NW-SE between 1999 and 2011.

N

S

E W

Maximum compressive direction by the proposed method is close to that by seismological technique.

Maximum compressive

direction

31

Discussion

• The proposed method tends to estimate not recent strain increment but total amount of regional strain stored in shallow crust.

N

S

E W

32

The regional strain and stress states and elastic

constants in the district surrounding the Torigatayama

mine in Japan were estimated by a back analysis for

GPS data.

Reliability of the estimation has been improved with an

increase in displacement due to mining progression.

The proposed method tends to estimate total amount of

regional strain stored in shallow crust.

The method can provide a useful basis for predicting

mining-induced deformation and clarifying the effect of

regional stress on rock slope stability.

Conclusions

33

Thank you for

your kind attention

34

35

-13.3×10-6

+0.85×10-6

8.0°

36

GPS

measurement

Estimated by gravity 重力場解析

により得られる

採掘変位

広域ひずみ場解析

により得られる

採掘変位

ずり堆積の解析

により得られる

変位

広域ひずみ場解析

により得られる

広域ひずみの変化に伴う変位

GPS座標値から求まる岩盤の回転変位 　ω　

　　

　　

　　

⊿

⊿⊿

⊿⊿

⊿⊿

)~,~(

),;(

),;(

),;(

000

000

000

xyt

ttt

ttt

ttt

Gxy

xy

xy

Gxy

yy

yy

Gyy

xx

xx

Gxx

XY

Y

X

xu

xu

xu

),,;(),,;( 00000

00 EgtEgttE

E

G xuxu ⊿

),;(),;(

),;(),;(

),;(),;(

00

000

00

000

00

000

xyxy

xy

Gxy

yyyy

yy

Gyy

xxxx

xx

Gxx

ttt

ttt

ttt

XYXY

YY

XX

xuxu

xuxu

xuxu

⊿

⊿

⊿

　

　

　

),',;(),',;( 000

00 EgtEgttE

E DD

G xuxu ⊿

)(xu

逆解析

Displacement due to gravity release

広域ひずみに起因する岩盤変位

参照値

最小二乗法

地盤ヤング率・広域ひずみ・広域ひずみ速度を同定

採掘に伴う岩盤変位

ずり堆積

に伴う岩盤変位

広域ひずみ速度に起因する岩盤変位

回転速度に 起因する 岩盤変位

ヤング率に依存

広域ひずみに依存

ヤング率に依存しない

),,;(),,;( 000000 EgtEgtt xuxu ⊿

期間 において、

採掘後にあたる の解析

モデルに対して、ヤング率を とし、

単位体積重量 を作用させた時の

点 における岩盤変位

tt ⊿0

ttt ⊿～ 00

g

0E

x

期間 において、

採掘前にあたる の解析

モデルに対して、ヤング率を とし、

単位体積重量 を作用させた時の

点 における岩盤変位

0tttt ⊿～ 00

g

0E

x

重力場解析に得られる採掘変位

37

GPS measurement Estimated by

numerical analysis

Estimated by

numerical analysis

Estimated by

numerical analysis

Estimated by regional

displacement measurement

by GPS

),,;(),,;( 00000

00 EgtEgttE

E

G xuxu ⊿

),;(),;(

),;(),;(

),;(),;(

00

000

00

000

00

000

xyxy

xy

Gxy

yyyy

yy

Gyy

xxxx

xx

Gxx

ttt

ttt

ttt

XYXY

YY

XX

xuxu

xuxu

xuxu

⊿

⊿

⊿

　

　

　

)(xuDue to gravity

release

Due to horizontal

stress release

参照値

最小二乗法

Estimation of Young’s modulus of ground and regional strain state

Due to excavation

Due to dumping

Due to change in regional strain state

Due to rigid rotation

Depends on

Young’s modulus Independent of

Young’s modulus

　ω　

　　

　　

　　

⊿

⊿⊿

⊿⊿

⊿⊿

)~,~(

),;(

),;(

),;(

000

000

000

xyt

ttt

ttt

ttt

Gxy

xy

xy

Gxy

yy

yy

Gyy

xx

xx

Gxx

XY

Y

X

xu

xu

xu

),',;(),',;( 000

00 EgtEgttE

E DD

G xuxu ⊿

Ground displacement at when

gravity is applied to a model for

after excavation state at

is unit Young’s modulus

tt ⊿0

g

0E

x

),,;(),,;( 000000 EgtEgtt xuxu ⊿

Displacement obtained from gravity field analysis

0t

Ground displacement at when

gravity is applied to a model for

before excavation state at

is unit Young’s modulus 0E

gx