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11
Naruki WakabayashiShimizu Corporation Tokyo Japan
Study on the Jointed Rock Mass forStudy on the Jointed Rock Mass for the Excavation of Hyper-KAMIOKANDE Cav the Excavation of Hyper-KAMIOKANDE Cav
ern at Kamioka Mineern at Kamioka Mine
NNN07 Hamamatsu, Japan 3-5 October 2005
22
Topics ・ Previous Geological Survey and Stability Analysis for the Hyper-K cavern ・ Site Selection ・ Isotropic Elastic FEM Analysis for the Investigation of Cavern Shape, Size and Type
・ Ongoing Investigation and Analysis for Jointed Rock Mass ・ Investigation of Joint Orientation ・ Obtaining In-Situ Rock Joints and Investigation of Joint Mechanical Properties ・ Pull-out Test of Two Types of Cable Bolt ・ Two Type Analysis for Consideration Joint Effects
33
Mozumi mine
Tochibora mine
Proposed Area
Kamioka Mine Location
Kamioka Mine
Hamamatsu
Tokyo
Super-K
Proposed Area in Mozumi Mine is about 10km South from the Super-Kamiokande.
Site Selection
44
Hyper-K Hyper-K proposed Siteproposed Site
HornblendeHornblendeBiotite GneissBiotite Gneiss& Migmatite& Migmatite
Biotite GneissBiotite Gneiss
LimestoneLimestone
”” AN
KO
” Fa
ult
AN
KO
” Fa
ult
”” 240
240
゜゚- M
E” F
au
lt- M
E” F
au
lt
””NAMARI” FaultNAMARI” Fault
Skarn OreSkarn Orebody Zonbody Zonee
Core BoringCore Boring
ExistingExistingTunnelTunnelSurveyedSurveyed
Geological Map of Proposed Siteat Tochibora Mine Plan View of + 550mEL
N
Proposed Site Formation is Hornblende Biotite Gneiss and Migmatite.
55
18m
42m
60m
ƒÓ 60m (r=30m)
Cylindrical Dome Larger than Super-K Huge Tunnel
Comparison of the Hyper-K Cavern from Various View PointsMultipleDomes
Single TunnelTwo Parallel
Tunnels
× ○ ○
△ △ ○
○ × ○
× ○ △
◎ ○ ○
× △ ○ Height 60.0 54.0 54.0 Width Φ 60 48.0 48.0 Length - - - 500 250
3,368 2,076 2,076152,600 1,038,000 519,000
7 1 21,068,200 1,038,000 1,038,000 Total Volume of Caverns (m3)
Size of oneCavern (m)
Cost Performance of Detector Tank
Construction Period & Cost
Cavern Stability
Total Evaluation
Observation during Maintenance
Early Observation Startup
Cavern Type
Vertical Cross Section Area (m2) Volume of one Cavern (m3) Required No. of Caverns
Two Parallel TunnelsIsotropic Elastic FEM Analysis
Image Design of Two 250m Long Parallel Tunnels
Spacing
Spacing
Offset
Offset
””NAMARI” FaultNAMARI” Fault”” AN
KO
” Fau
ltA
NK
O” F
ault
”” 240°-ME
” Fau
lt240°-M
E” F
ault
66
Summary of Previous StudySite Selection : Tochibora Mine, +480mEL~+550m EL is the most appropriate location with very competent rock condition.Cavern Design: Two 250m Long Parallel Tunnels with Section of 2,076m2 are capable of being safely excavated.Cavern Layout : Two Parallel Tunnels as above should be Located with 80m –100m Spacing and 50m-100m Offset to avoid the poor Zone of Surrounding Faults.
In Isotropic Elastic FEM Analysis of Previous Study, Young’s Modulus was empirically decreased as Jointed Rock Mass.It is Important and Necessary to Consider Numerically the Influence of Joint Orientation and Mechanical Properties.
77
Analysis for Jointed Rock Mass
Anisotropic Young’s Modulus Considering Joint Orientation and Mechanical Properties
Composition of Elastic Blocks Surrounding Joints
Equivalent Continuum Analysis
Discontinuous Analysis
Damage TensorCrack Tensor
Key BlockDistinct Element
Method (DEM)
・ Characteristics of Joint Orientation・ Mechanical Properties of Joint and Rock Core・ Mechanical Properties of Support such as Cable Bolt
88
Investigation of Jointed Rock Mass
B-ⅡB-Ⅰ
B-ⅡB-Ⅲ
B-Ⅳ
D-Ⅴ
C-Ⅳ
C-Ⅲ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
C-Ⅲ
B-Ⅲ
B-Ⅳ
C-Ⅳ
B-Ⅰ
B-Ⅰ
B-Ⅱ
B-Ⅱ
B-Ⅰ
B-ⅡB-Ⅰ
B-Ⅱ
B-Ⅰ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅲ
B-Ⅲ
D-Ⅳ
B-Ⅱ
C-Ⅳ
B-Ⅲ
B-Ⅱ
B-ⅡB-Ⅲ
B-Ⅲ
B-Ⅱ
B-Ⅱ
B-Ⅲ
C-Ⅳ
B-ⅡB-Ⅲ
B-Ⅱ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅱ
B-ⅡB-Ⅲ
B-Ⅲ
B-Ⅳ
B-Ⅳ
-200
+200
- 200
+100
0
-200
- 100
Ap
Ap
Ap
Ap
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
70
70
70
75
80
Ao
Ap
Ap
Ap
Ap
Ap
Ap
ApAp
Ap
Ap
ApAp
Ap
Ap
Ap
ApAp
Ap
85
75
80
85
80
80
70
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
Ap
Ap
Ap
Ap Ao Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
AoAo
AoAo
AoAo
Ao
AoAo
Ao
Ao
Ao
Ao
Ao
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
60
S70E
240°目断層
~~
~~
~~
~
300
220
230
240
250
260
270
280
290
310
320
330
340
350
360
370
380
390
400
210
200
190
140
150
160
170
180
110
120
130
100
90
80
70
60
50
40
30
20
10
0
調査終了点
調査開始点
大規模地下空洞立地可能性調査400m 1:300坑道調査( )縮尺
凡例
伊西岩角閃石片麻岩スカルンアプライト緑泥石化片麻岩片理面
割れ目
滴水あり
岩盤分類凡例
B B- B-( Ⅰ、 Ⅱ)
CH B- C-( Ⅲ、 Ⅱ)
CM B- C-( Ⅳ、 Ⅲ)
CL D- C- C-( Ⅲ、 Ⅳ、 Ⅴ)
D D- D-( Ⅳ、 Ⅴ)
AP
Ao
巻末資料3岩盤分類図
B-ⅡB-Ⅰ
B-ⅡB-Ⅲ
B-Ⅳ
D-Ⅴ
C-Ⅳ
C-Ⅲ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
B-Ⅲ
C-Ⅲ
B-Ⅲ
B-Ⅳ
C-Ⅳ
B-Ⅰ
B-Ⅰ
B-Ⅱ
B-Ⅱ
B-Ⅰ
B-ⅡB-Ⅰ
B-Ⅱ
B-Ⅰ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅱ
B-Ⅲ
B-Ⅲ
D-Ⅳ
B-Ⅱ
C-Ⅳ
B-Ⅲ
B-Ⅱ
B-ⅡB-Ⅲ
B-Ⅲ
B-Ⅱ
B-Ⅱ
B-Ⅲ
C-Ⅳ
B-ⅡB-Ⅲ
B-Ⅱ
B-Ⅱ
B-Ⅲ
B-Ⅲ
B-Ⅱ
B-ⅡB-Ⅲ
B-Ⅲ
B-Ⅳ
B-Ⅳ
-200
+200
- 200
+100
0
-200
- 100
Ap
Ap
Ap
Ap
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
70
70
70
75
80
Ao
Ap
Ap
Ap
Ap
Ap
Ap
ApAp
Ap
Ap
ApAp
Ap
Ap
Ap
ApAp
Ap
85
75
80
85
80
80
70
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
ApAp
Ap
Ap
Ap
Ap
Ap
Ap
Ap Ao Ao
Ao
Ao
Ao
Ao
Ao
Ao
Ao
AoAo
AoAo
AoAo
Ao
AoAo
Ao
Ao
Ao
Ao
Ao
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
Ap
60
S70E
240°目断層
~~
~~
~~
~
300
220
230
240
250
260
270
280
290
310
320
330
340
350
360
370
380
390
400
210
200
190
140
150
160
170
180
110
120
130
100
90
80
70
60
50
40
30
20
10
0
調査終了点
調査開始点
大規模地下空洞立地可能性調査400m 1:300坑道調査( )縮尺
凡例
伊西岩角閃石片麻岩スカルンアプライト緑泥石化片麻岩片理面
割れ目
滴水あり
岩盤分類凡例
B B- B-( Ⅰ、 Ⅱ)
CH B- C-( Ⅲ、 Ⅱ)
CM B- C-( Ⅳ、 Ⅲ)
CL D- C- C-( Ⅲ、 Ⅳ、 Ⅴ)
D D- D-( Ⅳ、 Ⅴ)
AP
Ao
巻末資料3岩盤分類図
Pull-out Test of Cable bolt (6 Places)
Obtaining Rock Joint (3 Places)
+550m EL
N
Rock Classification B Very Good CH Good CM Medium
Measurement of Joint Orientationin this Existing Tunnel
Rock Types Gneiss Migmatite
99
Investigation of Joint Orientation・ Major Joint Set : Strike E-W and Dip ±70 ~ 90°・ Another Joint Set : Strike NE-WS and Dip ± 40 ~ 50°
Projection of Poles
Pole Density Contours
0
Equal angle projection, lower hemisphere
n=130 (P)Num total: 130
0
Equal angle projection, lower hemisphere
n=131 (P)Num total: 131
0
Equal angle projection, lower hemisphere
n=130max. dens.=5.82 (at 344/ 15)min. dens.=0.00Contours at:0.00, 1.00, 2.00, 3.00,4.00, 5.00,(Multiples of random distribution)
0
Equal angle projection, lower hemisphere
n=131max. dens.=9.44 (at 180/ 5)min. dens.=0.00Contours at:0.00, 1.00, 2.00, 3.00,4.00, 5.00, 6.00, 7.00,8.00, 9.00,(Multiples of random distribution)
Gneiss MigmatiteN
W
S
E
N
W
S
E
N
W
S
E
N
W
S
E
N
S
W E
Strike
Dip
Pole
Joint
×
1010
Situation of Obtaining In-Site Rock Joints
Recovered Core with Joint
Diamond Drilling
Joint
Joint
1111
・ Joint Deformability Parameters such as Normal and Shear Stiffness, Dilatancy Angle ・ Joint Shear Strength such as Cohesion and Internal Friction Angle
Normal Stress
Shear Displacement
Joint Mechanical Properties
Direct Shear Test of Rock Joints
Shear Test Equipment(Normal and Shear load are 1MN)
Rock Joint Specimen with extensometers
1212
0.00 0.05 0.10 0.15 0.20 0.25 0.300
2
4
6
8
10
12shear-3-1-v
(mm)垂直変位
(N
/mm
垂直
応力
2 )σn=10N/mm2
Normal Stiffness=67N/mm2/mm
Normal Displacement (mm)
No
rmal
Str
ess
(N/m
m2 )
- 0.2
- 0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 1.0 2.0 3.0 4.0 5.0
(mm)せん断変位
(mm
)垂
直変
位
3- 1(σ n=10MPa)2- 1(σ n=5MPa)1- 1(σ n=5MPa)2- 2(σ n=2MPa)
Di l atancy angle=2.4°
Shear Displacement (mm)
No
rmal
Dis
pla
cem
ent
(mm
)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12
(N/ mm2)鉛直応力
(N/m
m2)
せん
断強
度
τ =0.5+σ n tan33°
τ =σ n tan54°
Normal Stress (N/mm2)
Sh
ear
Str
eng
th (
N/m
m2 )
Cohesion=0.57N/mm2
Internal Friction angle =33°
Results of Direct Shear Test
0
2
4
6
8
10
12
14
16
0.0 1.0 2.0 3.0 4.0 5.0
(mm)せん断変位
(N/m
m2)
せん
断応
力
3- 1(σ n=10MPa)2- 1(σ n=5MPa)1- 1(σ n=5MPa)2- 2(σ n=2MPa)
=60N/ mmせん断剛性 2/ mm
Shear Displacement (mm)
Sh
ear
Str
ess
(N/m
m2 ) Shear Stiffness=60N/mm2/mm
Shear Strength
1313
Pull-Out Test of Two Type Cable Bolts
Economical Support System should be used ・ Usual Support System for Large Cavern is Rock Anchor → Expensive ・ Proposed Support System is Rock Bolt and Cable Bolt → Economical ・ Special Cable Bolt with Dimples has very high Strength ・ Mechanical Properties of Cable bolt was estimated by Pull-Out Test
Usual Cable Bolt without Dimples( PC-Cable Bolt )
Special Cable Bolt with Dimples( ST-Cable Bolt )
1414
Situation of Pull-Out Tests
PC-Cable bolt
ST-Cable Bolt
Jock and Dial Gauge Pressure Pump
Diamond Drilling Inserting Cable Bolts
Pull-Out TestSetting up Equipments
1515
Results of Pull-Out TestsB片麻岩 級
0
50
100
150
200
250
0 2 4 6 8 10 12 14(mm)変位
(kN)
荷重
No.1- LNo.2- LNo.2- 上No.1- RNo.2- RNo.2- 下
ST
PC
Displacement (mm)
Load
(kN
)
Gneiss (B)
B伊西岩 級
0
50
100
150
200
0 2 4 6 8 10 12 14
(mm)変位
(kN
)荷
重
No.3- LNo.6- LNo.3- RNo.6- R
ST
PC
Displacement (mm)
Load
(kN
)
Migmatite (B)
0.00E+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
1.20E+05
1.40E+05
0 50 100 150 200 250 300 350 400(kN/ m)付着強度
(kN/m
/m)
付着
剛性
B ST片麻岩 級( ) CM ST片麻岩 級( )B ST)伊西岩 級( CH ST)伊西岩 級(B PC片麻岩 級( ) CM PC片麻岩 級( )B PC)伊西岩 級( CH PC)伊西岩 級(
PC 53kN/ m:付着強度 以上 40100kN/ m/ m.付着剛性 以上
ST 270kN/ m:付着強度 以上 53900kN/ m/ m.付着剛性 以上
Strength (kN/m)
Stif
fnes
s (k
N/m
/m)
ST
PC
□Gneiss (B) ◇Migmatite(B) □Gneiss (B) ◇Migmatite(B)
△Gneiss (CH) ○Migmatite(CH)△Gneiss (CH) ○Migmatite(CH)
PC Strength above 53kN/m Stiffness above 40MN/m/m
ST Strength above 270kN/m Stiffness above 53MN/m/m
付着剛性付着強度
Stiffness (kN/m/m)Strength (kN/m)
Cable bolt model
1616
Mechanical Properties of Intact Rock Core Migmatite Gneiss
Compressive Strength (N/mm2) 191 176
Young’s Modulus (kN/mm2) 60.4 64.3
Poisson’s Ratio 0.24 0.26
Density (MN/m3) 0.027 0.027
Mechanical Properties Properties
Rock MassSame as Intact Rock
Young’s Modulus=64.3 kN/mm2 Poisson’s Ratio=0.25Density=0.26NM/m3
JointNormal Stiffness=67N/mm2/mm Shear Stiffness=60N/mm2/mm Dairatancy Angle=2.4°Cohesion=0.57N/mm2 Internal Frictional angle=33°
ST-Cable Bolt Shear Strength= 270kN/m Shear Stiffness=53MN/m/m
PC-Cable Bolt Shear Strength= 53kN/m Shear Stiffness=40MN/m/m
1717
Analysis Cases
SupportSupport In-Situ StressIn-Situ Stress
Case 1Case 1 Without SupportWithout SupportIsotropic Stress
σH=σv=14.4
( N/mm2 )(Overburden:500m)
Case 2Case 2Rock Bolt (Length=6m :Space=2m)Rock Bolt (Length=6m :Space=2m)
Double PC-Cable Bolt (Length=15m :Space=2m)Double PC-Cable Bolt (Length=15m :Space=2m)
Case 3Case 3Rock Bolt (Length=6m :Space=2m)Rock Bolt (Length=6m :Space=2m)
Double ST-Cable Bolt (Length=15m :Space=2m)Double ST-Cable Bolt (Length=15m :Space=2m)
Discontinuous Analysis by DEM
DEM Analysis is Performed to Establish the Behavior of Jointed Rock Mass and the Effect of Support System.
Cavern Direction is East and West
Huge TunnnelW48m×H54m
2070m2
”” AN
KO
AN
KO
””F
au
ltF
au
lt
”” 240
240 ゜゚--
ME
ME
””F
au
ltF
au
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fa
ult
Fa
ult
”” 240
240 ゜゚--
ME
ME
””F
au
ltF
au
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fa
ult
Fa
ult
”” 240
240 ゜゚--
ME
ME
””F
au
ltF
au
lt
””NAMARINAMARI”” FaultFaultNNN
Cavern Type and Direction
1818
Procedure of Analysis
Establishing Support System after Each Excavation Step
First Step SecondStep
Third Step
FourthStep
Analysis Model
200m
200m
Strike NS-WS Dip ± 40 ~ 50°
Strike E-W Dip ±70 ~ 90°
Joints are Generated Statistically According to the Joint Orientation
1919
Displacement Vector and Cable Axial Force
Case 3: RB+ST-Cable Bolt (Double)
Displacement of Right and Left Side Wall are nearly same because of Symmetrical Joint Dip Angle (±70 ~ 90°).
Displacement of Case-3 is smaller than Case-2 because of Support Effect
Case 1 : Without Support Case 2 : RB+PC-Cable Bolt (Double)
89 17
15
93
17
45
67 13
15
41
10
35
60 13
15
37
10
32
284
464415
( kN )
474
618620
( kN )×
Failure
(mm)
(mm)
(mm)
2020ModelX
Z
Equivalent Continuum Analysis by Crack Tensor
Cavern Type and Region (528m×528m)
240m 240m48m
240
m23
4m54
mHuge TunnnelW48m×H54m
2070m2
Crack Tensor Analysis is Performed to Estimate the Relation between Tunnel Direction and Joint Orientation.
In-Situ Stress is Isotropic σH=σv=14.4 ( N/mm2 )Case 1:Cavern Direction is East and West, parallel Joint StrikeCase 2:Cavern Direction is North and South, right-angled Joint Strike
”” AN
KO
AN
KO
””F
ault
Fau
lt
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultNNN ”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultNNN
Case 1 Case 2
Join
t S
trik
e
Join
t S
trik
e
2121
Displacement
Case 1 Case 2Output Set: I- DEAS Case 1Deformed(0.0391): Total Translation
9mm
15mm
39mm39mm
Output Set: I- DEAS Case 1Deformed(0.0391): Total Translation
9mm
15mm
39mm39mm
Output Set: I- DEAS Case 1Deformed(0.0181): Total Translation
12mm
18mm8mm
18mm
Output Set: I- DEAS Case 1Deformed(0.0181): Total Translation
12mm
18mm8mm
18mm
”” AN
KO
AN
KO
””F
ault
Fau
lt
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultNNN
Join
t S
trik
e ”” AN
KO
AN
KO
””F
ault
Fau
lt
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultN”” A
NK
OA
NK
O””
Fau
ltF
ault
”” 240240 ゜゚--
ME
ME
””F
ault
Fau
lt
””NAMARINAMARI”” FaultFaultNNN
Join
t S
trik
e
Side Wall Displacement of Case 1 is 2 times Larger than Case 2 because of influence of Joint Strike Direction.
2222
Summary
Joint Orientation : At Proposed Site in Tochibora Mine, Major Joint Set Strike Direction is E-W and Dip Angle is ±70 ~ 90°Joint Properties : Normal and Shear Stiffness, Shear Strength are Estimated. Cable Bolt Properties : Shear Strength and Stiffness of ST and PC Cable Bolt are Estimated. Shear Strength of ST-Cable Bolt is 5 Times Higher than PC-Cable Bolt. ST-Cable Bolt is very Effective Support.Results of Analysis : Discontinuous and Equivalent Continuum Analysis are able to Estimate the Effect of Rock Support System and the Anisotropic Behavior of Jointed Rock Mass. Joint Orientation is very Important factor to decide the Cavern Axis.Further Investigation : It is Necessary for Accurate Joint Orientation to investigate in Different Direction Tunnel or Bore Hole. Measurements of In-Situ Initial Stresses and In-Situ Tests on Rock Mass Deformability are indispensable.
2323
END
2424
2525
ST cable bolt
0
50
100
150
200
250
0 2 4 6 8 10 12 14
displacement (mm)
load
(kN
)
in- situ test
simulation
cable bolt
0
20
40
60
80
100
0 2 4 6 8 10 12 14
dispplacement (mm)
load
(kN
)
in- situ test
simulation
ボルトの引き抜き試験の解析補強要素(ボルト)
グラウト孔掘削
ボルトの軸剛性
付着節点
すべり(ボルト/グラウトの粘着力= sbond)
ボルト/グラウトのせん断剛性= kbond
m
m
m
2626
空洞の安定解析 南北の鉛直面に亀裂傾斜を投影し、統計的に亀裂を発生させてモデルを作成
200m
200m
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
伊西岩
例数
範囲
個 数 :125 平均値 :87.0° 標準偏差:10.6°
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
片麻岩
例数
範囲
個 数 :123 平均値 :91.8° 標準偏差:24.8°
傾斜角 (deg)
傾斜角 (deg)
2727
クラックテンソルによる解析手法の概要
・岩盤基質部の弾性係数、ポアソン 比 (E, ν )・不連続面の垂直剛性とせん断剛性 に関する パラメータ (h, g)・不連続面の幾何学特性を表す 2階、4階の クラックテンソル (Fi j , Fi j kl)a:垂直方向の スプリング
b:せん断方向の スプリング多数の不連続面
を含む岩盤
垂直剛性 , せん断剛性(h, g)
クラックテンソル(Fi j , Fi j kl)
r
n (+)
n(-)
ba
τ σn
クラックテンソルによる不連続性岩盤の巨視的な応力とひずみ関係
kljkjljkililjkjlikijklklijjlikij FFFFg4
1F
g
1
h
11
E
1
2828
不連続性岩盤を対象とした解析手法不連続性岩盤を対象とした解析手法解析手法 亀裂のモデル化
弾性解析 ×亀裂の存在を岩盤の物性低下で考慮
弾塑性解析FEM連続体解析
非線形粘弾性解析
等方
等価
NAPI S ○無数にある亀裂の効果を等価な連続体で表現。
「亀裂の開口」と「亀裂の卓越方向に沿った変形」を剛性低下で表現可能。
適用岩盤の概念
亀裂がない、または、ランダムな方向性の無数の亀裂を有する岩盤
方向性を持った無数の亀裂を有する岩盤
比較的少数の特定の長い亀裂を有する岩盤や有限個の亀裂に囲まれた岩盤ブロック
MBC
EQR
複合降伏モデルクラックテンソル損傷テンソルジョイント要素 ○
個々の亀裂を解析メッシュ上でモデル化。
「亀裂の開口」と「亀裂の卓越方向に沿った変形」を表現可能(キーブロック解析を除く)。
RBSM
DEM
キーブロック解析DDA
マニホールド法
不連続体解析
2929
1.原位置岩盤のクラックテンソルの決定クラックテンソルの算定
2000
02908000
33
1311
..Sym
..
N.Sym
NN
0840
00601160
024008407160
3131
33313333
113111331111
.
..
...
N.Sym
NN
NNN
0290
00500480
007000400890
0020003000500550
00400080027004804930
002000700230029008901200
3131
23312323
123112231212
3331332333123333
22312223221222332222
113111231112113311221111
..Sym
..
...
....
.....
......
N.Sym
NN
NNN
NNNN
NNNNN
NNNNNN
1320
01206300
008005502380
33
2322
131211
..Sym
..
...
N.Sym
NN
NNN
■三次元の Nij , Nijkl
■二次元断面上の Nij , Nijkl
■F0の算定
■二次元断面上の Fij , Fijkl
2000
02908000
33
1311
..Sym
..
F.Sym
FF
0840
00601160
024008407160
3131
33313333
113111331111
.
..
...
F.Sym
FF
FFF
ijklijklijij NFFNFF 00 ,
(1)
(2)
(3)
(4)
2. 6m
2.6m
10m
調査坑道を横切る不連続面
・調査坑道 10mあたり 4本の不連続面を想定・不連続面の寸法(等価円の直径 r) 不連続面の面積: S=2.6m×2.6m=6.76m2
・ F0の算定
m..Sr 9276622
131
4921062624
4
3
1
30
.
...
rV
FM
k
)k(
∴F0=1.0
(5)
(6)
(7)(8)
(9)
(10)
3030
クラックテンソルによる解析手法の概要
・岩盤基質部の弾性係数、ポアソン 比 (E, ν )・不連続面の垂直剛性とせん断剛性 に関する パラメータ (h, g)・不連続面の幾何学特性を表す 2階、4階の クラックテンソル (Fi j , Fi j kl)a:垂直方向の スプリング
b:せん断方向の スプリング多数の不連続面
を含む岩盤
垂直剛性 , せん断剛性(h, g)
クラックテンソル(Fi j , Fi j kl)
r
n (+)
n(-)
ba
τ σn
クラックテンソルによる不連続性岩盤の巨視的な応力とひずみ関係
kljkjljkililjkjlikijklklijjlikij FFFFg4
1F
g
1
h
11
E
1
3131
解析結果
ケース1 ケース3
Output Set: I- DEAS Case 1Deformed(0.0391): Total Translation
Output Set: I- DEAS Case 1Deformed(0.0522): Total Translation
Output Set: I- DEAS Case 1Deformed(0.0181): Total Translation
変形図( 200倍)
等方弾性解析
N
W
S
E
調査
坑道
方向
X
空洞
軸
Y
Z軸
は鉛
直方
向N
W
S
E
調査
坑道
方向 X
空洞
軸
YZ
軸は
鉛直
方向
47mm52mm
36mm 9mm
15mm
39mm
12mm
18mm8mm
18mm39mm52mm
空洞軸を東西方向とするケース2では、二次元断面上の不連続面が鉛直方向(Z方向)に卓越するためそれに垂直な方向となるX方向に変形が大きく生じる変形モードとなる。一方、空洞軸を南北方向とするケース3では、空洞軸方向に対して直交する不連続面が卓越するため、XZ方向の変形は小さく、空洞軸方向の変形が大きく生じる変形モードとなる。
3232
解析結果
ケース1 ケース2 ケース3最大主応力分布( N/mm2)
等方弾性解析
N
W
S
E
調査坑道方向
X
空洞軸
Y
Z軸は鉛直方向
N
W
S
E
調査坑道方向
X
空洞軸
YZ軸は鉛直方向
0.
- 5.
- 10.
- 15.
- 20.
- 25.
- 30.
- 35.
- 40.
Output Set: I- DEAS Case 1Contour: Solid Y Normal Stress
0.
- 5.
- 10.
- 15.
- 20.
- 25.
- 30.
- 35.
- 40.
Output Set: I- DEAS Case 1Contour: Solid Y Normal Stress
0.
- 5.
- 10.
- 15.
- 20.
- 25.
- 30.
- 35.
- 40.
Output Set: I- DEAS Case 1Contour: Solid Y Normal Stress
①
②
③
④
⑤⑥
①
②
③
④
⑤⑥
①
②
③
④
⑤⑥
ケース1ケース1 ケース2ケース2 ケース3ケース3天端①天端① -36.18 -36.18 -35.21 -35.21 -35.88 -35.88
右側壁②右側壁② -24.39 -24.39 -23.77 -23.77 -24.23 -24.23
右偶角③右偶角③ -36.14 -36.14 -35.71 -35.71 -36.21 -36.21
左側壁④左側壁④ -24.39 -24.39 -23.69 -23.69 -24.26 -24.26
左偶角⑤左偶角⑤ -36.14 -36.14 -35.73 -35.73 -36.18 -36.18
底盤⑥底盤⑥ -18.65 -18.65 -20.55 -20.55 -19.34 -19.34
3333
解析結果
ケース1 ケース2 ケース3
最小主応力分布( N/mm2)
等方弾性解析
N
W
S
E
調査坑道方向
X
空洞軸
Y
Z軸は鉛直方向
N
W
S
E
調査坑道方向
X
空洞軸
YZ軸は鉛直方向
0.
- 2.5
- 5.
- 7.5
- 10.
- 12.5
- 15.
- 17.5
- 20.
Output Set: I- DEAS Case 1Contour: Solid X Normal Stress
0.
- 2.5
- 5.
- 7.5
- 10.
- 12.5
- 15.
- 17.5
- 20.
Output Set: I- DEAS Case 1Contour: Solid X Normal Stress
0.
- 2.5
- 5.
- 7.5
- 10.
- 12.5
- 15.
- 17.5
- 20.
Output Set: I- DEAS Case 1Contour: Solid X Normal Stress
①
②
③
④
⑤⑥
①
②
③
④
⑤⑥
①
②
③
④
⑤⑥
ケース1ケース1 ケース2ケース2 ケース3ケース3
天端①天端① -1.49 -1.49 -1.45 -1.45 -1.46 -1.46
右側壁②右側壁② -0.48 -0.48 -0.47 -0.47 -0.47 -0.47
右偶角③右偶角③ -4.80 -4.80 -5.10 -5.10 -5.06 -5.06
左側壁④左側壁④ -0.48 -0.48 -0.46 -0.46 -0.48 -0.48
左偶角⑤左偶角⑤ -4.80 -4.80 -4.95 -4.95 -5.14 -5.14
底盤⑥底盤⑥ -0.03 -0.03 -0.03 -0.03 -0.03 -0.03
3434
解析結果
ケース1 ケース2 ケース3
安全率分布
等方弾性解析
N
W
S
E
調査坑道方向
X
空洞軸
Y
Z軸は鉛直方向
N
W
S
E
調査坑道方向
X
空洞軸
YZ軸は鉛直方向
4.
3.5
3.
2.5
2.
1.5
1.3
1.
0.
Output Set: I- DEAS Case 1Contour: Solid Z Normal Stress
4.
3.5
3.
2.5
2.
1.5
1.3
1.
0.
Output Set: I- DEAS Case 1Contour: Solid Z Normal Stress
4.
3.5
3.
2.5
2.
1.5
1.3
1.
0.
Output Set: I- DEAS Case 1Contour: Solid Z Normal Stress
3535
0 5 10cm
1 0~2
J RC=20
50cm
500cm
J RC=10
50cm
500cm
J RC=5
50cm
500cm2
3
4
5
6
8
J RC値に対応する典型的な粗さ形状
2~4
4~6
6~8
8~10
10~12
14~16
9 16~18
10 18~20
7 12~1410cm
500cm50cm
30
20
10
0
JRC= (Df-1)/(4.413×10-5)
1. 00 1. 01 1. 02 1. 03
フラクタル次元
JRC
Lee et al.
ラフネスの定量的評価
亀裂面のラフネスを測定し、フラクタル次元
を算出↓
JRC を評価
フラクタル次元
y = - 0.0125x + 0.0162
y = - 0.0157x + 0.0238
y = - 0.0158x + 0.0286
00.0050.01
0.0150.02
0.0250.03
0.0350.04
0.0450.05
- 1.5 - 1 - 0.5 0 0.5 1 1.5
log(r)半径( )
(log(
N*r
+ε))
総延
長
2- 1- 12- 1- 22- 1- 3
(2- 1- 3)線形 (2- 1- 1)線形 (2- 1- 2)線形
3636
60
70
80
0 20 40 60 80 100 120 140
mm距離( )
LD m
m
60
70
80
0 20 40 60 80 100 120 140 160
LD m
m
60
70
80
0 20 40 60 80 100 120 140 160 180
LD m
m
ラフネスの測定例(1)
- 10
0
10
0 20 40 60 80 100 120 140 160 180
mm距離( )
LD m
m
-10
0
10
0 20 40 60 80 100 120 140 160 180
LD m
m
- 10
0
10
0 20 40 60 80 100 120 140 160 180
LD m
m
Df=1.0071→JRC=12
Df=1.0264→JRC=24
Df=1.0302→JRC=26
Df=1.0121→JRC=16
Df=1.0072→JRC=12
Df=1.0082→JRC=13
片麻岩
片麻岩
3737
80
90
100
0 20 40 60 80 100 120 140 160
mm距離( )
LD m
m
80
90
100
0 20 40 60 80 100 120 140 160
LD m
m
80
90
100
0 20 40 60 80 100 120 140 160
LD m
m
90
100
110
0 20 40 60 80 100 120 140
mm距離( )
LD m
m
80
90
100
0 20 40 60 80 100 120 140 160
LD m
m
80
90
100
0 20 40 60 80 100 120 140 160
LD m
m
ラフネスの測定例(2)
Df=1.0125→JRC=16
Df=1.0158→JRC=18
Df=1.0157→JRC=18
Df=1.0077→JRC=13
Df=1.0117→JRC=16
Df=1.0108→JRC=15
片麻岩
片麻岩