11. Application to underground rock cavern...wall displacement. 1、2、3 is stable since yield zone...

11. Application to underground rock cavern

‡：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。

11.1 Stability in excavation of rock cavern

Stress concentration is the cause of failure around a rock cavern.In the case where the initial stress is almost uniaxial stress state

Tensile tangential stress can occur.Tensile fracture which is normal to the free surface will appear.

Actually, initial stress is usually triaxial stress state and cavern geometry is designed not to induce tensile stresses.

It is not likely that tensile fracture becomes severe problems.Failure due to concentration of compressive stress is the problem in excavation of rock cavern.

Stress concentration on roadway wall

Stress concentration is small near the face since the face acts as a support. It increases when the face goes ahead and is almost converged when the distance to the face becomes identical to the diameter of the roadway.Instantaneous failure due to stress concentration occurs (1) in the way of excavation or (2) in the period before the distance to the face becomes identical to the diameter of he roadway.

Rockbursts in mountain tunnels were observed in (2)After that, mainly creep deformation occurs under a constant stress.

Special cases

CAES cavernFatigue deformation due to cyclic loading of the inner pressure.

Geological waste disposal of high-level nuclear waste and underground storage of LNG.

Thermal stress.

Roadways in mines.Stress disturbances by excavation.

Stress concentration around a circular cavern

A circular cavern having the radius R in a homogeneous and isotropic elastic medium subjected to stress p1 and p2 at an infinite distance

p2

p1 θ

σr

r σθ

τrθ

x

y

O

R

Stress concentration around a circular cavern

Stresses σ r, σθ, τrθ at a point ( r, θ ) (Kirsch's solution, ex. Jaeger and Cook, 1979）

p2

p1 θ

σr

r σθ

τrθ

x

y

O

R

θσ 2cos341)(211)(

21

4

4

2

2

212

2

21 ⎟⎟⎠

⎞⎜⎜⎝

⎛+−−+⎟

⎟⎠

⎞⎜⎜⎝

⎛−+=

rR

rRpp

rRppr

θσθ 2cos31)(211)(

21

4

4

212

2

21 ⎟⎟⎠

⎞⎜⎜⎝

⎛+−−⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

rRpp

rRpp

θτ θ 2sin321)(21

4

4

2

2

21 ⎟⎟⎠

⎞⎜⎜⎝

⎛−+−−=

rR

rRppr

In the case where only p2 is applied

Distribution along x-axis Distribution along y-axis

0 1 2 3 4 50

1

2

3

x / R

σ / p

2

σr

σθ

0 1 2 3 4 5-1

-0.5

0

0.5

y / R

σ / p

2

σr

σθ

p2

p1 θ

σr

r σθ

τrθ

x

y

O

R

Significant stress concentartionoccurs on the roadway wallRock mass near roadway wall may failure due the stress concentration

Large stress cvoncentration is transfered to outer area.

↓

This is the reason why the initial stress measurement should be done at least roadway width from the roadway wall

0 1 2 3 4 50

1

2

3

x / R

σ / p

2

σr

σθ

Lithostatic pressure case (p1 = p2 = p)

Stress which is concentrated on the wall deceases with rand converged to the stress at infinite.Average stress (σr + σθ) / 2 is independent on r and keep a constant value p.

0 1 2 3 4 50

1

2

r / Rσ

/ p

σr

σθ

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

21

rRprσ

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2

21

rRpθσ

0=θτ r

Elasto-plastic solution

Analysis which also considers failureA circular roadway under lithostatic pressureBray's solution (Goodman, 1980)Coulomb's criterion is assumed for failure and residual strength criterion.

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. 234,

Fig. 7.10』

を省略させて頂きます。


『Goodman (1980), Introduction to Rock Mechanics, John Wiley and Sons,

p. 236, Fig. 7.11』


Radius of plastic zone R

strength residual in angle friction :

strength residual in cohesion : :

pressure internal : pressure external :

hole theof radius : boundary plastic-elasto theof radius :

245

1)tan(

tan

)cot(2

45tan1

cot2

45tan12

j

j

i

j

j

1

jjij2

jj2

u

φ

φδ

φδδ

φφ

φφ

SUCSq

ppaR

Q

Sp

Sqp

aR

u

Qj

+=

−−

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

+⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛++

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+++−

=


『Goodman (1980), Introduction to Rock Mechanics, John Wiley and Sons, p. 234,

Fig. 7.10』


Stress in elastic zone

friction internal of angle :

12

45tan

12

45tan2

2

u2

2

2

φ

φ

φ

σ

σ

θ

Rqp

b

rbp

rbpr

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−⎟⎠⎞

⎜⎝⎛ +

+⎭⎬⎫

⎩⎨⎧

−⎟⎠⎞

⎜⎝⎛ +

=

+=

−=


『Goodman (1980), Introduction to Rock Mechanics, John Wiley and

Sons, p. 234, Fig. 7.10』


Stress in the plastic zone

jjj

jji

jjjji

cot)tan(

tan)cot(

cot)cot(

φφδ

δφσ

φφσ

θ SarSp

SarSp

Q

Q

r

−⎟⎠⎞

⎜⎝⎛

−+=

−⎟⎠⎞

⎜⎝⎛+=



Sons, p. 234, Fig. 7.10』


Example

Calculate the radius of the plastic zone. Uniaxial compressive strength and the angle of internal friction are 60 MPa and 30°, respectively. Cohesion and friction angle after failure are 0and 30° , respectively. Eaternal and internal pressure are 40 MPa and 1 MPa, respectively.Answer: 2.24 a.

Analysis for practical cases

Actual cavern is not always circular.Inhomogeneity, anisotropy, planes of weakness etc. sholwd be considered.

There are some analytical soltions.Circular roadway in an anisotropic rock mass (Hefny & Lo, 1999)Circular roadway in a rock mas having Hoek-Brown type failure criterion (Carranza-Torres & Fairhurst, 1999)Roadway having a geometry which can be approximated by a mathematical function (Exadaktylos & Stavropoulou, 2002), etc等

Generally, numerical analyses can be adopted.Finite Element MethodBoundary Element Method

Finite element methodThe entire region of interest is divided into finite elements.

Simultaneous equations which relates displacement and forc at elements' nodes are solved according to the boundary conditions.

FEM is suitable to finite, inhomogeneous and elasto-plastictc. prblems.It was very tedius to the data preparation, displaying the calculated results.

Excellent pre- and post-prosessors have been developed.

You can find many entry level texts in university library.

Very easy texts are recomendedoe the first one. Tensile stress is taken as positive

Boundary element methodOnly the boundary is divided into boundary elements

Ex. Simultaneous equations which relates displacement discontinuity to traction, displacement and displacement discontinuity are solved for displacement discontinuity in the Displacement DiscontinuityMethod.

BEM is suitable for infinite and semi-infinite problems.DDM is suitable for analysis of fracture propagation.

Coastline Land

Pacific Ocean Distribution of extensile strain due to excavation at K Coal Mine

Boundary Element Method

BEM is not a general purpose one since some professional knowledge is required for analysis.

0 1 2 3 4 50

1

2

3

4

5

x (m)

y (m

)

11.2 Support

Main members for support

ShotcreteRockbolt

Example of an NATM tunnel社団法人地盤工学会（1986）、NATM工法の調査・設計から施工まで、p. 159図-3.24

制限資料

ロックボルト

Why is support needed?

The limited stand-up time of unsupported span.

Ex. Unsupported roof stands up one month at most when RMR is 60.

Rock cavern can't be used for practical purpose without support.


『Goodman (1980), Introduction to Rock Mechanics, John Wiley and Sons, p. 239, Fig.

7.13』


Concept of support

Extent of loosening decreases with initial support pressure.

Initial support pressure and extent of loosening (Goodman, 1980)

strength residual in angle friction :

strength residual in cohesion : :

pressure internal : pressure external :

hole theof radius : boundary plastic-elasto theof radius :

245

1)tan(

tan

)cot(2

45tan1

cot2

45tan12

j

j

i

j

j

1

jjij2

jj2

u

φ

φδ

φδδ

φφ

φφ

SUCSq

ppaR

Q

Sp

Sqp

aR

u

Qj

+=

−−

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

+⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛++

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+++−

=


『Goodman (1980), Introduction to Rock Mechanics, John Wiley and Sons,

p. 237, Fig. 7.12a』


Concept of support

The dotted lines denote relationship between support pressure and deformation of the support. Slope of the lines represent the stiffness of support system. Deformation begins from the left side and stops at the crossing point of the solid line and the dotted line.

Support pressure and wall displacement (Goodman, 1980)



Sons, p. 237, Fig. 7.12c』


Concept of supportRock mass behaves elastically for small displacement. Consequently, support pressure decreases with wall deformation.Yield zone extends for large displacement. Support pressure increases with wall deformation in this case.

Support pressure and wall displacement (Goodman, 1980)



Sons, p. 237, Fig. 7.12c』


Concept of supportThe earlier the support is installed (1, 2 and 3 than 4 and 5) or the stiffer the support is (1 and 2 than 3 or 4 than 5), the less the wall displacement.1、2、3 is stable since yield zone is small.4 is potentially stable since the displacement exceeds the critical value although the solid and doted lines cross with each other.5 is very unstable since the solid and dotted line do not cross with each other. Support pressure and wall

displacement (Goodman, 1980)



Sons, p. 237, Fig. 7.12c』


Excavation and support of tunnel

NATM (New Austrian Tunneling Method)Mainstream in Japan at present

NATM

国土交通省北海道開発局旭川開発建設部上川道路建設事業所、中越トンネルパンフレット制限資料

Example of support pattern for a NATM tunnel (JSGS, 1986）

社団法人地盤工学会（1986）、NATM工法の調査・設計から施工まで、p. 159図-3.24

制限資料

Excavation and support of roadway

Example of bolted roadway in Taiheiyo Coal Mine in Japan (JCOAL and KCOAL, 1999)


図表を省略させて頂きます。

Example of bolted roadway in Taiheiyo Coal Mine in Japana (JCOAL and KCOAL, 1999)


図表を省略させて頂きます。

11.3 Evaluation of stability of rock cavern

Tunnel and roadway after excavationInner size decreases with time (convergence)

Creep deformation of the surrounding rock massPressure on the concrete lining due to Creep deformation of the surrounding rock massGround water pressureEarthquakeFreezing pressureVibration and air pressure disturbances by trains or carsDegeneration of concrete lining due to various causes

They can't serve as expected and detachment of concrete block and/or roof fall may occur if convergence exceeds a critical value.

Stability evaluation of underground cavernDeformation of concrete liningAxial load and bending moment of rockboltStress disturbances and displacement in rock massAE

Strength of rock mass is given in stressIt is expected that stress measurement is required for precise stability analysis...Displacement is measured much more than stress analysis since the former is much easier than the latter.

Relationship between strain and tunnel failure （Sakurai, 1998, 1：difficulties in maintain face, 2：failure and cracking of shotcrete, 3：buckling of steel arch, 4：breakage of rockbolts, 5：roof fall, 6：floor heave of invert, 7：others)

"Reprinted from Tunneling and Underground Space Technology, Vol. 12, Sakurai, S., Lessons Learned from Field Measurements in Tunneling, p. 456 Fig. 4, Copyright (1998), with permission from Elsevier".

制限資料

Strain

1%

Estimated yield zone

Schematic figure showing strain measurement in bolt roadway in a coal mine

Example of stability monitoring

CSIRO, 2005


『CSIRO EXPLORATION AND MINING REPORT P2005/138, p. 2 』


Roof monitoring of ULAN Mine from Japan

11.4 Prediction of failure around rock cavern

Inward displacement of rock cavern increases gradually even under a constant condition.

This means gradual extension of failure zone if wall is already fractured.Creep deformation is occurring if wall is not already fractured.

Failure may occur as a result of creep deformation just as rock specimen.

Strain in the tertiary creep

log (tF - t)

ε

Tertiary creep

CttB +−−= )log( Fε

Fukui & Okubo （1997）

Example of in-situ deformation monitoring

Face

Target Laser Sensor head

Differentiating the both sides with respect to t

Failure time can be predicted measuring strain rate in the tertiary creep region (Fukada, 1999).Measurement of rock mass surrounding a rock cavern can't be started just after the excavation.

Total strain is not known.Using strain rate can be an advantage

CttB +−−= )log( Fε

εdd

FtBtt −=

t

dt / dε

tF O

Example

Strain rate was 1 × 10-4 s-1 at 1 o'clock and 1 × 10-3 s-1 at 2 o'clock. Predict failure time.Answer：2:06:40'

11.5 Subsidence

Deformation may occur on the ground surface due to excavation of underground cavern.

Longwall coal excavationSurface subsidence

Shallow excavation (ex. Oya-ishi, room and pillar)Sinkhole

Subsidence due to longwall coal mining （Whittaker & Reddish, 1989）"Reprinted from, Subsidence, Whittaker & Reddish, p. 21 Fig. 10, Copyright (1989), with permission from Elsevier".

制限資料

Surface deformation above oldworkings by room and pillar method (Bruhn et al., 1978）

Bruhn R. W., Mangnuson M. O. & Gray R. E. (1978), Survey of ground surface conditions affecting structural responce to subsidence, ASCE Spring Convention, Pittsburgh, ASCE, Preprint, 3293, 26-55

制限資料

Formation of a sinkhole (Whittaker & Reddish, 1989) "Reprinted from, Subsidence, Whittaker & Reddish, p. 197 Fig. 116, Copyright (1989), with permission from Elsevier".

制限資料

11.6 Rockburst

Violent failure of rock mass sometimes occur due to deep excavation.The failure phenomena is called rockburst.Rockbursts may give severe damage to machines and workers.

South AfricaGold minesbreakouts

著作権処理の都合で、

この場所に挿入されていた

写真を省略させて頂きます。

Kolar Gold Fields

著作権処理の都合で、

この場所に挿入されていた

写真を省略させて頂きます。

11. Application to underground rock cavern11.1 Stability in excavation of rock cavernStress concentration on roadway wall Special casesStress concentration around a circular cavernStress concentration around a circular cavernIn the case where only p2 is appliedLithostatic pressure case (p1 = p2 = p) Elasto-plastic solutionRadius of plastic zone RStress in elastic zone Stress in the plastic zoneExampleAnalysis for practical casesFinite element methodBoundary element methodBoundary Element Method11.2 SupportロックボルトWhy is support needed?Concept of supportConcept of supportConcept of supportConcept of supportExcavation and support of tunnelNATMExcavation and support of roadway11.3Evaluation of stability of rock cavernExample of stability monitoring11.4 Prediction of failure around rock cavernStrain in the tertiary creepExample of in-situ deformation monitoringExample11.5 Subsidence11.6 Rockburst

11. Application to underground rock cavern...wall displacement. 1、2、3 is stable since yield zone...

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