LECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office ... · PDF fileLECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office / T1-A13-15C Tel : 016-5320264 [email protected]

LECTURE : 3 HRS / WEEK

Kamaruzzaman Mohamed

Dean Office / T1-A13-15C

Tel : 016-5320264

[email protected]

mailto:[email protected]

Rock at depth is subjected to stresses resulting from the

weight of the overlying strata and from locked in stresses of

tectonic origin.

When an opening is excavated in this rock, the stress field

is locally disrupted and a new set of stresses are induced in

the rock surrounding the opening.

Knowledge of the magnitudes and directions of these in situ

and induced stresses is an essential component of

underground excavation design since, in many cases, the

strength of the rock is exceeded and the resulting instability

can have serious consequences on the behaviour of the

excavations.

Introduction

Introduction

Besides basic material properties, equally important is in-

situ stress

In-situ stress is important to define the boundary conditions

for mechanical analysis

Rock engineering is concerned mainly with the effect of

altering the geometry of a pre-stresses material, hence

changing the pre-existing

stress state when extra loads are applied or when rock is

excavated

In-situ stress is important for underground engineering

1.1 Factors influencing the stress state

- Surface topography

- Erosion and temperature

- Non-homogeneity

- Discontinuities

- Time (e.g, postglacial rebound, viscosity)

- Presence of excavations

- Representative volume element (RVE)

1 Initial Stress

World Stress Map

Surface Topography


Higher stress

Lower stress

Higher stress

Lower stress

These effects may influence the

vertical stress to some extent. The

effect of topography on vertical

stresses depends on the height of the

hill or valley in relation to its width.

Topography


Stress conditions often may change

significantly across structures such

as faults, dyke contacts and major

joints. Stiffer geological materials

tend to attract stress, so that stress in

say a dyke may be higher than in a

rock such as quartzite in close

proximity.

These effects may influence the

vertical stress to some extent. The

effect of topography on vertical

stresses depends on the height of the

hill or valley in relation to its width.

Discontinuities


Stiff material

Soft material

Stress of stiff layer

makes higher stress

Erosion


Eroded Height !!!!!

Stress reduces by γ∆H

σ1=γh

(Fresh rock, K = 1),

Presence of excavation


Presence of excavation


Stress vector

Representative volume

element (RVE) or

representative

elemental volume, VH

I << H << L

L

H

I

Macro

Meso

MicroH

I

Real heterogeneous

material in modeled at

the meso-scalled by a

continuum

RVEs in Rock Mass

Rock mass is a multiscale structure

(1) no unique choice of the RVE.

(2) several continuum media can be associated with the rock mass

Scale 2 Micro2 Meso2

Scale 1 Micro1 Meso 1

A A A A A A

H1 H2

A-A

Stresses at microscale

A-A

Stresses at macroscale

A-A

Stresses at mesoscale

x

σ

x

σ

x

σ

H1

H2

Representative Volume Element


A A A A

RVE

A-A

Stresses at microscale

A-A

Stresses at macroscale

x

σ

x

σ

H1

Borehole scale

Regional scale

Engineering

structure scale

Scale Effect in Stress Measurements

Size of the volume element (rock mass volume involved in the test)

A s

tres

s co

mponen

t

RVEs

RVEs

RVEs

Averaging over RVE

Meso

Micro

Macro

Representative Volume Element


Vertical stress & Horizontal stress

1.2 In-situ Stress Measurement

Depth, z

Horizontal stress, σh

Ver

tica

l st

ress

, σ

v

Vertical stress

The stress

acting at a point

below the

ground surface

is due to the

weight of

everything lying

above: rock,

water, and

surface loading.

Horizontal stress

The stresses

acting horizontally

on an element of

rock at a depth z

below the surface

are much more

difficult to

estimate than the

vertical stresses.

Ground level

Measurements of vertical stress at various mining and civil engineering sites around the world confirm that this relationship is valid although, as illustrated above, there is a significant amount of scatter in the measurements

Vertical stress


Normally, the ratio of the average horizontal

stress to the vertical stress is denoted by the

letter k such that:

Terzaghi and Richart (1952) suggested that,

for a gravitationally loaded rock mass in which

no lateral strain was permitted during

formation of the overlying strata, the value of k

is independent of depth and is given by

where ν is the Poisson's ratio of the rock

mass.

Horizontal stress


Horizontal stress


Horizontal stress


Variation of

horizontal to vertical

stress ratio with depth

below surface

Shorey, 1994

Average deformation modulus

Correlation of ratio σh/σv to depth (z)


Variation of average

horizontal to vertical

stress ratio with depth

below surface

Brown & Hoek, 1978


Correlation of mean ratio σh/σv to depth (z)m

inim

um

2.1 Method performed on rock surface

- Flat Jack

- Surface relief method

2.2 Methods performed in borehole

- Hydraulic Fracturing

- Borehole breakout

- Overcoring

2.3 Methods performed using a drill cores

- Acoustic Method

- Core discing

- Strain recovery method

2 Method of Stress Measurement

1.2 Method Performed in Borehole

Hydraulic Fracturing Method

Po

Ps

Pc2

Pc1

2. Measurement1.2 In-situ Stress Measurement

Hydraulic Fracturing : Analysis (Kirsch’s solution)

fractured

borehole

ppAA


Flat Jack Method


Flat Jack Method


Flat Jack Method : Analysis

Pin

se

pa

ratio

n

do

Time Jack pressure

σθ

Overcoring - measure of distortion (strain!).


(1) advance +76mm main borehole

to measurement depth,

(2) drill +36mm pilot hole and

recover core for appraisal,

(3) lower probe in installation tool

down hole,

(4) probe releases from installation

tool; gauges bonded to pilot-

hole wall under pressure from

the nose cone,

(5) raise installation tool; probe

bonded in place and

(6) overcore the probe and recover

to surface in core barrel.

Overcoring


Overcoring : Analysis


CHILE versus DIANE

Continuous

Homogeneous

Isotropic

Linearly

Elastic

Discontinuous

Inhomogeneous

Anisotropic

Non-Linearly

Elastic

Strength Criteria for isotropic rock-failure theory proposed to explain observed rock failure phenomena

Types of strength criterion:

• Peak strength criterion

stress components which will permit the peak strengths developed under various stress combinations to be predicted

• Residual strength criterion

used to predict residual strengths under varying stress conditions

• Yield strength criterion

is a relation between stress components which satisfied at the onset of permanent deformation

3 Theory of Rock Failure

• Mohr-Coulomb’s strength criterion

• Griffith Crack Theory

• Empirical criteria – Hoek and Brown

.


Methods of Analysis

φ

σ

τ


Mohr-Coulomb failure criterion

Normal stress

Shear

str

ess

σ

τ

τ = c

Normal stress

Shear

str

ess

c

Coulomb condition

(cohesive material)

Failure occurs when an applied

stress exceeds the intrinsic

bonding strength between sample

grains

Mohr condition

(cohessionless material)

Failure occurs when an applied

stress overcomes internal

resistance on incipient failure

surfaces

φ

σ

τ



Normal stress (Mpa)

Shear

str

ess (

Mpa)

Mohr-Coulomb condition

(c & φ material)

Strength characteristics are mobilised both by cohesive and frictional resistance effects

c











ROCK CONDITION

Where rock exists in an

undisturbed, intact state the

resultant failure envelope will

exhibit both cohesional and

frictional strength behaviour

Once the rock has been

broken, local cohesional

bonding strength can often be

assumed to be negligible

In badly fragmented condition,

little or no cohesional strength

will exist to impart shear

resistance

φ

σ

τ

Normal stress (Mpa)

Shear

str

ess (

Mpa)

c

φ



c

φ

σ3 = 0σ

τ

Intergranular

crushing which

occurs between

grain boundaries

within rock test

specimens under

high confining stress


σ1 = σcσT

Linear

compressionTension Non-linear

compression


Actual plot of shear versus normal stress data

NO FAILURE

JUST FAILING

FAILED

c

φ

σ3 σ1(a) σ1(b) σ1(c)

ROCK INSTABILITY DUE TO INCREASING AXIAL STRESS APPLICATION

For a fixed level of confinement, sample failure becomes more likely as the

magnitude of axial- applied stress is increased

σ

τ

When stress circle

contact is made

with the locus it is

assumed that the

rock failure will

take place



Circle shrinksc

φ

σ3(a) σ3(b) σ1

ROCK INSTABILITY DUE TO INCREASING CONFINEMENT STRESSWhen confining stress increase, the stress circles reduces in size, and it displace

further, thereby indicating that a position of greater stability can be achieved

σ

τ

This example

therefore

demonstrate the

necessity for

applying support

to rock excavation



c

φ

σ3 σ1

ROCK INSTABILITY DUE TO EXISTING OF GROUNDWATERWhere groundwater may exist, it is shown to remain of a fixed size but to be displace

left.

σ

τ

Such

displacement

towards the failure

locus indicated

that the action of

pore water

pressure serves

to destabilise rock

against failure

σ1- uσ3 - u




σ3

σ1

σ1

σ1

σ1

σ3

Uniaxial tension

Uniaxial compression

Triaxial compression

σ3

σ1

compressiontension

HOEK-BROWN

FAILURE LOCUS

Hoek-Brown failure criterion

Major principle stress at failure

Minor principle stress at failure

Unconfined compressive strength of intact rock

Rock constants


or Using table provided by Hoek

For fresh rock, s = 1

For GSI>25, α = 0.5



Hoek-Brown versus Mohr-Coulomb



Value of mi for

intact rock

(Hoek 2002)

Hoek and Bown (1980) described the peak triaxial

compressive strength of isotropic rock as shown in

the equation given below. The mean value of the

uniaxial compressive strength of the intact sample

(σc) was found to be 35 MPa. Given the Hoek and

Brown (1980) failure criteria is:

σ1/ σc = σ3 / σc + { m σ3 / σc +1}½

Taking the rock material constant m is equal to 15 for

sandstone, tabulate the peak strength of

sandstone(σ1) against the confining pressure (σ3)

when the triaxial test was carried out at the confining

pressure range from 0.2, 0.4, 0.6, 0.8 and 1.0 ,

hence plot the peak strength envelope .

If similar test is to be carried out for granite with the

material constant is twice of sandstone, roughly plot

the graphical peak strength envelope of granite. How

is the different rock type contributed to the peak

strength envelope of rock?


0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1



Griffith’s theory of tensile rock failure



σ3

σ1

8ST

ST

3ST



Strength envelope



LIMITATION

Not in the idealised elliptical form suggested such as

natural flaw shapes and their associated fracture

mechanism are much more complex

Many efforts within laboratory environments to

duplicate of simulation the Griffith’s fracture

mechanism, no development of crack growth and

macroscopic sample failure has been able to be

duplicated in the manner suggested by Griffith

Documents

LECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office ... · PDF fileLECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office / T1-A13-15C Tel : 016-5320264 [email protected]