SPE-28036-MS_Relationship Between Frictional Strength and Fault Gouge Generation From Direct Shear Testing Under Constant Normal Displacement Control

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SPE 28036

Relationship between frictional strength

and

fault

gouge

generation

from

direct

shear

testing under constant normal displacement control

La relation entre

la

force de friction et la generation de mylonite microgrenue

de

faille a 'aide

d'un appareil acontrainte dirigee avec un controle constant du deplacement

normal

Eine Beziehung zwischen der GleitfHichenreibungsstiirke und Trtimmerpartikelerzeugung

unter Verwendung einer Abschermaschine unter normaler gleichbleibender

Verschiebungskontrolle

B. R.Crawford, SPE,ISRM

B.G. D. Smart, SPE, ISRM Department

of

Petroleum Engineering, Heriot-Watt University, Edinburgh, UK

B.T.Ngwenya, Department of Geology Geophysics, Edinburgh University,

UK

Copyright 1994. Society

of

Petroleum Engineers

This paper was prepared for presentation at the 1994 Eurock SPE/ISRM Rock Mechanics n

Petroleum Engineering Conference held n Delft, The Netherlands, 29-31 August 1994.

Abstract: The production of

rictional

wear

debris

fault

gouge)

under optimum non-dilatant conditions

conducive to maximum dynamic fragmentation

has

been undertaken utilising a novel direct

shear

machine.

A wide variety of

sedimentary

lithologies

have been

tested under

constant

normal

displacement

control and

a

mechanistic model

for

the

evolution

of

frictional

resistance developed.

X-ray

diffraction

quantitative

mineral identification

and

laser diffraction particle sizing technologies have

been

employed to characterise

the induced debris distributions. A relationship is presented

between

the frictional strength

o

the sliding

surfaces and the specific surface area

of

he induced cataclastic debris.

Resume:

La

production de debris

defriction

mylonite microgrenue defaille) a ere effectuee a

l aide

d un

nouvel appareil a contrainte

dirigee

sous des

conditions

optimales non-dilatantes conduisant a une

fragmentation

dynamique maximale. Une large variete de lithologies

sedimentaires

a ete

testee

avec

un

controle

constant

du

deplacement

normal

et un modele mecanique de

I evolution de la

resistance a la

friction a ere developpe. Les techniques

d

identification quantitative de mineraux par diffraction de

rayons

X et

d

evaluation

de la taille des

particules

par diffraction

laser

ont

ete

employees pour caracteriser

les

distributions

des

debris induits. Une relation entre la force de friction

des

surfaces coulissantes et la surface

specifique

des

debris cataclastiques est presentee.

Zusammenfassung:

Unter

Verwendung einer neuartigen Abschermaschine ist bei optimalen,

ausdehnungsfreien Bedingungen

die eine

maxima

e

dynamische Zerkleinerung

erlauben

Abnutzungsabrieb

HohlmeifJel) erzeugt worden. Eine Vielzahl unterschiedlicher Sedimentgesteine wurde unter

normaler

gleichbleibender

Verschiebungskontrolle getestet und ein

mechanisches

Modell flir die Entwicklung des

Reibungswiderstandes erstellt.

Fur

die quantitative Mineralbestimmung wurde das Rontgendiffraktometer,

fur die Ermittlung der Partikelgroj3en das Laserdiffraktometer verwendet,

mit

der die Verteilung des

Abnutzungsabriebes

charakterisiert

wurde.

Eine Beziehung zwischen

der

Gleitflachenreibungsstarke und

der spezifischen Oberflache der erzeugten kataklastischen Trummerpartikel wird dargestellt.

Introduction

Current visualisation of fractured

hydrocarbon

reservoirs with regard

to

flow

simulation has significantly advanced from the

sugar-cube ideal

with,

in

particular, the

effects

of

observed power-law

size populations

of faults

and

the influence

of small-scale sealing

faults

below the

limits

of

seismic

resolution, now being

quantitatively

incorporated into

reservoir

simulation

model gridblocks

(Heath

et al )1. Also, stress

sensitivity

has

been

introduced into simulation

studies.

During reservoir

development, the stress

field

can

be severely modified

by

transients

in pore

pressure and temperature resulting from production

or

injection.

Heffer

et al simulated the

effects

of

such stress changes on existing fracture

deformation,

and

predicted new fracture genesis.

Bawden

et al

3

were

amongst the

first

to show

that,

contrary to the assumption of perfect rigidity,

fracture deformability could

be

an important

influence on fluid flow.

They

investigated the

effects of normal and shear deformation on

fracture

conductivity using

the

finite

element

technique,

assuming a

straightforward

coupling between

dilatancy

and

conductivity.

The

model

was found to

be very sensitive to input data, especially for

dilatant

shear problems,

depending on a complex

interaction

between normal

load,

maximum

fracture

closure,

normal

stiffness

and the geological (stress)

history. However,

with normal movement

becoming progressively

suppressed under

increasing normal stress and

hence

with

increasing

depth,

dilatant

shear

within many

hydrocarbon

reservoirs may

well

be a second

order parameter,

and

indeed may be wholly repressed

under some

in

situ conditions. Despite this, the

vast

majority of

experimental discontinuity shear testing

is

2



conducted within portable shear

box

type

equipment modified from the soil mechanics

field,

under low magnitude, constant normal

stress

conditions (zero normal stiffness mode) more akin

to

surface structures where the possibility

of

significant

dilation exists.

In keeping with the maxim that, the

powerful numerical simulators currently available

are only empty

shells

if

they

cannot be

filled

with

reliable

data, a series of direct shear

tests

have

been

conducted

in order

to

assess the

frictional

strength characteristics

of

fractures

subjected to

shear displacement under constant normal

displacement (zero

dilation

equivalent

to infinite

normal

stiffness)

conditions. Frictional strength

parameters derived

from the

direct

shear

programme

have been quantified for a

wide

variety

of sedimentary lithologies, and are envisaged as

representing

input data for coupled fluid flow

and

deformability reservoir simulation studies. Shearing

under high normal stiffness represents the optimum

conditions

for asperity fracture and comminution,

and

as

such might well offer

a

more realistic

analogy for

sealing

faults, in

which the

principal

mechanism

of porosity collapse has

been

cataclasis

and granulation (cataclastic slip bands

or

granulation seams). Other areas

of

applicability lie

within the

near-wellbore environment related to

stability, sand production and stress-induced skin

effects.

Theory

The n

situ frictional

response of a rock

discontinuity to shear loading is dependent, not

only on material parameters such as surface

roughness

and asperity hardness/toughness,

but

also

on the

boundary

conditions operative across the

fracture walls.

These boundary

conditions can

be

variable.

Saeb Amadei

4

represented the range of

discontinuity-normal loading conditions

by

modelling the deformability

of

the surrounding

rockmass

as a

spring

with

normal

stiffness, k

n

=

dan/dOn, where dan and d n

are the changes in

discontinuity normal stress and displacement

respectively.

The

stiffness,

k

n

can

thus

be

considered to vary

between zero

for a

discontinuity

under

constant

normal

stress (as in slope stability

analyses)

or in

a

highly compliant rockmass,

and

infinity for

a

discontinuity in

a

highly

stiff

rockmass

where

no

change in

discontinuity-normal

deformation

is possible (as for tightly constrained

fault

blocks). Whilst

constant

normal stiffness

conditions may result if the change in normal

stress

and

normal displacement

remain

proportional,

stiffness

may

also vary with loading

history.

Although

finite, constant

or

variable

stiffness,

discontinuity-normal boundary conditions

are more likely to exist

n s tu

than either the zero

or infinite k

n

states, constant

normal

displacement

shearing is of particular interest, representing

optimum conditions for dynamic fragmentation and

wear debris (fault gouge) production by the process

of

cataclasis.

However, although Goodman

5

devised a method of predicting the

shear

response

of discontinuities under

constant

normal

displacement, based

on

a knowledge of

their

normal

loading behaviour and shear response

under

constant normal stress, as far as the authors

are

aware

no

experimental

results have

been

published

on direct shear testing under constant normal

displacement control. Johnston et l 6 developed a

constant normal stiffness direct

shear machine,

and

demonstrated an

increase in

measured shear stress

on failure with increasing normal stiffness, from

which it

can

be

assumed that the shear resistance to

slip under the constant normal displacement

criterion

will

be

very

different

from, and

significantly

greater

than that appropriate to the

fixed

normal

stress

mode.

In

this

study,

the mechanism of frictional

sliding under minimum dilation,

maximum

fragmentation

conditions associated with extreme

normal stiffness boundaries, is quantified

experimentally for a wide range

of

sedimentary

rock types,

using a novel

new direct shear rig,

capable of imposing a

constant

normal

displacement state. Also, X-ray and

laser

diffraction

technologies have been applied

to

thoroughly

characterise

the

large quantities of resultant

comminution products, the latter facility

representing a new capability not yet fully

utilised

by

the

petroleum industry. Through quantification

of the shear debris

sub-micron

sized fractions,

achieved via

laser

particle

sizing,

a

relationship is

demonstrated between sliding surface frictional

strength and a

measure of

the

induced

particle size

distribution.

The

value

of

such small particle

statistical

analyses

is

corroborated by

a study of

induced shear fracturing under triaxially

compressive stress states, in

which

the permeability

of

faulted core plugs

was

found to correlate

with

the

fractal dimension of the produced gouge, measured

by the laser

particle sizer

(Crawford et l

7 .

Equipment

A scaled

schematic

diagram of the

servo

hydraulic direct

shear

rig is shown in Fig. 1. The rig

was fabricated by RDP-Howden

Ltd.,

U.K., to a

customer-specified

design.

The

frame consists of

two

steel

side plates with a fixed base,

and

an

adjustable top

beam on

which a

500kN

hydraulic

linear actuator with a vertical stroke of

200mm

is

mounted, to

provide vertical normal reaction. The

vertical

actuator piston

rod is

attached

to an upper

shear box. Specimen sliding

displacement,

up

to

a

maximum of

100mm,

is achieved by means of a

unique

design

of

shear

table

which

utilises

a

linear

hydrostatic bearing to provide

effectively

frictionless motion,

even when acted on by the

500kN

normal compressive load. The

shear table

is

attached to a

lower shear

box.

Specimen

shearing

is

achieved

by relative horizontal

displacement

of the

lower shear box

fixed to

the

base table,

with respect

to a stationary upper shear box, attached to the

122



piston

head of the vertical

ram.

Sliding

displacement is generated by two horizontal,

opposing 500kN linear actuators with strokes of

l00mm,

each ram

acting only

in

push.

A constant pressure oil

supply

for the

vertical and horizontal

actuator

servo

systems

is

Floating Tahle Control:

T r a l 1 ~ t l l l c c r Imlicat()fS

provided

by

a

mobile

hydraulic power pack

with

a

maximum system

pressure

of 30MPa.

This power

pack

also supplies a lOOT

stiff

servo-hydraulic

compression rig and pressure intensifier

for

conventional

triaxial

compression

testing of core

plugs. The

shear

table

linear

hydrostatic bearing

is

Shear Rig Front Elevation:

~

~ .

I--

flormal 1I1S1 aC l lCIIl

0

.(1

I amPlificrl

(L VDT'S) vertical

hydraulic D ctuator

accumulator mounted

y

R

on

Vertical

Ram

crosshcad

PRESSURE

Control:

P-

INTENSIFIER SL2000

J

Lr _ _ _iJ

COMMAND

- ~

OM P:I'a';S ION

MODULE

:1

~

Hydraulic : ; T : b i ~ :

r ~ l ~ a ~ ~ )-1

for F o3lilu

(Ioadccll)

~ m { t ~ ~ H

fixing

pOSiti()n7

1

shear lox

for crosshead _I>

specimen holder

floating ~ a l l e on

I l

~

discontinuity

hydrostatic hearing

l ~ = ~

shear surr ce

19

9

~ h ~ a r

power

pack

aCluator9

-

shear load (pressure

shear u

.. , u ·

-

(LVDT'S)

Shear Rig Back Elevation:

\P)

c

r:

~

R

normal load 2 /

Ire

l ;u::rp

pressure .. ,

{

servo valve

-

0

0

0

SERVO-HYDRAULIC CONTROLLED, STIFF,

P

IRECT SHEAR l\IACIIINE

-

I

,

I

I I I I

I

I I

~ ~

I

(metres)

1

I Iydraulic Supply

for

Actuators:

~

C O M P ~ E S S I 0 1

(

PRESSURE

J

servo valve

INTENSIFIER

_ I ~ h

•

•

(

POWER

PACK

I

hydraulic oil

~ s s u r e P

-

ydraulic oil

return, R

~

l

-

#

Fig. 1 A

scaled

schematic of the direct shear rig,

123

=-

II

shear \

supply

I



fed from

a

separate

mobile

hydraulic

power

pack

which

supplies

a

maximum

system pressure of up

to

20MPa,

and scavenges

the

spent

oil.

The bearing

action is

created by

feeding hydraulic oil

through

four orifices on

the

underside of

the shear table.

The 20MPa

system

pressure is dissipated

in

a

0.05mm gap between the rims of the orifices and a

lower

bearing

plate. The linear

actuator

providing

vertical thrust is suitable for operation under closed

loop control with displacement or pressure as the

controlling

parameter.

An

internal linear variable

differential transformer (L VDT) provides

measurement

of

piston travel for normal

displacement control, whilst

a

pressure

transducer

in the hydraulic feed line enables the actuator to

be

operated

under the alternative condition

of normal

load

control. The pair

of

single acting (push-only)

horizontal actuators

mounted either

side of the

hydrostatic shear table are controlled separately

from

the vertical ram. L

VDT'

s allow measurement

of horizontal displacement, whilst pressure

transducers in

the hydraulic feed-lines enable

measurement of shear loads. Hardcopy data from

tests performed under constant normal

displacement conditions

is

provided

in

the form

of

continuous line traces

of

normal

load,

shear load

and

normal displacement

against

shear

displacement, recorded

on a multi-channel,

moving-paper

chart-recorder.

To

characterise

size distribution of the

fragmented

frictional

wear products, a

Mastersizer laser

light

scattering-based, particle

size analyser, commercially available from

Malvern

Instruments

Ltd.,

was

employed.

As

far as is

known,

this

present study is the first to employ laser

diffraction technology to

assess

fault gouge. In

essence, the laser light scattering sizer comprises an

optical measurement unit that forms the basic

particle size sensor, and a computer

that

manages

the measurement and

performs results

analyses and

presentation.

The

system

utilises

composite laser

light diffraction patterns produced by the dispersed

particles to compute

size distributions.

The

Mastersizer

has

three standard user-defined

size

ranges:

600 - 1.2, 180 - 0.5 and

80

- O.lJ..lm. t

cannot

simultaneously

cover the

complete dynamic

range in one

measurement,

so the total span is

broken down into the above

size

ranges, each

selected by

fitting the appropriate

range

lens, of

focal

length 300mm,

100mm and 45mm

respectively. The

Mastersizer employs two forms

of

optical configuration to

achieve

its

wide

range.

Whilst conventional

Fourier

optics are used

for

the

two greater focal length

lenses,

the 45mm lens

utilises

a

reverse Fourier

optical

configuration to

minimise aberrations associated with large angle

scattering detection

(typically

>10

0

) from small

particles.

When

a particle scatters light (sourced

from

a low power

Helium-Neon laser) it produces

a

unique

light

intensity characteristic with angle

of

observation.

This light

is scattered

so that

the

measured energy on a detector has a peak at a

favoured scattering angle which is related to the

24

particle

diameter.

Large particles have peak

energies in small angles of scatter and

vice

versa, as

illustrated in Fig 2.

Over

the

size

range 2J lm and

upwards, the

scattering with angle is effectively

independent of the optical properties of the material

or supporting

medium,

resulting

primarily

from

diffraction of light around the particle, however at

the O.IJ..lm size range, interaction of

light

with the

particle is complex and strongly influenced by the

optical properties of the particle, necessitating full

Mie

theory

modelling

of

the

scattering (Mie

theory uses the solution of the electromagnetic

wave

equations

for a

spherical

particle

of

specific

optical

properties). Two

optical

constants

are

required

to

determine

the scattering

behaviour, the

differential refractive index

between the dispersant

and the particle, and the particle absorption, both of

which

are user

selectable.

Thus

it is possible

for

the computer to predict

the scattering

signal

that would be received from a

wide range of materials at a

given

size.

t

formulates

a table

that characterises

how a unit volume of

material, of a range of sizes throughout the working

range,

scatters light. Using

this

theoretical data the

computer deduces

the

volume size distribution

that

gives

rise to

the observed scattering

characteristics,

by

a

process of constrained least squares fitting of

the

theoretical scattering characteristics to

the observed

data. This

best

fit

result can

either

be obtained

with

no

assumed

form

of

size

distribution (model

independent) allowing

the

characterisation of multi

modal distributions

with high

resolution, or else the

analysis

can

be constrained to

a known form

of

distribution

such

as the

Rosin-Rammler

or

Log

normal in volume.

Results

A

dozen 118mm

=4.5 ) -diameter

specimens

sourced

from

blocks retrieved from

surface mining operations, were tested in direct

shear under

constant normal displacement mode.

A

comprehensive range

of

sedimentary lithologies

were tested including Permian red sandstone

(specimens #3, #5, and

#6) and Carboniferous

fissile mudstone (#8 and #9), carbonaceous

Large particles

scatter at

small angles

Small particles

scatter at

high

angles

Central

Detector

Radii

Fig Properties

of scattered

light for large and

small particles.



Sliding Displacement

(mm)

Fig. 3 Shear

and

normal stress versus

sliding

displacement

profiles,

specimen S I (slip

dependent contact area).

5

c

Pre-Peak

+

Post-Peak

4

2

3

'

'

Ci

2

'

..c

n

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

o 2

3

4

5 6

7

Normal Stress (MPa)

Fig. 4 Frictional strength parameters under non

dilatant

maximum

fragmentation conditions,

specimen #8.

laminated

siltstone (#11,

#12 and #14) and

heterolithic sandstone/siltstone (S1,

S2, S3 and

S4).

Each

specimen was tested dry and

under

a

pre

shear initial

normal

load

of less

than

3MPa,

to a

maximum shear displacement of around 25mm,

with normal displacement (generally <O.1mm)

normal load and shear load variations being

recorded as synchronous traces

on

a chart recorder.

Details of

the

experimental methodology and

example load-displacement traces for the four

general rock

types

are given in Smart

Crawford

8

.

Shear and normal

load

curves were converted to

the

appropriate

stress

profiles by dividing by a

slip

dependent contact area, corrected to allow for

progressive decrease in

mated

shear surface area

with

increasing

shear displacement. This

more

realistic variable

contact area

analysis, as

opposed

to

the assumption

of a

constant contact

area,

was

observed to have a

first

order

influence

on

calculated stress profiles, as shown in Fig. 3 for

specimen S 1. In shear stress

versus

normal stress

space, all lithologies exhibited the same overall

attributes irrespective of rock

type,

namely a

non

linear increase in pre-peak

strength

data to a

maximum

friction

value (designated

Ii*max,

and

defined following Amonton's law as the peak shear

load attained divided by the corresponding value of

normal reaction) with post-peak data delineating a

robust straight-line relation with high correlation

coefficients,

defined

by a slope (designated the

coefficient

of

sliding friction, lis

and an intercept

(designated the inherent cohesion of the contact

surfaces,

So).

These relations

and

the

frictional

strength parameters Ii*max, lis

and

So

are shown in

Fig. 4, for specimen

#8.

Tabulated

values

for

comparison

of relative

magnitudes

between

the

different

rock types are

given in

able 1.

With

regard

to a

mechanistic explanation

for these

observed phenomena under constant

normal

displacement conditions,

maximum friction is

interpreted as

representing

peak shear strength of

able Correlation of frictional strength, composition,

and

fault gouge distribution parameters.

Direct Shear Testing

XRD

Analyses

Particle Size Analyses

Friction

Parameters:

%

Mineral

Content: Fractal

Dimension,

D = 3 - n:

I.D.

J.l*max

I

J.ls

I

So

Qtz

I spar I Clay I Mica

Sieving

I

=300mm

I

=45mm

Sw

(MPa)

(cmI\2/g)

#3 0.50

0.36

0.16 94.5

5.5 0 0 1.05

2.12

2.07

1891

#5 0.62

0.50

0.54

82.5

17.5 0 0

1.11

2.15 2.01

2008

#6

0.65

0.48

0.42

--- ---

---

---

0.80 2.20

2.13

2487

#8 0.69

0.43

0.83

15.1 38.8 46.1 0 1.80 2.31

2.05 1319

#9

0.82 0.43 0.38

0 0

100

0 1.83

2.26 2.03 1202

11 0.54

0.15

0.79

---

---

---

--- 1.88 1.46

1.63 874

#12 0.69

0.30

0.82

76.4 4.6

14.5

4.6

1.77 1.95 1.91

891

#14

0.64

0.15 0.98

65.4 8.7 22.1 3.8

1.76

1.88 1.67 454

Sl

0.88

0.21 1.93

44.9 5.7 38.7 5.7 2.05

2.00

1.95

1543

S2

0.62 0.35 0.95 44.5

4.1 45.5

5.9

2.26 2.05 1.85

1340

S3 0.49

0.26 0.76

24.4

0

70.7

4.9

2.14

2.13 1.84

1231

S4

0.80 0.39

2.13

45.1 0 45.5 9.4 1.95 2.08 1.88

1271

125



the sliding

discontinuity, immediately

prior to

through-going

breaching

of the

interlocking

asperity system (usually associated with a

significant, and frequently audible

dynamic

stress

drop)

followed

by

frictional

sliding on

a newly

created, pervasive shear

plane.

Post-mortem

examination reveals

this

surface to

be

composed of

frictionally

comminuted wear debris (analogous to

natural

fault

gouge) frequently exhibiting steps and

slip-parallel striae (analogous to slickensides and

related features as observed on natural fault

surfaces).

Following

direct shear testing, the specimen

halves

were

separated and a small sample of debris

(covering approximately 5% of the initial pre-shear

contact

area)

removed

from corresponding patches

on the upper (TOP) and lower (BOT) sliding

surfaces.

These

samples were

then

sieved

independently using B.S. Sieve No.'s 30 (500f..lm),

36 (422f..lm), 52 (295f..lm), 60 (251f..lm), 100

(152f..lm), 120 (l24f..lm),

150

(l04f..lm) and 170

(89f..lm). The

remaining

debris from both surfaces

was then added together and the total sample sieved

into >500f..lm and <500f..lm fractions, the former

being used

for

X-ray diffraction

(XRD) analysis to

characterise percentage mineral

content

(Table

1)

the latter

for

laser diffraction particle sizing

utilising both

the

300mm

and

45mm focal length

lenses

(resulting

in particle distributions by volume

from

600 - 1.2f..lm

and

80 - O.If..lm respectively).

Such fragmentation

data

has been

analysed

in

terms

of the Rosin-Rammler

9

distribution function, an

empirical, two-parameter, Weibull-equivalent

relation originally developed for broken coal, in

which for the residual

weight

distribution:

Eqn.l

In Eqn. 1, R is the cumulative percent

oversize,

x

the particle size

and

n a n d

b a r e

constants. Taking logs

to

the

base

10, this

represents a straight line relationship between log

log

100 R

and

log x. For theoretically

perfect

grading so that all fragments are the same size, n

00

for

steady size reduction n

=

1, and

for

more

rapid

diminution in size, n < 1, characteristic

of

a

dusty

material.

The constant n is

thus

a

measure

of the closeness of grading, it

fixes

the distribution

of particle

size, and

is therefore called the

distribution constant . The absolute size

constant , X, measures the actual

size

of

the

material, large values meaning

coarse

material and

small

values fine material.

Turcotte

10

,

related

the

power-law

mass distribution

given

in Eqn.l

to

the

definition

of

a fractal

number

distribution, and

showed

that for the fractal dimension, D:

D = 3 n

Eqn.2

Fig. 5 shows both the

sieve

and laser

particle sizing data plotted

in accordance

with the

linear

form of the Rosin-Rammler law, for

Laser sizing:

x

f=300mm

m

f=45mm

0

Sieving:

......

•

Bar

-

eo

0

TOP

..9

-1

6 '

0

-

-

-2

o

g

eo

..9

-3

EEl

.

IDD I

-

4

.1

10 100

1000

Particle

Size

(microns)

Fig. 5 Power-law relations for sieving and laser

particle

sizing volume distributions,

specimen 3.

specimen #3. For

both

the conventional and reverse

Fourier optics configurations, the resultant volume

distributions

show quite marked

sigmoidal

profiles,

with greater slopes at the upper

and lower

ends

indicative of more closely sized products. However

for specimen #3, the central

portions

of each plot

are

linear

and

broadly

parallel,

indicative

of a

power-law distribution.

The best-fit

straight line to

such

portions of each

curve were

used to

define the

distribution constant, b, from which Eqn.2. was

used

to

generate an

inferred fractal dimension,

D,

as listed

in

Table 1.

For the

analyses

by

sieving,

straight

lines

were fitted to the entire size range

(500

- 90f..lm)

and the upper- and

lower-sliding

surface results

averaged to arrive at

aD-value.

The

sigmoidal shape to

some

distributions

may

well reflect

complex

fragmentation

occurring

within the

mUlti-component

specimens, different

mineral species possessing different specific

surface

energies and crystal structures.

Whilst

scale-invariance is

inherent in

the

definition of

a

fractal or

fractional

dimension, natural

as

opposed

to

mathematical fractals do possess

finite upper and

lower

fractal limits above

and

below which

this scale

invariance

breaks down.

Samples

with

clay contents

approximately

~ 5 0

(specimens #8, #9, S2, S3 and S4) show strong

convergence

of both

the

6OO-1.2f..lm and 80-0.1f..lm

size range distributions at around the If lm scale,

suggestive of the attainment of a critical lower

limit to

clay

fragmentation.

For

all samples, good

agreement (relative parallelism) is shown between

the distributions

by

sieving

and

the

300mm

focal

length laser sizing data over

the

equivalent size

range.

Discussion

126

Grady

Kippll

proposed that growing

evidence from a wide variety of different

fragmentation

methods, whilst far from being

complete or systematic, did tend

to

suggest that

the



broad range in size of the distribution constant, n,

might be related,

at least in

part,

to the

type

or

method of fragmentation. Several different

fragmentation processes are listed below in order of

decreasing n:

fragmenting munitions (bomb casings)

direct impact fragmentation (spalling)

Hopkinson bar

testing

(torsional)

Interplanetary debris

(asteroid

breakup)

Ball

milling

(multiple comminution)

6 4

3 2

1.8 - 1.2

::::1

1 -

0.6

From the above list, Grady Kipp

suggested that

single tensile

fragmentation

leads to

fragment

size distributions

with large values

of

n,

whereas

in contrast, fragmentation

with

significant

shearing and continued comminution

leads

to lower

values. In

Fig.

6, average

distribution

constants, n,

from the relatively large-size

fraction

sieving

analyses

are plotted against percentage

mineral

content,

determined

by

XRD of the

multilithologic

direct shear specimens. From this,

it is

evident that

the distribution constant

increases

fairly

systematically from

n :::: 1

to

n

=

2

with increasing

quartz content, and vice versa with increasing clay

content. As the

method

of

fragmentation has been

the same for all rock types, that

of direct

shear

testing under constant

normal displacement

control,

this

observed variation in distribution constant

therefore must

reflect

material

property

differences.

A

tentative

explanation can be

found by

considering

the

micromechanics

of

the

deformation. For

the

high

quartz content

sandstones

with grain-supported ball-bearing like

structures,

macroscopic shearing

will on

the

microscale

be

transmitted as

stress-concentrations

at the point-to

point quartz grain

contacts,

resulting in

predominantly tensile splitting exactly

analogous

to

axial

microcracking in

triaxial

compression

specimens. By contrast,

due

to the foliated nature

of

the clay-rich

lithologies,

macroscopic

shearing

may

activate this fabric

resulting in

foliation shearing as

I=l

~

n

I=l

0

U

§

.g

D

.5

on

is

U

U

;>

<:

2.5

2.0

I

. Quartz

I

• Clay

1.5

•

1.0

b

0.5

0.0 +-...-.--.--.- 'T-r-....-...-,........., .......-,..--.-....,....,-..--,.........-....-i

o

25

50

75

100

Percentage

Mineral Content

Fig.

6 Dependence

of

fault

gouge distribution

constant on source

lithology mineral

content.

observed in natural argillaceous fault gouge. Thus

the

mechanisms of strain accomodation on the

microscale are determined by initial rock

microstructure,

with the

relative

amounts of

resultant

shearing fragmentation to

tensile cracking

being reflected in the debris distrbutions.

As the

surface area of a bed of

powder is

inversely

related to

the

particle size, the

lowest

size-range distribution (laser particle

sizer

with

45mm focal length lens) yields the greatest estimate

of specific surface area, calculated according to

Herdan

12

, by:

Eqn.3

Sw is the specific surface area per unit

weight, p is

the

density of

the

mineral phase, wdh

is the harmonic mean of

the

weight distribution,

and

the 6

corresponds to the shape factor

of

the

particles

(the laser sizer assumes they

are

all

spheres). Tabulated values of

Sw are

given in

able

1, from which it is apparent

that the

sandstone lithologies generate the largest surface

areas of

fault

gouge.

An

interesting direct

correlation

is

shown between

the

specific surface

area,

Sw,

and the coefffcient

of

sliding

friction,

J.L

s

(Fig.

7) the

relatively

slippy carbonaceous

siltstones possessing low frictional coefficients and

generating low shear debris surface areas,

the

red

sandstones vice versa.

The

Sw

versus J.L

s

relationship

can

perhaps

be rationalised through consideration of

the

following:

For

each

direct shear test, an

empirical

Coulomb-type linear

friction

law has been

demonstrated for sliding on newly created,

slickensided

and

shear

debris

covered surfaces:

Eqn.4

However

implicit

in

this formulation

is

the

assumption of a p e r f e ~ t l y - m a t e d

contact area

127

0.75 . - - - - - - - - - - - - - - - - - . . . . .

S3

I SI

0.00

- t - r - . - . ~ . . . . ........................ .. .... .... .... ..... .... .............. . . . . . . ~

....

..... ..........j

o

500 1000

1500

2000

2500

3000

Specific

Surface

Area

cmI\2/g)

Fig.

7

Relationship

between

frictional

strength

and

fault gouge specific

surface

area.



(although

corrected

for

the

effect of shear

displacement) when converting the measured shear

forces and normal reactions to stresses. Thus an

apparent contact area.

Aapparent

is assumed which

will

be

greater

than the

actual contact

area. Area .

occurring at the tips of touching asperities

associated with

rough

surfaces

in contact. Thus in

Eqn.

4.

the

shear

and

normal stresses can be

annotated

with the subscript apparent'·.

The

actual

stresses.

'treal

and

O'reah are

given

by

multiplying

the

calculated stresses. 'tapparent

and

O'apparent by

the

ratio (Aapparent / Areal). On

rearrangmg. Eqn.

4

becomes:

_ S (Aapparent)

'treal

0

A

l iS = real E 5

-

• qn.

O real

In Eqn.

5

above.

J 1

s

oc -IIA

rea

l.

so

that

as

the contact

area increases.

the frictional coefficient

also increases.

For

post-maximum friction

conditions

under

infinite

normal

stiffness. residual

sliding

is occurring wholly upon

a

bed

of

powdered

rock fragments. so that the

contact

area

is

best

described. not by fault wall

roughness

and asperity

contact.

but rather by the

specific

surface area of

the debris bed.

Sw =Areal. For smaller particle

size

and

therefore

greater

surface area. the

real area of

contact tends

more and more

towards the assumed.

perfectly-mated

contact area. the

ratio

Aapparent:Areal

decreases and

from

Eqn. 5. the

frictIonal

coefficient increases. thus

explaining

the

relationship in

Fig.

7.

Conclusions

A

novel

servo-hydraulic direct shear

machine

operated under constant normal

displacement (maximum normal

stiffness)

control

has

been used

to test lithologies ranging

from

sandstones

to

mudrocks. Once interlocking

asperities

have

been sheared through. residual

sliding

takes place

on a new

pervasive

shear plane

of

comminuted rock debris.

with

frictional strength

conforming

to

a linear Coulomb-type>'

criterion.

Sliding coefficients are less than (down

to

0.15)

and cohesions

greater

than

(>2MPa)

those

usually

measured

under dilatant. constant normal stress

conditions.

Such data

is

considered

relevant to

coupled

fluid flow

and deformability

reservoir

simulation in

which

sealing faults are expressly

incorporated. t is also directly pertinent to the

near-wellbore environment. Induced shear debris

volume

distributions

have been

quantified

down to

0.1 J.1m using new laser diffraction technology. such

analyses proving valuable in understanding both

macroscopic strength

and

the micromechanics of

deformation.

Future experimentation should

focus

on

characterisation

of both constant normal

stiffness and dilatant shear frictional response.

ideally

in combination

with

development of a fluid

flow

capability to enable simultaneous

permeability

quantification

during

shearing.

128

Nomenclature

A:

D

wdh:

k

n

:

n:

R:

So:

Sw:

x:

x:

on:

J.1*max:

J 1s:

O n:

't:

p:

Subscripts:

direct

shear

specimen

contact area

fractal dimension

harmonic mean of weight distribution

normal

stiffness

Rosin-Rarnmler distribution constant

residual

weight

%

cohesion of sliding surfaces

specific surface area

per

unit weight

particle size

Rosin-Rarnmler absolute size

constant

normal displacement

maximum

friction

coefficient

coefficient

of

sliding

friction

normal stress

shear stress

density of single mineral phase

apparent: assumed perfectly-mated contact area

real:

true rough contact area

References

1

Heath.

A.E

•

Walsh.

J.J..

Watterson.

J.:

Estimation of the

effects of

sub-seismic

sealing faults on effective permeabilities in

sandstone

reservoirs.

In:

Aasen

et

al

(Eds.)

North

Sea Oil and Gas Reservoirs - III

(1994)

NTH.

Kluwer

Academic Publishers.

Ch.

9. pp.173-183.

2. Heffer.

K.J • Last. N.C.. Koutsabeloulis.

N.C

•

Chan.

H.C.M

•

Gutierrez.

M. Makurat.

A.:

The influence

of natural fractures, faults and

earth

stresses

on reservoir performance -

geomechanical

analysis

by numerical

modelling;' In:

Aasen

et al

(Eds.)

North

Sea

Oil

and Gas Reservoirs - III (1994)

NTH.

Kluwer Academic Publishers.

Ch.

11.

pp.201-211.

3. Bawden. W.F • Curran. J.H. Roegiers. J.C.:

Influence of fracture deformation on

secondary permeability - a numerical

approach, Int.

J

Rock Mech. Min. Sci.

Geomech. Abstr. (1980) Vol.

17.

pp.265-279.

4. Saeb.

S.

Amadei. B.:

Modelling joint

response

under

constant or variable

normal

stiffness boundary

conditions;' Int. J Rock

Mech.

Min. Sci.

& Geomech. Abstr.

1990)

Vol.

27. No.3. pp. 213-217.

5. Goodman.

R.E.: Introduction to Rock

Mechanics

(2nd.

Edn.). John Wiley Sons.

New

York

(1989) 562pages.

6.

Johnston.

I.W

•

Lam. T.S.K

• &

Williams.

A.F.: Constant normal stiffness direct shear

testing for socketed

pile design

in weak

rock.

Geotechnique (1987) Vol. 37. No.1.

pp.83-

89.

7.

Crawford. B.R.. Main.I.G.

Smart,

B.G.D.:

Influence of the fractal structure of

fault

gouge on fluid

permeability

across faults

during

deformation,

(1994) J

Struct. Geol.

(in prep.).



8. Smart,

B.G.D.

Crawford, B.R.: An

investigation

of shear

debris

comminution as

a

mechanism

of

strain energy release for

frictional sliding

on dominant parting

planes,

In:

Brummer,

R. (Ed.)

Static

and Dynamic

Considerations In Rock

Engineering

1990)

A.A.Balkema, Rotterdam, pp.389-400.

9. Rosin,

P.

Rammler, E.: The laws

governing

the fineness of powdered

coal,

J

Inst.

Fuel (1933) Vol. 7, pp.29-36.

10.

Turcotte,

D.L.:

Fractals

and

Chaos In

Geology

and

Geophysics (1992) Cambridge

University Press, 221pages.

11. Grady,

D.E.

Kipp, M.E.:

Dynamic

rock

fragmentation,

In: Atkinson, B.K. (Ed.)

Fracture Mechanics o Rock 1987)

Academic Press, London, Ch. 10, pp.429-475.

12. Herdan, G.: Small Particle Statistics 1960)

Butterworths,

London,

418pages.

29

Documents

SPE-28036-MS_Relationship Between Frictional Strength and Fault Gouge Generation From Direct Shear Testing Under Constant Normal Displacement Control