properties of rock discontinuities

7/31/2019 Properties of Rock Discontinuities

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Chapter 5 Properties of Rock Discontinuities 1

CHAPTER 5

PROPERTIES OF ROCK DISCONTINUITIES

Properties of rock discontinuities govern the overall behaviour of the rock masses. This

Chapter addresses properties of rock discontinuities.

Rock discontinuities include joints, fractures, faults and other geological structures.Rock joints are by far the most common discontinuity encountered in rock masses. Rock

fractures are random features. Rock faults and folds are major but localised geological

structures and therefore are dealt individually.

5.1 Geometrical Characteristics of Rock Joints

5.1.1 Joint Sets and Length: Joints and Fractures, Set Number, and Persistence

As discussed early in the chapter dealing with rock formation, joints are generally in sets,

i.e., parallel joints. The number of joint sets can vary from 0 to as many as 5 (Table

5.1.1a). Typically one joint set cuts the rock mass into plates, two perpendicular sets cut

rock into column and three into blocks, and more sets cut rocks into mixed shapes ofblocks and wedges, as shown in Figure 5.1.1a.

The mechanical properties of the rock mass is obviously influenced by the presence of

joint sets and the number of joint sets. More joint sets provide more possibilities of

potential slide planes for rock wedges or blocks to slide and fall.

Figure 5.1.1a Rock masses showing one and three joint sets.

Table 5.1.1a ISRM suggested description of joint sets

I Massive, occasional random fractures

II One joint set

III One joint set plus random fractures

IV Two joint sets

V Two joint sets plus random fractures

VI Three joint sets

VII Three joint sets plus random fractures

VIII Four or more joint sets

IX Crushed rock, earth-like

Different from joints, rock fractures are considered as a non-systematic discontinuous

feature of rock masses. They are not in sets or parallel. They could be large in term of

numbers but their distribution is generally random. Rock mass quality is influenced by

the number of rock fractures and they are usually considered in the overall degree of

fracturing of a rock mass, in term of joint spacing and RQD, discussed in later sections.


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Persistence is the areal extent or size of a discontinuity, and can be crudely quantified by

observing the trace lengths of discontinuities on exposed surfaces. The persistence of

joint sets controls large scale sliding or 'down-stepping' failure of slope, dam foundation

and tunnel excavation. Figure 5.1.1b gives diagrams showing persistence of various

joint sets, while Table 5.1.1b presents the classification of persistence commonly adopted.

Figure 5.1.1b Sketches indicating persistence of various joint sets.

Table 5.1.1b ISRM classification of discontinuity persistence

Description Surface Trace Length (m)

Very low persistence < 1

Low persistence 1 3

Medium persistence 3 10

High persistence 10 20

Very high persistence > 20

5.1.2 Joint Orientation: Joint Plane Orientation and Representation

Orientation of a discontinuity is described by its dip and dip direction or its dip and strike.

The orientation of major joint set relative to an engineering structure largely controls the

possibility of unstable conditions or excessive deformations developing. The mutual

orientation of discontinuities will determine the shape of the individual blocks and beds

comprising the rock mass.

Orientation of a plane is measured by the degree of inclination and the direction of facing

of the plane. It does not fix its position. Therefore, two parallel planes have the same

orientation. In rock mechanics and engineering geology, the orientation of a plane is

generally defined by dip angle (inclination), dip direction (facing) or strike (running), as

illustrated in Figure 5.1.2a.

Figure 5.1.2a Representation of joint plane orientation.

Dip or dip angle represents the degree of inclination. It is the acute angle between the

plane and the horizontal plane. It is also the acute angle between a line with maximum

dip in the inclined plane and its horizontal projection. Dip angle is generally expressed

by an acute angle between 0 and 90.

Dip direction represents the facing direction. It is the bearing measured clockwise from

the north (0) of the line with maximum dip in the inclined plane. Dip direction is

generally expressed by a direction angle of 0 to 360.


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Strike is the alignment or run. It is the bearing of an imaginary horizontal line in the

inclined plane. Strike is generally expressed by a direction angle of 0 to 180.

Dip direction and strike direction are always perpendicular. In rock mechanics, dip

direction/dip format is generally used, e.g., 210/35, or 030/35, where dip directions

always have 3 digitals. Sometime, when strike is used instead of dip direction, the

general direction of plane dip must be given, otherwise, it could means two possible

planes, e.g., dip/strike 120/35 would be either dip direction/dip 210/35, or 030/35.Therefore correctly it should be presented as strike/dip 120/35SW which is the plane in

dip direction/dip 210/35, or 120/35NE which is the plane in dip direction/dip 030/35.

Normal to the plane is the imaginary line at right angle to the plane. Therefore the

orientation of the normal is given by,

trend of normal = dip direction of the plane 180,

plunge of normal = 90 dip.

Orientation of a joint plane can be represented graphically using hemispherical projection

method. The projection method is to represent a 3D plane by a 2D presentation. The

most common projection is the low hemispherical equal angle projection. Use the

projection, joint orientation data can be assessed in 2D form.

Figure 5.1.2b Analysis of joint orientation data using projection method.

It is a powerful tool to analyse large number of joint data and examine the rock slope

stability, slide of rock block in underground excavation, stability of rock foundation on

jointed rock mass. The use of the hemispherical projection method is given in a later

section in this chapter.

5.1.3 Joint Spacing: Joint Spacing, Frequency, Block Size, and RQD

The degree of fracturing of a rock mass is controlled by the number of joint in a givendimension. A rock mass contains more joints is also considered as more fractured. More

joints also mean that average spacing between joints is less. Several parameters can be

used to express the fracturing degree of a rock mass.

The spacing of adjacent joints largely controls the size of individual blocks of intact rock.

It controls the mode of failure. A close spacing gives low mass cohesion and circular or

even flow failure. It also influences the mass permeability.

Joint spacing for a particular pair of joint is the perpendicular distance between the two

joints. For a joint set, is usually expressed as the mean spacing of that joint set.

However, when the expose is limited, often the apparent spacing is measured. Figure

5.1.3a shows the relationship between spacing of individual joint set, apparent spacing

and average spacing. In the assessment of rock fracturing degree, the overall average


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spacing is considered. However, as illustrated in the figure, measurements of the overall

average joint spacing are different on different measuring faces.

Figure 5.1.3a Joint spacing, apparent spacing and true spacing.

ISRM recommends the use of the terms in Table 5.1.3a to describe joint spacing. Thedescription ranges from extremely close spacing to extremely wide spacing.

Table 5.1.3a Classification of discontinuity spacing

Description Joint Spacing (m)

Extremely close spacing < 0.02

Very close spacing 0.02 0.06

Close spacing 0.06 0.2

Moderate spacing 0.2 0.6

Wide spacing 0.6 2

Very wide spacing 2 6

Extremely wide spacing > 6

Joint frequency (), is defined as number of joint per metre length. It is therefore simply

the inverse of joint spacing (sj), i.e.,

= 1 / sj

Another measure of fracturing degree is the Rock Quality Designation (RQD). Is is

defined as the percentage of rock cores that have length equal or greater than 100 mm

over the total drill length (Figure 5.1.3b).

Length of cores >100 mmRQD =

Total length of drilling

100%

Figure 5.1.3b Example of measuring RQD from core logging.

Although RQD was initially proposed as an attempt to describe rock quality, in reality, it

only describes fracturing degree, by in fact considering the spacing of joints. Therefore,

statistically, RQD can be correlated to joint spacing or joint frequency the following

equation:

RQD = 100 e0.1

(0.1 +1)

For values of in the range 6 to 16/m, the above equation can be approximated by,


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RQD = 110.4 3.68

Joint space also defines the size of rock blocks in a rock mass. When a rock mass

contains more joints numbers, the joints have lower average spacing and smaller block

size. Block size can be classified by the volumetric joint count, Jv, defined as number of

joint per m3 volume of rock mass, as presented in Table 5.1.3b.

Table 5.1.3b ISRM suggested block size designations

Designation Volumetric Joint Count, joints/m3

Very large blocks < 1

Large blocks 1 3

Medium-sized blocks 3 10

Small blocks 10 30

Very small blocks > 30

Crushed rock > 60

RQD can be related approximately to Jv

by:

RQD = 115 3.3 Jv, for Jv between 4.5 and 30.

For Jv < 4.5, RQD is taken as 100%, and for Jv > 30, RQD is 0%.

5.1.4 Joint Surface and Opening: Roughness, Matching, Aperture and Filling

A joint is an interface face of two contacting surfaces. The surfaces can be smooth or

rough; they can be in good contact and matched, or they can be poorly contacted and

mismatched. The condition of contact also governs the aperture of the interface. The

interface can also be filled with intrusive or weathered materials.

Joint surface roughness is a measure of the inherent surface unevenness and waviness of

the discontinuity relative to its mean plane. The roughness is characterised by large

scale waviness and small scale unevenness of a discontinuity. It is the principal

governing factor the direction of shear displacement and shear strength, and in turn, the

stability of potentially sliding blocks.

Roughness can be distinguished between small scale surface irregularity or unevenness

and large scale undulation or waviness of the discontinuity surface, as illustrated in Figure

5.1.4a.

Figure 5.1.4a Definition of joint roughness at different scale.


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A classification of discontinuity roughness has been suggested by ISRM, and is

reproduced in Figure 5.1.4b. It describes the roughness first in metre scale (step,

undulating, and planar) and then in centimetre scale (rough, smooth, and slickensided).

The classification is useful to describe the joint surface but does not give any quantitative

measure.

Figure 5.1.4b Typical joint surface profile and suggested descriptions andcorresponding joint roughness coefficient (JRC) at different scales.

Another commonly used roughness classification is proposed by Barton, termed as Joint

Roughness Coefficient (JRC). JRC number is 0 for the smooth flat surface and 20 for

the very rough surface. The proposed JRC is reproduced in Figure 5.1.4b. Joint

roughness is affected by geometrical scale. In the JRC classification, the value of JRC

decreases with increasing size.

It should be noted that in realty, profiles of joint surfaces are 3D features (Figure 5.1.4c).

The above descriptions are 2D based. It is therefore suggested to take several linear

profiles of a surface for the description and JRC indexing.

Figure 5.1.4c 3D presentation of joint surface.

Joint surface is a rough profile that can be described by statistic method and fractal.

(A section on fractal describing surface profile.)

Fractal method is applicable not only in 2D (linear profile), but also in 3D (surface plane

profile), as shown in Figure 5.1.4d. It is a very powerful tool to quantify the surface

profile.

(More)

Figure 5.1.4d 3D joint surface profiles and fractal numbers.

However, a joint is an interface of two surfaces. The properties of a joint are therefore

controlled by the relative positioning of the two surfaces, in addition to the profiles of

both surfaces. For example, joints in fully contacted and interlocked positions has little

possibility of movement and is also difficult to shear, as compared to the same rough

joints in point contact where movement can easily occur. Often, joints are differentiated

as matched and mismatched (Figure 5.1.4e). A Joint Matching Coefficient (JMC) has

been suggested by considering the contact percentage of two surfaces, as shown in Figure

5.1.4f. JMC various from 0, representing completely mismatched with a few contact

points only in the joint interface, to 1, representing completely matched with fully in

contact of the joint.


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Figure 5.1.4e Matched and mismatched joint surface.

Figure 5.1.4f Scheme of Joint Matching Coefficient (JMC) for rock joints.

In a natural joint, it is very seldom that the two surfaces are in complete contact. There

usually exists a gap or an opening between the two surfaces. The perpendicular distance

separating the adjacent rock walls is termed as aperture. Descriptions of aperture are

suggested in Table 5.1.4a. Joint opening is either filled with air and water (open joint)

or with infill materials (filled joint), as illustrated in Figure 5.1.4g. Open or filled joints

with large apertures have low shear strength. Open aperture also associates with high

permeability and storage capacity.

Figure 5.1.4g Joint aperture and joint with filling.

Table 5.1.4a Classification of discontinuity aperture

Aperture Description

< 0.1 mm Very tight

0.1 ~ 0.25 mm Tight

0.25 ~ 0.5 mm Partly open

"Closed feature"

0.5 ~ 2.5 mm Open

2.5 ~ 10 mm Widely open"Gapped feature"

1 ~ 10 cm Very widely open

10 ~ 100 cm Extremely widely open

> 1 m Cavernous

"Open feature"

Aperture can be separated by mechanical aperture or real aperture and equivalenthydraulic aperture or conducting aperture. The later is particularly important when

permeability is concerned.

Filling is material in the rock discontinuities. The material separating the adjacent rock

walls of discontinuities. The wide range of physical behaviour depends on the

properties of the filling material. In general, filling affects the shear strength,

deformability and permeability of the discontinuities.

5.1.5 Correlation between Various Geometrical Properties

Figure 5.1.5a is an illustration of all the important geometrical properties of rock joints

and fractures. As all the features in a rock mass have undergone the same geological

processes, some of the geometrical features has certain degree of correlation.


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Figure 5.1.5a Illustration of various geometrical characteristics of rock joints and

fractures.

(Discussions on correlations between: joint set number and joint spacing/RQD, JRC and

aperture, etc)

5.2 Mechanical and Hydraulic Properties of Rock Joints and Fractures

5.2.1 Normal Stiffness and Displacement

Normal deformation characteristics and normal stiffness of rock joints are important

parameters for analysis and design. As discussed in an earlier chapter, a joint represents

a discontinuity of stress and displacement. A natural joint always has opening aperture

of less than 1 mm to a few mm. With increasing normal stresses, the opening closes,

and contact areas of the joint surfaces increase. Therefore as shown in Figure 5.2.1a, the

normal stress normal displacement curve can be highly non-linear. The normalstiffness, slope of the curve, is therefore not a constant.

Figure 5.2.1a Normal stress - normal displacement relation of joints in a granite

There are several mathematical models describing the normal stress displacement

relationship. In developing a joint element finite element model, Goodman (1976) used

a hyperbolic relation between normal stress, n, and normal displacement, dn,

n ni dn

ni= A (

dmax dn)

t

where dmax is the maximum possible closure, ni = a seating pressure defining the initial

normal stress conditions for measuring normal displacement, and A and t are

experimentally determined constants.

Based on a great number of laboratory experiments on matched rock fractures in dolorite,

limestone, siltstone and sandstone, Bandis et al. (1983) proposed a hyperbolic function to

express the normal effective stress-closure relation of a matched fracture. Assuming

positive signs for compression and fracture closure and negative signs for tension and

fracture opening, the normal effective stress-closure relation is,

kni dnn =

1 (dn/dmax)


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or

ndn =kni + (n/dmax)

where n is the normal effective stress, dn is the fracture closure, dmax is the maximum

allowable closure, kni is the normal stiffness of the fracture at initial stress. Whennormal stress becomes infinite, fracture closure approaches the maximum allowable

fracture closure, and simultaneously, normal fracture specific stiffness becomes infinite.

The fracture becomes a welded interface. On the other hand, when normal stress is zero,

fracture closure becomes zero, and the corresponding normal fracture specific stiffness is

named as initial normal fracture specific stiffness. The initial normal stiffness (kni) and

maximum allowable closure (dmax) can be determined from regular static fracture

deformation tests or fracture properties, i.e., fracture wall compressive strength (JCS),

fracture roughness coefficient (JRC) and average aperture thickness (ai) at initial seating

normal stress, as described by Barton et al. (1985). The model is commonly known as

the BB (Barton-Bandis) model.

The above hyperbolic BB model of the fracture normal behaviour is commonly used in

rock mechanics and engineering. Under cyclic loading/unloading condition, the BB modeldescribes that the initial load and unload cycles may cause a hysteresis between them.

Successive load/unload cycles can continue to stiffen the fractures, and the BB model

eventually tends to a hyperbolic elastic model without the hysteresis between the load and

unload cycles.

On the other hand, in the laboratory experiments on mismatched rock fractures, Bandis et

al. (1983) also found that the mismatched rock fractures exhibit much reduced normal

stiffness, compared to the matched fractures. A semi-log function was used to fit the

normal stress-closure curves, as expressed in the following:

log n = p + q dn

where n is normal effective stress, dn is the fracture closure, p and q are materialconstants.

Logarithmic functions have also been used by others to describe the normal behaviour of

rock fractures. For example, Zhao and Brown (1992) found that the normal stress -

normal displacement could be fitted by a function below,

dmax dn

dmax dni= 1 A ln(n/ni)

where dni = displacement at a reference normal stress ni, usually equal to the seating

pressure, and A is constant varies from 0.16 to 0.21.


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The curve shown in Figure 5.2.1a indicates that at high normal stress, when the joint is

highly closed, the normal stiffness approaches that corresponding to the elastic modulus

of the rock material. When the joint is completely closed, there is no further closure of

the joint, the displacement is therefore only by the elastic deformation of the rock

material.

5.2.2 Shear Strength of Rock Joints and Fractures

Shear behaviour of rock joints is perhaps one of most important feature in civil

engineering rock mechanics. Conditions for sliding of rock blocks along existing joints

and faults at slope or excavation opening are governed by the shear strengths developed

on the sliding rock discontinuities. As seen in Figure 5.2.2a, in slope, shear is subjected

to a constant normal load generated by the weight of the blocks; while in tunnel, shear is

subjected to constant stiffness due to the constraints of lateral displacement.

Figure 5.2.2a Controlled normal load (a, c) and controlled normal displacement (b, d)

shearing modes and tests.

The shear properties are usually determined by direct shear test shown in Figure 5.2.2a.

Detailed description of test preparation and methodology is given in a later section.

As shown early in chapter on mechanics, sliding between two smooth horizontal contact

surfaces gives the relationship between the friction angle , the normal force (N) and

shear force (Fs), as Fs = N tan.

It is therefore not surprised that shear tests carried out on smooth, clean fracture surfaces

at controlled normal load condition generally give shear strength (s) - effective normal

stress (n) curve (Figure 5.2.2b) and it follows the simple Coulomb law:

= n tan

where is the effective angle of friction of the fracture surfaces. For the case shown in

Figure 5.2.2b, = 35, a typical value for quartz-rich rocks.

Figure 5.2.2b Shearing of smooth quartzite surfaces under various conditions.

Naturally occurring discontinuity surfaces are far from being smooth. Figure 5.2.2c is

typical of the results obtained for clean, rough fractures. As observed in the tests, shear

stress quickly mobilised and reaches a peak. When shearing is progressed, the shear

strength stablised to a residual level. The peak is usually term as the peak shear strength

and the residual is the residual shear strength. For rough joints, peak shears strength is

significantly higher than the residual strength.


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Figure 5.2.2c Results of a direct shear test on a clean rough rock joint.

Observations of shear test results show that residual strength follows the linear friction

law, i.e.,

r= n tan r

On the other hand, peak shear strength does not follow the linear fiction law. The peak

strength for rough joints does not linearly proportional to normal stress. The gradient of

the peak shear strength normal stress decreases with increasing normal stress.

As shown early in Chapter 3, for idealized rough fracture models by Patton (1966) shown

in Figure 5.2.2d, it is similar as sliding between two contact surface at an inclination.

Therefore, at low normal stress and at relatively short shear distance, shear strength is also

influenced by the inclination angle,

= n tan(+i)

It was found that when the normal stress is increased above a critical value, shear stress

can eventually be developed so high that it causes shear failure through the asperities.

When such shearing through asperity occurs, the shear strength is somehow related to the

shear strength of the materials of the asperities. Comparing to rock joint, rock materials

have higher cohesion and internal friction angle of generally around 30.

Figure 5.2.2d Idealized surface roughness models and bilinear peak strength envelope.

Therefore, shear strength for a rough fracture could exhibit two features, a lower portion

representing shearing by climbing the asperity angle, and an upper portion representing

shearing off the asperities. This leads to a bilinear shear strength model shown in Figure5.2.2d, and is expressed by the equations below. In the equation, n is the critical

normal stress when shearing of asperity is assumed to start.

n tan (+i) fornn = {

c + n tan fornn

However, in reality, there is not clear boundary between shearing by climbing the asperity

angle and shearing off the asperities. With increasing normal stress, asperity shearing

off increases progressively. Therefore, the actual shear stress normal stress relation is

represented by a curve, as shown in Figure 5.2.2c.


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Based on extensive test results and noticing the progressive damage of asperities, Barton

(1973) proposed that the peak shear strengths of joints could be represented by the

empirical relation below,

JCS = n tan [JRC log10

( n) + r]

where n = effective normal stress, JRC = joint roughness coefficient on a scale of 1 forthe smoothest to 20 for the roughest surfaces, JCS = joint wall compressive strength, and

r= drained residual friction angle.

(Discussion on dilation and dilation angle.)

5.2.3 Other Factors Affecting Joint Shear Behaviour

Roughness effect can cause shear strength to be a directional property. Figure 5.2.3a

illustrates a case in which rough discontinuity surfaces were prepared in slate specimens.

Directional effects are not just in foliated rocks, but rather universal. As discussed in the

geometrical properties, surface profile is a 3D feature while shearing is a directional

activity. Surface profile along a particular direction would be different along anotherdirection and hence gives different shear strength.

Figure 5.2.3a Effect of shearing direction on the shear strength of a joint in a slate.

The natural discontinuities normally suffered weathering and alteration, which in term,

also change the degree of matching of the discontinuity surfaces. It was found that the

mismatched discontinuities generally have much lower shear strength than matched

(interlocked) ones (Figure 5.2.3b).

Figure 5.2.3b Shear strength of matched and mismatched fractures in a granite.

When a joint is wet, it has generally a lower friction angle than a dry joint. The shear

strength of a wet joint is calculated use the wet friction angle. If the joint is subjected to

groundwater pressure, the normal stress in the shear strength equation is the effective

normal stress, i.e., total stress water pressure.

The JRC-JCS shear strength equation shows that the shear strength of a rough joint is

both scale dependent and stress dependent. As n increases, the term log10(JCS/n)

decreases, and so the net apparent friction angle decreases. As the scale increases, the

steeper asperities shear off and the inclination of the controlling roughness decreases.

Similarly, the asperity failure component of roughness decreases with increasing scale


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because the material compressive strength, JCS, decreases with increasing size, as

illustrated in Figure 5.2.3c.

Figure 5.2.3c Influence of scale on the three components of discontinuity shear

strength.

5.2.4 Flow and Permeability of Rock Joints

From the early chapter on mechanics, it showed that flow in parallel plates is governed by

the cubic flow law. The parallel plates theory is applicable to flow in rock joints.

Therefore, flow and permeability of a rock joint are given as,

w i g de3

Q =12

(5.2.4a)

g de2

k =12

(5.2.4b)

where g = acceleration due to gravity, = kinematic viscosity of the fluid, w = width ofthe joint, and d = aperture of smooth plates or equivalent hydraulic aperture of the rough

joint.

The parallel plates theory is assumed for smooth plates and laminar flow. When it is

applied to actual rock joints with rough surfaces, which are far from smooth, the equation

does not truly represent the real case. The original equation therefore, does not account

for the deviations from the ideal conditions due to the joint surface geometry and other

effects. Somehow, modification has to be introduced to reflect the effects of joint

roughness and flow path. Therefore, in the above equation, instead of the aperture of

smooth plates, in natural rock joints, equivalent hydraulic aperture is used. The equivalent

hydraulic aperture of a rock joint (de)is estimated from,

de = f d (5.2.4b)

where d is the actual aperture of the rock joint, and f is a factor that accounts for

deviations from the ideal conditions that are assumed in the parallel smooth plate theory,

and f 1.

It is found that for a given joint, f is a constant at different apertures, without change of

joint surface profile (Witherspoon et al 1980). It is also noted that f value is generally

lower when the joint surfaces are rougher. This means that rougher joints deviate more

from smooth parallel plates and hence require higher corrections.

5.3 Correlations between Geometrical, Mechanical and Hydraulic Properties


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5.3.1 Joint Surface Profile and Normal Stiffness

It was observed that closure under load was more complete in smooth joints than in rough

joints. Conversely, rough joints in strong rocks close least under normal stress. The initial

normal stiffness and maximum closure were dependent on roughness (JRC) and wall

strength (JCS).

The effect of joint surface mismatch was noticed. Earlier experiments performed by

Bandis (1980) suggested that when mismatch occurs the number of contact points may

reduce, although the individual areas of contacting asperities may become larger.

5.3.2 Joint Surface Profile and Shear Strength

The JRC-JCS joint shear strength criterion has already highlighted the relationship

between joint roughness and strength. It is evident that rougher joint surface leads to

higher shear strength.

(Discussion on correlation between fractal and shear strength.)

5.3.3 Joint Surface Profile and Permeability

Many studies have been conducted on strength, deformation and conductivity coupling of

rock joints in an attempt to relate these to the joint surface roughness. A relationship

between equivalent hydraulic aperture and real joint aperture based on the Joint

Roughness Coefficient (JRC) was proposed by Barton and Choubey [1977]:

JRC2.5

de = (d/de)

2

(5.2.5b)

where de is the equivalent hydraulic aperture and d is the real aperture of a joint.

5.3.4 Joint Closure and Permeability

The permeability and hydraulic aperture of rock joints changes with effective normal

stress. As shown in Figure 5.3.4a, joint permeability reduces asymptotically and

approaches to zero with increasing effective normal stress.

Figure 5.3.4a Changes of permeability with effective normal stress of rock joints in a

granite.


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A hydraulic model describing the hydraulic behaviour of discontinuities was proposed by

Walsh (1981) and modified by Zhao and Brown (1992). The model suggested a

logarithmic relation between the joint permeability, kj and the effective normal stress,

(n),

kj n

kr= [1 B Ln (

r) ]

2(5.3.4a)

where kr= the rock joint permeability at a reference effective normal stress r, and B is a

parameter dependent on surface properties of the joint.

5.3.5 Joint Shear, Aperture and Permeability

For an originally matched and closed joint, shear will start to general separation of the

joint surface and creating larger aperture and high permeability, as illustrated in Figure

5.3.5a. As seen from the figure, when shear occurs, dilation occurs due the climbing

effects. The climbing effects may be less obvious if the joint is under high normal

stress. In this case, the asperities would be crashed and crashed particles may be filled in

the joint. This may still result in increasing of permeability but not as significant as in theprevious case.

Figure 5.3.5a Change of aperture with shear displacement of a matched joint.

For a non-matched joint, the situation may be quite different. Depending on the original

situation, the aperture could be reduced if shearing of the joint causes close up of the

joint, or vice versa.

5.4 Behaviour of Joints under Cyclic and Dynamic Loading

5.4.1 Joint Surface Damage under Cyclic Loading

5.4.2 Joint Behaviour under Dynamic Loads

5.4.3 Factors affect Rate Dependent Characteristics of Joints

5.5 Effects of Joints on Transient Stress Wave Propagation

5.5.1 General Concept of Dynamic Stress and Transient Waves


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5.5.2 Effects of Single Joint on Wave Transmission

5.5.3 Effects of Joint Set on Wave Transmission

5.6 Characteristics of Rock Faults and Folds

5.6.1 Single Fault

Single fault should be characterised similarly as joint, including orientation, persistence,

surface roughness, aperture and filling. Persistence or length of the fault is particularly

important in order to appreciate the impact and influence of the fault.

Another aspect of importance is groundwater flow in the fault. Faults are usually of

great length; they generally are better connected than most of the joints, and hence create

a water flow channel.

5.6.2 Fault Zone of Extended Thickness

In addition to the characteristics of planer fault, thickness of a fault zone has important

influence on the overall properties. Together with the thickness, the materials within the

fault zone should be properly described and understood. The materials can vary from

crushed to completely decomposed rocks. The properties of those materials need to be

tested and determined in order to estimate the strength and deformation characteristics.

Similarly to single fault, fault zones also often become major groundwater flow channel.

Major faults sometimes are associated with and connected to surface geographic

depression and water body.

5.6.3 Bedding Planes and Rock Formation Interfaces

Bedding planes of sedimentary rocks without being folded are planner. Important

characteristics need to be described are the orientation and interface types.

In most cases, conformable or unconformable bedding planes are cemented and do not

represent a separation with an opening. Unconformable bedding planes may be

represented by a mixed interface in which materials of both rocks of each side are mixed

and hence dose not show a clear line separating the two rocks.

Non-conformable interfaces are the interfaces between sedimentary rocks with non-

sedimentary (igneous and metamorphic) rocks. They may not be planner, and may be


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represented by mixed interfaces containing fragments of rocks on both sides, or may be

represented by localised contact metamorphism caused by intrusion.

Dykes and sills are localised intrusions of igneous materials into existing rocks. The

interfaces between dykes/sills with the existing rocks are represented by contact

metamorphism.

Interfaces between two non-sedimentary rocks are usually well welded, by intrusion or bymetamorphism. The interfaces therefore only represent a discontinuity of materials but

not necessarily a weak zone or failure plane.

The condition of rocks, particularly carbonate sedimentary rocks (limestone and dolomite)

close to the interface needs to be carefully examines. For example, at an interface

between porous sandstone and limestone with active groundwater flow, limestone may be

weathered and showing well developed cavities.

5.6.4 Intensively Folded Thin Layers

Sedimentary layers of relative thin thickness and intensively folded often represent a zone

of fractured and weak rock. Description of discontinuities is not easy. However,general descriptions should include the layer thickness, materials in the layers, degree and

type of folding, and groundwater condition.

In the Chapter dealing with rock mass, such zones will be discussed in term of rock mass

classification.

5.7 Field and Laboratory Characterisation of Rock Joints

5.7.1 Overview on Field and Laboratory Methods

Characterisation of rock discontinuities are done by three means, most convenient and

best mean is by mapping at outcrops. Therefore outcrop mapping should always be thefirst choice of exposure of rock face is available. Rock cores from boreholes provides

many useful information on rock discontinuities, and core logging remains an important

exercise of rock discontinuity characterisation. In addition to core logging, further

information can often be supplemented by log the borehole. Geophysical borehole

logging becomes increasingly useful in rock discontinuity and rock mass characterisation.

Table 5.7.1a provides an overview on the applicability of various methods to measure

rock discontinuities from outcrop mapping and core logging.

Table 5.7.1a Measurement of discontinuity geometrical features

Feature Measurement Method Outcrop

Mapping

Core

Logging

Borehole

Logging


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Discontinuities type Visual good good medium

Orientation Compass-clinometer good medium good

Spacing Measuring tape good good medium

Persistence Measuring tape good poor poor

Roughness Profile gauge good medium poor

Wall strength Schmidt hammer good medium poor

Aperture Scale or feeler gauge good poor poorFilling Visual good poor poor

Seepage Timed observation good poor good

Number of joint sets Hemispherical projection good medium poor

Block size 3-D fracture frequency good poor poor

5.7.2 Identification of Joint Sets

Measurements on joint set number are usually done by observation and orientation

measurements at outcrops.

Descriptions of joint sets are suggested by ISRM, as reproduced in Table 5.7.2a.

Table 5.7.2a ISRM suggested description of joint sets

I Massive, occasional random fractures

II One joint set

III One joint set plus random fractures

IV Two joint sets

V Two joint sets plus random fractures

VI Three joint sets

VII Three joint sets plus random fractures

VIII Four or more joint sets

IX Crushed rock, earth-like

It is not easy to measure joint set number by logging the rock cores. Often dominating

joint sets or joint sets most perpendicular to drilling can be identified. Joints parallel and

sub-parallel to drilling are not well represented in core and hence not easily notified.

5.7.3 Measurement of Joint Orientation

(a) By Outcrop Mapping

The most convenient way to measure joint orientation is from accessible outcrops or

exposed faces of slope cuts or underground excavation. The measurements can be made

by a geological compass, which gives readings of dip direction (bearing) and dip angle

(inclination), as shown in Figure 5.7.3a.


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Orientation of a joint plane daylighted on exposed surfaces may be obtained by surveying

methods from an inaccessible outcrop. The measurement may give orientations of the

daylighted lines. Orientation of the joint plane can be calculated from the orientations of

the daylighted traces of the same joint plane, as shown in Figure 5.7.3b.

Assume the orientations of the two trace lines are 1, 1, and 2, 2 (plunge and trend),

from 3D geometry, the orientation of the joint plane (dip angle , dip direction ) is givenby the equation below,

tan 1

tan = cos (| 1|)

and

tan 2

tan = cos (| 2|)

By combining the above two equations, we have,

tan 1 cos (| 1|)

tan 2=

cos (| 2|)

With given 1, 1, and 2, 2, dip direction of the plane can be calculated by the above

equation. Dip angle can be calculated by substitute to one of the earlier equations.

The determination of plane orientation from the two daylighted lines can also be done by

projection method, which will be presented in a later section in this Chapter.

The dip angle shown by the trace of the daylighted joint plane is called apparent dip.

Apparent dip is always smaller then the true dip, as the true dip is defined as the

maximum dip angle of the plane.

(b) By Core and Borehole Logging

Joint are intersected by borehole drilling and hence can be seen from the cores obtained

from coring. Boreholes mostly are drilled vertically. Therefore, dip angle of joints and

fractured can be easily estimated, as the angle between the joint plane (when core is

placed vertically) and the horizontal. However, drilling is by rotational coring and

usually the bearing of cores is not fixed. Therefore, the dip direction cannot be

determined, in normal drilling.

Dip direction determination is possible if core orientation is known. Core orientation is

possible in reasonably good quality rock, where joints are reasonable close and matched.

mark, indicating, say, north, is printed on the core before drilling and when the cores are

taken out and reconnected, the whole core samples can be reoriented and dip directions of

all the joints and fractures can be determined, as illustrated in Figure 5.7.3c.


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In inclined and horizontal drilling, core orientation can be done within a drilling system.

The core barrel can have a steel ball which sit at the lowest position, i.e., lower side of the

core. The steel ball is locked in the core barrel and kept therefore the in the same

orientation as the cores. When the cores are taken out from the borehole, cores can be

reoriented with the aid of the steel ball, as shown in Figure 5.7.3d.

Orientation can also be determined by log the borehole, for example, by impressionpacker or acoustic imaging. Those methods are aimed at obtaining the images of the

borehole walls. The images can be reconstructed to produce the joint plane cutting

through the borehole. With know orientation of the image, the orientation of the joint

can be easily determined, as shown in Figure 5.7.3e.

5.7.4 Measurement of Joint Spacing and RQD

(a) By Outcrop Mapping

At an outcrop where rock is exposed, a scanline, say, horizonally along a straight outcrop

surface is planed. Along the scanline, using a measuring tape, spacing of joint

daylighted on the outcrop can be measured. Measurements can be done in three ways:(a) measuring the total amount of joint numbers with the scanline length, to calculate the

joint frequency; (b) measuring all the individual spacing between all the joints, to

calculate average spacing of all the joints: (c) measuring spacing of joints of individual

joint sets, to calculate joing spacing for different joint sets; and (d) measuring all the

spacing longer than 10 cm, to calculate RQD. Various measurements are illustrated in

Figure 5.7.4a.

It should be noted that the measurements on the outcrop surface give the apparent spacing

of joints. The measurements are also directional, i.e., if the scanline is in different

direction, say vertical, the measurements will be different.

(b) By Core and Borehole Logging

Measuring RQD is almost a standard practice during core logging. It is usually

measured for each core run (generally 1 3 m), or for the length of cores in a core box

(generally 1 1.5 m). By placing a measuring tape along one side of the core length,

rock cores have a length longer than 10 cm are noted and summed, dividing to the drilling

length, giving the RQD. Alternatively, the total number of fractures can be counted to

calculate the joint frequency. The measurements are illustrated in Figure 5.7.4b.

In core logging for RQD or frequency, the length to be divided is the total drilling length,

not the core length. In competent rock and with good drilling practice, the core length

can be the same as drilling length. Sometimes, rock cores are not fully recovered from

drilling, and then the core length is shorter than the drilling length. The ratio of

recovered core length to the drilling length is termed as core recovery. When coring


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through a highly fractured rock mass or a faulted zone, core recovery could be low due to

loss of loss materials in the fractured and faulted zones.

5.7.5 Joint Surface Profile Measurements

(a) Measurement of Large Scale Waviness at Site

Large scale waviness of a joint at site can be obtained by placing a long ruler over the

joint surface and then to measurement at a fixed interval the gap between the ruler and the

profile surface, as indicated by illustration in Figure 5.7.5a.

(b) Measurement of Roughness at Small Scale

Roughness measurements are usually done by a profile gauge shown in Figure 5.7.5b.

More precise measurement can be obtained by using a laser device, as shown in Figure

5.7.5c. A simple profile gauge provides a profile along a scanline and each profile is

then compared with a typical profile to give the roughness description or the roughness

number. Alternatively, fractal number can be computed.

With a laser profile capable to move along x and y directions, a series linear profiles can

be scanned to provide a 3D profile plane. With the 2D profile or 3D profile, toughness

can be described, or fractal numbers be calculated.

5.7.6 Description of Joint Surface and Filling

(a) Weathering and Alteration

Weathering and alternation is usually visible at outcrops or from the cores. When the

joint surface is weathered, it often shows the change of colour and appearance. Often,

weathered products, such as grain particles may also remain inside the joint. Detailed

description is necessary. Table 5.7.6a gives the suggested description by ISRM.

Table 5.7.6a ISRM suggested descriptive terms for joint surface alteration

Term Description

Fresh No visible sign of weathering of rock material at joint wall.

Discoloured Colour of the original fresh rock material is changed. The

degree of change from the original colour should be indicated.

If the colour change is confined to particular minerals this

should be mentioned.

Decomposed Rock is weathered to the condition of a soil in which the

original materials fabric is still intact, but some or all of the

mineral grains are decomposed.


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Disintegrated Rock is weathered to the condition of a soil in which the

original materials fabric is still intact. The rock is friable, but

the mineral grains are not decomposed.

(b) Filling in Joint

Joint can be clean or filled with weathered products and deposits, ranging from sandyparticles to swelling clays. Descriptions of filling materials need be given in details, in

term types of the materials, thickness, and particle sizes. If swelling clays are found,

swelling characteristics should be described.

(c) Estimating Joint Wall Strength

Joint wall strength is also an indicating of weathering and alteration of joint wall. When

the joint is weathered, the strength of the rock at joint wall reduces significantly. As we

discussed earlier, this affects greatly the shear strength of the joint.

Joint wall strength can be estimated by a Schmidt hammer. With the Schmidt hammer

number, uniaxial compressive strength can be estimated.

5.7.7 Estimation of Joint Aperture and Contact Areas

(a) By Outcrop Mapping and Core Logging

At outcrop mapping, joint aperture can only be roughly estimated, through direct

observation of joint exposed at outcrop, according to the ISRM suggested description

represented in Table 5.1.4a. The actual measurement is rather difficult, if not

impossible.

(b) By Laboratory Measurements

Specific methods have been developed in the laboratory to measure the aperture and

contact area of rock joints. The most common method is by impress trace. Materials are

injected into the joint and are allowed to set. When the joint is opened, the hardened

injected material gives the impression of the joint, including gaps and contacts. Contact

points and areas as well as aperture can then be estimated.

5.7.8 Permeability Measurements of Rock Joints

(a) In Situ Tests


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In situ permeability tests usually are done in boreholes for a section of rock mass, and

they will be described in details in the next Chapter. For measuring permeability of

individual joint, tests can be done in a borehole with packers.

From core or borehole logging, the joint to be tested should be selected. The joint

should be able to be isolated by a pair and packer and between the packers, there should

be only that joint within the tested section. A pair of packers are lowered down into the

borehole to the positions, to include the joint between the packers. The packers areinflated to seal the section. Permeability tests are conducted by injecting high pressure

water within the section sealed by the packers. The test is often referred as borehole

packer test, and is illustrated in Figure5.7.8a. Permeability (often expressed as

transmissivity) can be calculated from flow characteristics, flow transmitting rate and

flow pressure.

(b) Laboratory Tests

Permeability tests on joint in laboratory can be set up using a system similar to Darcys

experiment. In addition, normal stress may be applied to the joint to determine the flow

rate and permeability at various stress conditions. A typical set-up using a triaxial cell is

shown in Figure 5.7.8b.

Permeability can be calculated from the flow rate measurements, hydraulic gradient and

specimen geometry, when the water flow is steady state laminar flow in the joint. Using

the parallel plates theory, equivalent hydraulic aperture can be estimated.

Change of pressure in the cell causes change of normal stress acting on the joint, and

leads to change of joint aperture. Such change will also be reflected in the change of

permeability.

5.7.9 Normal Compression and Stiffness Measurement of Joints

Rock sample containing a joint is prepared. Ideally, the joint should be placedhorizontally, parallel to the loading plane. The specimen can be cut into circular cylinder

or rectangular block and cross section area is measured. The joint surface is carefully

protected from mechanical damage during cutting and preparation. The profiles of joint

surfaces are recorded using a profiling gauge. The specimen is loaded under a standard

compression machine with load measurement. LVDTs or dial gauges are placed near

and across the joint to measure the normal displacement of the section containing the

joints, as shown in Figure 5.7.9a.

Load and displacement measurement should be taken regularly. If the displacement are

measured a relative large section of the rock, the displacement of the rock material should

be subtracted from the total displacement to give the net displacement of the joint.


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Stress (load/cross-section area) and joint normal displacement are plotted to give the

stress-normal displacement behaviour of the joint. Normal stiffness at a specific stress

level is the gradient of the tangent to the stress-normal displacement curve at that stress,

as illustrated in Figure 5.7.9b. It should be noted that the stress-normal displacement

behaviour of a rough joint is a curve.

5.7.10 Direct Shear Strength Test of Joints

Rock sample containing discontinuity is prepared and encapsulated in laboratory shear

box, with the discontinuity laid horizontally. The discontinuity is carefully protected

from mechanical damage during cutting and preparation. The sample is then mounted in

shear box using plaster, as shown in Figure 5.7.10a. The profile of discontinuity surface

are recorded using a profiling gauge. Area of the discontinuity is also measured. The

discontinuity is loaded under a constant normal load, and shear force is applied using a

mechanical gear-drive system (Figure 5.7.10b). Shear displacement, shear force and

normal displacement are recorded at a constant shear displacement interval (0.2-0.25

mm). The tests are continued until residual shear strength is obtained or about 10% of

the specimen length (Figure 5.7.10c).

Normal stress (n), peak shear strength (p) and residual shear strength (r) are calculatedas normal load, peak shear force and residual shear force divided by the shear area.

Peak shear strength, normal stress and angle of friction () can be adjusted to account for

dilation. The angle of dilation (i) is estimated from normal displacement (n) - shear

displacement curve (h) as i = n / h

Adjusted basic angle of friction () = ( i ).

Adjusted normal stress (n) = ( n cos i + p sin i ) cos i

Adjusted peak shear strength (p) = ( pcos i n sin i ) cos i

Reporting of results includes description of rock specimen and discontinuity, surface

roughness profile, shear stress - shear displacement and normal displacement - shear

displacement curves, peak shear strength, residual shear strength at each normal stress,

plots of peak shear strength and residual shear strength against normal stress .

5.8 Hemispherical Projection Method

5.8.1 Principle of Projection

5.8.2 Projection of Planes and Lines

5.8.3 Use of Projection for Geometrical Analysis


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5.8.4 Applications of Projection Methods


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5.7.8 Permeability Measurements of Rock Joints

(a) In Situ Tests

In situ permeability tests usually are done in boreholes for a section of rock mass, and

they will be described in details in the next Chapter. For measuring permeability of

individual joint, tests can be done in a borehole with packers.

From core or borehole logging, the joint to be tested should be selected. The joint

should be able to be isolated by a pair and packer and between the packers, there should

be only that joint within the tested section. A pair of packers are lowered down into the

borehole to the positions, to include the joint between the packers. The packers are

inflated to seal the section. Permeability tests are conducted by injecting high pressure

water within the section sealed by the packers. The test is often referred as borehole

packer test, and is illustrated in Figure5.7.8a. Permeability (often expressed as

transmissivity) can be calculated from flow characteristics, flow transmitting rate and

flow pressure.

The basic injection flow test procedures are outlined below:

(a) Open water feeding system valve and maintain constant pressure (PA), record theelapsed time and total volume of consumed water every 0.5 minute, for the first 3minute, then every minute, for about 10-15 minutes, until the pressure appears to

have stabilised.

(b) After pressure PA has stabilised for approximately 3 minutes, increase the waterpressure to pressure PB. Record the time and flow the same way as for PA, for about

10-15 minutes, until the pressure appears to have stabilised.

(c) After pressure PB has stabilised for approximately 3 minutes, increase the waterpressure to pressure PC. Repeating the same procedure by recording the time and

flow until pressure stabilised.

(d) Continue the tests for pressures PD and PE, following the same procedure.


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5.1.1a

5.1.1a


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Dip angle

Dip direction

StrikeN

N

Horizontal planeOrientation:

Dip direction / Dip

220/55

Measured clockwise on horizontal plane: 220

Measured on vertical plane: 55

Vertical plane

5.1.2a

Line of maximum dip

5.1.2b


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5.1.3a

Apparent spacingin x direction

Apparent spacingin y direction

True spacingApparent spacingOn the plane

5.1.3b


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5.1.4a

5.1.4b


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5.1.4c

5.1.4d


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5.1.4e

5.1.4f


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5.1.4g

5.1.5a


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5.2.1a

5.2.2a

(a) (b)

(c)

(d)


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5.2.2b

5.2.2c

(a)

(b)

Peak

Residual

ShearStrength

Normal Stress

ShearForce

Shear Displacement


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5.2.2d

N

S

N

S

N

S

N

S

S

N

S

N

S

N

ii

+i +i

i

5.2.3a


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5.2.3b

5.2.3c


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5.3.4a

5.3.5a


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5.7.3a

5.7.3b

Apparent spacingin 3 directions

Apparent spacing onthe measuring surface

Orientation of thejoint daylighted


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5.7.4a

RQD = (L1 + L2 + + Ln) / L x 100%

= number of joints / length = n / L

X X XX XL1 L2 L3 L4 L5 LnLi


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properties of rock discontinuities

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