Properties of Rock Discontinuities

Chapter 5

Properties of Rock Discontinuities

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CHAPTER 5 PROPERTIES OF ROCK DISCONTINUITIES Properties of rock discontinuities discontinuities govern the overall behaviour of the rock masses. Chapter addresses properties of rock discontinuities.

This

Rock discontinuities include joints, fractures, faults and other geological structures. Rock joints are by far the most common common discontinuity discontinuity encountered in rock masses. masses. Rock fractures are random features. features. Rock faults faults and folds folds are major major but localised geological geological structures and therefore are dealt individually.

5.1

Geometrical Characteristics of Rock Joints

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

As discussed early in the chapter dealing with rock formation, joints are generally in sets, i.e., parallel parallel joints. The number of joint sets can vary from 0 to as many as 5 (Table ( Table 5.1.1a). 5.1.1a ). Typically one joint set cuts the rock mass mass into plates, two two perpendicular sets cut rock into column and three into blocks, and more sets cut rocks into mixed shapes of blocks and wedges, as shown in Figure 5.1.1a. 5.1.1a. The mechanical properties of the rock mass is obviously influenced by the presence of joint sets and the number number of joint sets. More joint sets provide provide more possibilities possibilities of potential slide planes planes for rock wedges or blocks to to slide and fall.

Figure 5.1.1a

Table 5.1.1a

I II III IV V VI VII VIII IX

Rock masses showing one and three joint sets.

ISRM suggested description of joint sets Massive, occasional random fractures One joint set One joint set plus random fractures Two joint sets Two joint sets plus random fractures Three joint sets Three joint sets plus random fractures Four or more joint sets Crushed rock, earth-like

Different from joints, rock fractures are considered as a non-systematic discontinuous feature of rock masses. masses. They are not in sets or parallel. They could be large in term term of numbers but their distribution distribution is generally random. random. Rock mass mass quality is influenced 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 lengths of discontinuities on exposed surfaces. The persistence 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

Table 5.1.1b

Sketches indicating persistence of various joint sets.

ISRM classification of discontinuity persistence

Description Very low persistence Low persistence Medium persistence High persistence Very high persistence

Surface Trace Length (m) <1 1–3 3 – 10 10 – 20 > 20

5.1.2 Joint Orientation: Orientation: Joint Plane Plane Orientation Orientation and Representation 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 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 the plane. It does not fix its position. Therefore, two parallel planes have the the same same orientation. In rock mechanics and engineering engineering geology, the orientation orientation of a plane is generally defined by dip angle (inclination), dip direction (facing) or strike (running), as illustrated in Figure 5.1.2a. 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 acute angle between a line line with maximum maximum dip in the inclined plane and its horizontal projection. Dip angle is generally expressed by an acute angle between 0° and 90° 90°. Dip direction direction represents the facing direction. It is the bearing measured clockwise clockwise from the north (0° (0°) of the line with maximum maximum dip in the inclined plane. Dip direction direction is generally expressed by a direction angle of 0 ° to 360° 360°.

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Strike is the the alignment or run. It is the bearing of an imaginary imaginary horizontal horizontal line in the inclined plane. plane. Strike is is generally generally expressed by a direction angle of 0 ° to 180° 180°. Dip direction direction and strike direction direction are always perpendicular. 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, direction, the general direction of plane dip must be given, otherwise, it could means two possible planes, e.g., dip/strike dip/strike 120/35 would be either dip direction/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 imaginary line at right angle to the plane. orientation of the normal is given by, trend of normal = dip direction of the plane ± 180, plunge of normal = 90 – dip. dip.

Therefore the

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 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 hemispherical projection method method is given in a later later section in this chapter.

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

The degree of fracturing of a rock mass is controlled by the number of joint in a given dimension. A rock mass contains more joints is also considered as more fractured. fractured. More joints also mean that that average spacing between 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 circular or even flow failure. It also also influences 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 is usually expressed as the 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 average

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spacing is considered. However, as illustrated in the figure, measurements 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. description ranges from extremely close spacing to extremely wide spacing.

The

Classification of discontinuity spacing

Table 5.1.3a

Description Extremely close spacing Very close spacing Close spacing Moderate spacing Wide spacing Very wide spacing Extremely wide spacing

Joint Spacing (m) < 0.02 0.02 – 0.06 0.06 – 0.2 0.2 – 0.6 0.6 – 2 2–6 >6

Joint frequency (λ (λ), is defined as number of joint per metre length. length. the inverse of joint spacing (s j), i.e.,

It is therefore simply simply

λ = 1 / s j Another measure measure of fracturing fracturing degree is the Rock Quality Designation (RQD). (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 ( Figure 5.1.3b). 5.1.3b). RQD =

ΣLength of cores >100 mm × 100% Total length of drilling

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, degree, by in in fact considering the spacing of joints. Therefore, statistically, RQD can be correlated to joint spacing or joint frequency the following equation: –0.1λ –0.1λ

RQD = 100 e

(0.1λ (0.1λ +1)

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

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RQD = 110.4 – 3.68λ 3.68λ Joint space also defines the size of rock blocks in a rock mass. mass. When a rock rock mass contains more joints numbers, the joints have lower average spacing and smaller block size. Block size size can be classified classified by the volumetric volumetric joint count, J v, defined as number of 3 joint per m volume of rock mass, as presented in Table 5.1.3b. 5.1.3b.

Table 5.1.3b

ISRM suggested block size designations

Designation Very large blocks Large blocks Medium-sized blocks Small blocks Very small blocks Crushed rock

Volumetric Joint Count, joints/m3 <1 1–3 3 – 10 10 – 30 > 30 > 60

RQD can be related approximately to J v by: RQD = 115 – 3.3 J v,

for Jv between 4.5 and 30.

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

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

A joint is an interface face of two contacting surfaces. surfaces. The surfaces can be smooth 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 discontinuity relative relative to its its mean plane. The roughness is characterised characterised by large large scale waviness and small scale unevenness of a discontinuity. 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.. 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. 5.1.4b. It describes the roughness roughness first first in in metre metre scale scale (step, (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 and corresponding joint roughness coefficient (JRC) at different scales.

Another commonly used roughness classification is proposed by Barton, termed as Joint Roughness Coefficient Coefficient (JRC). (JRC). JRC number number is 0 for the smooth flat surface and 20 for the very rough surface. surface. The proposed proposed JRC is reproduced in Figure 5.1.4b. 5.1.4b. Joint roughness is affected by geometrical scale. In the JRC classification, 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). 5.1.4c). The above descriptions are 2D based. It is therefore suggested suggested to take take several linear profiles of a surface for the description and JRC 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. 5.1.4d. It is is a very powerful powerful tool to to quantify 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 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 in fully contacted and interlocked interlocked positions has little little possibility of movement movement and is also difficult to shear, as compared to the same same rough joints in point contact where movement can easily occur. Often, joints are differentiated as matched and mismatched (Figure ( Figure 5.1.4e). 5.1.4e). A Joint Matching Coefficient (JMC) has been suggested by considering the the contact percentage of two surfaces, as shown in Figure 5.1.4f . JMC various from 0, representing completely completely mismatched mismatched with a few contact points only in the joint interface, to 1, representing representing completely completely matched with fully in contact of the joint.

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Figure 5.1.4e


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Matched and mismatched joint surface.

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

In a natural joint, it is is very seldom that the two two surfaces are in complete contact. There usually exists a gap or an opening opening between the two surfaces. The perpendicular perpendicular distance separating the adjacent rock walls is termed as as aperture. Descriptions of aperture are suggested in Table 5.1.4a. 5.1.4a. Joint opening is either filled with air air and water (open (open joint) or with infill materials (filled joint), as illustrated in Figure 5.1.4g. 5.1.4g. Open or filled joints with large apertures have low shear strength. Open aperture also associates with high permeability and storage storage capacity.

Figure 5.1.4g

Joint aperture and joint with filling.

Table 5.1.4a

Classification of discontinuity aperture

Aperture < 0.1 mm 0.1 ~ 0.25 mm 0.25 ~ 0.5 mm 0.5 ~ 2.5 mm 2.5 ~ 10 mm 1 ~ 10 cm 10 ~ 100 cm >1m

Description Very tight Tight Partly open Open Widely open Very widely open Extremely widely open Cavernous

"Closed feature" "Gapped feature" "Open feature"

Aperture can be separated by mechanical aperture or real aperture and equivalent hydraulic aperture aperture or conducting aperture. aperture. The later later is particularly important when permeability is concerned. Filling is material in the rock discontinuities. discontinuities. The material material separating separating the adjacent rock walls of discontinuities. discontinuities. The wide wide range of physical behaviour depends on the properties of the filling filling material. In general, filling affects the shear strength, 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 features has certain degree of correlation.

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Figure 5.1.5a fractures.


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Illustration of various geometrical characteristics of rock joints and

(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 deformation characteristics and and normal stiffness stiffness of rock joints are important important parameters for analysis analysis and design. As discussed in an earlier earlier chapter, a joint joint represents a discontinuity of stress and displacement. displacement. A natural joint always always has opening opening aperture of less than 1 mm to a few mm. With increasing normal stresses, stresses, the opening closes, and contact areas of the joint surfaces increase. increase. Therefore as as shown in Figure 5.2.1a, 5.2.1a, the normal stress – normal displacement curve can be highly non-linear. The normal normal stiffness, 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 finite element element model, Goodman (1976) used a hyperbolic relation between normal stress, σn, and normal displacement, d n,

t dn σn – σ – σni =A( ) dmax – dn σni

where dmax is the maximum possible closure, σni = a seating pressure defining the initial normal stress conditions for measuring normal displacement, 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 compression and fracture closure closure and negative signs for tension tension and fracture opening, the normal effective stress-closure relation is, σn =

k ni ni dn 1 – (dn/dmax)

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or dn =

σn k ni (σn/dmax) ni + (σ

where σn is the normal effective stress, d n is the fracture closure, d max is the maximum allowable closure, k ni at initial initial stress. stress. When ni is the normal stiffness of the fracture at normal 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. 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 normal fracture fracture specific stiffness. The initial normal stiffness stiffness (k ni ni) and maximum allowable closure (d max) 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 (a i) at initial seating normal stress, stress, as described by Barton et al. (1985). The model is commonly 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 model describes 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 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 σn = p + q d n where σn is normal effective stress, d n is the fracture closure, p and q are material constants. 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 = 1 – A ln(σ ln( σn/σni) dmax – dni where dni = displacement at a reference normal stress σni, usually equal to the seating pressure, and A is constant varies from 0.16 to 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 rock material. material. When the joint is completely completely closed, 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 Strength of Rock Joints and Fractures Fractures

Shear behaviour of rock joints is perhaps one of most important feature in civil engineering rock mechanics. Conditions for sliding sliding of rock blocks along existing 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, 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 φ, the normal force (N) and shear force (F s), as Fs = N tanφ tanφ. 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 (σ (σn) curve (Figure (Figure 5.2.2b) 5.2.2b) and it follows the simple Coulomb law: τ = σn tanφ tanφ where φ is the effective angle of friction of the fracture surfaces. surfaces. Figure 5.2.2b, φ = 35° 35°, a typical value for quartz-rich rocks.

Figure 5.2.2b

For the case shown in

Shearing of smooth quartzite surfaces under various conditions.

Naturally occurring discontinuity discontinuity surfaces are far from being smooth. smooth. Figure 5.2.2c is typical of the results obtained for clean, rough fractures. As observed in the tests, shear stress quickly quickly mobilised mobilised and reaches a peak. When shearing is progressed, progressed, the shear strength stablised stablised to a residual level. The peak is usually term as the peak shear strength and the residual residual is the residual shear strength. For rough joints, joints, peak shears strength is significantly higher than the residual strength.

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Figure 5.2.2c


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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., τr = σn tan φr On the other hand, peak shear strength does not follow the linear fiction law. law. The peak strength for rough joints does not linearly proportional proportional to normal stress. 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, 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, τ = σn tan(φ tan(φ+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. asperities. Comparing to to rock joint, joint, rock materials materials have higher cohesion and internal friction angle of generally around 30° 30°.

Figure 5.2.2d

Idealized surface 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 Figure 5.2.2d,, and is expressed by the equations 5.2.2d equations below. below. In the equation, σn’ is the critical normal stress when shearing of asperity is assumed to start.

τ=

{

σn tan (φ (φ+i)

for σ for σn ≤ σn’

c + σn tan φ

for σ for σn ≥ σn’

However, in reality, there is not clear boundary between shearing by climbing the asperity angle and shearing off off the asperities. With increasing increasing normal stress, asperity shearing off increases progressively. Therefore, the the actual shear stress stress – normal normal stress relation is represented by a curve, as shown in Figure 5.2.2c. 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, τ = σn tan [JRC log 10 JCS ) + φr ] ( σn where σn = effective normal stress, JRC = joint roughness coefficient on a scale of 1 for the smoothest to 20 for the roughest surfaces, JCS = joint wall compressive strength, and φr = drained residual friction angle. (Discussion on dilation and dilation angle.)

5.2.3 Other Factors Affecting Joint Shear Behaviour 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 foliated rocks, but rather universal. universal. As discussed in the geometrical properties, surface profile is a 3D feature while shearing is a directional activity. Surface profile profile along a particular direction would would be different along another direction 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 (Figure 5.2.3b). 5.2.3b).

Figure 5.2.3b

Shear strength of matched and mismatched fractures in a granite.

When a joint is is wet, it has generally a lower friction friction angle than than a dry joint. The shear strength of a wet joint is calculated use the wet friction angle. If the joint is subjected to 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 stress dependent. As σn increases, the term log 10(JCS/σ (JCS/σn) decreases, and so the net apparent friction friction angle decreases. As the scale increases, 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 material compressive strength, strength, JCS, decreases with increasing size, size, as illustrated in Figure 5.2.3c. 5.2.3c.

Figure 5.2.3c strength.

Influence of scale on the three components of discontinuity shear

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 theory is applicable applicable to flow in rock joints. Therefore, flow and permeability of a rock joint are given as, 3

Q=

w i g de 12 ν

k=

g de 12 ν

(5.2.4a)

2

(5.2.4b)

where g = acceleration due to gravity, ν = kinematic viscosity of the fluid, w = width of the 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 modification has to be introduced to reflect the effects of joint roughness and flow flow path. Therefore, in in the above equation, instead instead of the the aperture of smooth plates, in natural rock joints, equivalent hydraulic aperture is used. The equivalent hydraulic aperture of a rock joint (d e)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 ≤ f ≤ 1. It is found that for a given joint, f is a constant at different apertures, without change of joint surface profile (Witherspoon (Witherspoon et al 1980). It is also noted that that f value is generally 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 Normal Stiffness

It was observed that closure under load was more complete in smooth joints than in rough joints. Conversely, rough joints joints in strong rocks close close least under normal 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. strength. It is evident that rougher 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 to relate these to the joint surface roughness. roughness. A relationship relationship between equivalent hydraulic hydraulic aperture and real joint joint aperture based on the Joint Joint Roughness Coefficient (JRC) was proposed by Barton and Choubey [1977]: 2.5

de =

JRC 2 (d/de)

(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, 5.3.4a, joint permeability reduces asymptotically and approaches to zero with increasing effective normal stress.

Figure 5.3.4a granite.

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

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A hydraulic model describing the hydraulic behaviour of discontinuities was proposed by Walsh (1981) and modified modified by Zhao and Brown (1992). The model model suggested a logarithmic relation between the joint permeability, k j j and the effective normal stress, (σn ), ′

k j 2 σ = [1 – B Ln ( n ) ] k r r σr ′

′

(5.3.4a)

where k r = the rock joint permeability at a reference effective normal stress σr , and B is a parameter dependent on surface surface properties of the joint. 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 high permeability, as as illustrated in Figure 5.3.5a.. As seen from the figure, when shear occurs, dilation occurs 5.3.5a occurs due the climbing effects. The climbing climbing effects may be less obvious if the joint is under high normal normal stress. In this case, the asperities would be crashed crashed and crashed particles particles may be filled in the joint. This may still result in increasing of permeability but not as significant as in the previous case.

Figure 5.3.5a

Change of aperture with shear displacement of a matched joint.

For a non-matched non-matched joint, the situation 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 Cyclic Loading

5.4.2 Joint Behaviour under Dynamic Loads

5.4.3 Factors affect Rate Dependent Dependent Characteristics Characteristics of Joints

5.5

Effects of Joints on Transient Stress Wave Propagation

5.5.1 General Concept Concept of Dynamic Stress Stress and Transient Waves 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 particularly important in order to appreciate the impact and influence of the fault. Another aspect of importance importance is groundwater flow 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 h as important influence on the overall properties. Together with with the thickness, the materials within the fault zone should be properly described described and understood. The materials materials can vary from crushed to completely decomposed rocks. The properties properties of those those materials 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 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 interfaces are the interfaces interfaces between sedimentary sedimentary rocks with nonsedimentary (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 intrusions of igneous materials 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 by metamorphism. metamorphism. The interfaces interfaces therefore only represent a discontinuity discontinuity of materials 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 interface needs to be carefully examines. examines. For example, example, at an interface between porous sandstone and limestone limestone with active 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 Field and Laboratory Laboratory Methods Methods

Characterisation of rock discontinuities are done by three means, most convenient and best mean is by mapping mapping at outcrops. Therefore outcrop mapping mapping should always be the first choice of exposure of rock face face is available. Rock cores from boreholes boreholes provides many useful information on rock discontinuities, and core logging remains an important exercise of rock discontinuity discontinuity characterisation. characterisation. In addition addition to core logging, further information can often be supplemented 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

Feature

Measurement of discontinuity geometrical features Measurement Method

Outcrop Mapping

Core Logging

Borehole Logging

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18

Discontinuities type

Visual

good

good

medium

Orientation Spacing Persistence Roughness Wall strength Aperture Filling Seepage Number of joint sets sets Block size

Compass-clinometer Compass-clinometer Measuring tape Measuring tape Profile gauge Schmidt hammer Scale or feeler gauge Visual Timed observation Hemispherical projection projection 3-D fracture frequency

good good good good good good good good good good

medium good poor medium medium poor poor poor medium poor

good medium poor poor poor poor poor 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 I II III IV V VI VII VIII IX

ISRM suggested description of joint sets Massive, occasional random fractures One joint set One joint set plus random fractures Two joint sets Two joint sets plus random fractures Three joint sets Three joint sets plus random fractures Four or more joint sets Crushed rock, earth-like

It is not easy to measure joint set number by logging the rock cores. Often dominating dominating joint sets or joint sets sets most perpendicular perpendicular to drilling can be identified. 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. excavation. The measurements measurements can be made by a geological compass, which gives readings of dip dip direction (bearing) and dip dip angle (inclination), as shown in Figure 5.7.3a. 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 measurement may may give orientations of the daylighted lines. lines. Orientation of the joint plane can be calculated calculated from the orientations orientations of the daylighted traces of the same joint plane, as shown in Figure 5.7.3b. 5.7.3b. Assume the orientations of the two trace lines are α1, β1, and α2, β2 (plunge and trend), from 3D geometry, the orientation of the joint plane (dip angle α, dip direction β) is given by the equation below, tan α1 = cos (|β (|β – β – β1|) tan α and tan α2 = cos (|β (|β – β – β2|) tan α By combining the above two equations, we have, tan α1 cos (|β (|β – β – β1|) = tan α2 cos (|β (|β – β – β2|) With given α1, β1, and α2, β2, dip direction of the plane β can be calculated by the above equation. Dip angle α can be calculated by substitute β to one of the earlier equations. The determination of plane orientation from the two daylighted lines can also be done by projection method, which 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 b e 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 is by rotational coring and and usually the bearing of cores is not fixed. Therefore, the dip direction direction cannot be determined, in normal drilling. Dip direction direction determination determination is possible if core orientation orientation is known. Core orientation orientation is possible in reasonably good quality 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. 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 locked in the core barrel and kept therefore the in the same same orientation as the cores. When the cores cores are taken out from the the borehole, cores can be reoriented with the aid of the steel ball, as shown in Figure 5.7.3d. 5.7.3d. Orientation can also be determined by log the borehole, for example, by impression packer or acoustic imaging. imaging. Those methods are aimed aimed at obtaining obtaining the images of the borehole walls. The images can be reconstructed reconstructed to produce the joint plane cutting through the borehole. With know orientation of the image, the orientation orientation of the the joint can be easily determined, as shown in Figure 5.7.3e. 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 spacing of joint daylighted on the outcrop can be measured. measured. Measurements can be done in three three ways: (a) measuring the total amount of joint numbers with the scanline length, to calculate the joint frequency; (b) measuring measuring all the individual individual spacing between all all the joints, to calculate average spacing of all the joints: (c) measuring spacing of joints of individual joint sets, to calculate calculate joing spacing for different different joint sets; and (d) measuring all the spacing longer than 10 cm, cm, to calculate calculate RQD. RQD. Various measurements measurements are illustrated illustrated in Figure 5.7.4a. 5.7.4a. It should be noted that the measurements on the outcrop surface give the apparent spacing of joints. The measurements measurements are are also directional, i.e., i.e., if the scanline is in different direction, say vertical, the measurements will be different. (b) By Core and Borehole Logging Measuring RQD 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). m). By placing a measuring measuring tape along along one side 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 to calculate the joint joint frequency. frequency. The measurements are illustrated illustrated in Figure 5.7.4b. 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, practice, the core length can be the the same as drilling length. Sometimes, rock cores are not fully recovered recovered from drilling, and then the core length is shorter than the drilling length. 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 the gap between the ruler and the profile surface, as indicated by illustration illustration in Figure 5.7.5a. 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. 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 5.7.5c along a scanline 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 profile plane. With the 2D profile or 3D profile, toughness can be described, or fractal numbers be calculated.

5.7.6 Description of Joint Joint Surface Surface and Filling Filling

(a) Weathering and Alteration Weathering and alternation is usually visible at outcrops or from the cores. When the joint surface is weathered, weathered, it often shows shows the change of colour and appearance. Often, weathered products, products, such as grain particles particles may also remain 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


22

Rock is weathered to the condition of a soil in which the original materials materials fabric is still intact. The rock is friable, 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 sandy particles to swelling swelling clays. Descriptions of filling filling materials need be given in details, in term types types of the the materials, materials, thickness, thickness, and particle particle sizes. sizes. If swelling 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 estimated by a Schmidt hammer. number, uniaxial compressive strength can be estimated.

With the Schmidt hammer hammer

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. 5.1.4a. The actual actual measurement 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 The most common common method method is by impress impress trace. Materials are injected into the joint and are allowed to set. When the joint joint is opened, the hardened injected material material gives gives the impression impression of the joint, including gaps and contacts. Contact points and areas as well well as aperture can then then be estimated.

5.7.8 Permeability Measurements of Rock Joints

(a) In Situ Tests

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23

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 measuring permeability 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 within the tested section. section. A pair of packers are are lowered down into the borehole to the positions, 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 within the section sealed sealed by the the packers. The test is often referred as borehole packer test, and is illustrated in Figure5.7.8a 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 Darcy’s experiment. In addition, normal stress may be applied to the joint to determine the flow rate and permeability permeability at various stress conditions. A typical set-up using a triaxial cell is shown in Figure 5.7.8b. 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 o f normal stress acting on the joint, and leads to change of joint aperture. Such change will will also be reflected 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 placed horizontally, 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 mechanical damage during cutting cutting and preparation. The profiles of joint joint surfaces are recorded using a profiling gauge. The specimen specimen is loaded loaded under a standard compression machine machine with load measurement. 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. 5.7.9a. Load and displacement displacement measurement measurement should be taken regularly. 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 displacement to give the net displacement of the the joint.

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24

Stress (load/cross-section area) and joint normal displacement are plotted to give the stress-normal displacement behaviour of the joint. Normal stiffness 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. 5.7.9b. It should 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 discontinuity laid horizontally. horizontally. The discontinuity is is carefully protected from mechanical mechanical damage during cutting and preparation. The sample sample is then mounted in shear box using plaster, as shown in Figure 5.7.10a. 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 (Figure 5.7.10b). 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 residual shear strength is obtained or about 10% of the specimen length (Figure (Figure 5.7.10c). 5.7.10c). Normal stress (σ (σn), peak shear strength (τ ( τ p) and residual shear strength (τ ( τr ) are calculated as normal load, peak shear force and residual shear force divided by the shear area. Peak shear strength, normal stress and angle of friction ( φ) can be adjusted to account for dilation. The angle of dilation (i) is estimated from normal normal displacement displacement (n) - shear displacement curve (h) as i = δn / δh Adjusted basic angle of friction ( φ′) φ′) = ( φ − i ). Adjusted normal stress (σ ( σn′) = ( σn cos i + τ p sin i ) cos i Adjusted peak shear strength (τ ( τ p′) = ( τ p cos i − σn 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 strength and residual shear strength 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

25

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26

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 measuring permeability 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 within the tested section. section. A pair of packers are are lowered down into the borehole to the positions, 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 within the section sealed sealed by the the packers. The test is often referred as borehole packer test, and is illustrated in Figure5.7.8a 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 (P A), record the elapsed time and total volume of consumed water every 0.5 minute, for the first 3 minute, then every minute, for about 10-15 minutes, until the pressure appears to have stabilised. (b) After pressure P A has stabilised for approximately 3 minutes, increase the water pressure to pressure PB. Record the time and flow the same way as for PA, PA, for about 10-15 minutes, until the pressure appears to have stabilised. (c) After pressure P B has stabilised for approximately 3 minutes, increase the water pressure to pressure PC. Repeating the same same procedure by recording the time time and flow until pressure stabilised. (d) Continue the tests for pressures P D and PE, following the same procedure.

5.1.1a

5.1.1a

1

Strike

N

Vertical plane

Dip direction

Dip angle Measured on vertical plane: 55

N

Line of maximum dip Horizontal plane Measured clockwise on horizontal plane: 220

Orientation: Dip direction / Dip 220/55

5.1.2a

5.1.2b

2

Apparent spacing On the plane

Apparent spacing in x direction

Apparent spacing in y direction

True spacing

5.1.3a

5.1.3b

3

5.1.4a

5.1.4b

4

5.1.4c

5.1.4d

5

5.1.4e

5.1.4f

6

5.1.4g

5.1.5a

7

5.2.1a

(a)

(b)

(c) (d)

5.2.2a

8

5.2.2b

(a)

e c r o F r a e h S

Shear Displacement

h t g n e r t S r a e h S

(b) Peak

Residual

Normal Stress

5.2.2c

9

N

N S

S

i

N

N

S

S i

i

S

S

S

φ

φ

N

φ +i +i

N

φ +i +i

N

5.2.2d

5.2.3a

10

5.2.3b

5.2.3c

11

5.3.4a

5.3.5a

12

5.7.3a

Orientation of the joint daylighted

Apparent spacing on the measuring surface

Apparent spacing in 3 directions

5.7.3b

13

RQD = (L1 + L2 + … + Ln) / L x 10 100% 0% = number number of join joints ts / length length = n / L Outcrop Face

L1

Tape

2

1

L2

L3

X

i

X

L4

X

L <10 cm

L5

n

Li

< 10 cm

X X

Ln

<10 cm fault

5.7.4a

<10 cm L1

L2

L3

X

<10 cm L4

X

X

<10 cm core loss L5

Li

X X

Ln

L

RQD = (L1 + L2 + … + Ln) / L x 100%

5.7.4b

14

Load measured by load cell

Displacements measured by LVDTs

5.7.9a

15

Properties of Rock Discontinuities

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