Rock Mechanics and Ground control

Course Material

For

Singareni Collieries Limited (SCCLtd)

Ramagundem AP

By

Dr.K.U.M.Rao

Professor Department of Mining Engineering

Indian Institute of Technology Kharagpur 721302

Chapter 1 Introduction 1.1 Rock Mechanics as a Discipline Rock mechanics is a discipline that uses the principles of mechanics to describe the behaviour of rocks. Here, the term of rock is in the scale of engineering. The scale is generally in the order of between a few metres to a few thousand metres. Therefore, the rock considered in rock mechanics is in fact the rock mass, which composes intact rock materials and rock discontinuities. What is so special of rock mechanics? For normal construction materials, e.g., steel and concrete, the mechanical behaviours are continuous, homogeneous, isotropic, and linearly elastic (CHILE). Properties of the manmade materials are known and can often be controlled. For rocks, due to the existence of discontinuities, the behaviours are discontinuous, inhomogeneous, anisotropic, and non-linearly elastic (DIANE). Properties of the natural geomaterials are unknown and often can not be controlled. It is important to be award that in rock mechanics, rock discontinuities dominate the mechanical and engineering behaviours. The existence of discontinuity depends on the scale. The discontinuous nature and scale dependence feature is not common in other man-made materials. Rock mechanics is applied to various engineering disciplines: civil, mining, hydropower, petroleum. In civil engineering, it involves foundation, slope and tunnel. In structural engineering, the design process generally is as following:

Calculate external loading imposed on the structure; Design the structure and analyse loading in structure elements; Design the structure element and select materials.

In rock engineering, or geotechnical engineering, the whole process is different. Loading condition is not easily calculateable, rock engineering, being sloping cutting or underground excavation, does not impose loading, but disturbs the existing stress field of the ground and redistribute the load. Therefore, the key process in rock engineering is to understand the how the stress field is disturbed by engineering activities and how the rock is behaving (responding) to the change of boundary conditions, and yet the material does not has a characteristics controlled by man. The objectives of learning rock mechanics are:

• To understand of the mechanical behaviour of rock materials, rock discontinuities and rock masses.

• To be able to analyse and to determine mechanical and engineering properties of rocks for engineering applications.

CHAPTER 2 ROCK FORMATION AND ROCK MASS 2.1 Rock Formations and Types Rock is a natural geo-material. In geological term, rock is a solid substance composed of minerals, of which can consist in particulate form (soil particles) or in large form (mountains, tectonic plates, planetary cores, planets). In common term, rock is an aggregate of minerals. Rocks are formed by three main origins: igneous rocks from magma, sedimentary rock from sediments lithfication and metamorphic rocks through metamorphism. Figure 2.1.1a shows the geological process involved in the formations of various rocks. It should be noted that the processes are dynamic and continuous.

Figure 2.1.1a Rock cycle illustrating the role of various geological processes in rock formation. 2.1.3 Igneous Rocks Igneous rocks are formed when molten rock (magma) cools and solidifies, with or without crystallization. They can be formed below the surface as intrusive (plutonic) rocks, or on the surface as extrusive (volcanic) rocks. This magma can be derived from either the Earth's mantle or pre-existing rocks made molten by extreme temperature and pressure changes. Figure 2.1.1a shows the origin of magma and igneous rock through the rock cycle. As magma cools, minerals crystallize from the melt at different temperatures. The magma from which the minerals crystallize is rich in only silicon, oxygen, aluminium, sodium,

potassium, calcium, iron, and magnesium minerals. These are the elements which combine to form the silicate minerals, which account for over 90% of all igneous rocks. Igneous rocks make up approximately 95% of the upper part of the Earth's crust, but their great abundance is hidden on the Earth's surface by a relatively thin but widespread layer of sedimentary and metamorphic rocks. 2.1.4 Sedimentary Rocks Sedimentary rock is formed in three main ways – by the deposition of the weathered remains of other rocks (known as 'clastic' sedimentary rocks); by the deposition of the results of biogenic activity; and by precipitation from solution. Sedimentary rocks include common types such as sandstone, conglomerate, clay, shale, chalk and limestone. Sedimentary rocks cover 75% of the Earth's surface, but count for only 5% of the rock in the earth crust. Four basic processes are involved in the formation of a clastic sedimentary rock: weathering (erosion), transportation, deposition and compaction. All rocks disintegrate slowly as a result of mechanical weathering and chemical weathering. Mechanical weathering is the breakdown of rock into particles without producing changes in the chemical composition of the minerals in the rock. Chemical weathering is the breakdown of rock by chemical reaction. 2.1.5 Metamorphic Rocks Metamorphic rock is a new rock type transformed from an existing rock type, through metamorphism. When an existing rock is subjected to heat and extreme pressure, the rock undergoes profound physical and/or chemical change. The existing rock may be sedimentary rock, igneous rock or another older metamorphic rock (Figure 2.1.1a). Metamorphic rocks make up a large part of the Earth's crust and are classified by texture and by mineral assembly. They are formed deep beneath the Earth's surface by great stresses from rocks above and high pressures and temperatures, known as regional metamorphism. The high temperatures and pressures in the depths of the Earth are the cause of the changes. Metamorphic rocks are also formed by the intrusion of molten rock (magma) into solid rock and form particularly at the place of contact between the magma and solid rock where the temperatures are high, known as contact metamorphism. Another important mechanism of metamorphism is that of chemical reactions that occur between minerals without them melting. In the process atoms are exchanged between the minerals, and thus new minerals are formed. Many complex high-temperature reactions may take place, and each mineral assemblage produced provides us with a clue as to the temperatures and pressures at the time of metamorphism. Heat and pressure are the causes of metamorphism. When above 200°C, heat causes minerals to recrystallise. Pressure forces some crystals to re-orient. The combined effects of recrystallisation and re-orientation usually lead to foliation, which is a unique feature

of metamorphic rocks. It occurs when a strong compressive force is applied from one direction to a recrystallizing rock. This causes the platy or elongated crystals of minerals, such as mica and chlorite, to grow with their long axes perpendicular to the direction of the force. This result in a banded, or foliated, rock, with the bands showing the colours of the minerals that formed them. 2.2 Rock Discontinuities 2.2.1 Joints A geological joint is a generally planar fracture formed in a rock as a result of extensional stress. Joints are always in sets. Joints do not have any significant offset of strata either vertically or horizontally (Figure 2.2.1a).

Figure 2.2.1a Typical joints seen (i) one dominant set, (ii) three sets. Joints can be formed due to erosion of the overlying strata exposed at the surface. The removal of overlying rock results in change of stresses, and hence leads to the fracturing of underlying rock. Joints can also be caused by cooling of hot rock masses, which form cooling joints. Columnar jointing or columnar basalts are typical joint features by cooling. Joints are also formed by tectonic movement. Joints are often in sets. A joint set is a group of parallel joints. Typically, a rock mass can have between one to a few joint sets. Joints are the most common type of rock discontinuities. They are generally considered as part of the rock mass, as the spacing of joints usually is between a few centimetres and a few metres. 2.2.2 Faults Geologic faults are planar rock fractures which show evidence of relative movement. Large faults within the Earth's crust are the result of shear motion and active fault zones are the causal locations of most earthquakes. Earthquakes are caused by energy release during rapid slippage along faults. The largest examples are at tectonic plate boundaries, but many faults occur far from active plate boundaries. Since faults usually do not consist of a single, clean fracture, the term fault zone is used when referring to the zone of complex deformation associated with the fault plane. Figure 2.2.2a.

Figure 2.2.2a Faults, fault zone and shear zone.

A shear zone is a wide zone of distributed shearing in rock. Typically this is a type of fault but it may be difficult to place a distinct fault plane into the shear zone. Shear zones can be only inches wide, or up to several kilometres wide. As faults, particularly fault zone and shear zone, are large scale geological features. They are often dealt separately from the rock mass. Small scale single faults often have the similar effects as a joint. The behaviour large scale fault and shear zones require specific investigation and analysis, if a project is to be constructed over or close such zones. 2.2.3 Folds The term fold is used in geology when originally flat and planar rock strata are bent as a result of tectonic force or movement. Folds form under very varied conditions of stress. Folds can be commonly observed in sedimentary formation and as well as in metamorphic rocks (Figure 2.2.3a). Folds are usually not considered as part of the rock mass. However, folds can be of the similar scale as the engineering project and hence the significance of folds on the behaviour of the rock mass must be taken into consideration. It should be noted that fold has huge variation of features. Folds, particularly intense folds, are often associated with high degree of fracturing and relatively weak and soft rocks. Although the folding feature may not be directly taking into account of rock mass, but the results of folding is often reflected in the rock mass consideration. 2.2.4 Bedding Planes As sedimentary rocks are formed in layers, the interfaces between layers are termed as bedding planes. Bedding plane therefore is a discontinuity separating different rocks (Figure 2.2.4a). Bedding plane often can be fully closed and cemented.

Figure 2.2.3a Folds in a sedimentary formation.

Figure 2.2.3b Folds in a sedimentary formation.

Bedding planes are isolated geological features to engineering activities. It mainly creates an interface of two rock materials. However, some bedding planes could also become potential weathered zones and pocket of groundwater. For example, an interface between porous sandstone and limestone may lead to extensive weathering of the limestone, which leads to cavities along the interface. 2.3 Rock Material and Rock Masses 2.3.1 Engineering Scale and Rock Engineering in and on rock has different scales, varying from a few centimetres to a few kilometres. A borehole can be typically around 8 cm while a mine can spread up to a few km. For civil engineering works, e.g., foundations, slopes and tunnels, the scale of projects is usually a few ten metres to a few hundreds metres. When such engineering scale is considered, then rock in such scale is generally a mass of rock at the site. This mass of rock, often termed as rock mass, is the whole body of the rock in situ, consists of rock blocks and fractures, typically seen in Figure 2.3.1b.

Figure 2.2.4a Some typical bedding planes.

Figure 2.2.4b Some typical bedding planes.

Figure 2.3.1b Typical rock masses.

2.3.2 Composition of Rock Mass A rock mass contains (a) rock material, in the form of intact rock plates, blocks and wedges, of various sizes, and (b) rock discontinuities that cuts through the rock, in the forms of fractures, joints, and faults. Rock materials and discontinuities together form rockmass. In addition, rock mass may also include filling materials in the discontinuities and dyke and sill igneous intrusions (Figure 2.3.2a). Faults are often filled with weathered materials, varying from extremely soft clay and fractured and crushed rocks.

Figure 2.3.2a A dyke intrusion. 2.3.3 Role of Joints in Rock Mass Behaviour Rock joints change the properties and behaviour of rock mass in the following terms:

(i) Cuts rock into slabs, blocks and wedges, to be free to fall and move (Figure 2.3.3a);

(ii) Acts as weak planes for sliding and moving; (i) Provides water flow channel and creates flow networks; (ii) Gives large deformation; (iii)Alters stress distribution and orientation;

Because the rock materials between rock joints are intact and solid, they have relative small deformation and low permeability. It is therefore obvious that rock mass behaviour by large is governed by rock joints. 2.4 Inhomogeneity and Anisotropy 2.4.1 Inhomogeneity of Rock Materials Inhomogeneity represents property varying with locations. Most of the engineering materials have varying degrees of inhomogeneity. Rocks are formed by nature and exhibits great inhomogeneity. 2.4.2 Inhomogeneity of Rock Masses Inhomogeneity of a rock mass is primarily due to the existence of discontinuities. Rock masses are also inhomogeneous due to the mix of rock types, interbedding and intrusion.

2.4.3 Anisotropy Anisotropy is defined as properties are different in different direction.Anisotropy occurs in both rock materials and rock mass. Some sedimentary rocks, e.g., shale, have noticeable anisotropic characteristics. Other sedimentary may not have clear anisotropy. However, under the influence of formation process and pressure, small degree of anisotropy is possible. Rock with most obvious anisotropy is slate. Phyllite and schist are the other foliated metamorphic rocks that exhibit anisotropy, as seen in Figure 2.4.3a.

Figure 2.4.3a Some common anisotropic rocks, (i) slate and (ii) sandstone. Rock mass anisotropy is controlled by (i) joint set (Figure 2.4.3b), and (ii) sedimentary layer (Figure 2.4.2a).

Figure 2.4.3b A Limestone rock mass with one dominating joint set.

CHAPTER 3 PROPERTIES OF ROCK MATERIALS Rock material is the intact rock portion. This Chapter addresses properties of rock material. 3.1 Physical Properties of Rock Material The physical properties of rocks affecting design and construction in rocks are:

1. Mineralogical composition , structure, and texture; 2. Specific gravity G 3. Unit weight γ 4. Porosity n 5. Void ratio e 6. Moisture content w 7. Degree of saturation, S 8. Permeability to water k

Mineralogical composition is the intrinsic property controlling the strength of the rock Although there exist more than 2000 kinds of known minerals, only about nine of them partake decisively in forming the composition of rocks. They are:

• Quartz • Feldspar • Mica • Hornblende(Amphiboles) • Pyroxenes • Olivine • Calcite • Kaolinite, and • Dolomite

These minerals are glued together by four types of materials such as silicates, calcites, argillaceous and ferrous minerals. The Rocks containing quartz as the binder are known as siliceous rocks and are the strongest while the rocks with calcium and magnesium carbonates are the weakest. The term “rock texture” refers to the arrangement of its grains. Thus the texture is the appearance, megascopic or microscopic, seen on a smooth surface of a mineral aggregate, showing the geometrical aspects of the rock including shape, size, and arrangement. One distinguishes between coarse-texture (coarse-grained) and fine-textures rock. A coarse-grained rock is one in which the large crystals are seen easily while the fine grained rocks need to be seen under a microscope. Rock structure and texture affect the strength properties of the rock.

3.1.1 Specific Gravity, Density, Porosity and Water Content Specific gravity is the ratio of the density of solids to the density of water.

WS

S

VM

Gρ1

⋅=

(where SM = mass of solids and SV -volume of solids)

Unit weight ( )γ

VW

=γ

( W is the total weight of the sample and V the total volume of the sample) Density is a measure of mass per unit of volume. Density of rock material various, and often related to the porosity of the rock. It is sometimes defined by unit weight and specific gravity. Most rocks have density between 2,500nd 2,800 kg/m3. Void ratio (e) is the ratio of the volume of voids (VV) to the volume of solids (VS)

S

V

VV

e =

we

GV

WW

dDry +

=⋅+

==11γγγ

Porosity (n) describes how densely the material is packed. It is the ratio of the non-solid volume (VV) to the total volume (V) of material. Porosity therefore is a fraction between 0 and 1.

V

GWVe

eVV

n WSV )/(1

γ−=

+==

VV

eS=

+11

(The unit weight of water = 1 g/cm3 = 1 t/m3 = 9.81 kN/m3 = 62.4 lb/ft3) Where dW = dry weight of the sample SW = weight of solids SV VandV = volume of voids and volume of solids V = total volume of the sample G = specific gravity e = Void ratio of the sample wγ = Unit weight of water = 9.81 kN/m3 w = moisture content of the sample

The value is typically ranging from less than 0.01 for solid granite to up to 0.5 for porous sandstone. It may also be represented in percent terms by multiplying the fraction by 100%. Water content is a measure indicating the amount of water the rock material contains. It is simply the ratio of the weight of water (Ww) to the weight (WS) of the rock material.

100100 ×−

=×=S

S

S

w

WWW

WW

w

Degree of saturation S is

100×=V

w

VV

S

Density is common physical properties. It is influenced by the specific gravity of the composition minerals and the compaction of the minerals. However, most rocks are well compacted and then have specific gravity between 2.5 to 2.8. Density is used to estimate overburden stress. Density and porosity often related to the strength of rock material. A low density and high porosity rock usually has low strength. Porosity is one of the governing factors for the permeability. Porosity provides the void for water to flow through in a rock material. High porosity therefore naturally leads to high permeability.

Figure Phase diagram illustrating the weights and volume relationship

Table 3.1.1a gives common physical properties, including density and porosity of rock materials. 3.1.2 Hardness Hardness is the characteristic of a solid material expressing its resistance to permanent deformation. Hardness of rock materials depends on several factors, including mineral composition and density. A typical measure is the Schmidt rebound hardness number.

Table 3.1.1a Physical properties of fresh rock materials

3.1.3 Abrasivity Abrasivity measures the abrasiveness of a rock materials against other materials, e.g., steel. It is an important measure for estimate wear of rock drilling and boring equipment. Abrasivity is highly influenced by the amount of quartz mineral in the rock material. The higher quartz content gives higher abrasivity.Abrasivity measures are given by several tests. Cerchar and other abrasivity tests are described later. 3.1.4 Permeability Permeability is a measure of the ability of a material to transmit fluids. Most rocks, including igneous, metamorphic and chemical sedimentary rocks, generally have very low permeability. As discussed earlier, permeability of rock material is governed by porosity. Porous rocks such as sandstones usually have high permeability while granites

have low permeability. Permeability of rock materials, except for those porous one, has limited interests as in the rock mass, flow is concentrated in fractures in the rock mass. Permeability of rock fractures is discussed later. 3.1.5 Wave Velocity Measurements of wave are often done by using P wave and sometimes, S waves. P wave velocity measures the travel speed of longitudinal (primary) wave in the material, while S-wave velocity measures the travel speed of shear (secondary) wave in the material. The velocity measurements provide correlation to physical properties in terms of compaction degree of the material. A well compacted rock has generally high velocity as the grains are all in good contact and wave are traveling through the solid. For a poorly compact rock material, the grains are not in good contact, so the wave will partially travel through void (air or water) and the velocity will be reduced (P-wave velocities in air and in water are 340 and 1500 m/s respectively and are much lower than that in solid). Typical values of P and S wave velocities of some rocks are given in Table 3.1.1a. Wave velocities are also commonly used to assess the degree of rock mass fracturing at large scale, using the same principle, and it will be discussed in a later chapter. 3.2 Mechanical Properties of Rock Material 3.2.1 Compressive Strength Compressive strength is the capacity of a material to withstand axially directed compressive forces. The most common measure of compressive strength is the uniaxial compressive strength or unconfined compressive strength. Usually compressive strength of rock is defined by the ultimate stress. It is one of the most important mechanical properties of rock material, used in design, analysis and modeling. Figure 4.2.1a presents a typical stress-strain curve of a rock under uniaxial compression. The complete stress-strain curve can be divided into 6 sections, represent 6 stages that the rock material is undergoing. Figure 3.2.1b and Figure 3.2.1c show the states of rock in those stages of compression.

Figure 3.2.1a Typical uniaxial compression stress-strain curve of rock material. Stage I – The rock is initially stressed, pre-existing microcracks or pore orientated at large angles to the applied stress is closing, in addition to deformation. This causes an initial non-linearity of the axial stress-strain curve. This initial non-linearity is more obvious in weaker and more porous rocks,

Figure 3.2.1c Samples of rock material under uniaxial compression test and failure. Stage II – The rock basically has a linearly elastic behaviour with linear stress-strain curves, both axially and laterally. The Poisson's ratio, particularly in stiffer unconfined rocks, tends to be low. The rock is primarily undergoing elastic deformation with minimum cracking inside the material. Micro-cracks are likely initiated at the later portion of this stage, of about 35-40% peak strength. At this stage, the stress-strain is largely recoverable, as the there is little permanent damage of the micro-structure of the rock material. Stage III – The rock behaves near-linear elastic. The axial stress-strain curve is nearlinear and is nearly recoverable. There is a slight increase in lateral strain due to dilation. Microcrack propagation occurs in a stable manner during this stage and that microcracking events occur independently of each other and are distributed throughout the specimen. The upper boundary of the stage is the point of maximum compaction and zero volume change and occurs at about 80% peak strength. Stage IV – The rock is undergone a rapid acceleration of microcracking events and volume increase. The spreading of microcracks is no longer independent and clusters of cracks in the zones of highest stress tend to coalesce and start to form tensile fractures or shear planes - depending on the strength of the rock. Stage V – The rock has passed peak stress, but is still intact, even though the internal structure is highly disrupt. In this stage the crack arrays fork and coalesce into macrocracks or fractures. The specimen is undergone strain softening (failure)

deformation, i.e., at peak stress the test specimen starts to become weaker with increasing strain. Thus further strain will be concentrated on weaker elements of the rock which have already been subjected to strain. This in turn will lead to zones of concentrated strain or shear planes. Stage VI – The rock has essentially parted to form a series of blocks rather than an intact structure. These blocks slide across each other and the predominant deformation mechanism is friction between the sliding blocks. Secondary fractures may occur due to differential shearing. The axial stress or force acting on the specimen tends to fall to a constant residual strength value, equivalent to the frictional resistance of the sliding blocks. In underground excavation, we often are interested in the rock at depth. The rock is covered by overburden materials, and is subjected to lateral stresses. Compressive strength with lateral pressures is higher than that without. The compressive strength with lateral pressures is called triaxial compressive strength. Figure 3.2.1d shows the results of a series triaxial compression tests. In addition to the significant increase of strength with confining pressure, the stress-strain characteristics also changed. Discussion on the influence of confining pressure to the mechanical characteristics is given in a later section. Typical strengths and modulus of common rocks are given in Table 3.2.1a.

Figure 3.2.1d Triaxial compression test and failure

3.2.2 Young's Modulus and Poisson’s Ratio Young's Modulus is modulus of elasticity measuring of the stiffness of a rock material. It is defined as the ratio, for small strains, of the rate of change of stress with strain. This can be experimentally determined from the slope of a stress-strain curve obtained during compressional or tensile tests conducted on a rock sample.

Table 3.2.1a Mechanical properties of rock materials.

Similar to strength, Young’s Modulus of rock materials varies widely with rock type. For extremely hard and strong rocks, Young’s Modulus can be as high as 100 GPa. Poisson’s ratio measures the ratio of lateral strain to axial strain, at linearly-elastic region. For most rocks, the Poisson’s ratio is between 0.15 and 0.4. As seen from the tests that at later stage of loading beyond, that is, beyond the linearly elastic region the increase in lateral strain is faster than the axial strain and hence indicates a higher ratio. 3.2.3 Stress-Strain at and after Peak A complete stress-strain curve for a rock specimen in uniaxial compression test can be obtained, as shown in Figure 3.2.3a. Strain at failure is the strain measured at ultimate stress. Rocks generally fail at a small strain, typically around 0.2 to 0.4% under uniaxial compression. Brittle rocks, typically crystalline rocks, have low strain at failure, while soft rock, such as shale and mudstone, could have relatively high strain at failure. Strain at failure sometimes is used as a measure of brittleness of the rock. Strain at failure increases with increasing confining pressure under triaxial compression conditions. Rocks can have brittle or ductile behaviour after peak. Most rocks, including all crystalline igneous, metamorphic and sedimentary rocks, behave brittle under uniaxial compression. A few soft rocks, mainly of sedimentary origin, behave ductile.

Figure 3.2.3a Complete stress-strain curves of several rocks showing post peak behaviour (Brady and Brown). 3.2.4 Tensile Strength Tensile strength of rock material is normally defined by the ultimate strength in tension, i.e., maximum tensile stress the rock material can withstand. Rock material generally has a low tensile strength. The low tensile strength is due to the existence of microcracks in the rock. The existence of microcracks may also be the cause of rock failing suddenly in tension with a small strain. Tensile strength of rock materials can be obtained from several types of tensile tests: direct tensile test, Brazilian test and flexure test. Direct test is not commonly performed due to the difficulty in sample preparation. The most common tensile strength determination is by the Brazilian tests. Figure 3.2.4a illustrates the failure mechanism of the Brazilian tensile tests.

Figure 3.2.4a Stress and failure of Brazilian tensile tests by RFPA simulation. 3.2.5 Shear Strength Shear strength is used to describe the strength of rock materials, to resist deformation due to shear stress. Rock resists shear stress by two internal mechanisms, cohesion and internal friction. Cohesion is a measure of internal bonding of the rock material. Internal friction is caused by contact between particles, and is defined by the internal friction angle, φ. Different rocks have different cohesions and different friction angles.

Shear strength of rock material can be determined by direct shear test and by triaxial compression tests. In practice, the later methods is widely used and accepted. With a series of triaxial tests conducted at different confining pressures, peak stresses (σ1) are obtained at various lateral stresses (σ3). By plotting Mohr circles, the shear envelope is defined which gives the cohesion and internal friction angle, as shown in Figure 3.2.5a.

Figure 3.2.5a Determination of shear strength by triaxial tests.

Tensile and shear strengths are important as rock fails mostly in tension and in shearing, even the loading may appears to be compression. Rocks generally have high compressive strength so failure in pure compression is not common. 3.3 Effects of Confining and Pore Water Pressures on Strength and Deformation 3.3.1 Effects of Confining Pressure Figure 4.3.1a illustrates a number of important features of the behaviour of rock in triaxial compression. It shows that with increasing confining pressure,

(a) the peak strength increases;

(b) there is a transition from typically brittle to fully ductile behaviour with the introduction of plastic mechanism of deformation;

(c) the region incorporating the peak of the axial stress-axial strain curve

flattens and widens;

(d) the post-peak drop in stress to the residual strength reduces and disappears at high confining stress.

The confining pressure that causes the post-peak reduction in strength disappears and the behaviour becomes fully ductile (48.3 MPa in the figure), is known as the brittle-ductile transition pressure. This brittle-ductile transition pressure varies with rock type. In general, igneous and high grade metamorphic rocks, e.g., granite and quartzite, remain brittle at room temperature at confining pressures of up to 1000 MPa or more.

Figure 3.3.1a Complete axial stress-axial strain curves obtained in triaxial compression tests on Marble at various confining pressures (after Wawersik & Fairhurst 1970). 3.3.2 Effects of Pore Water Pressure The influence of pore-water pressure on the behaviour of porous rock in the triaxial compression tests is illustrated by Figure 4.3.2a. A series of triaxial compression tests was carried out on a limestone with a constant confining pressure of 69 MPa, but with various level of pore pressure (0-69 MPa). There is a transition from ductile to brittle behaviour as pore pressure is increased from 0 to 69 MPa. In this case, mechanical response is controlled by the effective confining stress (σ3' = σ3 – u). Effect of pore water pressure is only applicable for porous rocks where sufficient pore pressure can be developed within the materials. For low porosity rocks, the classical effective stress law does not hold.

Figure 3.3.2a Effect of pore pressure on the stress-strain behaviour of rock materials.

3.4 Other Engineering Properties of Rock Materials 3.4.1 Point Load Strength Index Point load test is another simple index test for rock material. It gives the standard point load index, Is(50), calculated from the point load at failure and the size of the specimen, with size correction to an equivalent core diameter of 50 mm. 4.5 Relationships between Physical and Mechanical Properties 3.5.1 Rock Hardness, Density, and Strength Schmidt hammer rebound hardness is often measured during early part of field investigation. It is a measure of the hardness of the rock material by count the rebound degree. At the same time, the hardness index can be used to estimate uniaxial compressive strength of the rock material. The correlation between hardness and strength is shown in Figure 3.5.1a. The correlation is also influenced by the density of the material.

Figure 3.5.1a Correlation between hardness, Young’s Modulus and Strength. 3.5.2 Effect of Water Content on Strength Many tests showed that the when rock materials are saturated or in wet condition, the uniaxial compressive strength is reduced, compared to the strength in dry condition. 3.5.3 Velocity and Modulus While seismic wave velocity gives a physical measurement of the rock material, it is also used to estimate the elastic modulus of the rock material. From the theory of elasticity, compressional (or longitudinal) P-wave velocity (vp) is related to the elastic modulus sE and the density (ρ) of the material as,

If ρ in g/cm3, and vp in km/s, then Es in GPa (109 N/m2). The elastic modulus estimated by this method is the sometime termed as seismic modulus (also called dynamic modulus, but should not be mistaken as the modulus under dynamic compression). It is different from the modules obtained by the uniaxial compression tests. The value of the seismic modulus is generally slightly higher than the modulus determined from static compression tests. Similarly, seismic shear modulus Gs may be determined from shear S-wave velocity vs,

Gs is in GPa, when density ρ is in g/cm3, and S-wave velocity vs is in km/s. Seismic Poisson’s ration νs can be determined from,

Alternatively, seismic Young’s modulus Es can be determined from shear modulus (Gs) and Poisson’s ratio (νs), Es = 2 Gs (1 + νs) 3.5.4 Compressive Strength and Modulus It is a general trend that a stronger rock material is also stiffer, i.e., higher elastic modulus is often associated with higher strength. There is reasonable correlation between compressive strength and elastic modulus. The correlations are presented in Figure 3.5.4a. It should be noted that the correlation is not precisely linear and also depends on the rock type, or perhaps on the texture of the rocks.

Figure 3.5.4a Correlation between strength and modulus.

3.6 Failure Criteria of Rock Materials 3.6.1 Mohr-Coulomb criterion Mohr-Coulomb strength criterion assumes that a shear failure plane is developed in the rock material. When failure occurs, the stresses developed on the failure plane are on the strength envelope. Refer to Figure 3.6.1a, the stresses on the failure plane a-b are the normal stress σn and shear stress τ.

Figure 3.6.1a Stresses on failure plane a-b and representation of Mohr’s circle.

Applying the stress transformation equations or from the Mohr’s circle, it gives:

Coulomb suggested that shear strengths of rock are made up of two parts, a constant cohesion (c) and a normal stress-dependent frictional component, i.e.,

where c = cohesion and φ = angle of internal friction. Therefore, by combining the above three equations,

or

In a shear stress-normal stress plot, the Coulomb shear strength criterion τ = c + σn tanφ is represented by a straight line, with an intercept c on the τ axis and an angle of φ with

the σn axis. This straight line is often called the strength envelope. Any stress condition below the strength envelope is safe, and once the stress condition meet the envelope, failure will occur. As assumed, rock failure starts with the formation of the shear failure plane a-b. Therefore, the stress condition on the a-b plane satisfies the shear strength condition. In another word, the Mohr-Coulomb strength envelope straight line touches (makes a tangent) to the Mohr’s circles. At each tangent point, the stress condition on the a-b plane meets the strength envelope. As seen from the Mohr’s circle, the failure plane is defined by θ, and θ = ¼ π + ½ φ Then

Figure 3.6.1b Mohr-Coulomb strength envelope in terms of normal and shear stresses and principal stresses, with tensile cut-off. If the Mohr-Coulomb strength envelope shown in Figure 4.6.1b is extrapolated, the uniaxial compressive strength is related to c and φ by:

An apparent value of uniaxial tensile strength of the material is given by:

However, the measured values of tensile strength are generally lower than those predicted by the above equation. For this reason, a tensile cut-off is usually applied at a selected value of uniaxial tensile stress, σt′, as shown in Figure 4.6.1b. For most rocks, σt′ is about 1/10 σc.

The Mohr-Coulomb strength envelope can also be shown in σ1–σ3 plots, as seen in Figure 4.6.1b. Then,

and

or

The Mohr-Coulomb criterion is only suitable for the low range of σ3. At h igh σ3, it overestimates the strength. It also overestimates tensile strength. In most cases, rock engineering deals with shallow problems and low σ3, so the criterion is widely used, due to its simplicity and popularity. 3.6.2 Griffith strength criterion Based on the energy instability concept, Griffith extended the theory to the case of applied compressive stresses. Assuming that the elliptical crack will propagate from the points of maximum tensile stress concentration (P in Figure 4.6.2a), Griffith obtained the following criterion for crack extension in plane compression:

Figure 3.6.2a Griffith crack model for plane compression.

where σt is the uniaxial tensile strength of the material. When σ3 = 0, the above equation becomes

It in fact suggests that the uniaxial compressive stress at crack extension is always eight times the uniaxial tensile strength

Figure 3.6.2b Griffith envelope for crack extension in compression. The strength envelopes given by the above equations in principal stresses and in normal and shear stresses are shown in Figure 3.6.2b. This criterion can also be expressed in terms of the shear stress (τ) and normal stress (σn) acting on the plane containing the major axis of the crack:

When σn = 0, τ = 2σt, which represents the cohesion. 3.6.3 Hoek-Brown criterion Because the classic strength theories used for other engineering materials have been found not to apply to rock over a wide range of applied compressive stress conditions, a number of empirical strength criteria have been introduced for practical use. One of the most widely used criteria is Hoek-Brown criterion for isotropic rock materials and rock masses. Hoek and Brown (1980) found that the peak triaxial compressive strengths of a wide range of isotropic rock materials could be described by the following equation:

or

Where m is a parameter that changes with rock type in the following general way:

Figure 3.6.3a shows normalized Hoek-Brown peak strength envelope for some rocks. It is evident that the Hoek-Brown strength envelope is not a straight line, but a curve. At high stress level, the envelope curves down, so it gives low strength estimate than the Mohr-Coulomb envelope.

Figure 3.6.3a Normalized peak strength envelope for (i) granites and (ii) sandstones

(after Hoek & Brown 1980). The Hoek-Brown peak strength criterion is an empirical criterion based on substantial test results on various rocks. It is however very easy to use and select parameters. It is also extended to rock masses with the same equation, hence makes it is so far the only acceptable criterion for both material and mass. 3.7 Effects of Rock Microstructures on Mechanical Properties 3.7.1 Strength of rock material with Anisotropy Rocks, such as shale and slate, are not isotropic. Because of some preferred orientation of fabric or microstructure, or the presence of bedding or cleavage planes, the behaviour of those rocks is anisotropic. There are several forms of anisotropy with various degrees of complexity. It is therefore only the simplest form of anisotropy, transverse isotropy, to be discussed here. The peak strengths developed by transversely isotropic rocks in triaxial compression vary with the orientation of the plane of isotropy, plane of weakness or foliation plane, with respect to the principal stress directions. Figure 3.7.1a shows some measured variations in peak principal stress difference with the angle of inclination of the major principal stress to the plane of weakness.

Figure 3.7.1a Variation of differential stresses with the inclination angle of the plane of

weakness (see Brady & Brown 1985) Analytical solution shows that principal stress difference (σ1–σ3) of a transversely isotropic specimen under triaxial compression shown in Figure 3.7.1a can be given by the equation below (Brady & Brown 1985):

Where: wc = cohesion of the plane of weakness;

wϕ = angle of friction of the plane; β = inclination of the plane.

The minimum strength occurs when

The corresponding value of principal stress difference is,

Figure 3.7.1b shows variation of σ1 at constant σ3 with angle β, plotted using the above equation. When the weakness plane is at an angle of 45° + ½ φw, the strength is the lowest. For rocks, φw is about 30° to 50°, hence β is about 60° to 70°. In compression tests, intact rock specimens generally fail to form a shear plane at an angle about 60° to 70°. This in fact shows that when the rock containing an existing weakness plane that is about to become a failure plane, the rock has the lowest strength.

Figure 3.7.1b Variation of σ1 at constant σ3 with angle β.

3.8 Time Dependent Characteristics of Rock Materials 3.8.1 Rheologic Properties of Rock Materials 3.8.2 Effect of Loading Rate on Rock Strength 3.8.3 Failure Mechanism of Rock Material under Impact and Shock Loading 3.9 Laboratory Testing of Rock Materials 3.9.1 Compression Tests (a) Uniaxial Compression Strength Test Specimens of right circular cylinders having a height to diameter ratio of 2 or higher are prepared by cutting and grinding. Two axial and one circumferential deformation measurement devices (LVDTs) are attached to each of the specimen. The specimen is then compressed under a stiff compression machine with a spherical seating. The axial stress is applied with a constant strain rate around 1 μm/s such that failure occurs within 5-10 minutes of loading. The load is measured by a load transducer. Load, two axial deformations and one circumferential deformation measurements are recorded at every 2- 5 KN interval until failure. Uniaxial compressive strength, Young's modules (at 50% of failure stress) and Poisson's ratio (at 50% of failure stress) can be calculated from the failure load, stress and strain relationship.

Uniaxial compressive strength, cσ is calculated as the failure load divided by the initial cross sectional area of the specimen. Axial tangential Young's modulus at 50% of uniaxial compressive strength, Et50% is calculated as the slope of tangent line of axial stress - axial strain curve at a stress level equals to 50% of the ultimate uniaxial compressive strength. Poisson's ratio at 50% of uniaxial compressive strength, ν50%, is calculated as:

c

c

ofatcurvestrainstresslateralofslopeofatcurvestrainstressaxialofslope

vσσ

%50%50

%50 −−

=

Reporting of results includes description of the rock, specimen anisotropy, specimen dimension, density and water content at time of test, mode of failure, uniaxial compressive strength, modulus of elasticity, Poisson's ratio, stress-strain (axial and lateral) curves to failure.

Figure 3.9.3a A typical uniaxial compression test set-up with load and strain

measurements. (b) Triaxial Compression Strength Test Specimens of right circular cylinders having a height to diameter ratio of 2 or higher are prepared by cutting and grinding. Two axial and two lateral deformation (or a circumferential deformation if a circumferential chain LVDT device is used), measurement devices are attached to each of the specimen. The specimen is placed in a triaxial cell (e.g., Hoek-Franklin cell) and a desired confining stress is applied and maintained by a hydraulic pump. The specimen is then further compressed under a stiff compression machine with a spherical seating. The axial stress is applied with a constant strain rate arou nd 1 μm/s su ch that failu re occu rs with in 5-15 minutes of loading. The

load is measured by a load transducer. Load, 2 axial strain or deformation and 2 lateral strains or deformation (or a circumferential deformation if a circumferential chain LVDT device is used) are recorded at a fixed interval until failure. Triaxial compressive strength, Young's modules (at 50% of failure stress) and Poisson's ratio (at 50% of failure stress) can be calculated from the axial failure load, stress and strain relationship. Triaxial compressive strength, 1σ , is calculated as the axial failure load divided by the initial cross sectional area of the specimen. Axial tangential Young's modulus at 50% of triaxial compressive strength, Et50% is calculated as the slope of tangent line of axial stress - axial strain curve at a stress level equals to 50% of the ultimate uniaxial compressive strength. Poisson's ratio at 50% of triaxial compressive strength is calculated with the same methods as for the uniaxial compression test. For a group of triaxial compression tests at different confining stress level, Mohr's stress circle are plotted using confining stress as 3σ and axial stress as 1σ . Failure envelopes (Mohr, Coulomb or Hoek and Brown) and parameters of specified failure criterion are determined. Reporting of results includes description of the rock, specimen anisotropy, specimen dimension, density and water content at time of test, mode of failure, triaxial compressive strength, modulus of elasticity, Poisson's ratio, stress-strain (axial and lateral) curves to failure, Mohr's circles and failure envelope.

Figure 3.9.3b Triaxial compression test using Hoek cell.

3.9.4 Tensile Tests (a) Direct Tension Test Direct tension tests on rock materials are not common, due to the difficulty in specimen preparation. For direct tension test, rock specimen is to be prepared in dog-bone shape with a thin middle. The specimen is then loaded in tension by pulling from the two ends. Deformation modulus can be measured by having strain gauges attached to the specimen. calculation and the Young’s modulus and the Poisson’s ratio is similar to that for the uniaxial compression test. (b) Brazilian Tensile Strength Test Cylindrical specimen of diameter approximately equals to 50 mm and thickness approximately equal to the radius is prepared. The cylindrical surfaces should be free from obvious tool marks and any irregularities across the thickness. End faces shall be flat to within 0.25 mm and square and parallel to within 0.25°. The specimen is wrapped around its periphery with one layer of the masking tape and loaded into the Brazil tensile test apparatus across its diameter. Loading is applied continuously at a constant rate such that failure occurs within 15-30 seconds. Ten specimens of the same sample shall be tested. The tensile strength of the rock is calculated from failure load (P), specimen diameter (D) and specimen thickness (t) by the following formula:

DtP

T636.0

−=σ

Reporting of results includes description of the rock, orientation of the axis of loading with respect to specimen anisotropy, water content and degree of saturation, test duration and loading rate, mode of failure.

Figure 3.9.4b Brazilian tensile test. 3.9.5 Shear Strength Tests

(a) Direct Punch Shear (b) Shear Strength Determination by Triaxial Compression Results Shear strength parameters, cohesion (c) and international friction angle (φ) can be determined from triaxial compression test data. The Mohr’s circle can be plotted for a series of triaxial tests results with 1σ at different 3σ , forming a series circles, as typically shown in the figure below. A straight line is draw to fit best by tangent to all the Mohr’s circles. The line represents the shear strength envelope. The angle of the line to the horizontal is the internal friction angle φ, and the intercept at τ axis is the cohesion c. Alternatively, a series equation can be formed for sets of 1σ and 1σ , based on the Mohr- Coulomb criterion,

Cohesion c and friction angle ‘φ’ can be computed by solving the equations. 3.9.6 Point Load Strength Index Test Point load test of rock cores can be conducted diametrically and axially. In diametrical test, rock core specimen of diameter D is loaded between the point load apparatus across its diameter. The length/diameter ratio for the diametrical test should be greater than 1.0. For axial test, rock core is cut to a height between 0.5 D to D and is loaded between the point load apparatus axially. Load at failure is recorded as P. Uncorrected point load strength, Is, is calculated as:

2e

s DPI =

where eD , the "equivalent core diameter", is given by: 22 DDe = for diametrical test; π/4A= for axial, block and lump tests;

A = H D = minimum cross sectional area of a plane through the loading points. The point load strength is corrected to the point load strength at equivalent core diameter of 50 mm. For eD ≠ 50 mm, the size correction factor is:

45.0

50

= eDF

The corrected point load strength index )50(sI is calculated as:

ss IFI .)50( =

Figure 3.9.6a Point load test.

3.9.7 Ultrasonic wave velocity Cylindrical rock sample is prepared by cutting and lapping the ends. The length is measured. An ultrasonic digital indicator consist a pulse generator unit, transmitter and receiver transducers are used for sonic pulse velocity measurement. The transmitter and the receiver are positioned at the ends of specimen and the pulse wave travel time is measured. The velocity is calculated from dividing the length of rock sample by wave travel time. Both P-wave and S-wave velocities can be measured.

Figure 3.9.7a Measuring P and S wave velocity in a rock specimen.

3.9.8 Hardness (a) Schmidt Hammer Rebound Hardness A Schmidt hammer with rebound measurement is used for this test. The Schmidt hammer is point perpendicularly and touch the surface of rock. The hammer is released and reading on the hammer is taken. The reading gives directly the Schmidt hammer hardness value. The standard Schmidt hardness number is taken when the hammer is point vertically down. If the hammer is point to horizontal and upward, correction is needed to add to the number from the hammer. At least 20 tests should be conducted on any one rock specimen. It is suggest to omit 2 lowest and 2 highest reading, and to use the remaining reading for calculating the average hardness value.

Figure 3.9.8a Schmidt hammer rebound hardness test.

3.9.10 Abrasivity (a) Cerchar Abrasivity Test The Cerchar abrasivity test is an abrasive wear with pressure test . It was proposed by the Laboratoire du Centre d’Etudes et Recherches des Charbonnages (Cerchar) in France. The testing apparatus is featured in Figure 3.9.10a. It consists of a vice for holding rock sample (1), which can be moved across the base of the apparatus by a hand wheel (2) that drives a screwthread of pitch 1 mm /revolution turning. Displacement of the vice (1) is measured by a scale (3). A steel stylus (4), fitting into a holder (5), loaded on the surface of the rock sample. A dead weight (6) of 70 N is applied on the stylus.

Figure 3.9.10a Cerchar abrasivity test West apparatus (West 1989).

To determine the CAI value the rock is slowly displaced by 10 mm with a velocity of approximately 1 mm/s. The abrasiveness of the rock is then obtained by measuring the resulting wear flat on the tip of the steel stylus. The CAI value is calculated as,

dCAI 210−= where ‘d’ is the wear flat diameter of the stylus tip in μm. 3.9.12 Slake Durability Test Select representative rock sample consisting of 10 lumps each of 40-60g, roughly spherical in shape with corners rounded during preparation. The sample is placed in the test drum of 2 mm standard mesh cylinder of 100 mm long and 140 mm in diameter with

solid removable lid and fixed base, and is dried to a constant mass at 105°C. The mass of drum and sample is recorded (Mass A). The sample and drum is placed in trough which is filled with slaking fluid, usually tap water at 20°C, to a level 20 mm below the drum axis, and the drum is rotated at 20 rpm for 10 minutes (Figure 3.9.12a). The drum and sample are removed from trough and oven dried to a constant mass at 105°C without the lid. The mass of the drum and sample is recorded after cooling (Mass B). The slaking and drying process is repeated and the mass of the drum and sample is recorded (Mass C). The drum is brushed clean and its mass is recorded (Mass D).

Figure 3.9.12a Slake durability test. The slake-durability index is taken as the percentage ratio of final to initial dry sample masses after to cycles,

Slake-durability index, %1002 ×−−

=DADCI d

The first cycle slake-durability index should be calculated when 2dI is 0-10%,

Slake-durability index, = %100×−−

DADB

Table 3.9.12a Slake Durability Classification

Special Note AE Activity in rocks under compression The term acoustic emission (AE) is widely used to denote the phenomenon in which a material or structure emits elastic waves of shock type and sometimes of continuous type caused by the sudden occurrence of fractures or frictional sliding along discontinuous surfaces. Acoustic Emission (AE) is a naturally occurring phenomenon whereby external stimuli, such as mechanical loading, generate sources of elastic waves. AE occurs when a small surface displacement of a material is produced. This occurs due to stress waves generated when there is a rapid release of energy in a material, or on its surface. The wave generated by the AE source, or, of practical interest, in methods used to stimulate and capture AE in a controlled fashion for study and/or use in inspection, quality control, system feedback, process monitoring and others. The application of AE to non-destructive testing of materials in the ultrasonic regime, typically takes place between 100 kHz and 1 MHz.

Figure Two fundamental cases of stress application (a) and (b), and temporal variations of strain (ε ) and the frequency (n) of AE events in these cases

Figure Temporal variations of number of AE events and axial strain ( 1ε ), lateral strain

( θε ) and non-elastic volumetric strain (neV

V

∆

CHAPTER 6 ROCK MASS CLASSIFICATION Rock mass property is governed by the properties of intact rock materials and of the discontinuities in the rock. The behaviour if rock mass is also influenced by the conditions the rock mass is subjected to, primarily the in situ stress and groundwater. The quality of a rock mass quality can be quantified by means of rock mass classifications. This Chapter addresses rock mass properties and rock mass classifications. 6.1 Rock Mass Properties and Quality 6.1.1 Properties Governing Rock Mass Behaviour Rock mass is a matrix consisting of rock material and rock discontinuities. As discussed early, rock discontinuity that distributed extensively in a rock mass is predominantly joints. Faults, bedding planes and dyke intrusions are localised features and therefore are dealt individually. Properties of rock mass therefore are governed by the parameters of rock joints and rock material, as well as boundary conditions, as listed in Table 6.1.1a.

Table 6.1.1a Prime parameters governing rock mass property

The behaviour of rock changes from continuous elastic of intact rock materials to discontinues running of highly fractured rock masses. The existence of rock joints and other discontinuities plays important role in governing the behaviour and properties of the rock mass, as illustrated in Figure 6.1.1a. Chapter 4 has covered the properties of intact rock materials, and Chapter 5 has dealt with rocks contains 1 or 2 localised joints with emphasis on the properties of joints. When a rock mass contains several joints, the rock mass can be treated a jointed rock mass, and sometimes also termed a Hoek-Brown rock mass, that can be described by the Hoek-Brown criterion (discussed later). 6.1.2 Classification by Rock Load Factor (Terzaghi 1946) Based in extensive experiences in steel arch supported rail tunnels in the Alps, Terzaghi (1946) classified rock mass by mean of Rock Load Factor. The rock mass is classified into 9 classes from hard and intact rock to blocky, and to squeezing rock. The concept used in this classification system is to estimate the rock load to be carried by the steel arches installed to support a tunnel, as illustrated in Figure 6.1.2a. The classification is presented by Table 6.1.2a.

Figure 6.1.2a Terzaghi’s rock load concept. For obtaining the support pressure (p) from the rock load factor (Hp), Terzaghi suggested the equation below, p = Hp γ H where γ is the unit weight of the rock mass, H is the tunnel depth or thickness of the overburden. Attempts have been made to link Rock Load Factor classification to RQD. As suggested by Deere (1970), Class I is corresponding to RQD 95-100%, Class II to RQD 90-99%, Class III to RQD 85-95%, and Class IV to RQD 75-85%. Singh and Goel (1999) gave the following comments to the Rock Load Factor classification: (a) It provides reasonable support pressure estimates for small tunnels with diameter up to 6 metres. (b) It gives over-estimates for large tunnels with diameter above 6 metres. (c) The estimated support pressure has a wide range for squeezing and swelling rock conditions for a meaningful application. 6.1.3 Classification by Active Span and Stand-Up Time (Stini 1950, Lauffer 1958) The concept of active span and stand-up time is illustrated in Figure 6.1.3a and Figure 6.1.3b. Active span is in fact the largest dimension of the unsupported tunnel section. Stand-up time is the length of time which an excavated opening with a given active span can stand without any mean of support or reinforcement. Rock classes from A to G are assigned according to the stand-up time for a given active span. Use of active span and stand-up time will be further discussed in later sections.

Figure 6.1.3a Definition of active span.

Figure 6.1.3b Relationship between active span and stand-up time and rock mass classes

(Class A is very good and Class G is very poor) Table 6.1.2a Rock class and rock load factor classification by Terzaghi for steel arch supported tunnels

6.1.4 Rock Quality Designation (RQD) (Deere 1964)

Rock quality designation (RQD) was introduced in 1960s, as an attempt to quantify rock mass quality. Table 6.1.2a reproduces the proposed expression of rock mass quality classification according to RQD. As discussed earlier, RQD only represents the degree of fracturing of the rock mass. It does not account for the strength of the rock or mechanical and other geometrical properties of the joints. Therefore, RQD partially reflects on the rock mass quality. Table 6.1.2a Rock mass quality classification according to RQD

RQD has been widely accepted as a measure of fracturing degree of the rock mass. His parameter has been used in the rock mass classification systems, including the RMR and the Q systems. 6.2 Rock Mass Rating – RMR System 6.2.1 Concept of RMR System (1973, 1989) The rock mass rating (RMR) system is a rock mass quality classification developed by South African Council for Scientific and Industrial Research (CSIR), close associated with excavation for the mining industry (Bieniawski 1973). Originally, this geomechanics classification system incorporated eight parameters. The RMR system in use now incorporates five basic parameters below. (a) Strength of intact rock material: Uniaxial compressive strength is preferred. For

rock of moderate to high strength, point load index is acceptable. (b) RQD: RQD is used as described before. (c) Spacing of joints: Average spacing of all rock discontinuities is used. (d) Condition of joints: Condition includes joint aperture, persistence, roughness,

joint surface weathering and alteration, and presence of infilling. (e) Groundwater conditions: It is to account for groundwater inflow in excavation

stability. Table 6.2.1a is the RMR classification updated in 1989. Part A of the table shows the RMR classification with the above 5 parameters. Individual rate for each parameter is

obtained from the property of each parameter. The weight of each parameter has already considered in the rating, for example, maximum rating for joint condition is 30 while for rock strength is 15. The overall basic RMR rate is the sum of individual rates. Influence of joint orientation on the stability of excavation is considered in Part B of the same table. Explanation of the descriptive terms used is given table Part C. With adjustment made to account for joint orientation, a final RMR rating is obtained, it can be also expresses in rock mass class, as shown in Table 6.2.1b. The table also gives the meaning of rock mass classes in terms of stand-up time, equivalent rock mass cohesion and friction angle. RMR was applied to correlate with excavated active span and stand-up time, as shown in Figure 6.2.1a. This correlation allow engineer to estimate the stand-up time for a given span and a given rock mass. Table 6.2.1b Rock mass classes determined from total ratings and meaning

Figure 6.2.1a Stand-up time and RMR quality

6.2.2 Examples of using RMR System (a) A granite rock mass containing 3 joint sets, average RQD is 88%, average joint spacing is 0.24 m, joint surfaces are generally stepped and rough, tightly closed and unweathered with occasional stains observed, the excavation surface is wet but not dripping, average rock material uniaxial compressive strength is 160 MPa, the tunnel is excavated to 150 m below the ground where no abnormal high in situ stress is expected. Selection of RMR parameters and calculation of RMR are shown below:

The calculated basic RMR is 76. It falls in rock class B which indicates the rock mass is of good quality. (b) A sandstone rock mass, fractured by 2 joint sets plus random fractures, average RQD is 70%, average joint spacing is 0.11 m, joint surfaces are slightly rough, highly weathered with stains and weathered surface but no clay found on surface, joints are generally in contact with apertures generally less than 1 mm, average rock material uniaxial compressive strength is 85 MPa, the tunnel is to be excavated at 80 m below ground level and the groundwater table is 10 m below the ground surface. Here, groundwater parameter is not directly given, but given in terms of groundwater pressure of 70 m water head and overburden pressure of 80 m ground. Since there is no indication of in situ stress ratio, overburden stress is taken as the major in situ stress as an approximation. Joint water pressure = groundwater pressure = 70 m × γw In situ stress = Overburden pressure = 80 m × γ Joint water pressure / In situ stress = (70 × 1)/(80× 2.7)

= 0.32 Selection of RMR parameters and calculation of RMR are shown below:

The calculated basic RMR is 52. It falls in rock class C which indicates the rock mass is of fair quality. (c) A highly fractured siltstone rock mass, found to have 2 joint sets and many random fractures, average RQD is 41%, joints appears continuous observed in tunnel, joint surfaces are slickensided and undulating, and are highly weathered, joint are separated by about 3-5 mm, filled with clay, average rock material uniaxial compressive strength is 65 MPa, inflow per 10 m tunnel length is observed at approximately 50 litre/minute, with considerable outwash of joint fillings. The tunnel is at 220 m below ground. In the above information, joint spacing is not provided. However, RQD is given and from the relationship between RQD and joint frequency, it is possible to calculate average joint spacing, with the equation below,

RQD = 100 e–0.1λ (0.1λ +1) (where λ is the mean number of discontinuities per meter) Joint frequency is estimated to be 20, which gives average joint spacing 0.05 m Selection of RMR parameters and calculation of RMR are shown below:

The calculated basic RMR is 34. It falls in rock class D which indicates the rock mass is of poor quality. Judgement often is needed to interpret the information given in the geological and hydrogeological investigation reports and in the borehole logs to match the descriptive terms in the RMR table. Closest match and approximation is to be used to determine each of the RMR parameter rating. 6.2.3 Extension of RMR – Slope Mass Rating (SMR) The slope mass rating (SMR) is an extension of the RMR system applied to rock slope engineering. SMR value is obtained by adjust RMR value with orientation and excavation adjustments for slopes, i.e., SMR = RMR + (F1⋅F2⋅F3) + F4 where F1 = (1 - sin A)2 and A = angle between the strikes of the slope and the joint = |αj - αs|. F2 = (tan βj)2

B = joint dip angle = βj. For topping, F2 = 1.0 Value of F1, F2 and F3 are given in Table 6.2.3a. Table 6.2.3b gives the classification category of rock mass slope. Details on rock slope analysis and engineering including excavation methods and support and stabilisation will be covered in a later chapter dealing slope engineering.

Table 6.2.3a Adjustment rating of F1, F2, F3 and F4 for joints

Table 6.2.3a Classification of Rock Slope according to SMT

6.3 Rock Tunnel Quality Q-System 6.3.1 Concept of the Q-System The Q-system was developed as a rock tunnelling quality index by the Norwegian Geotechnical Institute (NGI) (Barton et al 1974). The system was based on evaluation of a large number of case histories of underground excavation stability, and is an index for the determination of the tunnelling quality of a rock mass. The numerical value of this index Q is defined by:

RQD is the Rock Quality Designation measuring the fracturing degree. Jn is the joint set number accounting for the number of joint sets. Jr is the joint roughness number

accounting for the joint surface roughness. Ja is the joint alteration number indicating the degree of weathering, alteration and filling. Jw is the joint water reduction factor accounting for the problem from groundwater pressure, and SRF is the stress reduction factor indicating the influence of in situ stress. Q value is considered as a function of only three parameters which are crude measures of: (a) Block size: RQD / Jn (b) Inter-block shear strength Jr / Ja (c) Active stress Jw / SRF Parameters and rating of the Q system is given in Table 6.3.1a. The classification system gives a Q value which indicates the rock mass quality, shown in Table 6.3.1b. Q value is applied to estimate the support measure for a tunnel of a given dimension and usage, as shown in Figure 6.3.1a. Equivalent dimension is used in the figure and ESR is given in Table 6.3.1c.

Table 6.3.1a Rock mass classification Q system

quantities of swelling clays

Table 6.3.1b Rock mass quality rating according to Q values

Figure 6.3.1a Support design based on Q value

Table 6.3.1c Excavation Support Ratio (ESR) for various tunnel categories

6.3.2 Examples of Using the Q-System

(a) A granite rock mass containing 3 joint sets, average RQD is 88%, average joint spacing is 0.24 m, joint surfaces are generally stepped and rough, tightly closed and unweathered with occasional stains observed, the excavation surface is wet but not dripping, average rock material uniaxial compressive strength is 160 MPa, the tunnel is excavated to 150 m below the ground where no abnormal high in situ stress is expected. Selection of Q parameters and calculation of Q-value are shown below:

The calculated Q-value is 29, and the rock mass is classified as good quality. (b) A sandstone rock mass, fractured by 2 joint sets plus random fractures, average RQD is 70%, average joint spacing is 0.11 m, joint surfaces are slightly rough, highly weathered with stains and weathered surface but no clay found on surface, joints are generally in contact with apertures generally less than 1 mm, average rock material uniaxial compressive strength is 85 MPa, the tunnel is to be excavated at 80 m below ground level and the groundwater table is 10 m below the ground surface. Selection of Q parameters and calculation of Q-value are shown below:

The calculated Q-value is 4.4, and the rock mass is classified as fair quality. (c) A highly fractured siltstone rock mass, found to have 2 joint sets and many random fractures, average RQD is 41%, joints appears continuous observed in tunnel, joint surfaces are slickensided and undulating, and are highly weathered, joint are separated by about 3-5 mm, filled with clay, average rock material uniaxial compressive strength is 65

MPa, inflow per 10 m tunnel length is observed at approximately 50 litre/minute, with considerable outwash of joint fillings. The tunnel is at 220 m below ground. Selection of Q parameters and calculation of Q-value are shown below:

The calculated Q-value is 0.85, and the rock mass is classified as very poor quality. Again, judgement is frequently needed to interpret the descriptions given in the geological and hydrogeological investigation reports and in the borehole logs to match the descriptive terms in the Q table. Closest match and approximation is to be used to determine each of the Q parameter rating. 6.3.3 Extension of Q-System – QTBM for Mechanised Tunnelling Q-system was extended to a new QTBM system for predicting penetration rate (PR) and advance rate (AR) for tunnelling using tunnel boring machine (TBM) in 1999 (Barton 1999). The method is based on the Q-system and average cutter force in relations to the appropriate rock mass strength. Orientation of joint structure is accounted for, together with the rock material strength. The abrasive or nonabrasive nature of the rock is incorporated via the cutter life index (CLI). Rock stress level is also considered. The new parameter QTBM is to estimate TBM performance during tunnelling. The components of the QTBM are as follows:

where RQD0= RQD (%) measured in the tunnelling direction, Jn, Jr, Ja, Jw, and SRF ratings are the same parameters in the original Q-system, σm is the rock mass strength (MPa) estimated from a complicated equation including the Q-value measured in the tunnel direction, F is the average cutter load (ton) through the same zone, CLI is the cutter life index, q is the quartz content (%) in rock mineralogy, and σθ is the induced biaxial stress (MPa) on tunnel face in the same zone. The constants 20 in the σm term, 20 in the CLI term and 5 in the σθ term are normalising constants.

The experiences on the application of QTBM vary between projects. Example of using the QTBM is given in Figure 6.2.3a. It appears that the correlation between QTBM and Advanced Rate is not consistent and varies with a large margin. Rock mass classification systems, including RMR and Q, when developed, were intended to classify rock mass quality to arrive a suitable support design. The systems were not meant for the design of excavation methodology. In general, with increasing of rock mass quality, penetration decreases. However, very poor rock mass does not facilitate penetration. Parameters in those rock mass classifications were related to support design, they were not selected to describe rock mass boreability. Although QTBM has added a number of parameters to reflect cutting force and wear, the emphasis is obviously not be justified. The original rock mass classifications are independent of TBM characteristics, while penetration however is a result of interaction between rock mass properties and TBM machine parameters (Zhao 2006). 6.4 Geological Strength Index GSI System and Others 6.4.1 GSI System The Geological Strength Index (GSI) was introduced by Hoek in 1994. It was aimed to estimate the reduction in rock mass strength for different geological conditions. This system is presented in Tables 6.4.1a. The system gives a GSI value estimated from rock mass structure and rock discontinuity surface condition. The direct application of GSI value is to estimate the parameters in the Hoek-Brown strength criterion for rock masses. Although it was not aimed at to be a rock mass classification, the GSI value does in fact reflect the rock mass quality. GSI system has been modified and updated in the recent years, mainly to cover more complex geological features, such as sheared zones. The use of GSI requires careful examination and understanding of engineering geological features of the rock mass. Rock mass structure given in the chart is general description and there may be many cases that does not directly match the description. In general, the following equivalent between rock mass structural descriptions of blocky to the block size description is suggested below. However, simple block size description does not include geological structural features, such as folds and shear zones.

GSI does not include the parameter of rock strength, as GSI was initiated to be a tool to estimate rock mass strength with the Hoek-Brown strength criterion. In the Hoek-Brown

criterion, rock material uniaxial strength is used as a base parameter to estimate rock mass uniaxial strength as well as triaxial strengths of rock material and rock mass. The use of GSI to estimate rock mass strength is given later in the section dealing with rock mass strength. GSI system did not suggest a direct correlation between rock mass quality and GSI value. However, it is suggested that GSI can be related to RMR (GSI = RMR – 5), for reasonable good quality rock mass. An approximate classification of rock mass quality and GSI is suggested in Table 6.4.1b, based on the correlation between RMR and GSI

Table 6.4.1a Geological Strength Index (GSI)

Table 6.4.1b Rock mass classes determined from GSI

6.4.2 Examples of Using the GSI System Examples of estimating GSI is given below, with the same rock masses used previously to estimate RMR and Q.

(a) Granite rock mass containing 3 joint sets, average RQD is 88%, average joint spacing is 0.24 m, joint surfaces are generally stepped and rough, tightly closed and unweathered with occasional stains observed, the excavation surface is wet but not dripping, average rock material uniaxial compressive strength is 160 MPa, the tunnel is excavated to 150 m below the ground where no abnormal high in situ stress is expected.

Refer to the GSI chart, Rock Mass Structure for the above granite is blocky, and Joint Surface Condition is very good. Therefore GSI is 75±5. The rock mass is classified as good to very good quality.

(b) A sandstone rock mass, fractured by 2 joint sets plus random fractures, average RQD is 70%, average joint spacing is 0.11 m, joint surfaces are slightly rough, highly weathered with stains and weathered surface but no clay found on surface, joints are generally in contact with apertures generally less than 1 mm, average rock material uniaxial compressive strength is 85 MPa, the tunnel is to be excavated at 80 m below ground level and the groundwater table is 10 m below the ground surface.

Refer to the GSI chart, Rock Mass Structure for the above sandstone is very blocky, and Joint Surface Condition is fair to poor. Therefore GSI is 40±5. The rock mass is classified as fair quality.

(c) A highly fractured siltstone rock mass, found to have 2 joint sets and many random fractures, average RQD is 41%, joints appears continuous observed in tunnel, joint surfaces are slickensided and undulating, and are highly weathered, joint are separated by about 3-5 mm, filled with clay, average rock material uniaxial compressive strength is 65 MPa, inflow per 10 m tunnel length is observed at approximately 50 litre/minute, with considerable outwash of joint fillings. The tunnel is at 220 m below ground.

Refer to the GSI chart, Rock Mass Structure for the above siltstone is blocky /folded/ faulted, and Joint Surface Condition is very poor. Therefore GSI is 20±5. The rock mass is classified as very poor to poor quality.

It is advised that while selecting an average value of GSI, it is perhaps better to select a range of the GSI value for that rock mass. Summary of RMR, Q and GSI from the above three examples are given below,

6.4.3 Correlation and Comparison between Q, RMR and GSI Correlation between Q and RMR are found to be, RMR = 9 lnQ + A A varies between 26 and 62, and average of A is 44. Figure 6.4.3a shows the comparison and correlation between RMR and Q.

Figure 6.4.3a Correlation between RMR and Q values.

Several other correlation equations have been proposed, one of which is:

RMR = 13.5 logQ +43.

They are all in the general form of semi-log equation. For generally competent rock masses with GSI > 25, the value of GSI can be related to Rock Mass Rating RMR value as, GSI = RMR – 5 RMR is the basic RMR value by setting the Groundwater rating at 15 (dry), and without adjustment for joint orientation. For very poor quality rock masses, the value of RMR is very difficult to estimate and the correlation between RMR and GSI is no longer reliable. Consequently, RMR classification should not be used for estimating the GSI values for poor quality rock masses. It should be noted that each classification uses a set of parameters that are different from other classifications. For that reason, estimate the value of one classification from another is not advisable. 6.4.3 Other Classification Systems Several other classification approaches have been proposed. In section, a few will be briefly discussed due to their unique application in certain aspect. (a) Rock Mass Number, N Rock Mass Number (N) is the rock mass quality Q value when SRF is set at 1 (i.e., normal condition, stress reduction is not considered). N can be computed as, N = (RQD/Jn) (Jr/Ja) (Jw) This system is used because the difficult in obtaining SRF in the Q-system. It has been noticed that SRF in the Q-system is not sensitive in rock engineering design. the value assign to SRF cover too great range. For example, SRF = 1 for σc/σ1 = 10~200, i.e., for a rock with σc = 50 MPa, in situ stresses of 0.25 to 5 MPa yield the same SRF value. The importance of in situ stress on the stability of underground excavation is insufficiently represented in the Q-system. Another application of N number is to the rock squeezing condition. Squeezing has been noted in the Q-system but is not sufficiently dealt, due to the special behaviour and nature of the squeezing ground. The use of N in squeezing rock mass classification will be presented in a later section in this chapter.

(b) Rock Mass Index, RMi Rock Mass Index is proposed as an index characterising rock mass strength as a construction material. It is calculated by the following equation, RMi = σc Jp where σc is the uniaxial compressive strength of the intact rock material, and Jp is the jointing parameter accounting for 4 joint characteristics, namely, joint density (or block size), joint roughness, joint alteration and joint size. Jp is in fact a reduction factor representing the effects of jointing on the strength of rock mass. Jp = 1 for a intact rock, Jp = 0 for a crushed rock masses. 6.5 Rock Mass Strength and Rock Mass Quality 6.5.1 Strength of Rock Mass As discussed earlier, strength and deformation properties of a rock mass are much governed by the existence of joints. In another word, the mechanical properties of a rock mass are also related to the quality of the rock mass. In general, a rock mass of good quality (strong rock, few joints and good joint surface quality) will have a higher strength and high deformation modulus than that of a poor rock mass. 6.5.2 Hoek-Brown Strength Criterion of Rock Mass Hoek and Brown criterion discussed in Chapter 4 is not only for rock materials. It is also applicable to rock masses (Figure 6.5.2a). The Hoek-Brown criterion for rock mass is described by the following equation:

or

Figure 6.5.2a Applicability of Hoek-Brown criterion for rock material and rock masses. The equation above is the generalised Hoek-Brown criterion of rock mass. The Hoek- Brown criterion for intact rock material is a special form of the generalised equation when s =1 and a = 0.5. For intact rock, mb becomes mi, i.e.,

Note in the Hoek-Brown criterion, σci is consistently referred to the uniaxial compressive strength of intact rock material in the Hoek-Brown criterion for rock material and for rock mass. In the generalised Hoek-Brown criterion, σ1 is the strength of the rock mass at a confining pressure σ3. σci is the uniaxial strength of the intact rock in the rock mass. Parameter a is generally equal to 0.5. Constants mb and s are parameters that changes with rock type and rock mass quality. Table 6.5.2a gives an earlier suggestion of mb and s values.

Table 6.5.2a Relation between rock mass quality and Hoek.Brown constants

Development and application of the Hoek-Brown criterion lead to better definition of the parameters mb and s. Table 6.5.2b presents the latest definition of mi values for the intact rock materials, according to different rocks.

Table 6.5.2b Values of constant mi for intact rock in Hoek-Brown criterion

The values in the above table are suggestive. As seen from the table, variation of mi value for each rock can be as great as 18. If triaxial tests have been conducted, the value of mi should be calculated from the test results. Once the Geological Strength Index has been estimated, the parameters which describe the rock mass strength characteristics, are calculated as follows,

For GSI > 25, i.e. rock masses of good to reasonable quality, the original Hoek-Brown criterion is applicable with,

and a = 0.5 For GSI < 25, i.e. rock masses of very poor quality, s = 0, and a in the Hoek-Brown criterion is no longer equal to 0.5. Value of a can be estimated from GSI by the following equation,

Uniaxial compressive strength of the rock mass is the value of σ1 when σ3 is zero. From the Hoek-Brown criterion, when σ3 = 0, it gives the uniaxial compressive strength as,

Clearly, for rock masses of very poor quality, the uniaxial compressive strength of the rock masses equal to zero. Example of using the Hoek-Brown equation to determine rock mass strength is given below by the same three examples used for determining the rock mass qualities RMR, Q and GSI. Calculation in the example uses average values only, although in practice, range of values should be used to give upper and lower bounds. (a) Granite rock mass, with material uniaxial strength 150 MPa, mean GSI 75. From the mi table, mi given for granite is approximately 32.

The Hoek-Brown equation for the granite rock mass is,

Uniaxial compressive strength of the rock mass is, when σ3 = 0,

(b) Sandstone rock mass, with material uniaxial strength 85 MPa, mean GSI 40. From the mi table, mi given for sandstone is approximately 17.

Similarly the uniaxial compressive strength is,

(c) Siltstone rock mass, with material uniaxial strength 65 MPa, mean GSI 20. From the mi table, mi given for siltstone is approximately 7.

Similarly the uniaxial compressive strength is,

6.5.4 Correlations between Rock Mass Quality and Mechanical Properties Correlations between rock mass strength and rock mass quality are reflected in Table 6.5.2a and the Hoek-Brown criterion relating GSI. The better rock mass quality gives high rock mass strength. When the rock mass is solid and massive with few joints, the rock mass strength is close to the strength of intact rock material. When the rock mass is very poor, i.e., RMR < 23, Q < 0.1, or GSI < 25, the rock mass has very low uniaxial compressive strength close to zero. Attempts have also been made to correlated deformation modulus of the rock mass with rock mass quality. In situ rock mass modulus (Em) can be estimated from the Q and the RMR systems, in the equations below,

The above Em-RMR equations are generally for competent rock mass with RMR greater than 20. For poor rocks, the equation below has been proposed,

For rock mass with σci < 100 MPa, the equation is obtained by substituting GSI for RMR in the original Em-RMR equation. The Em-GSI equation indicates that modulus Em is reduced progressively as the value of σci falls below 100. This reduction is based upon the reasoning that the deformation of better quality rock masses is controlled by the discontinuities while, for poorer quality rock masses, the deformation of the intact rock pieces contributes to the overall deformation process. 6.5.4 Relationship between Hoek-Brown and Mohr-Coulomb Criteria There is no direct correlation between the linear Mohr-Coulomb Criterion and the nonlinear Hoek-Brown Criterion defined by the two equations. Often, the input for a design software or numerical modelling required for rock masses are in terms of Mohr- Coulomb parameters c and φ. Attempts have been made by Hoek and Brown to estimate c and φ from the Hoek-Brown equation. At the same time, they caution the user that is a major problem to obtain c and φ from the Hoek-Brown equation. If a series tests have been conducted on the rock mass, obviously test results should be used directly to obtain parameters c and φ, using for example, plotting the Mohr circle and fitting with the best strength envelope, where c and φ can be readily calculated Common problems were there is no or limited test results on rock mass. The suggested approach to obtain rock mass Mohr-Coulomb parameters c and φ is by generate a series σ1–σ3 results by the Hoek-Brown equation. Then plotting the Mohr circle using the generated σ1–σ3 data and fitting with the best linear envelope, where c and φ can be readily calculated. Care must be taken when deciding the ‘best’ linear line in fitting the Mohr circles. It depends on the stress region of the engineering application. For a tunnel problem, if the depth and stress range is known, the line should be fitting best for the

Mohr circles in that stress region. For a slope problem, the stress region may vary from 0 to some level of stress, and the fitting a line at low stress level (where the curvature is the greatest for the non-linear Hoek-Brown strength envelope) is very sensitive to the stress level. Also, pore pressure needs to be considered as this affects the effective stress level. 6.6 Squeezing Behaviour of Rock Mass 6.6.1 Squeezing Phenomenon ISRM (Barla 1995) defines that squeezing of rock is the time dependent large deformation, which occurs around a tunnel and other underground openings, and is essentially associated with creep caused by exceeding shear strength. Deformation may terminate during construction or may continue over a long time period. The degree of squeezing often is classified to mild, moderate and high, by the conditions below, (i) Mild squeezing: closure 1-3% of tunnel diameter; (ii) Moderate squeezing: closure 3-5% of tunnel diameter; (iii) High squeezing: closure > 5% of tunnel diameter. Behaviour of rock squeezing is typically represented by rock mass squeezes plastically into the tunnel and the phenomenon is time dependent. Rate of squeezing depends on the degree of over-stress. Usually the rate is high at initial stage, say, several centimetres of tunnel closure per day for the first 1-2 weeks of excavation. Closure rate reduces with time. Squeezing may continue for years in exceptional cases. Squeezing may occur at shallow depths in weak and poor rock masses such as mudstone and shale. Rock masses of competent rock of poor rock mass quality at great depth (under high cover) may also suffer from squeezing. 6.6.2 Squeezing Estimation by Rock Mass Classification Based on case studies, squeezing may be identified from rock class classification Q-value and overburden thickness (H). As shown in Figure 6.6.2a, the division between squeezing and non-squeezing condition is by a line H = 350 Q1/3, where H is in metres. Squeezing condition may occur above the line, i.e., H > 350 Q1/3. Below the line, i.e., H < 350 Q1/3, the ground condition is generally non-squeezing.

Figure 6.6.2a Predicting squeezing ground using Q-value

Another approach predicting squeezing is by using the Rock Mass Number (N). As discussed in the previous section, N is the Q-value when SRF is set to be 1. The parameters allow one to separate in situ stress effects from rock mass quality. In situ stress, which is the external cause of squeezing is dealt separated by considering the overburden depth. From Figure 6.6.2b, the line separating non-squeezing from squeezing condition is,

Where H is the tunnel depth or overburden in metres and B is the tunnel span or diameter in metres.

Figure 6.6.2b Squeezing ground condition is presented by: H > (275 N1/3) B–0.1. It is also possible to characterise the degree of squeezing base on the same figure. Mild squeezing occurs when (275 N1/3) B–0.1 < H < (450 N1/3) B–0.1 Moderate squeezing occurs when (450 N1/3) B–0.1 < H < (630 N1/3) B–0.1 High squeezing occurs when H > (630 N1/3) B–0.1. Theoretically, squeezing conditions around a tunnel opening can occur when, σθ > Strength = σcm + Px A/2 where σθ is the tangential stress at the tunnel opening, σcm is the uniaxial compressive strength of the rock mass, Px is the in situ stress in the tunnel axis direction, and A is a rock parameter proportion to friction. Squeezing may not occur in hard rocks with high values of parameter A. The above equation can be written in the form below for a circular tunnel under hydrostatic in situ stress field, with overburden stress P, P=γH,

ISRM classifies squeezing rock mass and ground condition in Table 6.6.2a. Table 6.6.2a Suggested predictions of squeezing conditions

The prediction equations for squeezing require the measurements of in situ stress and rock mass strength. Overburden stress can be estimated from the overburden depth and rock unit weight. Uniaxial compressive strength of the rock mass can be estimated from the Hoek-Brown criterion with rock mass quality assessment (e.g., GSI). Studies carried out by Hoek (2000) indicate that squeezing can in fact start at rock mass strength / in situ stress ratio of 0.3. A prediction curve was proposed by Hoek and reproduced in Figure 6.6.2c, relating tunnel closure to rock mass strength/in situ stress ratio. The prediction curve was compared with tunnel squeezing case histories.

Figure 6.6.2c Squeezing prediction curve and comparison with case histories.

CHAPTER 3 In situ Stress In situ stress measurements have been compiled and presented in Figure 2.5.2a. Change of vertical stress with depth is scattered about the tend line, σv = 0.027 z, which represents the overburden pressure.

Dep

th, Z

(m)

Dep

th, Z

(m)

Figure 3.2a In situ stress measurements at various (Brady and Brown 157).

The horizontal stresses are presented in the figure by a ratio of average horizontal stress to vertical stress, k. It is very common in rock mechanics that one of the horizontal stresses represent the major principal stress, while the vertical stress or the other horizontal stress represents the minor principal stress.While vertical stress can be estimated with reasonable reliability. The horizontal stress should not be estimated. For projects that maximum stress direction and magnitude may be important, in situ stress measurements is required. In situ stress measurement Instrumentation For the development of information for the design of underground openings and their supporting structures, four principal classes of measurements are of interest. These are:

1. Measurement of strains in the ground surrounding an opening. 2. Measurement of convergence movements of rock surfaces. 3. Measurements of pressures on mine void filling material. 4. Measurement of loads on structures for supporting ground and stresses in

the supporting structures. The following stresses are important in influencing the behaviour of rock around subsurface openings:

1. The magnitude and directions of natural (pre-existing, inherent) stresses in rock.

2. The magnitude and directions of induced (concentrated or re-aligned) stresses. These are induced by creation of an opening.

The physical characteristics which may be measured are: Following physical features of a rock are modified when it is subjected to the stresses induced by creation of an opening:

1. Closure of roof and floor or closure of sides 2. Tangential deformation of exposed surfaces 3. Changes in velocity of sound waves passed through the ground 4. Changes in the modulus of elasticity of the ground 5. Nature of sub-audible vibrations originating in rock 6. Deformation of boreholes 7. Deformation and restoration of slots in the rock surfaces

Measurements of strains and stresses include the following: 1. Measuring strains in rock at exposed rock surface 2. Measuring strains in rock remote from a free surface 3. Measuring convergence of roof and floor( or HW and F 4. Measuring absolute movements of roof and floor ( or HW and FW) 5. Measuring pressures on mine filling materials 6. Measuring ground pressures in supporting structures 7. Measuring stresses in supporting structures

Measuring Strain (deformation) in rock The closure of roof and floor, or of walls and ribs, is the most conspicuous phenomenon associated with underground openings and the easiest to measure. However, such measurements do not yield information as to the stresses existing in the rock. Methods for determining the actual magnitudes of stresses within the rock involve measurements of deformation of rock blocks which are freed from the main mass and allowed to expand. The deformation in rocks is very small and therefore the determination of stresses depends on the measurement of extremely small deformations. The modulii of elasticity of rocks ranges from 20 to 70 610× KPa. For example in a rock with an elastic modulus of 7 0 610× KPa (70,000 MPa), the deformation in the rock is 0.0005 mm. Thus, large changes in stress values are produced by very small changes in dimensions (strain). In order to measure these minute changes in dimensions of the openings it is necessary to employ instruments capable of measuring to within a few ten-thousands of a cm. In an elastic material a stress concentration is created near the boundary of the opening. The rock stresses are not measured directly, but the measuring techniques are designed to measure strains and the stresses are then computed by using the values of the rock modulus of elasticity. There are two general methods for determining absolute rock strain. These are:

1. The strain relief method, and 2. The strain restoration method

In the Strain relief method strain gauges are fixed to the opening walls at selected locations. A groove is then cut around the location of the strain gauge, freeing the rock surface to expand. The amount of the expansion is a function of the initial stress within the rock and of the modulus of elasticity of the rock. In the Strain restoration method strain gauges are fixed to the rock surface and readings are taken. A deep slot is then cut into the rock above the gauges and the rock in allowed to expand. A flat jack is cemented into the slot and expanded by application of hydraulic pressure until the strain gauges indicate that the rock has been restored to the state of strain existing prior to cutting of the slot. The pressure in the jack is then assumed to be equal to the original pressure in the rock normal to the slot surface. Strain relief method Method 1: The strain gauge is cemented on the surface of the wall rock and a standard diamond drill is used to cut an annular slot in the rock around the gauges, thus allowing the portion of rock to expand.

The surface on which the gauges are mounted required careful selection and preparation. The surface is ground smooth with a hand grinding wheel. The rock surface is thoroughly dried before the gauges are cemented to the rock and dried with a hear lamp after gauges are cemented in place. Strain gauges are sealed with waterproof mastic to protect them against moisture. Method 2 Measurement of Diametral Borehole Deformation for Stress Determination Another method for determining rock stresses is the accurate measurement of borehole horizontal and vertical axes to determine the relative deformation produced in the cross-section of the borehole by stresses in the rock. Maximum deformation is caused to the vertical axis of a horizontal borehole due to the vertical stress (assuming the horizontal stress is in effective). When the vertical and horizontal stress in the rock is equal there will be no differential deformation along the two axes of the borehole.

Figure Borehole deformation gauge Theory and Equations Uni-axial stress

The deformation of the hole in a uni-axial stress and in plan stress is given by

)2cos21( θ+=EdSU (1)

Where U = deformation of hole (change in length of a diameter) a = radius of hole d = diameter of hole = 2a S, T = perpendicularly applied stress (for a uniaxial stress field T = 0) θ = angle (counterclockwise) from S to r E = modulus of elasticity

θ

r

SS

T

T

θ

r

SS

T

T Figure Schematic representation of biaxial stress acting across a borehole When θ = 00, the deformation is in the direction of the applied uniaxial stress, and equation 1 reduces to

EdSU 3

= (2)

When θ = 900, the deformation is

EdSU −= (3)

And the minus sign signifies that, as the stress increases, the hole (at the point) is expanding. The deformation versus the angle θ for one quadrant of the hole (θ = 00 to θ = 900) is plotted in the figure below

Figure Borehole deformation gauge

-1

0

1

2

3

15 30 40 60 70 90

4

5

8050

Def

orm

atio

n (a

rbitr

ary

units

)

Angle ( in degrees)

-1

0

1

2

3

15 30 40 60 70 90

4

5

8050-1

0

1

2

3

15 30 40 60 70 90

4

5

8050

Def

orm

atio

n (a

rbitr

ary

units

)

Angle ( in degrees)

Figure Sectional View of a borehole deformation gauge

Bi-axial stress For bi-axial stress field and plane stress, the deformation is related to the biaxial stresses S and T by

]2cos)(2)[( θTSTSEdU −++= (4)

When θ = 00,

)3( TSEdU −= (5)

When θ = 900,

)3( STEdU −= (6)

If the deformation is measured across three different diameters and the modulus of elasticity and Poisson’s ratio are known, the magnitude and direction of the stresses S and T can be computed. The equations for these conditions will be

θ

600

600

600

d/2

22U

21U

23U

22U

21U

23U

S

S

θ

600

600

600

d/2

22U

21U

23U

22U

21U

23U

S

S

In this investigation rock stress was determined by measuring the deformation (change in diameter) of a borehole before and after the hole was stress-relieved. . It has been shown that the borehole deformation in a biaxial stress field is related to the magnitude and direction of the applied stresses in the plane perpendicular to the axis of the hole by the following equations:

)(3 321 UUUdETS ++=+

212

132

322

21 ])()()[(62 UUUUUUdETS −+−+−=−

321

23

2)(3

2tanUUU

UU−−

−=θ

Where U1, U2, U3 = borehole deformation at a 600 separation (600 deformation rosette) in cm, U is +ve for increase in the diameter a = radius of hole d = diameter of hole = 2a S, T = perpendicularly applied stress (for a uniaxial stress field T = 0) θ 1 = angle (counterclockwise) from S to U1 E = modulus of elasticity Strain restoration methods In this method a slot is cut, as shown in the figure, to accommodate a flat jack. The measuring points A-Bare established prior to cutting slot and the distance between the points is accurately determined. The flat jack is then placed in the slot and cemented tightly in place with quick-setting cement mortar. Hydraulic pressure is applied to the flat jack until measurements show that the distance between points A and B has been restored to its original dimension. The pressure in the flat jack is then a function of the original pressure in the rock before the slot was cut. It has been reported from extensive experimentation with this system that the pressure required to restore the original strain with the locations of the measuring points relative to the slot. And best results were obtained when the measuring points were placed within a distance equal to about two-thirds the length of the flat-jack. In practice when a flat jack 70cm long and 70cm wide was used the distance A-B was made about 30cm.

Flat jack method does not require any knowledge of the elastic properties of the rock and hence it is considered to be a true stress measuring method. Because of the difficulty in cutting deep flatjack slots the method is restricted to near-surface measurements.

Figure Stress measurement using a flatjack

Figure Modified Flakjack method

Measurement of Rock Movement/deformation Convergence Measurement The mechanically simplest deformation measuring devices are deformeters, also called extensometers, of which convergence gagues are special types. This class of instruments consists of a length-sensing device, such as a vernier scale, micrometer, dial gauge. Multipoint extensometers installed in boreholes have been used to detect roof movements. Mechanical extensometers, consisting of a top and bottom anchor, steel wire or rigid tubing, and some kind of micrometer or dial gauge, have been used for decades in metal mines Figure.

Figure roof sag measuring station

Figure Axial deformation gauges

Figure dial gauge deformeter

The relative amount of closure between roof and floor, or between HW and FW, is an indication of the magnitude of the pressure on the rock above the opening. The amount of strain depends upon several factors, such as the amount of ground which is open, the amount and quality of filling material, characteristics of the country rock, etc. Measurement of convergence may be useful in predicting the imminence of failure of roof or floor rock. Convergence Measurement Monitoring technology and techniques to provide early warning of hazardous roof fall conditions have been a longstanding goal for safety engineers and practitioners working in the mining sector. Roof-to-floor convergence monitors are perhaps the oldest and most common method of measuring roof deflection as a means to detect roof rock instabilities. This type of instrument consist of an anchor device mounted on the mine roof and floor and connected by a ridged bar or a metal wire. The relative movement of the anchor points is measured with either mechanical or electromechanical devices. Extensometers are used to determine the magnitude, position and rate of movement of rock surrounding an excavation. Extensometers are installed into boreholes. The essential features of an extensometer installation are a stable reference anchor position at the far end of the borehole, a borehole mouth anchor at the tunnel wall and a means of indicating or measuring change in distance between them.

The simplest form of extensometer makes use of a stainless steel spring reference anchor with a tube indicator attached to it by stainless steel wire and visible at the hole mouth. Movement is indicated by coloured reflective bands on the indicator, which are progressively covered as movement develops. In mining a simple extensometer such as this is known as a “telltale” because it gives a visual indication of roof movement.

Telltale extensometer is a very simple and general design to measure deformation in the roof of coal mines at 4 or 6 different points up to 6 meter height. Model SME 248- has four/six spider type strong leaf spring anchors (Above figure). These anchors will be installed in a 42 mm hole at four different heights with the help of installation tool. The steel wire will be attached with each anchor before pushing of anchors. The steel wire will be brought to the down surface of roof. Each wire will be attached with steel scale of different colour for identification of the anchor height. After installation of all the anchors the reference head will be installed leaving all the scales hanging freely. When the bed/roof separation is taking place the reading will change in the respective scale.

Figure Evolution of Dual height Telltale

Here roof movement is converted to rotation of a pointer around a dial. This has the advantage that small roof movements can be easily read even when the tunnel height approaches 5m (Figure above). The most common form of telltale is the dual-height version. This was developed and patented by British Coal in 1992 as a safety device for coal mine tunnels where rockbolts were being introduced as support. The device is installed at the same time as the rockbolts into a 5m long roof hole of 27mm-35mm diameter. Loads in support systems and linings The load distribution in rockbolts and cablebolts is an important support design parameter, but one which is difficult to measure. British Coal began producing strain gauged bolts for this purpose in 1990. To date RMT have manufactured around 4000 strain gauged rockbolts, supplied to mine and tunnel projects in seven countries. They typically have pairs of diametrically opposed resistance strain gauges, allowing calculation and display of mean and bending strains. The technology has recently been extended to include flexible bolts, which are encapsulated multi-wire steel strands. Instruments installed in two coal mine shaft linings were found to be still returning consistent readings twenty five years later. Support system and lining condition Acoustic Energy Meter (AEM) is a simple nondestructive testing device for checking the ‘looseness’ of exposed rock surfaces in tunnels, and for the detection of voids behind tunnel linings. The AEM is a hand held device comprising an integral geophone and readout unit. It measures the reverberation decay rate of a surface when struck with a hammer. Examples of recent civil engineering use of the instrument include a steel lined water tunnel in the UK where voids behind the 45mm thick lining were detected, an underground wastewater plant in Finland and the Joskin tunnel in the UK, where areas of detached shotcrete lining were delineated.

Figure Strain gauged rock bolts

Observational methods of in situ stress determination or estimation Observations of the behaviour of openings or holes made in stressed rock can provide very valuable indications of the magnitudes and, more particularly, the orientations of in situ stresses. Borehole breakouts (dog earing) “Borehole breakout” is the more widely used term for what is known in South African mining as “dog earing”. This phenomenon refers to the stress induced failure that occurs on the walls of a borehole resulting in spalling or sloughing of material from the borehole wall as shown in Figure 7. It is commonly observed in deep boreholes.

Figure 7 Example of stress induced sloughing of material from a borehole wall

The locations of the breakouts on diagonally opposite sides of the borehole are usually aligned with the orientations of the secondary principal stresses acting in the plane normal to the borehole axis. They can therefore often provide a reliable indication of the orientations of in situ stress fields. Attempts have been made to use breakout data to estimate the magnitudes of in situ stresses (Zoback et al, 1985; Zoback et al 1986; Lee and Haimson, 1993; Haimson and Song, 1993). In these attempts, the width and depth of the breakout have been measured as a basis for estimating the stresses. Haimson and Herrick (1986) found that the depth and circumferential extent of the completed breakout were directly proportional to the state of stress normal to the borehole axis. Whilst this approach may have some potential for estimating indicative values of stress, and relative or comparative values of stress, it is unlikely that it will be successful in the adequate quantification of stress magnitudes. This is due to the fact that breakout mechanisms will be different for different types of rock, and extents of breakout will vary depending on rock properties and in situ conditions (water, temperature, drilling, etc).

Core discing Core discing appears to be closely associated with the formation of borehole breakouts. In brittle rocks it has been observed that discing and breakouts usually occur over the corresponding lengths of core and borehole. The thinner are the discs the higher is the stress level. However, the formation of discs depends significantly on the properties of the rock and the magnitude of the stress in the borehole axial direction (Stacey, 1982). In addition, the type and technique of drilling, including the drill thrust, can significantly affect the occurrence of discing (Kutter, 1991). It is therefore unlikely that observation and measurements of discing will be successful in quantifying the magnitudes of in situ stresses. Nevertheless, the shape and symmetry of the discs can give a good indication of in situ stress orientations (Dyke, 1989). If the discs are symmetrical about the core axis, as shown in Figure 8, then it is probable that the hole has been drilled approximately along the orientation of one of the principal stresses. A measure of the inclination of a principal stress to the borehole axis can be gauged from the relative asymmetry of the disc. For unequal stresses normal to the core axis, the core circumference will peak and trough as shown in Figure 9. The direction defined by a line drawn between the peaks of the disc surfaces facing in the original drilling direction indicates the orientation of the minor secondary principal stress. If the discs are uniform in thickness as shown in Figure 8, the two secondary principal stresses normal to the core axis will be approximately equal. Lack of symmetry of the discing, as shown in Figure 10, indicates that there is a shear stress acting the borehole axis that the axis is not in a principal stress direction.

Figure 8 Core discs symmetrical with respect to the core axis

Orientation of the minor secondary principal stress

Drilling direction

Disc peaks Orientation of the minor secondary principal stress

Drilling direction

Disc peaks

Figure 9 Core discs resulting with unequal stresses normal to the core axis

Figure 10 Non-symmetrical cores discing, indicating that the core axis is not a

principal stress direction Observations of failures in excavations Excavations can be considered as large boreholes, and observations of the behaviour of the walls of the excavations in response to the in situ stresses can provide very valuable indications of the in situ stress field. Dog earring in bored excavations can be equally pronounced as in boreholes. Figure 11 shows a classic dog ear in the sidewall of a 5 m diameter tunnel. This shows that the major secondary principal stress normal to the tunnel axis (i.e. the maximum stress in the plane perpendicular to the tunnel axis) is vertical at this location. Similarly, the dog earring in the tunnel in Figure 12 shows that the major secondary principal stress is inclined at about 120 to the horizontal.

Figure 11 Dog earing (photograph provided by Dr C D Martin)

Hydraulic Fracturing for In situ Stress measurement Hydraulic fracturing is now a well established method for determining in situ stress magnitudes. It has been widely used in the oil well industry. Although hydraulic fracturing had been used previously for other purposes such as borehole stimulation for increasing the yield of water supply or dewatering boreholes, Scheidegger (1962) and Fairhurst (1964) were the first to suggest its use for the determination of in situ stresses. Haimson (1968; 1977; 1983; 1993), Cornet (1993a), Rummel (Rummel, 1987; Rummel et al, 1983) and Zoback (Zoback et al, 1977; Zoback et al, 1980; Zoback et al, 1986) played a major role in developing and promoting the use of the hydraulic fracturing technique. The method involves the pressurization of a length of borehole and the measurement of the pressure required to fracture the rock or reopen existing fractures. 4.3.1 Hydraulic fracturing Conventional hydraulic fracturing involves the pressurizing of a short length of borehole, isolated using hydraulic packers on either side of it, until the hydraulic pressure causes the rock to fracture. The characteristics of the pressure induced breakdown and the subsequent reopening of the fracture under repressurisation are monitored carefully. The orientation of the induced fracture is measured using a borehole television camera or a special impression packer to obtain a physical record of the surface of the borehole. From all these data the orientations of the secondary principal stresses normal to the axis of the borehole can be interpreted. Vertical boreholes are usually used and it is assumed that the in situ principal stresses are vertical and horizontal. The application of the method is illustrated diagrammatically in Figure 14.

Figure 14 Hydraulic fracture applications

The method requires special equipment, and associated services and personnel, to carry out a measurement. The borehole must be diamond drilled. Since packers are inserted in the borehole to seal off the test sections, the straightness and wall quality of the borehole are important. A system for hydraulic fracturing stress measurements in deep boreholes is illustrated in Figure 15. Although this represents the full sophistication of the method, it is illustrative of the sort of requirements that would be necessary for quality measurements at greenfields sites. A simpler set-up would be applicable for in mine tests. After hydrofracturing, the borehole has to be inspected using a television camera, or a special impression of its surface taken using an impression packer, to determine the orientation of the induced fracture. The classical stress determination from hydraulic fracturing tests is generally based on a few assumption and they are:

1. the borehole axis is parallel to the direction of one of the principal stress components

2. the pressurization occurs sufficiently fast to avoid fluid permeating into

the rock and thus alter the pore pressure within the rock matrix

3. Fracture generation occurs at the location of the least tangential stress at

the borehole wall and the fracture propagates perpendicular to the direction of the least principal stress

4. the shut-in pressure is equal to the stress component perpendicular to the

fracture plane.

Fig 15 System for hydraulic fracturing stress measurements

(after Tunbridge et al, 1989)

The schematic arrangements of hydro-fracturing technique is as shown below in the figure 16

Figure 16 Schematic arrangement of hydro-frac technique

In non-porous rocks the minimum principal stress is given by the shut-in pressure. If a borehole is drilled in the vertical direction, and it is assumed that this is a principal stress direction, and that the minimum principal stress is horizontal, the major horizontal principal stress SH can be determined from the following equation: Testing Procedure A single or double straddle packers system is set (inflated) at the required depth so as to isolate a test cavity. A liquid is injected into the test cavity and its pressure raised while monitoring the quantity injected. A sudden surge of fluid accompanied by sudden drop in pressure indicates that hydrofracture of rock formation (fracture inititation or break down) has occurred. The hydrofracture continues to propagate away from the hole as fluid is injected, and is oriented normal to the least principal stress direction (Fig.17) Once the hydro-fracturing has traveled about 10 drillhole diameters, injection is stopped by shutting a valve, and the instantaneous shut-in pressure is measured. The process is repeated several times to ensure a consistent measurement of this pressure, which is equal to the minimum principal stress.

Figure 17 Fracture propagation

ZSV .γ= Sih PS =

ChH PSTS −+= .3

RC PPT −=

Where T is the tensile strength of the rock Sh and SV are the minor and major horizontal principal stress Pc is the breakdown pressure at fracture generation PR is the pressure necessary to re-open the induced fracture (T=0) PSi is the shut-in pressure to merely keep the fracture open against the normal stress acting in the fracture plane Z is the depth of the over burden and γ is the unit weight of the rock.

Interpretation of hydrofracture records can require expert input if the shut-in pressure is not distinct. Interpretation of test results is not a straightforward activity, and the experience of the interpreter has some effect on the in situ stress values ultimately determined. Different interpreters may derive somewhat different results from the same set of field data. In porous rocks in particular, interpretation of hydraulic fracturing tests may be very difficult and, owing to the pore pressure, definition of the major principal stress may be doubtful. In sedimentary rocks, beds with a thickness of at least 2 to 3m are necessary for satisfactory testing to be carried out.

Hydraulic fracturing stress measurements have been carried out at depths in the 6km to 9km range (Amadei and Stephannson, 1997) and therefore the method is, in theory, suitable for the high stress conditions encountered in deep mines. At such high pressures, valves, tubing and packers must be of special design to be able to perform as required. In boreholes in which spalling or breakouts are occurring, there may be a risk of not being able to insert (or recover) the packers, and it may also not be possible to seal off the borehole satisfactorily. Borehole breakouts due to high stress levels may also interfere with the location of the fracture on the borehole wall, and this may lead to inaccuracy in determining stress directions.

Table 1 Hydrofracture Field Data

Test No

Depth (m)

BreakDown Pressure-PC MPa

Shut-in Pressure-PR MPa

T=PC-PR MPa

PSi MPa

Underground Borehole –Sub-level 40 1 23.5 17.2 15.0 2.2 11.5 2 21.5 28.0 19.0 9.0 13.0 3 18.5 18.2 12.0 6.2 10.0 4 12.5 18.4 15.0 3.4 12.0 5 9.5 32.4 27.2 5.2 20.5 6 4.15 45.5 42.5 3.0 33.5 7 1.95 40.6 33.0 7.6 32.0

It is clear from the above that the application of the hydraulic fracturing method is theoretically possible, but would be expensive, and demanding on services. Perhaps the most severe restriction, however, is the requirement that the borehole be drilled in the direction of one of the principal stresses. In mining situations this is usually not known and is one of the in situ stress parameters to be determined. Bibliography Dyke, C G (1989) Core discing: its potential as an indicator of principal in situ stress directions, Rock at Great depth, ed Maury & Fourmaintraux, Balkema, pp 1057-1064. Fairhurst, C (1964) Measurement of in situ rock stresses with particular reference to hydraulic fracturing, Rock Mech. & Engng Geol., Vol 2, pp 129-147. Haimson, B C and Herrick, C G (1986) Borehole breakouts – a new tool for estimating in situ stress? Proc. Int. Symp. Rock Stress and Rock Stress Measurements, Stockholm, Centek Publishers, pp 271-280. Haimson, B C, Lee, C F and Huang, J H S (1986) High horizontal stresses at Niagara Falls, their measurement and the design of a new hydroelectric plant, Proc. Int. Symp. Rock Stress and Rock Stress Measurements, Stockholm, Centek Publishers, pp 615-624. Haimson, B C, Lee, M, Chandler, N and Martin, D (1993) Estimating the state of stress for subhorizontal hydraulic fractures at the Underground Research Laboratory, Manitoba, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol 30, No 7, pp 959-964. Haimson, B and Song, I (1993) Laboratory studies of borehole breakouts in Cordova Cream: a case of shear failure mechanism, Int. J. Rock Mech. Min. Sci., Vol 30, No 7, pp1047- 1056. Kutter, H (1991) Influence of drilling method on borehole breakouts and core disking, Proc. 7th Int. Cong. Int. Soc. Rock Mech., Aachen, Balkema, Vol 3, pp 1659-1664. Martin, C D and Chandler, N A (1993) Stress heterogeneity and geological structures, Int. J. Rock Mech. Min. Sci., Vol 30, No 7, pp 993-999. Rummel, F (1987) Fracture mechanics approach to hydraulic fracturing stress measurements, in Fracture Mechanics of Rocks, Academic Press, London, pp 217-239. Scheidegger, A E (1962) Stress in earth’s crust as determined from hydraulic fracturing data, Geol. Bauwesen, Vol 27, pp 45-53.

Stacey, T R (1997) Practical method of in situ stress measurement for deep level mines, Proc. 1st Southern African Rock Engineering Symp., SARES 97, S. Afr. National Group of Int. Soc. Rock Mech., pp 502-514. Tunbridge, L W, Cooling, C M and Haimson, B (1989) Measurement of rock stress using the hydraulic fracturing method in Cornwall, UK – Part I, Int. J. Rock Mech. Min. Sci & Geomech. Abstr., Vol 26, pp 351-360. Zoback, M L, Healy, J H and Rolles, J C (1977) Preliminary stress measurements in Central California using the hydraulic fracturing technique, Pure Appl. Geophys., Vol 115, pp 135-152. Zoback, M D, Mastin, L and Barton, C (1986) In-situ stress measurements in deep boreholes using hydraulic fracturing, wellbore breakouts, and stonely wave polarization, Proc. Int. Symp. Rock Stress and Rock Stress Measurements, Stockholm, Centek Publishers, pp 289- 299.