PLANES OF WEAKNESS IN ROCKS, ROCK FRCTURES AND FRACTURED ROCK. Contents

Transcription

1 PLANES OF WEAKNESS IN ROCKS, ROCK FRCTURES AND FRACTURED ROCK Contents 7.1 Introduction 7.2 Studies On Jointed Rock Mass Joint Intensity Orientation Of Joints Joint Roughness/Joint Strength Joint Roughness Coefficient (JRC) Wall Strength Aperture Gouge Scale Effect Discontinuity Type Joint Friction Angle 7.3 Barton s equation for Shear Strength 198

2 LECTURE INTRODUCTION Rock Strength reduces with increase in discontinuities/ fractures/ joints. Discontinuity can be of same scale as the excavation, but this may not be the case for soils. Moreover, discontinuities are not necessarily fully interconnected. It's the discontinuity and their decisive role in the behaviour of rock mass, makes Rock Mechanics, a domain outside the domain of soil mechanics. Figure 7.1 shows a typical view of the jointed rock mass found in the field which signifies the difficulties in characterizing jointed rock mass and the scale of different joints fractures. Most of the times these joints or fractures comes in sets and Figure 7.2 represents the typical joints occurring in rock mass expressed in different sets. The intensity of jointed rock or rock mass is also dependent on the scale of the problem as depicted in the Figure 7.3. Figure 7.3 depicts how the transition of intact to heavily jointed rock happens, as the domain of the problem changes. In Figure 7.3, different circles represents the intensity of joints in the domain and represents intact rock for the smallest circle and heavily jointed for the biggest circle. Figure 7.1: A typical view of the jointed rock mass found in the field 199

3 Figure 7.2: Typical joints occurring in rock mass expressed in different sets Figure 7.3: Transition of intact to heavily jointed rock as the domain of the problem changes 200

4 Joints or fracture is a generic term usually used any type of weak planes. But there are some differences among various terms usually used in rock engineering. Fissures are small cracks usually ranges from millimetres to several centimetres in scale. Joints are parallel planar cracks separated by several centimetres up to as much as 10m. Igneous and metamorphic rocks found to have regular jointing systems with three or more sets of weak planes. Rocks which are deformed by folds - observed to have shear joints and usually spaced more widely ranging from several millimetres to meters. In faults, spacing is much more, in several meters. To understand strength and deformation behaviour of rock mass, full range of planar weaknesses with their statistical distributions of spacing and orientations at all levels need to be considered. 7.2 STUDIES ON JOINTED ROCK MASS Characteristics of discontinuities in the jointed rock mass play a major role in controlling the engineering behaviour of rock masses. Characteristics of discontinuities that affect the behaviour of rock mass, as listed by Piteau (1970), are as follows: (a) nature of their occurrence, (b) orientation and position in space, (c) continuity, (d) intensity, (e) surface geometry, (f) genetic type, and (g) nature and thickness of infilling gouge material. The discontinuity intensity is described by various researchers as follows: (a) measurement of discontinuities per unit volume of rock mass, (b) Rock quality designation(rqd) technique (Deere, 1963), (c) Scan line survey technique (Piteau, 1970). The properties of joints that have maximum influence on the mechanical behaviour of rock mass are described in the following paragraphs Joint Intensity The joint intensity is the number of joints per unit distance perpendicular to the plane of joints in a set. Joint intensity has maximum influence on the strength and deformation behaviour of the rocks. The strength of the rock mass decreases with increasing number of joints and joint intensity is expressed as number of joints per meter and it is denoted by J n. Arora (1987) studied the effect of location of a single joint with respect to loading surface defined by, 201

5 d j = D j /B Where, D j is depth of joint and B is the width of loaded area. Arora (1987) has also presented the empirical relationships between the uniaxial compressive strength of intact/jointed specimens and d j Orientation of Joints Orientation of the joint pattern has very significant influence on the behaviour of the rock mass. It influences the shear stress distribution and zone of failure in the rock mass. Jaeger and Cook (1979) presented analysis of sliding on a plane of weakness in two dimensions as shown in figure 7.4 and gave the equation for slip criterion on the weak plane as τ = S 0 + µσ n (7.1) Where σ n and τ are normal and shear stresses along the weak plane and S 0 is the inherent shear strength of contact surface and µ is the coefficient of friction. They also gave the expressions for variation of stress difference (σ 1 -σ 3 ) necessary to cause failure with variation of β (orientation of joint with respect to the major principal stress direction) for fixed value of σ 3 and µ as 2S0 + 2µσ 3 = (7.2) ( σ σ ) 1 3 ( 1 µ cot β ) σin 2β Variation of σ 1 with β for the case µ = 0.5 is shown in Figure 7.5 for various values of σ 3. Arora (1987) has defined joint inclination parameter to quantify the effect of orientation of joints. He observed that the strength of single inclined joint at β = 30 0 (1J-30) is equivalent to 24 joints per meter inclined at β = 30 0 (24J-90). Similarly the effect of (1J-40) is equivalent to effect of (14J-90) and the effect (1J-50) is equivalent to the effect of (3J-90). The variation of single inclined joint with equivalent number of horizontal joints is given in Figure 7.6. The joint inclination parameter n is evolved from the figure for different β and is given in Table 7.1 and the plot between n and β is given in Figure 7.7. The values of n were obtained by taking the ratio of the log of strength reduction at β = 90 to the log of strength reduction at the desired value of β. These values of n were found to be almost the same irrespective of the number of joints per metre i.e. J n. 202

6 σ 1 σ 3 τ σ σ 3 β σ σ 1 τ φ c σ 3 2β σ 1 σ Figure 7.4: State of stress in a specimen with planar discontinuity under triaxial stress field Figure 7.5: Variation of σ 1 with β (number on the curves are values of σ 3 /c) 203

7 25 (J nh ) Number of horizontal joints J ni = β (deg.) Figure 7.6: Relationship of single inclined joint (J ni = 1) with equivalent number of Horizontal joint (J nh ) Table 7.1: Joint inclination parameter n for different β Orientation of joint β in degrees Joint inclination parameter n

8 1 Joint inclination parameter 'n' β in degrees Figure 7.7: Variation of inclination parameter with orientation of joint Joint Roughness/Joint Strength The frictional resistance between the joint faces is quantified as joint roughness. When a fractured surface of rock is viewed under magnification, the profile exhibits a random arrangement of peaks and valleys called asperities forming a rough joint surface. An asperity is quantified by the angle it makes with the plane of the joint (Patton, 1966). Friction angle along the joint is determined as φ µ + i, where φ µ is the friction angle of the smooth joint and i is the inclination of asperity as illustrated in Figure 7.8. The value of φ µ has been reported by many researchers. The coefficient of friction for smooth and rough surfaces is same at high normal stresses and they differ at low normal stresses (Coulson, 1970). The reason for this is that at low normal pressure the damage to the surface is minimal. It was observed by Handin et al. (1964) that if the dilation and rotation of the blocks are taken into account, the friction values seems to be independent of the nature of the surface. Jaeger (1970) has shown that there is no scale effect on the friction and the coefficient of friction measured on small surfaces is also applicable to larger surfaces. Based on experimental data of the direct shear tests on tension fractures, Barton (1971) gave a relationship between the joint roughness and the joint shearing strength. Subsequently Barton and Choubey (1977) gave a preliminary guide to Joint Roughness Coefficient. Arora (1987) quantified the roughness by a parameter r as a tangent value of friction angle of the joint. It was observed 205

9 from the data collected that for clean joints, the strength parameter r depends upon the value of σ ci of the rocks and the suggested values of r for various values of σ ci are presented in Table 7.2 (Ramamurthy and Arora, 1994). When a joint has gouge material of sufficient thickness to submerge the joint roughness, it is the frictional parameter of the gouge which will control the development of strength during shear. Based on information from the studies of Skempton (1964), Lambe and Whitman (1969) and Attewell and Farmer (1976), the values of friction angles for various gouge materials present in a dense state at or near the residual stage are suggested and the same is presented in Table 7.3 in the absence of any field shear test data by Ramamurthy and Arora (1994). When some cohesion exists along the joints due to cementation or otherwise, the value of parameter r could be calculated as r = τ j /σ nj, where τ j is the peak shear strength along the joint and σ nj is the expected normal stress on the joint plane. Usually, along slickensides and fault planes the cohesion values are found to be negligible. Figure 7.8: The basis for Patton s law for joint strength 206

10 Table 7.2: Values of r for different values of σ ci Uniaxial compression strength of intact Joint strength parameter r rock, σ ci (MPa) Table 7.3: Suggested joint strength parameter r for gauge material in joints near residual state Gauge material Friction angle (degrees) Joint strength parameter r = tanφ j Gravelly sand Course sand Fine sand Silty sand Clayey sand Clay-silt Clay-25% Clay-50% Clay-75%