International Journal of Rock Mechanics and Mining Sciences
Anisotropic strength and deformational behavior of Himalayan schists
Introduction
Out of the three generic categories of rocks, metamorphic rocks exhibit highest degree of anisotropy [1]. Segregation of constituent minerals, in response to high pressure and temperature gradients, is associated with tectonic evolution and development of layers of contrasting mineralogical assemblages. Rocks flow and recrystallize under new tectonic stresses to form weak foliation planes. Such planes of weakness (i.e. schistosity) affect the strength and deformational behaviors of rocks with orientation to the applied stresses. Irrespective of the size of the engineering projects, either dealing with inherent intact rock anisotropy from an exploratory borehole or induced rock anisotropy due to in situ fracturing [1], where stability of large rock mass is concerned, evaluation of intact rock anisotropy in terms of strength and modulus is inevitable. Prediction of the anisotropic responses of strength and deformation of rocks involves study of specimens at different orientation angles, β (the angle between the major principal stress direction and the foliation plane).
In the past, many investigators have carried out the measurement of the strength anisotropy for various rock types e.g. Donath [2], Chenevert and Gatline [3], McLamore and Gray [4], Hoek [5] Attewell and Sandford [6] and Brown et al. [7] on shales and slates, Deklotz et al. [8], Akai et al. [9] McCabe and Koerner [10] Nasseri et al. [11], [12] and Singh and Singh [13] on gneisses and schists, Ramamurthy et al. [14], [15], on phyllites Horino and Ellicksone [16], Rao et al. [17] and Al-Harthi [18] on sandstones, Pomeroy et al. [19] on coal, Allirote and Boehler on diatomite [20] and Tien and Tsao [21] on artificial material. An overall analysis and review of their works exhibit that maximum failure strength is either at β=0° or 90° and the minimum value usually is around β=30°, more precisely at (45–φ/2) where φ is the friction angle along the plane of weakness, fracture or sliding. The shape of the curve between the uniaxial compressive strength (σc) and the orientation angle, β, is designated as the ‘type of anisotropy” and is found to be generally of three types namely ‘U-shaped”, “shoulder shaped” and “wavy shaped” as shown in Fig. 1 [1].
In spite of many attempts made in the past to delineate the engineering behavior of intrinsically anisotropic rocks still their nature is not adequately understood. Prediction of strength of anisotropic rocks through various criteria proposed by Jaeger [22], Walsh and Brace [23], McLamore and Gray [4] and Hoek and Brown [24] requires a large amount of pre-evaluated experimental data, loosing the simplicity in their form and hence the practical application. Adoption of these failure criteria necessitates performance of at least three triaxial tests at different confining pressures and at three different orientations of plane of weakness.
Keeping in view the inadequate knowledge of transverse anisotropy of deformational and strength responses of schists over the entire range of β, an attempt has been made through a comprehensive investigation on four varieties of schists obtained from two Hydroelectrical power project sites in the Himalayas. The main objectives of the present investigation are, therefore:
- (i)
To study the transverse anisotropic behavior of schists in terms of compressive strength and deformational responses in uniaxial and in triaxial compression up to high confining pressures.
- (ii)
To evaluate the applicability of the non-linear strength criterion proposed by Ramamurthy and co-workers for the prediction of triaxial compressive strength of schists.
- (iii)
To develop a methodology to predict the tangent modulus and stress-strain response with minimum pre-evaluation of experimental data.
Section snippets
Non-linear criterion for anisotropic rocks
Based on the test results of four intact sandstones and from the analyses of available test data from more than 80 intact rocks, Ramamurthy et al. [14] and Rao et al. [17], proposed an empirical strength criterion to account for the non-linear strength response of isotropic intact rocks in the following form:where σci is the uniaxial compressive strength of intact rock without a weak plane, σ1 and σ3 are the principal stresses, αi is the slope of the plot between (σ1−σ3)/
Modulus in unconfined state
It has been pointed out by Chenevert and Gatline [3], that only two elastic constants i.e. E (Young's modulus) and ν (Poisson's ratio) are required for the linear theory of elasticity for isotropic homogeneous body, whereas evaluation of nine elastic constants are required to completely describe the elastic behavior of an orthotropic anisotropic body. They have however reduced the number of elastic constants to five to describe the deformational behavior of a transverse anisotropic rock through
Modulus in confined state
Investigators working on the effect of confining pressure on modulus demonstrated that modulus increase with increase of confining pressures. This increase has been related to the closure of the micro cracks and pore spaces in response to confinement. Preferential orientation of micro cracks along the foliation planes is considered to be another cause of anisotropy at microscopic level, [31]. Hobbs [32], in an attempt to study the effect of confining pressure on Young's modulus of seven coals
Geology of the site and rock tested
Keeping the objectives in view four anisotropic schistose rocks have been collected from the tectonically active and complex geological sequence of rocks in the foothills of the Himalayas for laboratory investigation.
Quartzitic and chlorite schists were collected from the Uri hydroelectrical project in Baramula District, Kashmir. This project envisages construction of a concrete dam on the river Jhelum with a 10 km long and 8 m diameter of head race tunnel in quratazitic schist belonging to the
Experimental work
In accordance with the objective mentioned earlier various tests were conducted on the four schistose rocks following ISRM [34] and IS (Indian Standard) practices [35]. The tests are classified under the following three major categories: (i) petrography and petro-fabric, (ii) physical properties and (iii) geotechnical properties.
Petrography
X-ray diffraction and scanning electron micrograph (SEM) studies revealed the following:
- (a)
Quartzitic schist is predominantly made up of crypto-crystalline to fine grained flaky micaceous minerals, preferably oriented with fine grained recrystallized quartz, which are in abundance. Quartz constitutes about 43%, mica 15% and feldspar 12.6% of the rock, with clay minerals such as kaolinite, illite and chlorite forming the rest.
- (b)
Chlorite schist is very fine grained, highly chloritized basaltic rock
Conclusions
In the past, many researchers have studied the anisotropic behavior of the schistose rocks, but only in a very few studies, systematic tests were performed to observe and analyze the strength and deformational responses of schistose rocks in uniaxial and triaxial states over the entire range of orientation angle (β) varying from 0° to 90° with respect to vertical. In the present study strength and deformational behavior of four schists, transversely anisotropic, are affected by the schistose
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