JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III ROCK MECHANICS ENGINEERING Previous Question Paper (February/March - 2022 - R18)

Physical properties of rocks are fundamental parameters that dictate their mechanical behavior and suitability for engineering applications. These properties are defined as follows:

Density: Density is defined as the mass per unit volume of a rock material. It is typically expressed in g/cm³ or kg/m³. In rock mechanics, it is categorized into bulk density (including pore spaces) and grain density (the density of the solid mineral constituents). It is a critical indicator of the rock's compactness and strength.

Porosity: Porosity is the ratio of the volume of void spaces (pores, cracks, and fissures) to the total volume of the rock sample. It is expressed as a percentage. High porosity generally correlates with lower strength and higher compressibility, as the voids reduce the effective contact area between mineral grains.

Moisture content: This represents the amount of water present in the rock pores at a given time, expressed as a percentage of the weight of the dry rock. It is calculated by measuring the weight of the rock in its natural state versus its weight after oven-drying at 105°C. Moisture content significantly influences the rock's strength, as water can act as a lubricant or induce chemical weathering.

Permeability: Permeability is the capacity of a rock to allow fluids (water, gas, or oil) to flow through its interconnected pore spaces or fractures. It is governed by Darcy's Law. Rocks with high connectivity between pores exhibit high permeability, which is a vital factor in groundwater studies and petroleum reservoir engineering.

Water absorption: This is the measure of the amount of water a rock can take in when immersed under specified conditions (usually atmospheric pressure or vacuum saturation) until it reaches a saturated state. It is expressed as a percentage of the dry weight of the rock. It provides an indirect measure of the rock's open porosity and its potential for degradation due to freeze-thaw cycles or chemical alteration.

The mechanical properties of rocks are determined through standardized laboratory testing procedures to assess their performance under different stress conditions.

1. Compressive Strength (Uniaxial Compressive Strength - UCS): This test measures the maximum load a rock specimen can withstand under axial compression. A cylindrical core sample with a length-to-diameter ratio of 2:1 is prepared. The sample is placed in a compression testing machine and loaded at a constant rate until failure. The UCS is calculated as:

where P is the peak load at failure and A is the cross-sectional area of the specimen.

2. Tensile Strength (Brazilian Test): Since rocks are weak in tension, the Brazilian test is the standard indirect method. A thin disc specimen (diameter-to-thickness ratio of 2:1) is placed diametrically between two parallel loading platens. A compressive load is applied until the disc splits along the vertical diameter. The tensile strength is calculated using:

where P is the failure load, D is the diameter, and t is the thickness of the disc.

3. Flexural Strength (Modulus of Rupture): This test evaluates the bending strength of rock beams. A rectangular rock prism is supported at two points and subjected to a central point load (three-point bending) or two-point loads (four-point bending) until fracture. The flexural strength is calculated based on the beam theory:

where P is the maximum load, L is the span length, b is the width, and d is the depth of the specimen. This test is critical for understanding the behavior of rock layers in underground excavations and roof stability.