Physical Properties of Rocks The study of rock deformation needs a knowledge of the physical properties of rocks in relation to deformation. These properties are concerned either with elastic or with plastic deformation or with rupture. If a body is subjected to directed forces lasting over a short period of time – minutes or hours – it usually passes through three stages of deformation. At first, the deformation is elastic, that is, if the stress is withdrawn, the body returns to its original shape and size. There is always a limiting stress, called the elastic limit, if this is exceeded, the body does not return to its original shape. Below the elastic limit, the deformation obeys Hook’s law, which states that strain is proportional to stress. If the stress exceeds the elastic limit, the deformation is plastic; that is, the specimen only partially returns to its original shape even if the stress is withdrawn. Steel rods under tension, for example, begin to get thinner or neck in the middle, and, even after the stress is released, the constriction remains in the rod. When there is a continued increase in the stress, one or more fractures develop, and the specimen eventually fails by rupture. All most all the deformations in which we are interested lie in a zone between the plastic fields, and that rupture and plastic deformation can hardly be distinguished from the physical point of view.

Physical Properties of Rocks Brittle Substances Brittle substances are those that rupture before any significant plastic deformation takes place. Ductile Substances Ductile substances are those that undergo a large plastic deformation before rupture. After the elastic limit has been exceeded ductile substances undergo a long interval of plastic deformation, and in some instances they may never rupture.

Stages of Deformation Elastic (Material is stretched, but returns to its original position.) Plastic (Material behaves in a ductile manner. Once stretched, it remains deformed.) Brittle (When enough stress is applied, the material will fracture.)

Stages of Deformation The type of deformation that occurs is dependent upon: Rate of stress ( As stress is increased, the material goes from being elastic to plastic and finally fracturing. Temperature ( At lower temperatures, the material fractures sooner. At higher temperatures, the material behaves like a plastic longer before fracturing.) Confining Pressure (The lower the pressure, the sooner the material will fracture.)

Physical Properties of Rocks Elastic Properties An elastic property is defined as the phenomenon in which the body comes back to its original position after removal of the load which caused the change of shape and size, i.e. deformation. This complete return to its original shape and size is never realized in actual materials, since there is always some retardation, known as hysteresis, in the unloading process. The three constants – Young’s Modulus (E), Shear Modulus or Rigidity (G) and Compressibility (K) are elastic properties of the material, but they are not independent of one another. With purely elastic deformation the strain is a linear function of the stress, i.e., the deformation obeys Hook’s law. If a solid rock bar is subjected to stress parallel to its long axis, it will lengthen under tension and shorten under compression. The ratio of the stress to the deformation is a measure of the property of the rock to resist deformation. Expressed by the equation E = s /e Where E is Young’s Modulus, also called Modulus of Elasticity, s is stress and e is strain. E is constant for the material of the bar. Since E is constant, the deformation curve in a stress – strain diagram is a straight line. Stress (a) Strain (e)

Physical Properties of Rocks Elastic Properties Rigidity or Shear Modulus: Instead of using a normal stress s, if we use a shearing stress t, the deformation will be known as simple shear. In purely elastic material, the simple shear will be given by Where G is known as the Shear Modulus or Rigidity, which is also constant for the material. t is the shear stress and is shear strain. Rigidity or shear modulus measures the resistance to change in shape. Compressibility or Bulk Modulus: When a body is subjected to a change of hydrostatic stress, the volume change per unit pressure change is called Compressibility. It is expressed by the equation Where DV is change in volume, Vo is original volume and DP is change in hydrostatic pressure. Compressibility is the reciprocal of Bulk Modulus n t _ G n = K = DV/Vo DP b = 1 K

Physical Properties of Rocks Plastic Property A material is said to behave plastic if, at stresses below a critical level, it reacts as solid; while at stresses at or above the critical level (or yield stress), it flows continuously without rupture to become permanently strained. Although most rocks at room temperatures and pressures fail by rupture before attaining a stage of plastic deformation, but at sufficiently high temperature and confining pressure, most rocks deform plastically even in experiments lasting for a short period. The plastic deformation is not recoverable or is only partially recoverable. That is, if the stress is removed, the material does not return to its original shape. The mathematical theory of plastic flow is mostly built up around the concept of idealised isotropic and homogeneous materials and their special models known as Rigid Plastic and Elastic Plastic types can be illustrated diagrametically. s e s e Rigid Plastic Elastic Plastic

Physical Properties of Rocks Rupture When there is a continued increase in the stress, one or more fractures develop, and the material eventually fails by rupture. Rocks may be subjected to an unlimited compressive hydrostatic stress; they suffer only a volume change. If subjected to tensile hydrostatic stress, they break apart with explosive violence. It is well known that rock will fail more easily under a tensile stress than under compressive stress. When rock fail it is found they break on two sets of planar shear surfaces with a certain angle (a) with the deformative stress. Theoretically, this angle a, is 450 but experimentally it is found to be 300 with F. F a

Stress – Strain Diagram The relation existing between stress and strain is commonly expressed in graphs known as stress-strain diagram. The stress is plotted on the ordinate (vertical axis), where as the strain is plotted on the abscissa (horizontal axis). Let us assume a compressive stress in pounds per square inch applied to a material, cylindrical in shape, parallel to its axis. With increasing stress the specimen becomes shorter and the strain is plotted in terms of the percentage of the shortening of the specimen. 1 2 3 4 5 6 Strain – shortening in percent Stress in pounds per square inch 10,000 20,000 30,000 40,000 Proportional Elastic Limit Rupture Ultimate Strength D B A C

Stress – Strain Diagram Curve A is the stress—strain diagram of a brittle substance. It deforms elastically up to a stress of 20,000 lb/in2 and has shortened 0.5%; it then fails by rupture. 1 2 3 4 5 6 Strain – shortening in percent Stress in pounds per square inch 10,000 20,000 30,000 40,000 Proportional Elastic Limit Rupture Ultimate Strength D B A C

Stress – Strain Diagram Curve B is an ideal plastic substance. It behaves elastically at first. At a stress of about 24,000 lb/in2 it reaches the proportional elastic limit, which is the point at which the curve departs from the straight line. The shortening is slightly less than 1%. Thereafter the specimen deforms continuously without any added stress. 1 2 3 4 5 6 Strain – shortening in percent Stress in pounds per square inch 10,000 20,000 30,000 40,000 Proportional Elastic Limit Rupture Ultimate Strength D B A C

Stress – Strain Diagram Curve C represents a more normal type of plastic behaviour. At a stress of about 28,000 lb/in2 and a strain of somewhat over 1%, the specimen reaches the proportional elastic limit and thereafter deforms plastically. But for every increment of strain an increase in stress is necessary. This is the result of what is called work hardening; that is, the specimen becomes progressively more difficult to deform. 1 2 3 4 5 6 Strain – shortening in percent Stress in pounds per square inch 10,000 20,000 30,000 40,000 Proportional Elastic Limit Rupture Ultimate Strength D B A C

Stress – Strain Diagram Curve D represents a very common type of plastic deformation. The specimen deforms elastically up to a stress of about 28,000 lb/in2 and a shortening of somewhat less than 2%. At first an increase in stress is necessary for continued deformation. But when the shortening is somewhat over 3%, progressively less stress is necessary to continue the deformation. The high point on the curve is the ultimate strength. However, the ultimate strength of a rock is a function of many variables, such as confining pressure and temperature. 1 2 3 4 5 6 Strain – shortening in percent Stress in pounds per square inch 10,000 20,000 30,000 40,000 Proportional Elastic Limit Rupture Ultimate Strength D B A C