rock mechanics pt2

STRESSSTRESSand and

STRAINSTRAINASPECTS OF ROCKASPECTS OF ROCK

Part 2Part 2

• Unlike soils, Unlike soils, pure rockpure rock (solid material (solid material between joints) is an between joints) is an elasto-plastic materialelasto-plastic material, , subject to elastic recovery AND permanent subject to elastic recovery AND permanent deformation, as shown in this Stress vs deformation, as shown in this Stress vs strain plot.strain plot.

• Physical phenomena associated with Physical phenomena associated with uniaxial compression tests of rock uniaxial compression tests of rock cylinders, under near zero confinement.cylinders, under near zero confinement.

• Unconfined compression testsUnconfined compression tests on rock cylinders generally on rock cylinders generally exhibit significant propagation of extension cracks after peak exhibit significant propagation of extension cracks after peak strength is exceeded, followed by friction and interlocking strength is exceeded, followed by friction and interlocking between cracked sections of the sample. between cracked sections of the sample.

• Example of a Example of a full-range stress-strain plotfull-range stress-strain plot, , showing how showing how post-failure stiffnesspost-failure stiffness is is estimated estimated

• Physical phenomena associated with gradual Physical phenomena associated with gradual breakdown of rock cylinders on the post-failure breakdown of rock cylinders on the post-failure side of a stress-strain plot side of a stress-strain plot

• The stress strain behavior of a natural rock like The stress strain behavior of a natural rock like sandstone is a combination of its mineralogical sandstone is a combination of its mineralogical components, in this case: quartz and calcitecomponents, in this case: quartz and calcite

• Most rocks exhibit Most rocks exhibit increasingly plastic behavior with increasingly plastic behavior with increasing levels of confinementincreasing levels of confinement, as shown in this , as shown in this series of jacketed triaxial tests on a marble. So, the series of jacketed triaxial tests on a marble. So, the most brittle behavior is typically exhibited under most brittle behavior is typically exhibited under conditions of the least confinement, at the Earth’s conditions of the least confinement, at the Earth’s surface.surface.

• Elasto-plastic behavior of Solenhofen Elasto-plastic behavior of Solenhofen Limestone, as seen in Limestone, as seen in measured relaxationmeasured relaxation in in percent axial strain after triaxial compression percent axial strain after triaxial compression under significant lateral confinement under significant lateral confinement

Plastic deformationPlastic deformation

ElasticElasticdeformationdeformation

• The most common physical attributes of The most common physical attributes of laboratory tests on intact rock are portrayed laboratory tests on intact rock are portrayed here. The true elastic modulus can only be here. The true elastic modulus can only be determined by employing load cycles.determined by employing load cycles.

• Goodman’s concept of Goodman’s concept of Modulus of Permanent Deformation, M,Modulus of Permanent Deformation, M, was introduced in 1980. It is important to appreciate in porous was introduced in 1980. It is important to appreciate in porous rocks which often exhibit “permanent set” with each loading rocks which often exhibit “permanent set” with each loading cycle, such as sandstone. cycle, such as sandstone.

Mohr CirclesMohr Circles are the most common technique used to describe the are the most common technique used to describe the failure envelopefailure envelope and the and the strength parametersstrength parameters frictionfriction and and cohesioncohesion

Rock tends to exhibit a slightly curvalinear failure envelope with Rock tends to exhibit a slightly curvalinear failure envelope with low tensile strengthlow tensile strength, shown at upper right, shown at upper right

• Be careful when evaluating elastic modulus values. Be careful when evaluating elastic modulus values. The terms used connote different kinds of calculations, The terms used connote different kinds of calculations, as shown here. as shown here.

• The elastic modulus (E) varies with the stress The elastic modulus (E) varies with the stress level and the induced strainlevel and the induced strain