Rock Mechanic Theories

•Rock Mechanic TheoriesThe study of rock mechanics deals w/ stresses and deformation in solid materials, there are two (2) theories adapted, namely:1. Theory of Elasticity2. Theory of Plasticity

• THEORY OF ELASTICITY: Rocks have elastic properties whereby all strains created by externally applied loads are instantaneously and totally recoverable upon removal of all external loads. A material is perfectly elastic if it recovers completely upon removal of external loads. • Main Objections Against the Theory of Elasticity

1. Because of the presence of discontinuities and various defects in the rock in-situ, thus affecting the mechanical properties of the rock;

2. Presence of internal (residual) stresses in the rock mass;

3. Dependence on time of the deformation.

• THEORY OF PLASTICITY: When rock mass will be under the action of large enough

stresses, there is strain permanent deformations which remain after the removal of the externally applied load.

The theory as applied to an ideal rock assumes that on a certain plane in rock there exist a state of failure or rupture at any point in a plane.

Fracture, as a rule, precedes plastic deformation. Minerals and brittle rocks maybe brought into the plastic state.

Plasticity is also of great interest to mining industry, as well as to geology and geophysics.

CHAPTER 5STRESS AND STRAINS

Stress – is the force applied to a plane divided by the area of the plane and it is what causes rocks to deform.

Strain – The result of stress applied to a body, causing deformation of its shape and/or a change of volume.

Types of Stresses 1. Compressive Stress (which results in shortening or flattening) – it is the stress generated by forces directed toward one another on opposite sides of a real or imaginary plane.2. Tensile Stress (which results in stretching and elongation) – it is the stress generated by forces directed away from one another or opposite sides of a real or imaginary plane.3. Shear Stress (which results in a sort of smearing) – it is the stress (force per unit area) that acts parallel to a (fault) plane and tends to cause the rocks on either side of the plane to slide by one another.

Primary Stresses in Sound Rock

Stress Components in Sound Rock

•Primary Stresses in Rock1. weight of the superimposed or overburden rock;2. weight of the rock3. tectonic forces

•Virgin Stresses1. Gravitational Stress – is due to the effect of gravity on the overburden;2. Tectonic Stress – is due to the previous or present-day straining in the earth’s crust (regional faulting);3. Residual Stress – is the stress remaining after the cause has been removed (e.g. thermal stresses or stresses caused by swelling or heat).

• Main Uses of Rock Stresses:1. designing the tunnel linings, walls, pillars, roof arches, and

domes of U/G openings;2. evaluation of rock stability of various kinds of structures in rock,

including stability in rock slopes made in open pits3. evaluation of the rock abutment system of high dams• Main internal natural stresses of rock mass in-situ are:

1. weight of overburden rock material2. hydrostatic pressure3. pore water pressure4. thermal stresses in rocks5. residual tectonic in the rock6. possible stresses caused by chemical processes in

the rock mostly by recrystallization of rock minerals.

Factors Affecting Natural Stresses in Rock are:1. local stresses brought about by

excavating in rock2. effects of blasting3. seismic forces4. changes in hydrostatic pressure5. changes in pore water pressure6. changes in rock thermal regimen7. variation and alteration in physical and chemical

factors of the rock mass and minerals

• Factors Controlling Behavior of Rocks under Tectonic Stress1. Temperature & Pressure – rocks under high temperature

and pressure tend to undergo deformation without breaking (plastic/ductile deformation) when subjected to a tectonic stress. Rocks under low temperature and pressure tend to fracture (brittle deformation) when subject to a tectonic stress.

2. Time (over which the tectonic stress is applied) – Tectonic stresses applied to rock over a long period of time are more likely to result in permanent deformation.When rocks undergo permanent plastic/ductile deformation, a FOLD develops.When rocks undergo brittle deformation, a FAULT develops.

ROCK LABORATORY TESTS

•Purpose of In-situ Rock Testing1. to assess the general suitability of a site for

contemplating engineering work;2. to facilitate adequate, safe, and economical

design of geotechnical structures for that site;3. to foresee and to provide against

geotechnical problems during and after construction

•In-situ Rock Tests1. Plate Loading (bearing)2. Jacking3. Pressure Chamber (tunnel)4. Compression5. Borehole Deformation6. Tension7. Shear Strength8. Torsion

• Plate Loading Test – will determine the extent to which the rock mass deform under various externally applied loads. In this test, a normal load is applied to an exposed, flat surface of the rock by means of hydraulic jack, and the resulting displacement of the rock is measured. The formula used :

Wo = m. l - µ2 . N E . √A where: Wo = surface displacement of rock

m = displacement coefficient µ = Poisson’s ratio E = Young Modulus of Elasticity A = area of the loading plate N = total normal surface load

• Jacking Tests – Deformability of in-situ rocks is usually determined by jacking (jack loading test). The test is carried out in excavated underground test galleries in rock. The jacks are supported against the rock ceiling and floor of an U/G opening. The load is applied by means of a jack placed on a flat surface of the rock, and resulting deformation is measured.• Pressure Chamber Test (Pressure Tunnel test), consist of

sealing off a part of the tunnel by means of bulkhead. But prior to that to avoid loss of water from tunnel to rock, a concrete lining is place over the test tunnel surface of the rock, and the inside surface of the tunnel lining is coated with a waterproofing material for water tightness.

• Compression Test – the rock mass compressive strength is determined from test on rock pillar which is then compressed.• Borehole Deformation Test – use a borehole deformation

meter.• In-situ Tension Test – Any incompetent rock mass in its

natural state cannot sustain tensile stresses due to the presence of joints, fractures, fissures and other rock defects, hence, tensile strength is not of great importance• In-situ Shear Strength Test – to obtain shear strength values

that comprehend the effect of the various rock defects. This is done by the use of hydraulic jacks. In U/G opening, the jacks are supported against the ceiling and wall of rock.

• The testing of rock conducted for measuring and evaluating the changes of rock properties as well as its properties by applied loading or force. The properties will include physical, index and strength whereby the behavior include deformation and failure mode.• Testing of the rocks is not always straightforward : There are a

number of method for testing the rocks, both to determine the in-situ stress on the rock, as well as the rock's ability to withstand this stress. • A rock may be very resistant to weathering, but may have also have

been subjected to a very long period of time, which may result in significant weathering. In general, the strength and resistance to weathering of a rock is derived from the class of rock. Igneous and metamorphic rocks, in general, are more resistant to deformation and weathering than sedimentary rocks.

ROCK SAMPLE TESTS

Definition of TermsBedrock – a formation at some depth beneath a mantle of soil

and is formed from the crust of the earth. It is dry, solid rock exposed to the surface of the earth or overlain by unconsolidated materials

Homogeneous Rock- is one in w/c the physical proper-ties of all of its parts or elements are the same.

Heterogeneity – is a characteristic of a material which have unlike unlike qualities.

Competent Rock – is one w/c is sufficiently strong to transmit a compressive force under given conditions.

Competent Ground – is one that does not require support when a tunnel is excavated through it.

Intact Rock- a rock material w/c can be sampled and tested in the laboratory & w/c is free of larger scale structural fractures such as joints, bedding planes, partings, and shear zones.

Matte (regolith)- is a loose fragments of rock and soil that act as a cover for bedrock. Soil above bedrock are called “Overburden”.

Rock Mass – is the in-situ rocks made up of the rock substance plus structural discontinuities.

Isotropic- is one that has the same physical, viz elastic properties in every direction at any point.

Anisotropic – is one w/ certain of its properties varies with direction at any point.

• Intact Rock are block of rocks that do not contain mechanical discontinuities and do have tensile strength.• Discontinuities are plane or surface that marks a change in

physical and chemical characteristics in rock material. They are considered plane of weakness and includes: bedding planes, joints, fractures, faults, etc.• Discontinuity is a plane that marks an interruption in the

continuity and normally has low or zero tensile strength.• Discontinuous rock mass is a rock mass containing

discontinuities.

Bedrock – a formation at some depth beneath a mantle of soil and is formed from the crust of the earth. It is dry, solid rock exposed to the surface of the earth or overlain by unconsolidated materials

Homogeneous Rock- rock which the physical properties of all of its parts/elements are the same.

Heterogeneity – is a characteristic of a material which have unlike qualities.

Competent Rock – rock sufficiently strong to transmit a compressive force under given conditions.

Competent Ground – is one that does not require support when a tunnel is excavated through it.

Intact Rock- a rock material w/c can be sampled and tested in the laboratory & w/c is free of larger scale structural fractures such as joints, bedding planes, partings, and shear zones.

Matte (regolith)- is a loose fragments of rock and soil that act as a cover for bedrock. Soil above bedrock are called “Overburden”.

Isotropic- is one that has the same physical, viz elastic properties in every direction at any point.

Anisotropic – is one w/ certain of its properties varies with direction at any point.

Inhomogeneous – is one that has different properties at different locations.

• Persistence – refers to the lateral extent of a discontinuity plane either the overall dimensions of the plane, or whether it contains rock bridges.• Roughness – is used to denote the deviation of a

discontinuity surface from perfect planarity, which can rapidly become complex mathematical procedure utilizing 3-dimensional surface characterization techniques whether these be by polynomials.• Aperture – is the distance between adjacent walls of a

discontinuity, e.g. it is the openness of the discontinuity.