Time Dependent Deformation Of RocksTime Dependent Deformation Of Rocks

RESPECTED TEACHER:

Sir Agha Shafi Jawaid Pathan

PRESENTED BY:GROUP-0812MN65 Ali Bux Wassan

(Group Leader)12MN34 Attique-er-Rehman Qureshi12MN43 Hassan Nawaz Arain12-10MN58 Shoaib Qureshi

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INTRODUCTIONINTRODUCTION

INTRODUCTION: The strength and deformation of rocks is time dependent Under long term constant loading most rocks suffer a

reduction in strength of about 50% The studies have indicated that deformation of pillars The studies have indicated that deformation of pillars

does not occur instantaneously but increases with time. Pillars which appear stable after mining may deteriorate with time and subsequently fail due to the development of limiting vertical deformation.

Pillar failure takes place at a range of vertical stresses; failure at high stresses taking place earlier than at low stresses.

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INTRODUCTION:INTRODUCTION:

Some rocks, such as gabbro and granite show little time-dependent strain whereas in other rocks such as salt, potash, trona, coal, alabaster, time dependent strain greatly exceeds the instantaneous elastic deformation.deformation.

An understanding of time-dependent behaviour of rocks is considered essential for further development in the fields of underground mine design, strata control, seismology and in understanding many other geological and geophysical phenomena occurring in the earth's crust.

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INTRODUCTION:INTRODUCTION:

The knowledge of deformational characteristics of the supporting pillars is essential for designing the mine workings, and also helps in determining the life of the pillars underground. pillars underground.

The time taken by a pillar to reach an unstable condition can be calculated from an experimental value of the maximum possible vertical deformation and the rate of convergence measured in situ.

The value of deformation at which the deformation rate starts to accelerate is chosen as the boundary between stability and instability

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INTRODUCTION:INTRODUCTION:

Creep studies are important in the study of rock- bursts as well. The influence of creep on rock-bursts

is as:

Firstly, the time-dependent deformation may cause a gradual release of abutment stress and hence diminish the gradual release of abutment stress and hence diminish the danger of rock-bursts.

Secondly, the occurrence of rock-bursts in between the shifts when the ground is not influenced by mining operations, can be explained satisfactorily, if the time-dependent strength of rocks is taken into consideration

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Introduction:Introduction:

Depending on the time dependent behavior, a rock can be divided into: I. Perfectly Elastic Material II. Real Material 1. Perfectly Elastic Material A perfectly elastic material undergoes elastic deformation on the

application of stress and instantaneous recovery on the removal of load.application of stress and instantaneous recovery on the removal of load.2. Real Material

In a Real-life material, the deformation is accompanied by a time lag during the application of the stress.

Both reversible and irreversible time dependent deformations are exhibited even though the stress level may remain below the elastic limits.

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Time Dependent EffectsTime Dependent Effects

Rheology is the study of the Flow in Rocks.

Rheology is science that is concerned with flow offluids and deformation of solid.

Study of flow properties of liquids is important influids and deformation of solid.

Study of flow properties of liquids is important inunderstanding the systems .

These systems can change their flow behaviorwhen exposed to different stress conditions.

Stress Models are used to describe fundamental types and behaviors of the Rheology.

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Rheological ModelsRheological Models

1. Hookean Model/ Elastic Deformational Model

Example: Spring

S = K S = K

Where,

s = Stress

K = Spring Constant

= Strain

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Rheological Models:Rheological Models:

2. Newtonian or Viscous Model Represents a Newtonian Liquid

S = he OR e = (s t)/h

Where,Where,

s = Stress

h = Time dependent Viscosity coefficient

e = Strain and

t = time

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Rheological Models:Rheological Models:

3. St Venant Model

Showing Frictional Material

Plastic Frictional Contact containing a St Venant Plastic Frictional Contact containing a St Venant Element and its inclusion in the model represents the Visco-Plastic behaviour of the material

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Rheological Models:Rheological Models:

4. Maxwell Material Model

A Perfectly Visco-Elastic Liquid

combination of a spring and dashpot series combination of a spring and dashpot series

The spring represents the elastic behaviour of the material whereas the dashpot incorporates the time dependent behavior of the material.

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Rheological Models:Rheological Models:

5. Kelvin or Voigt Model

Visco-Elastic Solid

Spring and dash pot arranged in parallel

Many rocks behave in this manner

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CREEPCREEP

Definition:

When materials under severe service conditions are required to sustain steady loads for long periods of time, they undergo a time dependent periods of time, they undergo a time dependent deformation.

This is known as creep

It can also be defined as

the slow and progressive deformation of a material with time at constant stress.

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CREEPCREEP

Creep curve:The creep curve is obtained by applying a constant

tensile load below the yield point to a specimen maintained at constant temp.

As soon as the specimen is loaded, there will be an maintained at constant temp.

As soon as the specimen is loaded, there will be an instantaneous strain which is denoted by o on the creep curve

Further deformation of the rock only after the instantaneous strain is considered as creep deformation

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Creep curve:Creep curve:

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Stages of creepStages of creep

Creep deformation of materials up to failure are divided into 3 stages i) primary creep ii) secondary creep iii) tertiary creep.

Primary creep: OR TRANSIENT CREEP This is the first stage of the creep which represents a region of decreasing creep rate. This is the first stage of the creep which represents a region of decreasing creep rate. In this region the rate at which the rock deforms decreases with time until it reaches a

constant valueThe creep rate goes on reducing because as the rock deforms ,it undergoes strain

hardening and offers more and more resistance to further elongation. The principal characteristic of transient creep is the decreasing rate in

deformation. Deformation is rapid at first but gradually becomes slower and slower as the rate

approaches some fixed value. Transient creep in rocks is observed at all temp, even near absolute zero. Hence it

is some times referred to as cold creep

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Stages of creepStages of creep

Secondary creep: [steady state creep]/Viscous creepNearly constant creep rate ,because strain hardening and recovery effects balance

each other. Creep in this region takes place by the viscous flow in the rocks It is characterized by the viscous flow of the material means that there is a constant

or a steady increase in deformation at constant stress Although strain hardening is present, its effect is just balanced by the recovery Although strain hardening is present, its effect is just balanced by the recovery

process which has the opposite effect i.e softening the rock. viscous creep is stopped when there is considerable reduction in cross sectional

area and enters the tertiary stage .

The rate of deformation increases rapidly in this 3rd stage and fracture occurs at the end of this stage.

Viscous creep also known as hot creep', since it is observed only at higher temperature.

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Stages of creepStages of creep

Tertiary creep : This stage is period of increasing strain rate. Tertiary creep occurs when there is an effective

reduction in cross-sectional area due to necking or internal void formation.reduction in cross-sectional area due to necking or internal void formation.

If the stress is kept constant of the load or if true strain is taken into consideration

then the resulting fracture due to creep would be at B.

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Fact ors Affecting CreepFact ors Affecting Creep

Nature of stress (compressive, tensile, shear, uni-axial, bi-axial , tri-axial)

Stress level (intensity of stress)

Confining pressure (depth of overburden)Confining pressure (depth of overburden)

Temperature

Humidity/Moisture Content

Grain Size and Geometry of mineral grains

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InIn--situ creep measurementsitu creep measurement

Need for Controlling Test Environment in Creep Testing

Constant temperature chamber

Need to idealise humidity Need to idealise humidity

Need to keep load constant- hydraulic machines not suitable

Precise displacement devices without tendency to drift

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