Rock Mechanics IRock Mechanics I MinEMinE 311311

Objectives:Objectives:

(a) To understand of the mechanical (a) To understand of the mechanical behavior of rock materials, rock behavior of rock materials, rock fractures and rock masses;fractures and rock masses;(b) To be able to analyze and to (b) To be able to analyze and to determine mechanical properties of determine mechanical properties of rocks for mining engineering rocks for mining engineering applications.applications.

Schmidt Hammer Rebound HardnessThe Schmidt hammer is point perpendicularly and touch the surface of rock. The hammer is released andreading on the hammer is taken. The reading gives directly the Schmidt hammer hardness value. The standard Schmidt hardness number is taken when the hammer is point vertically down. If the hammer is point to horizontal and upward, correction is needed to add to the number from the hammer. The correction number is Table below.At least 20 tests should be conducted on any one rock specimen. It is suggest to omit 2 lowest and 2 highest reading, and to use the remaining reading for calculating the average hardness value. Report of results should include descriptions of rock type, location, size and shape, and orientation of hammer axis.

AbrasivityAbrasivity are are measured by tests, measured by tests, e.g.,e.g.,Los Anglos Abrasion Los Anglos Abrasion MachineMachine

Slake Durability TestSelect representative rock sample consisting of 10 lumps each of40-60g, roughly spherical in shape with corners rounded during preparation. The sample is placed in the test drum of 2 mm standard mesh cylinder of 100 mm long and 140 mm in diameter with solid removable lid and fixed base, and is dried to a constant mass at 105°C. The mass of drum and sample is recorded (Mass A). The sample and drum is placed in trough which is filled with slaking fluid, usually tap water at 20°C, to a level 20 mm below the drum axis, and the drum is rotated at 20 rpm for 10 minutes. The drumand sample are removed from trough and oven dried to a constant mass at 105°C withoutthe lid. The mass of the drum and sample is recorded after cooling (Mass B). The slaking and drying process is repeated and the mass of the drum and sample is recorded (Mass C). The drum is brushedclean and its mass is recorded (Mass D).The slake-durability index is taken as the percentage ratio of final to initial dry sample masses after to cycles,Slake-durability index, Id2 = (C-D)/ (A-D) × 100%The first cycle slake-durability index should be calculated when Id2 is 0-10%,Slake-durability index, Id1 = (B-D)/(A-D) × 100%

Ultrasonic wave velocity

Rock Strength TypesRock Strength Types

Geology 229Engineering and

Environmental Geology

Lecture 5

Engineering Properties of Rocks(West, Ch. 6)

Outline of this Lecture

1. Triaxial rock mechanics test• Mohr circle• Combination of Coulomb shear failure criterion and

Mohr circle• Expressing Coulomb criterion by principal stresses

2. Engineering classification of intact rock3. Engineering tests for strength and durability

Triaxial Compression Test

In a triaxial compression test, the direction of the load is called the maximum principal direction and the direction of the confining pressure applied is the minimum principal direction. Attention should be exercised to the fact that the convention for defining the principal direction and principal stress may be different from earth science and physics. In physics, it is usually define the tensile stress, the extensional deformation as positive, whereas in earth science it is the opposite. We define compressive stress, and compressional deformation as positive, simply because the nominal status in the crust is compressive and compressional(think about a diver at the depth of 100 m, but the material is not water but rock now).

In the directions of the principal stresses (σ1, and σ3) there is no shear stress. Rock mechanic experiments show that the shear stress reaches its maximum in the direction of about 30 degrees from the maximum principle stress σ1. Theoretical prediction is 45 degrees from the principle directions.

Mohr’s Circle

Mathematically, it can be shown that the normal stress σ and the shear stress τ on any plane that has an angle of θ from the minimum principle stress σ3 direction related to the maximum and minimum stress in the following equations. These relationships can also be expressed graphically by the Mohr’s Circle:

θσστ

θσσσσσ

2sin)(21

2cos)(21)(

21

31

3131

−=

−++=

)(21:radius

)(21:center

31

310

σσ

σσσ

−=

+=

r

Mohr’s Circle (cont.)In a triaxial test, the normal stress and shear stress on a given plane are the functions of σ1 and σ3 and fall on a circle.

Mohr-Coulomb shear failure criterion

The combination of the Coulomb’s criterion on shear failure and the Mohr’s circle representation of the relationship between the principal stresses and the shear and normal stresses on a shear plane. Now we can examine not the τ−σ pair, but also the σ1 - σ3 pair to see if their relativity satisfies the stable/unstable condition.

Mohr-Coulomb shear failure criterion (cont.)When 2θ = 0.5π - φ, or θ = 0. 25π - 0.5φ, τ = τff , at this point the circle touches the straight line and this is the point of failure. Remember: θ is the angle of the shear plane with respect to the minimum compressive principal stress, on which the normal and shear stress are calculated, and φ is the angle of friction on the shear plane.

When shear failure is occurring, equivalent to express the failure criterion by the Coulomb criterion:

τ >= S0 + µσ

We can also find that the principal normal stresses are related as:

σ1 >= C0 + σ3tan2αwith

C0 = 2S0tanα, and α = π/4+φ/2

Thus, when the circle touches the Coulomb failure criterion (the straight line) shear failure occurs. There are three ways for the circle reach the straight line to reach failure:

1) Increase σ1;2) Decrease σ3 ;3) Decrease both σ1 and σ3 at the same amount

(equivalent to increase the pore pressure on the shear plane that we will discuss later)

Engineering classification of intact rock

There are two ways to classify the intact rock in terms of 2 parameters:

1) using compressive strength alone (C0) 2) use the ratio of E/ C0

Engineering classification of intact rock (cont.)

Using compressive strength alone (C0) we can classify the rocks in to 5 classes:

A, B, C, D, E

For rocks with very high compressive strength to very low compressive strength.

Engineering classification of intact rock (cont.)

Using the ratio of Young’s modulus to the compressive strength E/ C0 we can classify the rocks into 3 classes:

H (for high);M (for mediate);L (for low).

So by combining the 2 methods we may have rocks classified as BH, BM, CM, etc.

Engineering Classification of Intact Rock Based on Compressive Strength

Clay-shale, rock salt25.54,000Very lowE

Friable sandstones, porous tuff

27.5-554,000-8,000LowD

Most shales, porous sandstones, and limestones

55-118,000-16,000

MediumC

Most igneous rocks, most limestones, and dolomite, well-cemented sandstones and shales

110-22016,000-32,000

HighB

Quartzite, diabase, and dense basalt

22032,000Very highA

Representative Rocks

Strength in MPa

Strength in psi

Level of Strength

Class

200LowL

200-500MediumM

500HighH

E/C0Level of StrengthClass

Engineering Classification of Intact Rock Based on E/C0

Igneous Rocks

Sedimentary Rocks

Metamorphic Rocks

Aggregate are the most frequently used engineering materials for construction.

What is Aggregate?

An aggregation of sand, gravel, crushed stone slag;Used in cement concrete, mortar, asphalt pavement, etc., or used along in railroad ballast.

By surface excavation we can get these materials.

Quarry: - production of bedrocks;Pit: - production of gravel, sand, or other

unconsolidated materials.

For rock as engineering material we care about its strength and durability.

For getting the strength test we can use abrasion test.

For durability test we can use the sulfate soundness test and freezing and thawing test.

Abrasion resistance test:

Sample weight 5 kg, specific size gradation specific number of steel spheres, interior projecting shelf, 500 revolutions, then use #12 sieve with d=0.141 mm.

Percent loss = (material finer than #12 sieve) / (original weight)

For highway construction, we need percent loss less than 35 – 50 %.

For durability test there are two major methods:

1) sulfate soundness:

Soaking the material under test into sulfate solution and put it into oven for drying to crystal for 5 cycles, then use the same sieve and get the percent loss;

2) freezing-thawing test:

Freezing and thawing the material for 25 cycles, then use the same sieve and get the percent loss;

For highway construction material, the maximum loss for concrete aggregate is 12-15%, and for base course this number is 15-18%.

For durability Concern, different geographic regions may have different emphases. For example, in Florida, the heating-cooling, wetting-drying are the main processes for material deterioration; while in our New England, freezing-thawing, and the chemical reaction caused by road salt are the major damager for road material.

Readings:

Ch. 6, 7

Homework:

Chapter 6, Problems:

5, 6, 7, 8, 9