The Mechanics of Rock Failure

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The Mechanics of Rock Failure

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E MECHANICS OF HOCK FAILURE

By

J o h n P . Cogan

ProQuest N um ber: 10781401

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uest ProQuest 10781401 Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

i

53305

A t h e s i s s u b m i t t e d t o t h e F a c u l t y and t h e Board o f T r u s te e s o f the C olorado S c h o o l o f H in es in p a r t i a l f u l f i l l m e n t o f the r eq u ire m en ts f o r the d e g r ee o f M aster o f S cien ce.

C o-* (f Jo hn P . CoganQ

0££S

S ign ed :

Approved:

G olden, Colorado D ate:

2+

, 1950

CONTENTS Page 1

Abstract Introduction ............................... •

. . . . . . . .

2

3 General Aspects of Failure...... ....................... . . . . . . . Properties of Liquids........................ . . . . . . . . . 3 Deformation and Failure of Metals. . . . . . . . 4 Properties of Hock Crystals ......................... 6 Crystal Deformation .......................... . . . . . . 9 Patterns .of Failure in Polycrystalline Materials* 9 Failure Patterns in A rtific ia l Substances ♦ 10 Failure Patterns in Nature . . . . . . . . . 11 Hock Failure • • • . • • • • • . . . • ........................................ 16 Properties of Hocks • • • • • • • . . . » • . • • 16 Hock Fabrics . . . . . . . . . . • 16 Elastic Constants of Hocks . . . . . . . . . 17 Other Hock Properties • . • • • • • « • • • 19 Strength of Hooks .20 Effect of Confining Pressure. . . . . . . . 21 Effect of Temperature .............................. 22 ..................................23 Effect of Time and Solutions Hock as a Construction Material • • • • . • • . . 24 Natural Arching in Caves • . ......................................... 24 Natural Arches and Bridges .....................................30 33 'The Earth*s Crust . . . . . . . ......................... Temperature-Pressure•Depth Relations • . • • 33 The Mechanism of Earthquakes and Volcanoes . 36 Failure Patterns in the Earth’s Crust . . . 37 Classical Theories of Hock Failure . . . . .-*• . 45 The Mechanics of Hock Failure and Mining . . . . . . . Natural Stresses . . . . . . . ......................................... Model Studies . . * • • • • • • • • • .......................... Shape Preference of Underground Openings . . . . Shock Failure and Blasting . . . • • • • • . • • Subsidence « « » . . « • * # « . • . « . » • • * Rock Bursts .............................. Causes of Rock Bursts . ........................................* Prevention of .Bursts • • ......................... Prediction of Rock B u r s t s . Drilling and Blasting . . . * • • ......................... Mine Support ................................... Roof-Bolting . .................................................................. Block Caving

47 47 48 50 56 58 60 61 62 63 64 66 66 68

Conclusion

69

Bibliography

71

ILLUSTRATIONS Figure

Subject

Page

1.

Fracture pattern in Valley Glacier

14

2.

Typical Antarctica ice-pack

15

3.

Directions of greatest strength, in rocks

20

4.

Section showing overhang in Mesa Verde National Park

26

5.

Typical cave at Mesa'Verde showing arching In two directions

26

6.

A high arch over a narrow opening

27

7.

An opening with a short f l a t back and sloping abutments

27

8.

Flat-arched caves

28

9.

A cave near Moab, Utah showing arching and slabbing

29

C.lose-up of the cave at Moab showing the mechanics of arching and slabbing

29

11.

Rainbow Natural Bridge In Utah

31

12.

General shape of Rainbow Natural Bridge-

32

10.

13.

Structural zones within the earth

*

34

14.

Strain Elliposoid

38

15.

Tilted fau lt blocks and curved fault planes

39

16.

Sub-rounded fractures caused by rapid temper­ ature changes

40

17.

Rock slabbing because of v ertical pressure

42

18.

Close-up of slabbing rock

42

19.

Shear fractures

43

20.

Broken rock from natural block-caving

43

21.

Failing block in Grand Canyon twenty-five miles west of Cameron, Arizona

44

F i pare 22. 23. 24. 25.

Sub-L Lj e c t

Pa go

E f f e c t o f sh a p e on maximum s t r e s s tra tio n

concen­ 51

The e f f e c t o f r o o f - a r c h i n g i n a u n d i r e c t i o n a l field

52

S t r e s s c o n c e n tr a t io n a t the ends o f e l l i p s e axes in h y d r o s ta tic s t r e s s f i e l d

53

D irection s of g r e a te st s tr e s s sta tic fie ld

54

in hydro­

26.

P r e f e r r e d sh ap es o f underground o p e n in g s

55

27.

S t r a i n e l l i p s o i d o r i e n t e d t o an e x p l o s i v e charge

66

Method o f r o o f - b o l t i n g

57

28.

ACKNOWLEDGMENTS The author wishes to express his appreciation to Professors E. G. Fisher of the English Department, and C. W. Livingston of the Mining Department for their assistance in the compilation of this th esis, and to W * G. Fisher for the pictures of Rainbow Natural Bridge and Grand Canyon.

ARTHUR LAKES LIBRARY COLORADO SCHOOL OF MINES GOLDEN, CO 8 0 4 0 1

This paper on ^The Mechanics of Hoek Failure11 Is divided Into three parts s

the f ir s t: doa Is with thegeneral aspects

pf failure and properties of various materials, a feowledge of 'which Is necessary to an understanding of the underlying principles of a ll failure phenomena; the second part con­ cerns rock failure and Includesexamples of natural failure in rock formations; and the third part tr e a ts th e applica­ tion of rock failure to mining problems. The theoretlcai and mathematical aspects of the problem are generalized as much as possible, and the p ractic a b ility of the info r a t i o n is stressed wherever possible.

INTRODUCTION There are -two basic methods of approaching a problem such as rock failures

to s ta r t with fundamental concepts and

build up a theory to include a l l variations of fa ilu re , or to consider a ll types of fa ilu re , and from this information de­ rive general theories regarding i t . Because of the complexity and diversification of rocks and rock masses, and because failure may involve both mo­ lecular and large-scale disturbances, I t seems logical f i r s t to consider a ll information pertaining to the problem.

Then,

the value and limitations of fundamental theories may be more accurately evaluated. At the present time, considerable work Is being done In determining physical properties of rock materials.

Most of

this information is being applied to geophysics, ore dress­ ing, and rock crushing.

In mining there is l i t t l e

correla­

tion between experimental work and methods of mining or min­ ing support.

Mining methods are determined by the mine

manager, who bases his judgment on experience, and problems arising are eventually answered by cut-and-try methods. Practical applications of the various theories have been few.

GENERAL ASPECTS OF FAILURE Properties of Liquids Some properties exhibited by liquids are important in the study of solids because under conditions of high temper­ ature and pressure, under which solids become p la stic , there is an indefinite boundary line between the solid and liquid s ta te s • Liquids are slightly compressible and completely e la s tic . Pressure Is transmitted hydrostatically by the molecules of the liquid being forced closer together, and the viscosity Is thus increased. This property of viscosity, or resistance to flow, Is caused by the cohesion and interaction between fluid mole­ cules, and the resulting tangential and ,shear stresses are set up In moving fluid layers. Temperature of liquids Is a measurement of the molecular energy and molecular action involved.

As the temperature is

increased, there is an increase in volume and a decrease In viscosity.

Exceptions are to be found.

For instance, when

water nears the freezing point, i t s volume increases.

This

is due not to molecular energy but to molecules arranging 1 / themselves in position to form a crystal la ttic e .- ' T7 Vennard, J.K., Elementary fluid mechanics, 3 5 1 pp., New York, John Vs?iley & Sons, Inc., 1 9 4 0 . _ _

Deformation and Failure of lifeta ls Metals are often used in the study of failure phenomena for the following reasons: 1.

Metals have been more thoroughly studied and are

b etter understood than any other material* 2* 3.

They are easily available in pure form# The physical properties of metals change under vari­

ances of pressure and temperature available in the labora­ tory; and they are easily handled under these conditions. 4*

Metals exhibit p lastic failure and d u c tility easily ,

whereas locks show these properties only under extreme con­ ditions or over a long period of time, especially when the major force is ten sile, p

y/hereas rocks are b r i t t l e , have high compressive~ strength,

I weak tensile strength, and are not easily transformed Into the i _

...

|

p lastic sta te , metals possess strength, m alleability, d u etil-

V ity , good heat conductivity, and e le c tric a l and thermoe-

j

le c trlc properties. Metals have more allotropic modifications than rock p a rticles, and also have a higher degree of syrnmetry^by be­ longing to the Isometric, hexagonal, and tetragonalsystems only. Metallic crystals have an atomic space la ttic e , which permits the existence of free electrons and high specific cohesion between the atoms.

In rock crystals the valence

electrons are locked In a stable molecular or ionic la ttic e . As a re su lt, rock crystals are b r ittle and have l i t t l e or no

e le c tric a l conductivity* Metals have b etter tensile properties than rocks because the metal grains are more ductile and the bonding material is

$•

stronger*

When metals are subjected tt>. tension, the long

fibers come to lie p a ralle l to the axis of tension, especial­ ly near the center of the specimen*

I t is more d iffic u lt to

bring about failure along slip planes in metals of the hexa­ gonal system than the cubic system where there are many identical glide planes.

In la ttic e s of low symmetry where

the translation systems are few, the direction of movement corresponds to the crystaliographic gliding directions. The junctions of grains Is a locus of stress and de­ formation unless the crystals are oriented In identical directions. Metals like polycrystalline zinc deform easily under low hydrostatic pressure when intergranular movement may take place.

Under high confining pressures the same metals

deform less easily because they must f a l l with less crystal orientation. Intergranular movement or cold working In metals causes preferred orientation of crystalline grains and results In strain hardening, which can be relieved by re st, heat, or the application of slower rates of deformation*

These

remedies allow the crystals a chance to reorient themselves to the stress by p lastic movement. 1/ Newton, Joseph, Introduction to metallurgy, New York, John Wiley & Sons, Inc., 1938.

Properties of Rock Crystals The smallest particle of a rock vshich can be studied as a unit is the rock crystal*

The individual crystals are im­

portant In the study of rock deformation, because much of the failure Involved Is within the crystal la ttic e . The shape of a crystal is determined by the molecular structure, unless I t is Influenced by outside forces.

In

nature, crystalline grains are often weathered and deformed so that their orientation must follow a study of th eir in ­ ternal structure.

While metals have the advantage of being

easily handled, they must be studied In d etail by X-ray analysis to determine much of their molecular structure.

On

the other hand, Ionic crystals are at times transparent or translucent so that th eir structure can be examined directly. Natural distortion of natural crystals usually Involves the shape and size of faces and rarely Includes any change in the in te r-fa c ia l angles.

The growth of faces may d isto rt

the general shape and cover or obliterate adjacent faces. This Is known as Irregular distortion.

Symmetrical distortion

is caused by an equal growth of faces so that the general shape is maintained.

For instance, galena crystals remain

rectangular even when they follow & cubic pattern. Surfaces of crystals may be striated because of the growth pattern, eroded by weathering or a ttr itio n , or curved. The curving may 6© due to oscillatory combinations of mole­ cular la ttic e s , some independent molecular condition, or a mechanical cause.

General shapes are usually described as

columnar or fibrous, laminar, or granular* Solid, liquid, or gaseous inclusions often occur within crystals and may distribute themselves within the molecular system and so form a symmetrical pattern, or may be scattered and so disrupt the structure* Directions which are crystallographlcally Identical have like physical properties; and, in directions crystallographi­ cally dissimilar there may be a variation in the physical characters*

There are a few exceptions to th is rule*

Two fundamental strength properties are the Interrnolecular cohesion and that force called cohesion which tends to restore the molecules of a body to th e ir original position a fte r they have been disturbed by deformation*

The varying

degrees of cohesion and e la s tic ity are shown by cleavage, fracture, tenacity, and hardness*

Further knowledge of a

crystal Is derived from percusslon-figurea, pressure-figures, etching-figures, and the glide planes* Cleavage occurs along a plane in which there i s .minimum cohesion between systems of molecules and is described by Its direction in relation to the crystal orientation, the ease by which I t is obtained, and the smoothness of the resulting surface. Gliding planes are closely related to the cleavage directions in that they also represent surfaces of weak molecular bonding*

Where molecular slippage is accompanied

by a half-revolution of the molecules into a new position, the action is called twinning, or more correctly, secondarya r t h u b l a k e s l ib r a r y

COLORADO SCHOOL OF MINE GOLDEN. CO 8 0 4 0 1

twinning*

Any break along a twinning plane, which, may not

be a cleavage plane, is called parting*

A general term ap­

plied to any break other than one along a cleavage plane is ttfracture Several fundamental differences In the action and re­ sults of twin-gliding and translation-gliding are to be con­ sidered.

In translation-gliding the movement can proceed In

both senses of the prescribed direction and can continue un­ t i l strain hardening brings the deformation to an end.

It

Is d iffic u lt to t e l l that the structure has been deformed, except possibly by irre g u la ritie s of the grain boundaries. In metals where both actions may a ssist each other, most of the movement is charged to translation movement. Twin-gliding Is limited to one direction along a given plane and to a prescribed distance determined by molecular distances.

Twinning is Identified by the reversed pattern

of the mblecjalar structure. Minerals may d iffe r In hardness In different directions, and th is difference is most marked In those minerals having d istin c t cleavage.

The hardest face is that which Is in te r­

sected by the plane of most complete cleavage.

The direction

perpendicular to the cleavage-direction is the softest, and the direction p a ralle l to I t the hardest.

There is a direct

relationship between the specific gravity and hardness of minerals after the molecular weights of involved elements are accounted for.

W e expect minerals formed from heavy

molecules to be heavy.

However, the weight is further In-

creased, as is the hardness, by close molecular compaction* The tenacity of crystals or minerals is. described as b rittle ,

se c tile , malleable, and flexible.*^

3/ Dana, S.S*, Textbook of mineralogy, 4th ed*, pp. 180-340, Hew York, John Wiley & Sons, Inc*, 1932*___________________________ Crystal Deformations

Induced pressure, and tensile

stress caused by temperature variations changes the spacing and relation of molecules to each other*

The thermal con-

d ucitivlty , diathermancy, optical properties, and e le c tric a l properties are also changed. Microscopic analysis of deformed calcite shows that the plane of flattening Is a compromise between two slip planes determined by the crystal la ttic e structure*

The two planes

intersect at a low angle, and the flattening plane bisects 2/ the angle

W ~ Knopf, S.B., Study of experimentally deformed rocks; Science, vol* 103, no* 2665, pp* 99-103, Jan* 25, 1946*______ Patterns of Failure in Polyorysta1line Materials Patterns of fa ilu re may be determined mathematically and by photoelastic methods*

Even so, there Is a question of the

application of these results to heterogeneous rock masses. Failure In rocks is often so irregular that I ts relation to theoretical failure is doubtful*

A possible answer to the

problem may be the use of materials that have properties re­ lated both to "perfect1 1 materials and heterogeneous rock masses.

Certain polycrystalline substances and even certain

rocks are suitable for further study Failure Patterns in A rtific ia l Substances:

In tension,

metals and ductile materials f a i l along shear planes oriented at an angle of about.45 degrees to the stress*

As deforma­

tion continues, and the necking action gives way to complete fa ilu re, a "cone and cup" shape is formed in the area of complete failure*

B rittle materials f a i l along planes normal

to the vtensIle. sire ss * In compression, p la stic s, p laster, and the like f a i l slong shear planes forming an angle of less than 45 degrees with the direction of principle stre ss, and to a lesser ex­ tent along extension fractures p arallel to the principle stress*

This pattern corresponds to that postulated by v a ri­

ous theories to be considered later* I t is Interesting to note that cracks produced in plaster in buildings from vibrations or shock waves intersect at ob­ lique angle s.-i/

T T Leet, D.L., Vibrations from blasting; Hercules Powder Co.* pamphlet, 34 pp., 1946. These cracks are produced by slight and temporary com­ pressive forces.

Theoretically such cracks should in tersect

at right angles, and i t Is thought that fric tio n a l resistance to shear causes them to form at acute angles In the direction of stress*

Trlaxial tests show that the angle of intersec­

tion varies with the confining pressure.

This relationship,

treated In Mohr’ s theory of rock fa ilu re , Is thoroughly dis-

cussed by McCutchen.

1/

McCutchen, W.R., Behavior of rocks and rock masses in relation to m ilitary geology: Quarterly of the Colorado School of Mines, vol. 44, no* I , pp* 17-42, January 1949. Earthquakes have been known to form intersecting sets of

cracks in both the horizontal and v ertica l directions in con­ crete structures*

The orientation of these cracks gives a

clue to the direction of the earthquake center* ' Failure Patterns in Haturei

Shrinkage cracks in mud

form many patterns, depending on the type of mud.

They may

be curved, radiating, or polygonal, or conform to no particu­ la r pattern.

In playa bottoms, where the texture Is constant

and the material may be considered polycrystalline, tensile stresses, caused by dessication, form hexagonal p lates?

Rec­

tangular or polygonal cracks tend to form where mud is homogeneous, and Irregular cracks form where mud Is made up of various minerals or different sized grains, or contains organic debris. Likewise, balanced tensile stresses cause basalt to fracture into polygonal shapes*

The basaltic formation on

the coast of Ireland known as the "Giants Causeway" has columns which have three, five, six, seven, eight, and nine sides.

Most of the columns are v ertica l and are six-sided

as are other basalt formations throughout the world. Whether or not I t is Important, I t seems definite that tension cracks have a tendency to occur In three directions intersecting at 180 degrees to each other, to relieve a

multi-directional tensile stre ss. One of the most interesting polycrystalline substances is ice.

While i t lacks the strength and weight of rocks, i t

possesses some of th e ir characteristics and could hC studied as a model*

Some of I ts properties which might make i t s u it­

able for model study ares 1.

I t Is easily obtainable in a pure form.

2*

I t f a ils both e la s tic a lly and p la stic a lly , and ma|

be made to recrystallize under pressure.

The time element

for p lastic deformation Is short compared to that for rocks* 3*

Ice has from five to seven allotropic forms, which

fact complicates I ts studies although the same problems arise In rock studies. 4.

Blasting problems might be simplified by experimental

tion with ice.

I t is certainly easy to bore a hole In ice

and excavate the broken material to Investigate the model ratios to correspond to rock. 5.

Ice will expand and contract with temperature

changes. Ice, as found in glaciers, resembles the crust of the earth.

The crust of the earth is made up of relatively

loosely consolidated rock and sediments, containing, many voids, near the surface.

At a depth of about eighty kilo­

meters, the rock becomes compacted and more like glass, ac­ cording to the Interpretations of seismic vibrations. 2/

2/

Gutenberg, B., and Richter, C.F., Seismicity of the earth, 271 pp., Princeton, N .J., Princeton TJniv* Press, 1949.

Ice has been deposited in glaciers and compacted into layers to resemble sedimentary deposits.

At a depth of from

f i f ty to one hundred fe e t, i t becomes compacted, and re­ sembles glass.

At depth, i t is b r i t t l e , has a conchoidal

fracture, and contain# no a ir pockets or voids. Various pressures may act on ice masses.

Mountain

glaciers are in tension \dien they bend over convex surfaces or when the gradient rapidly increases.

The pressure of ‘up­

stream ice may cause compression, and the ice along the bottoms of glaciers may be acted on by confining pressure. Various cracks develop in valley glaciers, as shown in P ig *

1*

The ice-packs of Western Antartica break into zigzag patterns and contain lakes, which f i t into the same pattern,-^ 37 Hobbs,W.H., Characteristics of existing glaciers; 301 pp., New York, Macmillan Co., 1911. The ice at the head of the glacier is shown to be under compression by the intersecting fracture (1),

Longitudinal

and traverse crevasses (2) and (3) are caused by d iffe re n tia l movement within the ice and represent p lastic deformation. The strain ellipse

(4) is orientated to explain the angle

fractures on the edge of the glacier where fric tio n effects a compressive force p a ralle l to these side fractures. I t is thought that wind pushing against these huge ice masses creates sufficient force to cause shear fractures to form.

In one instanc©< ice shoved against an island broke

into a similar group of quadrangular elements.

Fig* 1

Valley Glaeier (Adapted from Hobbs)

These Antarctica icebergs are up to two hundred feet thick and contain no rock matter*

The s tra tific a tio n and

v e rtic a l jointing have been compared to that found in lime­ stone c l i f f s .

The top part is made up of granular ice,

which consolidates with depth, u n til a t the bottom the ice is glassy and crystal clear, and has a conchoids! fracture. Faces

following planes of fracturing are often miles in

-Lake w it h in the ice-p a ck

Pig. 2

T y p ic a l Antarctica Ice-pack

In Greenland, trough faults are found in the continental glaciers*

These extend for great distances in straight lines

and intersect an indefinite system of fractures at oblique angles*

I t is not known whether these faults are a resu lt

of expansion and contraction of the Ice with temperature changes or whether they have been formed by earth faults underneath*

They duplicate, on a small scale, r i f t valleys

as found In Africa*

ROCK FAILURE Properties of Rocks Because rocks are so complex and diversified in nature, i t is impossible to attrib u te to them specific properties without making numerous exceptions*

Therefore, this paper

will tre at them under the following headingst Rock Fabrics Elastic Constants of Rocks Other Rock Properties Strength of Rocks The Effect of Confining Pressure The Effect of Temperature The Effect of Time and Solutions Rock Fabricss

The mineral constituents of most rocks

have been found to be arranged In some sort of a preferred dimensional or crystallographic pattern.

1/

T7

Knopf,E.B., arid Ingerson, Earl, Structural petrology; Geol* Soc* of America, Memoir 6, 1938* ______________________ Sedimentary rocks may show depositional fabrics caused

by a chronological sequence of deposition or a sorting action by wind or water* In metamorphic rocks, mica and other minerals causing sh isto sity are arranged with th e ir f l a t sides normal to. the greatest stress*

This orientation Is caused by crystal

growth and plastic movement*

Solutions Injected through weak

zones in rocks cause an orientation of particles in the d i­ rection of movement. Crystals making up Igneous rocks show orientation of crystal axes and usually lie in a direction showing a definite relationship to the direction of the source of the material* Pressure may also contribute to the type of fabric. E lastic Constants of Rocks;

The four most commonly

used elastic constants of rocks are; Young*s modulus Modulus of rig id ity Poisson*s ratio Cubic compressibility The elastic properties of an e la s tic , homogeneous, and Isotropic substance can be determined by any two of these properties*

However, because rock materials are never per­

fe c t, more than two constants are often necessary to define their elastic properties fully* According to Birch and Bancroft^/, i t might require

T T Birch, Francis and Bancroft, Dennison, Effect of pres­ sure on the rig id ity of rocks; Jour* Geology, vol. 64, no. 1 & 2, Jan.-Feb*, Feb.-March, 1938* twenty parameters to' define the elastic characteristics of a complex crystal fu lly .

A rock made up of various crystals

becomes too complex to consider, unless the specimen is large enough to obtain^ average results and unless the crystalline components are disregarded. The e la stic constants are closely related to the rate ARTHUR LAKES LIBRARY rnL O R A D O SCHOOL OF MINES

GOtDEfTcO 80401

of sound and seismic vibrations, and are involved in geo­ physical computations*

Because of the velocity of torsional

waves and the compressibility of a substance are easily de­ termined, they are often used as a basis for approximating the other constants.** l/ Ide, J*M., Slastic properties of rocks: A correlation of theory and experiment: Hat. Acad. Sci., vol. 22, no. 1, •_______________ pp* 482-496, 1956. ________ Ihe equations relating the elastic constants are given: Symbols t E — ¥oungf s modulus B

Cubic compressibility

u ——Modulus of regidity m - — Poisson*s ratio p - — Density V — Velocity of longitudinal waves v —- Velocity of traverse waves

.

1

v2 = S-

1T”

o

v 2 - SL

1

3.

EB = 3 (l-2m)

4.

E/u = 2(1 •* -in)

5*

uB _ l-2m 3~ = 27TT¥T

F (l+m) (l - 2m)

=

4u-E/u _

3P-S/U

3

3 +EB

FE 9 "TgB

_ 1 ____ 3

~ P 2(1 * m) “ P(9-KB)

Poisson*s ratio may also be found from relations between the overtones in longitudinal vibration*

I t is somewhat

larger in rock specimens cut perpendicular to the bedding than

in those cut p a ralle l to the “ bedding*

The other constants

vary somewhat also, depending on the direction. The vibration of solid bodies is accompanied by dissipa­ tion of energy.

This loss of energy is known as Internal

fric tio n and is thought to be caused by p la stic flow or stra in hardening.

I t Increases with strain and is decreased

by any action which tends to close the Intererystalline spaces in rocks. Other Hock Properties i

Other properties of rocks,

many of which have more practical applications than the elastic properties, are: Compressive, te n sile , and shear strength Modulus of rupture Toughne s s Hardness Weathering properties D rilling, crushing, and grinding properties Breaking and shattering properties with blasting Specific gravity, porosity, and permeability All rock properties are determined by the composition, sise , strength, and qualities of the individual grains mak­ ing up the rock, the orientation of these grains, the char­ a c te ris tic s of the bonding material, and the distribution of the intercry stallin e voids. The rock is further affected by i t s environment, includ­ ing the confining pressure, temperature, solutions present,

and the rate of any active deforming process* Strength of Rocksg

The term wstrength” when referring

to rocks denotes the stress they will withstand before f a i l ­ ing by rupture or p lastic flow.

In geology, the term has

l i t t l e meaning, unless confinlng pressure, temperature, and the time element are considered. Rocks have l i t t l e crystals have l i t t l e

tensile strength, as the individual

tensile strength, and the bonding Is

usually weak and has poor adhesive qualities* The strength of rocks varies In different directions and is related to the fabric*

An example of this strength

difference is given for a typical example of marble and granite by Knopfi/.

l / Knopf , E.B,*, Study of 'experimentally deformed rocks; Science, new. ser. vol. 103, no* 2665, pp. 99-103, Jan. 25, 1946._______________________________________ ______________________________ The strength difference amounts to as much as 38 per cent In marble and 15 per cent In granite. Greatest strength

le a st strength Least strength Intermediate strength arb le Greatest strength Granite Pig. 3

Directions of greatest strength in rocks

As a r o c k i s

com pressed,

i t behaves at f i r s t e l a s t i c a l l y

e v e n t h o u g h d i f f e r e n t i a l s t r e s s e s may b e s e t up b e t w e e n t h e in d iv id u a l c r y sta ls occur.

and i n c i p i e n t f a i l u r e s

As t h e s t r e s s

is

in creased ,

ruptu re o r deform p l a s t i c a l l y . i n t e r g r a n u l a r m o v em e nt, s l i p p a g e tw in n in g,

r ec ry sta lliza tio n ,

the rock w i l l e i t h e r

P la stic

It

ate p l a s t i c how s m a l l ,

f a i l u r e may i n c l u d e

w ith in the l a t t i c e

structure

and e v e n c h e m i c a l c h a n g e s .

v o i d s may c h a n g e s h a p e o r d i s a p p e a r , stretch.

and m ovem ents n a y

and b o n d i n g m a t e r i a l may

ta k e s a s t r e s s o f a d e f i n i t e magnitude to i n i t i ­ f a i l u r e , w h e r e a s a n y u n b a l a n c e d f o r c e , no m a t t e r

w i l l c a u s e movement i n a v i s c o u s medium.

S f f e c t o f C on fin in g P r e s s u r e s be a p p r o x i m a t e d u n d e r f i e l d

C o n f i n i n g p r e s s u r e may

c o n d i t i o n s and d u p l i c a t e d i n

l a b o r a t o r y up t o p r e s s u r e s o f t h o u s a n d s o f a t m o s p h e r e s . ever,

A ir

in n a tu r e , c o n f in in g p ressu re

w ith h ig h tem p eratu res,

so lu tio n s,

is

the Kow-

alw ays accom panied

and o t h e r I n f l u e n c i n g

a g e n t s t h a t c a n n o t be d u p l i c a t e d e a s i l y .

It is

a lso thought

t h a t c o m b in a tio n s o f t h e s e i n f l u e n c i n g a g e n c i e s w i l l change r o c k p r o p e r t i e s more p r o p o r t i o n a t e l y , C on fin in g p ressu re

than s i n g l e

in c r e a s e s the v i s c o s i t y o f l i q u i d s ,

and t h e r i g i d i t y and s t r e n g t h o f r o c k m a t e r i a l . r ig id ity is also

in creased ,

in creased .

a g en cies.

3ven though

the ten d en cy to f a i l p l a s t i c a l l y i s

I t w o u ld t a k e a g r e a t e r s t r e s s

to i n i t i a t e

p l a s t i c deform ation. The process of preparing a rock sample for laboratory tests somewhat disrupts i t s structure, and the f i r s t pressure

applied tends to consolidate i t again.

As the pressure Is

Increased, .the intercrystalline voids are squeezed out, and s t i l l more pressure seems to involve molecular compression. The nature of the effects of compression or confining pres­ sure is shown by the elastic constants*

They vary with the

pressure along an e rra tic curved line under low pressures when consolidation i s taking place, and along a fa irly uni­ form straight line under high pressures*

A straight line

corresponds with the theoretical curve applied to a perfect medium. The density of many minerals is greater when they are in the crystalline state than when they are In the liquid state*.

Therefore, confining pressure should in no way

cause rock materials to become viscous.

And the fact that,

with pressure, rocks do become more plastic shows that there is considerable difference between the plastic and the viscous states when considering volume-pressure relations. Effect of Temperature:

An increase in temperature in­

creases the heat energy and consequently the molecular ac­ tiv ity of any substances.

The density, strength,

and

r ig id ity are decreased, and the p la stic ity Is increased. Very high temperatures will cause rock p articles to change *

into the liquid sta te , even when they are highly compressed. Thus we see th at the a b ility of a rock to f a i l p la stic a lly Is Increased by pressure, and i t s e la stic or strength quali­ tie s are decreased by a raise in temperature.

A combination

o f pressure and high temperature could easily make a rock act like a metal, by retaining i t s strength and losing some of I ts brittleness* Effect of Time and Solutionsz

Time is an important

factor when considering geological formations*

^-Creep" is

a term applied to gradual failure and may take the form of >

¥M & P CJ CO«r4 «m 03 O 1x0 CJ CJ *H O CJ co a> •H f t k O & 3 O O

H

O q

-$«

j.

s p r s

a o tr fu

oq.

u O fB y r

rl C-j O .H P ft *r4 CD r~4 H • Q 53 •H'm l*« O

54.

Ratio r / h n 0.16

■5qjnare C r o n in a

oo n e . O

0

1i

r\

>

npO

r~O

nm y a-;1 c I ' r R . a r

o e in s 5 i

iron v e rtic a l

s : i t r x or z x on i'or s an ar e O J. o 1 field

L o . ‘t a t i c

55,

elo'oraent hGe.dInrs

o p e n in g s

*o t

sto p e s

se

1 or

^ e^er : :i 151 :me. --?rpr ound. open5.nr:s

velopment headings should he as near e llip tic a l in shape as possible.

At least the back should be arched.

A high arch

has l i t t l e

advantage over a simple circular arch, because

stress approaches a constant value as the height to width (H/W) ra tio becomes large. 2.

Y*hen the H/W ratio is near unity, there is l i t t l e

advantage in one shape of opening over another. 3.

How, as the Il/W ra tio becomes less than one, the

order of shape preference is reversed and a rectangular shaped opening will withstand v e rtica l pressure better than ovaloid or e llip tic a l shaped ones.

As the ratio becomes

smaller, the necessity of using rectangular openings becomes rapidly acute. 4.

In normal openings,-which are assumed to have rounded

corners, the maximum stress is located where the rounded part meets the side walls. 5.

Equid linens Ional openings such as circular or square

ones should be used when possible in'hydrostatic stress fields Shock Failure and 31asting Hocks fracture more easily when the force is applied

t

rapidly than when i t is applied 3lowly.

This is especially

true when the force Is applied amost instantaneously as in blasting.

The more b r i tt le

a material is,- the more i t is

affected by waves and vibrations.

A diamond, the hardest

material known,' w ill shatter and practically disintegrate i f tapped with just sufficient force to cause destructive waves to be set up within I ts crystalline la ttic e structure.

Glass

may be shattered by sound waves.

I t is thought that even

organic substances might be made to disintegrate i f subjected to waves of proper frequency and intensity whereby the vibra­ tion energy of the molecules would exceed the inter-molecular attraction# The energy from explosives is dissipated as heat energy,: wave energy, and propulsive energy.

Most; of the heat originates

from the chemical reactions Involved in the explosion, some heat may be formed by rock movements, and some my be formed by a transformation of wave energy.

I t Is absorbed by the

rocks and removed by the gases formed.

If the b la st is ex­

posed, heat energy w ill be radiated and also dispelled into the atmosphere. In b r i tt le rocks the shattering effect is caused by shear and compressional waves, which may disrupt the rock inter-granularly or Intra-granularly.

I t is in the study

and eventual control of these waves that progress will be made in blasting.

An adaptation of control Is featured by

shaped charges, in vhich the direction of the waves is con­ fined to a limited area, and a penetration effect is pro­ duced.

Milli-second delay blasting gives a timing effect,

in which wave fronts can be somewhat controlled to give more or less shattering as desired, or to Increase the blast efficiency. The propulsive power of an explosive is caused by the formation of gases, the increase in volume of gases due to increased temperatures, and to a slight degree by the force

of the wave fronts.

The propulsive energy is more Important

than the shattering energy in soft rocks or where rock ma­ te ria ls have to be moved.

Certain problems of-blasting per­

taining to mining w ill be considered la te r. Subsidence Most subsidence is caused by mining* although some has been attributed to the removal of water and o il from under­ ground s tra ta , where i t acts as support somewhat like solid materials.

A secondary cause is the drying and shrinkage

of clay beds a fte r the water table has been lowered. Considerable damage is done to surface structures by the d iffe re n tia l movement accompanying subsidence and per­ manent problems arise from changes in elevation along water­ ways, transportation routes, and so forth.

Another problem

sometimes present is the danger of flooding the mine.

Crumb1

ing of overlying s tra ta allows water from the sea, lakes, old workings, and other formations to enter the mine, and many disasters have resulted from ju st such entry.

In England

coal is mined underneath the sea, and several Inrushes of water have occurred.

In Alaska, sudden subsidence along a

fa u lt flooded the Alaska-Treadwell group of mines* Hiere are two alternatives in considering subsidence* I f the ore Is valuable in relatio n to the damage to be caused there Is l i t t l e

need to curb subsidence.

On the other hand,

i f caving has to be prevented, p illa rs must be l e f t or the stopes must be f ille d .

The trend in modern methods of mining is to eliminate the p illa r s wherever possible by using a long-wall method of extraction.

The calculation of the size and spacing of

p illa r s poses a problem; and then, if p illa r s do f a i l , the overlying beds are more completely disrupted than I f they had failed under controlled conditions in the f i r s t place. P illa rs interfere with the use of modern machinery and are something of a fire hazard. There is a difference of opinion among B ritish and American authorities on the relation of surface subsidence areas to the mined area.

However, general rules governing

this relation can be given:, 1.

Room-and-piliar miningcauses arching to take place

and may prevent surface subsidence.

However, \dien an arch

or dome breaks the surface, subsidence continues outward to a point directly above the p illa r or rib , or beyond, i f the depth of subsidence is great.

The la te ra l extent of the draw

Is governed by the support given by the broken rock. 2.

Y/hen mining is continuous and no p illa r s are l e f t ,

subsidence precedes the mining operation by a distance deter­ mined by the angle of draw and det)th of the operations.

The

angle of draw varies from 65 to 75 degrees depending on the nature of the rock.

The movement of the rock follows a

plane of s ta b ility , which Is v e rtic a l near the surface and curved to meet the minlng-face a t an angle of about 30 de­ grees from the horizontal. 3.

The depth of subsidence varies from one-half to two-

t h i r d s o f th e 4.

t h i c k n e s s o f d e p o s i t rem oved* S u b s id e ix e

a lth o u g h th e d i r e c t i o n

is

The d i r e c t i o n o f f a i l u r e beds*

The a c t u a l l i n e

and a r c h i n g a c t s v e r t i c a l l y i n g e n e r a l , i n f l u e n c e d b y th e d ip o f th e beds* t e n d s to w a r d a l i n e

of fa ilu r e

norm al to

th e

i s u s u a l l y a c o m p ro m ise b e ­

t w e e n t h e v e r t i c a l and n o r m a l d i r e c t i o n s . S u b s i d e n c e c a n be c o n t r o l l e d b y f i l l i n g su ffic ie n t p illa r su b sid e n c e

a rea f o r perm anent s u p p o r t.

c a u se s th e su r fa c e

.to be s u b j e c t to

or by le a v in g

to f a i l f i r s t

c o m p r e ssiv e f o r c e ,

h a ter,

P r o g r e ssiv e

in t e n s io n , sta b ility

th en

is

a c q u i r e d •1/ T T P e e l e , R o b e r t , M in in g e n g l n e e r s f h a n d b o o k , 3rd e d . , S e c . 1 0 , p o . 5 1 9 - 5 3 2 , New Y o r k , Jo h n W i l e y & S o n s , I n c . , 1941. B r i g g s , H e n r y , M in in g s u b s i d e n c e , 2 1 5 p p . , L o n d o n , Edward A r n o ld fc C o . , 1 9 2 9 . _______________________________ '____________ Rock B u r s t s Rock b u r s t s i n c l u d e rock s underground. so n n e l,

t h e s u d d e n and u n e x p e c t e d f a i l u r e

of

B e s i d e s being a c o n s t a n t t h r e a t t o p e r ­

t h e y o f t e n c a u s e damage t o n i n e

tr a n sp o r ta tio n f a c i l i t i e s .

s u p p o r t s and d i s r u p t

T h ey o c c u r I n t u n n e l s and m in e s

I n v a r i o u s p l a c e s and o f t e n w here l e a s t e x p e c t e d .

Large

b u r s t s a r e u s u a l l y f o u n d I n d e p t h and I n h a r d s t r o n g r o c k . M in or b u r s t s o c c a s i o n a l l y o c c u r i n c o a l m in e s and t u n n e l h e a d in g s. The t e r m tfc r u s h b u r s t s ” may be a p p l i e d

to

th o se c a u s in g

c o n s i d e r a b l e dam age and I n v o l v i n g a m a jo r r o c k d i s t u r b a n c e .

They may Include the crushing of p illa r s , the shearing of the back or stra ta adjacent to the mine.

Some bursts occur deep

within rock formations and cause vibrations similar to those caused by slight earthquakes. "Strain bursts” include slabbing, popping, and smallscale rock fa ilure s • Causes of Rock Bursts:

Whenever d iffe re n tia l stress ex­

ceeds the strength of rocks, bursts may occur.

The removal

of rock by mining may change a system of confining stress to t

one of d iffe re n tia l stre ss.

The distribution and concentra­

tion of this stress Is determined by the system of mining and support.

The p o ssib ility off bursts increases with the

rig id ity and strength of the rocks, because when rocks f a i l p la s tic a lly , a l l movement will be gradual, .and the stress dis tributed evenly throughout the rock.

Then too, in p illa rs

and ribs p lastic failure is obvious and steps will be taken to correct the situation , whereas in highly e la stic materials the true stress condition may never be recognized in time to prevent a burst or major fa ilu re . Strain bursts are related to slabbing except for the fact that they are sudden.

The walls of an underground open­

ing may act under pressure much as a deck of cards when com­ pressed edgewise.

A combination of la te ra l stra in and v e r t i­

cal compression causes an outward bending, and In b r itt le rocks sudden rupture will occur.

Slabbing takes place In

softer rocks and those containing imperfections that weaken

th eir strength.

The stra in which causes slabbing may act

over a period of days or weeks*

Immediately after blasting,

a slab of rock may appear to f i t tig h tly against the rib or back; la te r a crack will form behind i t and continually widen* Investigation w ill show that such rocks cannot be made to f i t in to .the depression from whence they came, because la te ra l stra in w ill have changed the shape of the opening. Sagging within an arch causes stra ta to separate* one stratum f a i l s ,

When

i t closes the gap between i t and the lower

one, and an air-rush may be Initiated*

The cantilever forces,

which act along the sides of the arch, are a t the same time reversed so th at a shock wave is transmitted through the p illa rs or arch supports and further failu re may be induced.^

y

Jeppe, C.3., Gold mining on the Witv/atersrand, pp. 785826, vol. 1, Johannesburg, Transvoal Chamber of Mines, 1946 Prevention of Bursts:

The only positive way to avoid

bursts is to prevent the accumulation of stresses exceeding the strength of rocks.

All mining operations should be

planned with this fact in mind*

Openings

should be made

corresrjonding In shape to the, ideal shape a3 much as possible* Heavy timbered support, i f in stalled before sagging takes place, will help prevent bursts and protect men to some extent*

Strong e la stic supports like ste e l beams are ex­

cellent, while b r i t t l e materials such as concrete are danger­ ous in hard ground because the concrete may act like rock i t ­ self*

F i l l i n g may n o t p r e v e n t a l l b u r s t s b e c a u s e may s t i l l

occur.

s l i g h t sag

H o w e v e r , m a jo r movem ent and f a i l u r e s

w ill

be h i n d e r e d . Main e n t r a n c e s t o m in e s s h o u l d be p r o t e c t e d f r o m p r e s s u r e and b u r s t s b y l e a v i n g l a r g e p i l l a r s d r ifts

and t h e s l o p i n g a r e a s .

I f p o s s i b l e , e n tr a n c e s sh o u ld

b e d e e p w i t h i n t h e f o o t w a l l , and i f dangerous, w o rk in g s

b e t w e e n th e s h a f t s o r

c o n d it io n s are e x tr e m e ly

a p i l o t e n t r y c a n b e d r i v e n b e t w e e n t h e e n t r y and

t o a c t a s a b u f f e r t o s h o c k s and t o d i s t r i b u t e

stress b etter. above in c lin e d

On t h e R and, p i l o t e n t r i e s a r e o f t e n u s e d s h a f t s t o p r o t e c t them fr o m t h e v i o l e n t

s h o c k s a c c o m p a n y in g r o c k b u r s t s . P r e d i c t i o n o f Rock B u r s t s :

T h ere I s no s i m p l e f o o l -

p r o o f m eth o d o f p r e d i c t i n g b u r s t s . c e r t a i n m in in g d i s t r i c t s

T h ey a r e common i n

and r a r e i n o t h e r s .

V a r i o u s m e th o d s

h a v e b e e n u s e d i n p r o d u c i n g them : 1.

The amount o f c l o s u r e

In d r i l l h o l e s in p i l l a r s h a s

b e e n m easu red to a p p ro x im a te

th e s t r e s s

W h ile t h i s

sy s te m m ig h t g iv e

an i n d i c a t i o n o f i m p e n d in g

fa ilu r e

s o f t fo r m a tio n s,

in

w ith in th e p i l l a r .

I t h a r d l y w o u ld i n b r i t t l e

rocks

i n w h ic h d a n g e r o u s b u r s t s o c c u r . 2.

S a g h a s b e e n m e a s u r e d b y t h e u s e o f s a g m e t e r s , and

c o r r e l a t i o n s h a v e b e e n made b e t w e e n t h e am ount o f s a g and b u r s t In c id e n c e • 3. tio n s,

P i l l a r s have been t e s t e d f o r freq u en cy o f v ib r a ­ c o n d u c t i v i t y o f e l e c t r i c a l f i e l d s , v e l o c i t y o f sound

waves, and temperature as an indication of them.

the stress

within

Sudden temperature changes may show incipient move­

ment and impending rupture. Drilling and Blasting Variable factors in d rillin g and blasting a round in a mine are: Humber of holes Pattern and spacing of holes Size and depth *of holes Strength and velocity of detonation of explosive Distribution of explosive in the

holes

Amount and type of stemming used Timing of shots The- overall efficiency and cost of any round is affected by a change in any one of the above factors.

In general,

mines adopt a standard round, one which miners are accustomed to using, and adjust i t by using more or fewer holes to ob­ tain b etter re su lts.

Many miners have favorite rounds, which

they continually use with slig h t modifications.

That much

is to be desired in planning rounds is sometimes shown by results achieved accidentally or by individual miners, who have acquired special s k ill in d rillin g and blasting.

One

such miner at Lark, Utah, d r i l l s a round in shale or soft limestone from two positions of the machine.

From near the

center of the face, he d r i l l s a ll of the holes except the l i f t e r s , which he d r i l l s horizontally.

He has excellent re-

s u its , even In d r if ts eight feet by eight fe e t. A miner at Cobol, Alaska, averaged over six feet per round over a measured distance in a five-by seven-foot d r i f t in graywacke. The effectiveness of a blast and shape of the crater re­ sulting from a single b last is determined by the bore-hole pressure and explosion

p

r

e

s

s

u

r

e

.

pressure relations

IT

Livingston, C.W., Lecture on rock excavation, Colorado School of Mines, 1949.

y

Burwash, E.M.J., Bomb craters in different so ils: Ab­ s tr a c t, Geol. Soc. Amorica B ull., vol. 51, no. 12, p. 1922, _________ 1940. ^

depend on the type, and amount of explosive, the distance to the free faces, and the internal fric tio n and strength of. the rock, and are Influence*|||fc>y Imperfections In the rock.

Frac­

tures are formed along shear and tension planes by compression and shear waves.

(See Fig. 27)

The rock is thrown clear of

the crater partly by the force of the wave fronts and partly by gas pressure.

In quarrying or wherever large charges are

fire d , the propulsive force of the explosive is derived a l ­ most entirely from pressure exerted by the explosive gases. The use of fast-delay blasting has Increased the ef«* ficieney of some rounds.

When shots are detonated within a

short time interval, the shock waves may support each other to give b etter fragmentation. fragments may'be formed.

Occasionally, larger rock

Added fragmentation may be caused

by rock from one b la st being thrown against the rock from

the previous blast before it falls to the ground.

A, B, and C represent three major shapes of craters which may be formed depending on the amount of explosive. PPf _____________________| Is the direction of ma opposing force. Pig. 27

Strain ellipsoid oriented to an explosive charge

Mine Support The trend in mining -practice is toward a system of con­ tinuous mining whereby temporary support is necessary only for a short time, a fte r which,-the excavation is f ille d or i

allowed to cave.

Where possible, natural stresses are be­

ing used to a s s is t in breaking rock.

In longwall rnin

the weight of the overlying rock on the working face causes stre ss, which may aid or hinder the operation.

The caving

methods of mining make the greatest use of natural forces to break and crush rock. Roof-Bolting;

Roof-bolting is becoming a common way

of supporting the back* Although i t lias been used in a few mines for years, only recently has i t been recognized as an economical method of support*

These bolts tie s tra ta together

so that the f u ll strength of the rocks is u tiliz e d as support. (See Pig. 28)

r*/ ^ /s ,

Fig. 28

Method of roof-bolting

The following advantages of roof-bolting should be con­ sidered: 1.

Steel rods are cheap and durable.

2.

In stallatio n costs are often less than those for tim­

bering. 3.

Development d rifts are not cluttered up with timber.

4.

Rods can be Installed close to the face almost im­

mediately a fte r blasting.

That dangerous i n i t i a l sag is

eliminated, loose slabs are supported, and the beds are made •to act like thick beams and thus support themselves. 5.

The stress acting on rods Is easily determined and

extra rods may be added as needed.

Bolts have been used successfully where timber support has failed .

However * in plastip rock^ timber support might

be necessary to seal the d r i f t complately* Block Caving;

Haturally forming arches within the broken

material in cave-stopes are a constant source of trouble In mining.

Vertical arphlng w ill cause d iffic u lty in drawing

the ore through the raises and horizontal arching causes v e rtic a l channels to extend upward to the surface.

Both

conditions cause dilution and poor recovery, and complicate draw control.

.

Closely spaced raises and careful draw con­

tr o l are the only’ preventives known?to keep arches from form­ ing,*

Lateral draw from outside the block I s often unpre­

dictable, and lar ge unbroken boulders may cause uneven move' ' V ■: ' d ..."'I- TV ment within the block — a prelude to further complications. I r i tioek^laving, rockhas rather than by shear and toform

a tendency to

f a i l by tension 1/ ■ / v e rtic a l c o l u m n s H i g h

l / VancSrwilt, J.W.,Ground movement adjacent to a caving blockx Am.Inst,Min.Met.Eng. , Mining Technology Tech. Pub. "2000, May 1946. _______ - ' ■ ■ ■■ //___________________y: