##### Document Text Contents

Page 1

.

. "' . .." . .,; 1'",

:t~ ~, . - " .

" .. ' .. '.' "., ,t ., ., n ' c... . • -ffll,.'t: a- • ..., ~- '

~. -' , . '. :.... .

.' 1"',_ ,: '. '1' •. ,. ~, . ' ,', ~,. ::~~

. . .

. . .

. Mechanic$

r

Page 2

'. {. ,

Introduction to

Rock Mechanics

Second Edition

Richard E. Goodman

University of California at Berkeley

Jahn Wiley & Sans

New York I Chichester I Bri.bane I Toronto I Singapore

.. , .".

. . "

Page 144

272 Applications of Rock Mechanics in Engineering for Underground Openings

E

w E

lb)

Figure 7.28 (b) Projection in the tunnel

section of the maximum remoyable block

corresponding to JP 010.

limit plane must pass through both the comer and its opposite. Ifthe comer has

distance x from the center of the reference circle, its opposite has distance R2/X

from the center in the opposite direction (where R is the radius ofthe reference

circle). In the case of Figure 7.28a, the lP lies inside each of the enveloping

great circles, so the lP is above both of them. The angles of inclination of the

orthographic projections of the comers in the tunnel section are transferred to

the tunnel section in Figure 7.28b, and the removable block is found as the

region simultaneously aboye each. In this case, the maximum removable block

is not a key block if gravity is the main contributor to the resultant force

direction in the block.

Figure 7.29a shows a similar construction but for lP 001. The comer 1,2 of

this lP is off the paper so its opposite -1'2 has been drawn. (The opposite is the

upper hemisphere line that is perpendicular to both ofthe normal s n, and n2 and

therefore perpendicular to the great circle connecting normals n, and n2.) Great

circles through each comer in tum intersect the tunnel section at the points

shown and the limiting great circles are established as those through lz3 and 113 ,

intersecting the tunnel section respectively 24° aboye east and 83° aboye west.

The lP is outside the first of these and inside the second so JP 001 is below the

first and aboye the second. Figure 7.29b transfers this information to the tunnel

section.

7.S Underground Openings in Blocky Rock-"Block Theory" 273

Having performed an analysis of maximum key block s for two lPs, we now

proceed to find all the rest. Since JPs 000 and 111 contain the tunnel axis, they

have no maximum key block areas in the tunnel section. The maximum key

block regions of all the other lPs are shown on Figure 7.30, where each tunnel

section is drawn in the curved polygon corresponding to the lP in question. We

.

· · ·

. . .

N

....... t. ............ ~./Aa .......

.... --....-. .... ," , ....

..... ,." l' ....

.. ' "" l' ....

.... ",,"" I , ....

.

...... / I \\ ..... \------

... // I \ \\-----

/ I \ ... ~----

/ I ,

I I \

" " \ ® í' ' - 12 ,

I ,

I

I

I ,

JP 001

~----7-- Tunnel

section

Limit plane 2 ,

~

• I

~ I

'. ;<.......

.... -1 1" ;1' " "'- .' .7 •• -----

•••• 13 ." "" Lim it plane 1

_ 11'"' , •• '

: A

123 .-

~.~----~~-----~--

/ .'

Reference

circle

/{/ ..... 1" ....

.... J .."",. ~ ..... . ~-- .

~···· •••••••••••••••••• II ••• ••••

(a)

JP 001 is below limit plane 1

and aboye limit plane 2

Figure 7.29 (a) Construction for the projections of the edges of the maximum

remoyable block in the tunne! section, corresponding to JP 001.

Page 145

274 Applications of Rock Mechanics in Engineermgfor Underground Openings

W------~~--~~--~--------E

(b)

Figure 7.29 (h) Projection in the tunnel

section of the maximum removable block

corresponding to lP 001.

see at a glance that under gravity loading JPs 101, 100, and 001 may generate

block s that require support. A1though these drawings are two dimensional, the

three-dimensional maximum keyblocks can be drawn corresponding to each of

thesejoint pyramids and subjected to a limit equilibrium analysis. The direction

of sliding under gravity is determined by a mode analysis, based upon the

direction of the resultant force and the description of the joint pyramid, as

discussed by Goodman and Shi (1985). Then when friction angles are input on

each face, the support force vector can be computed for each maximum key

block using methods of analysis discussed in the next chapter. It may be that

none of the blocks require support; on the other hand, in certain tunnel direc-

tions, the same set of joint planes and friction angles may create the need for a

large support force. This is largely due to the changing size of the maximum key

block s as the direction of the tunnel is varied.

CASE HISTORY--"TUNNEL SUPPORT SPECTRUM"

The effect of tunnel direction on rock mass support requirements will be illus-

trated for the rock mas s of Figure 7.20 by studying the SUpport force for

7.S Underground Openings in Blocky Rock-"Block Theory" 275

Figure 7.30 Tunnel sections showing maximum removable block s for each lP super-

imposed on the stereographic projection of the lPs.

equilibrium of the most critical block as a function of a complete sweep of

tunnel directions. AH the examples considered thus far correspond to a hori-

zontal tunnel axis in direction N 21 0 E. Consid~ring only horizontal tunnels, for

the time being, we can observe the relative size of the most critical key block,

for five tunnel directions, in Figure 7.31. The maximum key block s become

d.ramaticaHy larger as the direction 3150 (N 450 W) is approached. Limit equilib-

num analysis of this system, for a horseshoe tunnel 6 m wide and 5.4 m high,

yields required support forces for the maximum k~y block varying from a low

of less than 1 me trie ton per meter length of tunnel, to a maximum of 33 metric

Page 288

560 Inde~

Photoelastic stress gage, 116

Piles and piers, 346

load distribution in, 370-374

load tests, 372, 373

settlement of, 376, 377

Pillars, 231

Plane sliding, see Block sliding

Plane stress and plane strain, 452

Plastic analysis of tunnels, 242-249, 454-464

Plate bearing test, 188-190

Point load index, 36

Poisson's ratio, 67, 181

measurement, 184

for permanent and total strain, 220

typical values, 186

variation with deviatoric compression,

70, 185

Pore "crush-up", 69

Pore pressure:

and fault slip, 171-173

and rock failure, 85, 86

and stress measurement, 140

Porosity:

effect of age on rocks, 29

measurement, 31

types of pore spaces, 13, 28, 29

values for selected rocks, 29, 83

and water content, 32

Poulos, H. G., 352, 370

Pratt, H. R., 91, 92

Principal strains, 412

Principal stresses, 133, 134, 393,402,403

Principal stress ratio:

effect on strength, 74-76, 87

initial values, 106-113

Principal symmetry directions, 182

Punching failure of footing, 351, 352

, Q system (classification), 47-49

Quartzite, 142, 144

compressive and tensile strength, 61

Hoek-Brown constants, 99

Lundborg's strength parameters, 90

modulus ratio and Poisson's ratio, 186

Mohr-Coulomb parameters, 83

Radial jacking test, 191

Radial permeability test, 34, 35

Raleigh, C. B., 172

Rangeley oil field, 172

Raphael, J., 363

Rate of load effects, 213-215

Reichmuth, D. R., 62

Relaxation, 203

Removable blocks, 258

Rengers, N., 166, 167, 169

Reservoir induced seismicity, 86, 171-172

Residual strength, 81, 161

Residual stresses, 116

Rhyolite, 20

density, 33

Riley, P. B., 116

Ring shear test, 66, 88-90

Roberts, A., 116

Rocha, M., 36, 116, 121, 134

Rock boIt design:

to control plastic zone of tunnels, 246

to prevent slip of joints in tunnels, 241

for rock slope stability, 279, 283, 317-319

to secure roof beams in layered rock, 236,

237, 281, 290, 334, 387

Rock bursts, 102

Rock classification:

comparison of Q and RMR, 47

fabrics, 20, 21

fissuring, 39-42

geological, 19, 419-425

NGI (Q) system, 47

RMR (Geomechanics) system, 43-46

for tunneling, 43-47

Rock loosening, 53, 247

Rock mas s rating, see Geomechanics

classification

Rock noise, 69

Rock reinforcement, 249. See also Rock bolt

design

Rock slopes:

buckling of, 337

types, 293, 294

Rock socket, 345, 371, 377

Rock test preparation equipment, 58, 59

Roof beams, buckling of, 233

Roof design, underground, 233-237

Rosettes, strain gages, 411, 412

RQD,44 '

Rummel, F., 63

Rutter, E. H., 206

Safety, see Factor of safety

Salem, A., 190

Sallstrom, S., 419

Salt, 15

creep properties, 252

density, 252

ductility, 74

Sandstone, 143, 144, 146

compressive and tensile strength, 61

(

foundations, 349, 350

Hoek-Brown constants, 99

joints in, 146

modulus ratio and Poisson's ratio, 186

Mohr-Coulomb parameters, 83

permeability, 35

point load strength, 37

porosity, 29, 83

in triaxial compression, 75

Schist, 8, 20, 21, 161

bearing capacity, 350

compressive and tensile strength, 61

density, 33

modulus ratio and Poisson's ratio, 186

permeability, 35

Schistosity, 13

and strength, 61, 83

Schneider, B., 147, 190, 199-201

Schneider, H. J., 157, 168, 169

Scratch hardness, 416-418

"Seamy rock" in building code, 349

Seismicity, reservoir induced, 87, 172

Serpentinite, 20, 21

Shale, 144-146

bearing capacity, 350

compressive and tensile strength, 37, 61

ductility, 74

Hoek-Brown constants, 99

modulus ratio and Poisson's ratio, 140, 186

Mohr-Coulomb parameters, 83

permeability, 35

pore water pressure, induced, 85

porosity, 29, 83

residual strength, 81

swelling pressure, 380

Shear failure, 56

Shear modulus, 182

of jointed rock, 196

Shear zones, 141

Shear stiffness, 163, 196

Shear strength intercept, 81

typical values, 83

variation with direction, 93

Shi, G. H., 257

Shi's theorem, 259, 260

Shield, R. T., 362

Shtenko, V. W., 382

Siltstone, 145, 146

compressive and tensile strength, 61

Mohr-Coulomb parameters, 83

porosity, 83

Size effect on strength, 90-93, 229

tests, 90, 91, 231, 233

Skinner, E. H., 42

Slake durability classification, 38

Slaking,37

Slate,20

anisotropy in strength, 93

bearing capacity, 350

Inde~ 561

Lundborg's strength parameters, 90

Mohr-Coulomb strength parameters, 83

Snow, D. T., 35

Sonic velocity, 39-42

Sowers, G., 39, 378

Specific gravity, 30-33

Spillways, 9

Splitting tension test, see Brazilian test

Squeezing ground, 104, 286

Stability analysis:

of block on aplane, 312-319

of general polyhedron, 325-331

of 2d active/passive system, 333-334

of 2d block, 287

of wedge, 319-320

Stagg, K. G., 189

Standards, 17

for compression tests, 60

Stephenson, D. E., 117

Stereographic projection, 475-493

equations for drawing great circles, 261

joint orientation analysis, 150-154

of joint system, 263

kinematic analysis of slopes, 301-310

limit equilibrium analysis for a given JP,

325-331

roughness angles of joints, 167

stability analysis of slopes, 312-320

Stereonet, 479, 480

Stiffness of joints, 196

of testing machines, 76

Strain in two dimensions, 409-413

Strength, 34, 36, 37, 76

Stress concentrations, 225, 228-231

Stresses, manipulation and operations,

389-408

Stress history related to sedimentation and

erosion, 176

Stresses in the crust map, 112

Stress measurement, 116, 117

complete state of stress, 132-135

doorstopper test, 127-129

flat jack method, 121-123

hydraulic fracturing, 117-121

inclusion methods, 116, 127

overcoring, 123-127

undercoring, 130, 131

Page 289

562 Inde~

Stress-strain relations:

deviatoric values in terms of, 218

elastic, 181

for jointed rock, 195-197, 220

viscoelastic, 206

Strike and dip, defined, 400

Subsidence over old mines, 379

Swelling rock, 380-382

mineral s responsible for, 343, 419

Syenite, 33

Ta ehien dam site, 147

Taylor, H. W., 46

Temperature gradient in ground, 220

Tensile failure, 56, 57

Tensile strength, 82, 119

Terratek, Inc., 12,64,92

Terzaghi, K., 242

Terzaghi, R., 153

Three-dimensional analysis of stresses in situ,

134, 135

Tiedemann, H. R., 42

Timoshenko, S., 189, 468

Tincelin, M. E., 121

Toews, N. A., 126, 135

Topographic effects on stresses, 102,

104, 105, 107

Toppling failure, 298-300

kinematic analysis, 304-306

Tourenq, e., 65

Townsend, F. e., 81

Transversely isotropic rock, 183

Triaxial compression:

equipment, procedures, 61-65

for joints, 160-164

Tributary area, 231, 232

Trona, 20

Tuff,20

compressive and tensile strength, 61

modulus ratio and Poisson's ratio, 186

porosity, 29

Tunnel support spectrum, 274-280

Twin gliding, 74

Two block sliding analysis of slopes, 333, 334

Unconfined compressive strength, see

eompressive strength

Undercoring, 130, 131

Underground openings:

circular, elastic rock, 220, 225

circular, plastic rock, 242-249, 454-464

elliptical, oval, rectangular, 230

spherical, 230

time dependency, creep, 250-256

U.S. Bureau of Mines gage, 124

Van Heerden, W. L., 91

Velocity of sound in rocks, 39-42

longitudinal ve!ocity in minerals, 40

Virgin stresses, see Initial stress

Viscoelasticity:

spring and dashpot models, 204-206

and stress measurement, 117

Viscosity, 202

for water, 34

Vogler, U. W., 61

Voight, B., 116

Volcanic rocks, 20. See alsa individual

rack type

point load strength, 37

Volumetric strain, 68

Wagner, P. L., 546

Water, effect on rock strength, 84-87

Water loss coefficient, 52

Wave equation, 442

Wave velocity, 39-42

Wawersik, W. R., 69, 71

Weathering:

effect on foundations, 341, 343

effect on porosity, 24, 28, 30

Wedge slides, 295-297

kinematic analysis, 304

stability analysis, 319, 320

Wickham, G. E., 42

Willett, D. e., 224

Wilson, L. e., 385

Wittke, W., 318

Woodward, R. J., 370, 377

X-ray measurement of stresses, 117

Young's modulus, 181

fractured or jointed rocks, 195-202

measurement, 183-195

ratio to compressive strength, 186

variation with strain, 185

Yudhbir,99

Zaruba, Q., 132

Zienkiewicz, O. e., 189,352

Zoback, M., 112

.

. "' . .." . .,; 1'",

:t~ ~, . - " .

" .. ' .. '.' "., ,t ., ., n ' c... . • -ffll,.'t: a- • ..., ~- '

~. -' , . '. :.... .

.' 1"',_ ,: '. '1' •. ,. ~, . ' ,', ~,. ::~~

. . .

. . .

. Mechanic$

r

Page 2

'. {. ,

Introduction to

Rock Mechanics

Second Edition

Richard E. Goodman

University of California at Berkeley

Jahn Wiley & Sans

New York I Chichester I Bri.bane I Toronto I Singapore

.. , .".

. . "

Page 144

272 Applications of Rock Mechanics in Engineering for Underground Openings

E

w E

lb)

Figure 7.28 (b) Projection in the tunnel

section of the maximum remoyable block

corresponding to JP 010.

limit plane must pass through both the comer and its opposite. Ifthe comer has

distance x from the center of the reference circle, its opposite has distance R2/X

from the center in the opposite direction (where R is the radius ofthe reference

circle). In the case of Figure 7.28a, the lP lies inside each of the enveloping

great circles, so the lP is above both of them. The angles of inclination of the

orthographic projections of the comers in the tunnel section are transferred to

the tunnel section in Figure 7.28b, and the removable block is found as the

region simultaneously aboye each. In this case, the maximum removable block

is not a key block if gravity is the main contributor to the resultant force

direction in the block.

Figure 7.29a shows a similar construction but for lP 001. The comer 1,2 of

this lP is off the paper so its opposite -1'2 has been drawn. (The opposite is the

upper hemisphere line that is perpendicular to both ofthe normal s n, and n2 and

therefore perpendicular to the great circle connecting normals n, and n2.) Great

circles through each comer in tum intersect the tunnel section at the points

shown and the limiting great circles are established as those through lz3 and 113 ,

intersecting the tunnel section respectively 24° aboye east and 83° aboye west.

The lP is outside the first of these and inside the second so JP 001 is below the

first and aboye the second. Figure 7.29b transfers this information to the tunnel

section.

7.S Underground Openings in Blocky Rock-"Block Theory" 273

Having performed an analysis of maximum key block s for two lPs, we now

proceed to find all the rest. Since JPs 000 and 111 contain the tunnel axis, they

have no maximum key block areas in the tunnel section. The maximum key

block regions of all the other lPs are shown on Figure 7.30, where each tunnel

section is drawn in the curved polygon corresponding to the lP in question. We

.

· · ·

. . .

N

....... t. ............ ~./Aa .......

.... --....-. .... ," , ....

..... ,." l' ....

.. ' "" l' ....

.... ",,"" I , ....

.

...... / I \\ ..... \------

... // I \ \\-----

/ I \ ... ~----

/ I ,

I I \

" " \ ® í' ' - 12 ,

I ,

I

I

I ,

JP 001

~----7-- Tunnel

section

Limit plane 2 ,

~

• I

~ I

'. ;<.......

.... -1 1" ;1' " "'- .' .7 •• -----

•••• 13 ." "" Lim it plane 1

_ 11'"' , •• '

: A

123 .-

~.~----~~-----~--

/ .'

Reference

circle

/{/ ..... 1" ....

.... J .."",. ~ ..... . ~-- .

~···· •••••••••••••••••• II ••• ••••

(a)

JP 001 is below limit plane 1

and aboye limit plane 2

Figure 7.29 (a) Construction for the projections of the edges of the maximum

remoyable block in the tunne! section, corresponding to JP 001.

Page 145

274 Applications of Rock Mechanics in Engineermgfor Underground Openings

W------~~--~~--~--------E

(b)

Figure 7.29 (h) Projection in the tunnel

section of the maximum removable block

corresponding to lP 001.

see at a glance that under gravity loading JPs 101, 100, and 001 may generate

block s that require support. A1though these drawings are two dimensional, the

three-dimensional maximum keyblocks can be drawn corresponding to each of

thesejoint pyramids and subjected to a limit equilibrium analysis. The direction

of sliding under gravity is determined by a mode analysis, based upon the

direction of the resultant force and the description of the joint pyramid, as

discussed by Goodman and Shi (1985). Then when friction angles are input on

each face, the support force vector can be computed for each maximum key

block using methods of analysis discussed in the next chapter. It may be that

none of the blocks require support; on the other hand, in certain tunnel direc-

tions, the same set of joint planes and friction angles may create the need for a

large support force. This is largely due to the changing size of the maximum key

block s as the direction of the tunnel is varied.

CASE HISTORY--"TUNNEL SUPPORT SPECTRUM"

The effect of tunnel direction on rock mass support requirements will be illus-

trated for the rock mas s of Figure 7.20 by studying the SUpport force for

7.S Underground Openings in Blocky Rock-"Block Theory" 275

Figure 7.30 Tunnel sections showing maximum removable block s for each lP super-

imposed on the stereographic projection of the lPs.

equilibrium of the most critical block as a function of a complete sweep of

tunnel directions. AH the examples considered thus far correspond to a hori-

zontal tunnel axis in direction N 21 0 E. Consid~ring only horizontal tunnels, for

the time being, we can observe the relative size of the most critical key block,

for five tunnel directions, in Figure 7.31. The maximum key block s become

d.ramaticaHy larger as the direction 3150 (N 450 W) is approached. Limit equilib-

num analysis of this system, for a horseshoe tunnel 6 m wide and 5.4 m high,

yields required support forces for the maximum k~y block varying from a low

of less than 1 me trie ton per meter length of tunnel, to a maximum of 33 metric

Page 288

560 Inde~

Photoelastic stress gage, 116

Piles and piers, 346

load distribution in, 370-374

load tests, 372, 373

settlement of, 376, 377

Pillars, 231

Plane sliding, see Block sliding

Plane stress and plane strain, 452

Plastic analysis of tunnels, 242-249, 454-464

Plate bearing test, 188-190

Point load index, 36

Poisson's ratio, 67, 181

measurement, 184

for permanent and total strain, 220

typical values, 186

variation with deviatoric compression,

70, 185

Pore "crush-up", 69

Pore pressure:

and fault slip, 171-173

and rock failure, 85, 86

and stress measurement, 140

Porosity:

effect of age on rocks, 29

measurement, 31

types of pore spaces, 13, 28, 29

values for selected rocks, 29, 83

and water content, 32

Poulos, H. G., 352, 370

Pratt, H. R., 91, 92

Principal strains, 412

Principal stresses, 133, 134, 393,402,403

Principal stress ratio:

effect on strength, 74-76, 87

initial values, 106-113

Principal symmetry directions, 182

Punching failure of footing, 351, 352

, Q system (classification), 47-49

Quartzite, 142, 144

compressive and tensile strength, 61

Hoek-Brown constants, 99

Lundborg's strength parameters, 90

modulus ratio and Poisson's ratio, 186

Mohr-Coulomb parameters, 83

Radial jacking test, 191

Radial permeability test, 34, 35

Raleigh, C. B., 172

Rangeley oil field, 172

Raphael, J., 363

Rate of load effects, 213-215

Reichmuth, D. R., 62

Relaxation, 203

Removable blocks, 258

Rengers, N., 166, 167, 169

Reservoir induced seismicity, 86, 171-172

Residual strength, 81, 161

Residual stresses, 116

Rhyolite, 20

density, 33

Riley, P. B., 116

Ring shear test, 66, 88-90

Roberts, A., 116

Rocha, M., 36, 116, 121, 134

Rock boIt design:

to control plastic zone of tunnels, 246

to prevent slip of joints in tunnels, 241

for rock slope stability, 279, 283, 317-319

to secure roof beams in layered rock, 236,

237, 281, 290, 334, 387

Rock bursts, 102

Rock classification:

comparison of Q and RMR, 47

fabrics, 20, 21

fissuring, 39-42

geological, 19, 419-425

NGI (Q) system, 47

RMR (Geomechanics) system, 43-46

for tunneling, 43-47

Rock loosening, 53, 247

Rock mas s rating, see Geomechanics

classification

Rock noise, 69

Rock reinforcement, 249. See also Rock bolt

design

Rock slopes:

buckling of, 337

types, 293, 294

Rock socket, 345, 371, 377

Rock test preparation equipment, 58, 59

Roof beams, buckling of, 233

Roof design, underground, 233-237

Rosettes, strain gages, 411, 412

RQD,44 '

Rummel, F., 63

Rutter, E. H., 206

Safety, see Factor of safety

Salem, A., 190

Sallstrom, S., 419

Salt, 15

creep properties, 252

density, 252

ductility, 74

Sandstone, 143, 144, 146

compressive and tensile strength, 61

(

foundations, 349, 350

Hoek-Brown constants, 99

joints in, 146

modulus ratio and Poisson's ratio, 186

Mohr-Coulomb parameters, 83

permeability, 35

point load strength, 37

porosity, 29, 83

in triaxial compression, 75

Schist, 8, 20, 21, 161

bearing capacity, 350

compressive and tensile strength, 61

density, 33

modulus ratio and Poisson's ratio, 186

permeability, 35

Schistosity, 13

and strength, 61, 83

Schneider, B., 147, 190, 199-201

Schneider, H. J., 157, 168, 169

Scratch hardness, 416-418

"Seamy rock" in building code, 349

Seismicity, reservoir induced, 87, 172

Serpentinite, 20, 21

Shale, 144-146

bearing capacity, 350

compressive and tensile strength, 37, 61

ductility, 74

Hoek-Brown constants, 99

modulus ratio and Poisson's ratio, 140, 186

Mohr-Coulomb parameters, 83

permeability, 35

pore water pressure, induced, 85

porosity, 29, 83

residual strength, 81

swelling pressure, 380

Shear failure, 56

Shear modulus, 182

of jointed rock, 196

Shear zones, 141

Shear stiffness, 163, 196

Shear strength intercept, 81

typical values, 83

variation with direction, 93

Shi, G. H., 257

Shi's theorem, 259, 260

Shield, R. T., 362

Shtenko, V. W., 382

Siltstone, 145, 146

compressive and tensile strength, 61

Mohr-Coulomb parameters, 83

porosity, 83

Size effect on strength, 90-93, 229

tests, 90, 91, 231, 233

Skinner, E. H., 42

Slake durability classification, 38

Slaking,37

Slate,20

anisotropy in strength, 93

bearing capacity, 350

Inde~ 561

Lundborg's strength parameters, 90

Mohr-Coulomb strength parameters, 83

Snow, D. T., 35

Sonic velocity, 39-42

Sowers, G., 39, 378

Specific gravity, 30-33

Spillways, 9

Splitting tension test, see Brazilian test

Squeezing ground, 104, 286

Stability analysis:

of block on aplane, 312-319

of general polyhedron, 325-331

of 2d active/passive system, 333-334

of 2d block, 287

of wedge, 319-320

Stagg, K. G., 189

Standards, 17

for compression tests, 60

Stephenson, D. E., 117

Stereographic projection, 475-493

equations for drawing great circles, 261

joint orientation analysis, 150-154

of joint system, 263

kinematic analysis of slopes, 301-310

limit equilibrium analysis for a given JP,

325-331

roughness angles of joints, 167

stability analysis of slopes, 312-320

Stereonet, 479, 480

Stiffness of joints, 196

of testing machines, 76

Strain in two dimensions, 409-413

Strength, 34, 36, 37, 76

Stress concentrations, 225, 228-231

Stresses, manipulation and operations,

389-408

Stress history related to sedimentation and

erosion, 176

Stresses in the crust map, 112

Stress measurement, 116, 117

complete state of stress, 132-135

doorstopper test, 127-129

flat jack method, 121-123

hydraulic fracturing, 117-121

inclusion methods, 116, 127

overcoring, 123-127

undercoring, 130, 131

Page 289

562 Inde~

Stress-strain relations:

deviatoric values in terms of, 218

elastic, 181

for jointed rock, 195-197, 220

viscoelastic, 206

Strike and dip, defined, 400

Subsidence over old mines, 379

Swelling rock, 380-382

mineral s responsible for, 343, 419

Syenite, 33

Ta ehien dam site, 147

Taylor, H. W., 46

Temperature gradient in ground, 220

Tensile failure, 56, 57

Tensile strength, 82, 119

Terratek, Inc., 12,64,92

Terzaghi, K., 242

Terzaghi, R., 153

Three-dimensional analysis of stresses in situ,

134, 135

Tiedemann, H. R., 42

Timoshenko, S., 189, 468

Tincelin, M. E., 121

Toews, N. A., 126, 135

Topographic effects on stresses, 102,

104, 105, 107

Toppling failure, 298-300

kinematic analysis, 304-306

Tourenq, e., 65

Townsend, F. e., 81

Transversely isotropic rock, 183

Triaxial compression:

equipment, procedures, 61-65

for joints, 160-164

Tributary area, 231, 232

Trona, 20

Tuff,20

compressive and tensile strength, 61

modulus ratio and Poisson's ratio, 186

porosity, 29

Tunnel support spectrum, 274-280

Twin gliding, 74

Two block sliding analysis of slopes, 333, 334

Unconfined compressive strength, see

eompressive strength

Undercoring, 130, 131

Underground openings:

circular, elastic rock, 220, 225

circular, plastic rock, 242-249, 454-464

elliptical, oval, rectangular, 230

spherical, 230

time dependency, creep, 250-256

U.S. Bureau of Mines gage, 124

Van Heerden, W. L., 91

Velocity of sound in rocks, 39-42

longitudinal ve!ocity in minerals, 40

Virgin stresses, see Initial stress

Viscoelasticity:

spring and dashpot models, 204-206

and stress measurement, 117

Viscosity, 202

for water, 34

Vogler, U. W., 61

Voight, B., 116

Volcanic rocks, 20. See alsa individual

rack type

point load strength, 37

Volumetric strain, 68

Wagner, P. L., 546

Water, effect on rock strength, 84-87

Water loss coefficient, 52

Wave equation, 442

Wave velocity, 39-42

Wawersik, W. R., 69, 71

Weathering:

effect on foundations, 341, 343

effect on porosity, 24, 28, 30

Wedge slides, 295-297

kinematic analysis, 304

stability analysis, 319, 320

Wickham, G. E., 42

Willett, D. e., 224

Wilson, L. e., 385

Wittke, W., 318

Woodward, R. J., 370, 377

X-ray measurement of stresses, 117

Young's modulus, 181

fractured or jointed rocks, 195-202

measurement, 183-195

ratio to compressive strength, 186

variation with strain, 185

Yudhbir,99

Zaruba, Q., 132

Zienkiewicz, O. e., 189,352

Zoback, M., 112