Principal Symbols. f. Skin friction G Shear modulus. Cu Coefficient of uniformity Cc Coefficient of curvature

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1 Principal Symbols A, a Area A Air content A, A Pore pre.ssure coefficients a' Modified shear strength parameter (effective stress) a Dial gauge reading in oedometer test B Width of footing B, B Pore pressure coefficients Cu Coefficient of uniformity Cc Coefficient of curvature c. Isotropic compressibility of soil skeleton C. 0 Uni-axial compressibility of soil skeleton Cv Compressibility of pore fluid Cc Compression index C~ Rate of secondary compression c Shear strength parameter c" Undrained (total stress) shear strength parameter c' Drained (effective stress) shear strength parameter c~ Drained residual shear strength parameter cw Wall adhesion cv Coefficient of consolidation (vertical drainage) ch Coefficient of consolidation (horizontal drainage) D Depth of footing; depth of excavation D Depth factor D Particle size Db Depth of embedment of pile in bearing stratum d Length of drainage path d Diameter E Young's modulus e Void ratio e Eccentricity F Factor of safety f. Skin friction G Shear modulus 408

2 G, Specific gravity of solid particles g 9 8 m/s 2 H,h Height H Layer or specimen thickness h Total head I Influence factor Ip Plasticity index (or PI) IL Liquidity index (or LJ) In Relative density (or RD) IB Brittleness index i Hydraulic gradient i Inclination factor J Seepage force j Seepage pressure K Bulk modulus K Lateral pressure coefficient KA Active pressure coefficient Kp Passive pressure coefficient Ko Coefficient of earth pressure at rest K Absolute permeability k Coefficient of permeability L, l Length LL Liquid limit (or wl) LI Liquidity index (or IL) M Mass mv Coefficient of volume compressibility N Normal force N Standard penetration resistance Nd Number of equipotential drops N~ Number of flow channels NY Bearing capacity factor Nc Bearing capacity factor Nq Bearing capacity factor N, Stability coefficient n Porosity nd Equipotential number PA Total active thrust Pp Total passive resistance PL Plastic limit (or wp) PI Plasticity index (or Jp) p Stress invariant 409

3 p Pressure PA Active pressure PP Passive pressure Po At-rest pressure Q Surfaceload Q 1 Ultimate load q Flow per unit time q Stress invariant q Surface pressure; total foundation pressure qn Net foundation pressure qa Allowable bearing capacity q 1 Ultimate bearing capacity qnf Net ultimate bearing capacity qc Cone penetration resistance R, r Radius RD Relative density (or /D) r Compression ratio r u Pore pressure ratio S, Degree of saturation s Shape factor s Settlement sc Consolidation settlement s; Immediate settlement T, Time factor (vertical drainage) T, Time factor (radial drainage) t Time U Boundary water force U Degree of consolidation u, uw Pore water pressure ua Pore air pressure V Volume v Specific volume v Discharge velocity v' Seepage velocity W Weight w Water content wl Liquid limit (or LL) wp Plastic limit (or PL) z Depth coordinate z Elevation head a' Modified shear strength parameter (effective stress) 410

4 lx Angle of wall inclination lx Skin friction coefficient p Skin friction coefficient p Slope angle y Shear strain y Unit weight y 4 Dry unit weight Ysat Saturated unit weight y' Buoyant unit weight Yw Unit weight of water {J Angle of wall friction e Normal strain '7 Dynamic viscosity " Slope of isotropic swelling/recompression line A. Slope of isotropic normal consolidation line Jl. Settlement coefficient M Slope of critical state line v Poisson's ratio p Bulk density Pd Dry density Psat Saturated density Pw Density of water u Total normal stress u' Effective normal stress u 1, u 2, u 3 Total principal stresses u~, u~, u3 Effective principal stresses t Shear stress t 1 Shear strength; peak shear strength t, Residual shear strength 4> Potential function 4> Shear strength parameter 4>u Undrained (total stress) shear strength parameter 4>' Drained (effective stress) shear strength parameter 4>; Drained residual shear strength parameter x Parameter in effective stress equation for partially-saturated soil t/1 Flow function 411

5 Answers to Problems Chapter SW, MS, ML, CV, (SW, SM, ML, CH) , 46 6%, 2 10 Mgjm\ 20 4% kn/m 3, 19 1 kn/m 3, 9 9 kn/m 3, 18 7 kn/m\ 19 3% % Mg/m 3, 0 38, 83 7%, 4 5%; no %, 1 83 Mg/m 3, 3-5% Chapter x 10-8 m/s x 10-6 m 3 /s (perm) x to-s m 3 /s (perm), 316kN/m x 10-6 m 3 /s (perm) x 10-6 m 3 /s (perm) 2.6 H x 10-6 m 3 /s (perm) x 10-s m 3 /s (perm) x 10-s m3js (perm) Chapter kn/m kn/m 2, 33 4 knjm kn/m (a) 94 0 kn/m 2, kn/m 2, (b) 94 0 knjm 2, kn/m kn, 73o below horizontal kn/m 2, 10 6 knjm , 14 kn/m 2, 90 knjm , 0 65 m Chapter kn/m

6 kn/m2, oo 205 kn/m J..o 170 kn/m2 ' 2 ' 15 kn/m 2, kn/m , 0 23 Chapter kn/m kn/m kn/m kn/m kn/m 5.6 7mm Chapter kn/m, 122 kn/m kn/m, 8 57 m kN/m, 160kN/m kn/m 2, 69 kn/m 2, m kn/m 2, 35 kn/m 2, 1.2, m, 226 kn , 321 kn kn Chapter Cv = 2 7, 2 6m 2 /year, mv = 0 98m 2 /MN, k = 8 1 X m/s mm, 38 mm (four sublayers) years, 0 95 years kn/m mm, 95 mm mm, 38 mm, 72 mm, 65 mm mm (six sublayers) years, 0 7 years 413

7 Chapter knfm knjm , , kn , 5 3, kn/m mm, 22 mm kN kN kn Chapter , , ,

8 Index Active pressure, 187 Active Rankine state, 188 Activity, 8 Adsorbed water, 4 Air content, 26 Allowable bearing capacity, 294 of clays, 308 of sands, 309 Anchored sheet pile walls, 216 Angle of shearing resistance, 107 Angular distortion, 295 Apparent cohesion, 107 Arching, 222, 330 Artesian conditions, 39, 393 Augers, 388 Back pressure, 118 Band drains, 285 Base failure in excavations, 225, 307, 349 Bearing capacity, 294 allowable, 294, 308, 309 factors, 30 l of piles, 327 ultimate, 296 Bearing value, presumed, 295 Bell's analysis for slopes, 372 Bentonite, 225 Bernoulli's theorem, 39 Bishop's method of slices, 365 Boiling, 99 Bookhouse structure, 5 Boreholes, 386, 388, 390, 391 Borehole logs, 400 Borehole tests, 45 Boundary water force, 95 Boussinesq equations, 165 Braced excavations, 223 British soil classification system, 15 Brittleness index, 145 Buisman-DeBeer method, 321 Bulb of pressure, 169, 336 Bulkheads, 216 Buoyant unit weight, 28 Cantilever retaining walls, 207 Cantilever sheet pile walls, 216 Capillary rise, 39, 90 Casing, 312, 388 Cation exchange, 3 Chimney drain, 74 Chisel, 386 Classification of soils, 10 Clay, 5, 13, 14, 16, 21, 41, 122, 136, 143, 199,225,240,295,308,331,337, 346,352,373 Clay cutter, 388 Clay minerals, 1 Coarse-grained soils, 6 Coefficient of consolidation, 260, 265 Coefficient of curvature, 7 Coefficient of permeability, 40, 265, 270 Coefficient of uniformity, 7 Coefficient of volume compressibility, 241 Cohesion intercept, 107 Cohesive soil, 5 Compaction, 30 equipment, 34 in the field, 36 standard tests, 30 Compatibility equation, 160 Compressed air sampler, 398 Compressibility characteristics, 240 Compression index, 241 Compression ratios, 269 Cone penetration resistance, 319, 331 Consolidated-undrained triaxial test, 117 Consolidation, 88, 114, 122, 237 analogy, 89 Terzaghi's one-dimensional theory,

9 Consolidation settlement, 237, 308, 338 one-dimensional method, 246 Skempton-Bjerrum method, 249 Constant head permeability test, 42 Constant rate of penetration test, 335 Construction period correction, 274 Continuity equation, 48 Continuous sampler, 398 Coulomb theory of earth pressure, 201 Critical hydraulic gradient, 97 Critical state, 136, 145, 162, 374 Darcy's law, 40 Deformation requirements of Rankine theory, 200 Degree of consolidation, 257 Degree of saturation, 25 Density, 26 Diaphragm walls, 225 Differential settlement, 294, 309 Dilatancy test, 12 Direct shear test, 110 Discharge velocity, 40 Dispersed structure, 4 Displacements from elastic theory, 176 Dissipation, 88 Double layer, 4 Drainage, 88 Drained condition, 88, 118, 190, 372 Drained triaxial test, 117 Dry density/water content relationship, 30 Dry strength test, 12 Dutch cone test, 319 Dynamic consolidation, 347 Earth dams: pore pressure conditions, 376 seepage control, 73 seepage theory, 67 stability, 376 Earth pressure at rest, 197 Earth pressure coefficients, 206, 208 Earth-retaining structures, 207 Eccentric loading of foundations, 303 Effective size, 7, 41 Effective stress, 84 in partially saturated soils, 93 principle of, 84 Elastic modulus, 163 Elasticity, 159 Electrical resistivity method, 405 Elevation head, 39 Embankments, 30, 284, 375 Equilibrium equations, 160 Equipotentials, 49 Excavations, 223, 307, 347, 373 Excess pore water pressure, 88, 118, 258,332,337,373,376 Expansion index, 241 Fadum's chart, 172 Failure envelope, 108 Falling head permeability test, 42 Fellenius method of slices, 365 Filter cake, 226 Filter requirements, 74 Fine-grained soils, 6 Fissured clay, 41, 124, 332, 374 Flocculated structure, 4 Flow function, 49 Flow lines, 50 Flow nets, 52 Flow rule, 162 Footings, 294 Foundation pressure, 302 Foundations, 294 factor of safety, 294, 302, 308, 309 fundamental requirements, 294 significant depth, 296, 385 Free earth support method, 217 Frost heave, 79 Cap-graded soil, 7 General shear failure, 297 Geophysical methods, 402 Graded filter, 75 Gravel, 5, 13, 14, 16, 20, 41, 295 Gravity retaining walls, 207 Grid rollers, 35 Ground anchors, 218, 350 Ground investigation, 384 Group symbols, 18, 19 Grouting, 78 Half-closed layer, 261 Headings, 386 Heaving, 98,

10 Horizontal drainage layers, 377 Hvorslev surface, 139 Hydraulic gradient, 40, 52 Hydraulic oedometer, 270 Illite, 3 Immediate settlement, 178, 237, 249, 308 Impermeable blanket, 74 Inclined loading of foundations, 303 Initial compression, 266 Isochrones, 261 Isomorphous substitution, 2 Isotropic consolidation, 122 Kaolinite, 3 Kozeny's basic parabola, 71 Limit theorems of plasticity, 184 Limiting equilibrium, 201, 360 Liquid limit, 8 Liquidity index, 8 Local shear failure, 297 Log time method, 266 Lower bound theorem, 184 Maintained load test, 335 Method of slices, 363 Mohr-Coulomb failure criterion, 107 Moisture content, 25 Montmorillonite, 3 Morgenstern-Price analysis for slopes, 371 Negative skin friction, 344 Newmark's chart, 173 Normally consolidated clay, 123, 129, 137,148,162,240,253,272,309, 333,361 Oedometer test, 238, 270 Open drive sampler, 395 Open layer, 261 Optimum water content, 31 Organic soil, 12, 13, 14, 16, 21 Overconsolidated clay, 123, 129, 139, 149,162,240,253,309,333,374 Overconsolidation ratio, 123 Particle shape, 1, 13 Particle size, 5 Particle size analysis, 6 Passive pressure, 188 Passive Rankine state, 188 Peat, 12, 13, 14, 15, 16, 21 Penetration tests, 312, 319, 331 Perched water table, 39, 393 Percussion boring, 386 Permeability, 40 Phase relationships, 25 Phreatic surface, 39 Piezometers, 152, 237, 270, 376, 393 Piles, 294 bearing capacity, 327 driving formulae, 339 groups, 335 load factor, 328, 333 load tests, 335 settlement, 337 Piping, 73 Plane slip analysis, 369 Plane strain, 155 Plastic equilibrium, 183, 297 Plastic limit, 8 Plasticity, 7 Plasticity chart, 17, 19 Plasticity index, 8 Plasticity theory, 161, 183, 298 Plate anchor, 218 Plate bearing test, 311 Pneumatic tyred rollers, 34 Poisson's ratio, 163, 249 Poorly graded soil, 7 Pore air pressure, 93 Pore pressure coefficients, 145 Pore pressure ratio, 366 Pore water pressure, 39, 85 Pore water pressure measurement, 115, 152 Porosity, 26 Potential function, 49 Power rammers, 35 Preconsolidation pressure, 241, 272, 309 Presumed bearing values, 295 Pressuremeter test, 163 Primary consolidation, 266 Principle of effective stress,

11 Progressive failure, 374 Punching shear failure, 297 Quick clay, 128 Quick condition, 97 Quicksand, 98 Raft, 294 Rankine's theory of earth pressure, 185 Rapid assessment procedures, 11 Rapid drawdown, 378 Recompression, 124, 240 Reinforced earth, 228 Relative density, 28 Residual shear strength, 143, 374 Residual soil, 1 Resultant body force, 94 Retaining walls, 207 Ring shear apparatus, 144 Rock flour, 1, 5 Root time method, 268 Rotary drilling, 391 Sampling, 394 Sand,5, 13, 14, 16,20,41, 120,199, 224,295,309,329,336,346,351 Sarma's analysis for slopes, 372 Saturation line, 32 Schmertmann's method, 322 Secondary compression, 266, 271 Sedimentation, 6 Seepage, 39 anisotropic soils, 61 basic theory, 47 earth dams, 67 flow nets, 52 force, 94 non-homogeneous soils, 64 pressure, 96 transfer condition, 65 velocity, 41 Seismic refraction method, 402 Sensitivity of clays, 128 Settlement, 178, 237, 246, 249, 255, 294, 308,309,313,321,337 Shafts, 386 Shear strength, 107 in terms of effective stress (of clays), 128 parameters, 107, 122, 128 residual (of clays), 143 sands, 120 saturated clays, 122 tests, 110 undrained (of clays), 124 Sheepsfoot rollers, 34 She11,386 Shrinkage limit, 8 Sieving, 6 Significant depth, 296 Silt, 5, 13, 14, 16, 21, 41, 295, 308, 309, 331 Single grain structure, 1 Skin friction,"327, 331, 332 Slip line field, 186 Slope stability, 359 4>. = 0 analysis, 360 method of slices, 363 Bishop solution, 365 Fellenius solution, 365 plane slip analysis, 369 pore pressure conditions, 372 progressive failure, 374 Slurry trench stability, 227 Smooth wheeled rollers, 34 Soil classification, 10 Soil description, 10 Soil fabric, 10, 15, 125, 270, 308, 402 Soil suction, 40, 93 Sokolovski's earth pressure solution, 207 Specific gravity of particles, 26 Specific surface, 1 Specific volume, 26 Split barrel sampler, 312, 397 Standard penetration resistance, 312, 331 Standard penetration test, 312 State boundary surface, 139 Static pore water pressure, 87 Stationary piston sampler, 397 Steady-state pore water pressure, 88 Stokes' law, 6 Strain hardening, 161 Strain softening, 161 Stress paths, 130, 137, 139, 141, 199, 251,255 Stress path method,

12 Stress point, 109 Stresses from elastic theory, 164 circular area, 171 line load, 166 point load, 165 rectangular area, 171 strip area, 169, 170 Surcharge pressure, 190 Swelling, 89, 237, 240 Taylor's slope stability coefficients, 362 Tension zone, 188 Terzaghi's theory of one-dimensional consolidation, 258 Thin walled sampler, 397 Thorburn's SPT correction, 316 Total active thrust, 189 Total head, 39 Total passive resistance, 189 Total stress, 84 Toughness test, 12 Transported soil, 1 Trial pits, 385 Triaxial test, Ill Turbostratic structure, 5 Ultimate bearing capacity, 296 Unbalanced hydrostatic pressure, 221 Unconfined compression test, 115 Unconsolidated-undrained triaxial test, 117 Undrained condition, 88, 118, 178, 191, 249,255,308,372 Unified classification system, 19 Uniform soil, 7 Unit weight, 27 Upper bound theorem, 184 Vane shear test, 119 Vertical drains, 284 Vibrating plates, 35 Vibratory rollers, 35 Vibro-compaction, 346 Vibro-replacement, 346 Virgin compression, 240 Void ratio, 26 Void ratio/effective stress relationship, 122,240 Wall adhesion, 201 Wall friction, 201 Wash boring, 391 Water content, 25 Water table, 39 Wave equation, 340 Well graded soil, 7 Well pumping test, 44 Yield criterion, 161, 178, 324 Young's modulus, 163 Zero-air-voids line,

Introduction to Soil Mechanics

Introduction to Soil Mechanics Sela Sode and Colin Jones WILEY Blackwell Contents Preface Dedication and Acknowledgments List of Symbols Soil Structure 1.1 Volume relationships 1.1.1 Voids ratio (e) 1.1.2