Answers to exercises

Chapter 2

2.1 2.65 Mglm3

2.2 100,99.1,95.9,93.8,90.2,84.4,75.2,63.8, 50.4,38.9,27.8, 15.2,3.8 %

2.3 12.2 %, 2.22 Mglm3, 21.8 kN/m3, 1.98Mgm3,

19.4 kN/m3

2.4 0.38,0.27,88 %,3.3 % 2.5 55 %, 27 %, 28 %, CH 2.6 0.29,0.71

Chapter 3

3.1 8.6 x 10-5 mls 3.2 2.7 x 10-8 mls 3.3 2.4 x 10-7 mls 3.4 60.5 m3/day 3.5 2.9 x 10-5 mls 3.6 8.6 x 10-4 mls 3.7 5 litres/minlm 3.8 23 litres/minlm 3.9 4.0,2.3 3.10 22.5 litreslhour

Chapter 4

4.1 139,98, 41 kN/m2

4.2 90,49,41 kN/m2

4.3 a) 105,29.4, 75.6 kN/m2

b) 195, 78.4, 116.6 kN/m2

4.4 42.8,67.4 kN/m2 4.5 1) 41.1, 69.1, 97.1 kN/m2

2) 57.7, 69.1, 97.1 kN/m2

3) 57.7, 85.7, 113.7 kN/m2

4.6 19.6 kN/m2

4.7 1.0, 1.50, 1.18 4.8 0.96 4.9 0.34,0.58,0.74,0.88,0.95,0.98 4.10 0, 0.22, 0.16, 0.08, 0.01, -0.07, -0.13

350

Chapter 5

5.1 62 kN/m2

5.2 172 kN/m2

5.3 59.2,37.2,9.4 kN/m2

5.4 50,21 kN/m2

5.5 48, 20 kN/m2 5.6 57,23 kN/m2 5.7 45 kN/m2

Chapter 6

6.1 0.856,0.852,0.848,0.840,0.803,0.753, 0.704,0.712,0.726,0.737

6.2 125 kN/m2, 2.2 6.3 0.086,0.087,0.087,0.201,0.138,

0.070m2/MN 0.09,0.15 m2/MN

6.4 0.16 6.5 3.3 m2/year, 0.20 m2/MN, 2.0 x 10-10 mls 6.6 70mm 6.7 a) 12 kN/m2 b) 42 kN/m2 6.8 46mm 6.9 53 weeks 6.10 83 % 6.11 1.35 m

Chapter 7

7.1 57.7,20.2 kN/m2

7.3 24kN/m2

7.4 21.5Q

7.5 15 kN/m2, 39Q

7.6 1.5 7.7 248.1, 238.1, 244.3 kN/m2

124,119,122 kN/m2

7.8 a = 16 kN/m2 a= 30.5Q

c' = 20kN/m2 <p' = 36Q

7.9 a = IOkN/m2 a= 26.6Q

c' = 11.5 kN/m2 tP' = 30Q

7.10 A=0.14 7.11 0.87

N = 2.47

7.12 184 kN/m2

7.13 0.60,0.50 7.14 a) 65, 97 kN/m2

Chapter 8

8.1 a) 586 8.2 2393 kN 8.3 3.1 m 8.4 9.3 8.5 a) 2380 kN/m2

8.6 a) 4065 kN/m2

8.7 a) 4.2 8.8 a) 3.1

Chapter 9

9.1 28 mm, 11 mm 9.2 1) 14mm 9.3 1) 21 mm 9.4 42mm,l2mm 9.5 1) 19 mm 9.6 164mm 9.7 165mm 9.8 41 mm, 14mm 9.9 84mm, 177mm 9.10 19mm,28 mm 9.11 22 mm, 33 mm

Chapter 10

10.1 1086kN 10.2 16.4m 10.3 1477kN 10.4 9498 kN 10.5 a) 4570 kN 10.6 1206 kN 10.7 729 kN

b) 129, 195 kN/m2

b) 686 kN/m2

b) 9.2 b) 15.7 b) 8.0 b) 4.9

2)9mm 2) 23 mm

2) 29 mm

b) 5890kN

Answers to exercises 351

Chapter 11

11.1 96 kN, 1.43 m 11.2 806 kN, 1.76 m 11.3 82 kN, 1.49 m 11.4 1) 86 kN, 1.39 m 11.5 1) 6.4 2) 2.4 11.6 1) 6.5 m 2) 312 kN 11.7 1) 2.5 mm 2) 1.8

Chapter 12 12.1 1.51,1.23, l.l3 12.2 3.53, 2.24, 1.81 12.3 15.7Q 12.4 17 kN/m2

12.5 1.38 12.6 17 kN/m2

12.7 2.5 12.8 302 12.9 1.34 12.10 1.30 12.11 1.90 12.12 1.30

Chapter 13

13.1 14.4 13.2 32,0.8 13.3 1) 16447 m3

2) 1221

2) 18.5 kN 3) 172, 54 kN/m2

3) 303 bankm3/hour, 54.3 hours 13.4 18.5%, 1.76 Mglm3

13.5 0.55,0.35,92%,2.7%

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Skempton, A.W. (1959). Cast in-situ bored piles in London Clay. Geotechnique, 9, p. 153-178.

Skempton, A.W. (1961). Horizontal stresses in an overconsolidated eocene clay. Proc. 5th ICSMFE, Paris, 1, p. 352-357.

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Skempton, A. W. (1964). Long-tenn stability of slopes. Geotechnique, 14, No.2, p. 77-101.

Skempton, A.W. (1966). Summing up. Proc. Symp. on Large Bored Piles, London.

Skempton, A.W. (1986). Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, ageing and overconsolidation. Geotechnique, 36, No.3, p. 425-447.

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358 Soil Mechanics - Principles and Practice

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Index

A parameter, see pressure, parameters abutments, bridge, 254 activity, 28, 29 active pressure, 135,240-241 active thrust, 243-244, 246 adhesion, 184,223-226,246,248,257 aeolian soils, 4 air voids,

content, 31, 317 lines, 19,316,321

allowable bearing pressure, 168 sand, 184-186

allowable settlements, 168, 184, 229 anchors, 260-261 anchored walls, 259-260 angle of shearing resistance, 142

clay, 151 sand,142,226,227,228

angular strain, 210 anisotropic soil, 42 aquicludes, 36 aquifers, 36 area ratio, 146, 147 artesian, 36, 38 at rest, see earth pressure augering, 333-334

see also hand augering

B parameter, see pressure, parameters back pressure, 118, 152 band drains, 119 base-exchange, see cation-exchange basements, 135, 137,252-254 bearing capacity, see also piles, retaining structures

depth factors, 178, 180 eccentric loading, 179-181 effect of compressibility, 183-184 effect of water table, 182 factor of safety, 182-183 factors, 178-179 inclined loading, 181, 182 modes of failure, 176, 177 net ultimate, 182 pile groups, 232-233 safe, 168 shape factors, 178-179 strength cases, 181

theory, 178-184 ultimate, 168

bearing pressure, 182, 184, 255 bedding, 13 bentonite, see montmorillonite boiling, 37, 58-59 borehole record, 347 boulders, 3, 12

description, 16 boulder clay, 3, 321 British Soil Classification System, 12, 13 brucite, 5 bulbs of pressure, 94-95, 230 bulking, 309, 311-312 bulk density, see density

cable percussion boring, 330-331, 332-333, 346, 347, 349 capillaries, 39 capillary rise, 83-84 cation-exchange capacity, 7, 8 CBR,320 chlorite, 7 cohesion, undrained, see strength cohesion intercept, 151, 184, 248-249, 280-281 classification, 12 clay

auger, 333-334 classification, 12-14 content, 27, 148, 160, 172 cutter, description, 12-14, 18 fissured, see fissures minerals, 5-8, 10, 148 partially saturated, 148 sensitivity, 4, 144,205,310-311 settlements, see settlements size, 5 softening, 310-311 soil,5 strength, effective 150 et seq strength, undrained, 143-150 strength, in situ, 149-150, 222 strength, residual, 159-160

cobbles, 5, 12 description, 15-16

coefficient of curvature, 22, 23

359

360 Soil Mechanics - Princivles and Practice

compressibility, 113-114, 200 consolidation, 113-116, 119 consolidation, in situ, 116, 117 permeability, 39-41 secondary compression, 204-205

cofferdams effect of flexibility and propping, 242-243 flow around, 37, 38 flow net, 55 piping, 59-60 stressing on, 241-245 strutted excavations, 261-263

colour, terms, 14 compaction

acceptability, 306 compactive effort, 313-314 field, 314-316, 319 laboratory, 319-321 moisture content, 313 soil type, 314 specification, 316-318

compressibility, 104, 183 compression index, 113-114, 198-200 cone penetrometer, 207, 228, 339-340 consistency

index, 10 limit, 25-29

consolidation analogy, 80 cell, 116-118 coefficient of, 113-116, I 19 curve-fitting, 114-116 degree of, 110-111, 120 in situ curve, 106-107 in triaxial text, 152 isochrones, 111 oedometer test, 111-113 one-dimensional theory, 109-111 radial, 119-121 settlement, 198-200 two and three dimensional, 118 void ratio-pressure plot, 104-107

constant head test, 43, 46-47, 49-50 contact pressure, 91-92 contaminated soils, I, 329, 345 coring, rotary, 334-335 crib wall, 254 critical depth, 226-227 critical hydraulic gradient, 59 critical state, theory, 153-159 cuttings, 135, 136, 137,274,276,277

see also slope stability

damage to buildings, 210-212 deflection ratio, 210-212 density, 8, 15,22-24

bulk, 10, 22-24, 31, 113 dry, 10,31,113,313-314,321 in situ, 10 maximum, 10 minimum, 10 relative, 9-10, 142, 184

depth correction, 195, 196, 201 factors, 178,201,207,235 of exploration, 330 of foundations, 172-176 pile group, 235

description, 12-18, 346, 347, 349 desiccated crust, 75-76 desk study, 328-329 dewatering, 37 differential settlement, 209, 211 dilatancy, 14, 15, 130, 139-140, 144, 226 discontinuities, 13, 14 dispersed structure, 11 disturbance, 106, 143, 147,222,335,337 drainage

drained condition, 133-136, 137, 151, 157 gravity, 37, 285 in hydraulic cell, 117 stress change, due to, 79-80, 133-137 undrained condition, 133-136, 137, 157,248, 250, 281-284

drained, see drainage drawdown, 50-51 drumlins, 4 dunes, 4

earth dams, see also slope stability, earthworks flow through, 37, 38, 60-61 stability, 137,275-276,279,290-291

earth pressure active, 135,240-241 at rest, 76-79, 108, 135, 139, 154-156,226,

240,242,341 coefficients, 246-247 due to surface loads, 251, 252 passive, 135,241-242

earthworks acceptability, 305, 306-309 bulking, 309, 311-312 construction plant, 303-304, 308 efficiency, 306, 309, 310

material requirements, 304, 306 Mev, 307-309 softening, 309-311

eccentric loading, see bearing capacity effective

area, 179-181, 184 size, 23, 40

embankments, see also earth dams, slope stability, earthworks

stability, 137,275,276 equivalent

raft, 235 fluid pressure, minimum, 248-249

erosion, 3, 71,175-176 excavations, see also cuttings

flow into, 37 stability, 38,135,137,274 strutted, 261-263

factor of safety, 130, 168, 182-183, 184, 196,229,255, 259,265,294 failure modes, 176-178, 221-222, 232, 254-256 falling head test, 44, 46-47 falls, 274, 275 fill, I filters, 37 fines, 13, 22 fissures, 4, 10, 13, 136, 148-149, 222, 307 flocculated structure, II flow nets, 53-56 flow slides, 274, 275 fluvio-glacial drift, 4 foundation

allowable settlement, 209-212 depth, 168, 172-176 effect of tree roots, 172-175 pad, 170-171 pier and beam, 169 raft, 91-92,168,171,172 spread, 168 stiffness, 91-92, 230-231 strip, 169-170

freezing/thawing, 4, 175

gabion walls, 253, 254 gibbsite, 5 glacial deposits, 3 gleying,4 grading, see particle size distribution gravel, 3, 5, 12

correction for, 25, 321 description, 15-16, 18

gravity walls, 254-257

groundwater, see also water table occurrence, 36 lowering, 37, 50-51 observations, 346

halloysite, 7, 8, 15 hand augering, 330, 331-332, 346 head, 39, 40, 57 heave, 209 heaving, 38, 224 humus, 12 Hvorslev surface, 155,158-159 hydraulic consolidation cell, 44-46, 116-118 hydraulic gradient, 39-40

critical, 59 ice

soils deposited by, 3 lenses, 175

illite, 7, 8, 29 inclined loading, see bearing capacity

Index 361

index tests, see liquid, plastic and shrinkage limits in situ curve, 106-107 in situ testing

Dutch cone penetrometer, 339-340 pressuremeter,341-342 SPT,339

instrumentation, see piezometers isochrones, II I isomorphous substitution, 7

joints, see discontinuities

kaolinite, 7, 8, 29 Ko condition, see earth pressure at rest

laminated clay, 4,10, 13, 136 layered profiles, 42, 221, 281 layering, principle of, 192, 194 leaching, 4 line load, 92, 93 liquidity index, 10, 26 liquid limit, 10, 14, 17,25,26-27,200 local shear failure, 176, 177 loess, 5 log-time method, 114-116, 125

made ground, I, 12, 18, 276 method of slices, 282-283, 284-286 middle third rule, 255-256 minimum and maximum

density, 10 pressures, 255-256

model, soil, 29-30, 313

362 Soil Mechanics - Principles and Practice

modulus drained, 203 increasing, 195, 197 undrained, 198,341-342

Mohr-Coulomb relationship, 132, 147,227 Mohr's circle, 76, 77 moisture condition value, 307-309 moisture content, see water content montmorillonite, 7, 8, 29, 205, 222 mudflows, 274

Normally consolidated clay, 72-74, 76, 78,105-106,150, 151-153,157,177,199,223,277,278 oedometer

test, 111-113 settlement, 200

organic soils, see peat outwash deposits, 4 overconsolidated clay, 74, 78,105-107,130,149-150, 151-153,158,177,199,223,277,278 overconsolidation ratio, 74-75, 78, 105 overturning, 178-179,255,265

packer test, see permeability packing, state of, 8- 10, 141-142 particle, 5

clay, 10 density, 17, 19,31,32 effect on strength, 141-142 shape, 19-20 size distribution, 20-23

passive pressure, 135,241-242 passive thrust, 245 peat, 3,12

classification, 17, 28 description, 16-18 secondary compression, 204-205

perched water table, 36 permeability

borehole tests, 46-48 coefficient, 39-41 empirical values, 40-41 laboratory tests, 43-46 layered soils, 42 packer test, 48 piezometer test, 49-50 pumping test, 50-51 typical values, 39, 41

phreatic surface, 36, 54, 60-61, 291 piezometer

hydraulic, 344-345 pneumatic, 344, 345

standpipe, 343-344 test, 49-50 vibrating wire, 345

piezometric head, 36 level, 39 observations, 346

piles bored, in clay, 222 bored, in sand, 229 design of single, 221-230 driven, in clay, 223-224 driven, in sand, 226-229 factor of safety, 229-230 layered deposits, 221 types, 220

pile groups block failure, 232 efficiency, 231-232 individual pile penetration, 232 load variation, 230 settlements, 233-234 spacing, 230

piping, 38, 59 piston sampler, 337-338 plasticity

chart, 14, 15,27-28 index, 27,149,151,160,172,173,200,203

plastic limit, 10,25,26,27,307 point load, 92, 93 polluted soils, I pore pressure,. see pressure porosity, 8, 31, 39 preconsolidation pressure, 73-74,105-106,198,204 pressure, 39, see also head

change in pore, 79-80, 135-136, 200, 223, 276-279

initial pore, 58, 70-71, 77 minimum equivalent fluid, 248 parameters, pore, 81-83,135,151,201,291 pore pressure ratio ru' 281, 287

pressuremeter test, 341-342 principal stress, 76-77 pumping test, see permeability

quick clays, 4 quick condition, 58-59

raft foundations, 91-92 rapid drawdown, 290-291 reinforced earth, 263-265 relative deflection, 210

relative density, 9-10, 142, 184 reports, 345-348 residual strength, see strength ring shear test, 139, 159 rollers, compaction, 314-315, 318 root-time method, 114, 115 Roscoe surface, 155, 157 rotary drilling, 334-335 rotation, 209 rotational failure, 255, 265, 275 Rowe cell, 44-46, 116-118 running sand, 37

safety margin, 130 sampling

block, 335 Delft continuous, 338-339 piston, 337-338 quality, 335, 337 split-barrel SPT, 336-337 thin-walled tube, 336 U100, 335, 337,347

sand description, 15-16, 18 drains, 119 replacement test, 10 settlements, 205-209 shear strength, 139-142

saprolite, 2 saturation

back pressure, 152 capillary rise, 83-85 degree of, 29, 30, 31 partial, 71, 148 zone of, 36

secondary compression, 115, 120,203-205 sedimentation test, 19, 20, 22 seepage

anisotropic soils, 55-56, 57 effect on slope stability, 280-281 flow nets, 53-56 force, 58, 59 pressure, 58 quantities, 57 theory, 51-53

selected materials, I sensitivity, 4, 144,205,310-311 serviceability, 211 settlement, consolidation

compression index, 198-200 oedometer,200

settlement, immediate average, 195,196 depth correction, 195,196 general method, 192-194 rigidity correction, 195 modulus increasing, 195, 197 modulus estimates, 198 yielding, 195-196, 198

settlements, permissible allowable, 168, 184, 229 definitions, 209-210 criteria for movements, 210-211 routine limits, 211-212 damage criterion, 211-212

settlements, sand, 205 Burland and Burbridge method, 207-209 Schmertmann method, 206-207

settlements, secondary general method, 204 coefficient, 204-205

settlements, total elastic drained method, 201-203 modulus, drained, 203 pile groups, 233-234 Skempton-Bjerrum method, 200-201

shear box text, 138, 140 shear surfaces, 4, 159 sheet piling, see also cofferdams

anchored or propped, 259-260 cantilever, 258-259

shell and auger, see cable percussion boring shell fragments, 5 shrinkage, 26, 172, 312 shrinkage limit, 26, 28-29 sieving, see particle size distribution silt, 3, 8, 12-15,18 site reconnaissance, 329 skin friction, 227-229, 256, 340 slickensided surfaces, 4, 14 slides, see slope stability sliding, 184

Index 363

slope stability, see cuttings, earth dams, embankments Bishop simplified method, 286 critical circle, 284, 286, 287, 297, 299 circular arc, undrained, 281-284 effective stress, 284-293 Fellenins method, 286 method of slices, 282-283, 284-286 non-circular, 291-292 plane translational slide, 280-281 pore pressure ratio, 287 rapid drawdown, 290-291

364 Soil Mechanics - Principles and Practice

stability coefficients, 287-290 stability number, 283-284 submerged slopes, 290 tension crack, 283 water table, 287-290 wedge method, 292-293

smectite, see montmorillonite softening, 3 10-311 soil

aeolian, 4 classification, 18-29 description, 12-18 formation, 1-4 model, 29-30, 313 section, 349 strength terms, 13 structure, 8-11 tropical, I, 2, 25, 27

solum, 2 specific gravity, see particle density specific volume, 31,153 spread foundations, 168 stability coefficients, 287-290 stability number

excavations, 262 slopes, undrained, 283-284 slopes, effective stress, 287-290

standard penetration test, 9, 10, 184-185,207,228,339, 347 standpipe, 343 standpipe piezometer, 343-344 stone, see gravel strength

critical state, 131, 132, 142, 156 effective stress, clay, 150 et seq peak, 131, 132, 141 residual, 131, 132, 159-160 sand, 139-142 test procedures, 136, 138 ultimate, 131, 141 undrained, clay, 143,307,309,341 yield, 131

stress effective, 70-72, 77, 223, 225 effective, above water table, 84-85 history, 70-75,105,151 horizontal, 76-79, 135 see also earth pressures in the ground, 76 paths, 132-134, 135, 153 total, 70, 71,77, 222, 276-279, 281-284

stress distribution bulbs of pressure, 94-95, 230

line load, 92, 93 Newmark's method, 97 on walls, 251, 252 point load, 92, 93 principle of superposition, 96-97 rectangle flexible, 96-97, 98-99 rectangle, rigid, 99 uniform pressure, 94-95 strip load, 95, 96

structure, 8-11, 13, 14, 39, 116, 143 submerged

density, 72 slopes, 290

suction, 71, 84, 281 sump pumping, 37 super-elevation, 176 superposition, principle, 96-97, 192, 194 swelling, 79-80, 104, 156, 172,312 swelling index, 199

temperature, effect of, 24, 25, 27, 40 tension cracks, 250-251, 283 till

ablation, 4 lodgement, 3 melt-out, 4

tilt, 209-210 time factor, 110-116, 120, 121 topsoil, 12 translational slides, 275, 280-281 trees, effects of, 172-175 trial pits, 331, 346 triaxial apparatus, 145 triaxial test, 136, 138, 139, 145-148

consolidated drained, 146, 153 consolidated undrained, 146, 151-153 multi-stage, 147 quick undrained, 146-147 rate of strain, 146, 152

tropical soils, 1,2,25,27

unconfined compression test, 138,143 undisturbed samples, see sampling undrained, see drainage uniformity coefficient, 22, 23, 24, 142 unit weight, 9, 22-23, 31, 70

submerged, 72 uplift, 38, 58

vane test, 138, 143-145,340-341 varved clay, 4, 10, 13 void ratio, 9, 31, 40, 73, 104, 204

constant, 142 voids, 30, 38-39 volcanic ash, 5, 15

wall friction, 228, 243-246,248, 256 walls

basement, 252 cofferdam, see cofferdams crib, 254 embedded, 253-254 gabion, 253,254 gravity, 254-257 masonry, 251-253 reinforced earth, 263-265 reinforced concrete, 252-253 sheet pile, see sheet piling

waste materials, see made ground water-borne soils, 3 water content, 10, 17,24-25,31,307,321 water table, 36, 54, 70-71, 76, 176

capillary rise above, 83-84 correction, 186 effective stresses above, 84 effect on bearing capacity, 182 effect on earth pressures, 248-249 effect on slope stability, 280-281,287-289 instruments for, 342-345 on borehole record, 347 on soil section, 349

weathering chemical, I grades, I, 14 mechanical, I oxidation, 4

wedge method active thrust, 243-245 passive thrust, 245-246 slope stability, 292-293

weight, see unit weight Westergaard material, 93 wind-blown soils, 4

yield, 131, 196, 198, 242-243

Index 365