43
APPENDIX A SI UNITS IN GEOTECHNICAL ENGINEERING Introduction There has always been some confusion with regards to the system of units to be used in engineering practices and other commercial transactions. FPS (Foot-pound-second) and MKS (Meter- Kilogram-second) systems are still in use in many parts of the world. Sometimes a mixture of two or more systems are in vogue making the confusion all the greater. Though the SI (Le System International d'Unites or the International System of Units) units was first conceived and adopted in the year 1960 at the Eleventh General Conference of Weights and Measures held in Paris, the adoption of this coherent and systematically constituted system is still slow because of the past association with the FPS system. The conditions are now gradually changing and possibly in the near future the SI system will be the only system of use in all academic institutions in the world over. It is therefore essential to understand the basic philosophy of the SI units. The Basics of the SI System The SI system is a fully coherent and rationalized system. It consists of six basic units and two supplementary units, and several derived units. (Table A.I) Table A.1 Basic units of interest in geotechnical engineering 1. 2. 3. 4. 5. Quantity Length Mass Time Electric current Thermodynamic temperature Unit Meter Kilogram Second Ampere Kelvin SI symbol m kg S A K 987

Appendix & Index

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Page 1: Appendix & Index

APPENDIX ASI UNITS IN GEOTECHNICAL ENGINEERING

IntroductionThere has always been some confusion with regards to the system of units to be used in engineeringpractices and other commercial transactions. FPS (Foot-pound-second) and MKS (Meter-Kilogram-second) systems are still in use in many parts of the world. Sometimes a mixture of twoor more systems are in vogue making the confusion all the greater. Though the SI (Le SystemInternational d'Unites or the International System of Units) units was first conceived and adoptedin the year 1960 at the Eleventh General Conference of Weights and Measures held in Paris, theadoption of this coherent and systematically constituted system is still slow because of the pastassociation with the FPS system. The conditions are now gradually changing and possibly in thenear future the SI system will be the only system of use in all academic institutions in the worldover. It is therefore essential to understand the basic philosophy of the SI units.

The Basics of the SI System

The SI system is a fully coherent and rationalized system. It consists of six basic units and twosupplementary units, and several derived units. (Table A.I)

Table A.1 Basic units of interest in geotechnical engineering

1.2.

3.

4.

5.

Quantity

Length

Mass

Time

Electric current

Thermodynamictemperature

Unit

Meter

Kilogram

Second

Ampere

Kelvin

SI symbol

m

kgS

A

K

987

Page 2: Appendix & Index

988 Appendix A

Supplementary UnitsThe supplementary units include the radian and steradian, the units of plane and solid angles,respectively.

Derived UnitsThe derived units used by geotechnical engineers are tabulated in Table A.2.

Prefixes are used to indicate multiples and submultiples of the basic and derived units as givenbelow.

Factor

106

103

io-3

io~6

Quantity

acceleration

area

density

force

pressure

stress

moment or torque

unit weight

frequency

volume

volume

work (energy)

Prefix Symbol

mega Mkilo k

milli mmicro (i

Table A. 2

Unit

meter per second squared

square meter

kilogram per cubic meter

newton

pascal

pascal

newton-meter

newton per cubic meter

hertz

cubic meter

liter

joule

Derived units

SI symbol

---N

Pa

Pa

N-m

N/m3

Hz

m3

L

J

Formula

m/sec2

m2

kg/m3

kg-m/s2

N/m2

N/m2

kg-m2/s2

kg/s2m2

cycle/sec

-

10-3m3

N-m

MassMass is a measure of the amount of matter an object contains. The mass remains the same even ifthe object's temperature and its location change. Kilogram, kg, is the unit used to measure thequantity of mass contained in an object. Sometimes Mg (megagram) and gram (g) are also used asa measure of mass in an object.

TimeAlthough the second (s) is the basic SI time unit, minutes (min), hours (h), days (d) etc. may be usedas and where required.

ForceAs per Newton's second law of motion, force, F, is expressed as F = Ma, where, M = massexpressed in kg, and a is acceleration in units of m/sec2. If the acceleration is g, the standard valueof which is 9.80665 m/sec2 ~ 9.81 m/s2, the force F will be replaced by W, the weight of the body.Now the above equation may be written as W = Mg.

Page 3: Appendix & Index

SI Units in Geotechnical Engineering 989

The correct unit to express the weight W, of an object is the newton since the weight is thegravitational force that causes a downward acceleration of the object.

Newton, N, is defined as the force that causes a 1 kg mass to accelerate 1 m/s2

.kg-mor 1N = 1—E-r—

s2

Since, a newton, is too small a unit for engineering usage, multiples of newtons expressed askilonewton, kN, and meganewton, MN, are used. Some of the useful relationships are

1 kilonewton, kN = 103 newton = 1000 N

meganewton, MN = 106 newton = 103 kN = 1000 kN

Stress and PressureThe unit of stress and pressure in SI units is the pascal (Pa) which is equal to 1 newton per squaremeter (N/m2). Since a pascal is too small a unit, multiples of pascals are used as prefixes to expressthe unit of stress and pressure. In engineering practice kilopascals or megapascals are normallyused. For example,

1 kilopascal = 1 kPa = 1 kN/m2 = 1000 N/m2

1 megapascal = 1 MPa = 1 MN/m2 = 1000 kN/m2

DensityDensity is defined as mass per unit volume. In the SI system of units, mass is expressed in kg/m3. Inmany cases, it may be more convenient to express density in megagrams per cubic meter or in gm percubic centimeter. The relationships may be expressed as

1 g/cm3 = 1000 kg/m3 = 106 g/m3 = 1 Mg/m3

It may be noted here that the density of water, p^ is exactly 1.00 g/cm3 at 4 °C, and the variation isrelatively small over the range of temperatures in ordinary engineering practice. It is sufficientlyaccurate to write

pw = 1.00 g/cm3 = 103 kg/m3 = 1 Mg/m3

Unit weightUnit weight is still the common measurement in geotechnical engineering practice. Therelationship between unit weight, 7 and density p, may be expressed as 7= pg.For example, if the density of water, pw = 1000 kg/m3, then

,..,„, = ,000 4 x 9*1 i = 9810 4-!|mj s2 m3 s2

Iro rn NSince, 1N = 1 -£—, y =9810—- = 9.81 kN/m3

s2 m j

Page 4: Appendix & Index

990 Appendix A

Table A.3 Conversion factors

To convert

Length

Volume

Force

Stress

Unit weight

Moment

Moment of inertia

Section modulus

Hydraulicconductivity

Coefficientof consolidation

SI to FPS

From

mmcmmm

m2

m2

cm2

mm'

m3

m3

cm3

NkNkNkN

N/m2

kN/m2

kN/m2

kN/m2

kN/m2

kN/m3

kN/m3

N-mN-m

mm4

m4

mm3

m3

m/mincm/minm/seccm/sec

cm2/secm2/yearcm2/sec

To

ftininin

ft2

in2

in2

in2

ft3

in3

in3

IbIbkipUS ton

lb/ft2

lb/ft2

US ton/ft2

kip/ft2

lb/in2

lb/ft3

lb/in3

Ib-ftIb-in

in4

in4

in3

in3

ft/minft/minft/secin/sec

in2/secinVsecft2/sec

Multiply by

3.28139.370.39370.03937

10.76415500.1550.155x 10~2

35.3261,023.40.06102

0.2248224.80.22480.1124

20.885 xlO-3

20.8850.0104420.885 x 10-3

0.145

6.3610.003682

0.73758.851

2.402 x KT6

2.402 x 106

6.102 x 1Q-5

6.102 x 104

3.2810.032813.2810.3937

0.1554.915 x 10-5

1.0764 x lO'3

FPS to SI

From

ftininin

ft2

in2

in2

in2

ft3

in3

in3

IbIbkipUS ton

lb/ft2

lb/ft2

US ton/ft2

kip/ft2

lb/in2

lb/ft3

lb/in3

Ib-ftIb-in

in4

in4

in3

in3

ft/minft/minft/secin/sec

in2/secin2/secft2/sec

To

mmcmmm

m2

m2

cm2

mm2

m3

m3

cm3

NkNkNkN

N/m2

kN/m2

kN/m2

kN/m2

kN/m2

kN/m3

kN/m3

N-mN-m

mm4

m4

mm3

m3

m/mincm/minm/seccm/sec

cm2/secm2/yearcm2/sec

Multiply by

0.30480.02542.5425.4

929.03 xlO^6.452x10^6.452645.16

28.317xlO-3

1 6.387 x 10~6

16.387

4.4484.448 x 10'3

4.4488.896

47.880.0478895.7647.886.895

0.1572271.43

1.35580.11298

0.4162 x 106

0.4162 x KT6

0.16387 x 105

0.16387 x 10-4

0.304830.480.30482.54

6.45220.346 x 103

929.03

Page 5: Appendix & Index

SI Units in Geotechnical Engineering 991

Table A.4 Conversion factors —general

To convert from

Angstrom units

Microns

US gallon (gal)

Pounds

Tons (short or US tons)

Tons (metric)

kips/ft2

Pounds/in3

Poise

millipoise

ft/mm

ft/year

cm/sec

To

inchesfeetmillimeterscentimetersmeters

inches

cm3

m3

ft3

liters

dynesgramskilograms

kilogramspoundskips

gramskilogramspoundskipstons (short or US tons)

lbs/in2

lbs/ft2

US tons/ft2

kg/cm2

metric ton/ft2

gms/cm3

kg/m3

lbs/ft3

kN-sec/m2

poisekN-sec/m2

gm-sec/cm2

ft/dayft/year

ft/min

m/minft/minft/year

Multiply by

3.9370079 10~9

3.28084 x 10-'°1 xio-7

1 x io~8

1 x io-10

3.9370079 x 1(T5

37853.785 x io-3

0.1336803.785

4.44822 x io5

453.592430.45359243

907.187420002

1 x IO6

10002204.62232.20462231.1023112

6.9444510000.50000.4882444.88244

27.679927679.9051728

io-4

io-3

io-7

icr6

14405256 x IO2

1.9025 x 1Q-6

0.6001.96851034643.6

Page 6: Appendix & Index
Page 7: Appendix & Index

APPENDIX BSLOPE STABILITY CHARTS AND TABLES

As per Eq.( 10.43), the factor of safety Fs is defined as

Fs = m-nru

where, m, n = stability coefficients, and ru = pore pressure ratio. The values of m and n may beobtained from Figs. B.I to B.I4

3:1 4:1Slope cot/?

5:1 3:1 4:1Slope cot /3

Figure B.1 Stability coefficients m and n for c'lyH = 0 (Bishop andMorgenstern, 1960)

993

Page 8: Appendix & Index

994 Appendix B

= >'40°

= J>40°

2:1 3:1 4:1 5:1 2:1 3:1 4:1 5:1Slope cot ft Slope cot /?

Figure B.2 Stability coefficients for c'ljH = 0.025 and nd = 1.00(Bishop and Morgenstern, 1960)

2:1 3:1 4:1 5:1

40° 5

2:1 3:1 4:1 5:1

Figure B.3 Stability coefficients m and /? for c'lyH = 0.025 and nd = 1.25(Bishop and Morgenstern, 1960)

Page 9: Appendix & Index

Slope Stability Charts 995

3:1 4:1 5:1 2:1 3:1 4:1cot/J cot/3

Figure B.4 Stability coefficients m and n for c'/yH = 0.05 and nd = 1.00(Bishop and Morgenstern, 1960)

2:1 3:1 4:1 5:1 2:1 3:1 4:1 5:1cot/? cot/3

Figure B.5 Stability coefficients m and n for c'lyH = 0.05 and nd = 1.25(Bishop and Morgenstern, 1960)

Page 10: Appendix & Index

996 Appendix B

40°

30 4

5:1 2:1 5:1

Figure B.6 Stability coefficients m and n for c'lyH = 0.05 and nd = 1.50(Bishop and Morgenstern, 1960)

3 4cot/?

40°

35° 5

30" 4

25° n

20° 3

40°

35°

30°

25°

20°

3 4cot/?

Figure B.7 Stability coefficients m and /? for c'lyH = 0.075 toe circles(O'Connor and Mitchell, 1977)

Page 11: Appendix & Index

Slope Stability Charts 997

0

40°

35°

30°

25°

20°

3 4 5 "2 3 4 5cot/3 cot/3

Figure B.8 Stability coefficients m and n for c'lyH = 0.075 and nd = 1.00(O'Connor et al., 1977)

03 4 5

cot/?

Figure B.9 Stability coefficients m and n for c'lyH = 0.075 and nd = 1.25(O'Connor and Mitchell, 1977)

Page 12: Appendix & Index

998 Appendix B

2 =~

3 4cot 3

35° 5

30°4

25° n

20° 3

40°

35°

30°

25°

20°

3 4cot/3

Figure B.10 Stability coefficients m and A? for c'lyH = 0.075 and nd = 1.50(O'Connor and Mitchell, 1977)

3 4cot/?

40°

35C

30°

25°

20°

3 4cot/3

40°

35°

30°

25°

20°

Figure B.11 Stability coefficients m and n for c'ljH = 0.100 toe circles(O'Connor and Mitchell, 1977)

Page 13: Appendix & Index

Slope Stability Charts 999

40°

7

35°

30°

25°

90°/u n

2 3 4 5cot/3

Figure B.12 Stability coefficients m and n for c'/yH = 0.100 and nd = 1.00(O'Connor and Mitchell, 1977)

40°

35°

30°

25°

20°

2 3 4 5cot/3

Figure B.13 Stability coefficients m and n for c'lyH = 0.100 and nd = 1.25(O'Connor and Mitchell, 1977)

Page 14: Appendix & Index

1000 Appendix B

40°

35°

30°

25°

20°

5 2 3 4 5

cot/3

Figure B.14 Stability coefficients m and n for c'lyH = 0.100 and nd = 1.50(O'Connor and Mitchell, 1977)

Page 15: Appendix & Index

Slope Stability Charts 1001

Bishop and Morgenstern (1960) Stability Coefficients are Presented inTabular FormF - m -n.r

c' _Table B1 Stability coefficients m and n for ~77 ~ °yh

Stability coefficients for earth slopes

0'

10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2:1

m

0.3530.4430.5360.631

0.7280.8280.9331.041

1.1551.2741.4001.535

1.678

n

0.4410.5540.6700.789

0.9101.035.166.301

.444

.593

.7501.919

2.098

Slope 3:1

m

0.5290.6650.8040.946

1.0921.2431.3991.562

1.7321.9112.1012.302

2.517

n

0.5880.7390.8931.051

1.2131.3811.5541.736

1.9242.1232.3342.588

2.797

Slope 4:1

m

0.7050.8871.0721.261

1.4561.6571.8652.082

2.3092.5482.8013.069

3.356

n

0.7490.9431.1391.340

1.5471.7611.9822.213

2.4542.7082.9773.261

3.566

Slope 5:1

m

0.8821.1091.3401.577

1.8202.0712.3322.603

2.8873.1853.5013.837

4.196

n

0.9171.1531.3931.639

1.8922.1532.4242.706

3.0013.3113.6393.989

4.362

Table B2 Stability coefficients m and n for ~TJ - 0-025 anc| n^ = <|

<t>'10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2:1

m

0.6780.7900.9011.012

1.1241.2391.3561.478

1.6061.7391.8802.030

2.190

n

0.5340.6550.7760.898

1.0221.1501.2821.421

1.5671.7211.8852.060

2.247

Slope 3:1

m

0.9061.0661.2241.380

1.5421.7051.8752.050

2.2352.4312.6352.855

3.090

n

0.6830.8491.0141.179

1.3471.5181.6961.882

2.0782.2852.5052.741

2.933

Slope 4:1

m

1.1301.3371.5441.751

1.9622.1772.4002.631

2.8733.1273.3963.681

3.984

n

0.8461.0611.2731.485

1.6984.9162.1412.375

2.6222.8833.1603.458

3.778

Slope 5:1

m

1.3651.6201.8685.121

2.3802.6462.9213.207

3.5083.8234.1564.510

4.885

n

1.0311.2821.5341.789

2.0502.3172.5962.886

3.1913.5113.8494.209

4.592

Page 16: Appendix & Index

1002 Appendix B

Table B3 Stability coefficients m and n for ~77 ~ °-025 and nd = 1.25

0'

10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2:1

m

0.7370.8781.0191.162

1.3091.4611.6191.783

1.9562.1392.3312.536

2.753

n

0.6140.7590.9071.059

1.2161.3791.5471.728

1.9152.1122.3212.541

2.775

Slope 3:1

m

0.901.076.253.433

.618

.8082.0072.213

2.4312.6592.9013.158

3.431

n

0.7260.9081.0931.282

1.4781.6801.8912.111

2.3422.5882.8413.112

3.399

Slope 4:1

m

1.0851.2991.5151.736

1.9612.1942.4372.689

2.9533.2313.5243.835

4.164

n

0.8671.0891.312.1.541

1.7752.0172.2692.531

2.8063.0953.4003.723

4.064

Slope 5:1

m

1.2851.5431.8032.065

2.3442.6102.8973.196

3.5113.8414.1914.563

4.988

n

1.0141.2781.5451.814

2.0902.3732.6692.976

3.2993.6383.9984.379

4.784

|_,

Table B4 Stability coefficients m and n for ~T = 0>05 and nd = 1.00

0'

10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2: 1

m

0.9131.0301.1451.262

1.3801.5001.6241.753

1.8882.0292.1782.336

2.505

n

0.5630.6900.8160.942

1.0711.2021.3381.480

1.6301.7891.9582.138

2.332

Slope 3:1

m

1.1811.3431.5061.671

1.8402.0142.1932.380

2.5742.7772.9903.215

3.451

n

0.7170.8781.0431.212

1.3871.5681.7571.952

2.1572.3702.5922.826

3.071

Slope 4: 1

m

1.4691.6881.9042.117

2.3332.5512.7783.013

3.2613.5233.8034.103

4.425

n

0.9101.1361.3531.565

1.7761.9892.2112.444

2.6932.9613.2533.574

3.926

Slope 5:1

m

1.7331.9952.2562.517

2.7833.0553.3363.628

3.9344.2564.5974.959

5.344

n

1.0691.3161.5761.825

2.0912.3652.6512.948

3.2593.5853.9274.288

4.668

Page 17: Appendix & Index

Slope Stability Charts 1003

rv rvcTable B5 Stability coefficients m and n for ~ = °-05 and n = 1.25

0'10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2:1

m

0.9191.0651.2111.359

1.5091.6631.8221.988

2.1612.3432.5352.738

2.953

n

0.6330.7920.9501.108

1.2661.4281.5951.769

1.9502.1412.3442.560

2.791

Slope 3:1

m

1.1191.2941.4711.650

1.8342.0242.2222.428

2.6452.8733.1143.370

3.642

n

0.7660.9411.1191.303

1.4931.6901.8972.113

2.3422.5832.8393.111

3.400

Slope 4:1

m

1.3441.5631.7822.004

2.2302.4632.7052.957

3.2213.5003.7954.109

4.442

n

0.8861.1121.3381 .567

1.7992.0382.2872.546

2.8193.1073.4133.740

4.090

Slope 5:1

m

1.5941.8502.1092.373

2.6432.9213.2113.513

3.8294.1614.5114.881

5.273

n

1.0421.3001.5621.831

2.1072.3922.6902.999

3.3243.6654.0254.405

4.806

_ _ _

Table B6 Stability coefficients m and n for 777 = °-05 and nd = 1.50

<t>'10.012.515.017.5

20.022.525.027.5

30.032.535.037.5

40.0

Slope 2:1

m

1.0221.2021.3831.565

1.7521.9432.1432.350

2.5682.7983.0413.299

3.574

n

0.7510.9361.1221.309

1.5011.6981.9032.117

2.3422.5802.8323.102

3.389

Slope 3:1

m

1.1701.3761.5831.795

2.0112.2342.4672.709

2.9643.2323.5153.817

4.136

n

0.8281.0431.2601.480

1.7051.9372.1792.431

2.6962.9753.2693.583

3.915

Slope 4:1

m

1.3431.5891.8352.084

2.3372.5972.8673.148

3.4433.7534.0824.431

4.803

n

0.9741.2271.4801.734

1.9932.2582.5342.820

3.1203.4363.7714.128

4.507

Slope 5:1

m

1.5471.8292.1122.398

2.6902.9903.3023.626

3.9674.3264.7075.112

5.543

n

1.1081.3991.6901.983

2.2802.5852.9023.231

3.5773.9404.3254.735

5.171

Page 18: Appendix & Index

1004 Appendix B

Extension of the Bishop and Morgenstern Stability Coefficients (O'Connorand Mitchell, 1977)

Table B7 Stability coefficients m and n for ~77 - 0.075 ancj toe cjrc|eyn

<t>'2025303540

Slope 2:1

m

1.5931.8532.1332.4332.773

n

1.1581.4301.7302.0582.430

Slope 3:1

m

2.0552.4262.8263.2533.737

n

1.5161.8882.2882.7303.231

Slope 4:1

m

2.4982.9803.4964.0554.680

n

1.9032.3612.8883.4454.061

Slope 5:1

m

2.9343.5204.1504.8465.609

n

2.3012.8613.4614.1594.918

Table B8 Stability coefficients m and n for 777 = 0-°75 ancj = 1 .00

0'2025303540

Slope 2:1

m

1.6101.8722.1422.4432.772

n

1.1001.3861.6862.0302.386

Slope 3:1

m

2.1412.5022.8843.3063.775

n

1.4431.8152.2012.6593.145

Slope 4: 1

m

2.6643.1263.6234.1774.785

n

1.8012.2592.7583.3313.945

Slope 5:1

m

3.1733.7424.3575.0245.776

n

2.1302.7153.3314.0014.759

Table B9 Stability coefficients m and n for — = 0.075 and nd =

0'

2025303540

Slope 2: 1

m

1.6882.0042.3522.7823.154

n

1.2851.6412.0152.3852.841

Slope 3:1

m

2.0712.4692.8883.3573.889

n

1.5431.9752.3852.8703.428

Slope 4:1

m

2.4922.7923.4994.0794.729

n

1.8152.3152.8573.4574.128

Slope 5:1

m

2.9543.5234.1494.8315.063

n

2.1732.7303.3574.0434.830

Table B10 Stability coefficients m and n for ~rj - 0.075 ancj n^ = i 50

0'

2025303540

Slope 2:1

m

1.9182.3082.7353.2113.742

n

1.5141.9142.3552.8543.397

Slope 3:1

m

2.1992.6603.1583.7084.332

n

1.7282.2002.7143.2853.926

Slope 4:1

m

2.5483.0833.6594.3025.026

n

1.9852.5303.1283.7864.527

Slope 5:1

m

2.9313.5524.2184.9615.788

n

2.2722.9153.5854.3435.185

Page 19: Appendix & Index

Slope Stability Charts 1005

Table B11 Stability coefficients m and n for ~77 ~ 0-100 ancj toe cjrc|eyh

0'

2025303540

Slope 2:1

m

1.8042.0762.3622.6733.012

n

1.2011.4881.7862.1302.486

Slope 3:1

m

2.2862.6653.0763.5184.008

n

1.5881.9452.3592.8033.303

Slope 4:1

m

2.7483.2463.7704.3394.984

n

1.9742.4592.9613.5184.173

Slope 5:1

m

3.1903.7964.4425.1465.923

n

2.3612.9593.5764.2495.019

Table B12 Stability coefficients m and n for ~~ °-100 and nd = 1 .00

0'2025303540

Slope 2:1

m

1.8412.1022.3782.6923.025

n

1.1431.4301.7142.0862.445

Slope 3:1

m

2.4212.7853.1833.6124.103

n

1.4721.8452.2582.7153.230

Slope 4: 1

m

2.9823.4583.9734.5165.144

n

1.8152.3032.8303.3594.001

Slope 5:1

m

3.5494.1314.7515.4266.187

n

2.1572.7433.3724.0594.831

Table B13 Stability coefficients m and n for 777 - °-100 and nd = 1.25

<t>'2025303540

Slope 2:1

m

1.8742.1972.5402.9223.345

n

1.3011.6422.0002.4152.855

Slope 3:1

m

2.2832.6813.1123.5884.119

n

1.5581.9722.4152.9143.457

Slope 4: 1

m

2.7513.2333.7534.3334.987

n

1.8432.3302.8583.4584.142

Slope 5:1

m

3.2533.8334.4515.1415.921

n

2.1582.7583:3724.0724.872

Table B14 Stability coefficients m and n for — - 0.100 anc| n^ _ 1 59

0'2025303540

Slope 2:1

m

2.0792.4772.9083.3853.924

n

1.5281.9422.3852.8843.441

Slope 3:1

m

2.3872.8523.3493.9004.524

n

1.7422.2152.7283.3003.941

Slope 4:1

m

2.7683.2973.8814.5205.247

n

2.0142.5423.1433.8004.542

Slope 5:1

m

3.1583.7964.4685.2116.040

n

2.2852.9273.6144.3725.200

Page 20: Appendix & Index
Page 21: Appendix & Index

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Page 38: Appendix & Index
Page 39: Appendix & Index

INDEX

Activity 57Adsorbed water 15, 16Angle of obliquity 253Angle of wall friction 254, 421Anisotropic soil 116Apparent cohesion 255, 300Aquifer 97

confined 99, 100unconfined 97, 98

Atterberg limits 46flow curve 48liquid limit 46-50plastic limit 49shrinkage limit 50

BBase exchange 16, 17Beaming capacity, shallow foundation 481

based on CPT 518based on SPT 518, 519bearing capacity factors 489^1-90, 493-

494, 504case history, Transcona 533-534depth factors 505design charts 555, 558effect of compressibility 509

effect of eccentric loading 515, 588effect of size of footings 554effect of water table 494-496empirical correlations 558-559equation, Terzaghi 489footings on stratified deposits 521-526foundation on rock 532foundations on slope 529general equation 503gross allowable 484, 493load inclination factors 505net allowable 484, 493, 545net ultimate 484, 493plate load tests 548safe bearing pressure 485safety factor 484, 493seat of settlement 562settlement charts 555settlement computation 561-571settlement differential 547settlement permissible 548settlements (max) 547shape factors 505ultimate 483-484, 489, 491

Boiling condition 148Boring of holes

auger method 318rotary drilling 320

1025

Page 40: Appendix & Index

1026 Index

wash boring 319Boussinesq point load solution 3, 174

Capillary water 149, 154, 156contact angle 150pressure 149rise in soil 149siphoning 154surface tension 149, 150

Classical earth pressure theory 2Coulomb's theory 2Rankine' theory 2

Classification of soils 69AASHTO 70textural 69USCS 73

Clay mineral 11composition 11formation 12Ulite 11, 14Kaolinite 11, 12Montmorillonite 11, 14structure 11-15

Clayshigh sensitivity 219low to medium sensitivity 219normally consolidated 217, 220overconsolidated 217, 220

Coefficient of friction 254at rest earth pressure 422compressibility 222consolidation 236, 240earth pressure, active 427earth pressure, passive 428volume compressibility 222

Collapse potential 795Collapse settlement 796Compression 209

immediate 209primary 209secondary 209

Compression index 219, 223, 224Conjugate confocal parabolas 127Consistency index 55Consistency limits 3, 45Consolidation 207, 208

degree of consolidation 238one-dimensional 209, 210, 233settlement 209

test 213time factor 236

Consolidometer 212Coulomb's earth pressure 452

coefficient for active 454coefficient for at-rest 422coefficient for passive 456for active state 452for passive state 455

Critical hydraulic gradient 148Curved surfaces of failure 462

earth pressure coefficient 466for passive state 462

DDarcy's law 89Degree of consolidation 238Density 21Diffused double layer 15Dilatometer test 349Discharge velocity 91Drilled pier foundation 741

design considerations 751estimation of vertical settlement 765lateral bearing capacity 779methods of construction 743types 741uplift capacity 777vertical bearing capacity 754vertical bearing capacity equation 755vertical load transfer 752vertical ultimate skin resistance 760, 763,

764

Effective diameter 154Effective stress 144, 274Electrical resistivity method 354Embankment loading 191Expansion index 810

Factor of safety with respect to cohesion 368safety with respect to heave 132with respect to height 368with respect to shearing strength 368

Floating foundation 595Flow net construction 116Flow value 263

Page 41: Appendix & Index

Index 1027

Free swell 804

Geophysical exploration 352Grain size distribution 43

coefficient of curvature 44gap graded 43uniformity coefficient 43uniformly graded 43well graded 43

HHydraulic conductivity 90, 91

by bore-hole tests 101by constant head 92by pumping test 97empirical correlations 103falling head method 93for stratified layers 102of rocks 112

Hydraulic gradient 87, 147critical 148

Hydrometer analysis 35, 38, 39

I

Isobar 198

Laminar flow 88Laplace equation 114Lateral earth pressure 419

active 420at rest 420passive 420

Leaning Tower of Pisa 2Linear shrinkage 56Liquid Limit

by Casagrande method 47by fall cone method 49by one-point method 48

Liquidity index 54

MMeniscus 39, 41, 152Meniscus correction 41Mohr circle of stress 264-266

diagram 265, 269, 270

Mohr-coulomb failure theory 268, 269

NNewmark's influence chart 188, 190

influence value 189

oOedometer 212Origin of planes 266, 271Overconsolidation ratio 306

Percent finer 40Permeability test 92-101Phase relationships 19-25Pile group 674

allowable loads 690bearing capacity 678efficiency 676negative friction 691number and spacing 674settlement 680, 689uplift capacity 694

Piles batter laterally loaded 731Piles, vertical 605

classification 605driven 607installation 610selection 609types 606

Piles, vertical load capacity 613adhesion factor a 633jS-method 633Coyle and Castello's method 628bearing capacity on rock 670general theory 618Janbu's method 628A-method 633load capacity by CPT 652load capacity by load test 663load capacity by SPT 635load capacity from dynamic formula 666load transfer 614methods of determining 617Meyerhof's method 624settlement 680static capacity in clays 631t-zmethod 683Tomlinson's solution 622

Page 42: Appendix & Index

1028 Index

ultimate skin resistance 629uplift resistance 671Vesic's method 625

Piles vertical loaded laterally 699Broms' solutions 709case studies 722coefficient of soil modulus 703differential equation 701direct method 716Matlock and Reese method 704non-dimensional solutions 704p-y curves 706Winkler's hypothesis 700

Piping failure 131, 945Plastic limit 49Plasticity chart 59, 75Plasticity index 53Pocket penetrometer 304Pole 266Pore pressure parameters 298Pore water pressures 144Porosity 21Preconsolidation pressure 218Pressure bulb 198Pressuremeter 343Pressuremeter modulus 346Principal planes 260, 263Principal stresses 260, 263, 275Proctor test 952

modified 954standard 953

Pumping test 97

QQuick sand condition 148

Radius of influence 99Rankine's earth pressure 425Relative density 24, 44Reynolds Number 89Rock classification 5

minerals 5, 6weathering 7

Rock quality designation 326, 532

Secondary compression 224coefficient 224

compression index 225settlement 224

Seepage 114determination 120flow net 114-116, 127Laplace equation 114line location 130loss 128pressure 122, 123, 147

Seepage velocity 91Seismic refraction method 353Settlement

consolidation settlement 219-223secondary compression 224Skempton's formula 223

Settlement rate 242Shear tests 276

consolidated-drained 277consolidated-undrained 277unconsolidated-undrained 277

Shrinkage limit 50Shrinkage ratio 55Sieve analysis 33Significant depth 199Soil classification 10, 339Soil particle 9

size and shape 9, 32size distribution 43specific gravity 22specific surface 9structure 17, 18

Soil permeability 87Soils

aeolin 8alluvial 8classification 69colluvial 8glacial 8identification 68inorganic 8lacustrine 8organic 8residual 8transported 8

Specific gravity 22correction 42

Stability analysis of finite slopesBishop and Morgenstern method 404Bishop's method 400Culmann method 376Friction-circle method 382

Page 43: Appendix & Index

Index 1029

(f)u = 0 method 380Morgenstern method 405slices method, conventional 393Spencer method 409Taylor's stability number 389

Standard penetration test 322, 327standardization 327

Static cone penetration test 332Stokes' law 36Stress, effective 143-144

pore water 143-144Suction pressure 149Surface tension 149-150, 155Swell index 223, 811Swelling potential 804, 812-813

pressure 804

Taj Mahal 2Taylor's stability number 389, 390Thixotropy 59Torvane shear test 302Toughness index 54Transcona grain elevator 533, 536Turbulent flow 88

uUnconfined aquifer 97Unconfined compressive strength 58

related to consistency 58Uplift pressure 123

VVane shear test 300Velocity

discharge 90, 91seepage 90, 91

Void ratio 21Volumetric Shrinkage 56

wWater content 21Westergaard's point load formula 175

Zero air void line 955