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FIG. 2. Values of Friction Angle 4' for Natural Clay Compositions

c4

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Relationship between Cohesion Intercept and Preconsolidation Pressure

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Figure by MIT OCW.

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Relationship between normalized shear stress and effective normal stress forPortuguese Bend bentonitic tuff. Ca Mont. LL = 98 PI = 61 CF = 68

200 300Effective Normal Stress (kPa)

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tanφ

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R Rupturesurface at residual

gatu( (),~~Xc (a)

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Fig. 21. Rupture surfaces predicted by the analyses on 3:1 slopes, 10 m high,with surface suction 10 kPa and varying Ko

Q.

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Note:Accumulated deviatoric plastic strains during excavation εoP < 5%.

Note:Strain-softening starts whenεoP = 5%. It is complete when εoP = 20%.

εoP = 5%εoP = 20%

Rupture Surface

t = 9yr

t = 14.5yr

9 years After Excavation

Rupture Surface

Peak

BetweenResidual

0 25mScale

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P

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a

14.5 years After Excavation - Just Before Collapseb

Typical Analysis (S3): 3:1 slope, 10 m high, Ko = 1.5, Surface Suction 10 kPa. Contours of Accumulated Deviatoric Plastic Strain, εo

Figure by MIT OCW.

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Test on Intact specimens +

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-_ t ¢ ~ * ~ Peak (0I IX Residual

0 O 10O 200 300 400 300 600 700 800 900

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300 - Resia\ -I kN/m Rethsdul strength

IC er ' 150 kN/m 2

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0 I 2 3 4 S 6 7 8 9Displacement: mm

(b)

Fg. 5S. Typical shear stress-displacement curves and strength envelope for direct drained shear tests on LowerOxford Clay specimens sheared parallel to the bedding

co0-

a

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0)O cZ L

4

I

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Plasticity Index, Ip, %

100

φs'

φr'

φr

σn = 100 kPa

'

'

σn = 400 kPa'

σn = 50 kPa'

φr'

φs'

φs'

150

150

10

20

30

40

200 250

0

10

20

Seca

nt F

rictio

n A

ngle

, deg

rees

30

40

0

10

20

30

40

HomogeneousAlong scarpAt residualReactivated slide

Stratified and/or fissured}

Mobilized friction angles back-calculated from reactivated and first-time slope failures compared to the range from empirical information.

Figure by MIT OCW.Adapted from:

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0,'~4

TABLE II. RESULTS OF RESIDUAL STRENGTH TESTS ON M I XTURES.

MineralContent Residual Statem dry wt. - k1.0kg/cms '

Miture a w tI, ..•gtnA. MIXTURES CONTAINING MONTMORILLONITEMontmorillonite - Na 0 50/50 200 92 0.09

andQuartz 25/75 25 75 96 s0 0.1110/90 10 90 44 60 0.426/95 5 95 39 54 0.01

Moatmorillonite - Na 30 50/50 60 50 72 84 0.24and Quartz 25/76 2S 75 51 69 0.36

10/90 10 90 34 64 0.56Montmorillonite- Na 30 50/50 50 50 150 90 0.21

and Amorphous SiO. 25/75 25 75 87 78 0.24Bentoniteand Quartz 0 75/25 44 56 61 84 0.12

50/50 62 38 52 75 0.2626/76 81 19 42 63 0.4015/85 89 11 82 53 0.64

Bentonite and 0 91/9 32 68 70 89 0.10Amorphous SiO 82/18 39 61 A6 84 0.11

68/32 49 51 68 81 0.1347/53 65 35 60 76 0.1826/7 S81 19 47 66 0.2710/90 92 8 51 61 0.49

B. MIXTURES CONTAINING KAOLINITE AND GRUNDITEKaolinite and Quart 0 75/25 25 ' 75 40 88

50/50 50 50 30 7325/75 75 25 23 54

Kaolinite and 0 75/25 25 75 44 89Amorphous Si 50/50 50 50 31 74

Grundite- Na 0 75/25 25 75 67 91and Quatz 50/5 0 50 49 79

25/75 76 25 36 62Grundite - Na 0 75/25 25 75 63 91

and Quartz 50/50 50 50 40 7725/75 75 25 36 62

C. MIXTURES CONTAINING HYDROUS MICAIydrous mica I -N 0 75/2 48 52

and Quaurt 50/50 65 35IHydrous mica I - Na 30 76/25 48 52

and Quatz 50/50 66 35Hydrous mia I - K 0 75/25 48 52

and Quart 50/50 6s 35Hydrous mica I - K 30 75/25 48 52

and Quartz 50/50 6 35Hydrous iica It- Na 0 75/25 33 67

50/50 65 45Hydrous mica II - Na 30 75/25 33 67

ao/so 55 45Hydrous mica I - Ns 0 7/ 33 67

5/5 6 45Hydrous mica III - Na 30 75/25 33 67

50/50 65 45

.1}CY

n17-

Conentt o00 800.32

0.490.650.320.410.250.400.620.220.400.62

ID-

08

i 0630 74 0.3531 65 0.4432 75 0.3833 66 0.4630 74 0.4130 65 0.4741 78 0.4935 67 0.5031 80 0.3222 66 0.4641 83 0.4527 67 0.4754 85 0.4440 74 0.4852 85 0.4446 76 0.50

02

&

I tt"4344ep 4w44a* l~/cppcnsdid

/o, ,-,e/minenI---

A Koolinite II Grundte m

MontmorillcmixturesSymbols-s

O I- -

O 20o| 6P

(0)

-(C)

UonTenT Ofr mcoi ilnruld urw ulr. U W ur. N

Fig. 4. Relative residual strength

O"I

e oav. - e

=

+ZZ.. :.

'-1t I~iZ·IU

n7 O4 (l1xJ t) - (C y)

Ton I rC (laJsy) - 7an (C/#y)

.4

-

f I C-1 W r 'f 0 ~~~46 " I fq-'_-- R7I 't lOf _11

n

---

1'e I d11110 7 J 2 1.7

9 f4 1 .5 M FF Ya/ / ISS I-1/ C

Z

4*1

t

,

0o0 20 40

Plasticity Index Ip %Residual Strength : Correlations with Plasticity Index

DRAINED RESIDUAL STRENGTH OF COHESIVES SOILS

60 80 100

10o

Res

idua

l Fric

tion

Ang

le, φ

R'

20o

30o

40o

0o0 10

P.I. %

10o

φres'

20o

30o

20 30 40 50 60 70 80

40o

Vaughan et al. (1978) σn = 130 - 180 kPa'

Bucher (1975) σn = 72.5 - 269.5 kPa'

Kanji (1974) σn = 147 kPa'Seycek (1978) σn = 300 kPa'Fleischer (1972)Voight (1973)

Figure by MIT OCW.

00

200

400

Dra

ined

Res

idua

l She

ar

Stre

ss (k

Pa)

200

Effective Normal Stress (kPa)

Effect of Clay Mineralogy on Drained Residual Failure Envelopes

400

Incr

easi

ng

liqui

d lim

it

600

35LL

800 1000

010

12

14

16

18

20

22

50

25% 45%

100

Liquid Limit (%)

Reduction in Secant Residual Friction Angle from Effective Normal Stresses of 50 kPa to 700 kPa

(φr)

50 / (

φ r) 70

0'

'

150 200 250 300

0.39

52 0.51

62 0.44

184 1.54288 2.7798 0.9068 0.86

Ag391112

192832

Soil Number(Table 1)

< CF <

45%CF <

20%CF <

Liquid Limit (%)

Seca

nt R

esid

ual F

rictio

n A

ngle

(D

egre

es)

Relationship between Drained Residual Friction Angle and Liquid Limit

<

20%CF <

50%CF <

45%25% CF <<

00 40 80 120 160 200

Effectivenormal stress(kPa)

100400700100400700100400700

20

<50

< <CF 4525

Clay size fraction(%)

240 280

4

8

12

16

20

24

28

32

}

}

}

Figures by MIT OCW.Adapted from:

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