shear strength of soils fars science and research branch, islamic azad university

Shear Strength of Soils

Fars Science and Research Branch,

Islamic Azad University

2

Mohr-Coulomb Failure Criterion(in terms of total stresses)

f is the maximum shear stress the soil can take without failure, under normal stress of .

tancf

c

failure envelope

Cohesion

Friction anglef

3

Mohr-Coulomb Failure Criterion(in terms of effective stresses)

f is the maximum shear stress the soil can take without failure, under normal effective stress of ’.

’

'tan'' cf

c’

’

failure envelope

Effective

cohesion

Effectivefriction angle

f

’

u '

u = pore water pressure

4

Mohr-Coulomb Failure Criterion

'tan'' ff c

Shear strength consists of two components: cohesive and frictional.

’f

f

’

'

c’ c’cohesive

component

’f tan ’ frictional component

s’

2

'3

'1 '

3 '1

PD = Pole w.r.t. plane

q

(s’, tf)

Orientation of Failure Plane

f’

’1

’1

’3’3

’

’1

’1

’3’3

’

Failure envelope

(90 – )q

Therefore,

90 – + q f’ = q = q 45 + f’/2

6

Other laboratory tests include,Direct simple shear test, torsional ring shear test, plane strain triaxial test,

Determination of shear strength parameters of soils (c, f or c’, f’)

Laboratory tests on specimens taken from representative undisturbed samples

Field tests

Most common laboratory tests to determine the shear strength parameters are,

1.Direct shear test2.Triaxial shear test

1. Vane shear test2. Torvane3. Pocket penetrometer4. Pressuremeter5. Static cone penetrometer6. Standard penetration test

7

Laboratory tests

Field conditions

z svc

svc

shcshc

Before construction

A representative soil sample

z svc + Ds

shcshc

After and during construction

svc + Ds

8

Laboratory testsSimulating field conditions in the laboratory

Step 1

Set the specimen in the apparatus and apply the initial stress condition

svc

svc

shcshc

Representative soil sample taken from the site

0

00

0

Step 2

Apply the corresponding field stress conditions

svc + Ds

shcshc

svc + DsTraxial t

est

svc

svc

t

t

Direct shear test

9

Direct shear testSchematic diagram of the direct shear apparatus

10

Direct shear test

Preparation of a sand specimen

Components of the shear box Preparation of a sand specimen

Porous plates

Direct shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays

11

Direct shear test

Leveling the top surface of specimen

Preparation of a sand specimen

Specimen preparation completed

Pressure plate

12

Direct shear test

Test procedure

Porous plates

Pressure plate

Steel ball

Step 1: Apply a vertical load to the specimen and wait for consolidation

P

Proving ring to measure shear force

S

13

Direct shear test

Step 2: Lower box is subjected to a horizontal displacement at a constant rate

Step 1: Apply a vertical load to the specimen and wait for consolidation

PTest procedure

Pressure plate

Steel ball


S

Porous plates

14

Direct shear test

Shear box

Loading frame to apply vertical load

Dial gauge to measure vertical displacement

Dial gauge to measure horizontal displacement


15

Direct shear testAnalysis of test results

sample theofsection cross of Area

(P) force Normal stress Normal

sample theofsection cross of Area

(S) surface sliding at the developed resistanceShear stressShear

Note: Cross-sectional area of the sample changes with the horizontal displacement

16

Direct shear tests on sands

Sh

ear

str

ess

, t

Shear displacement

Dense sand/ OC clay

tfLoose sand/ NC claytf

Dense sand/OC Clay

Loose sand/NC Clay

Ch

ang

e in

hei

gh

t o

f th

e sa

mp

le Exp

ansi

on

Co

mp

ress

ion Shear displacement

Stress-strain relationship

17

tf1

Normal stress = s1

Direct shear tests on sandsHow to determine strength parameters c and f

Sh

ear

stre

ss,

t

Shear displacement

tf2

Normal stress = s2

tf3

Normal stress = s3

Sh

ear

stre

ss a

t fa

ilu

re,

tf

Normal stress, s

fMohr – Coulomb failure envelope

18

Direct shear tests on sandsSome important facts on strength parameters c and f of sand

Sand is cohesionless hence c = 0

Direct shear tests are drained and pore water pressures are dissipated, hence u = 0

Therefore,

f’ = f and c’ = c = 0

19

Direct shear tests on clays

Failure envelopes for clay from drained direct shear tests

Sh

ear

stre

ss a

t fa

ilu

re,

tf

Normal force, s

f’

Normally consolidated clay (c’ = 0)

In case of clay, horizontal displacement should be applied at a very slow rate to allow dissipation of pore water pressure (therefore, one test would take several days to finish)

Overconsolidated clay (c’ ≠ 0)

20

Advantages of direct shear apparatus

Due to the smaller thickness of the sample, rapid drainage can be achieved

Can be used to determine interface strength parameters

Clay samples can be oriented along the plane of weakness or an identified failure plane

Disadvantages of direct shear apparatus

Failure occurs along a predetermined failure plane

Area of the sliding surface changes as the test progresses

Non-uniform distribution of shear stress along the failure surface

21

Triaxial Shear Test

Soil sample at failure

Failure plane

Porous stone

impervious membrane

Piston (to apply deviatoric stress)

O-ring

pedestal

Perspex cell

Cell pressureBack pressure Pore pressure or

volume change

Water

Soil sample

22

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Edges of the sample are carefully trimmed

Setting up the sample in the triaxial cell

23

Triaxial Shear Test

Sample is covered with a rubber membrane and sealed

Cell is completely filled with water

Specimen preparation (undisturbed sample)

24

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Proving ring to measure the deviator load

Dial gauge to measure vertical displacement

25

Types of Triaxial Tests

Is the drainage valve open?

yes no

Consolidated sample

Unconsolidated sample


yes no

Drained loading

Undrained loading

Under all-around cell pressure c

cc

c

cStep 1

deviatoric stress ( = q)

Shearing (loading)

Step 2

c c

c+ q

26

Types of Triaxial Tests


yes no

Consolidated sample

Unconsolidated sample

Under all-around cell pressure c

Step 1


yes no

Drained loading

Undrained loading

Shearing (loading)

Step 2

CD test

CU test

UU test

27

Consolidated- drained test (CD Test)

Step 1: At the end of consolidationsVC

shC

Total, s = Neutral, u Effective, s’+

0

Step 2: During axial stress increase

s’VC = sVC

s’hC = shC

sVC + Ds

shC 0

s’V = sVC + Ds = s’1

s’h = shC = s’3

Drainage

Drainage

Step 3: At failuresVC + Dsf

shC 0

s’Vf = sVC + Dsf = s’1f

s’hf = shC = s’3fDrainage

28

Deviator stress (q or Dsd) = s1 – s3


s1 = sVC + Ds

s3 = shC

29

Vo

lum

e ch

ang

e o

f th

e sa

mp

le

Exp

ansi

on

Co

mp

ress

ion

Time

Volume change of sample during consolidation


30

De

via

tor

str

ess

, D

sd

Axial strain

Dense sand or OC clay

(Dsd)f


Loose sand or NC clay

Vo

lum

e ch

ang

e o

f th

e sa

mp

le Exp

ansi

on

Co

mp

ress

ion Axial strain

Stress-strain relationship during shearing


Loose sand or NC Clay(Dsd)f

31

CD tests How to determine strength parameters c and fD

evia

tor

stre

ss,

Ds

d

Axial strain

Sh

ear

stre

ss,

t

sor s’

fMohr – Coulomb failure envelope

(Dsd)fa

Confining stress = s3a(Dsd)fb

Confining stress = s3b

(Dsd)fc

Confining stress = s3c

s3c s1cs3a s1a

(Dsd)fa

s3b s1b

(Dsd)fb

s1 = s3 + (Dsd)f

s3

32

CD tests

Strength parameters c and f obtained from CD tests

Since u = 0 in CD tests, s = s’

Therefore, c = c’ and f = f’

cd and fd are used to denote them

33

CD tests Failure envelopesS

hea

r st

ress

, t

sor s’

fd

Mohr – Coulomb failure envelope

s3a s1a

(Dsd)fa

For sand and NC Clay, cd = 0

Therefore, one CD test would be sufficient to determine fd

of sand or NC clay

34

CD tests Failure envelopes

For OC Clay, cd ≠ 0

t

sor s’

f

s3 s1

(Dsd)f

csc

OC NC

35

Some practical applications of CD analysis for clays

t t = in situ drained shear strength

Soft clay

1. Embankment constructed very slowly, in layers over a soft clay deposit

36


2. Earth dam with steady state seepage

t = drained shear strength of clay core

t

Core

37


3. Excavation or natural slope in clay

t = In situ drained shear strength

t

Note: CD test simulates the long term condition in the field. Thus, cd and fd should be used to evaluate the long term behavior of soils

38

Consolidated- Undrained test (CU Test)

Step 1: At the end of consolidationsVC

shC


0

Step 2: During axial stress increase

s’VC = sVC

s’hC = shC

sVC + Ds

shC ±Du

Drainage

Step 3: At failuresVC + Dsf

shC

No drainage

No drainage ±Duf

s’V = sVC + Ds ± Du = s’1

s’h = shC ± Du = s’3

s’Vf = sVC + Dsf ± Duf = s’1f

s’hf = shC ± Duf = s’3f

39

Vo

lum

e ch

ang

e o

f th

e sa

mp

le

Exp

ansi

on

Co

mp

ress

ion

Time

Volume change of sample during consolidation


40

De

via

tor

str

ess

, D

sd

Axial strain


(Dsd)f


Loose sand /NC Clay

Du

+-

Axial strain

Stress-strain relationship during shearing


Loose sand or NC Clay(Dsd)f

41

CU tests How to determine strength parameters c and fD

evia

tor

stre

ss,

Ds

d

Axial strain

Sh

ear

stre

ss,

t

sor s’

(Dsd)fb

Confining stress = s3b

s3b s1bs3a s1a

(Dsd)fa

fcuMohr – Coulomb failure envelope in terms of total stresses

ccu

s1 = s3 + (Dsd)f

s3

Total stresses at failure(Dsd)fa

Confining stress = s3a

42(Dsd)fa

CU tests How to determine strength parameters c and fS

hea

r st

ress

, t

sor s’s3b s1bs3a s1a

(Dsd)fa

fcu

Mohr – Coulomb failure envelope in terms of total stresses

ccus’3b s’1b

s’3a s’1a

Mohr – Coulomb failure envelope in terms of effective stresses

f’

C’ ufa

ufb

s’1 = s3 + (Dsd)f - uf

s’3 = s3 - uf

Effective stresses at failure

uf

43

CU tests

Strength parameters c and f obtained from CD tests

Shear strength parameters in terms of total stresses are ccu and fcu

Shear strength parameters in terms of effective stresses are c’ and f’

c’ = cd and f’ = fd

44

CU tests Failure envelopes

For sand and NC Clay, ccu and c’ = 0

Therefore, one CU test would be sufficient to determine fcu and f’(= fd) of sand or NC clay

Sh

ear

stre

ss,

t

sor s’

fcuMohr – Coulomb failure envelope in terms of total stresses

s3a s1a

(Dsd)fa

s3a s1a

f’

Mohr – Coulomb failure envelope in terms of effective stresses

45

Some practical applications of CU analysis for clays

t t = in situ undrained shear strength

Soft clay

1. Embankment constructed rapidly over a soft clay deposit

46


2. Rapid drawdown behind an earth dam

t = Undrained shear strength of clay core

Core

t

47


3. Rapid construction of an embankment on a natural slope

Note: Total stress parameters from CU test (ccu and fcu) can be used for stability problems where,

Soil have become fully consolidated and are at equilibrium with the existing stress state; Then for some reason additional stresses are applied quickly with no drainage occurring

t = In situ undrained shear strength

t

48

Unconsolidated- Undrained test (UU Test)Data analysis

sC = s3

sC = s3

No drainage

Initial specimen condition

s3 + Dsd

s3

No drainage

Specimen condition during shearing

Initial volume of the sample = A0 × H0

Volume of the sample during shearing = A × H

Since the test is conducted under undrained condition,

A × H = A0 × H0

A ×(H0 – DH) = A0 × H0

A ×(1 – DH/H0) = A0z

AA

10

49

Unconsolidated- Undrained test (UU Test)

Step 1: Immediately after sampling0

0

= +

Step 2: After application of hydrostatic cell pressure

Duc = B Ds3

sC = s3

sC = s3 Duc

s’3 = s3 - Duc

s’3 = s3 - Duc

No drainage

Increase of pwp due to increase of cell pressure

Increase of cell pressure

Skempton’s pore water pressure parameter, B

Note: If soil is fully saturated, then B = 1 (hence, Duc = Ds3)

50


Step 3: During application of axial load

s3 + Dsd

s3

No drainage

s’1 = s3 + Dsd - Duc Dud

s’3 = s3 - Duc Dud

Dud = ABDsd

Duc ±

Dud

= +

Increase of pwp due to increase of deviator stress

Increase of deviator stress

Skempton’s pore water pressure parameter, A

51


Combining steps 2 and 3,

Duc = B Ds3 Dud = ABDsd

Du = Duc + Dud

Total pore water pressure increment at any stage, Du

Du = B [Ds3 + ADsd]

Skempton’s pore water pressure equation

Du = B [Ds3 + A(Ds1 – Ds3]

52


Step 1: Immediately after sampling

0

0


-ur

Step 2: After application of hydrostatic cell pressure

s’V0 = ur

s’h0 = ur

sC

sC

-ur + Duc = -ur + sc

(Sr = 100% ; B = 1)Step 3: During application of axial load

sC + Ds

sC

No drainage

No drainage

-ur + sc ± Du

s’VC = sC + ur - sC = ur

s’h = ur

Step 3: At failure

s’V = sC + Ds + ur - sc Du

s’h = sC + ur - sc Du

s’hf = sC + ur - sc Duf

= s’3f

s’Vf = sC + Dsf + ur - sc Duf = s’1f

-ur + sc ± Duf

sC

sC + DsfNo drainage

53


Total, s = Neutral, u Effective, s’+Step 3: At failure


= s’3f


-ur + sc ± Duf

sC

sC + DsfNo drainage

Mohr circle in terms of effective stresses do not depend on the cell pressure.

Therefore, we get only one Mohr circle in terms of effective stress for different cell pressures

t

s’s’3 s’1Dsf

54s3b s1bs3a s1aDsfs’3 s’1


Total, s = Neutral, u Effective, s’+Step 3: At failure


= s’3f


-ur + sc ± Duf

sC

sC + DsfNo drainage

t

s or s’

Mohr circles in terms of total stresses

uaub

Failure envelope, fu = 0

cu

55

s3b s1b


Effect of degree of saturation on failure envelope

s3a s1as3c s1c

t

s or s’

S < 100% S > 100%

56

Some practical applications of UU analysis for clays

t t = in situ undrained shear strength

Soft clay

1. Embankment constructed rapidly over a soft clay deposit

57


2. Large earth dam constructed rapidly with no change in water content of soft clay

Core

t = Undrained shear strength of clay core

t

58


3. Footing placed rapidly on clay deposit

t = In situ undrained shear strength

Note: UU test simulates the short term condition in the field. Thus, cu can be used to analyze the short term behavior of soils

59

Unconfined Compression Test (UC Test)

s1 = sVC + Ds

s3 = 0

Confining pressure is zero in the UC test

60

Unconfined Compression Test (UC Test)

s1 = sVC + Dsf

s3 = 0

Sh

ear

stre

ss, t

Normal stress, s

qu

Note: Theoritically qu = cu , However in the actual case qu < cu due to premature failure of the sample

61

Other laboratory shear tests

Direct simple shear test

Torsional ring shear test

Plane strain triaxial test

62





63


Direct shear testf = 80 mm

Soil specimenPorous stones

Spiral wire in rubber membrane


64





65


PeakResidual

t

Shear displacement

tf

s’

f’max

f’res

66


sN

Preparation of ring shaped undisturbed samples is very difficult. Therefore, remoulded samples are used in most cases

67





68


s’1, e1

s’2, e2

s’3, e3

Plane strain test

s’2 ≠ s’3

e2 = 0

s’1

s’2

s’3

s’2

Rigid platens

Specimen

69

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer

Pressuremeter

Static Cone Penetrometer test (Push Cone Penetrometer Test, PCPT)

Standard Penetration Test, SPT

70

In-situ shear tests

Vane shear test (suitable for soft to stiff clays)

Torvane

Pocket Penetrometer

Pressuremeter



71

PLAN VIEW

Vane shear test

This is one of the most versatile and widely used devices used for investigating undrained shear strength (Cu) and sensitivity of soft clays

Bore hole (diameter = DB)

h > 3DB)

Vane

D

H

Applied Torque, T

Vane T

Rupture surface

Disturbed soil

Rate of rotation : 60 – 120 per minute

Test can be conducted at 0.5 m vertical intervals

72

Vane shear test

Since the test is very fast, Unconsolidated Undrained (UU) can be expected

Cu

Cu

T = Ms + Me + Me = Ms + 2Me

Me – Assuming a uniform distribution of shear strength

2

0

).2(

d

ue rCrdrM

2

0

32

0

2

322

d

u

d

ue

rCdrrCM

1283

2 33 dCdCM uu

e

d/2d/2

Cu

h

73

Vane shear test


Cu

Cu

Ms – Shaft shear resistance along the circumference

22

2hdC

ddhCM uus

2122

32

dChd

CT uu

62

32 dhdCT u

62

32 dhd

TCu


74

Vane shear test


Cu

Cu


Me – Assuming a triangular distribution of shear strength

h

d/2d/2

Cu

82

32 dhd

TCu

Can you derive this ???

75

Vane shear test


Cu

Cu


Me – Assuming a parabolic distribution of shear strength

h

203

2

32 dhd

TCu

Can you derive this ???

d/2d/2

Cu

76

Vane shear test


Cu

Cu

h

After the initial test, vane can be rapidly rotated through several revolutions until the clay become remoulded

tpeak tultimate

t

Shear displacement

StengthUltimate

StengthPeakySensitivit

77

In-situ shear tests

Vane shear test

Torvane (suitable for very soft to stiff clays)

Pocket Penetrometer

Pressuremeter



78

Torvane

Torvane is a modification to the vane

79

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer (suitable for very soft to stiff clays)

Pressuremeter



80

Pocket Penetrometer

Pushed directly into the soil. The unconfined compression strength (qu) is measured by a calibrated spring.

81

Swedish Fall Cone (suitable for very soft to soft clays)

The test must be calibrated

Soil sample

Cu ∞ Mass of the cone

∞ 1/(penetration)2

82

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer

Pressuremeter (suitable for all soil types)



83

Pressuremeter

Pre – bored or self – bored hole

Guard cell

Measuring cell

Guard cell

Coaxial tube

Water

Air

84

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer

Pressuremeter

Static Cone Penetrometer test (Push Cone Penetrometer Test, PCPT) (suitable for all soil types except very course granular materials)


85

Static Cone Penetrometer test

Cone penetrometers with pore water pressure measurement capability are known as piezocones

40 mm

40 mm

40 mm

40 mm

86

Static Cone Penetrometer test

Force required for the inner rod to push the tip (Fc) and the total force required to push both the tip and the sleeve (Fc + Fs) will be measured

Point resistance (qc) = Fc/ area of the tip

Sleeve resistance (qs) = Fs/ area of the sleeve in contact with soil

Friction Ratio (fr) = qs/ qc ×100 (%)

Various correlations have been developed to determine soil strength parameters (c, , f ect) from fr

87

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer

Pressuremeter


Standard Penetration Test, SPT (suitable for granular materials)

88


SPT is the most widely used test procedure to determine the properties of in-situ soils

63.5 kg

0.76 m

Drill rod0.15 m0.15 m0.15 m

Number of blows = N1



Standard penetration resistance (SPT N) = N2 + N3

Number of blows for the first 150 mm penetration is disregarded due to the disturbance likely to exist at the bottom of the drill hole

The test can be conducted at every 1m vertical intervals

Various correlations have been developed to determine soil strength parameters (c, , f ect) from N

89


SPT (Manual operation)

shear strength of soils fars science and research branch, islamic azad university

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