Shear Strength of Soils · 2019-11-19 · The shear strength of the soil is related to • Material property of soil • Magnitude and method of loading • Previous stress history

19-11-2019

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Shear Strength of SoilsStrength of different

materials

Steel

Tensile

strength

Concrete

Compressive

strength

Presence of pore waterComplex

behavior

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2

In the most of the problems in soil engineering such as

• Foundation of structures (Deep and Shallow),

• Earthwork Engineering

• Design of Retaining Structures

• Canal and River embankment

• Design of Pavements etc,

the soil mass has to withstand the shearing stresses.

Shearing stresses tend to displace a part of soil mass relative to

the rest of the soil mass

Shearing strength of a soil is the capacity of the soil to resist

shearing stress.

It can be defined as the maximum value of shear stress that

can be mobilised within a soil mass.

If this value is equalled by the shear stress on any plane or a

surface at a point, failure will occur in the soil because of

movement of a portion of the soil mass along that particular

plane or surface.

The soil is then said to have failed in shear

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Shear failure mechanism

At failure, shear stress along the failure surface () reaches the shear strength (f).

All stability analysis, which use Limit Equilibrium Approach,

requires the determination of the limiting shearing resistance.

Hence, the shear strength is one of the most important

property of the soil.

However, its determination is quite complex.

The shear strength of the soil is related to

• Material property of soil

• Magnitude and method of loading

• Previous stress history

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a general shear failure ruptures and pushes up

the soil on both sides of the footing. For actual

failures in the field, the soil is often pushed up

on only one side of the footing with subsequent

tilting of the structure. A general shear failure

occurs for soils that are in a dense or hard state.

Local shear failure can be considered as a

transitional phase between general shear and

punching shear. Because of the transitional

nature of local shear failure, the bearing

capacity could be defined as the first major

nonlinearity in the load-settlement curve (open

circle) or at the point where the settlement

rapidly increases (solid circle). A local shear

failure occurs for soils that are in a medium

dense or firm state.

The process of deformation of the footing

involves compression of soil directly below the

footing as well as the vertical shearing of soil

around the footing perimeter. The load

settlement curve does not have a dramatic break

and for punching shear, the bearing capacity is

often defined as the first major non linearity in

the load-settlement curve (open circle). A

punching shear failure occurs for soils that are

in a loose or soft state.

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 .

f c tan

CohesionFriction angle

f

c

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(in terms of effective stresses)

f is the maximum shear stress the soil can take without

failure, under normal effective stress of ’.

’

c’

f c' ' tan'

’

Effective cohesion Effective

friction anglef

’

' u

u = pore water

pressure


’f

f

’

Shear strength consists of two components:

cohesive and frictional.

'

c’

’f tan ’

c’

f c' ' f tan'frictional component

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c and are measures of shear strength.

Higher the values, higher the shear strength.

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Mohr Circle of stress

Soil element

’1

’1

’3’3

’

Resolving forces in and directions,

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Soil element

’

Soil elementSoil element


’1

’1

’3’3

’

’1 3

2

2

' '

1 3

'

3 '

1 ' '

Soil element

’

Soil elementSoil element


’1

’1

’3’3

’

’1 3

2

'

3 '

1

PD = Pole w.r.t. plane

’,

2

' '

1 3

' '

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Mohr Circles & Failure Envelope

XY

Y ~ stable

X ~ failure

’

f c' ' tan '


Y c

c

Initially, Mohr circle is a point

c +

The soil element does not fail if

the Mohr circle is contained

within the envelope

GL

c

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Y c

c

As loading progresses, Mohr

circle becomes larger…

.. and finally failure occurs

when Mohr circle touches the

envelope

GL

c

’1 3

23

'

1

'

PD = Pole w.r.t. plane

f ’,

Orientation of Failure Plane

’

’1

’1

’3’3

’

Failure envelope

’

Therefore,

+ ’ = 2

45 + ’/2

' '

2

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Mohr circles in terms of total & effective stresses

Xh’

X

u

u

= +

vh ’

effective stresses

uv ’ h

X

v v’

h

total stresses

or

Failure envelopes in terms of total & effective

stresses

Xh’

X

u

u

= +

h’

effective stresses

uvv’ h

X

v v’

h

or

If X is on

failure

total stresses

Failure envelope in

terms of total stresses

’

c’ c

Failure envelope in terms

of effective stresses

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Mohr Coulomb failure criterion with Mohr circle

of stress

’v = ’1

’h = ’3X

X is on failure1

’3

effective stresses

’

c’

Failure envelope in terms


c’ Cot ,

,

2

Therefore,

, ,

2

’

Mohr Coulomb failure criterion with Mohr circle

of stress

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Types Of Soil Based On

Total Strength

1. Cohesion less soil (Ф- Soil)

These are the soils which do not have cohesion.

(C=0)

These soils derive the shear strength from the intergranular friction.

These soils are also called frictional soils.

Examples: Sands and gravels.

Equation for strength is,

S= σ . Tan Ф

2. Purely cohesive soil: (C-Soil)

These are the soils which exhibit cohesion

but, the angle of shearing resistance,Ф=0

These soils are called C-Soils.

Example: Saturated clays

Equation for shear strength is

S=C

3. Cohesive frictional soil: (C-Ф soil)

These are composite soil having c and Ф both.

These are also called C-Ф soils.

Example: Clayey sand, silty sand, sandy clay

The equation for shear strength is,

S= C + σ tan Ф

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Determination of shear strength parameters of

soils (c, or c’, ’

Laboratory

specimens

tests on

taken from

representative undisturbed

samples

Field tests

Most common laboratory tests

to determine the shear strength

parameters are,

1.Direct shear test

2.Triaxial shear test

Other laboratory tests include,

Direct simple shear test, torsional

ring shear test, plane strain triaxial

test, laboratory vane shear test,

laboratory fall cone test

1. Vane shear test

2. Torvane

3. Pocket penetrometer

4. Fall cone

5. Pressuremeter

6. Static cone penetrometer

7. Standard penetration test

Laboratory tests

Field conditions

z

vc

hchc

Before construction

A representative

soil sample

vc

zvc +

hc

After and during

construction

hc

vc +

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Laboratory tests

Simulating field conditions

in the laboratory

Step 1

Set the specimen in

the apparatus

apply the

and

initial

stress condition

vc

vc

hchc

Representative

soil sample

taken from the

site

0

00

0

Step 2

Apply

corresponding

the

field

stress conditions

vc +

hchc

vc +

vc

vc

The test is carried out on a soil sample confined in a metal box of

square cross-section which is split horizontally at mid-height. A

small clearance is maintained between the two halves of the box.

The soil is sheared along a predetermined plane by moving the

top half of the box relative to the bottom half. The box is usually

square in plan of size 60 mm x 60 mm.

Direct shear test

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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

If the soil sample is fully or partially saturated, perforated metal

plates and porous stones are placed below and above the sample

to allow free drainage. If the sample is dry, solid metal plates are

used.

A load normal to the plane of shearing can be applied to the soil

sample through the lid of the box.

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Direct shear test

Leveling the top surface

of specimen

Preparation of a sand specimen

Specimen preparation

completed

Pressure plate

Tests on sands and gravels can be performed quickly, and are

usually performed dry as it is found that water does not

significantly affect the drained strength.

For clays, the rate of shearing must be chosen to prevent excess

pore pressures building up.

As a vertical normal load is applied to the sample, shear stress is

gradually applied horizontally, by causing the two halves of the

box to move relative to each other. The shear load is measured

together with the corresponding shear displacement.

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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

Direct shear test

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

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

PTest procedure

Pressure plate

Steel ball

Proving ring

to measure

shear force

S

Porous

plates

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Direct shear test

Shear box

Loading frame to

apply vertical load

Dial gauge to

measure vertical

displacement

Dial gauge to

measure horizontal

displacement

Proving ring

to measure

shear force

A number of samples of the soil are tested each under different

vertical loads and the value of shear stress at failure is plotted

against the normal stress for each test.

Provided there is no excess pore water pressure in the soil, the

total and effective stresses will be identical.

From the stresses at failure, the failure envelope can be obtained.

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PRINCIPLE OF DIRECT SHEAR TEST

MN = plane of shear failure

N = vertical normal load

F = horizontal shear force

= Major principal stress = Minor principal stress

3

Sh

ea

r

str

es

s,

Shear displacement

Dense sand/

OC clay f

Loose sand/

NC clay f

Dense sand/OC Clay

Ch

an

ge

inh

eig

ht

of

the

sa

mp

le Ex

pa

nsio

nC

om

pre

ssio

n Shear displacement

Loose sand/NC Clay

Direct shear tests on sandsStress-strain relationship

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f1

Normal stress = 1

Direct shear tests on sands

Sh

ea

r

str

es

s,

Shear displacement

f2

f3

How to determine strength parameters c and

Normal stress = 3

Normal stress = 2

Sh

ea

rs

tre

ss

at

fail

ure

,

f

Normal stress,

Mohr – Coulomb failure envelope

Direct shear tests on sands

Some important facts on strength parameters c and of sand

Sand is cohesionless

hence c = 0

Direct shear tests are

drained and pore

water pressures are

dissipated, hence u =0

Therefore,

’ = and c’ = c = 0

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Direct shear tests on clays

Failure envelopes for clay from drained direct shear tests

Sh

ea

rstr

es

sa

tfa

ilu

re,

f

Normally consolidated clay (c’ = 0)

Normal force,

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)

Interface tests on direct shear apparatus

In many foundation design problems and retaining wall problems, it

is required to determine the angle of internal friction between soil

and the structural material (concrete, steel or wood)

af c ' tan

Where,

ac = adhesion,

= angle of internal friction

Soil

Foundation materialFoundation material

Soil

P

S

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MERITS OF SHEAR TEST

The sample preparation is easy. The test is simple and convenient.

As the thickness of the sample is small the drainage is quick and the pore

pressure dissipates very rapidly.

It is ideally suited for conducting drained tests on cohesion less soils.

The apparatus is relatively cheap.

DEMERITS OF SHEAR TEST

The stress conditions are known only at failure.

The orientation of the failure plane is predetermined. This may not be weakest

plane.

Control on the drainage condition is very difficult. Consequently only drained

tests can be conducted on highly permeable soils.

There is no provision for measuring pore water pressure in the shear box and

so it is not possible to determine effective stresses from undrained tests.

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Q. A series of Triaxial shear test were performed on a soil. Each testwas carried until the soil sample failed. The confining pressure andthe total axial stress are given in the Table. Find out the value ofshear strength parameter by graphical method (mohr’s circlemethod) and by analytical method.

Hint:1 =N2 2cN

Where;

N = tan(45+2

Test Confining Pressure,

(kN/m2)Total Axial Stress,

(kN/m2)

1 300 876

2 400 1160

3 500 1460

Triaxial Shear Test Problem:Triaxial Shear Test

Soil sample

at failure

Failure plane

Porous

stone

impervious

membrane

Piston (to apply deviatoric stress)

O-ring

pedestal

Perspex

cell

Cell pressure

Back pressure Pore pressure or

volume change

Water

Soil

sample

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Triaxial Shear Test

Specimen preparation (undisturbed sample)

Sampling tubes

Sample extruder

Triaxial Shear Test


Edges of the sample

are carefully trimmed

Setting up the sample

in the triaxial cell

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Triaxial Shear Test

Sample

with

is covered

a rubber

membrane and sealed

Cell is completely

filled with water


Triaxial Shear Test


Proving ring to

measure the

deviator load

Dial gauge to

measure vertical

displacement

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Types of Triaxial Tests

Is the drainage valve open?

yes no

Consolidated

sampleUnconsolidated

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

Types of Triaxial Tests


yes no

Consolidated

sampleUnconsolidated

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

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Consolidated- drained test (CD Test)

Step 1: At the end of consolidation

VC

hC

Total, = Neutral, u Effective,

+

0

Step 2: During axial stress increase

VC =

VC

hC =

hC

VC +

hC 0

V = VC +

= 1

h = hC

= 3

Drainage

Drainage

Step 3: At failure

VC + f

hC 0

Vf = VC +

f =

1f

hf = hC

= 3f

Drainage

Deviator stress (q or d) = 1 –3


1 = VC +

3 = hC

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Vo

lum

ech

an

ge

of

the

sa

mp

le

Ex

pa

nsio

nC

om

pre

ssio

n

Time

Volume change of sample during consolidation


Devia

tor

str

es

s,

d

Vo

lum

ech

an

ge

of

the

sam

ple Ex

pan

sio

nC

om

pre

ssio

n

Axial strain

Dense sand

or OC clay

Axial strain

Loose sand

or NC clay

Stress-strain relationship during shearing

Dense sand

or OC clay

d)f


Loose sand

or NC Clayd)f

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CD tests

Devia

tor

str

ess

,

d

Axial strain

Sh

ea

r

str

es

s,

or

Mohr – Coulomb

failure envelope

d)f

a

Confining stress = 3ad)f

b


d)f

c

Confining stress = 3c

Confining stress = 3b

3c 1c3a 1a

(d)f

3b 1b

( )d fb

1 3 = +

(d)f

3

CD tests

Strength parameters c and obtained from CD tests

Since u = 0 in CD

tests, = ’

Therefore, c = c’

and = ’

cd and d are used

to denote them

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CD tests Failure envelopes

Sh

ea

r

str

es

s,

Or ’

Mohr – Coulomb

failure envelope

3a 1a

(d)f

For sand and NC Clay, cd = 0

Therefore, one CD test would be sufficient to determine d

of sand or NC clay

CD tests Failure envelopes

For OC Clay, cd ≠ 0

or

3 1

(d)f

c

c

OC NC

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Some practical applications of CD analysis for

clays

= in situ drained

shear strength

Soft clay

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

deposit


clays

2. Earth dam with steady state seepage

Core

= drained shear

strength of clay core

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clays

3. Excavation or natural slope in clay

= In situ drained shear strength

Note: CD test simulates the long term condition in the field.

Thus, cd and d should be used to evaluate the long

term behavior of soils

Consolidated- Undrained test (CU Test)

Step 1: At the end of consolidation

VC

hC

Total, Neutral, u Effective,

= +

0

Step 2: During axial stress increase

VC =

VC

hC =

hC

VC +

hC ±

u

Drainage

Step 3: At failure

VC + f

hC

No

drainage

No

drainage ±uf

V = VC + ± u

= 1

h hC = ± u

= 3

f Vf = VC + ± uf

= 1f

hf hC f

= 3f

= ± u

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Vo

lum

ech

an

ge

of

the

sa

mp

le

Ex

pa

nsio

nC

om

pre

ssio

n

Time

Volume change of sample during consolidation


Devia

tor

str

es

s,

d

u

+-

Axial strain

Loose

sand /NC

ClayAxial strain

Dense sand

or OC clay

Stress-strain relationship during shearing

Dense sand

or OC clay

d)f


Loose sand

or NC Clayd)f

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CU tests How to determine strength parameters c and

Devia

tor

str

ess

,

d

Axial strain

Sh

ea

r

str

es

s,

or

d)f

b

3b 1b3a 1a

( )d fa

cuMohr – Coulomb

failure envelope in


ccu

1 = 3 +

(d)f

3

Total stresses at failure

d)f

a

Confining stress = 3b

Confining stress = 3a

(d)fa

CU tests

Sh

ea

r

str

es

s,

or

3b 1b

3a

d)fa

cu

Mohr – Coulomb

failure envelope in


ccu 3

b

11ba

3a

(

1a

Mohr – Coulomb failure

envelope in terms of

effective stresses

C’ ufa

ufb


1 = 3 + ( d)f -

uf

= 3 -

uf

Effective stresses at failure

uf

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CU tests

Shear strength

parameters in terms

of total stresses are

ccu and cu

Strength parameters c and obtained from CD tests

Shear strengthparameters in terms


are c’ and

c’ = cd and =

d

CU tests Failure envelopes

For sand and NC Clay, ccu and c’ = 0

CU testTherefore, one would be sufficient to determine

cu and =d) of sand or NC clay

Sh

ea

r

str

es

s,

or

cuMohr – Coulomb

failure envelope in


3a

(d)f

a

3a 1a 1a

’

Mohr – Coulomb failure

envelope in terms of

effective stresses

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Some practical applications of CU analysis for

clays

= in situ

undrained shear

strength

Soft clay

1. Embankment constructed rapidly over a soft clay deposit


clays

2. Rapid drawdown behind an earth dam

Core

= Undrained shear

strength of clay core

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clays

3. Rapid construction of an embankment on a natural slope

Note: Total stress parameters from CU test (ccu and cu) 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

= In situ undrained shear strength

Unconsolidated- Undrained test (UU Test)

Data analysis

C = 3

C = 3

No

drainage

Initial specimen condition

3 + d

3

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 – H) = A0 × H0

A ×(1 – H/H0) =A0

A

1 z

A 0

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Step 1: Immediately after sampling

0

0

= +

Step 2: After application of hydrostatic cell pressure

uc = B3

C = 3

C = 3 uc

3 = 3

- uc

3 = 3

- uc

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, uc = 3)


Step 3: During application of axial load

3 + d

3

No

drainage

1 = 3 + d - uc

ud

3 3 = - uc ud

ud =AB d

uc ± ud

= +

Increase of pwp due to

increase of deviator stressof deviatorIncrease

stress

Skempton’s pore water

pressure parameter, A

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u = uc + ud

Combining steps 2 and 3,

uc = B 3 ud =ABd

Total pore water pressure increment at any stage, u

u = B [3 + Ad]

Skempton’s pore

water pressure

equation

u = B [ 3 + A(1 – 3]


Derivation of Skempton’s pore water pressure equation

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Step 1 :Increment of isotropic stress

2

3

1

No drainage

1 + 3

3 + 3

2 + 3

No drainage

uc

Increase in effective stress in each direction = 3 - uc


Step 2 :Increment of major principal stress

2

3

1

No drainage

1 + 1

3 + 0

2 + 0

No drainage

uc

ud

Increase in effective stress in 1 direction = 1 -

Increase in effective stress in 2 and 3 directions = -u

dAverage Increase in effective stress = ( 1 - ud - ud – ud)/

3

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Typical values for parameter B Typical values for parameter A

1 – 3

u

Axial strain

NC Clay (low sensitivity)

(A = 0.5 – 1.0)

NC Clay (High sensitivity)

(A > 1.0)

Axial strain

u

1 – 3

Collapse of soil structure may occur in high sensitivity

clays due to very high pore water pressure generation

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Typical values for parameter A

1 – 3

Axial strain

OC Clay (Lightly overconsolidated)

(A = 0.0 – 0.5)

OC Clay (Heavily

overconsolidated)

(A = -0.5 - 0.0)

During the increase of major principal stress pore water

pressure can become negative in heavily overconsolidated

clays due to dilation of specimen

u

1 – 3

Axial strain

u

Typical values for parameter A

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Documents

Shear Strength of Soils · 2019-11-19 · The shear strength of the soil is related to • Material property of soil • Magnitude and method of loading • Previous stress history