shear strength of soil

Shear Strength of Soil

Prof. Samirsinh P ParmarAssistant Professor, Department of Civil Engineering,Dharmasinh Desai University, Nadiad, Gujarat, INDIAMail: samirddu@gmail.com

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DEFINITIONS OF KEY TERMS• Shear strength of a soil (τf) is the maximum internal resistance to applied shearing forces.• Effective friction angle (Ø´) is a measure of the shear strength of soils due to friction.• Cementation (Ccm) is a measure of the shear strength of a soil from forces that cement the

particles.• Soil tension (Ct) is a measure of the apparent shear strength of a soil from soil suction

(negative pore water pressures or capillary stresses).• Cohesion (Co) is a measure of the intermolecular forces.• Undrained shear strength (Su) is the shear strength of a soil when sheared at constant

volume.• Apparent cohesion (C) is the apparent shear strength at zero normal effective stress.• Critical state is a stress state reached in a soil when continuous shearing occurs at constant

shear stress to normal effective stress ratio and constant volume.• Dilation is a measure of the change in volume of a soil when the soil is distorted by shearing.

Strength of different materials

Tensile strength

Concrete

Compressive strength

Shear strength

Presence of pore waterComplexbehavior

TYPICAL RESPONSE OF SOILS TO SHEARING FORCES

Simple shear deformation of Type I and Type II soils

Ref: Muni Budhu

Embankment

Strip footing

Shear failure of soilsSoils generally fail in shear

Failure surface

Mobilized shear resistance

At failure, shear stress alongthe failuresurface

(mobilized shear resistance) reaches the shear strength.

Retaining wall

Shear failure of soilsSoils generally fail in shear

Retaining wall

Shear failure of soils

At failure, shear stress along the failuresurface(mobilized shear resistance) reaches the shear strength.

Failuresurface

Mobilized shear resistance

Soils generally fail in shear

Shear failure mechanism

failure surface

The soil grains slide over each other along the failure surface.

Nocrushing

of individual grains.

Shear failure mechanism

At failure, shear stressalongreaches the shear strength (f).

thefailure

surface()

INTERPRETATION OF THE SHEAR STRENGTH OF SOILS

Contribution of sliding friction, dilatancy,crushing, and rearrangement of particles onthe peak shear strength of soils.

Mohr-Coulomb Failure Criterion

f is the maximum shear stress the soil can takewithout failure, under normal stress of .

(in terms of total stresses)

Cohesion

Friction anglef

f is the maximum shear stress the soil can takewithout failure, under normal effective stress of ’.

(in terms of effective stresses)

f c' ' tan '

Effective cohesion

Effectivefriction angle

' uu = pore water

pressure

tan' f c' ' f

Shear strength consists of two components: cohesive and frictional.

’f tan ’

frictionalcomponent

c and are measures of shear strength.

Higher the values, higher the shear strength.

Mohr Circle of stress

Soil element

Resolving forces in and directions,

’3’3

Cos2 '

' ' 13

Mohr Circle of stress

PD = Pole w.r.t. plane

Soil elements at different locations

Failure surface

Mohr Circles & Failure Envelope

Y ~ stable

X ~ failure

f c' ' tan '

Initially, Mohr circle is a point

The soil element does not fail if the Mohr circle is contained within the envelope

As loading progresses, Mohrcircle becomes larger…

.. and finally failure occurs when Mohr circle touches the envelope

PD = Pole w.r.t. plane

’, f

Orientation of Failure Plane

’3’3

Failure envelope

Therefore,

– ’ =

45 + ’/2

Mohr circles in terms of total & effective stresses

v v’

h’ X

v’ hh’

effective stresses

total stresses

or ’

Failure envelopes in terms of total & effective stresses

v’ hh’

effective stresses

v v’

h’ X

total stresses

or ’

If X is onfailure

c’ c

Failure envelopein terms of total stresses’

Failure envelope in terms of effective stresses

Mohr Coulomb failure criterion with Mohr circle of stress

’v = ’1

’h = ’3

X is on failure ’1c’’3

effective stresses

’’

Failure envelope in terms of effective stresses

c’ Cot’ ’ ’

’ ’

c'Cot '

Therefore,

Mohr Coulomb failure criterion with Mohr circle of stress

c'Cot '

Sin' '2c'Cos

' 1 Sin' ' 1 Sin' 2c'Cos'

1 31 Sin ' '

1 Sin '

2c' Cos ' 1 Sin

' 2c'Tan 45

' ' Tan2 45

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

Determination ofsoils (c, or c’ ’

shear strength parameters of

Laboratory specimens

testson

taken fromrepresentativesamples

undisturbed

Field tests

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

1.Direct shear test 2.Triaxial shear test

1. Vane shear test2. Torvane3. Pocket penetrometer4. Fall cone5. Pressuremeter6. Static cone penetrometer7. Standard penetration test

LABORATORY TESTS

Laboratory testsHow to take undisturbed samples

Laboratory testsField conditions

zA representativesoil sample

Before construction

z + vc

After and duringconstruction

Laboratory testsSimulating field conditions in the laboratory

Step 1

Set the specimen inthe apparatus and

initialapply thestress condition

Representative soil sample taken from the site

Step 2

Applycorresponding

thefield

stress conditions

Direct shear testSchematic diagram of the direct shear apparatus

Direct shear testPreparation of a sand specimen

Porous plates

Components of the shear box Preparation of a sand specimen

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

Direct shear test Mould

Direct shear test

Leveling the top surface of specimen

Preparation of a sand specimen

Specimen preparation completed

Pressure plate

Direct shear testTest procedure

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

Pressure plate

Porousplates

Steel ballP

Proving ring to measure shear force

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 procedurePressure plate

Porousplates

Steel ball

Direct shear testShear box

Loading frameto apply vertical load

Dial gauge to measure vertical displacement

Dial gauge to measure horizontal displacement

Direct shear testAnalysis of test results

Area of crosssection of the sample

Normalforce(P) Normalstress

Shear stress Shear resistance developedat the sliding surface

(S)Area of cross section of the sampleNote: Cross-sectional area of the sample changes with the horizontal

displacement

Shear displacement

Dense sand/ OC clay

fLoose sand/NC clayf

Dense sand/OC Clay

Direct shear tests on sandsStress-strain relationship

Shear displacementLoose sand/NC Clay

f1Normal stress = 1

Direct shear tests on sands

How to determine strength parameters c and

Normal stress = 3

Normal stress = 2

Shear displacement

Normal stress,

Mohr – Coulomb failure envelope

Direct shear tests on sands

Some important facts on strength parameters c and of sand

Sand is cohesionlesshence c = 0

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

Therefore,

’ = and c’ = c = 0

Direct shear tests on clays

Failure envelopes for clay from drained direct shear testsSh

Normal force,

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)

Interface tests on direct shear apparatusIn 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)

f ca ' tan

Where,

ca = adhesion,

= angle of internal friction

Foundation materialFoundation material

Advantages of direct shear apparatus

Due to the smaller thickness of the sample, rapid drainage canbe 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

Triaxial Shear Test

Soil sample at failure

Failure plane

Porous stone

impervious membrane

Piston (to apply deviatoric stress)

O-ring

pedestal

Perspexcell

Cell pressure Back pressure Pore pressure or

volume change

Soil sample

Triaxial Test Equipment

The Cell (Chamber)

Loading Frame Control Panel

Triaxial Test Equipment

Triaxial Shear TestSpecimen preparation (undisturbed sample)

Sampling tubes

Sample extruder

Edges of the sample are carefully trimmed

Setting up the sample in the triaxial cell

Triaxial Shear Test

Cell is completely filled with water

Specimen preparation (undisturbed sample)

Sample is coveredwith amembrane an

rubber d sealed

Proving ring to measure the deviator load

Dial gauge to measure vertical displacementIn some tests

Types of Triaxial TestsDepending on whether drainage is allowed or not during

initial isotropic cell pressure application, and

shearing,there are three special types of triaxial tests that have practical significances. They are:

Consolidated

Drained (CD) test

Undrained (CU) testUnconsolidated Undrained (UU) test

Types of Triaxial Tests

Is the drainage valve open?

yes no

Consolidatedsample

Unconsolidatedsample

yes no

Drainedloading

Undrainedloading

Under all-around cell pressure c

cStep 1

deviatoric stress ( = q)

Shearing (loading)

Step 2

Types of Triaxial Tests

yes no

Consolidatedsample Unconsolidated

sample

Under all-around cell pressure c

Step 1

yes no

Drainedloading

Undrainedloading

Shearing (loading)

Step 2

CD test

CU test

UU test

Consolidated- drained test (CD Test)

Step 1: At the end of consolidationVC

Total, = Neutral, u Effective, ’+

Step 2: During axial stress increaseVC +

’VC = VC

’hC =hC

’V = VC + =’1

’h = hC = ’3

Drainage

Step 3: At failureVC + f

’Vf = VC + f = ’1f

’hf = hC = ’3fDrainage

1 = VC +

3 = hC

Deviator stress (q or d) = 1 – 3

Volume change of sample during consolidation

Axial strain

Dense sand or OC clay

Axial strain

Loose sandor NC clay

Stress-strain relationship during shearing

Loose sandor NC Clayd)f

CD tests How to determine strength parameters c and

Axial strain

Mohr – Coulomb failure envelope

or ’

Confining stress = 3a

Confining stress = 3c

Confining stress = 3b

CD tests

Strength parameters c and obtained from CD tests

Since u = 0 in CDtests, = ’

Therefore, c = c’and = ’

cd and d are used to denote them

CD tests

Failure envelopes

σ or ’

dMohr – Coulomb failure envelope

( d)fa

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 ’

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

2. Earth dam with steady state seepage

drained

strength of clay core

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

SHEAR STRENGTH OF SOIL

SELECTION OF TRIAXIAL TESTSoil type Type of construction Type of tests and shear strength

Cohesive Short term (end ofconstruction time)

Triaxial UU or CU for Undrained Strength with appropriatelevel of insitu strength

Staging Construction Triaxial CU for Undrained Strength with appropriate level of insitu strength

Long term Triaxial CU with pore water pressure measurement or Triaxial CD for effective shear strength parameter

Granular All Strength parameter ’ which is got from field investigation ordirect shear test

Material c- Long Term Triaxial CU with pore water pressure measurement or TriaxialCD for effective shear strength parameter

Consolidated- Undrained test (CU Test)

Step 1: At the end of consolidation VC

Total, = +Neutral, u Effective, ’

Step 2: During axial stress increase VC +

’VC = VC

Drainage

Step 3: At failure VC + f

No drainage

’V = VC

+ ± u = ’1

’h = hC

u = ’3

’Vf = VC + f

uf = ’1f

’hf =

uf = ’3f

Volume change of sample during consolidationConsolidated- Undrained test (CU Test)

Axial strain

Loose sand/NC Clay

Axial strain

Stress-strain relationship during shearing

Consolidated- Undrained test (CU Test)

Loose sandor NC Clay

CU tests How to determine strength parameters c and

Axial strain

or ’

cuMohr – Coulomb failure envelope in terms of total stresses

Total stresses at failure

Confining stress = 3b

Confining stress = 3a

1 = 3 + ( d)f

CU tests

or ’

’1b 1a

’1a( d)f

Mohr – Coulomb failure envelope in terms of effective stresses

Mohr – Coulomb failure envelope in terms of total stresses

C’ ufa

How to determine strength parameters c and ’1 = 3 + ( d)f - uf

’ = 3 - uf

Effective stresses at failure

CU testsStrength parameters c and obtained from CD tests

Shearstrengthparameters intermsof total stressesare ccu and cu

Shearstrength parameters in terms of effective stresses are c’ and ’

c’ = cd and ’ = d

CU tests Failure envelopesFor sand and NC Clay, ccu and c’ = 0

Therefore, one CU test would be sufficient to determinecu and ’= d) of sand or NC clay

or ’

cuMohr – Coulomb failure envelope in terms of total stresses

( d)fa

Mohr – Coulomb failure envelope in terms of effective stresses

Some practical applications of CU analysis for clays

= in situ undrained shear strength

Soft clay

1. Embankment constructed rapidly over a soft clay deposit

2. Rapid drawdown behind an earth dam

• • Core

• = Undrained shear

• strength of clay core

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 =

No drainage

Initial specimen condition

3 + d3

No drainage

Specimen conditionduring 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 z

Unconsolidated- Undrained test (UU Test)Step 1: Immediately after sampling

Step 2: After application of hydrostatic cell pressure

uc = B 3

C = 3 C =

’3 = 3 - uc

Nodrainage

Increase of pwp due to increase of cell pressure

Increase of cell pressure

Skempton’s pore waterpressure parameter, BNote: If soil is fully saturated, then B = 1 (hence, uc = 3)

Unconsolidated- Undrained test (UU Test)

Step 3: During application of axial load

No drainage

’1 = 3 + d - uc

’ = - u u3 3 c d

uc ± ud

ud = AB d

Increase of pwp due toincrease of deviator stress

Increase stress

ofdeviator

Skempton’s pore waterpressure parameter, A

Unconsolidated- Undrained test (UU Test)Combining steps 2 and 3,

uc = B 3 ud = AB d

Total pore water pressure increment at any stage, u

u = uc + ud

u = B [ 3 + A d]Skempton’s pore water pressure equation

u = B [ 3 + A( 1 – 3]

Derivation of Skempton’s pore water pressure equation

Step 1 :Increment of isotropic stress

No drainage

Increase in effective stress in each direction = 3 - uc

Step 2 :Increment of major principal stress

No drainage

Increase in effective stress in 1 direction = 1 - ud

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

Average Increase in effective stress = ( 1 - ud - ud – ud)/3

Typical values for parameter B

Typical values for parameter A 1 – 3

Axial strain

NC Clay (low

sensitivity) (A = 0.5 –

NC Clay (High sensitivity)

(A > 1.0)

Axial strain

1 – 3

Collapse of soil structure may occur in high sensitivity clays due to very high pore water pressure generation

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

Axial strain

1 – 3

Typical values for parameter A

Step 1: Immediately after sampling

Total, = +Neutral, u Effective, ’

Step 2: After application of hydrostatic cell pressure

’V0 = ur

’h0 = ur

-ur uc = -ur c

(Sr = 100% ; B = 1)

Step 3: During application of axial load

No drainage

No drainage -u ±

’VC = C + ur - C = ur

’h = ur

Step 3: At failure

’V = C + + ur - c u

h C r c

+ u - u

’hf = C + ur - c

= ’3f

’Vf = C + f + ur - c

uf = ’1f

-u ± u

r c fC

No drainage

Unconsolidated- Undrained test (UU Test)Effect of degree of saturation on failure envelope

or ’

S < 100% S > 100%

Some practical applications of UU analysis for clays

= in situ undrained shear strength

Soft clay

1. Embankment constructed rapidly over a soft clay deposit

Some practical applications of UU analysisfor clays2. Large earth dam constructed rapidly with

no change in water content of soft clay• • Core

• = Undrained shear

• strength of clay core

Some practical applications of UU analysisfor clays3. Footing placed rapidly on clay deposit

= 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

termbehavior of soils

True Triaxial Apparatus

FIGURE : Schematic of true triaxial cell and stresses imposed on a sample of soil.

• The purpose of a true triaxial test is to determine soil behaviour and properties by loading the soil in three dimensions.

• In a true triaxial test, a cuboidal sample is subjected to independent Displacements or stresses on three Cartesian axes.

• Displacements are applied through a system of rigid metal plates moving perpendicularly and tangentially to each face, as shown by the arrows in Figure

Unconfined Compression Test (UC Test)

1 = VC +

Confining pressure is zero in the UC test

Unconfined Compression Test (UC Test)

1 = VC + f

Normal stress, Sh

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

Stress Invariants (p and q)p (or s) = ( 1 + 3)/2 q (or t) = ( 1 - 3)/2

( 1 - 3)/2

3 1( 1 + 3)/2

p and q can be used to illustrate the variation of the stress state of a soil specimen during a laboratory triaxial test

Stress Invariants (p and q)

p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2

q or p

Mohr Coulomb failure envelope in terms of stress invariants

p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2

c 'Cot

221 31 3

Sin 'c'Cos '

3 1(1 + 3)/2

(1 - 3)/2

q pSin 'c'Cos '

p (or s) = (1 + 3)/2 q (or t) = (1 - 3)/2

Mohr Coulomb failure envelope in terms of stress invariants

Therefore, sin = tan = sin-1(tan

Stress path for CD triaxial test

p, p’ (or s, s’) = (1 + 3)/2

= (’1 + ’3)/2

q (or t) = (1 - 3)/2

q or p

In CD tests pore water pressure is equal to zero. Therefore, total and effective stresses are equal

Step 1 3

p, p’ (or s, s’) = 3 q (or t) = 0

Step 2 3 + d

p, p’ (or s, s’) = 3 + d/2 q (or t) = d/2d

Stress path for CU triaxial test

3 = ’3

p (or s) = (1 + 3)/2

p’ (or s’) = (1 + 3)/2 - uq (or t) = (1 - 3)/2

In CU tests pore water pressure develops during shearing

Step 1 3

p, p’ (or s, s’) = 3 q (or t) = 0

p (or s) = 3 + d/2d

Step 2 3 + d

q ’ or p, p’q (or t) = d/2

Other laboratory shear tests

Direct simple shear test

Torsional ring shear test

Plane strain triaxial test

Direct shear test = 80 mm

Soil specimenPorousstones

Spiral wire in rubber membrane

’max

’res

PeakResidual

Shear displacement

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

’1, 1

’2, 2

’3, 3

Plane strain test

’2 ≠ ’3

Rigid platens

Specimen

FIELD TESTS

In-situ shear tests

Vane shear test

Torvane

Pocket Penetrometer

Pressuremeter

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

Standard Penetration Test, SPT

In-situ shear tests

Vane shear test (suitable for soft to stiff clays)

Torvane

Pocket Penetrometer

Pressuremeter

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

PLAN VIEW

Vane shear testThis 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)

Applied Torque, T

Vane T

Rupture surface

Disturbed soil

Rate of rotation : 60 – 120 per minute

Test can be conducted at 0.5m vertical intervals

Vane shear test

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

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

Me – Assuming a uniformdistribution of shear strength

r 2 dr 2C

12 8 32C C d

3 d 3 M

M e (2rdr).C u r

Vane shear test

Ms – Shaft shear resistance along the circumference

22d 2h

dM s dhCu

d h Cu dT C

d 3 T Cu

d 3 d 2 h

Vane shear test

Me – Assuming a triangulardistribution of shear strength

hd/2d/2

Can you derive this ???

Vane shear test

Me – Assuming a parabolicdistribution of shear strength

3d 3 d 2 h

Can you derive this ???

d/2d/2

Vane shear test

After the initial test, vane can be rapidly rotated through several

the claybecome

revolutions until remoulded

peakultimate

Shear displacement

UltimateStengthPeak StengthSensitivity

Some important facts on vane shear test

Insertion of vane into soft clays and silts disrupts the natural soil structure around the vane causing reduction of shear strength

The above reduction is partially regained after some time

Cu as determined by vane shear test may be a function of the rate of angular rotation of the vane

Correction for the strength parameters obtained from vane shear test

Cu(design) = Cu(vane shear)

Where, = correction factor = 1.7 – 0.54 log (PI)

PI = Plasticity Index

Bjerrum (1974) has shown that as the plasticity of soils increases, Cu obtained by vane shear tests may give unsafe results for foundation design. Therefore he proposed the following correction.

TorvaneTorvane is a modification to the vane

FIELD VANE SHEAR TEST

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

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

PressuremeterAir

Coaxial tube

Pre – bored or self – bored holeGuard cell

Measuring cell

Guard cell

Pressuremeter

Pre – bored or self – bored hole

Guard cell

Measuring cell

Guard cell

Coaxial tube

Air Pres

sion Time

PressureVolu

Pseudo- elastic phase

Elastic phase

Static Cone Penetrometer test

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

Static Cone Penetrometer testForce 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, ect) from fr

Standard Penetration Test, SPTSPT is the most widely used test procedure to determinethe properties of in-situ soils

63.5 kg

The test can be conducted at every 10.76 m vertical intervals

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

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

SPT (Manual operation)

Various correlations for shear strengthFor NC clays, the undrained shear strength (cu) increases withthe effective overburden pressure, ’0

0.11 0.0037(PI ) '

cu Skempton (1957)

Plasticity Index as a %For OC clays, the following relationship is approximately true

(OCR)0.8

Overconsolidated Normally Consolidated

Ladd (1977)

For NC clays, the effective friction angle (’) is related to PI as follows

Sin ' 0.814 0.234 log(IP)

Kenny (1959)

Shear strength of partially saturated soilsIn the previous sections, we were discussing the shear strength of saturated soils. However, in most of the cases, we will encounter unsaturated soils in tropical countries like Sri Lanka

Saturated soils Unsaturated soils

Pore waterpressure, u

Effective stress, ’ Solid

Pore waterpressure, uw

Effective stress, ’

AirPore airpressure, ua

Pore water pressure can be negative in unsaturated soils

Shear strength of partially saturated soilsBishop (1959) proposed shear strength equation for unsaturated soils as follows

c'( u ) (u u)tan'

n a aw

Where,n – ua = Net normal stressua – uw = Matric suction= a parameter depending on the degree of saturation

( = 1 for fully saturated soils and 0 for dry soils)

Fredlund et al (1978) modified the above relationship as follows

b f c'( n ua ) tan '(ua uw ) tanWhere,tanb = Rate of increase of shear strength with matric suction

Shear strength of partially saturated soils

b f c'( n ua ) tan '(ua uw ) tan

Same as saturated soils Apparent cohesion due to matric suction

Therefore, strength of unsaturated soils is much higher than the strength of saturated soils due to matric suction

How it become possible build a sand castle ?

b f c'( n ua ) tan'(ua uw ) tan

Same as saturated soils Apparent cohesiondue to matric suction

Apparent cohesion

Ranges of Friction Angles for Soils (degrees)

*Higher values (32°–37°) in the range are for sands with significant amount of feldspar (Bolton, 1986). Lower values (27°–32°) in the range are for quartz sands.

Ref: Muni Budhu, page no. 282

Summary of Equations for the Four Failure Criteria

Correlation of N, N60, γ, Dr, and Ø´ for Coarse-Grained Soils

Correlation of N60 and su for Saturated Fine-Grained Soils

Empirical Soil Strength Relationships

Some practical cases and the laboratory strength tests to specify.

Questions ???

shear strength of soil

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