GEO-MECHANICSGEO-MECHANICS(CE2204)(CE2204)

Shear Strength of SoilsShear Strength of Soils

Lecture Week No 4

Mdm Nur Syazwani Noor RodiMdm Nur Syazwani Noor Rodi

LINTON UNIVERSITY COLLEGELINTON UNIVERSITY COLLEGESCHOOL OF CIVIL ENGINEERINGSCHOOL OF CIVIL ENGINEERING

NOTATIONS

σ - Total Stress [kN/m2; kPa]

σ’ - Effective Stress [kN/m2; kPa]

σN - Normal Stress [kN/m2; kPa]

σv - Vertical Total Stress [kN/m2; kPa]

σh - Horizontal Total Stress [kN/m2; kPa]

σ1 - Principle Stress [kN/m2; kPa]

σ3 - Minor Stress [kN/m2; kPa]

u - Pore Water Pressure [kN/m2; kPa]

- Shear Strength [kN/m2; kPa]

Φ - Angle of Friction [º]

Δ - Change in

C - Cohesion of Soils [kN/m2; kPa]

SHEAR FAILURE IN SOILS

WHAT IS SHEAR STRENGTH?

• The shear strength of a soil is its resistance to shearing stresses.

• It is a measure of the soil resistance to deformation by continuous displacement of its individual soil particles

• Shear strength in soils depends primarily on interactions between particles

• Shear failure occurs when the stresses between the particles are such that they slide over each other

SHEAR STRENGTH IN SOILS

STRIP FOOTING

q

Shear Resistance, f

Shear Stress,

At failure, shear stress along the failure surface () reaches

the shear strength (f).

The soil grains slide over each other along the failure

surface

SHEAR STRENGTH PARAMETERS

Soil derives its shear strength from two sources:

a) Cohesion (C), is a measurement of the forces that cement between particles of soils (stress independent component)

- Cementation between sand grains

- Electrostatic attraction between clay particles

b) Internal Friction angle (Φ), is the measure of the frictional resistance between particles of soils (stress dependent component)

MOHR-COULOMB FAILURE CRITERION

This theory states that a material failure is due to the critical combination of normal

stress and shear stress

The relationship between normal stress and shear is given as……

tanNf c MOHR-COULOMB FAILURE CRITERION

MOHR CIRCLE

v

σ3 σ1

SOILELEMENT

σ3

σ1 = σ3 + Δσv

σ3

f

N

tanc

General State of Stress

MOHR CIRCLE

As loading progresses, Mohr circle becomes

larger…

.. and finally failure occurs when Mohr circle

touches the envelopeInitially, Mohr circle is a point

SOILELEMENT

σ3

σ1 = σ3 + Δσv

σ3

f

N

General State of Stress

TYPES OF SHEAR TEST

Laboratory Tests:a) Shear Box

b) Triaxial Compression

In Situ Tests:a) Standard Penetration

b) Shear Vane

UNDRAINED TESTS• NO drainage of pore water• simulates short term condition (e.g. end of construction)• excess pore water pressure, Δu is often finite

DRAINED TEST• Drainage ALLOW for pore water• simulates long term condition (e.g. ‘many years’ after

construction)• excess pore water pressure, Δu = 0; however u is not

necessarily = 0

TYPES OF SHEAR TEST(DIRECT SHEAR BOX)

TYPES OF SHEAR TEST(DIRECT SHEAR BOX)

●(N1 , 1)

max (kN/m2)

N (kN/m2)

Cd

Φd

●(N2 , 2)

●(N3 , 3)

dNdf C tan

TYPES OF SHEAR TEST(DIRECT SHEAR BOX)

Example 1

A drained shear box test was carried out on a sandy clay and yielded for the following results:

Normal Load (N) 108 202 295 390 484 576

Shear Load at failure (N) 172 227 266 323 374 425

Area of shear plane = 60mm x 60mm

Determine the apparent cohesion and angle of friction for the soil

A

P

Example 2

Test

Maximum

Shear Stress

(kN/m2)

max

Normal Load, P

(kg)Normal Stress, N

(kN/m2)

1 70 36.7 100

2 130 73.4 200

3 220 128.4 350

206.01000

81.97.36

206.01000

81.94.128

206.01000

81.94.73

TYPES OF SHEAR TEST (TRIAXIAL TEST)

TYPES OF SHEAR TEST (TRIAXIAL TEST)

• The test is designed to mimic actual field or “in situ” conditions of the soil.

• Triaxial tests are run by:1. saturating the soil

2. applying the confining stress (σ3)

3. applying the vertical stress (known as deviator stress) until failure

• 3 main types of triaxial tests:a) Unconsolidated - Undrained

b) Consolidated – Drained

c) Consolidated – Undrained

0

0 u ≈ 0

Stage A

Sample Preparation

0 σ3

σ1

uf ≠ 0

Stage C

Undrained Failure

σ3

Undrained

UNDRAINED TEST (Unconsolidated-Undrained)

Stage B

Apply Cell Pressure

σ3

σ3

u ≠ 0σ3

Undrained

• Fast - Undrained - Short term

• Cu & Φu

• for saturated soils (S=1), NO Volume Change

0

0 u ≈ 0

Stage A

Sample Preparation

0 σ3

σ1

uf = 0

Stage C

Drained Failure

σ3

DRAINED TEST (Consolidated-Drained)

Stage B

Consolidation

σ3

σ3

u = 0σ3

• Extremely slow – Drained – Long term

• Cd & Φd

• for saturated soils (S=1), NO Volume Change

Drained Drained

0

0 u ≈ 0

Stage A

Sample Preparation

0

CONSOLIDATED UNDRAINED TEST

Stage B

Consolidation

σ3

σ3

u = 0σ3

• Intermediate – Drained – Long & Short term

• C’ & Φ’ ( ≈ Cd & Φd ) ; Cu & Φu

Drained

σ3

σ1

uf ≠ 0

Stage C

Undrained Failure

σ3

Undrained

Example 1

A drained triaxial compression test carried out on three specimens of the same soil yielded the following results:

Test No. 1 2 3

Cell pressure (kPa) 100 200 300

Deviator stress at failure (kPa) 210 438 644

Draw the shear strength envelop and determine the shear strength parameters, C’ & Φ’, assuming that the pore water pressure remain constant during the axial loading stage.

Example 2

Three consolidation undrained triaxial tests were carried out on 38mm diameter samples of the same clay. The applied axial force at failure of the samples were found to be as follows:-

Test No. 1 2 3

Cell pressure (kN/m2) 25 75 120

Applied axial force at failure (kN) 0.086 0.120 0.149

Determine the shear strength parameters of the clay in term of total stress.

Example 3

The following results were obtained from undrained triaxial tests on specimens of a saturated normally consolidated clay.

Test No. 1 2 3

Cell Pressure (kN/m2) 100 200 300

Ultimate Deviator Stress (kN/m2) 137 210 283

Ultimate Pore Pressure (kN/m2) 28 86 147

Determine the shear strength parameters of the clay in term of total and effective stress.

Example 4

The following results were obtained from undrained triaxial tests on specimens of an overconsolidated clay.

Test No. 1 2 3

Cell Pressure (kN/m2) 100 250 400

Deviator Stress at failure (kN/m2) 340 410 474

Deviator Pore Pressure (kN/m2) -42 64 177

Determine the shear strength parameters of the clay in term of total and effective stress.

Example 5

Referring to Example 2, if the shear strength parameters of the clay in term of effective stress were C’ = 10 kN/m2 and Φ’ = 30°, determine the pore water pressure in each sample at failure.

Example 6Consolidated undrained triaxial tested were carried out on 3 samples of the same clay soil and the following results were obtained at the point of failure:-

Sample No.

Cell Pressure (kN/m2)

Deviator Stress at

failure (kN/m2)

Pore Water

Pressure (kN/m2)

Cu

(kN/m2)

Φu

(°)

C’(kN/m2)

Φ’(°)

1 50 80.543 27.201

10 ?? ?? ??2 100 ?? 57.879

3 ?? 158.514 ??

Determine the 6 unknown value (??) in the table by Calculation and Graphical method

TYPES OF SHEAR TEST(SHEAR VANE TEST)

62

32 dhdCT u

TYPES OF SHEAR TEST(SHEAR VANE TEST)

• Suitable for determining the in-situ undrained shear strength of unfissured saturated clays and silts

• The vane consists of four rectangular blades in a cruciform at the end of a steel rod

• Shear strength is measure by pushing the vane into the soil and rotated by applying a torque at the surface end of the rod

• The vane is first rotated at 6-12° per minute to determine the undisturbed shear strength and then the remoulded strength is measured by rotating the vane rapidly

Example 1

A shear vane used to test a soft clay had a diameter of 75mm and a length of 150mm. The average torques recorded after slow and then rapid rotations were 64 and 26 Nm respectively. Determine the undrained strength of the clay.