shear strength of soil student handout
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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.