1. GEO-MECHANICS (CE2204) Shear Strength of Soils
LINTON UNIVERSITY COLLEGE
SCHOOL OF CIVIL ENGINEERING
GEO-MECHANICS (CE2204)
Shear Strength of Soils
Lecture Week No 4
Mdm Nur Syazwani Noor Rodi

2. NOTATIONS  - Shear Strength [kN/m2; kPa]
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]

3. SHEAR FAILURE IN SOILS

4. 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

5. SHEAR STRENGTH IN SOILS
STRIP FOOTING q
Shear Stress, 
Shear Resistance, f
The soil grains slide over each other along the failure surface
At failure, shear stress along the failure surface () reaches the shear strength (f).

6. SHEAR STRENGTH PARAMETERS
Soil derives its shear strength from two sources:
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
Internal Friction angle (Φ), is the measure of the frictional resistance between particles of soils (stress dependent component)

7. 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……

8. MOHR-COULOMB FAILURE CRITERION

9. General State of Stress
MOHR CIRCLE 
SOIL
ELEMENT σ3
σ1 = σ3 + Δσv f N
v σ1 σ3 
General State of Stress

10. MOHR CIRCLE   As loading progresses, Mohr circle becomes larger…
SOIL
ELEMENT σ3
σ1 = σ3 + Δσv f N
Initially, Mohr circle is a point 
General State of Stress
.. and finally failure occurs when Mohr circle touches the envelope

11. TYPES OF SHEAR TEST Laboratory Tests: In Situ Tests: Shear Box
Triaxial Compression
In Situ Tests:
Standard Penetration
Shear Vane

12. UNDRAINED TESTS DRAINED TEST 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

13. TYPES OF SHEAR TEST (DIRECT SHEAR BOX)

14. TYPES OF SHEAR TEST (DIRECT SHEAR BOX)

15. TYPES OF SHEAR TEST (DIRECT SHEAR BOX)
max (kN/m2) Φd ●
(N3 , 3) ●
(N2 , 2) ●
(N1 , 1) Cd
N (kN/m2)

16. 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

17. Example 2 max 70 130 200 220 350 Test Maximum Shear Stress (kN/m2)
Normal Load, P
(kg)
Normal Stress, N 1 70
36.7
100 2
130
73.4
200 3
220
128.4
350

18. TYPES OF SHEAR TEST (TRIAXIAL TEST)

19. 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:
saturating the soil
applying the confining stress (σ3)
applying the vertical stress (known as deviator stress) until failure
3 main types of triaxial tests:
Unconsolidated - Undrained
Consolidated – Drained
Consolidated – Undrained

20. UNDRAINED TEST (Unconsolidated-Undrained)
u ≈ 0
Stage A
Sample Preparation
Stage B
Apply Cell Pressure σ3
u ≠ 0 σ3 σ1
uf ≠ 0
Stage C
Undrained Failure
Undrained
Undrained
Fast - Undrained - Short term
Cu & Φu
for saturated soils (S=1), NO Volume Change

21. DRAINED TEST (Consolidated-Drained)
u ≈ 0
Stage A
Sample Preparation
Stage B
Consolidation σ3
u = 0 σ1 σ3
uf = 0 σ3
Drained
Drained
Stage C
Drained Failure
Extremely slow – Drained – Long term
Cd & Φd
for saturated soils (S=1), NO Volume Change

22. CONSOLIDATED UNDRAINED TEST
u ≈ 0
Stage A
Sample Preparation
Stage B
Consolidation σ3
u = 0 σ3 σ1
uf ≠ 0
Stage C
Undrained Failure
Undrained
Drained
Intermediate – Drained – Long & Short term
C’ & Φ’ ( ≈ Cd & Φd ) ; Cu & Φu

23. 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.

24. 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.

25. 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.

26. 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.

27. 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.

28. Deviator Stress at failure (kN/m2) Pore Water Pressure (kN/m2)
Example 6
Consolidated 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’ Φ’ 1 50
80.543
27.201 10 ? 2
100
57.879 3
Determine the 6 unknown value (?) in the table by Calculation and Graphical method

29. TYPES OF SHEAR TEST (SHEAR VANE TEST)

30. 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

31. 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.