1 Following dataare given for a direct shear test conducted on dry sand:
. Specimen dimensions: 63 mm X 63 mm X 25 mm (height)
. Normal stress: 105 kN/m2
. Shear force at failure: 300 N
a. Determine the angle of friction, Φ'
b. For a normal stress of 180 kN/m2, what shear force is required to cause failure?
2 Consider the specimen.
a. What are the principal stresses at failure?
b. What is the inclination of the major pnncipal plane with the horizontal?
3 For a dry sand specimen in a direct shear test box, the following are given:
. Size of specimen: 63.5 mm >: 63.5 mm X 31.75 mm (height)
. Angle of friction: 33'
. Normal stress: 193 kN/m2
Determine the shear force required to cause failure
4 The following are the results offour drained direct shear tests on undisturbed normally consolidated clay samples having a diameter of 50 mm. and height of 25 mm.
| Test no. |
Normal
force (N) |
Shear force at
failure (N) |
|
1
|
67
|
23.3
|
|
2
|
133
|
46.6
|
|
3
|
213
|
44.6
|
|
4
|
369
|
132.3
|
Draw a graph for shear stress at failure against the normal stress and determine the drained angle of friction from the graph.
5 Repeat Problem 12.4 with the following data. Given: Specimen diameter :
50 mm; specimen height : 25 mm.
|
Test no.
|
Normal
force (N)
|
Shear force at
failure (N)
|
|
1
|
250
|
139
|
|
2
|
375
|
209
|
|
3
|
450
|
250
|
|
4
|
540
|
300
|
6 Consider the clay soil in Problem 12.5. If a drained triaxial test is conducted on the same soil with a chamber confining pressure of 208 kN/m2, what would be the deviator stress at failure?
7 For the triaxial test on the clay specimen in Problem 6,
a. What is the inclination of the failure plane with the major principal plane?
b. Determine the normal and shear stress on a plane inclined at 30o with the major principal plane at failure. Also explain why the specimen did not fail along this plane.
8 The relationship betrveen the relativc density, D', and the angle of fiiction Φ', of a sand can be given as Φ' = 28 + 0. 18D,.(D,. in %). A drained triaxial test was conducted on the same sand with a chamber-confining pressure of 150 kN/mr2.
The sand sample was prepared at a relative density of 68%. Calculate the major principal stress at failire.
9. For a normally consolidated clay specimen. the results of a drained triaxial test are as follows:
Chamber-confining pressure : 12-5 kN/ml
Deviator stress at lailure - 17-5 kN/rnr
Determine the soil friction angle Φ'.
10. In a consoliclatecl-drained triaxial test on a clay, the specirlen failed at a deviator stress of 124 kN/m2. If the effective stress fiiction angle is known to be 31o. what was the effective confining pressure at failure?
11. Consider the clay sample problem 12 A consolidated-Undrained triaxial test was coducted on thc same clay with a charnber pressure of 103 kN/m2. The pore pressure at failure (Δud)f = 33 kN/m2. What rvould be the major principal stress.
12 following are the results of consolidated-undrained triaxial tests on undisturbed soils retrieved soil retrieved from a 4-m-thick saturated clay layer in the field (γsat = 19 kN/m3).
a. Estimate graphically the Mohr-Coulonrb shear strength parameters c' ancl Φ'.
b. Estirnate the shear strength in the middle of the clay layer.
Chamber Deviator stress, Pore pressure at
pressure,σ3 (Aork (kN/m2) failure, (Auk (kN/m2)
Test no. (kN/m2)
|
1
|
100
|
170
|
-15
|
|
2
|
200
|
260
|
-40
|
|
3
|
300
|
360
|
-80
|
13 A consolidated-drained triaxial test was conducted on a nonnally consolidated clay with a chamber pressure. σ3 = 172 kN/m2. The deviator stress at failure. (Δσd)f = 227 kN/m2. Detemine:
a. The angle of fricition, Φ'
b. The angle θ that the failure plane makes with the rnajor principal plane
c. The normal stress. σ'f and the shear stress, Τf on the failure plane
14. The results of two consolidated-drained triaxial tests on a clay are given below:
Chamber Deviator stress,
pressure, σ3 (σ1 - σ2),
Specimen (kN/m2) (kN/m2)
I 105 220
II 400 400
Calculate the shear strength parameters of the soil.