Shear Strength of soil —
In a soil mass there is various planes where normal stress and shear stress are acted. Besides there is 3 planes , where only normal stress are acted. These planes are known as principal planes and corresponding stresses are known as principal stress. Depending upon the quantum they are major and minor principal stresses.
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Shear failure of soil —
Mohr strength theory and Mohr coulomb theory are well acceptable. The points of this theory are -
1) Materials fail essentially by shear.
2) Ultimate shear stress depends on normal stress on the potential failure plane and properties of materials.
3) In three dimensional stress system the failure criterion is independent of intermediate principal stress α2.
If σ and τ are the normal and shear stresses on any place and B the angle of obliquity that is the angle made by resultant of σ and τ with the normal to plane,
we have τ = σ tan ß on potential failure plane ß will have limiting value φ and then the shear strength will be τ= σ tan φ .......(1)
As Mohr did not consider cohesion, this theory is applicable for cohesion less soil. The line represented by equation (1) is called Mohr strength envelope φ is angle of internal friction.
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Mohr Coulomb theory and concept of shear parameters ——
This theory was first proposed by coulomb and latter generalized by Mohr. If we plot shear stress at failure as ordinate and normal stress as abscissa we obtain a curve known as strength envelope which is τf = F( σ). Coulomb assumed the relation between
τf and σ to be linear and gave the following equation which is τf = c + σ tang [Coulomb's equation).
c= intercept of strength envelope on Ï„ axis.
tan ø= slope of strength envelope c is known as cohesion and φ is known as angle of internal friction or angle of shearing resistance. These c and φ are called shear strength parameter.
Strength envelope and strength equation for c-φ, cohesion and cohesion less soil.
The shear tests commonly used in laboratory are ——
1) Direct shear test
2) Unconfined compression test 3) Vane shear test
1) Direct shear test: ––
Soil specimen used in the test is usually square in plan of size 60mmx60mm and thickness about 20 to 25 mm. The shear equipment essentially consist of (i) Shear box (ii) loading yoke for applying normal force (iii) geared jack for applying shear force, displacement and vertical deformation for volume change.
A normal stress σ is applied on the specimen and is kept constant through out the test. The shear stress τ is caused by application of shear force is transmitted to the top half of the shear box. The shear stress is gradually increased until the force from lower half to top half of shear box. If test continues beyond 20% strain it is usual to stop the test and define failure point corresponding to any desired level of strain up to 20%. By plotting τf, against σ the failure envelope is obtained.
2) Unconfined compression test ——
In this test no lateral or confining pressure is applied so that σ2= σ3=0. Specimen is cylindrical in shape with length about 2 to 2.5 times its diameter. The laboratory equipment for conducting this test has facilities for compressing the specimen at uniform rate of strain and measuring the axial deformation and corresponding axial compressive force. The maximum compressive stress resisted by the specimen before failure is called
F unconfined compression test. It is denoted by, qu = F/Ac
F= axial compressive force at failure.
A = corrected area of cross section of specimen
Ä„.= Initial area of cross section of specimen
ε = Δ2/Lo = axial strain at failure point.
It is a quick test and no drainage is allowed. Un-drained shear strength parameters are Cu and φu
The angle d-which the failure plane makes with the horizontal is measured.
3) Vane shear test ——
It is a quick test used to determine un-drained shear strength of cohesive soils. The equipment essentially consist of 4 high tensile steel plates called vanes which are welded orthogonally to the bottom end of a steel rod called the torque rod with an arrangement to measure the torque and rotation. A typical arrangement consist of a calibrated torsion spring attached to the top of torque rod which are rotated by a combination of worm gear and worm wheel. This test can be conducted in laboratory and field also. Vanes have 20 mm height, diameter of 12mm across vanes with blade thickness of 0.5 to 1mm. The field set of vanes usually is 100 to 200 mm in height, 50 to 100 mm in diameter, blade thickness of 2.5 mm. To conduct the test vanes are gently pushed into the soil and torque rod is rotated at a uniform rate of usually 1° per minute. Torque T corresponding to θ at uniform interval are noted. T is plotted as ordinate against 8 as abscissa. Torque Tf at failure point is found
T= Ï„Ï€d2[H/2+d/12]
Short Answer Type Questions
1. Identity the wrong statement from the following –
Statement 'a': Vane shear test is applicable for soft clay only. Statement ‘b': Failure plane is predetermined in direct shear test.
(a) statement 'a' only
(b) statement ‘b' only
(c) both the statements
(d) none of the statements
Answer: (d)
2. The maximum shear strength occurs in the filament which makes an angle with the horizontal plane equal to -
(a) 30°
(b) 75°
(c) 45°
(d) 90°
Answer: (c)
3. Effective stress is —
(a) the stress at particles contact
(b) a physical parameter that can be measured
(c) important because it is a function of engineering properties of cont
(d) all of the above
Answer: (c)
4. Shear strength of a soil is a unique function of —
(a) effective stress only
(b) total stress only
(c) both effective stress and total stress
(d) none of above
Answer: (a)
5. The shear strength of a soil —
(a) is directly proportional to the angle of internal friction of the soil
(b) is inversely proportional to the angle of internal friction of the soil
(c) decreases with increase in normal stress
(d) decreases with decrease in normal stress
Answer: (d)
6. In sandy soil shear strength is mainly due to —
(a) Cohesion
(b) bulk density
(c) plastic limit
(d) angle of internal friction
Answer: (d)
7. Coulomb's equation for shear strength can be expressed as —
(a) s =σ +c tan φ
(b) s= σ +c sin φ
(c) s =c+ σ tan φ
(d) s= c + σ cot φ
Answer: (c)
8. Vane shear test is suitable for the following type of soil
(a) cohesion soil
(b) cohesionless soil
(c) cohesive-frictional soil
(d) none of these
Answer: (b)
9. In direct shear test the size of square box is -
(a) 60 mm x 60 mm
(b) 60 cm x 60 cm
(c) 60 m x 60 m
(d) 0.6 cm x 0.6 cm
Answer :(a)
10. For examination of the stability of the unstream slope of an earthen dam during rapid drawdown the shear parameters are used from —
(a) unconsolidated undrained test
(b) consolidated undrained test with pore pressure measurement
(c) consolidated drained test (d) unconsolidated undrained test with pore pressure measurement
Answer: (b)
11. For heavily over consolidated clay sample, Skempton pore pressure parameter A is —
(a) greater than 1
(b) less than 1
(c) equal to 1
(d) negative
Answer: (d)
12. In shear box test, failure plane is the —
(a) weakest plane
(b) vertical plane
(c) major principal plane
(d) horizontal plane
Answer: (d)
13. A footing is resting on a fully saturated clayey strata. For checking the initial stability, shear parameters are used from —
(a) consolidated drained test (b) unconsolidated drained test
(c) unconsolidated undrained test (
d) unconsolidated undrained test with pore pressure measurement
Answer: (c)
14. A direct shear test possesses the following disadvantages —
(a) the relatively thin thickness of sample permits quick dissipation of pore pressure developed during the test
(b) the relatively thin thickness of sample permits quick drainage
(c) as the test progresses, the area under shear gradually changes
(d) none of the above
Answer: (c)
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