University of Rajshahi

Shear Strength of soil

Direct Shear Test

Mohr-Coulomb Failure Criteria

– Total stress

– Effective stress

– Cohesion and friction angle

Normal and shear stresses Principal stresses

Mohr Circle of Stress and failure envelope

Direct Shear Test : Apparatus and

procedures

Mohr-Coulomb Failure Criterion ( in terms of total stresses )





_f

is the maximum shear stress the soil can take without failure, under normal stress of .







 f  c  tan

c



failure envelope

Cohesion Friction angle



_f



Mohr-Coulomb Failure Criterion ( in terms of effective stresses )



_f

is the maximum shear stress the soil can take without failure, under normal effective stress of ’.



’

' tan

'

'  

 f  c 

c’

’

failure envelope Effective

cohesion Effective

friction angle



_f

’

 u

 



^'

u = pore water

pressure

Mohr-Coulomb Failure Criterion

' tan

'

'  

 f  c  f

Shear strength consists of two components:

cohesive and frictional.

’

_f



_f

’



'

c’ c’

_cohe^{sive compone}

’

_f

tan ’

nt frictional component

Normal stresses and shear stresses on any plane can be obtained with the following equations

Principal stresses

or

Mohr Circle of stress

Soil element

’₁

’₁

’₃

’₃



’



 





 

 

 

2 2 2

2 2

' 3 '

1 '

3 '

' 1

' 3 '

1

Cos Sin

 

 

 

Resolving forces in  and  directions,

' 2 3 '

1 ' 2

3 '

' 1 2

2

2  





 



  

 

 



 



     



Mohr Circle of stress

' 2 3 '

1 ' 2

3 '

' 1 2

2

2  





 



  

 

 



 



     



Soil element

’₁

’₁

’₃

’₃



’



Soil element Soil element

’₁

’₁

’₃

’₃

’₁

’₁

’₃

’₃



’





’





’

2

' 3 '

1 

 

2

' 3 '

1 

 

'



3



₁^'

Mohr Circle of stress

' 2 3 '

1 ' 2

3 '

' 1 2

2

2  





 



  

 

 



 



     



Soil element

’₁

’₁

’₃

’₃



’



Soil element Soil element

’₁

’₁

’₃

’₃

’₁

’₁

’₃

’₃



’





’





’

2

' 3 '

1 

 

2

' 3 '

1 

 

'



3



₁^'

P

_D

= Pole w.r.t. plane



’, 

Soil elements at different locations

Failure surface

Mohr Circles & Failure Envelope

X

X

X ~ failure

Y

Y

Y ~ stable



’

' tan '

'  



_f

 c 

NEED AND SCOPE In many engineering problems such as

• design of foundation,

• retaining walls,

• slab bridges,

• pipes,

• sheet piling,

The value of the angle of internal friction and cohesion of the soil involved are required for the design.

Direct shear test is used to predict these parameters quickly.

Direct shear test

1. This test is performed to determine the consolidated - drained shear strength of a sandy to silty soil.

2. The shear strength is one of the most important engineering properties of a soil, because it is required whenever a structure is dependent on the soil’s shearing resistance.

3. The shear strength is needed for engineering situations such as determining the stability of slopes or cuts, finding the bearing capacity for foundations, and calculating the pressure exerted by a soil on a retaining wall.

Direct shear test

Apparatus

1. Direct shear box apparatus

2. Loading frame (motor attached).

3. Dial gauge.

4. Proving ring.

5. Tamper.

6. Straight edge.

7. Balance to weigh upto 200 mg.

8. Aluminum container.

9. Spatula.

PROCEDURE

• Check the inner dimension of the soil container.

• Put the parts of the soil container together.

• Calculate the volume of the container. Weigh the container.

• Place the soil in smooth layers (approximately 10 mm thick). If a dense sample is desired tamp the soil.

• Weigh the soil container, the difference of these two is the weight of the soil. Calculate the density of the soil.

• Make the surface of the soil plane.

• Put the upper grating on stone and loading block on top

of soil.

Direct shear test

Preparation of a sand specimen

Components of the shear box Preparation of a sand specimen Porous

plates

Direct shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays

Direct shear test

Leveling the top surface of specimen

Preparation of a sand specimen

Specimen preparation completed

Pressure plate

Direct shear test

Test procedure

Porous plates

Pressure plate Steel ball

Step 1: Apply a vertical load to the specimen and wait for consolidation

P

Proving ring to measure shear force

S

Direct shear test

Step 2: Lower box is subjected to a horizontal displacement at a constant rate Step 1: Apply a vertical load to the specimen and wait for consolidation

Test procedure P

Pressure plate Steel ball

Proving ring to measure shear force

S Porous

plates

PROCEDURE

8. Measure the thickness of soil specimen.

9. Apply the desired normal load.

10. Remove the shear pin.

11. Attach the dial gauge which measures the change of volume.

12. Record the initial reading of the dial gauge and calibration values.

13. Before proceeding to test check all adjustments to see that there is no connection between two parts except sand/soil.

14. Start the motor. Take the reading of the shear force and record the reading.

15. Take volume change readings till failure.

16. Add 5 kg normal stress 0.5 kg/cm2 and continue the experiment till failure

17. Record carefully all the readings. Set the dial gauges zero, before starting the experiment

Direct shear test

Shear box

Loading frame to apply vertical load

Dial gauge to measure vertical displacement

Dial gauge to measure horizontal displacement

Proving ring to measure shear force

Direct shear test

Analysis of test results

sample the

of section cross

of Area

(P) force

Normal stress

Normal 

 

sample the

of section cross

of Area

(S) surface

sliding at the

developed resistance

Shear stress

Shear 

 

Note: Cross-sectional area of the sample changes with the horizontal displacement

Direct shear tests on sands

Shear stress, 

Shear displacement

Dense sand/

OC clay



_f

Loose sand/

NC clay



_f

Dense sand/OC Clay

Loose sand/NC Clay

Change in height of the sample ExpansionCompression Shear displacement

Stress-strain relationship



_f1 Normal stress = ₁

Direct shear tests on sands

How to determine strength parameters c and 

Shear stress,

Shear displacement



_f2

Normal stress = ₂



_f3

Normal stress = ₃

Shear stress at failure, 

f

Normal stress,





Mohr – Coulomb failure envelope

Direct shear tests on sands

Some important facts on strength parameters c and  of sand

Sand is cohesionless hence c = 0

Direct shear tests are drained and pore water pressures are dissipated, hence u = 0

Therefore,

’ =  and c’ = c = 0

Direct shear tests on clays

Failure envelopes for clay from drained direct shear tests

Shear stress at failure, 

f

Normal force, 

’

Normally consolidated clay (c’ = 0) In case of clay, horizontal displacement should be applied at a very slow rate to allow dissipation of pore water pressure (therefore, one test would take several days to finish)

Overconsolidated clay (c’ ≠ 0)

Interface tests on direct shear apparatus

In many foundation design problems and retaining wall problems, it is required to determine the angle of internal friction between soil and the structural material (concrete, steel or wood)





 f  c a  ' tan

^Where, _c

a = adhesion,

= angle of internal friction

Foundation material Soil

P

S

Foundation material Soil

P

S

Advantages of direct shear apparatus

 Due to the smaller thickness of the sample, rapid drainage can be achieved

 Can be used to determine interface strength parameters

 Clay samples can be oriented along the plane of weakness or an identified failure plane

Disadvantages of direct shear apparatus

 Failure occurs along a predetermined failure plane

 Area of the sliding surface changes as the test progresses

 Non-uniform distribution of shear stress along the failure surface