Question

In a direct shear test on a sample of cohesionless sand, the vertical normal stress on the sample is 300 kPa and the horizontal shear stress at failure is 200 kPa. a) Assuming uniform stress distribution within the failure zone, determine the magnitude and direction of the principal stresses at failure. b) Explain if it is possible to determine the principal stresses in a direct shear sample for an applied horizontal shear stress which is not large enough to cause failure.

Answer 1

Let's Use Mohr's circle to solve for principal stresses and their orientation

Step 1:

Plot the normal and shear stress as shown below and draw the line which is passing exactly through the origin(As Cu=0)

the resultant line is Failure plane

And the angle of friction   $\phi _f=34^o$

Step 2:

Draw a line perpendicular to the failure plane which exactly intersects on the x-axis

The intersected point is Centre of Mohr's Circle

Step 3:

Draw the Mohr's Circle Which has a centre at C and passes through the point F as shown

Draw a horizontal line from P the intersected point on the circle is Pole(P)

Step 4:

Measure the Major and Minor Principal Stresses shown below

Step 5:

Measure the Directions of Major and minor Principal plane

b)

The major Drawback of the Direct shear test is it is not possible to attain the values of stresses and properties before the failure point.

So the soil should definitely fail by reaching failure point at failure shear stress to calculate Principal stresses.

It is not possible to Estimate Before Failure stress.

Answer 2

Зоо кра • 200 kPa T= ctotem o Griven, Т. 2 от 04 О. Qoy ka cao (Cohessionless sond). 2oo — Зоо n ф эфе erm" (5) — ф-р+9 (фа 37.69° ) DABE tenga 2 1= 2em »ф 22 123.23 с P\ - гг 2 -3 Oce ota ос. Ою+ 117.23 – ОС 432 .23

وليه ما a . cosa= P I - R= a e => R= 200 coso C01133.694) » R=240.27 Sol r2 = 0C-R 7 = 422.32-240.27 10=192.65 kPa 1 m or octra 10,= 673.7 kPa] (8). Y find hence failure points it doesn't occur then we can not. of failure (at mong circle) and u not possible to find principal spresses,

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