advanced soil mechanics 1 - chapter 1-1-12

Advanced Soil Mechanics I

SNU Geotechnical and Geoenvironmental Engineering Lab.

1-1

Chapter I

Shear Strength of Soils

1.1 Background (1) Principal Stresses and Mohr Circle

Principal planes: Three orthogonal planes on which there are zero shear stresses.

Principal stresses: The normal stresses that act on these three planes

The largest : major principal stress, 1 The smallest : minor principal stress, 3 The intermediate : intermediate principal stress, 2

At geostatic state in the horizontal ground, the horizontal plane and two vertical planes are principal planes.

When Ko(='h /'v) < 1, 'v = '1, 'h = '3 and '2 = '3 = 'h When Ko(='h /'v) > 1, 'h = '1, 'v = '3 and '2 = '1 = 'h

Some rules on stress description in soil mechanics Mostly, Ko< 1 and 2 = 3 or 2 = 3

(geostatic condition and axisymmetric condition). Stresses are positive when compressive. Shear stress is

positive when counterclockwise.



1-2

Mohr Circle: The graphical representation of stress state of material element. - It can be determined with the normal and shear stresses of two

orthogonal planes. - Given a Mohr circle, it is possible to find stresses in any direction

by graphical construction using the Mohr circle. (Using origin of plane (pole))

- The origin of plane (or the pole) is a point on the Mohr circle where a line through Op and any point of the Mohr circle is parallel to the plane on that given point.

2sin2

2cos)(21)(

21

31

3131

=

++=

- The maximum shear stress (max = (1 - 3)/2) occurs on planes lying at 45o to the major principal direction.

2

1

3

III

I

III

I 3 1

(, ) Op (Pole)

Soil Element.



1-3

Ex1)

GH is parallel to OpE and HJ is parallel to OpF. Fig E1. The way to find the plane that 1, 3 act.

Ex2)

CD is parallel to OpB and DH is parallel to AOp. Fig E2. The way to find the plane that 1 and 3 act.



1-4

p-q diagrams : - The stress state is plotted with stress point whose coordinates are

231 +

=p

+

=

horizontal the to45 than less inclined is if

vertical the to45 than lessor toequal inclined is if

21

1

31

q

- Effective way to represent, on a single diagram, many states for a given specimen of soil.

Representing the change of stress state during loading. Vector curve Stress path



1-5

Locations of failure plane and failure stress conditions are defined in terms of effective stresses. ( Based on drained strength envelope)

Drained tests (CD) (1 acts on horizontal plane.)

45+/2

c=0

'n

' Drained strength envelope

nff'

Initial condition (For isotropic consolidation)

45+/2

ff

Failure Plane.

1' f

3' f

ff' ff



1-6

UU tests

Notes : 2

31 ffus

=

ff = shear stress at failure at failure plane = uu ss



1-7

(2) Vector Curves

Vector Curves : Locus of stress states (shearing stresses and effective normal stresses) on a potential failure plane for loading to failure.

Shearing Phase (D : Drained, U : Undrained) Loading Method (C : Compression, E : Extension)

Ex) CID TXC Testing device (TX : Triaxial, PS : Plane Strain) Consolidation phase CI : Isotropic Consolidation (1=2=3=c) CA : Anisotropic Consolidation (1 2=3=c) CK0 : Consolidation with zero lateral strain U : Unconsolidation

To plot the curves, 1. Assume '. 2. Plot Mohr circle for each load. (1 and 3 are given from tests) 3. Find , n on potential failure plane for each circle. 4. Connect points. 5. Redraw if vector curve at peak or at large strain dose not match

with assumed failure envelope.

'n

'

45+/2

321 ''' ==



1-8

Pore pressure measurement

Ex) CIU TXC (1 , 3 and eu are given from tests)

Look at 1 Mohr circle (at failure).

1. Assume . 2. Plot total Mohr circle.

3. Find (= ff ), n( nff= ). (which is located at base line)

4. Find (= ff ), n(= 'nff ) with measured pore pressure.

' ( ' ) ( )3 3 3

uf c f e = = = ' ( ' ) ( )3 unff n nff en = = =

'

45+/2

(nff' , ff )

Base line

nn ,'

Vector

curve eu

3f 1f 1f c=3f

( nff , ff )



1-9

To draw vector curve,

1. Draw base line based on assumed ' . 2. Account for eu at each stress level. Vector curve.

'

45+/2

Base line

nn ,'

Vector

curve

eu



1-10

Major Points

Pore pressure development

Base line

nn ,'

To left (+ue)

To right (-ue)

Base line

nn ,'

0)( 31

advanced soil mechanics 1 - chapter 1-1-12

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