insitu stresses

Indian Institute of Technology Hyderabad (IITH)05 Feb 2015

1

Dr. B. Munwar Basha

Why do we learn about In situ Stresses ?

In a given volume of soil, the solidparticles are distributed randomly

with void spaces between.

The void spaces are continuous andare occupied by water and/or air.

To analyze problems (such as

compressibility of soils,

bearing capacity of foundations, stability of embankments, and lateral pressure on earth-retaining

structures

we need to know the nature of the

distribution of stress along a given

cross section of the soil profile.

3Stresses in Saturated Soil without Seepage

Figure shows a column ofsaturated soil mass with noseepage of water in anydirection.

The total stress at the elevationof point A can be obtainedfrom the saturated unit weightof the soil and the unit weightof water above it. Thus,

( )w A satH H H

HA = distance between point A and the water table, H =height of water table from the top of the soil column, at =saturated unit weight of the soil, w =unit weight of water

4The total stress, , given by above equation can be dividedinto two parts:1. A portion is carried by water in the continuous void

spaces. This portion acts with equal intensity in alldirections.

2. The rest of the total stress is carried by the soil solids attheir points of contact. The sum of the vertical componentsof the forces developed at the points of contact of the solidparticles per unit cross-sectional area of the soil mass iscalled the effective stress.

Stresses in Saturated Soil without Seepage


Drawing a wavy line, aa, through point A that passes onlythrough the points of contact of the solid particles.Let P1, P2, P3, . . ., Pn be the forces that act at the points ofcontact of the soil particles .

1( ) 2( ) 3( ) ( )...'

v v v n vP P P P

A


1( ) 2( ) 3( ) ( )...'

v v v n vP P P P

A

The sum of the vertical components of all such forces over the unit cross-sectional area is equal to the effective stress ,

P1(v), P2(v),, Pn(v) are the vertical components P1, P2, P3, . . ., Pn , respectively, and is the cross-sectional area of the soil mass under consideration.


If as is the cross-sectional area occupied by solid-to-solidcontacts (that is, as = a1+a2 +a3 ++an), then the spaceoccupied by water equals ( -as ).

So we can write

where u = HA w = pore water pressure (i.e., the hydrostaticpressure at A)a's =as /A = fraction of unit cross-sectional area of the soil massoccupied by solid-to-solid contacts

'( )' ' (1 )s su A a

u aA

8The value of a's is extremely small and can be neglected forpressure ranges generally encountered in practical problems.Thus the above equation can be approximated as

where u is also referred to as neutral stress.From previous equations, we get,

where = sat - w equals the submerged unit weight of soil.We can see that the effective stress at any point A isindependent of the depth of water, H, above the submergedsoil.

' u

[ ( ) ]w A sat A wH H H H

( )( )A sat wH H '(Height of the soil column)


9 Figure 1a shows a layer ofsubmerged soil in a tankwhere there is no seepage.

Figures b through d showplots of the variations of thetotal stress, pore waterpressure, and effective stress,respectively, with depth for asubmerged layer of soilplaced in a tank with noseepage.


10

Figures b through d show plots of the variations of the total stress, pore waterpressure, and effective stress, respectively, with depth for a submerged layer of soilplaced in a tank with no seepage.


11

In summary, effective stress isapproximately the force per unit areacarried by the soil skeleton.

The effective stress in a soil masscontrols its volume change andstrength.

Increasing the effective stressinduces soil to move into a denserstate of packing.

The effective stress principle isprobably the most important conceptin geotechnical engineering.

The compressibility and shearingresistance of a soil depend to a greatextent on the effective stress.


12

If water is seeping, the effectivestress at any point in a soil mass willdiffer from that in the static case.

It will increase or decrease,depending on the direction ofseepage.

Stresses in Saturated Soil with Upward Seepage

13

Figure shows a layer of granular soilin a tank where upward seepage iscaused by adding water through thevalve at the bottom of the tank.

The rate of water supply is keptconstant.

The loss of head caused by upwardseepage between the levels of A andB is h.


14

The loss of head caused by upward seepagebetween the levels of A and B is h.

At point A : z = 0, Seepage head = 0

At point C : z = 0, Seepage head = ?

At point B : z = H2, Seepage head = h


Fig. 2.1 Flow of water in a simple channel section

Seepage ForcePressure at A is w h1

and at B is w h2

hydraulic gradient =

Water In

Soil

Sample

P1 h1

Standpipes

h2

Water

Out

A B

21 hhi

wziSeepage pressureP2

16


Hydraulic Gradient, i = h / H2


At point C : z = z, Seepage head = z i



Seepage pressure = ziw

17


18


19


20


A comparison of Figures d of both cases shows that the effective stress at a point located at a depth z measured from the surface of a soil layer is

reduced by an amount because of upward seepage of water.

' ' 0c cr wz i z

Stresses in Saturated Soil with Seepage Stresses in Saturated Soil with Upward Seepage

21


If the rate of seepage is increased andthereby the hydraulic gradient gradually isincreased, a limiting condition will bereached, at which point

where icr = critical hydraulic gradient (forzero effective stress).

Under such a situation, soil stability is lost. This situation generally is referred to as boiling, ora quick condition. From above equation

For most soils, the value of icr varies from 0.9 to1.1, with an average of 1.

'cr

w

i

' ' 0c cr wz i z

22

Quick Condition in Granular SoilsDuring upward flow, at X:

' = ' z - wizflow

hw

LX

soil

z

hL

izw

w

'

Critical hydraulic gradient (ic)

If i > ic, the effective stresses is negative.

i.e., no inter-granular contact & thus failure.

- Quick condition

Quick Sand Condition23

Quick sand is not a type of sand but it is a flow conditionoccurring within a cohesionless soil when its effective stress

is reduced to zero due to upward flow of water.

The effective stress in the soil is the difference betweenthe total stress and the pore pressure inside the soil mass.

The higher the effective stress, the more tightly the soilgrains are held together, generally resulting in higher

strength.


A soil is said to be in a quick condition when the effectivestress drops to zero.

Quick sand occurs in nature when water is being forcedupward under pressurized conditions.

Quicksand is found where water and sand mix every day.A good place to find quick sand is in hilly country with

abundant caves and underground springs.


In this case, the pressure of the escaping water exceedsthe weight of the soil and the sand grains are forced

apart.

The result is that the soil has no capability to support aload.


In this case, thepressure of the

escaping water

exceeds the weight

of the soil and the

sand grains are

forced apart.

The result is thatthe soil has no

capability to

support a load.


Shear Strength ofthe sand is zero

during this

condition.

28

The water level in the soil tank isheld constant by adjusting thesupply from the top and theoutflow at the bottom.

Stresses in Saturated Soil with Downward Seepage

29

The hydraulic gradient caused bythe downward seepage equals i =h/H2.


30



At point C : z = 0, Seepage head = ?



31

The loss of head caused by downwardseepage between the levels of A and B is h.

Hydraulic Gradient, i = h / H2


At point C : z = z, Seepage head = z i



Seepage pressure = ziw

32


33


' 'c wz iz

Stresses in Saturated Soil with Seepage Stresses in Saturated Soil with Downward Seepage

34

Seepage Force

The preceding section showed that the effect of seepageis to increase or decrease the effective stress at a point

in a layer of soil. Often, expressing the seepage force

per unit volume of soil is convenient.

In Figure(1), it was shown that, with no seepage, theeffective stress at a depth z measured from the surface

of the soil layer in the tank is equal to z. Thus, theeffective force on an area A is '

1 'P z A

35

Seepage Force

If there is an upward seepage of water in the verticaldirection through the same soil layer (Figure 2), the

effective force on an area A at a depth z can be given

by

Hence, the decrease in the total force because ofseepage is

The volume of the soil contributing to the effective forceequals zA, so the seepage force per unit volume of soil is

'

2 ( ' )wP z iz A

' '

1 2 wP P iz A

' '

1 2

(Volume of soil)

ww

iz AP Pi

zA

Seepage Force36

Seepage Force37

Capillarity

Capillary rise in soils39

Because water is attracted tosoil particles and because

water can develop surface

tension, suction develops inside

the pore fluid when a saturated

soil mass begins to dry.

This suction acts like a vacuumand will directly contribute to

the effective stress or skeletal

forces.

The negative pore pressure isusually considered responsible

for apparent and temporary

cohesion in soils, whereas the

other attractive forces produce

true cohesion.


Trees 'drink' from capillarywater.

Their instrument to drink fromthe capillary water is the

primary root.

In this photo you can see theprimary roots going

downwards to the dark soil.

This soil is dark because of thewater content in the capillary

channels.


In soil, there are millions ofvertical channels - these are

called "capillary tubes."

Whenever there is a downpour,excess water runs underground

through these capillary tubes.

When it is dry, these sametubes transport water to the

surface.


Trees have their roots in thesecapillary tubes - which also

contain threads of fungi which

are hygroscopic (attracting

water); and with their lateral

roots, they soak up capillary

water when it is hot and dry.

This is how a tree survives heatand drought.

Even in rocks, invisible fissuresfunction as capillary tubes.


The continuous voidspaces in soil can

behave as bundles

of capillary tubes of

variable cross

section.

Because of surfacetension force, water

may rise above the

phreatic surface.

Figure below showsthe fundamental

concept of the

height of rise in a

capillary tube.


The height of rise of water in the capillary

tube can be given by summing the forces in

the vertical direction, or

where T = surface tension (force/length)

d = diameter of capillary tube

= angle of contactw = unit weight of water

2 cos4

c wd h dT


For pure water and clean glass, = 0. Thus, above equation becomes

For water, T = 72 mN/m.

From above equation, we see that the

height of capillary rise

4c

w

Th

d

1ch

d

46

Effective Stress in the Zone of Capillary Rise

Although the concept of capillaryrise as demonstrated for an ideal

capillary tube can be applied to

soils, one must realize that the

capillary tubes formed in soils

because of the continuity of voids

have variable cross sections.

The results of the nonuniformity oncapillary rise can be seen when a

dry column of sandy soil is placed

in contact with water (Figure

9.16).

47


After the lapse of a given amount oftime, the variation of the degree of

saturation with the height of the soil

column caused by capillary rise is

approximately as shown in Figure

9.16b.

The degree of saturation is about100% up to a height of h2, and this

corresponds to the largest voids.

Beyond the height h2, water canoccupy only the smaller voids; hence,

the degree of saturation

is less than 100%. The maximumheight of capillary rise corresponds

to the smallest voids.

Hazen (1930) gave a formula forthe approximation of the height of

capillary rise in the form

48


Beyond the height h2, watercan occupy only the smaller

voids; hence, the degree of

saturation is less than

100%.

The maximum height ofcapillary rise corresponds

to the smallest voids.

49


Hazen (1930) gave aformula for the

approximation of the

height of capillary rise in

the form

50


The general relationship among total stress, effective stress, and porewater pressure was given as

The pore water pressure u at a point in a layer of soil fully saturatedby capillary rise is equal to w h (h height of the point underconsideration measured from the groundwater table) with the

atmospheric pressure taken as datum.

If partial saturation is caused by capillary action, it can beapproximated as

where S = degree of saturation, in percent.

' u

100w

Su h

51


52

Partially saturated soils

In the case of partially saturated soils part of the void space is occupiedby water and part by air.

The pore water pressure (uw) must always be less than the pore airpressure (ua) due to surface tension.

Unless the degree of saturation is close to unity the pore air will formcontinuous channels through the soil and the pore water will be

concentrated in the regions around the inter-particle contacts.

The boundaries between pore water and pore air will be in the form ofmenisci whose radii will depend on the size of the pore spaces within the

soil.

Part of any wavy plane through the soil will therefore pass through waterand part through air.

53

Partially saturated soils

In 1955 Bishop proposed the following effective stress equation forpartially saturated soils:

Where is a parameter, to be determined experimentally, relatedprimarily to the

degree of saturation of the soil. The term (ua uw) is a measure of thesuction in the

soil. For a fully saturated soil (Sr 1), 1; and for a completely drysoil

(Sr 0), 0. Equation 3.5 thus degenerates to Equation 3.1 when Sr 1. The value

of is also influenced, to a lesser extent, by the soil structure and the waythe

particular degree of saturation was brought about. Equation 3.5 is notconvenient

for use in practice because of the presence of the parameter .

insitu stresses

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