Lecture16_4on1

8/10/2019 Lecture16_4on1

http://slidepdf.com/reader/full/lecture164on1 1/5

Lateral Earth PressureLateral Earth Pressure –– FineFine--grainedgrainedSoils and MSE WallsSoils and MSE Walls

Lecture No. 16

November 14, 2002

2

Unsupported Excavation in a FineUnsupported Excavation in a Fine--grained Soilgrained Soil

• So far, we’ve considered a drained case for thecalculation of lateral earth pressure.

• A drained case applies to general behaviour ofcoarse-grained soils and long-term behaviour offine-grained soils.

• The short-term behaviour of a fine-grained soil isundrained and therefore, the relevant parameteris the undrained shear strength (su) of the soil.

• In case of fine-grained soils, it is usually possible toexcavate a trench up to a critical depth without theneed for any support in the form of a retainingwall.

• The critical depth of an unsupported excavation ina fine-grained soil depends on its su value.

3

ττ

σσ

ssuu

Unsupported ExcavationUnsupported Excavation –– Dry TrenchDry Trench

• Let’s excavate the trench in six layersand draw a Mohr’s circle of stress ateach stage for an element of soil atthe corner of the trench.

• Since the trench is dry, the total

horizontal stress on the element iszero.

• As we excavate deeper, the totalvertical stress on the elementincreases.

• Maximum value of total vertical stressis reached when the Mohr’s stresscircle touches the su–line.

• At this point, the soil will begin to failand some form of support will be

needed.• The critical depth (zcr) is given by:

zzcrcr

0σh = crsatv zσ ⋅=γ

satucr 2sz γ=4

Unsupported ExcavationUnsupported Excavation –– WaterWater--filled Trenchfilled Trench

• Here, at every stage,the trench iskept filled with water.

• Therefore, the total horizontal stresson an element at the corner of thetrench is equal to the hydrostatic

pressure applied by the water in thetrench.

• As we excavate deeper, the totalvertical stress on the elementincreases but so does the totalhorizontal stress.

• As a result, the Mohr’s circle ofstress shifts to the right as well asexpands.

• Maximum total vertical stress is

reached when the Mohr’s circle ofstress touches the su–line.

• The critical depth (zcr) is given by:

ττ

σσ

ssuu

zzcrcr

crwh zσ ⋅= γcrsatv zσ ⋅=γ

( ) γγγ ′=−= uwsatucr 2s2sz

8/10/2019 Lecture16_4on1


5

Unsupported ExcavationUnsupported Excavation –– Slip PlaneSlip Plane• So far, we have established the

critical depth of an unsupportedexcavation using equilibrium ofstresses.

• However, the excavation failsonly by developing a slip planewithin the soil mass.

• We do not know the shape andlocation of this slip plane but it isreasonable to assume a straightline inclined at an angle withhorizontal and passing throughthe corner of the trench as shownin the figure on the right.

• The figure also shows variousforces acting on a wedge of soilabove the slip plane.

• The wedge of the soil isconsidered on the verge ofsliding downwards.

• Therefore, the disturbingforces are equal toresisting forces along theslip plane.

6

Slip Plane (Continued..)Slip Plane (Continued..)

• Resolving the forces along the slipplane:

WsinθTcosθPa =+

wherewhere T=sT=suuL=sL=suuHH00 /sin /sinθθ

andand W=½W=½γ γ satsatHH0022cotcotθθ

• Hence, the above equation yields:

sin2θ

H2s-H

cosθsinθ

Hs-HP 0u2

0sat210u2

0sat21

a γγ =⋅

=

• To find maximum lateral earth pressure, we differentiate the

above equation w.r.t. θ and equate the derivative to zero:

0csc2θcot2θH4sθ

P0u

a=⋅=

∂

∂θθ = 45°= 45°

7

Slip Plane (Continued..)Slip Plane (Continued..)

• Substituting θ = 45° in the expression for Pa, we get:

0u20sat2

1a H2s-HP γ=

• For an unsupported dry trench, Pa = 0. Therefore,

satucr00u20sat2

1

4szH 0H2s-H γγ ==→=

• For a water-filled trench, Pa = ½γ wH02 . Therefore,

γγγ ′==→= ucr020w2

10u

20sat2

1 4szH HH2s-H

• Therefore, we have two limits for maximum unsupporteddepth – 2su /γ and 4su /γ – from the considerations of stressequilibrium and assumed failure mechanism, respectively.

• The true answer for maximum unsupported excavation lies inbetween the two limits. In practice, zcr is taken as:

satucr 3.8sz γ= γ′= ucr 3.8sz

[dry trench][dry trench] [water[water--filled trench]filled trench] 8

(a) Gravity(a) Gravity (b) Cantilever(b) Cantilever

(d) Buttress(d) Buttress(c) Counterfort(c) Counterfort

Rigid Retaining WallsRigid Retaining Walls

• There are twomain categoriesof retainingwalls: rigid and

flexible.• Rigid retaining

walls consist ofconcrete ormasonry wallsthat rely ongravity fortheir stability.

• Four different rigid retaining walls are shown in thefigure above.

8/10/2019 Lecture16_4on1


9

(a) Cantilever(a) Cantilever (c) Propped(c) Propped(b) Anchored or Tie(b) Anchored or Tie--backback

Flexible Retaining WallsFlexible Retaining Walls

• Flexible retaining walls consist of slender membersof steel, concrete or wood and rely on passive

soil resistance, props or anchors for stability.

• Three different types of flexible retaining walls areshown in the figure above.

10

Failure Modes for Rigid Retaining WallsFailure Modes for Rigid Retaining Walls

(a) Sliding or translational failure(a) Sliding or translational failure (b) Rotational failure(b) Rotational failure

(c) Deep(c) Deep--seated failureseated failure (d) Structural failure(d) Structural failure

11

Failure Modes for Flexible Retaining WallsFailure Modes for Flexible Retaining Walls

(a) Deep(a) Deep--seated failureseated failure(b) Rotation about the(b) Rotation about the

anchor or propanchor or prop

(c) Rotation about the base(c) Rotation about the base(d) Failure of(d) Failure of

anchor/propanchor/prop(e) Failure by(e) Failure by

bendingbending 12

Design of Retaining WallsDesign of Retaining Walls

• The topic of retaining wall design is so vast that itcan be a full-fledged course on its own.

• This topic will be covered in two final-yearelectives:

– C E 416 Geotechnical Design Practice (Prof. I. Fleming)– C E 466 Modeling of Earth Structures (Prof. J. Sharma)

• The design of retaining walls requires the analysisof all possible failure modes.

• For each of the possible failure modes, there shouldbe sufficient factor of safety against failure.

• Flexible walls are popular as temporary supportstructures for deep excavation but rigid walls are

fast becoming obsolete and are being replaced byMechanically Stabilized Earth (MSE) walls.

8/10/2019 Lecture16_4on1


13

The Concept of MSEThe Concept of MSE

• The concept of soil reinforcement ormechanically stabilized earth (MSE) wasaccidentally discovered by Henri Vidal in 1967 while

playing with his son on a beach.

• He discovered that he could build sand hills at anangle greater than the angle of internal friction ofsand by reinforcing the sand with strips of palmleaves.

• He called the composite material Terre Armeé® orReinforced Earth®.

• The horizontal reinforcement mobilizes friction atits interfaces with the sand and therefore, increasesthe lateral effective confining stress.

14

The Concept of MSE (Continued..)The Concept of MSE (Continued..)

• This effect isshown usingMohr’s circle of

stress in thefigure on theright.

• For the MSE, theMohr’s circle ofstress is smallerand is further

away from thefailure line.

• Therefore, MSE is able to resist larger shear stressesthan ordinary soil.

15

Components of an MSE WallComponents of an MSE Wall

(a) Typical Cross(a) Typical Cross--sectionsection (b) Types of reinforcement(b) Types of reinforcement

16

Components of an MSE Wall (Continued..)Components of an MSE Wall (Continued..)

Front PanelFront Panel

Strip ReinforcementStrip Reinforcement

BackfillBackfill

8/10/2019 Lecture16_4on1


17

MSE WallMSE Wall –– Construction StagesConstruction Stages

Installing the front facing panelsAttaching strip reinforcement to the

facing panel

Compacting the backfill18

Examples of MSE WallsExamples of MSE Walls –– CanadaCanada

• Check out the

abutments of theCircle Drive bridgecrossing over 22nd

Street.

Toronto

Vancouver

• There are manyexamples of MSE

walls in Saskatoon.

19

Stability of an MSE WallStability of an MSE Wall

• A MSE wall has to satisfy two stability criteria:

– Internal stability

– External or overall stability

• The external stability of a MSE wall is determined

by using the same procedure as used for a gravityretaining wall with a vertical face.

• The internal stability depends on

– The tensile strength of the reinforcing material, and

– The slip at the soil-reinforcement interface.

• Tensile failure of the reinforcement at any levelleads to progressive collapse of the wall.

• Slip at the soil-reinforcement interface leads toredistribution of stresses and progressivedeformation of the wall.

20

Stability of an MSE Wall (Continued..)Stability of an MSE Wall (Continued..)

• Two methods of analysis are used to determine theinternal stability of a MSE wall.

• One method is analogous to treating the MSE wallas an anchored flexible retaining wall and is

generally used for reinforcing material with highextensibility such as geotextiles and geogrids.

• The other method is the coherent gravity methodand is used for reinforcement of low extensibilitysuch as metal strips.

• Both these design methods will be covered in thefinal-year electives (C E 416 and C E 466).

• The curious ones amongst you may want to readthe book on Earth Reinforcement by C.J.F.P Jones(Engin. Lib. Call Number TA710.J75 1996).

Documents

Lecture16_4on1