foundation analysis and design 1.pdf

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ENCE 461

Foundation Analysis andDesign

Retaining Walls

Lateral Earth Pressure Theory


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RetainingWalls

Necessary in situations where gradual transitionseither take up too much space or are impracticalfor other reasons

Retaining walls are analysed for both resistanceto overturning and structural integrity

Two categories of retaining walls

Gravity Walls (Masonry, Stone, Gabion, etc.)

In-Situ Walls (Sheet Piling, cast in-situ, etc.)


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Lateral Earth PressureCoefficient

K = lateral earth pressure coefficient

x = horizontal effective stress

K

x '

z '


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Mohrs Circle

and LateralEarth

Pressures

=z 'x '=


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Development of Lateral EarthPressure

Po

b1z1

2Ko

2

Note Pore Water Effect! subtract vertically add horizontally


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Groundwater Effects

Steps to properly compute horizontal stresses

including groundwater effects:

Compute total vertical stress

Compute effective vertical stress by removinggroundwater effect through submerged unit weight;plot on P

odiagram

Compute effective horizontal stress by multiplyingeffective vertical stress by K

Compute total horizontal stress by directly adding

effect of groundwater unit weight to effectivehorizontal stress


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Groundwater

Effects


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Conditions of Lateral EarthPressure Coefficient

At-Rest Condition

Condition where wall movement is zero or minimal

Ideal condition of wall, but seldom achieved in reality

Active Condition Condition where wall moves away from the backfill

The lower state of lateral earth pressure

Passive Condition

Condition where wall moves toward the backfill

The higher state of lateral earth pressure


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Effect of Wall Movement


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Wall Movements Necessary to

Achieve Active or PassiveStates


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Estimates of At Rest LateralEarth Pressure Coefficient

Jakys Equation

Modified for Overconsolidated Soils

Applicable only when ground surface is level In spite of theoretical weaknesses, Jakys

equation is as good an estimate of the coefficient

of lateral earth pressure as we have

Ko1sin '

Ko1sin 'OCRsin '


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Relationship of Poissons Ratio

with Lateral Earth PressureCoefficient

Ko 1

211

tan1

tan2(Normally Consolidated Soils)


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At Rest Pressure Example Compute at rest earth pressure coefficient

Compute Effective Wall Force

Ko1sin 'Ko1sin 300.5

Po

b1z1

2Ko

2

Po

b

1202020.52

Po

b

12000lbs

ft

12kips

ft

hPA

20

3 6.67 ft.

(valid for all theories)


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Development of Active Earth

Pressure

D l f P i E h


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Development of Passive EarthPressure


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Earth Pressure Theories


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Rankine Earth Pressure Equations

Level Backfills


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Rankine Theory with Inclined

Backfills


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Rankine Coefficients with

Inclined Backfills

Inclined and level backfill equations are identical when = 0

E l f R ki A i W ll


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Example of Rankine Active Wall

Pressure Given

Retaining Wall as Shown

Find

PA,

from At Rest Conditions


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Rankine Active Pressure

Example Compute at rest earth pressure coefficient


Po

b

1z1

2Ka

2Po

b

1202020.3332

Po

b 8000lbs

ft8kips

ft

KAtan245

2

KAtan24515

1

3


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Rankine Passive Pressure

Example


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Rankine Passive Pressure

Example Compute at rest earth pressure coefficient


Po

b

1z1

2Kp

2Po

b

12020232

Po

b 72000lbs

ft72kips

ft

KPtan245

2

KPtan245153

Summary of Rankine and At


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Summary of Rankine and AtRest Wall Pressures

72,000 lbs.

12,000 lbs. 8000 lbs.

K cos

2


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Coulomb Theory

Kpcos

2

cos2cos1

sin sin

coscos

2

Ka

cos2cos1

sin sin

coscos

2

Typical


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TypicalValues

of WallFriction

E l f C l b Th


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Example of Coulomb Theory

Given

Wall as shown above

Find

KA, K

P, P

A


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Solution for Coulomb Active

Pressures Compute Coulomb Active Pressure

KA = 0.3465

Compute Total Wall Force

PA

= 8316 lb/ft of wall


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Solution for Coulomb Passive

Pressures Compute Coulomb Passive Pressure

KP = 4.0196

Compute Total Wall Force

PA

= 96,470 lb/ft of wall


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Walls with Cohesive Backfill Retaining walls should generally have

cohesionless backfill, but in some cases cohesivebackfill is unavoidable

Cohesive soils present the following weaknesses as

backfill:

Poor drainage

Creep

Expansiveness

Most lateral earth pressure theory was firstdeveloped for purely cohesionless soils (c = 0)

and has been extended to cohesive soils afterward


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Rankine Pressures with


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a e essu es tCohesion (Level Backfill)

31 tan2

4

22 c tan

4

2

1H

KA3

1tan2

4

2

2 c

H

tan

4

2

Active

Passive

13 tan2

4

2

2 c tan

4

2

3H

KP13

tan2

4

2 2 c

H tan

4

2

Overburden Driving

Wall Driving

Comments on Valid if wall-soil


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Comments on

RankineEquations

friction is not taken in

to account Do not take into

consideration soil

above critical height

Do not take intoconsideration sloping

walls

For practical problems,

should use equations asthey appear in the book

Hc2c

Ka


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Equivalent Fluid Method Simplification used to guide the calculations of

lateral earth pressures on retaining walls Can be used for Rankine and Coulomb lateral

earth pressures

Can be used for at rest, active and passive earthpressures

Transforms the soil acting on the retaining wallinto an equivalent fluid

Example of Equivalent Fluid Method


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Example of Equivalent Fluid Method

Given

Wall as shown above

KA

= 0.3465

KP

= 4.0196

w = 3 degrees

Find

Forces acting on the

wall (both horizontaland vertical)


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Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Active

Case)

GhKa coswGh1200.3465cos3

Gh41.52 pcf

GvKa sinwG v1200.3465sin 3

Gv2.18 pcf


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Example of Equivalent Fluid Compute Wall Load (Active Case)

PabGh H

2

2

Pa

b 41.52202

2 8304 lb/ft

Va

b

Gv H2

2

Va

b

2.18202

2436 lb/ft


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Example of Equivalent Fluid Compute Equivalent Fluid Unit Weights (Passive

Case)

GhKp coswGh1204.0196cos3

Gh481.69 pcf

G vKp sinwG v1204.0196sin 3

G v25.24 pcf


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Example of Equivalent Fluid Compute Wall Load (Passive Case)

PpbGh H

2

2

Pp

b 481.69202

2 96338lb/ft

Vp

b

G v H2

2Vp

b

25.24202

2

5048 lb/ft

T hi


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Terzaghi

Model Assumes log spiral

failure surface behindwall

Requires use of

suitable chart for KA

and KP

Not directly used inthis course, but optionin SPW 911

P ti L t l E th


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Presumptive Lateral Earth

Pressures Based on Terzaghi theory

Suitable for relatively simple retaining walls inhomogeneous soils

Classifies soils into five types:1. Clean coarse grained soils

2. Coarse grained soils of low permeability; mixed with

fine grained soils3. Residual soils with granular materials and clay content

4. Very soft clay, organic silts, or silty clays

5. Medium or stiff clay, very low permeability

P ti L t l E th


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Presumptive Lateral Earth

Pressures

Presumptive


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p

LateralEarthPressures

Effects of


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SurfaceLoading


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Homework Set 5 Reading

McCarthy: Chapter 16

Coduto: Chapters 22, 23, 24 & 25

Homework Problems McCarthy: 16-1, 16-8, 16-12a, 16-17

Coduto: 25.3 (Hand and Chart Solutions); 25.5 (SPW

911)

Due Date: 17 April 2002


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Questions

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