soil dynamic handouts (amin)

7/29/2019 Soil Dynamic Handouts (Amin)

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Dynamics of Soil & FoundationLecturer: Dr. Amin Eisazadeh

INSPIRING CREATIVE AND INNOVATIVE MINDS

2

Chapter 1

Introduction to Geotechnical

Earthquake Engineering


3

What is Earthquake Engineering?

Earthquake engineering deals with the effect ofearthquakes on people and their environment andwith methods of reducing those effects.

Earthquakes are a global phenomenon and aglobal problem. They have occurred for millions ofyears and will continue in future as they have in thepast.

Introduction

4

Hazards associated with earthquakes are commonly referredto as seismic hazards:

1. Ground Shaking

2. Structural Hazards3. Liquefaction4. Landslides5. Retaining Structure Failures

6. Lifeline Hazards7. Tsunami Hazards

Types of Seismic Hazards


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Ground ShakingGround Shaking

When earthquake waves reach theground surface, they produce shakingthat may last from seconds tominutes.

It is considered to be the mostimportant of all seismic hazardsbecause all the other hazards arecaused by ground shaking.

The strength and duration of shakingat a particular site depends on the

size and location of the earthquakeand on the characteristic of the site

(filter).6

Structural HazardsStructural Hazards

The leading cause of death and economic loss in many earthquakes.

It can be due to the collapse of unreinforcedstructures or falling objectswithin a structure which have caused casualties in many earthquakes

7

LiquefactionLiquefaction

In this phenomenon, the strength of the soil is reduced, often drastically,to the point where it is unable to support structures or remain stable.

Liquefaction only occurs in saturated soils, hence, it is most commonlyobserved near rivers and other bodies of water. 8

LandslidesLandslides

Earthquake induced landslides can bury a entire town or a village.

It can result from liquefaction phenomena or the failure of slopes thatwere marginally stable under static conditions.


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Lifeline HazardsLifeline Hazards

A network of facilities that provide the services required for commerce and public

health such as electrical power, transportation, water and gas distribution.

Lifeline failures not only have severe economic consequences but can also

hamper emergency response and rescue efforts following an earthquake. 10

Tsunami HazardsTsunami Hazards

Rapid vertical seafloor movements caused by fault rupture during earthquakescan produce long-period sea waves called tsunami.

In the open sea, they have height of less than 1m and wavelengths of severalhundred km, but as it approaches the shore the decreasing water depth causes

its speed to decrease and the height of wave to increase.

11

Significant Historical EarthquakesSignificant Historical Earthquakes

Earthquakes occur almost continuously around the world. Fortunately,

most are so small that cannot be felt and only a small percentage arelarge enough to be considered major earthquakes. Throughout recordedhistory, some of these major earthquakes can be regarded as being

particularly significant, such as:

The most deadly earthquake in history (700,000 death)7.8China1976

Caused intense interest in liquefaction phenomenon7.5J apan1964

Probably the largest earthquake ever recorded9.5Chile1960

CommentMagnitudeLocationYear

12

Chapter 2

Seismology & Earthquakes



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Introduction

The study of geotechnical earthquake engineering

requires an understanding of the various processes bywhich earthquakes occur and their effects on groundmotion.

This chapter provides a brief introduction to the structureof earth, the reasons why earthquake occur, and theterminology used to describe them.


14

Internal Structure of the EarthInternal Structure of the Earth

The earth is roughly spherical andconsists of different layered structureswhich causes the refraction andreflection of seismic waves at theirboundaries.

The crust, on which human lives, isthe outermost layer of the earth. Itsthickness is only a small fraction ofearths diameter (5-70 Km thick).

The mantle which is located below

crust and is separated by boundaryknown as Mohorovichic discontinuity

is about 2900 Km thick.

15

Seismic WavesSeismic Waves

When earthquake occurs differenttype of seismic waves are produced,they are:

Body waves Surface waves

Body waves can travel through theinterior of the earth and are of twotypes:

P-waves S-waves

City

Epicenter

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Body WavesBody Waves

P-waves, also known as primary,compressional, or longitudinal waves,involve successive compression andrefraction of the material throughwhich they pass. The motion of an

individual particle that a p-wavetravels through is parallel to thedirection of travel.

S-waves, also known as secondary orshear waves, cause shearingdeformations as they travel through amaterial. The motion of an individualparticle is perpendicular to thedirection of s-wave travel.


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Surface WavesSurface Waves

Surface waves result from the interaction between body waves andthesurface and surficial layers of the earth.

For engineering purposes, the most important surface waves areRaylieghand Love waves.

Raylighwaves are produced by interaction of p-and SV-waves with theearths surface, involve both vertical and horizontal particle motion.(They are similar to the waves produced by a rock thrown into a pond)

Love waves result from the interaction of SH-waves with a soft surficial

layer and have no vertical component of particle motion.

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Surface WavesSurface Waves

P & S wave front

Rayleigh Surface wave

S wave front

Love Surface wave

Multiple reflections of(horizontal component)

SH wave trapped by surficiallayer creates Love wave

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Continental Drift

Wegener, believed that the earth had only one large

continent called Pangaea 200 million years ago which broke

into pieces that slowly drifted into the present configuration

of the continents.

This was confirmed by the long-term deformations that

were concentrated in narrow zones between relatively intact

blocks of crust.

The theory of continental drift had become the greatest

advance in the earth sciences in a century.

INSPIRING CREATIVE AND INNOVATIVE MINDS20

Continental DriftContinental Drift

Present 200 Million years ago

Alfred Wegener (1920s) noted that surface geologyand fossil records match at boundary indicating that

Africa and South America where once united


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Plate Tectonics

The basic hypothesis of plate tectonics is that the earths surface

consists of a number of large, intact blocks called plates, and

that these plates move with respect to each other.

The earths crust is divided into six continental-sized plates and

about 14 of subcontinental size.

The relative deformation between plates is due to the convection

currents in the semimolten rock of the mantle, which impose

shear stresses on the bottom of the plates, thus dragging them inthe various directions across the surface of the earth.


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Plate TectonicsPlate Tectonics

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Earthquake ZonesEarthquake Zones

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Plate Boundaries

1. Spreading Ridge Boundaries: The plates move apart from

each other and hence the molten rock from the underlying

mantle rises to the surface where it cools down and becomes

part of spreading plate.

2. Subduction Zone Boundaries: The plates move towards each

other where at the point of contact, one plate sunducts

beneath the other plate.

3. Transform Fault Boundaries: The plates move past each

other without creating new crust or consuming old crust.



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Plate BoundariesPlate Boundaries

26

Faults are planes of weakness along which the Earth has beenbroken.

Movements on a fault can be eitherslow(ductile deformation) orfast(brittle fracture).

When a fault behaves in a brittle manner and breaks, earthquakesare generated.

FaultsFaults

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Fault MovementFault Movement

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Elastic Rebound Theory

As relative movement of the plate occurs, elastic strain energy

is stored in the materials near the boundary as shear stresses

increase on the fault planes that separate the plates.

When the shear stress reaches the shear strength of the rock

along the fault, the rock fails and the accumulated strain energy

is released.

If the rock is strong and brittle, the failure will be rapid and the

rupture of rock will release the stored energy explosively in the

form of heat and stress waves that are felt as earthquakes.



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Earthquake EnergyEarthquake Energy

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Earthquake Terminology

Earthquakes result from rupture of the rock along a fault. The

point at which rupture begins and the first seismic waves

originate is called the focus of earthquake.

The point on the ground surface directly above the focus is

called the epicenter.

The distance on the ground surface between an observer or site

and the epicenter is known as the epicentral distance.


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Earthquake TerminologyEarthquake Terminology

32

Earthquake Terminology

The earthquake size can be describedin different ways:

Earthquake Intensity:

The intensity is the oldest measure ofearthquake size and is a qualitativedescription of the effects of theearthquake at a particular location.(e.g., MMI scale)

Earthquake Magnitude:

The quantitative measurement ofearthquake size with use of seismicinstruments is made.



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Earthquake IntensityEarthquake Intensity

I. Not felt except by a very few under especially favorable conditions.

II. Felt only by a few persons at rest, especially on upper floors of buildings.

III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do notrecognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck.Duration estimated.

IV. Felt indoors by many, outdoors by few during the day. A t night,some awakened. Dishes, windows, doorsdisturbed; walls make cracking sound. Sensation like heavy truckstriking building. Standing motor cars rockednoticeably.

V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned.Pendulum clocks may stop.

VI. Felt by all , many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage slight.

VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinarystructures; considerable damage in poorly built or badly designed structures; some chimneys broken.

VIII. Damage slight in special ly designed structures; considerable damage in ordinary substantial buildings withpartial collapse. Damage great in poorly built structures. F all of chimneys, factory stacks, columns, monuments,walls. Heavy furniture overturned.

IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb.Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations.

X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations.Rails bent.

XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly.

XII. Damage total. Lines of s ight and level are distorted. Objects thrown into the air.

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Earthquake Magnitude

1. Richter Local Magnitude: It is defined as the logarithm of

the maximum trace amplitude recorded on a Wood-

Anderson seismometer located 100 Km from the epicenter

of the earthquake. (for shallow and local earthquakes)

2. Surface Wave Magnitude: It is based on the maximum

ground displacement amplitude of Rayleigh waves.

3. Moment Magnitude: It is based on the seismic moment,

which is a direct measure of the factors that produce rupturealong the fault. (Is not dependent on ground shaking levels

and hence does not saturate)


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Richters Magnitude

As known as the local magnitude (ML ) Measured on a Wood-Anderson seismometer 100km from

the epicenter. Wood-Anderson is a short period instrument that records 0

to 1s period accurately. Thus is records the shaking that willbe structurally important range for buildings.

ML =Log ( peak amplitude in micro-metres)

Logarithmic scale means that each unit increase in Richter

magnitude is a 10 fold increase in earthquake size. Thus

7.3ML earthquake is 100 times larger than a 5.3ML event.

An event magnitude is usually recorded from as many

seismometers as possible and an mean taken.

Best known scale but is doesnt distinguish between different

types of seismic waves.

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Moment Magnitude - Mw

Mw =(2/3)log10Mo 10.7

Mo =Seismic Moment

Mo =Au

o =shear modulus (typically 30 x 109 N/m2 or 30x 1010 dyne/cm2)

oA =area of fault rupture

o u=average displacement along fault


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Earthquake Magnitude


38

Chapter 8

Local Site Effects & Design

Ground Motion


39

Introduction

The effect of local geologic and soil conditions on the

intensity of ground shaking and earthquake damage

has been known for many years.

Design ground motions are the motions that reflect the

levels of strong motion amplitude, frequency content,

and duration that a structure or facility at a particular

site should be designed for.


Local Site Effects

1. Evidence from Theoretical Ground Response Analysis:

If the effects of material damping is neglected, the conservation of elastic

wave energy requires that the flow of energy from depth to the ground

surface to be constant. Hence, since the density and s-wave velocity

decreases as waves approach the ground surface, the particle velocitymust increase.


S waves


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Local Site Effects

2. Evidence from Measured Amplification Functions:

The strong amplification measured at the natural frequencies

of the soil deposit shows the importance of local site

conditions on ground response.

3. Evidence from Measured Surface Motions:

By comparing the ground surface motions measured at

different locations of a particular site during an earthquake,

the importance of local site conditions can be confirmed.


42

September, 1985 Michoacan(Ms=8.1) earthquake, 350 Km from Mexico city

Earthquake DescriptionEarthquake Description

Foothill Zone: Shallow, compact deposits of mostly granular soils.

Lake Zone:Thick deposits of very soft soils. Ground water waslocated at depth of 2m.

Transition Zone: Located between Foothill and Lake Zone andcomprised of thin soft soil deposits.

Mexico City Soil ProfileMexico City Soil Profile

Mexico City, 1985

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UNAM: University National Autonoma de Mexico (Foothill Zone)

SCT: Secretary of Communications and Transportation (Lake Zone)

Location of SeismographsLocation of Seismographs

Mexico City, 1985

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Mexico City, 1985

Peak Accelerations: At SCT site were up to five times greater thanthose at UNAM. (0.03g-0.04g at UNAM site)

Spectral Acceleration: Response spectra computed from recordedmotions for SCT site were about 10 times greater than at UNAM.

Damages at SCT site:The characteristic site period for SCT sitewas estimated to be around 2 sec. Most buildings (5-20 storey high)with almost the same fundamental period were damaged.(Resonance effect)

Comparison of Measured Surface MotionsComparison of Measured Surface Motions


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Local Site Effects

4. Compilations of Data on Local Site Effects:

At low to moderate acceleration levels, peak accelerations at soft sitesare likely to be greater than on rock sites. At higher acceleration levels,however, the low stiffness and nonlinearity of soft soils often preventthem from developing peak accelerations as large as those observed onrock.


46

Local Site Effects

5. Effects of Surface Topography and Basin Geometry:

Increased amplification near the crest of a ridge was measured in fiveearthquakes in Japan (acrest= 2.5 abase)

The curvature of basin in which softer soils have been deposited can trapbody waves and produce surface waves. (The amplification at edges willbe different)


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I. Design Parameters

Design Earthquakes Design Spectra

II. Development of Design Parameters

Site-Specific Development

Code-Based Development

Design Ground Motion

Design ground motions are the motionsthat reflect the levels of strong motionamplitude (ah(max),vh(max)), frequencycontent, and duration that a structure orfacility at a particular site should be

designed for.

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Design Earthquake

Design earthquake have been associated with two-level

design, at first level, remain operational, and to avoid

catastrophic failure for more severe level.

The Maximum Credible Earthquake (MCE): Is usually defined

as the largest earthquake that can reasonably be expected.

Operating Basis Earthquake (OBE): It is an earthquake that

should be expected during the life of a structure.



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Design Earthquake

Safe Shutdown Earthquake (SSE): The earthquake that produces themaximum peak horizontal acceleration for the following case:

Moving the epicenter of the largest anticipated event in the surroundingseismotectonic province to the site.

Moving the epicenter of the largest anticipated event in the surroundingseismotectonic province to the nearest points on boundaries andattenuating their motions to the site

Moving the focus of the largest event on any capable faults to the closetpoint on the faults to the site and then attenuating their motions to the

site.

(SSE is used in design of nuclear power plants )


50

Design Spectra

Response spectra are often used to represent seismic loading for the dynamicanalysis of structures. As a result, design ground motions are often expressed interms of design spectra.

Newmark and Hall, for example, recommended that design response spectra bedeveloped from a series of straight lines on a tripartie plot.

A Newmark-Hall design spectrum is obtained by multiplying the peak groundacceleration, velocity, and displacement values by amplification factors given fordifferent structural damping ratios.


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Design Spectra


Development of Design Parameters Site-Specific Development: Site-specific design ground motions reflect the detailed

effects of the particular subsurface conditions at the site of interest. The usualprocess for developing site-specific ground motions involves a seismic hazardanalysis and a ground response analysis. The procedure is as follows:

Seismic hazard analysis that produce ground motion at the surface (point A)

Deconvolution through the soil profile to determine bedrock motion (point B) This is the bedrock motion at the base (point D) of the soil profile at the site.

A conventional ground response analysis is then performed to predict the motion atthe surface of the soil profile of interest (point E)



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Development of Design Parameters

Code-Based Development:

The purpose of these codes is to produce minimum standards tosafeguard life, health, property, and public welfare during anearthquake by regulating and controlling the design,construction, quality of materials and etc

The UBC and NEHRP are the most influential contemporarydocuments that describe minimum standards for earthquake-resistant design of buildings in the United States.


54

Uniform Building Code (UBC)

The UBC building code is not intended to eliminate earthquake damagecompletely, In general, structures designed based on this code is ableto:

1. Resist a minor level of earthquake ground motion without damage.

2. Resist a moderate level of earthquake ground motion without structuraldamage, but possibly experience some non-structural damage.

3. Resist a major level of earthquake ground motion having an intensityequal to the strongest either experienced or forecast for the buildingsite, without collapse, but possibly with some structural as well as non-structural damage.


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The UBC allows two basic approaches to the

earthquake-resistant design of a building:

Static Approach

Dynamic Approach


Static Approach:

This approach is based on determination of a design base shear force,which is then distributed in a specific form over the height of the

structure for structural resistance of lateral load resistance.

(The effect of ground motions are represented by static lateral force)

WR

ZICV

w

=


Seismic dead loadSeismic dead load

Structure Ductilitycoefficient

Structure Ductilitycoefficient

Z: Seismic Zone FactorI: Importance FactorS: Soil Coefficient

T: Fundamental Period

Z: Seismic Zone FactorI: Importance FactorS: Soil Coefficient

T: Fundamental Period

75.225.1

32

=T

SC


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58

Dynamic Approach:

This approach allows the response of the structure to be determined by

response spectrum analysis or by time-history analysis which are obtained

by site-specific ground response analysis or from smooth, normalized

spectral shapes.


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Chapter 9

Liquefaction


Liquefaction Phenomena

When cohesionless soils are saturated and rapid loading occursunder undrained conditions, the tendency for densification causesgeneration of excess pore pressure (main characteristic ofliquefaction) which results in reduction of effective stress.

Liquefaction phenomena that results from this process can be dividedinto two main groups:

Flow Liquefaction

Cyclic Mobility



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Liquefaction Phenomena

62

Liquefaction Phenomena Flow Liquefaction:

9 Flow liquefaction can occur when the shear stress required for staticequilibrium of a soil mass (the static shear stress) is greater than theshear strength of the soil in its liquefied state.

9The cyclic stresses may simply bring the to an unstable state atwhich its strength drops sufficiently. Once triggered the largedeformations produced by flow liquefaction are actually driven bystatic shear stresses.


63

Flow LiquefactionFlow Liquefaction

64

Liquefaction Phenomena Cyclic Mobility:

9 Cyclic mobility occurs when the static shear stress is less then the

shear strength of the liquefied soil. The deformations produced bycyclic mobility failures develop incrementally during earthquake andare driven by both cyclic and static shear stresses.

9 Level-ground liquefaction is an example of cyclic mobility whichresults in excessive vertical settlements and development of sand

boils on the ground surface.



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Cyclic MobilityCyclic Mobility

66

Evaluation of Liquefaction Hazards

1. Liquefaction Susceptibility:

Is the soil susceptible to liquefaction?

2. Liquefaction Initiation:

If the soil is susceptible, will liquefaction betriggered?

3. Liquefaction Effects:

If liquefaction is triggered, will damage occur?


67

Liquefaction Susceptibility

1. Historical Criteria:

A great deal of information on liquefaction behavior has comefrom post-earthquake field investigations. This can be used toidentify specific sites, or more general site conditions, that may

be susceptible to liquefaction in future earthquakes.

Post-earthquake field investigations have also shown thatliquefaction effects have historically been confined to a zone

within a particular distance of the seismic source.


2. Geologic Criteria:

9 Geologic process that sort soils into uniform grain size

distributions and deposit them in loose states produce soil

deposits with high liquefaction susceptibility.

9 The susceptibility of older soil deposits to liquefaction is generallylower than that of new deposits.

9 The liquefaction only occurs in saturated soils, so the depth ofground water influences liquefaction susceptibility and arecommonly observed at ground water tables within a few meters ofthe ground surface.




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3. Compositional Criteria:

9 The compositional characteristics that influence volume changebehavior affect the liquefaction susceptibility of the soil. Thesecharacteristics include particle size, shape, and gradation.

9 The liquefaction phenomena is mostly observed in sands whichare capable of generating excess pore pressures. Nonetheless,liquefaction of non-plastic fine silts have also been observed.

9 Well-graded soils are generally less susceptible to liquefactiondue to filling of voids with smaller particles and hence lowervolume change potential. Also, rounded particles densify moreeasily than angular grains and so are more susceptible toliquefaction.



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4. State Criteria:

9 Even if a soil meets all of the mentioned previous criteria, it maystill not be susceptible to liquefaction. This is due to the fact thatthe liquefaction susceptibility is also dependent on the initial stateof the soil (i.e., stress and density characteristics) which controlsthe tendency of soil to generate excess pore pressure.

9 The initial state of soil required for liquefaction susceptibility ofsoils to phenomena introduced before, i.e., Flow liquefaction andcyclic mobility are different and should be considered separately.

9 To evaluate soils liquefaction susceptibility in terms of statecriteria, a brief review of some basic concepts of cohesionless soilbehavior is required which will be discussed here.



71

Critical Void Ratio (CVR)Critical Void Ratio (CVR)

Strain-controlled drained triaxial test performed on initially loose anddense sands showed that all samples with the same effective confiningpressure approached the same density when sheared to large strain.

The void ration corresponding to this constant density was termed thecritical void ratio (ec) which is uniquely related to the effective confiningpressure and hence can be drawn as a CVR line. 72

Steady State of DeformationSteady State of Deformation

The steady state of deformation is reached only at large strains wheresoil flows continuously under constant shear stress (residual strength).

The relationship between void ratio and effective confining pressure inthe steady state deformation can be shown on a line similar to CVRknown as the steady-state line (SSL).


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State Parameter:

The SSL is useful for identifyingthe conditions under which aparticular soil may or may not besusceptible to flow liquefaction.

A soil whose state lies above theSSL (exhibits contractivebehavior) will be susceptible to

flow liquefaction only if the staticshear stress exceeds its steady

state (residual) strength.



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9 The fact that a soil deposit is susceptible to liquefaction does notmean that liquefaction will necessarily occur in a givenearthquake. Its occurrence requires a disturbance that is strongenough to trigger it.

9 In the following slides, the mechanism of both flow liquefactionand cyclic mobility will be discussed.


Initiation of Liquefaction

75

Flow Liquefaction MechanismFlow Liquefaction Mechanism

The conditions at the initiation of flow liquefaction can be seen most

easily when a loose saturated sand is subjected to monotonicallyincreasing stresses under undrained conditions in a stress-controlledtriaxial test.

76

The soil has an initial effective confining pressure, 3c , prior toundrainedshearing (point A).

When undrainedshearing begins, the contractive behavior causes thegeneration of positive excess pore pressure as soil resistance reaches

its peak value (shear strength) located at point B.

At point B, the soil becomes unstable and strains dramatically until itreaches steady state (point C) conditions.

Beyond point C the soil is in the steady state of deformation and theeffective confining pressure is only a small fraction of the initial effectiveconfining pressure.

The soil has exhibited flow liquefaction, the static shear stress requiredfor equilibrium (point B) were greater than the available shear strength ofthe liquefied soil (point C).



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We can determine the response of a

series of soils with the same initial

void ratio and having different

effective confining pressures.

As can be seen, samples C, D, and

E show contractive behavior and

also it reaches a peak undrained

strength after which they strain

rapidly towards the steady state.

The flow liquefaction was initiatedat points marked witho(point B)

which when connected forms astraight line.



78

This line is used to define Flow

Liquefaction Surface (FLS).

The FLS marks the boundarybetween stable and unstablestates in undrainedshear. So, ifthe stress conditions in an

element of soil reach the FLSunder undrained conditions,whether by monotonic or cyclicloading, flow liquefaction will betriggered and the shearing

resistance will be reduced tothe steady-state strength.



79

Unlike flow liquefaction,cyclic mobility can developwhen the static shear stressis smaller than the steady-state strength (shaded

region). Also, it can occur inboth loose and dense soils.

Three combinations of initialconditions and cyclic loadingconditions generally producecyclic mobility.


Cyclic Mobility MechanismCyclic Mobility Mechanism

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Cyclic Mobility MechanismCyclic Mobility Mechanism

1. No shear stress reversal and no exceedance of the steady-state strength:Significant permanent strains can develop with each loading cycle.

2. No shear stress reversal but steady-state strength is exceeded momentarily:Significant permanent strains can develop when it touches the FLS,momentarily.

3. Stress reversal occurs and steady-state strength is not exceeded:Initial liquefaction can occur where soil reaches the state of zero effectivestress.


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Cyclic Stress Approach

9 The cyclic stress approach is based on the assumption thatexcess pore pressure generation is fundamentally related to thecyclic shear stress.

9 Conceptually is quite simple as well, i.e., the earthquake-inducedloading, expressed in terms of cyclic shear stresses, is comparedwith the liquefaction resistance of the soil, also expressed in termsof cyclic shear stresses.

9 At locations where the loading exceeds the resistance,liquefaction is expected to occur.


Evaluation of Initiation of Liquefaction

82

Characterization of Earthquake Loading

9 Actual earthquake motions can have very irregular time history ofshear stresses.

9 On the other hand, the lab data from which liquefaction resistancecan be estimated are obtained tests in which the cyclic shearstresses have uniform amplitudes.

9 Hence, in order to be able to compare earthquake-inducedloading with lab-determined resistance, conversion of the

earthquake loading to an equivalent series of uniform stresscycles is required.



83

Seed et al. applied a weighting procedure

to a set of shear stress time histories from

recorded strong ground motions to

determine the number of uniform stress

cycles, Neq, at an amplitude of 65% ofthe peak cyclic shear stress, that would

produce an increase in pore pressure

equivalent to that of the irregular timehistory.



84


The uniform cyclic

shear stress amplitude

for level (or gently

sloping) sites can be

also estimated from asimplified procedure:


dvcyc

cyc

rg

a

max

max

65.0

65.0

=

=

amax: peak ground surface accelerationg: gravity acceleration

v: The total vertical stressrd: stress reduction factor

amax: peak ground surface accelerationg: gravity acceleration

v: The total vertical stressrd: stress reduction factor

0

20

40

60

80

100

0.000 0.200 0.400 0.600 0.800 1.000

Stress Reduction Factor, rd

Depth,

ftLow

Avg

High

Poly. (Low)


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85


Characterization of LiquefactionResistance Based on Lab Test

9 Stress conditions on horizontalplates beneath ground surface issimulated in lab by consolidatingthe soil samples isotropically.

9 In these tests, the liquefactionfailure is defined as the point whichinitial liquefaction or at which somelimiting cyclic strain amplitude has

been reached.


86


Characterization of LiquefactionResistance Based on Lab Test

9 The relationship betweendensity, cyclic stress amplitude,and number of cycles toliquefaction failure can beexpressed graphically bylaboratory cyclic strengthcurves.

9 These curves are frequentlynormalized by the initialeffective overburden pressure to

produce a cyclic stress ratio

(CSR).


87


The CSR for the cyclic simple

shear test and cyclic triaxial

obtained from the lab test and

the field can be written as:


txrssfield

c

dcrtxrss

v

cyc

ss

CSRcCSRCSR

cCSRcCSR

CSR

)(9.0)(9.0)(

2)()(

)(

3

0

==

==

=

1.150.692(1+2K

0

)/(330.5)

Castro

1.00.55VariesSeed

1.00.7(1+K0)/2Finn et al.

Cr0.4 1.0

EquationReference

88


Characterization of LiquefactionResistance Based on In Situ Test

9 Liquefaction case histories can beused to characterize liquefaction

resistance in terms of measured insitu test parameters.

9 In this approach, the cyclic stressratio is usually used as the loading

parameter, and in situ test parametersthat reflect the density and pore

pressure generation characteristics ofthe soil are used as liquefactionresistance parameters.



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89


Standard Penetration Resistance:

9 The most common method usedfor characterization ofliquefaction resistance.

9 Seed compared the corrected SPTresistance and cyclic stress ratiofor clean and silty sand sites atwhich liquefaction was or was notobserved in earthquake of M=7.5to determine the minimum cyclicstress ratio at which liquefactioncould be expected in a sand of agiven SPT number.


90



9 The presence of fines can affect SPTresistance and therefore must beaccounted for in the evaluation ofliquefaction resistance. Nonetheless,the liquefaction resistance of sandsis not influenced by fines unless thefines comprise more than 5% of thesoil.

9 The plasticity of fines can alsoinfluence the liquefaction resistance.Ishihara suggested that the effect of

plasticity could be accounted for bymultiplying CSR by the factor:


( ) 1010022.00.1100.1

>+=

=

PIPIF

PIF

91



9 The minimum cyclic stressratio required to initiateliquefaction decreases with

increasing magnitude.

9 The minimum cyclic stressratio for other magnitudesmay be obtained bymultiplying the cyclic stressration for M=7.5 earthquakesby the factors shown in thetable.



Cone Penetration Resistance:

9 The tip resistance from the CPTtest can be used as a measure ofliquefaction resistance. It has an

advantage over the SPT in itsability to detect thin seams ofloose soil.

9 In CP T-based liquefactionevaluations, the tip resistance isnormalized to a standardeffective overburden pressure of1 ton/ft2 by:


5.0

0

1

=

v

acc

pqq


24/36

93


Once the cyclic loading imposed by an earthquake and the liquefactionresistance of the soils have been characterized, liquefaction potential can beevaluated.

The cyclic stress approach characterizes earthquake loading by the amplitudeof an equivalent uniform cyclic stress and liquefaction resistance by theamplitude of the uniform cyclic stress required to produce liquefaction in thesame manner of cycles.

The evaluation of liquefaction potential is thus reduced to a comparison ofloading and resistance throughout the soil deposit of interest. First, the variationof equivalent cyclic shear stress (earthquake loading) with depth is plotted. Thevariation of the cyclic shear stress required to cause liquefaction (liquefactionresistance) with depth is then plotted on the same graph.


94


Liquefaction can beexpected at depths wherethe loading exceeds theresistance or when thefactor of safety againstliquefaction is less than 1.


CSR

CSRFS

key earthquainduced bear stresscyclic shequivalent

quefactiono cause lirequired tar stresscyclic sheFS

L

cyc

Lcyc

L

L

==

=

,

95

Evaluation of Liquefaction Hazards

1. Liquefaction Susceptibility:

Is the soil susceptible to liquefaction?

2. Liquefaction Initiation:If the soil is susceptible, will liquefaction betriggered?

3. Liquefaction Effects:

If liquefaction is triggered, will damage occur?


Effects of Liquefaction

1. Alteration of Ground Motion

2. Development of Sand Boils

3. Settlement



25/36

97

Alteration of Ground MotionAlteration of Ground Motion

The development of positive excess porepressures causes soil stiffness to decreaseduring an earthquake and hence soilbecomes much softer.

This softening prevents the transmittance ofthe high-frequency component of thebedrock motion to the ground surface.

98

Development of Sand BoilsDevelopment of Sand Boils

Liquefaction is often accompanied by the development of sand boils.During and following earthquake shaking, seismically induced pore

pressures are dissipated predominantly by the upward flow of pore water. This flow produces upward-acting forces on soil particles which carries

them through localized channels and cracks to the ground surface to formsand boils.

99

Dry sands densify very quickly, hence, the settlement of a dry sanddeposit is usually complete by the end of an earthquake.

The settlement of a saturated sand deposit requires more time and can

only occur as earthquake-induced pore pressure dissipate.

The time required for this settlement to occur depends on thepermeability and compressibility of the soil, and on the length of thedrainage path, it can range from a few minutes up to about a day.

Settlement

100

Settlement Value

9 Tokimatsu and Seed produceda chart that allows thevolumetric strain afterliquefaction in a M=7.5

earthquake to be estimateddirectly from the cyclic stressratio and SPT resistance.

9 The settlement of each layer isthen computed as the productof the volumetric strain and thelayer thickness.



26/36

101

Settlement Value

9 For earthquakes of othermagnitudes, an equivalentcyclic stress ratio, CSRM,can be determined from thefollowing equation andTable.


dvcyc rg

a max65.0=

102

Chapter 10

Seismic Slope Stability


103

Introduction

When an earthquake occurs, the effects of earthquake-inducedground shaking is often sufficient to cause failure of slopes that weremarginally to moderately stable before the earthquake.

The resulting damage from slope instability can range frominsignificant to catastrophic depending on the geometric and materialcharacteristic of the slope.

For instance, in the 1964 Alaska earthquake, an estimated 56% ofthe total cost of damage was caused by earthquake-inducedlandslides or in 1920 Haiyuan earthquake in China , more than100,000 deaths were reported due to large landslides.

Therefore, evaluation of seismic slope stability is one of the mostimportant activities of the geotechnical earthquake engineer.


Types of Earthquake-Induced Landslides

Earthquake-induced landslides can be divided into three maincategories:

Disrupted slides and falls:These type of failure, usually found in

steep terrain, can produce extremely rapid movements anddevastating damages such as rock and soil avalanches.

Coherent slides:These type of failure, usually found in moderate tosteeply sloping terrain, occur at lower velocities than disrupted slidesand falls and its generally consist of transition of few coherent blocksof rock or soil..

Lateral spreads and flows: Generally involve liquefiable soils, andhence, due to the low residual strength of these materials, sliding canoccur on remarkably flat slopes and produce very high velocities.



27/36

105

Earthquake-Induced Landslides

106

9 It is logical to expectthat the extent ofearthquake-inducedlandslide activityshould increase withincreasing earthquakemagnitude and alsothat the extent ofearthquake-inducedlandslide activityshould decrease withincreasing source-to-site distance.

Earthquake-Induced Landslide Activity

Rock slumps, rock block slides, lateral spreads5.0

Rock avalanches6.0

Soil avalanches6.5

Soil slumps, soil block slides4.5

Rock falls, soil falls, rock slides4.0

DescriptionML

107

9 Geological, hydrological, topographical, geometrical, and materialcharacteristicsall influence the stability of a particular slope andshould be considered in the slope stability evaluation.

9 For many sites, considerable useful information can be obtained

from previously published documents such as topographic andhazard maps. Also, field reconnaissance which involves carefulobservation and detailed mapping of a variety of sitecharacteristics associated with existing or potential slopeinstability such as displaced channels, cracked walls, leaningtrees and etc are useful in the slope stability evaluation.

9 Lab tests are often used to quantify the physical characteristics ofthe various subsurface materials for input into a numerical slopestability analysis. Only after this information is obtained can astability analysis be performed.


Evaluation of Slope Stability

108

Evaluation of Slope Stability

Slopes become unstable when the shear stresses required to maintainequilibrium reach or exceed the available shearing resistance onsomepotential failure surface.

For slopes in which the shear stress required to maintain equilibrium understatic gravitational loading are high, the additional dynamic stresses neededto produce instability maybe low.

Hence, the seismic stability of a slope is strongly influenced by its staticstability and often rely on static stability analysis.

Currently, the most commonly used methods of static slope stability analysisare:

Limit Equilibrium Analysis

Stress-Deformation Analysis



28/36

109


Assumptions:

Considers force/moment equilibrium of a mass of soil above a potentialfailure surface.

The potential failure surface is rigid. (shearing can only occuron thepotential failure surface)

The shear strength is mobilized at the same rate over the entirefailuresurface.

The soil on the potential failure surface shows rigid-perfectly plasticbehaviour.

110


Slope stability is usuallyexpressed in terms of an index,most commonly the factor ofsafety, which is usually definedas:

Typical minimum FS used in slopedesign are about 1.5 for long-term

loading conditions and about 1.3for temporary slopes or short-termloading.


mequilibriumaintaintorequiredstressshear

strengthshearavailable=FS

SoilStrength

111


Example of Limitations:

Considers rigid-perfectly plastic behaviour which suggests that the deformationwill happen in ductile manner.

Many soils exhibit brittle, strain-softening behaviour.

Hence, the peak shear strength may not be mobilized simultaneously at all pointson the failure surface.

In this case, as the stress redistribution process continues, the zone of failure maygrow until the entire slope become unstable (Progressive failure) even with the

limit equilibrium factor of safety well above 1.(Residual shear strength should beused in the limit equilibrium analysis)

112

Limit Equilibrium Analysis Limitations


29/36

113

Stress-Deformation Analysis

Stress-deformation analysis allow consideration of the stress-strain behaviourof soilare most commonly performed using the finite element methods.

Non-linear stress-strain behaviour, complex boundary conditions, irregulargeometries and etc can all be considered in a modern finite element analysis.

This method offers the advantage of predicting slope deformations up to the point offailure and locating the most critically stresses zones within a slope.

However, the accuracy of stress-deformation analysis is strongly influenced by theaccuracy with which the stress-strain model represents actual material behaviour.

114

Seismic Slope Stability Analysis

Seismic slope instabilities can be grouped into two main categories:

Inertial Instabilities: the shear strength of the soil remains relativelyconstant, but slope deformations are produced by temporaryexceedancesof the strength by dynamic stresses.

Weakening Instabilities: are those in which the earthquake serves toweaken the soil sufficiently that it can not remain stable underearthquake-induced stresses. Flow liquefaction and cyclic mobility

are the most common causes of weakening instability


115

Analysis of Inertial Instability

Earthquake motions can induce significant horizontal and vertical dynamicstresses in slopes.

These stresses produce dynamic normal and shear stresses along thepotential failure surfaces within a slope.

When superimposed upon the previously existing static shear stresses, thedynamic shear stresses may exceed the available shear strength of the soiland produce inertial instability of the slope.

Currently, the most commonly used methods of inertial instability analysisare:

Pseudostatic Analysis (produces a factor of safety)

Makdisi-Seed and Newmark Sliding Block Analysis (based on evaluatingpermanent slope displacement)


Pseudostatic Analysis

9 The seismic stability of earth structures can be analyzed by apseudostaticapproach in which the effects of an earthquake arerepresented by constant horizontal and/or vertical accelerations that

produce inertial forces (Fh and Fv) that act through the centre of thefailure mass.


Wkg

WaF

Wkg

WaF

vv

v

hh

h

==

==

ah: horizontal pseudostatic accelerationav: vertical pseudostaticacceleration

kh & kv: dimensionless coefficientsW: weight of the failure mass

ah: horizontal pseudostatic accelerationav: vertical pseudostaticacceleration

kh & kv: dimensionless coefficientsW: weight of the failure mass


30/36

117

Selection of Pseudostatic kh & kv

9 The results of pseudostatic analysis are critically dependent on thesecoefficients, since it controls the pseudostatic force on the failure mass.

9 If the slope material was rigid, the inertial force induced on a potential slidewould be equal to the product of the actual horizontal acceleration and the massof the unstable material which increases with rising acceleration.

9 In practice, the fact that actual slopes are not rigid and that the peakacceleration exists for only a short time so these coefficients generallycorrespond to acceleration well below amax.


ga.k

k

Wkg

WaF

h

h

hh

h

max50:FranklinandGriffin-Hynes

)earthquakeccatasrophie,destructiv(severe,0.50.2,0.1,:Terzaghi

=

=

==

118

Pseudostatic Analysis

9 The pseudostatic

analysis, produces a

factor of safety against

seismic slope failure

by resolving the forces

on the potential failure

mass in a direction

parallel to the failure

surface.


( )[ ]( )

cossin

tansincos

forcedriving

forceresisting

hv

hvab

FFW

FFWclFS

+

+==

W

Fh

Soil Strength

Fh = ahW/g = khW

Fv = avW/g = kvWFv

119

NewmarkSliding Block Analysis

9 The serviceability of a slope after an earthquake is controlled bydeformations, therefore, analysis that predict slope displacementprovide a more useful indication of seismic slope stability.

9 Newmarkuses a block resting on an inclined plane analogy to developa method for prediction of the permanent displacement of a slope that issubjected to ground motions and is in unstable conditions.


Newmark Sliding Block Analysis

9 Considering the block is in stableconditions under static forces andthat the blocks resistance to sliding

is purely frictional:


cos)(sin

tan]sin)(cos[

forcedrivingicpseudostat

forceresisting)(

kh(t)gah(t)withplaneinclinedtheofvibrationhorizontalby

blockthetoedtransmittforcesinertialofeffectsthegConsiderin

tan

tan

sin

tancos

forcedrivingstatic

forceresisting

tk

tktFS

W

WFS

h

hd

+

==

=

=== W

hN

Kh(t) W R


31/36

121


9 Obviously, the dynamic factor of safety decreases as kh increases and there willbe some positive values of kh that will produce a factor of safety of 1.0 which isknown as yield coefficient (ky).

9 Hence, the yield acceleration corresponding to ky, is the minimum pseudostatic

acceleration required to produce instability of the block


( )

uphillsliding

tantan1

tantan

downhillslidingtan

+

+=

=

y

y

k

k

122


9 When a block on an inclined plane is subjected to a pulse of acceleration thatexceeds the yield acceleration, the block will move relative to the plane.

9 To illustrate the procedure by which the resulting permanent displacement canbe calculated, consider the case in which an inclined plane is subjected to asingle rectangular acceleration pulse of amplitude A and duration t.

9 If the yield acceleration, ay, is less then A, the acceleration of the block relativeto the plane during this period t0 to t0+t is:


)( 00 ttttaAa(t)ata yybrel +==

123


9 The relative movement of the block during this period can be obtainedby integrating the relative acceleration twice, that is:

[ ]( )

[ ]( )

2

1)(

)(

00

2

0

000

0

0

ttttttaAdt(t)vtd

ttttttaAdt(t)atv

t

tyrelrel

t

tyrelrel

+==

+==


9 After the base acceleration drops to zero (at t =t0+t), the block willcontinue to slide on the plane but with decreasing velocity due to the

friction force acting on the base:

0)( 10 ttttaaa(t)ata yyybrel +===

124


9 The relative displacement of the block continues to increase with time.Note that the total relative displacement of the block can be given as:

( ) ( ) yyrel aA

taAtd

2

1 2

1=


9 As can be seen, the total relative displacement depends stronglyonboth the amount by which and the length of time during which the yield

acceleration is exceeded.

9 Using the rectangular pulse solution,Newmark suggested the followingequations for peak base velocity and

permanent displacement produced: yy

y

y

rel

a

a

ad

A

a

ad

max

2

maxmax

2

max

2

1

2

=

=


32/36

125

Makdisi-Seed Analysis

9 Makdisi and Seed used average

accelerations computed by the Chopra and

sliding block analysis to compute

earthquake-induced permanent

deformations of earth dams and

embankments based on normalized charts.


126

Seismic Slope Stability Analysis

Seismic slope instabilities can be grouped into two main categories:

Inertial Instabilities: the shear strength of the soil remains relativelyconstant, but slope deformations are produced by temporaryexceedancesof the strength by dynamic stresses.

Weakening Instabilities: are those in which the earthquake serves toweaken the soil sufficiently that it can not remain stable underearthquake-induced stresses. Flow liquefaction and cyclic mobilityare the most common causes of weakening instability.


127

Analysis of Weakening Instability

Through a process of pore pressure generation and/or structural disturbance,earthquake-induced stresses and strains can reduce the shear strength of asoil.

Weakening instabilities can occur when the reduced strength drops belowthe static and dynamic shear stresses induced in the slope.

Flow Failures: occur when the available shear strength becomes smaller thanthe static shear stress required to maintain equilibrium of a slope.

Deformation Failures: occur when the shear strength of a soil is reduced tothe point where it is temporarily exceeded by earthquake-induced shearstresses.


Deformation Failure Analysis

9 Byrne Approach:

The method is based onmodeling a slope as a crust ofintact soil resting on a layer ofliquefied soil, Byrne used

work-energy principles todetermine the permanentdisplacement of the slope (D):


( )

( ) LstrLr

Lst

L

r

TDS

TSmvD

TDmvDT

SD

limlim

2

0

lim

2

02

lim

3

6

43

02

1

3

+=


33/36

129

Chapter 11

Seismic Design of Retaining Walls


130

Types of Retaining Walls

The problem of retaining soil is one of the oldest in geotechnical engineering.Retaining walls are often classified in terms of their relative mass, flexibility,and anchorage conditions, i.e.:

Gravity walls: Gravity walls are thick and stiff enough that they do not bend,their movement occurs essentially by rigid-body translation and/or roatation.

These walls usually fail by rigid-body mechanisms such as sliding and/oroverturning.

Cantilever walls:These walls bend as well as translate and rotate, rely ontheir flexural strength to resist lateral earth pressures. Cantilever walls aresubject to the same failure mechanisms as gravity walls, and also to flexuralfailure mechanisms.

Braced walls:These walls are constrained against certain types of movementby the presence of external bracing elements. They usually fail by grossinstability, tilting, flexural failure, and/or failure of bracing elements.


131

Gravity Walls

132

Static Pressures on Retaining Walls

Static earth pressures on retaining structures are strongly influenced by walland soil movements.

Active earth pressures develop as a retaining wall moves away from the soilbehind it, inducing extensional lateral strain in the soil. When the wall

movement is sufficient to fully mobilize the strength of the soil behind thewall, minimum active earth pressures act on the wall.

Passive earth pressures develop as a retaining wall moves towards the soilthereby producing compressive lateral strain in the soil. When the strength ofthe soil is fully mobilized, maximum passive earth pressures act on the wall.

Currently, the most commonly used methods for evaluating static loads are:

Rankine Theory

Coulomb Theory



34/36

133

RankineTheory (Active Earth Pressure)

9 Rankine developed the simplest

procedure for computing minimum

active earth pressures and expressed

it at a point on the back of retaining

wall as:


2

A

22

222

vA

vA

2

1

:basetheabove

3Hatloadpointaatacts,Presultant,pressureearthactivebackfill,sscohesionledryFor

angle)(backfillcoscoscos

coscoscoscos

245tan

sin1

sin1

soiltheofcohesion:stress,effectivevertical:pressure,earthactiveoftcoefficien:

2

HKP

KK

cK

KcKp

AA

AA

AA

=

+

=

=

+

=

=

134

RankineTheory (Passive Earth Pressure)

9 Rankine expressed

passive earth pressure

as:


2

P

22

222

v

vP

2

1

:basetheabove

3Hatloadpointaatacts,Presultant,pressureearthpassivebackfill,sscohesionledryFor

angle)(backfillcoscoscos

coscoscoscos

245tan

sin1

sin1

soiltheofcohesion:stress,effectivevertical:pressure,earthpassiveoftcoefficien:

2

HKP

KK

cK

KcKp

PP

PP

P

PP

=

+=

+=

+=

+=

135

Coulomb Theory (Active Earth Pressure)

9 Coulomb assumed that the force acting on

the back of a retaining wall resulted from

the weight of a wedge of a soil above a

planar failure surface. He then used force

equilibrium to determine the soil thrust:


( )

( ) ( ) ( )( ) ( )

( )

( ) ( ) ( )[ ] ( ) ( )[ ]( ) ( ) ( )[ ]{ }

+++=

+++=

=

++=

+

+++

=

=

cottantan1

cottan1cottantan

horizontalwithsurfacefailurecriticalofangletan

tan

figure.in theshownareandsoil,theandwallebetween thfrictioninternalofangle:

coscos

sinsin1coscos

cos

2

1

:basetheabove3Hatloadpointaatacts,Presultant,pressureearthactivebackfill,sscohesionledryFor

2

1

2

11

2

2

2

2

A

C

C

C

C

K

HKP

AA

A

AA

136

Coulomb Theory (Passive Earth Pressure)

9 Coulomb theory predicts

passive earth pressure as:


( )

( )( ) ( )( ) ( )

( )

( ) ( ) ( )[ ] ( ) ( )[ ]( ) ( ) ( )[ ]{ }

++++=

++++++=

=

++=

+++

+=

=

cottantan1

cottan1cottantan


tan

figure.in theshownareandsoil,theandwallebetween thfrictioninternalofangle:

coscos

sinsin1coscos

cos

2

1

2

1

4

31

2

2

2

2

C

C

C

C

K

HKP

AP

P

PP


35/36

137

Seismic Pressures on Retaining Walls

Common approach to the seismic design of retaining walls involves estimatingthe loads imposed on the wall during earthquake shaking and then ensuring thatthe wall can resist those loads.

Yielding Walls: retaining walls that can move sufficiently to developactive/passive earth pressures are referred to as yielding walls. The dynamicpressure acting on these walls are usually estimated by pseudostatic method.

Mononobe-Okabe Method:based on pseudostatic analysis of seismic earthpressures on retaining structures (also known as M-O method). It is the directextension of the static coulomb theory to pseudostatic conditions. Hence, the

pseudostatic accelerations are appl ied to a active/passive wedge and then fromforce equilibrium the total forces are obtained.


138

M-O method (Active Earth Pressure)

9 In addition to the forces that exist under

static conditions, the wedge is also acted

upon by horizontal and vertical

pseudostatic forces whose magnitude are

related to the mass of wedge by ah, av.


( )

( )

( )( ) ( )( ) ( )

( )[ ]

( )

( ) ( ) ( )[ ] ( ) ( )[ ]

( ) ( ) ( )[ ]{ }

basethefromactwillforcetotalreheight whethe:)6.0(3

cottantan1

cottan1cottantan


tan

1tan,,

coscos

sinsin1coscoscos

cos

12

1

2

1

2

11

1

2

2

2

2

hP

HPHPh

PPP

C

C

C

C

kkK

kHKP

AE

AEA

AEAAE

E

E

A

E

EAE

vhdAE

vAEAE

+=

+=++++=

++++=

=

++=

==

++

++++

=

=

139

M-O method (Passive Earth Pressure)

9 The total passive thrust

on a wall retaining a dry,

cohesionless backfill

is given by:


( )

( )

( )( ) ( )( ) ( )

( )[ ]

( )

( ) ( ) ( )[ ] ( ) ( )[ ]( ) ( ) ( )[ ]{ }

PEPPE

E

E

A

E

EPE

vhdPE

vPEPE

PPP

C

C

C

C

kkK

kHKP

+=

+++++=

+++++++=

=

++++=

==

+

++++

+=

=

cottantan1

cottan1cottantan


tan

1tan,,

coscos

sinsin1coscoscos

cos

12

1

2

1

4

31

1

2

2

2

2

140

Effects of Water on Wall Pressures

The presence of water plays a strong role in determining the loads

on waterfront retaining walls both during and after earthquakes.

Water outboard of a retaining wall can exert dynamic pressures on

the face of the wall. Water within a backfill can also affect the

dynamic pressures that act on the back of the wall.

Water Outboard of Wall: Hydrodynamic water pressure results

from the dynamic response of a body of water. For retaining walls,

this pressure is usually estimated from Westergaards solution. The

resultant hydrodynamic thrust is given by:


reservoirinwaterofdepththe:12

7 2 HHg

aP W

hW =


36/36

141

Effects of Water on Wall Pressures

Water in Backfill: for restrained water conditions (no relative movement of soil

and water), the M-O method can be modified to account for the presence of

porewater within the backfill. Representing the excess porewater pressure in the

backfill by the pore pressure ratio, ru, the active soil thrust can be calculated,

also, an equivalent hydrostatic thrust based on a fluid of unit weighteq must be

added to the soil thrust:


.

)1)(1(tan

)1(

1

3

buweq

vub

hsat

cexcessuub

r

kr

k

urr

+=

=

==

142

Seismic Displacement of Retaining Walls

9 Richards and Elms proposed a method for the seismic design of gravity wallsbased on allowable permanent wall di splacements. The method estimatespermanent displacement in a manner analogous to the Newmark sliding blockprocedure.

9 By defining yield acceleration as the level of acceleration that is just largeenough to cause the wall to slide on its base and calculating PAE using the M-O method, Richards and Elms proposed the following expression forpermanent block displacement:


( ) ( )g

W

PPa

a

avd

AEAEby

y

perm

++=

=

sincostan

087.04

3

max

2

max

soil dynamic handouts (amin)

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