Laterally Loaded Piles2005

7/30/2019 Laterally Loaded Piles2005

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Design of Laterally Loaded Piles for

Offshore Platforms

Don Murff, TAMU/OTRC

Introduction

The design of piles for lateral loading is a standard aspect of the offshore platform

design process. Most environmental agents such as wind, waves, currents,

earthquakes, and ice impose lateral forces on an offshore structure. These forces,along with the structure weights and operational loads, are ultimately transmitted to

the foundation as axial and lateral loads and moments on the pile heads.

Configuring the piles to have adequate strength and stiffness to efficiently carry

these loads into the soil is the objective of the pile design process.


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Contents

Overview of the design process

Derivation of governing equations History of analysis/design methods

Models for failure analysis

A case history

Summary

References


3/29

Idealized Soil Resistance Profiles in Normally

Consolidated Clay

Axial Soil Resistance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Normalized Axial Resistance

NormalizedDepth

Lateral Soil Resistance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.5 0 0.5 1

Normalized Lateral Soil Resistance

Norm

alized

Depth

Pile design has two rather distinct components:

The axial load is resisted by shear resistance along the pile shaft and end bearing at

the pile tip. As shown in the figure on the left, in normally consolidated profiles, nearsurface soils play a relatively minor role in resisting axial load. In this case less than

10% of the capacity is developed in the top 30% of the pile. This aspect of design is

covered in a separate lecture.

The lateral load and moment are resisted by the lateral bearing resistance of the soil

and the bending stiffness of the pile. As shown on the right, the resistance to lateral

loads and moments is mobilized in the near surface soils. In this case

approximately 85% of the lateral resistance is developed in the top 30% of the pile.

The pile stiffness and strength must be adequate to effect this load transfer

efficiently. This aspect of design is the focus of this discussion.


4/29

Steel Pipes as Structural Members in Platform

Construction

From the beginning of offshore platform design in the mid-nineteen forties it has

been recognized that circular pipe piles are best suited for their foundation support.

In fact tubular members are preferred for most of the platforms structural

components. There are a number of reasons for this including:

The ability to resist omni-directional loads

Facilitation of fabrication and installation

Steel pipe piles have thus been used almost exclusively for offshore fixed bottom

structures.


5/29

Vertical and Battered Platform Sides

Many of the earliest structures were vertically-sided truss-type templates with

relatively wide base dimensions relative to water depth and small diameter circular

piles driven through the structure legs into the seabed. As we will discuss, the

critical foundation failure modes for such structures is often dominated by the lateral

capacity of the piles. Such structures become less efficient in deeper water where

overturning failure becomes more critical and hence designs evolved to structures

with sloped or battered sides i.e. with piles driven at a small angle to vertical. This

configuration increases the foundation base width relative to the deck and, hence

increases overturning resistance. It also allows the foundation to react significant

lateral load at least partially from the piles axial capacity.


6/29

Forces on Vertical and Battered Piles

Fv

FH

Fv

FH

+

As shown, the lateral load on a vertically sided structure is transmitted as a shear

force directly to the pile head. In a battered structure the vertical load creates a

shear force (perpendicular to the pile axis) at the pile head that opposes and partly

compensates for the shear force due to the lateral load. Since the platform imposes

a rotational restraint on the pile head the moment tends to bend the pile back into

the load almost irrespective of the pile batter.

This schematic is somewhat over simplified for the purposes of illustration. For a

complex structure the loads transferred to the piles will also depend on the stiffness

of the pile and the stiffness of the structure near the pile head.


7/29

Pile Design for Lateral Loading

0

10

20

30

40

50

60

70

80

90

100

0.00 1.00 2.00 3.00

Required Wall Thickness, inches

Depth,

ft.

Required

Wall

Thickness

Design

Wall

Thickness

0

20

40

60

80

100

120

140

160

180

200

-1 50 00 0 - 10 00 00 - 50 00 0 0 5 00 00

Bending Moment, inch-kips

Depth,

ft

Design Data

Diameter: 48 inches

Length: 200 feet

Load: 400 kips

Soil: Soft Clay

Wall Thickness Top 100 FeetMoment DiagramNOTE Different depth scales are used in the above plots.

A typical bending moment diagram for a pile is shown on the left. We will discuss

how this moment profile is developed later but first we consider how it is used in

design. The large moment at the pile top is due to the rotational restraint imposed

by the platform. The moment is attenuated with depth as the lateral load is

transferred to the soil. In addition to the moment, an axial force due to platform

weight and overturning resistance also acts on the pile. The pile forces and

moments cause stresses to develop along the pile. The shear stresses across the

pile are usually of minor importance. The longitudinal stresses (tension and

compression parallel to the pile axis), due to both axial load and pile bending control

the design, that is, they determine the required wall thickness of the pile (the outer

diameter is constant for the entire pile). These stresses vary with depth, ultimately

attenuating so that the required wall thickness generally decreases with depth.

Here, for the purposes of illustration, we will consider only those stresses due to the

moments. The figure on the right shows the wall thicknesses that would be required

to maintain the bending stresses below allowables for the design parametersassumed in this analysis. To economize on pile steel and especially the time

required for welding pile sections together, the design pile wall thickness will

gradually decrease. Each pile segment or can is a uniform thickness so the

changes in pile cross section occur in steps at the welds, i.e. they are not tapered.

An example of wall thickness selection is shown on the right. Note that the wall

thickness of the pile will affect the moment profile so some iteration is required in

the design. Further, a minimum wall thickness is required to prevent pile damage

during handling and driving.


8/29

Equation for Bending of a Beam

2

2

dxydEIEIM ==

M = Bending moment at x

E = Youngs Modulus of the pile material

I = Moment of Inertia of the cross section at x

= Radius of curvature

y = Lateral displacement of the pile at x

x = Coordinate along pile axis

Original Deformed

x

y

M

M

To carry out the design we need a mathematical model of the pile-soil system. The

pile can be treated as a linearly elastic, beam-column, a model which provides a

high degree of accuracy within the underlying assumptions. A robust theory of

elastic beam columns was developed by Navier almost 200 years ago. The theory is

based on the relatively simple idea that the moment at a point on a beam is

proportional to the curvature in the beam at that point. This is shown in the figure.

The theory has a number of simplifying assumptions including that of small

displacements, i.e. the geometry of the deformed shape does not vary significantly

from the original shape. In this figure displacement magnitude is exaggerated for

clarity. This model is a fundamental tool of structural engineers and provides a

basic building block for developing the model of a laterally loaded pile.

The equation for moment in terms of beam curvature can be used to connect the

relationship between the lateral displacement of the pile and the resistance along

the pile that is provided by the soil.


9/29

Shear and Lateral Load

p(x)

VM

V+dVM+dM

x

4

4

3

3

)(

0

0

dx

ydEI

dx

dVxp

Forces

dx

ydEI

dx

dMV

Moments

==

=

==

=

The equations of equilibrium provide us with relationships between moment and

shear and subsequently between shear and lateral load as shown. Shear and lateral

load are then proportional to third and fourth derivatives of displacement.

The last relationship shown connecting the lateral load, p(x) and the displacement, yis the fundamental beam equation that must be solved to determine the piles

displaced shape.


10/29

Geometric Relationships

dxEI

Mdx

dx

dyy

dxEIMdx

dxyd

dxdy

==

==2

2

Curvature, M/EI Slope Displacement

Purely geometric relationships provide us with expressions among beam curvature,

slope and displacement. The change in beam slope between any two points is the

integral of the curvature and the change in displacement is the integral of the slope.

The equilibrium and geometric conditions and the boundary conditions(forces/displacements at the pile top and bottom) provide the relationships for

modeling and hence designing a pile.


11/29

Pile Soil Interaction Model

4

1

22

4

sinsinh

cossincoshsinh2

=

=

EI

kD

where

LL

LLLL

kD

F

FF

L

= Pile top lateral displacement

Pile diameter= D

Pile flexural stiffness= EI

Winkler spring stiffness=k (force per unit

area per unit displacement)

Hetenyi Solution

Pile-Soil Idealization

Uncoupled

Springs

Soil stress-strain behavior is highly complex so that characterizing soil resistance is

certainly the biggest challenge in formulating the pile-soil model. It is intuitive that

the more displacement imposed by the pile at a point in the soil, the larger will be

the resistance. Therefore, one of the earliest attempts to model this behavior was to

idealize the soil as a bed of linear springs. In this model there is no coupling of soil

resistance from point to point along the pile, i.e. the soil resistance at any point on

the pile is simply proportional to the displacement of that point. This is referred to as

a Winkler foundation after its creator. Although this behavior is clearly

oversimplified, the model does seem to capture the basic physics of the system and

is surprisingly robust. It also has the significant advantage that, for certain

simplifying assumptions (linear springs of uniform stiffness), the governing equation

can be solved in closed form.

This solution was published by Hetenyi in 1946 and has been used extensively in

structural design of shallow foundations such as strip footings as well as for

laterally loaded piles. A number of investigators (Palmer and Thompson 1948,

Gleser 1954, and others) have carried out experiments to characterize the soil

springs (determine the appropriate spring constants) and correlate their behavior

with measurable soil properties such as soil type, soil stress history and strength

parameters.


12/29

Early Field Tests of Laterally Loaded Piles

After McClelland and Focht (1956)

Many of the early land applications were in areas of relatively competent soil and

under modest loads the assumptions of linear, uniform, uncoupled behavior worked

reasonably well. In many if not most offshore applications however the soils are

very weak near the mudline and have significant strength and stiffness increases

with depth. Here, the simplified theory did not work so well.

A significant body of work has been undertaken to address the offshore problem

and to generalize the model to include nonlinear, nonhomogeneous behavior. One

of the first studies of this problem was carried out by McClelland and Focht (1956).

They analyzed a set of field experiments conducted in 1952 on a 24 inch diameter

pile embedded 75 feet in a soft clay off the Louisiana coast in 33 feet of water. The

test frame and configuration are shown in the schematic. The pile was attached to

an existing structure through the bracing system as shown. The test pile was

instrumented with strain gages along its length to determine bending moments. A

lateral load was applied in increments with corresponding moment measurements.


13/29

Experimentally Derived P-Y Curves

After McClelland and Focht (1956)

Given the moment profile and boundary conditions one can determine the soil

resistance vs. displacement relationship at any point on the pile (in principle) by

Integrating the diagram of M/EI twice to get displacements

Differentiating the diagram of M twice to get lateral load.McClelland and Focht analyzed the test results in this manner and developed the

reaction vs displacement curves at various depths shown here. These curves

represent the load vs displacement characteristics of the soil springs at each depth

shown. Several features of these curves are worth noting.

The curves are decidedly nonlinear, i.e. the reactions are nonlinear with

displacement.

The stiffness and strength of the curves increases significantly with depth.

The curves are only fully developed up to 5 ft. depth. Curves below that do notdevelop their full capacity.

This work was a very significant step forward but of course left many unanswered

questions and begged for further generalization (deeper depth, varying strength

profile, sandy soils, etc.)


14/29

Effects of Small Errors in Numerical Derivatives

0

10

20

30

40

50

60

70

80

90

100

-600 -400 -200 0 200 400

Second Derivative of Moment

Depth

Smooth Cubic

Cubic w/ 0.1 % random error

Cubic w/ 1.0% random error

( )211

2

2 2

x

MMM

dx

Md iii

+ +

i -1

i

i +1x

Finite Difference Approximation of

Second Derivative

X

X

DxCdx

Md

DxCxBxAM

62ReactionSoilThen

Let

2

2

32

+==

+++=

Here it is worth mentioning some of the experimental and analytical difficulties in

carrying out such a study. Since McClelland and Fochts data was in numerical form

these operations have to be done numerically rather than analytically. Numerical

integration is stable, straightforward and so slope and displacement can be

estimated with relatively small errors. Numerical differentiation using finite

difference methods, however, is inherently unstable and introduces large errors

which are much worse in the second derivative than in the first. It is not clear how

the authors carried out the latter operation but it probably required some trial and

error and considerable judgement.

To illustrate this difficulty a cubic spline was fit to a typical moment vs depth curve.

The straight line shown in the figure is the second derivative of the analytical curve

(the soil reaction) using finite differences and is clearly well behaved. The

oscillating lines are second derivatives of the analytical curves with a small random

error introduced. The random errors have a mean of zero and standard deviations

of 0.1% and 1.0% of the mean moment magnitude respectively. It would be

extraordinarily difficult to obtain this level of accuracy in an experiment. Clearly this

is a very sensitive operation.


15/29

Elastic Soil Springs

0)(4

4

=+ xpdx

ydEI

the soil reaction p(x) can be represented

by the soil spring equation:

In the governing differential equation

K(x) can be any function of depth,

x, such as

yxkxp )()( =

y

P(x)

1k

xp(x) = k(x)y

k(x) = k0xn

The work carried out by McClelland and Focht initiated a comprehensive study of

the problem that was funded by the offshore oil industry and carried out by Profs.

Hudson Matlock and Lymon Reese and their co-workers at the University of Texas

over twenty to thirty years. These studies resulted in a wide ranging set of models

which form the basis of the current API design practice RP2A and are used

throughout the world by geotechnical engineers. Here, it is useful to highlight a few

of the significant contributions to this body of engineering.

As discussed earlier the governing equation for the laterally loaded pile problem is

repeated in this slide. In 1960 Matlock and Reese published an ASCE paper in

which they obtained solutions for a wide range of soil spring variations with depth

such as the power law form shown here. Although these solutions were limited to

linearly elastic springs, the authors argue that increasing the soil stiffness with depth

can account, to some degree for both increasing stiffness with depth and nonlinear

behavior since the soil stiffness will be most affected (reduced) near the soil

surface. The authors solutions included an approach to account for both shear and

moment loading at the pile top. In addition the paper describes in detail the

numerical solution technique using finite difference approximations to the equations

that has become the standard solution technique for beam columns of almost any

type e.g. pipelines, bridges, etc.


16/29

Development of Nonlinear Soil Springs or p-y Curves

Nondimensional p-y curve

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10 11

Nondimensional Displacement, y/yc

Nondimensional

resistance,p/pultima

te

Dy

sD

xJsxsp

cc

uu

uult

5.2

93

=

++=

where

Su=undrained strength; = effective unit weight;

X = depth below mudline; D= pile diameter;

J, c =material constants

After Matlock, 1970

The next step was to develop specific soil spring characterizations for various soil

types which explicitly included the observed nonlinear behavior. This was done by

conducting large scale tests on laterally loaded piles in representative soils.

Matlock carried out tests on instrumented piles of 12.75 inches in diameter in soft

clay in two areas: near the mouth of the Sabine River in southeast Texas and atLake Austin (Matlock, 1970). The pile head loads and moments were increased

incrementally. To his considerable credit he was able to numerically double

differentiate the moment diagrams to determine sensible soil reactions as a function

of depth and numerically double integrate M/EI to determine the pile displacements.

Based on these results, he developed simple relationships between load (p) and

displacement (y) as shown here on the left for static or monotonic loading for

various depths. He further collapsed the p-y curves into a single nondimensional

curve as shown on the right. An equation for the maximum reaction, pultimate, at any

depth is shown here as a function of the undrained shear strength along with anequation for the characteristic displacement, yc as a function of pile diameter. A

similar set of curves was developed to represent the post cyclic resistance of the

soil which shows significant degradation in resistance compared to static curves.

With this rather simple recipe, p-y curves could then be developed for any soft clay

strength profile. This procedure has stood the test of time having been incorporated

in the API Recommended Practice RP2A and being used internationally as well.


17/29

Iteration Scheme for Nonlinear p-y Curves

F

p

y

p

y

p

y

Closure Points

Example finite difference equation at each station i

0),(464

4

2112 =+

++ ++ii

iiiiiyyxk

x

yyyyyEI

i

i-1

i+1

x

The nonlinear p-y curves are used in an analysis of laterally loaded piles in the

following manner:

1. Boundary conditions such as lateral load, moment, or displacement are specified

at the pile head.2. A linear, finite difference solution of the governing equation is determined using

the initial stiffnesses of the p-y curves. This involves solving a set of simultaneous

algebraic equations. Because the equations have a very small band width, very

efficient solution methods are available.

3. The displacement is determined at each p-y curve location and a secant

modulus is determined for each curve as shown in the top call out.

4. A new linear solution is obtained.

5. Steps 3 and 4 are repeated until the changes in secant stiffnesses at selected

points are within a specified tolerance.

6. A new load increment is applied and the process is repeated.

7. Primary results include a pile head load vs. displacement curve and a series of

moment diagrams for the various load increments.


18/29

Laterally Loaded Pile Tests in Sand

After Reese, et al., 1974

Matlocks work on piles in soft clay was followed up by work by Reese and his co-

workers on piles in sand (1974). This study was carried out on Mustang Island

along the central Texas coast using instrumented 24 inch diameter piles. Both static

and cyclic p-y curves were obtained. This study employed the idea of fitting smooth

spline functions to the moment data so that the curves could be differentiated

analytically. This process proved much less sensitive to small data errors than

numerical differentiation and has become a standard method for analyzing such

data. Using these results Reese, et al. developed generalized p-y curves for use

with piles in sands of varying density (strength). These results have also been

incorporated into RP2A (in a simplified form) and are used internationally as well.

Reese and his coworkers also carried out a similar study in stiff clays at a site just

east of Austin (Manor). The p-y curves from this work are specific to the

overconsolidated, jointed, slicken-sided clay soils at the site. They show a distinct

brittle behavior and are not necessarily applicable to stiff clays found offshore.


19/29

Response of a 48 Inch Diameter, Fixed-Head Pile

to Lateral Load

0

200

400

600

800

1000

1200

0 5 10 15 20 25

Displacement, inches

LateralLoad,

Kips

Normally

Consolidated

ClayMedium Dense

Sand

To develop some insight into the behavior of piles under lateral load it is useful to

consider the effect of soil type on pile response. This figure is a plot of the

predicted pile head load vs pile head displacement for a 48 inch diameter, fixed

head (no rotation) pile using API p-y curves for both soft clay and medium dense

sand. There is a comparable difference in the moments and stresses developed in

the piles. Clearly the soil properties can have a profound effect on pile response.


20/29

Continuum Approaches to Analysis of Laterally

Loaded Piles

After Templeton, 2002

While the p-y approach to analyzing and designing offshore pile foundations iswidely accepted, it should be mentioned that there are alternative methodsavailable. These generally fall into the category of continuum models, that is, thesoil is represented as a continuous medium so that coupling of the soil resistancesalong the pile is included. Within this category the two most common solutions

involve (1) integral equation solutions and (2) finite element solutions.The integral equation method has been popularized by Prof. Poulos at theUniversity of Sydney. In one rendition, the pile is idealized as a thin vertical stripwith constant bending stiffness and the soil is idealized as a uniform, linearly elastichalf space. Solutions are obtained using superposition of Mindlins solution to apoint load in an elastic half space. The appropriate elastic properties are based onbackfitting experimental results so that, in this authors opinion, the method is noless empirical than the p-y approach and offers no real advantages for offshoreapplications.

The finite element approach (as illustrated here) is a well known and highly flexiblenumerical method that can include complex geometries, load conditions, andconstitutive (stress-strain) behaviors. It can be used to great advantage for newapplications such as unusual soil conditions but it involves considerably more effortthan the simple p-y approach. Therefore, its use on conventional designs is notwarranted (at this time). This method continues to be improved and user interfacesare being simplified so it will probably find more widespread use in the future.


21/29

Group Pile Effects

There has been a wide range of studies, since those previously discussed, to further

generalize the p-y curves to include other aspects of behavior.

One important study was conducted by Stevens and Audibert (1979). They

investigated the validity of using the p-y curves for clay developed from the relativelysmall 12.75 inch diameter piles used by Matlock for the analysis of larger piles more

common in deeper water structures which may have diameters of 84 inches or

more. They found that the conventional p-y curves significantly over predicted the

displacements for larger diameters and published a correction for normalizing the

standard curves.

Another area of interest is the so-called group pile effect. If the piles are closely

spaced, say two to three diameters edge to edge, they can strongly influence each

other. Such foundations tend to be common for very heavy platforms such as those

used in the Central North Sea, indicated here by the schematic of the Tern Platformshown on the left. Notice the pile sleeves arranged around each leg of the platform

will result in closely spaced piles. A similar arrangement is shown on the platform

under tow on the right. A single pile will tend to displace the soil in its immediate

vicinity and thus push on other piles in close proximity. This has the effect of

softening the overall group response to something less than that of the same

number of piles acting alone. A comprehensive discussion of this topic was

published by ONeill (1983).


22/29

Foundation Collapse Mechanisms

Shear

Mechanism

Overturning

Mechanism

Reverse

Mechanism

To this point our discussion has focused on the design of piles using simplified p-ycurves and beam-column analyses. The design requires that the stresses in the pilesteel are maintained below specified allowable values for both operating andextreme environments.

To complete our discussion of laterally loaded piles we turn our attention here tomethods of estimating the ultimate capacity of pile foundation systems. The ratio ofultimate capacity to design load levels is sometimes referred to as the reservestrength ratio or RSR. With the improvement of non-linear model techniques it hasbecome relatively common to estimate the RSR as an additional check after theconventional design is completed.

The controlling failure mechanisms may be in the structure, in the foundation, or acombination of the two. As a part of this analysis it is possible to analyze thereserve strength of the foundation alone (assuming the structure remains elastic)using a much simpler model than the fully nonlinear structural model. One solution

approach to this problem using plastic limit analysis has been documented by theauthor(Murff,1999).

As shown above the typical failure mechanism for a platform foundation involves thedevelopment of plastic hinges at the pile head and at some depth below themudline. The critical mechanism for the entire foundation may be a pure horizontaltranslation (left) or a simple overturning (center). For battered piles with relativelywide foundations the mechanism may actually involve reverse rotation of theplatform (right).


23/29

Ultimate Lateral Load Capacity

0

0

2

2

R

ML

MRF

p

p

pultimate

=

=

ultimateF

Uniform Soil

Resistance Linear SoilResistance

Plastic Sections

Mp

Mp R0=Ultimate

resistance

per unit

length

Lp

3

1

3 1

2

6

2

9

R

ML

RMF

p

p

p

ultimate

=

=

R1=Gradient

of ultimate

resistance

per unit

length

Mp= Plastic moment Capacity

Pile head fixed

against rotation

This slide illustrates a method for estimating the lateral capacity of a single pile.

This model is an integral part of the pile foundation system model. It is assumed

that plastic moments develop in the pile at the pile head and at some (unknown)

depth below mudline. This is valid for long piles but other mechanisms are possible

for short piles. It is further assumed that the lateral soil resistance between the two

plastic moments is fully developed. One way to estimate this soil resistance is to

use the p-ultimate values from the p-y curves directly. More general methods have

also been proposed (Murff and Hamilton, 1993).

To find the piles ultimate lateral capacity we can apply the upper bound method of

plastic limit analysis. In short, we seek the depth of the second plastic hinge that

will minimize the pile head capacity using optimization methods. In this slide, exact

solutions are given for two idealized but useful models of soil resistance, a uniform

distribution (left) and a linearly increasing distribution (right). The depth Lp is the

value that minimizes the resistance. Note that the overall capacity of the pile is

dependent not only on soil resistance but on the plastic moment capacity of the pile.

The plastic moment capacity is, in turn, dependent on the yield stress of the steel,

the cross section of the pile, and the axial load at that cross section.


24/29

Strengthening of Bass Strait Platforms

An Example of p-y Curve Development

To complete this discussion of laterally loaded piles it may be of interest to consider

an example of p-y curve development for unusual situations. In the late 1960s five

first generation platforms were installed in Bass Strait off the southeast coast of

Australia. It was subsequently discovered that the design criteria used were

unconservative and a decision was made to strengthen the platforms. Because of

the highly directional nature of the storms in that area an unusual strengthening

scheme was developed. This involved the placement of pile-founded struts on one

side of the platform for additional support against the design sea states. To design

an effective strut it was important to have a good estimate of the lateral stiffness of

the pile foundation. Since the soils in that area are calcareous sands, conventional

p-y curves could not be used reliably. It was therefore decided to carry out a test

program to develop an appropriate soil resistance model.

In the above figures from left to right at the top:

A schematic of the strut and pile installation plan.

The pile struts in the construction yard.

Left to right at the bottom:

84 inch pipe piles used to found the strut.

Struts in place on one of the platforms.


25/29

P-y Criteria Development- Centrifuge Tests

One experimental method used in this program was scale model testing using a

geotechnical centrifuge. This technique allows one to achieve similitude in scaling

from model to prototype. In a geometrically scaled model of 1:n the gravitational

field is simulated by imposing an n x g centifugal acceleration. Thus for a scale

model of say 1:100, a one foot thick soil layer simulates a prototype thickness of

100 feet. The tests were carried out in prepared sand beds using actual calcareous

sand obtained from Bass Strait sites. This slide illustrates some elements of the

test.

From left to right at the top:

A schematic of a centrifuge showing the soil container with a pile in place. Note

that the soil surface is in a vertical plane during the tests.

The arm of the Cambridge centrifuge (5m radius) where the test was carried out.

From left to right at the bottom:

Model piles with strain gages along the axes. Note that different pile diameters

were used in the tests.

Model piles installed in the soil container.

Tests were carried out on single piles and pile groups for a variety of pile

geometries and soil conditions.


26/29

Analysis of Centrifuge Results

After Wesselink, et al., 1988

This slide illustrates the analysis of the centrifuge results. Various lateral load levels

were imposed on the model piles and moment diagrams were measured for each

load level. In this interpretation an analytical form of a p-y curve was assumed

which is a power law function of depth and displacement. The coefficients and

exponents in the p-y curve equation were then determined by minimizing the error

between the analytical form assumed and the measurements. Using this approach

a generalized set of p-y curves was developed.


27/29

P-y Criteria Development Field Tests

In addition to the centrifuge tests, a series of field tests was conducted oninstrumented piles in a prepared soil pit, again using actual Bass Strait soils. Thisseries of tests complemented the centrifuge tests and also served to help validatethe centrifuge scaling. The test pit was basically a cube 20 feet on a side. The soilwas placed in a controlled process to achieve void ratios similar to those found

offshore and to those used in the centrifuge tests. Aspects of the tests areillustrated here.

Left to right at the top:

A sample of calcareous soil. Large soil particles were sieved out of the test soils.

The test pit with the two 14 inch diameter test pile heads exposed.

Left to right at the bottom:

The test pile set up showing the yoke which was used to impose the lateral load tothe pile head.

A comparison between pile head load vs displacement for the field test and for ascaled up centrifuge test. The centrifuge tests included a model test of one of thefield tests which was intended to validate the centrifuge scaling. This was a trueclass A prediction in that the centrifuge test was conducted first and a predictionwas made prior to the field tests being performed.

The generalized p-y curves were used to design the strut foundation which wasinstalled in the late 1980s and has performed satisfactorily since then.


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Summary

Design of piles for lateral loading is a key

element of the foundation design process. Modeling lateral soil resistance with uncoupled,

non-linear springs (p-y curves) has proven to be

a very satisfactory model that is simple to use.

Generalized p-y curves are available to model a

wide range of pile and soil conditions but

specialized tests may be required for unusual

situations.


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References

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Lloyd, J. R. and Clawson, W. C., 1984. Reserve and Residual Strength of Pile Founded Offshore Platforms,Proc. Int. Symp. On the Role of Design, Inspection, and Redundancy in Marine Structural Reliability,Washington.

Matlock, H., 1970. Correlations for Design of Laterally Loaded Piles in Soft Clay, Proc. Offshore TechnologyConference, Houston.

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Palmer, L. A. and Thompson, J. B., 1948. The Earth Pressure and Deflection Along the Embedded Lengths ofPiles Subjected to Lateral Thrust, Proceedings, Second International Conference on Soil Mechanics andFoundation Engineering, Vol. 5.

Poulos, H. G. and Davis, E. H., 1980, Pile Foundation Analysis and Design, John Wiley and Sons.

Reese, L. C., Cox, W.R., and Koop, F. D., 1970. Field Testing and Analysis of Laterally Loaded Piles in StiffClay, Proc. Offshore Technology Conference, Houston.

Reese, L. C., Cox, W.R., and Koop, F. D., 1974. Field Testing and Analysis of Laterally Loaded Piles in Sand,

Proc. Offshore Technology Conference, Houston.Stevens, J. B. and Audibert, J. M. E., 1979. Re-examination of p-y Curve Formulations, Proceedings, OffshoreTechnology Conference, Houston.

Templeton, J.S., 2002. The Role of Finite Elements in Suction Foundation Design Analysis, Proceedings,Offshore Technology Conference, Houston.

Wesselink, B. D., Murff, J. D., Randolph, M. F., Nunez, I.L., and Hyden, A. M., 1988. Analysis of CentrifugeModel Test Data from Laterally Loaded Piles in Calcareous Sand, Proceedings, Int. Conference on CalcareousSediments, Perth, Australia.

Williams, A., Dunnavant, T. W., Anderson, S., Lamb, W. C. and Hyden, A. M., 1988. Performance and Analysisof Lateral Load Tests of 356mm Diameter Piles in Reconstituted Calcareous Sand, Proceedings, Int.Conference on Calcareous Sediments, Perth, Australia.

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