Lateral Load Analysis of Single Piles

8/10/2019 Lateral Load Analysis of Single Piles

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Lateral Load Analysis of Single Piles

ECI 281(a)Term Project

Instructor:

Boris Jeremic

Yung-Tsang Chen

University of California, Davis

2004


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Purpose

The purpose of this report is to provide knowledge of deep foundation analyses, and

provide commonly used method for structure engineers.

Piles are structural members

made of steel, concrete, or timber, but many structure engineers are not familiar with

the piles behavior. Therefore, in order to ensure structural safety, it is very essential toknow how to analyze the soil pile behavior.

Introduction

Most structures are subject to lateral loads as a result of wind, earthquake, impact,

waves, and lateral earth pressure. If these structures are supported on deep

foundations, the foundations have to be designed for lateral loads. Laterally loaded

piles should be safe against geotechnical failure, structure failure, and excessivedeflections. In general geotechnical failure is reached only at very large displacements.

Therefore, what we concerns about is mainly on the prediction of deflections and

maximum bending moments in long piles.

The problem of a deep foundation subjected to lateral loading involves the interaction

of soil and structure. Therefore, the solution to the problem usually requires the use of

iterative techniques because soil response is a nonlinear function of the deflection of

the foundation. However, most practical engineers are interested in how to obtain thedeflection and bending moment in the deep foundation. Hence, in the process of

analysis, it is crucial to obtain these values.

Analyses in which the interaction between the soil and the pile is modeled using

concepts of subgrade reaction have been developed by Hetenyi(1946), and a number

of other investigators. These analyses are based on the assumption that the soil

reaction p is proportional to the deflection of the pile y. The soil reaction divided by

the deflection is called the soil modulus Es. Solutions have been developed for Es

constant with depth (Hetenyi 1946), for Es varying with linearly with depth (Reese

and Matlock 1956), for Es varying nonlinearly with depth (Matlock and Reese 1960).

The p-y method, devised by McClelland and Focht(1958), appears to be the most

practically useful procedure for the design of deep foundations. The reaction of the

soil against the pile is related to the deflection of the pile by means of nonlinear p-y

curves. Methods for estimating the shapes of p-y curves for various types of soil and

loadi9ng conditions have been developed by Matlock (1970) for soft clay, Reese et al.

(1975) for stiff clay below the water table, Reese et al.(1974) for sand.


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Because p-y analyses are capable of representing a wide variety of soil and loading

conditions in a realistic manner, and because the results of p-y analyses have been

found to be in reasonable agreement with results of field loading tests in many cases,

these analyses provide good results in pile design. However, in practical engineering

design, how to reduce the analyzing time becomes very important. When engineersuse p-y analyses, they have to spend a lot of time on developing the input data and

performing the computer analyses. Thus, a simplified method on analyzing the pile

subjected to lateral load is needed. Evans and Ducan (1992) proposed a simplified

analyzing method, called Characteristic Load Method. (CLM)

In the following reports, I would like to introduce 3 commonly used methods,

including Elastic solution for single piles, P-y method of nonlinear behavior for lateral

load analysis, and Characteristic load method.

Elastic solution for single piles

Consider a pile of length L subjected to a lateral force Q and a moment M at the

ground surface=0), the soil reaction in the direction opposite to the pile deflection can

be written as

(1)pdx

yd

IE pp =

4

4

Figure 1. Lateral load pile(a)before deformation (b)after


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According to Winkler s model, an elastic medium can be replaced by a series of

infinitely close independent elastic springs; therefore, we can assume:

(2)

Where p=pressure on soil

k=modulus of subgrade reactiony=deflection

The subgrade modulus for granular soil at a depth x is defined as

(3)

Where nx=constant of modulus of horizontal subgrade reaction.

Combining the above equations, the soil reaction can be written as

(4)

By solving the above equations, pile deflection at any depth [y(x)] can be obtain

(5)

Slope of pile at any depth [c (x)] can be obtain

(6)

Moment of pile at any depth [m(x)] can be obtain

(7)

Where are coefficients, is the characteristic length

of the soil-pile system.

When L 5T, the pile is considered to be a long pile. For L 2T, the pile is

considered to be a rigid pile. Table 1. gives some representative values of nh. Table 2.

gives the values of the coefficients for long piles. Note that, in the first column of

Table 2, Z is the non-dimensional depth.

kyp =

xnk xx=

04

4

4

4

=+=+ xyndx

ydIEyk

dx

ydIE xppypp

pp

y

pp

yIE

MTB

IE

QTAxy

23

)( +=

pppp IE

MTB

IE

QTAx

23

)( +=

MBQTAxm mm +=)(

mmyy BABABA ,,,,, 5y

pp

n

IET=


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Table 1. Representative values of nh

Table 2. Coefficient for long piles(L 5T)


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P-y method of nonlinear behavior for lateral load analysis

When a deep pile is subjected to a lateral load, the equation can be written as

According to Winkler s model, an elastic medium can be replaced by a series of

infinitely close independent elastic springs; therefore, we can assume:(8)

Where p=pressure on soil

Es=soil modulus

y=deflection

However, soil modulus may not be a constant in all depth, and it may changes with

depth and with p-y curves. Therefore, if we can predict a set of p-y curves at all

depths, deflection, pile rotation, shear, soil reaction can be readily solved.

Figure 3 shows the p-y cures under different depth. From the figure, we can observe

that soil modulus is not a constant or a straight line. Soil will perform nonlinear

behavior under big soil deflection.

Hence, how to get a set of p-y curves under different depth has become an important

thing. We can obtain the results from the experiments, and predict some formulas.

Matlock (1970) proposed some procedures to obtain the p-y curves for soft clay;

Reese (1975) proposed some steps and procedures for stiff clay to get p-y curves; Cox

(1974) and Reese (1974) also proposed procedures to find the p-y curves.

pdx

yd

Pdx

yd

IE xpp =+

2

2

4

4

Figure 2. Lateral load pile (a)deformation (b)modeled as independent elastic

yEp s=


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The researchers mentioned above all proposed similar procedures for different soils.

Reese in 1975 proposed his procedures for making a set of p-y curves, and the steps

are as follows

Step1: Obtain the best possible estimate of the variation of shear strength c and

average effective unit weight with depth, and the value of 50, the strain

corresponding to one-half the maximum principal stress difference.

Step2: Compute the ultimate soil resistance per unit length of pile, pu, use the smaller

of the following values.

(9)

(10)

Figure 3. (a) soil modulus varies with depth (b) p-y curves under different depth

( Prakash S., and Sharma, H. D. 1990)

cbb

x

c

xpu

++= 5.03

cbpu 9=


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Step3: Compute the deflection, y50, at one-half the ultimate soil resistance

(11)

Step4: Points describing the p-y curve may be computed by following equation

(12)

The applications of p-y curves requires the use of computer programs, such as

COM622 (Reese 1977), COM624 (Reese 1984), LPILE (Reese 1985), LTBASE

(Borden and Gabr 1987). These programs can help us to solve the deflection, rotation,

shear, moment, and soil pressure of piles under lateral loads.

The advantages of using p-y analyses are that p-y curves are the p-y curves arecapable of representing a wide variety of soil and loading conditions in a realistic

manner, p-y curveshave been found to be in reasonable agreement with results of

field loading tests in many cases, and p-y analyses consider the nonlinear behavior of

soils. The disadvantages of using p-y analyses are that p-y curves separate the soil

into discrete elements; therefore, the soil pressure is converted to point loads. Another

disadvantage is that the amount of time required developing input and performing the

detailed computer analyses in engineering practice. Thus, we may need a more

simplified method to be used on engineering practice.

Characteristic Load Method (CLM)

In order to reduce the time of analyses, a simplified method may be needed in

engineering design. Evans and Ducan (1992) proposed CLM method, which closely

approximates the results of nonlinear p-y analyses, and this method obtains results

more quickly.

This method can be used to determine ground-line deflections due to

lateral load, ground-line deflections due to moments applied at the ground line,

maximum moments, and the location of maximum moments. In using the method,

first, we have to find the characteristic load and moment, which are

For clay

(13-1)

For sand

(13-2)

5050 5.2 by =

41

50

5.0

=

y

y

p

p

u

68.0

2 )(34.7

=

Ip

uIpc

RE

SREDP

68.0''2 )(57.1

=

Ip

p

Ipc

RE

KDREDP


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For clay

(14-1)

For sand

(14-2)

Where Pc= characteristic load, Mc=characteristic moment

D= pile width or diameter, Ep=pile modulus of elasticity

RI= moment of inertia ratio=ratio of moment of inertia of the pile to the

moment of inertia on a solid circular cross section

r= effective unit weight of sand, Su= undrained shear strength of clay

r = effective stress friction angle for sand

Kp= Rankine coefficient of passive earth pressure=tan2

(45+ r /2)

Deflection due to loads applied at ground line

To estimate the ground line deflection using Fig.4, calculate the value of Pcusing

(13-1) for clay or (13-2) for sand. Divide the ground line load by Pcto determine the

value of Pt/Pc. Using the appropriate curve in Fig. 2, determine the value of yt/D, and

multiply this value by D to determine the ground line deflection yt .

Fig.4 can also be used to determine the load corresponding to a given ground linedeflection, by determine the load corresponding to a given ground line deflection, by

entering the chart on the horizontal scale at yt/D, and determining the corresponding

value of Pt/Pcfrom the appropriate curve.

Deflection due to moments applied at ground line

To estimate the ground line deflection using Fig.5 calculate the value of Mc using

(14-1) for clay or (14-2) for sand. Divide the ground line moment by Mc to determine

the value of Mt/Mc. Using the appropriate curve in Fig. 5, determine the value of yt/D,

and multiply this value by D to determine the ground line deflection yt.

46.0

3 )(86.3

=

Ip

uIpc

RE

SREDM

4.0''3 )(33.1

=Ip

p

IpcREKDREDM


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Figure 4. Load-Deflection Curves(a) Clay(b) Sand

Figure 5. Moment-Deflection Curves(a) Clay(b) Sand


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Comparison of characteristic load and p-y analyses

The CLM was derived from the results of p-y analyses, and it would be expected that

these two types of analyses would agree fairly closely when used to analyze the sameconditions. However, because some simplifications and approximations were made in

the process of reducing the numerical p-y results to the simplified dimensionless from

of the CLM, there are some differences between the results calculated by the two

methods. From table 3, the results for clay calculated using the CLM are in close

agreement with static p-y results for the soft clay and the stiff clay above water p-y

formulations, and the CLM gives a conservative approximation for the static analyses

using the stiff clay below water p-y formulation. The results of the CLM also agree

fairly well with the cyclic results calculated using the soft clay formulation.

Table 3. Comparison of characteristic load and p-y methods of analyses


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Summary and Conclusion

Analyses of laterally loaded piles can be simplified by an elastic beam, and by using

elastic beam theory and Winklers model, we can easily solve the problem. For most

cases, we can use p-y curves and computer programs to obtain the results, while mostimportant parameters involved in the prediction of p-y curves are believed to have

been considered. However, the prediction methods for p-y curves for clay or sand are

based on a small amount of experimental data; therefore, for more exactly analyses,

we should use continuum mechanics of lateral soil-pile interaction to analyze the

problem in 3-D condition. In engineering practice, we can use CLM method to

quickly obtain the approximate results, but we have to be very careful until additional

data allow the method to be validated.

Reference:

1. Matlock, H., and Reese, L. C. (1960). Generalized solutions for laterally loaded

piles. Journal of Soil Mechanics and Foundation Division, ASCE, 86(5), 63-91.

2. McClelland, B., and Focht, J. A. Jr. (1958). Soil modulus for lateral loaded

piles. Trans., ASCE, 123 1046-1063.

3. Reese, L. C., and Welch, R. C. (1975). Lateral loading of deep foundations in

stiff clay. Journal of the Geotechnical Engineering Division, ASCE, 101(7),

633-649.4. Das, B. M. Principal of foundation engineering. PWS-KENT publishing.

5. Ducan, J. M. Lateral load analysis of single piles and drilled shafts.

6. Abedzadeh, F. and Pak, Y. S. (2004) Continuum mechanics of lateral soil-pile

interaction. Journal of Engineering Mechanics, 130(11), 1309-1318.

Documents

Lateral Load Analysis of Single Piles