lateral load analysis of single piles
TRANSCRIPT
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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.