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FINAL REroRr '!'HE APPLICABII1ITY OF '!'HE WFAP-86 PIIB CAPACI.'lY
imDlcrICN MEIH:>D :roR OONNECI'IaJr SOlIS ani
BEHAVIOR OF A SHEEI'PIIE WAIL FOR STABILIZATICN OF A SLOPE IN :EORl'I.AND
Project 86-7 by
Richard P. ~, Professor Kenneth R. Demars, Assoc. Professor William A. Shaheen, Grad. student Viroj Mekaga.roon, Grad. Student
JHR 88-181 octdber 1988
'!his research was sp:>nsored by the Joint Highway Research Advisory council of the University of cormecticut am the COrmecticut of the University of cormecticut ani the Connecticut Department of Transportation, am was carried out in the Civil Engineerirg Department of the University of Connecticut.
Table of Contents
I. WEAP.86
Introduction •
Scope of the Research
Background •
The WEAP-86 Program
Failure criterion
Analysis •
Conclusion •
II. Portland Embankment Stabilization
Introduction •
Background •
Instrumentation Program
Result.
Conclusion •
1
1
4
12
15
20
33
36
36
38
41
52
1
Introduction
The engineer requires reliable methcx1s for predicting the
capacity of piles as driven in the field. Early approaches used
semi-empirical methcx1s for making these predictions. The success of
these early attempts was mixed. The Federal Highway Administration
sponsored research to develop better methcx1s for predicting pile
capacity and a method evolved based on the work of Smith (1962) using
the wave equation analogy as a means of modelling the pile driving
operation and the resulting capacity of the pile. All mathematical
models must be calibrated to field conditions in an area. The
Connecticut Department of Transportation has conducted many load
tests on piles over the years. In this phase of the project, pile
capacity as predicted by WFAP was compared to the capacity measured
by field load tests.
Scope of the Research
This phase of the research conpares the pile capacity predicted
by the WFAP-86 version of the Wave Equation Analysis of piles (FHWA)
to available appropriate pile load test results. Included in this
project are the comparison of capacities for both monotube piles
which develop their resistance through skin friction and H-Piles in
glacial till whose capacity appears to be end bearing. The Soils and
Foundation Division of ConnIX:1.[l made the results of 240 pile load
tests available for comparison. These tests were screened for
suitability for this investigation and many had to be excluded. The
most common reasons for excluding individual tests from consideration
were: The pile was not loaded to failure or that the pile was driven
to bear on rock.
2
Field load tests are often "proof" tests to demonstrate that the
pile as driven, can withstand at least twice the design load without
excessive settlement. In these tests the ultimate capacity is not
determined and a comparison with a predicted value from WEAP can not
be made. When a pile is driven to rock, the load test shows
primarily the elastic shortening of the pile and yields no useful
infonnation on the soil pile interaction properties.
After reviewing available test data, seven steel H-piles. ranging
in size from liP 10 x 42 through liP 12 x 74 were selected for
comparison. 'lhe test data for the seven selected monotube piles
indicated that their ultimate capacity depended on skin-friction
together with an end-bearing component. Comparisons of field tests
and WEAP were made for these piles.
An example of the load tests used in this investigation is shown
in Fig. 1. 'lhe pile shown in Fig. 1 is an end-bearing pile driven
into glacial till. The pile size is liP 12x7 4.
txj ~.
1 .... .
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4
Background
Pile f01.U1dation design requires prediction of both pile capacity
and the length of pile. Prediction of the ultilnate bearing capacity
of pile may use two approaches; static analysis and dynamic
analysis. '!he static analysis estilnates capacity from soil
properties with little regard to the manner by which the pile is
placed, 'Whereas the dynamic approach uses cons&Vation of energy
principles without regard to soil properties and behavior. Each
approach has inherent advantages and disadvantages.
'!he static analysis requires accurate soil strength, soil unit
weight, pore pressure information, and lateral earth pressure
coefficients, together with pile dimensions to accurately predict
pile capacity. '!he soil information is usually estilnated. fran the
boring logs. '!he problems involved with static analyses have led to
the widespread use of simplistic energy-based fonnulas 'Which do not
consider soil properties in their development.
Dynamic analyses are based on equating the energy transferred to
the pile by the hammer to the work done by the pile in penetrating
the soil a finite distance. '!he penetration distance is called the
set. '!his approach is attractive since the set can be obBel:Ved in
the field and used to control capacity. However, the physical
properties of the pile and properties of the soil are not considered
in early dynamic fonnulations. '!he first such fonnula appeared in
Engineering News Reco:rd magazine and hence is known as the ENR
fonnula. '!he original ENR equation to calculate the ultilnate pile
load (Pu) as a function of the final pile set is given by:
Pu = Wr h s+l
where: Wr = weight of ram (kips)
h = height of fall (inches)
s = final pile set (inches)
5
'!he nominal factor of safety for this approach is 6 but field tests
have frequently shown that the actual factor of safety by this
equation can be less than 1, or greater than 6. Even though the ENR
fonnula is one of the most unreliable methods available to predict
Pu, it is still widely used. to control pile driving due to its
simplicity.
Soon after the development of the ENR fonnula, many others
developed dynamic fonnulas for predicting Pu. Among the available
fonnulas, the Hiley equation, and the Rational pile fonnula appear to
be most accurate. '!hese equations were the first to introduce a tenn
to account for soil stiffness. '!he Hiley equation is shown to be,
Pu = eWrh s + (IG. + K2 + 10)
Where: e = ~ efficiency
Wr = weight of ram
h = ram fall
s = final pile set
Wp = weight of pile
n = coefficient of restitution
kl = capblock and pile cap stiffness
k2 = pile stiffness
k3 = elastic compression of soil
6
'!he k3 tam is a first step fran the early dynamic formulations
to a more COlTp1ete model. '!he Hiley and Rational formulas were the
first to consider soil stiffness in an energy formulation.
Application of the wave equation to pile driving yielded a model that
allows for pile dimensions, variable soil stiffness along the pile
profile, soil and soil damping, system losses, etc. This was to
become known as the wave equation analysis of piles (WEAP).
rrbe wave equation was first, put into practical fonn by E.A.L.
Smith1 in 1962. rrbe greatest advantage of the wave equation is
that it attempts to account for variation in a large number of
physical parameters for any particular pile driving case. It
predicts ultilnate pile capacity as a function of the final blow
count, and estilnates stresses in the pile that develop during
driving.
The wave equation uses physical properties of the pile soil
system, accounts for energy losses in the system; and in-situ pile
driving infonnation to predict static pile capacity.
rrbe wave equation may be derived fran consideration of the
intemal forces and motion produced on a segment of a free1y
suspended elastic bar subjected to an inpact. at one end. rrbe
resulting 1-0 equation is:
where c = longitudinal wave velocity
U = longitudinal displacement
x = longitudinal coordinate
t = time
This one-dimensional wave equation has been derived fran the
equations of motion as outlined in Ko1~, and has been solved in
7
closed analytical form by ~ for a homogenous 1-0 bar
embedded in an homogeneous elastic medium. standard linear,
isotropic, elastic material properties are assumed for Pochh.aJmnerI s
exact solution. In practice; however, viscous soil damping, variable
pile cross-sections, and variable pile cushion stiffness
considerations all make exact analytical solutions impractical if not
impossible to solve in closed form.
In addition, for a pile with non-zero skin friction, the
resistance of the surrounding soil must also be considered.
Modifying the above equation yields:
d2U ? d2U dt2 = c- dx2 +/- R , where R is a soil resistance term.
'!he WFAP-86 computer program uses a finite-difference numerical
solution to solve the above modified equation.
'!he approach used by WFAP-86 was first developed by Smith to
determine the pile-set (or b101f1 count) for a given ultimate static
pile load. '!he pile system is idealized as shown in Figure 2 and
consists of the fo1101f1ing elements.
1. A weight (ram) to which an initial velocity is imparted from
the hannner.
2. A capb10ck (hannner cushion)
3. A pile cap (anvil)
4. A cushion block (for concrete piles)
5. '!he pile
6. '!he supporting soil
(A) ACTUAL .SYST.EM. DIESEL
AIR I STEAM
.. "'~I---- RA M --a ..
o - ANVIL---~~~ ~----r' CJ;n ' CAPBLOCK
::==:~ . LJ '1.I~HElMET --.. -.... -:..----.. ~., :t:l~ C·USHION~-~~ .
·o~ PILE -----..
(C) SOIL RESI'STANCE: ' o :::E ~ z >o a: "'--___ __
VELOCITY
8
-':.,.:;':"', ,
:'f
;,.. ', - .::~~ .... ,;, ... : . . :"; ., . -• .' _ ~ ;f. ~~. . .... ~
. ~ .i,·r:-: . .. : .... ':-:' / . . :t ~~ · f: " I~ > : .
-...... '. .' .. -, .:., ~ " \, - . ~ . .. ',"
I I .' .
~' . ...
DISPLACEMENT
Figure 2. Actual Soil-Pile System and Idealized Schematic Model
'!he ram, capblock, pile cap, cushion block, and pile are
represented by appropriate discrete weights and springs. '!he
frictional resistance on the side of the pile is represented by a
series of springs and dashpots, while the point resistance is
modelled by a single spring and dashpot.
9
Soil does not follow the constitutive laws for an isotropic
linear-elastic material by being highly nonlinear for laI:ge strains
and. able to defonn plastically as well. Smith I s model of the
constitutive laws of a typical soil subjected to a stress reversal is
shown in Fig. 3.
Load
Ru(m)JY(m.t )
·.~u(mj· -
D<zformation
Ru(ml·
D
Figure 3. Typical Response for Soil Undergoing a Stress Reversal
10
The loading path OABCDEFG represents loading and unloading in
side friction. For the pile point, only compressive loading is
considered and the loading and unloading path in OABCF. The Q(m)
tenn, called the quake, is defined as the maxllm:nn "linear"
defomation the soil may undergo before the onset of plastic
defonnation. A idealized load-defonnation diagram such as in Figure
4a may now be established separately for each spring, so that
K' (m) = Ru(m)
Q(m)
where K' (m) is the spring constant during elastic defonnation for the
extemal spring (m). To aCCOlmt for the effects of dynamic loading
during pile driving in increasing the instantaneous resistance of the
soil, a Kelvin-type rheological model is used (Figure 4b). In the
Kelvin model, the damping constant, J, represents the an additional
resisting force which is proportional to the velocity of loading.
Load
E
Friction link limits spring load.
Spring constant K'
Darormation
RJm)
o
Soil Rllsistancll \ R
..... _ ........ ___ . ---.J .=TI.isPlacamant D
Damping constant J.
11
Figure 4. Idealized Elasto-Plastic Stress-strain Behavior of
Soil (a), and Visco-Elastic MOdel (b)
'!here is considerable uncertainty regarding the selection of
quake and damping values to be used in a WEAP analysis. However; a
12
commercially available electronic pile driving analyzer, using a
sampling probe attached to the pile butt during driving, can monitor
and detennine in-situ quake and damping values. 'lhese values
together with a computer program, called CAPWAP4 , further refines
WFAP prediction accuracy.
'!he WEAP-86 Program
In order to model and predict pile load capacity using WEAP-86,
the soil and pile physical properties must be input to the computer
program via a data input program called wa6-IN. Required physical
properties include pile driving hammer infonnation, pile and helmet
cushion weights, lengths, and stiffnesses, pile-segment
discretization properties including masses, damping, and stiffnesses;
and soil-pile damping and soil quake values. The WFAP program
provides default values for the soil input parameters for toe and
side quake tams (.1 in.) and toe and side damping tams
(.1 sec./ft.).
The material properties required by the WEAP-86
finite-difference ccxie include the modulus of elasticity of the pile
helmet, pile segments, and pile cushion. In addition, assmned
skin-friction distriliution schemes and end-bearing/skin friction
percentages, soil quake values, and damping values all must be
specified. A sample input card is shown in Figure 6 which describes
the soil-pile system of Figure 1.
type II.Out 1
q~'~\j ECHO PRINT OF INPUT DATA
o " 1.200 .000 .0 .000 .0 .000
30.500 21.160 30000.l')OO VULCAN VOL 06 3 1 0
6.5000 39.19(~ 17.4q(~
. 00(1 • 000 • 8(10 2.~~0 2.350 .000 • (le)(I(I • (11)00 • (II)(H)
• 1 00 • 1 00 • 1 ()(I
0 ··0 0 .000 .500
492.000
3.0000 .010
21709.8 • ')0('(1 .100
ll~.O 150.0 2~0.0
.0 .0 .(1
15 0 .800 .010 .8'W
3.0000 2
21709.8 .0000
6 0 0 .010
.0 .010
.6700
.0
.0
WEAP8o: WAVE EQUATION ANALYSIS OF PILE FOUNDATlONS 1986, VERSION 1.(101
hpilf.! pg 1::'1 I
HAMMER MODEL OF; VUL 06 MADE BY: VULCAN
0 0 .0
.0
ELEMENT WEIGHT STIFFNESS COEFF. Of" D-NL. CAP DAMF'G
)
(
(KIPS) (KIlN) R£ST! TUnON FT H(lFT/S) 1 6.500
CAP/RAM 1.200 177183.5 .8l~ .0100 26.3
ASSEMBLV WEIGHT STIFFNESS COEFF. OF D-NL. ! (KIPS) (KIlN) REST !TUnON FT
1 2.350 21709.8 2 2.350 21709.8 .800 .0100
HAMMER OPT I DNS I HAMMER NO. FUEL SETTG. STROKE OPT. HAMMER TYPE DAMPNG-HAMR
206 1 0 3 2
HAMMER PERFORMANCE DATA RAM WEIGHT RAM LENGTH
(KIPS) (IN) b.50 ,!.9.19
RTD PRESS. (PSI)
.00
ACT PRESS. (PSI)
.00
MAX STROI:E (FT> 3.1)"
EFF. AREA ( IN2)
.00
STROKE EFFICIENCY 1FT)
3.00 .67(1
IMPACT VEL. (FT/S) 11.37
WEAP OF 1986 hpile P9 75 I
PILE PROFILEr LST \ AREA E-MOD SP.W. WAVE SP EAIC
(FT) ( IN2) (KS1) (LB/FT3) (FT/S) (K/FT/S)
.00 21.8 30000. 492.000 16806.8 ;sa. 8 ::SO. 50 21.8 30000. 492.000 16806.8 38.8
WAVE TRAVEL TIME - ·2L/C - • 3.629 MS
PILE AND SOIL MODEL FOR RULT .. 10CI.O KIPS
0
NO WEIGHT STlFFN D-NL SPLICE COR SOIL-S SOIL-D QUAKE L 8T
2 4 6
TOE
(t<IPS) (KIlN) (FT) .378 lu702. .010 • 37e 10702 • .(ltO .378 10702. .010 • 378 10702 • .010
PILE OPTIONSJ N/UNIFORM AUTO S.G.
o o
SOIL OPlIUNS: X SKIN FR % END BG
15 85
(FT> (KIPS) (SIFT} • (lOCI .8S0 2.5
-1. (IOu 1.000 2.5 -1.000 1.000 2.5 -1.000 1.000 2.5
8:1.0
SPLIC£S DAMPNG-P
DIS. NU. 5 DAMPING 6 SMln~-1
• 100 .100 .100 .100 .100
D-P VALUE O"-;/FT IS)
• 777
ANALYSIS/OUTPUT OPTIONS:
<IN} (FT)
.100 5.08
.100 10.17
.100 20.33
.100 30.50
.100 f l
ITERATNS DTeR/OT<X) RES STReSS lOUT (I
AUTO SGMNT OUTPT INCR o 160 (\
.0
AREA (INU2) 21.8 21.8 21.8 21.8
MAX T (MSl (I
13
Figure 5. WFAP-86 Input card for Pile Installation in Figure 1.
14
Of considerable interest to the geotechnical engineer are the
quake and damping values. These are very difficult to estimate from
available soil properties, but experience over the years suggest
certain guidelines. Forehand and Reese5 have compiled some
errpirical quake and damping values ' as shown in Table 1. Unless
otherwise stated, WFAP-86 provides a default value of .1 in. for toe
and side quakes (Smith), and .1 sec./ft. for toe and side damping.
'Ihese values are the recanunended default values for using WFAP-86,
unless values from any other rational basis, such as the
CMWAP/dynamic pile analyzer, are available.
Table 1. Empirical Values of Qr, or, and Percent Side Friction5
Soil .I(p) ·. (sec/ft)
Coarse sand 0.10 0.15 Sand gravel mix~d 0.10 0~15 Fine sand 0.15 0.15 Sand and clay . or .loanl', ::at leastSO% ,·/ 0.20 ;' :; 0~20," .
Q(pn. e.in .. ·san.d " . . Sitt and fine sand ,
: underWD ·~t·hai'd strata
,~ . , · ·~tt.~4~-·~.ii~'~.1s~.~· . strata
Side _ . Adhesion (%"ofRU> ..
35 75-100
100
15
Failure Criterion
lJhe tenns "ultimate load" and "failure" for a pile re<;;lUire some
discussion. As stated by Peck6 et. al., the ultimate or failure
load for a friction pile may be constructed graphically s:iJTq;>ly by
extending the two lines obtained from the load vs. settlement cm:ve.
For a friction pile these two lines are well-defined. HO\'Never, for
piles that develop significant end-bearing resistance, the load -
settlement cm:ve increases monotonically as the load increases due to
the skin friction being mobilized first, then the point resistance.
Van der veen7 has postulated that the load settlement cw::ve is of
the general form P = Pu(1-ebx), '\Nhere x is vertical settlement and
b is a constant determined by a least square cw::ve fitting scheme.
Van der Veen's criterion defines the failure load as the load
value corresponding to the vertical asymtote of the load vs. butt
defomation cw::ve. Van der Veen's criteria are shown schenatically
in Fig. 6. A least square cw::ve fitting computer routine was
developed to find Van der Veen's (VDVM) ultimate load from available
load - settlement infomation. However, VDVM indicates excessively
large pile capacities for some data. 'Iheoretically, Pu will occur at
an unbounded displacement value using the VDVM criterion.
16
Load Pu (Van der Veen)
~--====~------------------------------------- y
x
. ,.
Assume of form
y
ot
A x
=
~
> >
-<xx A( 1 - e )
@
@ @
Figure 6. Van der Veen's Approach for Detennining Pu.
Alternatively, one could use Terzaghi's criterion8 which
defines P ult. as the load at which pile settlement equals 10% of the
pile base diameter. Hawever, this approach fails to consider the
load - settlement curve of the pile and the associated. soil-pile
behavior and may also lead to somewhat high Pu values.
Another unpublished failure criterion, developed by Q'Nei119
plots the time rate change of settlement against applied load. The
17
generated curve consists of two lines, 'Whose point of intersection
corresponds to the failure load as described by O'Neill (Figure 7).
In o:r.U.er to use a 'Neill's criterion, time vs. settlement curves for
each load increment must be available. since this criterion has only
been presented recently, the CDNNDJr data base does not contain the
necessary info:t".ltlation.
Wi dt
Time tl t2
~~------------------------------------------~ t
s
Slope = ds PI dt
P2
P3 I increasing slope
Pu (O'Neill) o~ ____________________ ~~~~ ________ ~
o LOAD
Figure 7. O'Neill's Approach for Detennining Pu.
18
A useful definition for the failure load of a pile could be the
point of maximum curvature on the load-settlement curve. 'Ibis point
represents a finite settlement beyond which the settlement per load
increment increases. The point of maximum curvature can be
detennined by eyes.
An example is shown in Figure 8. The degree of curvature is
mathematically equal to the 2nd derivative of y with respect to x,
and in words represents the rate of change of slope with respect to
x. However, for practical purposes, one can locate the point of
maximum curvature (minimum radius of curvature) by inspection.
Load Pu (m.c.)
o~~----------------------------------------------. y
x
~---------- Min. radius of curvature located here by inspection.
Figure 8. Maximum CUIvature Approach for Determining Pu.
19
'!he concept of the maximum curvature criterion is along the same
lines Peck's criterion for friction piles.
Figure 9 shows a typical load vs. butt settlement curve and a
comparison of ultimate capacities obtained from using the VDVM,
Terzaghi, and maximum curvature failure criteria.
o
Pu Pu Pu Load (Me.) (VDVM.) (Terzaghi) ~O~ ______________________________________________ ~~ y
x
Pu (Terzaghi) is D at 19% 9.l*B'= D @ Pu(Ter)
H-Pile 12*53 EBT. (page.75)
Figure 9. Pu as Obtained by Three Methods
20
PILE ANALYSIS
The follow'ing OONNOOI' end-bearing H-pile and friction monotube
pile installations were modelled using WEAP-86 and the program
default values for quake and damping. Their actual measured capacity
from OONNIXYr load tests are shown in tabular fonn in Table 2 as
inteJ:preted by tvIo methods: VDVM and maximum cu.:rvature.
Table 2. :Physical Characteristics of piles studied.
Table 2
Pile capacity Prediction :ey
IDeation Pile VDVM. Max. AASHIO. WEAP.86 Note Size CUrv.
I-84 steel H 352 426 151 210 15% Skin #7 Hartford 12BP53 Dist., Smith Pier#4-WB wr = 0.75
I-84 steel H 282 250 135 450 25% skin #3 Hartford, l2BP53 Dist., Smith West - wr = 0.75 Abutment
I-84 West Steel H 318 270 140 305 15% skin #6 Hartford, 12BP53 Dist., Smith Pier 1 ST = 0.75
I-84 Steel H 278 190 124 180 10% skin #2 Hartford, 10BP42 Dist., Smith
wr = 0.75
I-84 Hf Steel H 318 220 131 130 25% skin #6 OVer 12BP74 Dist., Smith NY.NH. & wr = 0.75 HRR.
I-84 Steel H 356 300 175 405 5% skin #5 Hartford 12BP42 Dist., Smith E.B. Road wr = 0.75 Way
I-84 Steel H 280 222 117 140 5% skin #7 Hartford, 10BP42 E = 1450 psi.
den = 75 pcf
21 Table 2. (Continued)
Pile capacity Prediction By
location Pile VDVM. Max. AASHIO. WEAP.86 Note Size CUtv. DFSIGNIDAD
1-84 Precast 502 400 227 275 10% skin Hartford, Con. 24" #7 Dist., S-E Rdwy. Sq., Type wr = 1.0 Viaduct III tip.
1-84 Timber, 42 18 13 9 60% skin Nook - 12" dia. #7 Dist., FannSewer III tip. E = 1450 psi.
Derby, Concrete 222 156 75% skin Rt. 34 Monotube #2 Dist. Bridge over wt = 0.75 Naugatuk R.
Graton Concrete 250 180 125 151 50% Skin, Southington Manatube #3 Dist. 1-95 wt = 0.75
Coventry Concrete 304 264 144 168 75% Skin, Monotube #2 Dist.
wt = 0.75
Farmington Concrete 162 124 50 133 60% Skin, Manotube #7 Dist.
Coventry Concrete 212 150 105 178 75% Skin, 1-84 Manatube #2 Dist.
Derby, Concrete 224 156 85 75% Skin, Rt. 34 Manotube #2 Dist. Bridge over Naugatuk R.
-------- -------------------------------------------------------------------------------------------------------
22
It should be reiterated that the two program input parameters
with the greated uncertainty are the soil quake terms and the soil
damping terms. other input terms such as the mod.ulus of elasticity
of steel, unit weight of steel, length of pile, and to a somewhat
lesser extent, the skin friction distribution, hammer energy
transferred to the pile, and cushion stiffness are known to a
relatively high degree of accuracy.
'!he major focus of the study deals with the effect of the
selected quake and damping terms upon the predicted pile capacity for
end-bearing H-pile capacity; in addition, a mnnber of computer
modelled monotube piles considered the effect of different skin
friction distribution patterns as well as selected quake and damping
valve effects. WEAP-86 predictions were generally conducted by
varying only a single parameter at a time so that only the effect of
that particular parameter is noted.
a) End Bearing H-piles
A total of 7 steel H-piles driven into sand/glacial till were
selected for study based on availability of appropriate load test
infonnation for pile tested to failure. '!he required infonnation
includes soil boring infonnation and blow count data taken during
driving. Data from the soil borings are used to estilnate the
fraction of the ultilnate load carried in side friction as well as the
distribution of stresses along the pile shaft. WEAP program runs
were made using the physical properties of the hammer used, the type
of pile driven and the bearing soil. '!his phase of the analysis used
the program default values for the quake and damping (smith type)
terms. '!he results, shown in Table 2 and plotted in Figures 9a and
9b, suggest that the standard default values of quake (Qr=.1 in.)
23
and damping (DI'=.1 sec./ft) for end-bearing H-piles statistically
undet'predict measured pile capacity as intel:preted by either the Van
der Veen or maximum curvature failure criterion (Figs. lOa and lOb).
GOO
500
400 " . i' S:: '" J 300
3 200
100
o
WEAP.86 (Default OT = 0.1 DT - 0.1) Max. Curve.. Foilure Crfterfon
PeR. != 2 1/ V --
Va 1/ -_. / :/ ...
14° I~J ...
tJ
I I;: ..
kV i
o 200 400 eoo lOGd Predtcted by WEAPM (J<tpa.)
- FS. - 1.0
Figure 9a
4 I i
800
,.... 1-....,
! !
500
400
300
200
100
o
WEAP.86 (Default OT = 0.1 DT - 0.1) \'DVM. Fctlure Crlterton
// ~
..
+1 + /t J++ / +
...
/ 7 1/ i
o 200
Load Pred1cted by WEAP_80 (KIps.) - F& .. 1.0
Figure 9b
Pile Capacity Ratio & Freq.of Occurence
24
----
VDVM. Criterion 8~--------------------------.---------________ ~
0.2 - 0.4 0.6 1.0 1.2 1.4 1.6
PIle Ccrpo1\y Ratto .. (pu)*eap/(Pu)vdvm.
Figure lOa
t I
" j C
t i ~
J I ]
Pile Capacity Ratio & Freq.of Occurence Max. CUMt. Cnterlon
8~-----------------------------------------------
1
180
170
180
150
140
130
120
110
1C)()
90
80
70
eo 80
0.2 - 0.4 OA o.s 1.0 1.2 1.4 1.6 1.8./
Pile Copoo~ Ratto .. (Pu)weap/(Pu)mc.
Figure lOb
Monotube Pile: C.I.P. Concrete Load PredIcted By WEAP86 W/RSA &t WOjRSA
--+--"-+--/-1~
+/ I //
,.-+
80 100 120 140
Load Predfct.d By W!APM WO/RSA' (kfpe) - FS. .1.0
Figure 11
1to 180
26
b. Monotube piles
Seven monotube pipe piles were also modelled using WFAP-86.
Monotube piles are nonnally used as friction piles. '!he effect of
the assumed skin friction distribution along the pile shaft requires
consideration as to the residual stresses, damping, and quake
values. The i.Irportance of residual stresses developed in driven
piles has been demonstrated by HollowarQ• The compression of the
pile and soil on the downward stroke when the ram rebounds results in
the retention of compressive forces in the lower part of the pile,
and these appear to depend on the soil-pile interaction only,
independent of the impact driving apparatus used. The magnitude of
the residual loads increase as the axial stiffness of the pile
decreases. Impact driving of a pile with low axial stiffness will
cause the pile to compress in the vertical direction and expand in
the radial direction. As the hanuner rebounds the pile attempts to
return to its orginal length, but the soil along the pile resists
this expansion through friction. This soil-pile interaction in the
pile results in the development of a residual compressive force at
the pile tip which remains even without an applied force at the butt
end. When a residual load remains after driving, a portion of the
pile's end-bearing capacity has already been mobilized as noted by
Braud et ale ColWentional ·pile instrumenation are zeroed at this
time, ignoring any residual stresses in load test interpretation.
The actual end-bearing capacity of the pile is the measured value
plus the residual value. While the effects of residual loads are not
measured, failure to account for residual stresses in the WFAP
analysis leads to low predicted pile capacities (Fig. 11).
27
Monotube piles - Analysis
Seven monotube pipe piles bearing in sand were also modelled
using WEAP-86. The results, shown in Figures lOa and lOb, suggest
that the standard default values of quake (QI'=.01 sec.) and ~ing
(o:i:=.l sec./ft) together with use of the R.S.A. for monotube piles
statistically underpredict measured pile capacity as interpreted by
either the Van der Veen or maximum curvature failure criterion.
Sensitivity Analysis
A parametric sensitivity analysis was conducted to investigate
the effects of pile-soil parameter variance on H-pile and monotube
predicted capacities.
H-piles- A series of WFAP pile capacity prediction runs were
made capacity predicitions were made by varying the toe quake from .1
in. to .05 in. and by varying toe ~ing from .1 sec./ft. to .05
sec./ft. The variance in a given parameter was conducted while
holding the other constant in order to note the effect of varying the
parameter of interest only, holding all others at default values for
Figs. 13 and 14. Fig. 15 shows the effect of varying Qr and Dr at
the same time. Decreasing either parameter by 50% resulted in an
increase in predicted pile capacity of about 15%. Figures 16a. and
1Gb. show that for QI'=O.08 in., for example, the composite actual
capacity versus predicted capacity value reflect this increase in
predicted capacity by a shift of all points to the right. other Qr
and Dr values selected (See Figs. 17a, b; 18a, b) show similar
trends. A major result from this parameter variation study is that
the net accuracy of the solution remains essentially unchanged
regard.less of Qr or or, provided values near WEAP-86 recommendation
are selected. Hence, predicted pile load capacity is not highly
Monotube PiJe : C.I.P .. Concrete 28 W'i.AP.88 WIth and Without RSA.
180 -
110
" It
~ 160
"" ~ 150
~ 140 ~-
Q) GO r1. 1~
~ 120
~
J 110
t 100 0.
'8 90 .c3
80
/ :/ +
/' + "'
/~ +
// :/
:/ +
:/ :/
V. +' I
70 80 100 120 140" 180 180
Load Predtoted tJy WE'AP.8fS w/RSA.(Jdpe..)
Figure 12
WEAP.86 At DT - 0.1 Pile HP 12-53 EBl'.
250
240
230
220
~ 210
~- 200
~ 110
I 180
'R 170 0.
] 180
150
140
130
120 0.0& 0..1$ 0.25 0.35
QT. (tn.)
Figure 13
WEAP.86 At QT = 0.1 PIle HP 12'U l1li'. 29
~~~------------------------------------~
1. CI.04 0.1.
Figure 14
WEAP .86 At DT - QT -PIle HP 12*&3 EBT.
210
210
2-tO
; UO
• 220
I 210
1 200
110
1.
110 0.04 0.1.
Dr - QT (In.)
Figure 15
-" 8-l "V
~
400
~
200
+
0.40 0.80 0.80 (ThouecftcSs)
Lood Predtcted by WEAP.88 (Ktpe.) ---..- FS. .. 1.0
Figure 16a
1.00
WEAP.86 (Default OT = 0.08 DT = 0.1)
30
1 .. 20
ASSHTO. Max. Curvature cnt.rton
eoo T~- r I r T--r I -,-
t- ~ --t-~' ~ l~_I~-I---"~r' ~-+-i~-f ~ :~~~~!~~ ~- +J
200
0.00 - 0.40 0.80 0.80
Load Predtcted~~~ (Ktpa.) - FS. .. 1.0
1 .. 20
Figuie 16b
"
'" ~ j ]
600
100
o
WEAP.86 (Default QT = 0.05 DT = 0.1) VDVM. FGtlure Crfterton
I I IV I !
_t---_-t-· t-~-- ____ I ~.
_._,,~~~. I
t·~-r.-· ---
/ o
1/1
+ I +
+ .
+
~ -I
"":::ror..,.,,...~. r---
/ i
200 400 eoo 1.oOd Predfcted by WFAP..80 (KIPI-)
- FS." 1.0
Figure 17a
.
WEAP_86 (Default OT = 0.05 DT = 0.1) ASSHTO. Max. Curvoture Crfterton
I
31
-~
f500 -----r------r--l -T-- r "--""'--~I -----.----.-.--r\----,
I! i! I !
400
300
200
, I I
++ '-- ---t :--r-t--+----+----+---1 ---Y--::! +~t-+- I t·-
o~--~--~---+--~--~----~--~--~--~ o 200 400 eoo 800
load Predtcted by WEAP.8e (Kfpe..) - Fl. -1.0
Figure 17'0
400 '" .-2-.....,
J 300
"0
~ 200
400
t-g 11 3QO ~
] 200
100
Q
o
WEAP.86 (Default ·QT = 0.1 DT = 0.05) vovu .. FaUure Crtterion
+
200 400 600
Load Predtcted by WEAP.8& (Ktpe.) - FS. .1.0
Figure l8a
I \
800
WEAP.86 (Default OT = 0.1 DT = 0.05) ASSHTO. Max.. Curvature Criterion
I / ! ~ I
i ,: j
i
I IL I -~.-+-
t f---- ----1------- --f----
I I I I
ti/ . • -T
+ +
/ I
/ i
i •
32
-_.-
o 200 400 600 800.
Load PredIcted by WEAP.18 (Ktpe.) - FS.. -1.0 Figure l8b
33
sensitive to large, +1- 100%, changes in the quake and damping values
for end-bearing H-piles.
Monotube piles A series of WEAP pile capacity prediction runs
were made by va:tying the toe quake from .15 in. to .05 in. and by
va:tying toe damping from .15 sec./ft. to .05 sec./ft. Results
(Figs 18a, 18b) show that a total variation of 15% occurs over the
entire range of selected quake and damping values. Next, both
parameters were dried to note the composite effect of va:tying or and
Pr at the same time (Fig. 19). Finaly, variation of skin-friction
percentage as a fraction of total variation of about 15% occurs from
0% to 100% skin friction assumed of the pile shaft (Fig. 20).
COnclusions
The wave eq:uation analysis of piles (WEAP-86) finite difference
computer solution package applied to end-bearing H-piles and
friction-type monotube piles in sand show the following trends.
1. Selection of quake and. damping values do not appear to greatly
influence predicted pile capacity (± 15%).
2. Percent skin friction assumed for monotube piles changes
predocted capacity about 15%.
3 • Residual Stress Analysis should be used when modelling
monotube-type piles.
4. Default values of quake and damping yield predicted capacities
that are statistically lower than the measured capacities.
5. WEAP-86 provides the user with some insight into the pile
driving process and. effects of various properties on the pile
stresses and. capacities.
Monotube Pile: C.LP. Concrete 34
WIth RSA.
~r-- l 95 "-,
94 ~, 93 .'
92
91
90
89
"'" 88 .; ~ 87 'V ae :t 0- eo
84 83 82
81
80
79 78 17
0.05 0.07 0.0& 0.11 0.13 0.18
DT~ (tn.)
Figure 19a
Monotube Pile : C.I.P. Concrete WIth RSA.
87
86
95
94
93
92
91
" ! 00
a- u :t 88 0-
87
ae 86
84
83
82
81 0.05 0.07 0.08 0.11 0..13 O.1ij
aT. (Tn.)
Figure 19b
Monotube Pile: C.I.P. Concrete 35 WIth RSA.
106~----------------"------------------------------~
104
102
100
98
96
94
92
90
88
a8 84
82 80
18
76
14 72 ~4---~----~--~-----1~--~--~1----~---~(----~---~
0.08 om 0.09 0..11 0.13 0.15
01, ell OT. (tn.)
Figure 20
Monotube Pile: C.LP. Concrete wtth RSA.
~,---~-----"-----------------------------~---------------
87
86
86
84-
83
82
81
80
78
78
n;----.----.----r----.I----~--~I----~------~~~ o 20 -+0 eo 80 100
" Skfn Frfctton
Figure 21
PHASE II
Stabilization of a Highway Embankment Using steel Sheetpiling
with steel Batter Piles
I. OB.JECrIVE
To monitor the performance of steel PZ-35 sheeting used in
conjunction with steel HI? 10 x 53 batter piles as a methcxi of
stabilizing a highway embankment against slope movement.
II. BACKGROUND
36
'lhis project developed fran a field condition that was declared
an emergency in the Spring of 1987. '!he site, located on Route 66 in
Portland, COnn., was experiencing recurring highway pavement
settlement which inclinometers installed by Conn ror showed to be
progressive outward slope movements. This phenomenon has been
occurring for the past several decades. Available infonnation
indicated that the greatest slope movements tend to occur during the
spring high-water season, suggesting that pore pressures beneath the
embankment may be a contributing factor. Another contributing factor
may be the dynamic/vibrato:ty loading caused by heavy vehicles passing
the site.
r:Ihe subsurface profile, as shown in Fig. 1, consists mainly of
granular fill overlying peat, which rests on sand. Depth to bedrock
varies fran 20 feet (western edge of site) to 55 feet (eastern
side). Ee.drokc in primairly triassic sandstone of the portland
fonnation. '!he presence of the ol:ganic peat exacerbates the problem.
CDNNror engineers decided in May 1987 to attempt to stabilize
the slope by structural means using steel sheeting supported
~; ,~ / ,_,_ 7;"'" V CQIC C-.L..I Typicel Sec,h'on -Ap?fOX SfC/o 220-1- 10
,_4\=:~£~ '~::. \!~-i
K'1= ~.b'
.... t ('J " ,"
, £fnbcrnt . . "'n'll
5;;.'1 it:. /" -:: 4-() l Plan Treafmenf If-om sta. 219tO -to S-fc-:1. 222+ 75 (h~(¥ox, 375 ~.F.)
---+---1 --.0 . ~~Q. If(
'j(. " II C:;"fJrdFa,"r II --,.---~,:~,~ .. ,~----~------------~-------~
. LTopoP Slope . ~ U
I 22 • ~.fi. -
I . shed pi It. '><fa II viI lip ire PraCC5 6' {);t:.. 7 . :~" .. l II 1.1.' '" 1'1' , I It I ". t f" t t i,'I~::::'='=I='=I_t '_.1-----
c::.wtv/<. Toe. of Slope - . ~ Approx. H(9nwtty Line
Figure 22
38
laterally by steel batter piles. UCONN personnel instnnnented two
sheetpile sections with strain gages to measure the strains induced
in the sheeting. CONNlXYI' mounted slope indicator tubes at two other
locations on the sheeting to monitor the deflection of the sheeting.
UCONN and CONNlXYI' staff inplemented seperate instnnnentation
schemes which, would complement the evaluation of sheetpile
perfonnance.
III. INSTRUMENTATION PROGRAM
a. Underlying '!heo+Y'
'!he inclinometer directly measures vertical slope with respect
to a reference. '!he slopes along the vertical profile can be I
integrated, with an appropriate bounda:ty condition, to give a
deflection curve; or can be nun:terically differentiated using finite
differences to obtain,
Ely" = M, from SlTIa.ll deflection beam theo:ry,
which can be co.n:pared with the strain gage data directly and inplies
that the spatial rate of change of slope is proportional to the
internal bending moment at that section. However, accuracy and
vertical positioning error makes this numerical integration approach
only approximate at best.
b. UCONN Instnnnentation Design and Construction
A strain gage instnnnentation program was developed to detennine
the bending moment distribution along the vertical profile of the
sheeting. Several challenging problems had to be addressed. '!he
instnnnentation had to withstand, a. impact driving by a Vulcan #1
pile driving hammer, b. a subm.eJ:ged envirornnent below the ambient
water table, c. potential damage by vandals.
39
1'--_ .......... ·--9.00 "-_ .... ···· ..... ··--i
_ .... --1 2. 25" 1---4. 25 "~ 2. 25" 1----
L 3*3=:--~-.' ,
1 II
"'1"--,-------.--18.0"-, --- ,---,-----1
Figure 23a
I
i
cP'"
i i 0 I
j
j ~
- .- 0 -+----- ---1 ------ j -e--I \ I
I 1 I ! ! I
o I
I I !
o o
An
. ACl..G ~ fItS) MAulING' &P-N . ~~Lb ~1'{)
-.-. '- A' .
~,,..JG 7LArG7
(JjRCftL'j
Prd-oJa~ Af.>J.m~lY
Figure 23b
Advice was sought from Dr. J. Gartner of the University of
Connecticut Mechanical Engineering Department, a specialist in
instnnnentation, and engineers at Micro-Measurements group of
41
Raleigh, N. C. Electric resistance type strain-gages were selected
for this project. In addition to gage selection and attachment to
the pile, a means for protecting the instnnnentation and its
associated wiring required careful consideration. '!he cover scheme
selected consisted of steel 3" x 3" angles placed longitudinally onto
the flanges of the PZ-35 sheetpiling (Figure 23b). Ten foot long
segments of the angle would be welded to a pile with 1 foot gaps left
between them. within these gaps would be placed the strain gage
arrangment and protective coatings. Following gage installation, a 1
foot piece of steel angle would be bolted to the sheetpiling to
protect the instnnnentation assembly from physical damage during
driving. Any attempt to exclude water from inside the angle sections
would not be successful, hence individual waterproof coatings were
applied to the gages instead.
'!he bonding of the gages to the steel piling was to be
accomplished by spot-welding of the steel strain-gage backing to the
piling, a task which was done in the field. A special layered.
application of sealants was applied to the area surrounding the gages
after the necessaJ:Y electrical connections were made to the strain
gage (see Figure 24). Next, a steel 3X311 angle cover were bolted to
the pile above the gages to help protect the instnnnentation during
pile driving operations.
Data Collection
Soon after pile installation, reference "zerol1 readings were
taken on all strain gages using a Micromeasurements model P-3500
42
Silicone Sealant
Teflon Tape Covering
-_ .. - --- --~ ~~~-=NG __ '-~"'-'--"'''''''--''-"-'''''
Figure 24
digital strain readout unit. Following the next several sets of
observations, it was soon evident that the readings of the gages were
eroneous. '!he problem was that the readout box would not give a
stable reading: the reading drifted. with time during measurement.
'!he possibility of water or moisture getting to and possibly banning
the gages was of primary concern. At this point, Mr. John Fickiet,
Chief Electronic Technician at UCX:>NN, was called in to assist in the
investigation of this problem. Mr. Fickiet concluded that the design
of the box, being of a high ilrpedence input type, was picking up
stray electron:agnetic signals at the location and these signals were
responsible for the drift problem. A low in'pedence type bridge, such
as the older BIH type of wheatstone bridge circuitJ::y was reccommended
as a solution. Measurements taken with the BIH readout box indeed
gave stable strain gage readings and was used exclusively thereafter.
strain gages readings versus pile depth and gage readings versus
elapsed time are shown in Figures 25 thru 32 for both the east and
west instnnnented sheetpiles.
9
8
7
6 . '" c - 5 i 2~ 4 o· _"0 ~c "",0
3 • Ot::J co ijt 2 ~ • 1 Ot 0 0
0
-1
-2
-3 0 20 40
[] Depth - -6
STRAIN VS. TIME East Sheetplle, (Swamp aIde)
60 80 100
Elapsed time In days. Q -26 + -16
Figure .25
120 140
A -36
160
.p.. w
. ,..."..
c 2 .. e" o· _"0 ~c '"'g 0;, co iit f • at
&
STRAIN vs. DEPTH East Sheetplle, (embankment aide)
4 ~------------------------------------------------------------------~
3
2
1
0
-1
-2
-3
-4~1~------~--~--~--~--T---~--~--~--~--~--~---r--~--~
-~ -32 -28 -24 -20 -16 -12 -8
Elevation wlth Respect to Grade C 23 + 37 <> 93 A 120 X 151 Days
Figure 26
.j>
.j>-
.. " c -e 1i e" o· _"0 ;:ec '"'i 'O:s co ;;,t, f • 0
8
STRAIN vs. TIME East Sheetplle. (embankment aide)
4~i------------------------------------------~
3
2
1
0
-1
-2
-3
-4 o 20 40 60 80 100 120 140 160
C Depth = -6 Elapsed time In days.
+ -16 ~ -26 A -36
Figure 27
..p.. U1
STRAIN vs. TIME 2
west Sheetplle. (Swamp _Ide)
1
0
• '" -1 c -2 11 e~ -2 S" 2C ,-,0
-3 • Ut:J co It -4 ! • CIt -5 0 ()
-6
-7
-8 0 20 40 60 80 100 120 140 160
C Depth = 6 Elapsed time In daye.
+ -4 ~ -14 A. -24 .p-O'.
Figure 28
1.3
1.2
1.1
1
• 0.9 '" c -2 0.8 1» 2~ .2"0 0.7 ::EC '-'0 0.6 o! co 'Db 0.5 e
0.4 • OIl 0 0.3 0
0.2
0.1
0
-0.1 -24
[] 21
STRAIN VS. DEPTH west Sheetplle, (embankment .fde)
-20 -16 -12 -8 -4
Elevation with respect to grade + 37 <> 93 A 120
Figure 29
o
X 151 days
4
.+:'-.....J
2
1
0
. " -1 c -e 1i e" -2 o· _'0 ~c ,-,0
-3 • Ot:J co ;it -4 !
• 0' -5 0
" -6
-7
-8
-24
·0 21
STRAIN VS. DEPTH west Sheetptle. (Swamp side)
-20 -16 -12 -8 -4
Elevation with Respect to Grade + 37 ~ 93 A 120
Figure 30
o
X 151 Days
4
+:-co
9
8
7
6 . " c -e 5 ..-2" 4 o· _"0 ~c .....,0
3 • "':3 co ~t 2 ! • 1 Qt 0 ~
0
-1
-2
-3 -36
C 21
STRAIN vs. DEPTH East Sheetplle. (Swamp aide)
-32 -28 -24 -20 -16
Elevation with Reepect to Grade + 37 <> 93 It. 120
Figure 30
-12
X 151 Days
-8
+:-~
. 1.3
1.2
1.1
1 .
0.9 " c -f 0.8 • e~ 0.7 .2"0 :i C
- ,-,0 0.6 • 0:1 co
:gt 0.5 !
0.4 • 0 a 0.3 C
0.2
0.1
0
-0.1
STRAIN VS. TIME west Sheetpn •• (embankment aide)
0 20 40 60 80 100
Elapsed time In days. C Depth = 6 + -4 ~ -14
Figure 31
120 140
A -24
160
\J1 o
51
calculations indicate that the maximum internal bending moment
developed in the PZ-35 sheetpiling occurs at an elevation
approximately 10 feet above the pile tip. In addition, the internal
moment at the pile tip and pile butt appears to be quite small
suggesting that conditions at these points approach those of pinned
connections. Observation of the strain gage reading versus time
plots (Figs. 25 thru 32) suggest that the pile-soil system, and slope
has stabilized. 'Ihis is further substantiated by obse:r:ving that
vertical settlement of the Route 66 pavement surface appears to have
been arrested.
Bending moments were calculated by using linear-elastic
assu:rcptions together with simple beam theo:ty; with
M = S E 8b~ where 8b = (8 S - 8 e ) / 2
8 S = strain on swamp side of sheeting
8 e = strain on embankment side of sheeting
81;) = strain due to bending
E = Young's modulus
S = section modulus of sheeting (per foot of wall)
M = internal moment in sheetpile
Independent inclinometer readings support the general shape of
the moment versus depth cu:tVes. However; the magnitude of the
bending moments do not agree with infonnation obtained from
inclinometer readings taken by eonnooI' personnel.
'!he measured bending moments obtained from the strain gages are
several times higher than those back-calculated fran the
inclinomenter readings. Water infiltration onto the strain gages and
associated electrical connections was investigated as a possible
source of error. In light of the harsh envirornnental conditions
52
present, moisture may have worked its way onto the strain gages although
the methcxl of waterproofing recommended by the manufacture was used.
'!he university of COnnectiOlt geotechnical engineering laboratories
devised a simple laboratory experiment to measure the effect of moisture
upon gage performance. '!he perfonnance of a strain gage was measured by
inunersing the gage and associated electrical connections in a brackish
water bath (to model in-situ corrlitions) • '!he results, when conpared to
readings taken while the gage was dl:y, indicated that the microstrain
readings were essentially the Same after allowing for an initial drift
pericxl of several minutes duration for the gage to stabilize.
Electrically, water acts as a parallel shunt resistance across the 120
ohm strain gage grid which makes the effective resistance of the gage
slightly less than 120 ohms. Theoretically, this shunting effect should
lessen the sensitivity (gage factor) of the strain gage, and apparent
readings should be less than those actually occurring. However, as
detennined from the laboratory experiments, this effect is quite small.
Therefore, water seepage can be tentatively ruled out as the primary
reason for the abnonnally high strain gage readings.
Conclusions
1. The maximum bending moment in the sheetpile appears occur about 10
feet from the bottom of the pile.
2. The magnitude of the maximum moment is uncertain as strain gage
measurements and inclinometer data do not compare well.
3. '!he batter/sheetpile wall appears to have stabilized the slope
against continued outward movement.
4. The Continued use of electrical resistance type strain gages in
harsh environments is not reconunended.
REFERENCES
1. Smith, E.A.L. (1960), "Pile Driving Analysis by the Wave Equation", J .S.M.F.D., A.S.C.E., Vol.86, SM4: pp. 35-61.
2. Kolsky, H. (1963), STRESS WAVES m SOLIDS, Dover, New York.
3. Pochhammer, L. (1876), "J. Reine Angew" Math, Vol. 81, P. 324.
4. CAIWAP - Computer Analysis Program
5. Forehand, P.W. and Reese, J .L., (1964), "Pred.iction of Pile capacity by the Wave Equation", J.S.M.F.D., A.S.C.E. Vol. 90, 8M2, pp. 1-25.
6. Peck, R., Hansen, W. and Thombum, T., (1974), FOUNDATION ENGINEERING, 2nd ed., New York, Wiley, p. 215.
7. Van der Veen, C., (1953), "The Bearing capacity of a Pile", Proceedings of the Third Int. Conf. Soil Mech. Fed. Eng., Vol. 2, pp. 84-90.
8. Terzaghi, K., and Peck, R.B., (1967), Soil Mechanics in Engineering Practice, 2nd ed., Wiley, New York.
9. O'Neill, M., Unpublished information.
··53
10. Holloway, D.M., Clough, G.W., and vesic, A.S., "The Mechanics of Pile-Soil Interaction in Cohesionless Soils", Report for the Co:rp. of Engineers, Vicksburg, Miss., Dec., 1975.
REFERENCES
1. Smith, E.A.L. (1960), "Pile Driving Analysis by the Wave Equation", J.S.M.F.D., A.S.C.E., Vol.86, SM4: pp. 35-61.
2. Kolsky, H. (1963), S'rnESS WAVES rn SOLIIlS, D:wer, New York.
3. Pochh.a:rraner, L. (1876), "J. Reine Angew" Math, Vol. 81, P. 324.
4. c.ru::wAP - computer Analysis Program
5. Forehand, P.W. and Reese, J.L., (1964), "Prediction of Pile Capacity by the Wave Equation", J.S.M.F.D., A.S.C.E. Vol. 90, 8M2, pp. 1-25.
6. Peck, R., Hansen, W. and'Ihornbmn, T., (1974), FOUNDATION ENGINEERING, 2nd ed., New York, Wiley, p. 215.
7. Van der Veen, C., (1953), "'!he Bearing Capacity of a Pile", Proceedings of the Third Int. Conf. Soil Mech. Fed. Eng., Vol. 2, pp. 84-90.
8. Terzaghi, K., and Peck, R.B., (1967), Soil Mechanics in . Engineering Practice, 2nd ed., Wiley, New York.
9. O'Neill, M., Unpublished information.
10. Holloway, D.M., Clough, G.W., and Vesic, A.S., "'!he Mechanics of Pile-Soil Interaction in Cohesionless Soils",.' Report for the Corp. of Engineers, Vicksburg, Miss., Dec., 1975.