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' AND ITS VARIATION WITH DEPTH By James D. Hartley,1 A. M. ASCE,
and James M. Duncan,2 F. ASCE
(Reviewed by the Pipeline Division)
ABSTRACT: The modulus of soil reaction, E', characterizes the
stiffness of soil backfill placed at the sides of buried flexible
pipelines for the purpose of eval-uation deflection caused by the
weight of backfill above the pipe. In this study, the nature of E'
is investigated in detail to determine whether its magnitude
increases with increasing depth of embedment. The development of E'
in the literature is reviewed, and data from field installations
are presented to estab-lish that E' can be shown to increase with
depth on the basis of previous re-search. Analytical methods, based
on elastic theory and finite element tech-niques, are also used to
demonstrate the dependence of E' on depth. Design values of E',
which vary with depth, are presented, together with
recommen-dations regarding the use of E' in the Iowa formula.
INTRODUCTION
Deflections caused by the weight of overlying fill can be the
governing criterion in the design of buried pipelines, particularly
if the pipeline is lined or coated with cement mortar. Deflection
tolerances for those pipe-lines are typically set at about 2% of
the nominal diameter, in order to reduce the probability of cracks
in the lining and subsequent corrosion of the metal. The most
common formula used to calculate these deflec-tions for design
purposes is the Iowa formula, which includes the em-pirical modulus
of soil reaction, ' , to account for the restraint devel-oped by
the soil backfill at the sides of the pipe.
Because of its empirical nature , the parameter ' can introduce
a large degree of uncertainty in deflections calculated using the
Iowa formula. For many years only a limited number of design values
for ' were pub-lished, and typically only for "good" or "low
quality" backfills; in 1976, Howard (11) presented design
recommendations for ' for a variety of soil types and compacted
densities.
In spite of its empirical basis, ' is conceptually similar to a
soil mod-ulus (such as Young's modulus or the constrained modulus)
and can be reasonably thought to behave in a similar manner . Since
all soil moduli exhibit a dependence on confining pressure, it
might be expected that E' should depend not only on soil type and
density, but on the depth of backfill as well.
The dependence on depth of other structurally influenced soil
stiffness factors has been well established, for example by
Terzaghi for the coef-ficient of subgrade reaction (25), and by
Audibert and Nyman relative to the translational displacement of
buried rigid pipes (3). Common de-sign practice, however, does not
take into account the effect of backfill
'Proj. Engr., Woodward-Clyde Consultants, 3467 Kurtz St., San
Diego, CA 92110. 2W. Thomas Rice Prof, of Civ. Engrg., Virginia
Polytech. Inst, and State Univ.,
104 Patton Hall, Blacksburg, VA 24061. Note.Discussion open
until February 1, 1988. To extend the closing date one
month, a written request must be filed with the ASCE Manager of
Journals. The manuscript for this paper was submitted for review
and possible publication on February 29, 1984. This paper is part
of the Journal of Transportation Engineer-ing, Vol. 113, No. 5,
September, 1987. ASCE, ISSN 0733-947X/87/0005-0538/ $01.00. Paper
No. 21813.
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depth on ', and conflicting conclusions can be found in the
literature regarding the importance of depth on the value of E'.
This lack of com-mon understanding of the behavior of ' may be
contributing to over-conservatism in design and excess material
costs for pipelines under high fills.
Scope of Study.This study focused on the dependence of the
mod-ulus of soil reaction on depth of backfill. Its goal was to
determine the degree to which E', as a modulus influencing
deflection caused by fill placed over buried pipelines, is a
function of backfill depth, and to in-corporate the dependence on
depth, if significant, into a revised sched-ule of E' values for
design.
To achieve this goal, four approaches were taken: (1) A thorough
re-view of the published discussion on the dependence of E' on
backfill depth was conducted; (2) an examination was made of data
available over a range of backfill depths for individual pipe
installations; (3) a study was performed to investigate the
theoretical nature of E' and its relation to fundamental soil
moduli through elastic analyses; and (4) a finite ele-ment analysis
study was undertaken to simulate the field behavior of buried
pipelines and to obtain E' values for specified installation and
soil conditions.
The findings and conclusions of these efforts are presented
herein.
BACKGROUND INFORMATION
Development of Modulus of Soil Reaction, E' Following a series
of full-scale experiments on culverts, Spangler (22)
proposed the Iowa formula for computing the horizontal
deflection of buried flexible pipelines. The formula is based on
Spangler's observa-tions of culvert deflections, and is typically
presented as follows:
DiKW AX = z + 0.061E' (1)
R1
where AX = horizontal change in culvert diameter (L); Dj =
deflection lag factor, to account for time-dependent deflections; K
= culvert bed-ding constant; W = vertical soil load on culvert
(FL'1); E = Young's mod-ulus of culvert material {FL~2); I =
culvert section moment of inertia (L4/ L); R = mean culvert radius
(L); and E' = modulus of soil reaction (FL~2).
Conceptually, the formula may also be expressed in this way
(11): (Soil load)
Culvert deflection = (2) (Culvert stiffness + Soil stiffness)
Considerable work had been done before the Iowa formula was
pro-posed, particularly by Marston, to determine the soil load on
culverts, and this load and the stiffness of culverts could be
determined at that time with relatively little uncertainty. It was
not well known, however, how to characterize the soil stiffness,
although it was evident that for flexible culverts, this term could
dominate the values of deflection cal-culated using the Iowa
formula. Virtually no research had been per-
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formed on the stiffness of culvert backfill before Spangler's
study in 1941, and it was not until Spangler's work that its
importance was recognized or its value investigated.
In his original experiments, Spangler observed that the ratio
between the horizontal pressure acting on the culvert and its
horizontal deflection appeared to remain essentially constant for a
given soil. This ratio was denoted by the letter "e" and the name
"modulus of passive resistance," and was introduced into the Iowa
formula to account for the restraint provided by the backfill to
the culvert sides.
In 1958, Watkins and Spangler (29) modified the soil stiffness
factor in the Iowa formula to reflect their findings that the ratio
e was, in fact, not constant for a given soil, but that the
quantity e multiplied by the culvert radius (R) appeared to be
approximately constant, This quantity was presented by Watkins (26)
as ' (psi), and was given the name "modulus of soil reaction."
As developed by Spangler and Watkins, the modulus of soil
reaction is an empirical parameter, dependent on the deflection and
the pressure developed at culvert springline during installation.
For this reason, E' can be measured only under actual field
conditions, as it is a function not only of the soil but of the
entire backfill-culvert system.
Much work has been devoted to developing ' values for culvert
de-sign by measuring the deflections of installed culverts, and
back-calcu-lating the modulus of soil reaction required to yield
the given deflec-tions. Spangler was the first to do this, in 1941
(21), and later with Watkins in 1958 (29). In 1969, Spangler again
presented the data published in 1958, adding to the list values he
obtained in the Wolf Creek culvert (22) and bringing the number of
case histories available for analysis to 18. This list was greatly
expanded by the work of Howard (11), who col-lected deflection and
installation data on over 100 Bureau of Reclamation and other
culverts and buried pipelines.
Before the work of Howard, the lack of sufficient field data
prompted several researchers to find a means of determining
equivalent values of E' by laboratory testing and theoretical
analysis. The first model study to determine E' appears to have
been performed by Watkins (26) in 1959, and was followed by the
large-scale modeling work of Watkins and Niel-son (28), Howard
(10), and Howard and Selander (12). Other researchers have employed
the theory of elasticity solution for buried pipeline de-flections
and pressures, developed by Burns and Richard (6), to correlate E'
to fundamental soil properties and commonly performed index tests
(2,8,18,19).
By far the most extensive presentation of E' values for pipeline
design to date is that by Howard (11), which provides design values
according to soil type and backfill compaction.
Modulus of Soil Reaction, E', as Function of Fill Depth
Published Material.Throughout the study of E' in the laboratory
and in the field, researchers have attempted to establish the
relation-ships between E' and the variables on which it depends. It
has been convincingly established that ' varies with both soil type
and degree of compaction (15); this is reflected in the design
values for E' presented by Howard (11). It has not been generally
agreed upon, however, whether
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E' varies with the depth of fill above the culvert. Table 1
presents the published discussion of the dependence of the
modulus of soil reaction on cover depth. It can be seen that
evidence has been found to suggest both that E' is independent of
the depth of cover (11,19,21,26,29) and that it is not
(2,8,15,17,18,20,28). Conclusions that E' varies with depth of
cover are generally based on theoretical and laboratory analyses,
while statistical analyses of available field data have led to the
conclusion that E' is constant. It is significant that these
anal-yses of field data have often grouped together a wide variety
of soil types and installation conditions, whereas careful
reduction of data from a single case history (20) has shown a
distinct variation with fill height.
Based on information gathered during this study, it appears that
agen-cies using the Iowa formula have generally assumed that E'
does not vary with fill height (1,7,11,24).
Theoretical and Empirical Basis.There is a strong theoretical
basis for the dependence of ' on backfill depth. All soil moduli
increase with increasing confining pressure (except for completely
saturated clays un-der undrained loading), i.e., soils are
generally stiffer if they are buried more deeply. The modulus of
soil reaction, however, is not a true soil modulus, but depends on
the stiffness and dimensions of the culvert as well. For stiffer
backfill and more flexible culverts, though, the effect of the
culvert properties is small, and for these cases E' should behave
much like a true soil modulus, increasing in value with increasing
depth of cover.
Because of the empirical basis on which E' was proposed, any
theo-retical considerations of its behavior should be substantiated
by field measurements. Three sets of field data, in which
deflection measure-ments were made on a single project over a range
of backfill depths, were examined as part of this study and are
presented herein.
A survey of major California water agencies uncovered a large
number of previously unpublished deflection measurements taken in
1964 by the East Bay Municipal Utilities District (EBMUD). The
measurements were taken at 100-ft intervals along approximately
five miles of steel water mains installed northeast of San
Francisco. The pipes ranged in diameter from 42 to 60 in., and were
bedded in sand and backfilled with native soil (sandy silt) in
trenches ranging from 9 to 19 ft deep. The deflection measurement
stations were later carefully matched to as-built profiles in order
to compare the computed value of E' for each deflection
mea-surement with depth of backfill over the pipe. The results of
this com-parison are shown in Fig. 1(a), in which the average
computed values of E' are plotted against the depth of pipe
embedment.
The plot clearly shows a progressively stiffer backfill with
depth. The significance of this result is enhanced by the large
number of measure-ment data that were used to compute E' values,
and by the fact that these data were all taken from the same
pipeline project, reflecting sim-ilar soil conditions and
workmanship standards.
Some years earlier, near Chapel Hill, North Carolina, a series
of care-fully conducted field tests on buried culverts was
sponsored by the United States Bureau of Public Roads and the North
Carolina State Highway Commission (5). These tests had as their
scope the study of culvert be-havior under embankment loading, in
order to secure design data for
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TABLE 1.Published Material on E' as Function of Fill Height
Reference (D
Spangler 1941 (1)
Shafer 1948 (15)
Watkins and Spangler 1958 (3)
Watkins 1959 (4)
Watkins and Nielson 1964 (5)
Meyerhof 1966 (16)
Nielson 1967 (7)
Krizek, et al. 1971 (14)
Allgood and Takahashi 1972 (9)
Parmalee and Corotis 1972 (17)
Howard 1976 (2)
Chambers, et ai. 1980 (12)
E' increases with fill height?
(2) No
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Basis (3)
Full-scale field tests Ames, Iowa
Interpretation of Chapel Hill, North Carolina experi-ments
Spangler's 1941 con-clusions and "model studies"
"Previous work"
Large-scale testing (Modpares device)
Principles of soil me-chanics and Cana-dian experience
Theory of elasticity (bonded interface)
Comprehensive litera-ture review
Theory of elasticity (unbonded inter-face)
Statistical analysis of 18 published field measurements
Extensive field mea-surement analysis
Laboratory testing lit-erature review
Comments (4)
Unaccounted deflection lag effects may have reduced e-values at
greater fill heights.
Questioned e as depending only on soil properties.
Employed principles of similitude to find that er is constant,
rather than e.
Conclusions apparently based on work with Spangler.
Uncertainty in Modpares device too great to accurately determine
E'-values; however, increase in E' due to increasing overburden
pressure convincingly demon-strated (appendix I).
E' varies with depth for sands, not clays.
E' correlated to M, by elasticity the-ory, related to triaxial
testing through a and vs.
Recognized that "previous experi-mental work" seemed to indicate
that e is constant with depth, but advocated using the Iowa formula
with values of ' that increase as the height of the fill
increases.
' correlated to M,; finite element analyses are shown to use
values of Ms that increase with depth.
Too few data to develop significant correlation.
Wide scatter in computed values of ', probably due to variety of
in-stallation factors. No discussion of dependence on fill height
other than to limit E'-values given to fills of 50 ft or less.
E' recognized as a purely empirical factor, measurable only in
field installations. Analysis shows, however, that in the Iowa
for-mula, ' can be accurately re-placed by M,, which does vary with
depth.
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FIG. 1.Values of ' Calculated from Field Data: (a) EBMUO Data;
(b) Chapel Hill Data; and (c) Corrected Spangler Data
highway culverts. Twenty- to 30-in. diameter test culverts of
corrugated metal, steel, smooth iron, and concrete were loaded by a
clean sand embankment, built in 1-ft increments to a height of 12
ft above the cul-vert crowns. Deflection and pressure measurements
were made after each 1-ft increment of fill was added.
From these measurements, ' values for the backfill have been
com-puted, and these are presented in Fig. 1(b). The apparent
increase of E' with depth of embedment is distinct, and these data
illustrate the degree to which increasing confining pressure can
affect the backfill soil stiff-ness.
During the same years as the Chapel Hill tests, Marston was
con-ducting the tests at the Iowa Engineering Experiment Station
that Span-gler would later use as the basis for the Iowa formula.
These tests in-volved a variety of culvert sizes, a sandy clay loam
embankment up to 15 ft in height, and investigations into the
effects of backfill density and time on culvert pressures and
deformations. The investigation was ex-tremely thorough, and
pressure and deflection measurements were taken after each 6-in.
lift of fill was placed.
Plotted versus fill height and examined carefully, however, many
of the deflection records reported by Spangler (22) do not increase
with depth smoothly and gradually, as might be expected, but are
occasion-ally irregular. In some cases almost 10% of the completed
embankment deflection was found to have occurred due to a single
6-in. lift of fill. Fortunately, Spangler also provided information
on the time elapsed be-tween successive lifts and measurements, and
it becomes clear when the data are examined carefully that the
jumps in the deflection records and a good part of the apparently
excessive deflection increments caused by some lifts can be
directly linked to delays of up to 10 days between some lifts.
Indeed, such delays led to a construction time of four months for a
15-ft embankment. Given the soil used as backfill (sandy clay
loam), it is reasonable to assume that some of the deflections
measured during fill construction were time-dependent, separate
from the immediate de-flections that can be predicted by the
modulus of soil reaction. Accord-ingly, it appears that Spangler
overestimated the immediate deflections
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at greater fill depths and therefore underestimated the values
of e at these points, which would have suppressed any tendency for
those val-ues to increase with depth.
Fig. 1(c) presents E' values computed for Marston's Experiment 1
after the deflections that appear to have been caused by a delay in
construc-tion have been eliminated. The finer-grained nature of the
backfill yields a more gradual increase in E' with depth than was
the case with the clean sand backfill at Chapel Hill, but the trend
for ' to increase with depth is readily apparent.
ANALYTICAL STUDIES
General Because E' is an empirical parameter, it may be argued
that conclu-
sions regarding its behavior should be based on field
experience. Field data were used to calculate values of E' in the
previous section for three case histories, in which reliable data
for a range of depths are available. Unfortunately, very few such
sets of field data exist from which E' can be computed over a range
of depths for a single installation. Further-more, it appears that
this cannot be remedied by combining available field data; Parmalee
and Corotis (20) concluded that it is not possible to develop
statistical correlations based on data from a variety of
installa-tions because the scatter is too great to draw any
significant correlation between E' and depth. Howard (11) appears
to have encountered the same scatter in his study of a considerably
larger body of data.
The scatter of most available field data and the expense of
conducting full-scale field experiments have led some researchers
to theoretical studies of E'. The most common purposes of these
studies has been to establish a means of determining E', an
empirical soil-structure interaction param-eter, on the basis of
fundamental soil properties that can be determined from easily
performed laboratory tests. Many of these studies have re-lated E'
to the constrained soil modulus, which is denoted in this paper as
Ms, using the elastic solution for deflections and pressures of
buried pipes developed by Burns and Richard (6).
Analysis Using Theory of Elasticity Scope of Analysis.In this
investigation a study was performed to
verify the published correlations between E' and M s , and to
establish the range of conditions under which E' can be
approximated as being equal in value to the constrained soil
modulus. The purpose of this study was to determine the degree to
which E' behaves as a true soil modulus, independent of the
properties of the pipe embedded in the fill.
Previous Research.Allgood and Takahashi (2) suggested that the
constrained soil modulus, Ms/ is the parameter that best models the
stiffness behavior of soil under embankment loading, and Krizek, et
al. (15) described Ms as "the basic and logical" soil modulus for
problems of soil-structure interaction. Many researchers have used
Ms as the fun-damental soil modulus in their analyses of soil-pipe
systems, including Allgood and Takahashi (2), Kay and Abel (13),
Krizek and Kay (14), Luscher (16), and Watkins (27).
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In the attempt to overcome the empirical restrictions of ', some
re-searchers, notably Nielson (18), Stankowski and Nielson (23),
and more recently Chambers, et al. (8), have proposed that design
values of E' may be found by multiplying values of Ms by a
constant. The primary advantage of this approach is that values of
Ms may be obtained by per-forming conventional one-dimensional
(oedometer) tests on represen-tative soil samples at appropriate
strain levels, while E' can be deter-mined accurately only on the
basis of recorded field data. By this approach E' = kMs (3) where
fc is a constant whose value has been found by elastic analysis to
lie between 0.7 and 1.5 (8).
Description of Analysis.A linear elastic solution for pressures
on and deflections of buried pipelines was developed in 1964 by
Burns and Richard (6). In their analysis, the soil was assumed to
be homogeneous, elastic, and isotropic; it was also assumed that
the soil was subjected to a uniform overburden load of infinite
horizontal extent.
The modulus of soil reaction, ', may be computed from the Burns
and Richard solution for pressures and deflections using a
modification of the formula proposed by Spangler:
PrR
where Pr = horizontal pressure at culvert springline (FL~2); R =
mean culvert radius (L); and Wh = radial horizontal displacement
(L). Because of the complexity of the equations involved in the
elastic solution, a computer program was written to facilitate the
comparison of E' and Ms values for a range of soil and pipe
properties.
Findings.The range of soil and pipe property combinations
exam-ined with the Burns and Richard solution represents the range
of con-ditions that could be expected in the installation of
flexible pipe. It was found that the value of the coefficient fc
(Eq. 3) depended on two vari-ables only: The normalized pipesoil
stiffness, (MSR3/EI), and Poisson's ratio for the soil, vs. The
relationship between these variables and fc is shown in Fig. 2.
In Fig. 2, it may be seen that the value of fc for all soil and
pipe con-ditions closely matches the published range of 0.7 to 1.5.
Furthermore, for medium-dense or denser backfills and flexible
pipes [(MSR3/EI) > 250], this range of fc remains practically
constant, and its value depends primarily on the degree of bonding
assumed between the pipe and the soil.
One of the shortcomings of the elastic analysis developed by
Burns and Richard is that, while the exact solutions for bonded or
frictionless soil-pipe boundary conditions can be obtained, it is
not possible to ana-lyze partial slip or limiting stress boundary
conditions that would more accurately model the actual soil-pipe
interface behavior.
Fortunately, this does not lead to major uncertainties in the
results. The bonded and frictionless boundary conditions provide
upper and lower bounds to the actual field behavior, and do not
differ greatly. For prac-tical purposes, an average may be taken of
the values of fc corresponding
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I/, = 0.45 \ RANGE OF MOST FLEXIBLE -
PIPE INSTALLATIONS
BONDED INTERFACE UPPER LIMIT
AVERAGE OF BONDED AND UNBONDED V A L U E S ^
UNBONT)1>'WERT:ACE~LOWERHUMTT"
IQOOO 3000S" 300 1000 3000 MSR3/EI
FIG. 2.Values of K = E ' /M s Determined from Burns and
Richards' Elastic So-lution
to these two boundary conditions, which results in a value of k
for most flexible pipe installations very close to unity (see Fig.
2). On the basis of this analysis, then: E'~M. (5)
It seems reasonable that ' should depend mostly on the
properties of the backfill in the case of flexible pipe
installations, because of the small influence of the pipe stiffness
on the behavior. In fact, other re-searchers (8,15,24) have also
reached the conclusion that ' can be very closely approximated by
Ms; because of its more fundamental character, it has even been
suggested by Chambers, et al. (8) and by Krizek, et al. (15) that
the constrained soil modulus should be used in place of E' in the
Iowa formula. Because of the dependence of all soil moduli on
con-fining pressure, this relationship provides compelling evidence
for the increase of the modulus of soil reaction with depth, which
will be dem-onstrated further in the following section.
Finite Element Studies of ' Scope of Analysis.A series of finite
element analyses were per-
formed, for a variety of soil and pipe conditions, to
investigate design values of ' that would take into account the
effect of increasing depth of backfill. The analyses were limited
to studying only the range of pipe properties represented by
large-diameter, flexible steel pipe.
Description of Analysis.The finite element program used for this
analysis, SSTIPN, computes the stresses and strains in the pipe and
the soil at a series of construction increments, each representing
placement of a layer of backfill. In this way, SSTIPN permits a
realistic analysis of pipe-soil systems including nonlinear
behavior of the backfill and vari-ation of geometric conditions
during backfilling.
The finite element mesh used in the analyses is shown in Fig. 3.
By employing the principles of symmetry and taking the horizontal
diam-eter of the pipe as the system datum, it was possible to model
the entire system with a mesh covering 1 /4 of the pipe-soil
system.
A sequence of 12 backfilling steps was used to model the
behavior of
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^
_ 10 RELATIVE WIDTH
tfs; IVJ
% 5
FIG. 3.Finite Element Mesh Used for SSTIPM Analysis
the pipe-soil system under different heights of backfill. These
steps con-sisted of the seven layers shown in the mesh, and five
successive in-crements of uniform surcharge to simulate backfill
levels up to 40 ft above the springline of the pipe.
Table 2 shows the values of the hyperbolic soil properties used
in the finite element analysis. These properties are taken from the
results of extensive testing and analysis performed by Duncan, et
al. (9) to deter-mine representative soil parameters for finite
element analyses.
Ten steel pipe sections were analyzed, ranging in diameter from
4 to 12 ft and in diameter-to-thickness ratio from 100 to 400 ft.
Preliminary findings showed that, for a given ratio of diameter to
thickness, the per-centage deflections remained constant as the
pipe diameter was varied. In addition, it was found that the
deflections varied as predicted by the Iowa formula for conditions
of varying pipe wall thicknesses and con-stant soil properties.
Therefore, for the purpose of investigating the val-ues of E' with
the varying fill depth and soil properties, a single steel pipe
section with 8-ft diameter and 1/2-in. wall thickness (D/t = 200)
was used.
Findings.Given the pipe deflection and soil stress-strain data
pro-vided by the SSTIPN analysis, three procedures were used to
compute E'-values for the pipe-soil system.
1. Knowing the horizontal deflection of the pipe (8*) and the
hori-zontal soil stress in the adjacent element (ah), E' may be
calculated using the expression:
Oft E' = - R (6)
2. Knowing the horizontal deflection (8*) and stiffness (EI) of
the pipe and the overburden load of the fill {w), the Iowa formula
can be rear-ranged so that E' may be calculated using the
expression:
KW EI
E, = 28x R _ ( 7 ) 0.61
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TABLE 2.Soil Properties Used for SSTIPN Analysis
Soil material number
(D 1
2
3
4
5
6
7
Soil type (2)
Fine-grained soils (LL < 50) CL, ML, CL-ML
Fine-grained soils (LL < 50) CL, ML, CL-ML
Coarse-grained soils with fines SM-SC
Coarse-grained soils with fines SM-SC
Coarse-grained soils with
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F!G, 4,Comparison of Recommended Design Values with Field Data:
(a) Fine-Grained Soils CL, ML, CL-ML; (b) Coarse-Grained Soils with
Fines, SM-SC; and (e) Coarse-Grained Soils SP, SW, GP, GW
rived values for ', based on known soil properties and
construction conditions. These can serve as the yardstick for
evaluating design values of ' without the effects of spurious
deflections resulting from causes other than fill loads, which
inevitably affect measured field values.
RECOMMENDATIONS FOR DESIGN
General The previous sections have demonstrated empirically and
analytically
that the modulus of soil reaction should be expected to increase
in value with depth of embedment. In this section, design values
for ' that vary with depth, and a discussion on the uncertainties
of E' and the Iowa formula are presented. This discussion is
intended to provide perspec-tive on the selection of design
parameters for the Iowa formula, in par-ticular E', and on the
importance of careful field control during pipeline installation in
controlling pipeline deflections due to the weight of
over-fill.
Empirical Uncertainties in Iowa Formula The Iowa formula was
developed empirically to account for the con-
tributions of soil load, pipe stiffness, and soil stiffness on
horizontal pipe deflections. Though the pipe stiffness and soil
load were well under-stood theoretically at the time the formula
was introduced, empirical factors were necessary to account for the
effects of lateral soil resistance ('), pipe bedding (K), and
time-dependent deflections (Da).
Research subsequent to the development of the Iowa formula has
ex-amined the ranges of values that E', K, and Di can assume. Of
the three, K is known with the greatest certainty. If the vertical
pressure is as-sumed to be uniform across the entire width of the
bedding, K can be shown to vary from 0.110 for pipe laid on a flat
surface (no bedding) to 0.083 for pipe bedded up to springline
(22).
The deflection lag factor, Di, is associated with soil
plasticity, time after construction, and the trench or embankment
geometry. As a single factor representing the ratio of ultimate
horizontal deflection to imme-diate horizontal deflection, it has
been measured at values ranging from 1.2 to 6.0 (15).
Values of E' that have been back-calculated from field
measurements vary widely from site to site, and even along the same
pipeline. This is
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apparent in virtually every compilation of E'-values based on
field mea-surements, and is perhaps most clearly seen in the work
by Howard (11). It is evident that this is caused by a deviation in
deflections along a pipeline, or from pipeline "to pipeline, when
the pipelines were con-sidered to have similar soil types and
densities. When these deflections are used to back-calculate the
modulus of soil reaction, there is an in-evitable uncertainty as to
the "true" value of E' for the assumed con-ditions and the value
that should be used for design.
This uncertainty may be due to differences in the bedding or
deflec-tion lag effects at the points of measurement, changes in
soil type or compaction, or even subtle variations in standards of
workmanship (4). Deflection deviations between sites may be related
to different standards of measurement accuracy or to differences in
the handling or fabrication of the pipe. Whatever the cause, any
one of these factors could lead to deflections varying
significantly from those predicted by the Iowa for-mula and a given
value of '.
It is clear that, in designing pipe for deflection using the
Iowa formula, it is important to assess realistically all of the
factors that may affect pipe deflection, and to ensure that
construction operations adhere to the con-ditions considered in
design. In addition to proper construction control, it is important
to use values of E' that accurately represent stiffness of the
backfill. It is the intent of the following section to present such
val-ues of E', which have been developed from the results of finite
element analyses and checked against controlled field data.
Design Values of E' Fig. 4 presents sets of E'-values
recommended for use in the Iowa
formula, based on the findings of this study. The recommended
values
TABLE 3.Design Values of ' (psl)
Type of soil d)
Fine-grained soils with less than 25% sand content (CL, ML,
CL-ML)
Coarse-grained soils with fines (SM, SC)
Coarse-grained soils with little or no fines (SP, SW, GP,
GW)
Depth of cover (ft)
(2) 0-5 5-10
10-15 15-20 0-5 5-10
10-15 15-20 0-5 5-10
10-15 15-20
Standard AASHTO Relative Compaction
85% (3) 500 600 700 800 600 900
1,000 1,100
700 1,000 1,050 1,100
90% (4) 700
1,000 1,200 1,300 1,000 1,400 1,500 1,600 1,000 1,500 1,600
1,700
95% (5)
1,000 1,400 1,600 1,800 1,200 1,800 2,100 2,400 1,600 2,200
2,400 2,500
100% (6)
1,500 2,000 2,300 2,600 1,900 2,700 3,200 3,700 2,500 3,300
3,600 3,800
Note: AASHTO is the American Association of State Highway
Transportation Officials.
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are presented for three general soil types, various relative
compactions, and depths of fill cover up to 20 ft.
The field data presented earlier in this paper are shown
superimposed on the appropriate recommended values of E'. The field
data closely follow the trend of the curves with depth and tend to
approximate val-ues of E' for low relative compactions for all
three soil types. This is consistent with the low compactive
efforts with which these backfill soils were placed. Fig. 4 shows
that the design values given vary significantly with relative
compaction. It is therefore recommended that the method of
compaction to be used in the field is critically examined to
determine the value of relative compaction that can be expected,
and that this value of relative compaction is used to select an
appropriate value of E' for design.
The values of ' recommended in this study are summarized in
Table 3. The increase of E' with depth is approximated, for each
soil type and compacted density, by constant values that increase
in 5-ft increments. These values of E' may be considered equivalent
to those in Fig. 4 for the purpose of predicting deflections with
the Iowa formula.
SUMMARY
The modulus of soil reaction (') characterizes the stiffness of
the soil backfill at the sides of a buried pipeline, and is an
important factor in the Iowa formula for determining pipe
deflections. An empirical param-eter, E' has been the subject of
much research aimed at determining suitable values for design. This
and previous studies of E' have shown clearly that the value of E'
varies with soil type and degree of compac-tion, and that its value
can vary considerably from one location to an-other where the same
backfill and construction methods appear to be used. Designers
should bear these inevitable variations in mind, and use values of
E' with appropriate caution for estimating pipe deflections due to
fill loads. Though it has been clearly established experimentally
and in practice that E' varies with soil type and compacted
density, there have been conflicting opinions in the literature as
to whether E' should vary with depth of embedment as well.
This study has demonstrated, on the basis of empirical and
analytical evidence, that E' is indeed a function of depth, and
that depth has a significant effect on the value of E'. This effect
was examined empirically with sets of pipeline deflection data from
three installations, analytically with an elastic solution of
buried pipeline deflections and pressures, and with a finite
element computer program developed for the study of cul-verts
during and after construction. The results of these studies
pro-vided the basis for developing design E'-values for known soil
types, densities, and depths of embedment.
It was also established that, for the loading conditions
adjacent to a buried flexible pipeline, the value of the modulus of
soil reaction, E', is nearly equal to that of the constrained
modulus, Ms. This relationship between E' and Ms is fortunate, as
it provides a method to determine site-specific values of E' on the
basis of a relatively simple laboratory test in cases where that
may be desirable.
551
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ACKNOWLEDGMENTS
The writers wish to express their appreciation to the following
people for their contributions to this study: Frank Cortelessa,
Kaiser Steel Cor-poration, Fontana, California; Robert Moehle and
Sanford Belkin, Met-ropolitan Water District, Los Angeles,
California; Thomas Rulla and Ber-nard Gallie, Los Angeles
Department of Water & Power, Los Angeles, California; Buckley
F. Ogden, San Diego County Water Authority, San Diego, California;
and Art Thompson, East Bay Municipal Utilities Dis-trict, Oakland,
California.
Special appreciation goes to George Tupac for his instrumental
role in the development of this study, and to the American Iron and
Steel In-stitute for its financial support of the
investigation.
APPENDIX.REFERENCES
1. Adrian, G. W., "Steel Pipe Design for the Second Los Angeles
Aqueduct," Journal of the Pipeline Division, ASCE, vol. 93, No. 3,
Nov., 1967, pp. 33-43.
2. Allgood, J. F., and Takashi, H., "Balanced Design and Finite
Element Anal-ysis of Culverts," Highway Research Record No. 413,
1972, Washington, D.C., pp. 44-56.
3. Audibert, J. M. E., and Nyman, K. J., "Soil Restraint against
Horizontal Mo-tion of Pipes," Journal of the Geotechnical
Engineering Division, ASCE, Vol. 103, No. 10, Oct., 1977, pp.
1119-1142.
4. Boden, J. B., Farrar, D. M., and Young, O. C , "Standards of
Site Practice Implications for Innovation in the Design and
Construction of Buried Pipe-lines," TRRL Supplementary Report 345,
Berkshire, England, 1977.
5. Braune, G. M., Cain, W., and Janda, H. F., "Earth Pressure
Experiments on Culvert Pipe," Public Roads, Vol. 10, Nov., 1929,
pp. 153-176.
6. Burns, J. O., and Richard, R. M., "Attenuation of Stresses
for Buried Cyl-inders," Proceedings, Symposium on Soil-Structure
Interaction, University of Arizona, Tucson, Ariz., 1964, pp.
378-392.
7. Cates, W. H., "Design of Flexible Steel Pipe under External
Loads," Journal of the Pipeline Division, ASCE, Vol. 90, No. 1,
Jan., 1964, pp. 21-31.
8. Chambers, R. F., McGrath, T. J., and Heger, F. J., "Plastic
Pipe for Subsur-face Drainage of Transportation Facilities," NCHRP
Report 225, Transporta-tion Research Board, Washington, D.C., Oct.,
1980, pp. 122-140.
9. Duncan, J. M., et al., "Strength, Stress-Strain and Bulk
Modulus Parameters for Finite Element Analyses of Stresses and
Movements in Soil Masses," Re-port No. UCB/GT/80-01, University of
California, Berkeley, Calif., 1980.
10. Howard, A. K., "Laboratory Load Tests on Buried Flexible
Pipe," Journal of the AWWA, Vol. 64, No. 10, Oct., 1972, pp.
655-662.
11. Howard, A. K., "Modulus of Soil Reaction (') Values for
Buried Flexible Pipe," Engineering and Research Center, Bureau of
Reclamation, Denver, Colo., 1976.
12. Howard, A. K., and Selander, C. E., "Laboratory Load Tests
on Buried Rein-forced Thermosetting, Thermoplastic, and Steel
Pipe," Journal of the AWWA, Vol. 66, No. 9, Sep., 1974, pp.
540-552.
13. Kay, J. N., and Abel, J. F., "Design Approach for Circular
Buried Conduits," Transportation Research Record No. 616,
Transportation Research Board, 1976, Washington, D.C., pp.
78-80.
14. Krizek, R. J., and Kay, J. N., "Material Properties
Affecting Soil-Structure Interaction of Underground Culverts,"
Highway Research Board, No. 413, Washington, D.C., 1972, pp.
12-29.
15. Krizek, R. J., et al., "Structural Analysis and Design of
Pipe Culverts," Report No. 116, National Cooperative Highway
Research Program, Highway Re-search Board, 1971, Washington, D.C.,
155 pp.
552
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Luscher, U., "Buckling of Soil-Surrounded Tubes," Journal of the
Soil Me-chanics and Foundation Division, ASCE, Vol. 92, No. 6,
Nov., 1966., pp. 211-228. Meyerhof, G. G., "Composite Design of
Shallow-Buried Steel Structures," Proc, 47th Annual Convention of
the Canadian Good Roads Association, Sep., 1966, Halifax, Nova
Scotia. Nielson, F. D., "Modulus of Soil Reaction as Determined
from Triaxial Shear Test," Highway Research Record No. 185, 1967,
Washington, D.C., pp. 80-90. Parmalee, R. A., and Corotis, R. B.,
"The Iowa Deflection Formula: An Ap-praisal," Highway Research
Record No. 413, 1972, Washington, D.C., pp. 89-101. Shafer, G. E.,
"Discussion: Underground ConduitsAn Appraisal of Mod-ern Research,"
Trans., ASCE, Vol. 113, 1948, pp. 354-363. Spangler, M. G., "The
Structural Design of Flexible Pipe Culverts," Bulletin 153, Iowa
Engineering Experiment Station, Ames, Iowa, 1941. Spangler, M. G.,
"Discussion: Rebuilt Wolf Creek Culvert Behavior," High-way
Research Record, No. 262, Highway Research Board, Washington, D.C.,
1969, pp. 10-13. Stankowski, S., and Nielson, F. D., "An
Analytical-Experimental Study of Underground Structural Cylinder
Systems," Engineering Experiment Station, New Mexico State
University, Las Cruces, N. Mex., Oct., 1969. Steel PipeDesign and
Installation, American Water Works Association, Steel Pipe Manual
Mil , 1964. Terzaghi, K., "Evolution of Coefficients of Subgrade
Reaction," Geotechniaue, London, Vol. 5, No. 4, 1955, pp. 297-326.
Watkins, R. K., "Influence of Soil Characteristics on the
Deformation of Embedded Flexible Pipe Culverts," Bulletin 223,
Highway Research Board, Washington, D.C., 1959, pp. 14-24. Watkins,
R. K., "Structural Design of Buried Circular Conduits," Highway
Research Record No. 145, Washington, D.C., 1966, pp. 1-16. Watkins,
R. K., and Nielson, F. D., "Development and Use of the Modpares
Device," Journal of the Pipeline Division, ASCE, Vol. 90, No. 1,
Jan., 1964, pp. 155-178. Watkins, R. K., and Spangler, M. G., "Some
Characteristics of the Modulus of Passive Resistance of Soil: A
Study in Similitude," Proc, Highway Re-search Board, Vol. 37, 1958,
pp. 576-583.
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