HIGHWAY RESEA.

RCH
RECORD
Number 116

Culverts and Storm--D-rains

4 Reports

Presented at the
44th ANNUAL MEETING
January 11-15, 1965

SUBJECT CLASSIFICATION
23 Highway Drainage
34 General Materials

filGHWAY RESEARCH BOARD

of the
Division of Engineering and Industrial Research
National Academy of Sciences-National Research Council
Washington, D. C.
1966
 Department of Design
W. B. Drake, Chairman
Assistant State Highway Engineer
Kentucky Department of Highways, Lexington

HIGHWAY RESEARCH BOARD STAFF

F. N. Wray, Engineer of Design
R. C. Edgerton, Assistant Engineer of Design

GENERAL DESIGN DIVISION

W. L. Warren, Chairman
Engineer of Design
California Division of Highways, Sacramento

COMMITTEE ON SURFACE DRAINAGE OF HIGHWAYS

(As of December 31, 1964)

Carl F. Izzard, Chairman

Chief, Hydraulic Research Division, Office of Research and Development
U. S. Bureau of Public Roads, Washington, D. C.

C. R. Edgerton, Hydrographic Engineer, North Carolina State Highway Commission,

Raleigh ,
Kenneth S. Eff, Chief, Hydraulic Section, Civil Engineering Branch, Office, Chief of
Engineers, Department of the Army, Washington, D. C.
Kenneth M. Fenwick, Assistant Engineer of Design, California Division of Highways,
Sacramento
John G. Hendrickson, Jr., Director of Engineering Research, American Concrete
Pipe Association, Chicago, Illinois
S. W. Jens, Consulting Engineer, St. Louis, Missouri
Frank L . Johnson, Hydraulic Engineer , Region 6, U. S. Bureau of Public Roads , Fort
Worth, Texas
A. H. Koepf, Manager, Field Engineering-Highway Products, Kaiser Aluminum and
Chemical Sales, Inc., Oakland, California
Frank Leonard, Design Engineer , Idaho Department of Highways, Boise
Robert A. Norton, Engineer of Hydraulics and Bridge Maintenance, Connecticut State
Highway Department, Wethersfield
Ralph M. Peterson, Chief, Branch of Management Studies and Systems Planning, U. S.
Forest Service , Washington, D. C
A. L. Pond, Jr., Hydraulic Engineer, Virginia Department of Highways, Richmond
W. 0. Ree, Agricultural Research Service, Stillwater, Oklahoma
James K. Searcy, Hydraulic Engineer, Hydraulic Branch, Bridge Division, U. S.
Bureau of Public Roads , Washington , D. C.
E. P. Sellner, Manager, Water Resources Bureau, Portland Cement Association,
Chicago, Illinois
Roy E. Smith, Managing Director, National Corrugated Steel Pipe Association,
Chicago, Illinois
F. W. Thorstenson, Assistant Road Design Engineer , Minnesota Department of
Highways, St. Paul
Mainard Wacker, Chief Highway Designer (Hydraulics), Hydraulics Section, Advance
Plans Division, Wyoming Highway Department, Cheyenne
 Department of Materials and Construction
R. L. Peyton, Chairman
Assistant State Highway Engineer
State Highway Commission of Kansas, Topeka

HIGHWAY RESEARCH BOARD STAFF

H . .I!; • .Hollen, .l!;ngrneer ot Matena1s and Construction
W. G. Gunderman, Assistant Engineer of Materials and Construction

GENERAL MATERIALS DIVISION

John L. Beaton, Chairman
Materials and Research Engineer
Materials and Research Department
California Division of Highways, Sacramento

COMMITTEE ON CULVERTS AND CULVERT PIPE

(As of December 31, 1964)
Reynold K. Watkins, Chairman
Professor and Head
Mechanical Engineering Department
Utah State University, Logan

T. F. DeCapiteau, Drainage Products Engineer, Manufacturing Division, Republic

Steel Corporation, Youngstown, Ohio
W. B. Drake, Assistant State Highway Engineer, Kentucky Department of Highways,
Lexington
Kenneth S. Eff, Chief, Hydraulic Section, Civil Engineering Branch, Office, Chief of
Engineers, Department of the Army, Washington, D. C.
C. J. Francis, Director, Engineering Division, Soil Conservation Service, U. S.
Department of Agriculture, Washington, D. C.
R. T. Healy, Executive Secretary, Connecticut Concrete Pipe Association, Inc., South
Windham
John G. Hendrickson, Jr., Director of Engineering Research, American Concrete
Pipe Association, Chicago, Illinois
A. H. Koepf, Manager, Field Engineering-Highway Products, Kaiser Aluminum and
Chemical Sales, Inc., Oakland, California
J. Alan Myers, Manager, Highway Construction Marketing, United States Steel
Corporation, Pittsburgh, Pennsylvania
Eric Nordlin, Supervising Highway Engineer, Materials and Research Department,
California Di vision of Highways, Sacramento
C. E. Proudley, Materials Consultant, Raleigh, North Carolina
E. P. Sellner, Manager, Water Resources Bureau, Portland Cement Association,
Chicago, Illinois
Rockwell Smith, Research Engineer-Roadway, Association of American Railroads,
r,i,..; ...,,,.,.,....,.... T11.;"",....;,eo
\..,.ll.1.\..,C\.C,V, .L.1..1..1...1..I.V.1.1,;:J

M. G. Spangler, Civil Engineering Department, Iowa State University, Ames

Harold A. Swanson, Manager, Civil Engineering, International Pipe and Ceramics
Corporation, East Orange, New Jersey
H. L. White, Chief Engineer, Armco Metal Products Division, Middletown, Ohio
 Contents
HYDRAULIC DESIGN OF THE FORT CAMPBELL
STORM DRAINAGE SYSTEM
Laurence G. Leach and Benjamin L. Kittle . . . . . . . . . . . . 1

FRICTION FACTORS FOR HYDRAULIC DESIGN OF

CORRUGATED METAL PIPE
John L. Grace, Jr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

CAMBER DESIGN STUDY FOR

CONCRETE PIPE CULVERT
Robert C. Deen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

FIELD VERIFICATION OF RING COMPRESSION

CONDUIT DESIGN
J. Demmin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Discussion:
M. G. Spangler; J. Demmin . . . . . . . . . . . . . .. . . . . . . . 80
 Foreword
The four papers in this Highway Research Record cover subjects related to
highway culverts. Engineers involved in drainage design and in the structural
design, selection, and installation of culverts should find useful information
in these papers.
The paper by Leach and Kittle demonstrates the economies that can beef-
fected by the use of ponded storage in a storm drainage system.
John L. Grace, Jr., offers recommendations of friction factors for the
commonly used corrugations of annular corrugated pipe including the 2- x
6-in. corrugations of structural plate pipe and the 1- x 3-in. corrugations
used in some larger riveted sizes. The recommendations are based on model
test results extended by analytical methods.
In the third paper, Robert C. Deen describes a simplified method for pre-
dicting the required camber in highway culvert installations. Fairly close
agreement between predicted and observed settlements is reported.
Jurgen Demmin reports on a series of load tests on a large structural plate
pipe arch. The author interprets the results as a substantial verification of
the Ring Compression Method of conduit design.
Hydraulic Design of the Fort Campbell
Storm Drainage System
LAURENCE G. LEACH, Chief, Hydraulic Section, and
BENJAMIN L. KITTLE, Hydraulic Engineer, U. S. Army Engineer Division, South
Atlantic, Atlanta, Georgia

The Corps of Engineers, U. S. Army, awarded a contract in June 1963

for construction of a storm drainage system to serve a major portion of
the cantonment area of Fort Campbell, Kentucky. A total of 31, 000 lineal
feet of pipe, ranging in size from 12- to 84-in. diameter, was required
to drain 2, 000 acres of land in the main post area. The cost of this drain-
age system was approximately $2,000,000.
While the project is unusual, based on pipe quantities and construction
costs involved, it is also somewhat unique in that the original estimated
cost of $ 5, 500, 000 was drastically lowered by the use of temporary pond-
ing to reduce peak discharges in the main trunk sewer. The hydraulic
design of the system permits a limited amount of ponding (at the majority
of storm drainage inlets) as a result of a 10-yr frequency design storm.
This relatively small amount of temporary storage capacity reduced re-
quired pipe sizes considerably, but the largest percentage of cost savings
was effected by enlarging two major ponding areas in the upstream portion
of the project. These two excavated temporary retention basins permitted
large reductions in pipe diameters for nearly three miles of trunk sewer.

•FORT CAMPBELL is located on the Kentucky-Tennessee state line about 50 miles

northwest of Nashville, Tenn ssee. Th re ion is characterised by gently rolling ter-
rain having a thick clay overburden unde rlain by a cavernous limestone .formation.
The development of solution hannels in the 1mderlying limestone, with accompanying
erosion of the overburden due to circulating groundwat , r has resulted in the formation
of a typical Karst topography with sau er-shaped ct pressions on the ground surface
and, in some instances, open sinkholes. The cantonment area comprises about 6,000
acres located in the eastern part of the base adjacent to US 41A. Figure 1 is a map of
the main post area of Fort Campbell.
The central and western portions of the cantonment area occupy higher ground, con-
taining fewer sinkholes, than the eastern section. The central portion of the built-up
area was constructed on a low ridge which runs generally north and south. Because
this higher ground is relatively well drained, with few sinkholes, it was developed be-
fore the lower land to the east. The later development of Fort Campbell into a per-
manent army facility, however, necessitated the expansion of the cantonment to the
east. The eastern section had very few drainage lines and contained numerous large
sinks. The natural drainage provided by the sinkholes was not satisfactory. Following
a heavy rainstorm, wate r would sland Ior days or weeks in some sin.k s would b readily
drained from others, and would remain ponded in others almos t indefinitely. Dating
from World War II, attempts were made to drain lh sinks by constructing vertical
drainage wells thr0ugh th clay ove rburden into the underlying weathered limestone.
These wells were only moderately successful, since only a few would handle the run-
off from a storm of normal intensity without ponding, and all presented a continuing
maintenance problem to keep them functioning. When postwar expansion of the main

Paper sponsored by Commi ttec on Surface Drainage of Highwuys .

l
2

TENNESSEE KENTUCKY

>IIGH WAY 4/ A
BASIN

STORM DRAIN
NATURAL POND ~
SCALE IN FEET
EXCAVATED POND
0 1200· 2400 3600
DRAINAGE AREA ,., , .11,i11n,,.,11111w11u1
OPEN DITCH ······· ······ ..
CHUTE -------

F i gure 1. Luyout of s torm drainage s ystem .

post began to infringe upon the sink areas, it becam apparent that a positive drainage
system would have to be provided for Fort Campbe ll.

COMPARISON OF DRAINAGE SCHEMES CONSIDERED

Ea rly in 1955 a drainage study was pre pared for th Naslivill Dislricl (of the Corps
of Engineers) by a private consu lting e ngineer firm . T his study proposed a syste m of
w1der ground conduits lo re move the storm r unoff as Iast as i t was coll cled. T he sys-
tem i nvol ved reinforced concrete box condui ts having cross-sectional dim e nsions as
large as 17 by 14 feet and as much as 45 feel below the ground surface at the downstream
end of the pr oject. The e normity of such a project is reflected in its estimated cost
of $5,500,000.
The Nashville District, in an attempt to devise a satisfactory drainage system that
was economically feasible , prepared and submitted a drainage report in 1957 to the
Chief of Engineers . Five possible plans were considered in this s tudy . P lan A was
essentia lly a refinement of the original consu Ui.ng engineer repor t a nd provided for im -
mediate rem oval of storm r unoff . The estimated cos t of t his plan was $4, 600, 000.
Plan B permitted a minor amount of pondi~ in U1.e eXisting s ·nlt areas which 1·educed
the cost estimate considerably. Plans C and D wer a lternates to Plans A a nd B and
involved disposing of a major portion of the runoU into an existing large open sink.hole .
While bo th of these plans were probably feasible the uncertainties involved with under -
gr ound di sposal of s torm r 1 noff r11lPd out th ir us . Plan E was essentially Lhe same
as Plan B except for the use of certain open ditches instead of pipe to reduce costs.
The estimated cost of this plan was $3,370,000.
In addition to these five plans , consideration was also give n Lo Ll1e us e of a storm
water pumping station at a strategic location to reduce pipe sizes and to the construc-
tion of an unlined drainage tunnel driven through rock in the lowe r portion of the sys-
tem. Neither of these schemes proved to be economically feasible.
 3

0
,,. r-- ! ~ m-
-I "'
I .!. .!.. I .!.. <[
.!. I
CD
I- I- I- I- 0 I- I- I- 0
w w w w z w ww z
...J ...J ...J ...J ...J ...J ...J 0
I- 0 zz
560 ~ ~ ~ ~ Q. ~ Q.
w
w
LL

z
520
z
0

~
;::,;
w 480
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440 v - CHUTE AND STILLING BASIN

400
0 2 4 6 8 10 12 14 16 18 20 22
DISTANCE IN THOUSANDS OF FEET

Figure 2. Prof ile of mai n trunk sewe r.

Based on a preliminary design prepared by the South Atlantic Division, the Nashville
District submitted a revised drainage report in 1960 which provided additional storage
capacity by enlarging two key ponding areas by excavation. This was essentially Plan
E with the addition of two major ponding areas. The estimated construc tion c os l of this
plan was $2,000,000. This was the scheme that was later adopted for construction.

DESCRIPTION OF ADOPTED SCHEME

Superimposed on the street layout, shown in Figure 1, is the storm drainage system
including drainage area limits, open ditches , ponding areas , pipe , discharge chute, and
stilling basin. The cross hatching indicates the approximate limits of ponding for a 10-
yr frequency storm. All ponding occurs in natural sink areas except for excavated
Ponds A and B. Beginning at the upstream end of the system, the pipe sizes increase
progressively until an 84-in. diameter pipe is required to handle the flow entering
Pond A. Sufficient storage capacity is provided in Pond A to limit the outlet pipe size
to 30-in. diameter. Progressing downstream, pipe diameters increase again until the
required outfall pipe diameter is 78 inches. The flow discharging from the outlet pipe
enters a 6. 5-ft wide concrete chute, approximately 1, 800 feet long, which terminates
in a stilling basin at the elevation of the creek. Figure 2 is a profile of the main trunk
sewer .

OUTLINE OF THE HYDRAULIC DESIGN

The design rainfall used for the Fort Campbell drainage project has an expected
frequency of recurrence of once in ten years and a maximum hourly intensity of 1. 95
inches. Rainfall intensity-duration data for the Fort Campbell area were obtainedfrom
U. S. Weather Bureau publications. Accumulative volumes of rainfall were computed
by use of the developed intensity-duration curve. Rainfall excess values were then ob-
tained by applying estimated infiltration rates. The relationships between duration and
rainfall intensity, volume, loss , and excess are shown in Figure 3.
Drainage areas to be served by the system were delineated on topographical maps
and the times of concentration computed based on length of over land flow, slope of ter-
rain, and type of vegetive cover. Peak inflow rates were determined by use of the
Rational Formula using a runoff coefficient of 0. 90 for impervious areas and 0. 3 for
4

10-YEAR FREQUENCY DESIGN STORM RAINFALL

~
0
5 ~--~-- -------- -- -- -- -- -~
::c INTENSIT Y - OURATION
en o::
w ~
~
w 4 l-+- - - + - - - + - - - + - - - + - -- • ,- - - 1 - - - - - - + - - - - t

z ~ OEPTH-OURATION-:---..
z ~ I
z 3 1-----\---t---+---+----==-+""'""---+--

OEPTH- DURATION

Figure 3. Rainfall relationships for design stonn .

120 ...---- --,-----.----,---~--,-----,

0
z 10-YEAR FREQUENCY STORM
0
~ 100 1 -- , --++- - - - - + - - - - - + - - - t - - - - - + - --t 541
(/)

0:::
w
a. 80 1-1-----+- \, 540
1-- I-
w w
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t) 60 l -l•- ' - - l --,,£-- -',1----'~.A'
z
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::::, z
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(!) w
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t) 0
(/) z
0
0 a.
2 4 6 8 10 12
TIME IN HOURS
AREA I HYDROGRAPH RELATIONSHIPS

Figure 4. L."1flo-•.; outflcr,; hyd:rogr aph for 8.re8. 7~

pervious areas. Inflow hydrographs were developed for each drainage area by using
the peak rate of runoff and the time of concentration to define the crest and the rising
portion of the hydrograph and then drawing the recession side in such a manne1· as to
balance the total runoff (2. 1 inches in 8 hou1·s). Figure 4 shows the inflow hydrograph
for drainage area No. 1, which is the area tributary to the northernmosl natural pond
 5

400 527
I I I I I
10 -YEAR FREQUENCY STORM
0
z
0 r
(.)
Lu 300 "- ,_.STAGE
525
(/)

0:
I K

""
Lu
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Lu
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(.) 200 ' '
523

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al
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<I:
~ INFLOW
100

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;OUTFLOW
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0
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24 48
- r---
------72
TIME IN HOURS
96
--- 1-- -

120
- - 519
144

POND A HYDROGRAPH RELATIONSHIPS

Figure 5. Inf low- outflow hydr ograph for Pond A.

shown in Figure 1. For clarity, the limits of the individual drainage areas have not
been shown in Figure 1.
In addition to the numerous natural ponding areas, two large ponds were excavated
at hydraulically critical points. Pond B is approximately 600 feet long and 500 feet
wide. Pond A is approximately 1,200 feet long and varies in width from 400 to 800
feet. Each of the two excavated ponds provides approximately 130 acre-feet of tem-
porary storage capacity. To obtain this ponding volume, it was necessary to excavate
250, 000 cubic yards of earth (total for both ponds). The surplus material from the
excavation was used to fill and grade small sink areas throughout the cantonment area.
The runoff from each drainage area was routed through storage, where available,
to determine the outflow hydrograph or rate of contribution to the drainage system.
Figure 4 shows the routing for the natural pond serving drainage area No. 1. This
routing is typical for all natural ponds in the system. To induce temporary storage
and restrict the rate of runoff entering the drainage system, most of the inlets were
equipped with a short control pipe. When flowing partially full, critical flow with inlet
control was assumed. After the pipe was flowing full, the discharge was computed by
the conventional orifice formula. The long pipe lines draining Ponds A and B were
rated assuming friction control and an entrance loss of one-tenth of a velocity head.
The outflow hydrographs, separated by the travel time between design points, were
added to obtain the maximum rate of contribution to the drainage system. Figure 5
shows the inflow-outflow relationship for Pond A which receives inflow from drainage
areas 1 through 13. It will be noted that the peak discharge entering Pond A is 280 cfs
while the outflow is limited to 32 cfs. This reduction in peak discharge entering the
downstream system, together with a similar reduction upstream at Pond B, reduced
the cost of the project approximately $1,000,000. The reason for this large reduction
in pipe cost is apparent when it is realized that 13, 000 lin ft of trunk sewer lies be-
tween Pond A and the outfall. Provision of adequate storage capacity at Ponds A and
B permitted the outlet pipe from Pond A to be reduced from 90- to 30- in. diameter.
6

CHUTE 4.6 % SLOPE The ground surface, downstream of the

pipe outfall, falls rapidly (90 feet) to Little
18'-0" 21'-0"
West Fork Creek, the ultimate disposal
point for the storm drainage. To prevent

SECTION A-A
.... J erosion of the steep slope, a rectangular
concrete chute 6. 5 feet in width and 1, 800
feet in length was provided. The required
height of the side walls was determined by
backwater computations beginning at criti-
- - "_1 ___ .1..,_ ------ .l.1- - __ ,=. __ _ - - - . l . 1 - . l . - •• ..J ____ ______ _ _
\;d.1 Ut::}JLU 111::::d..J. LUt: }Jll,)t:: UUL.U::L d.UU 1,1.1 ~ J . t:.Oo-

ing downstream. Bulking of water due to

air entrainment was computed and found
ID
to be negligible. Super elevation required
A A
=U) ID =o at each of the horizontal curves in the chute
L ID_, :: _J
was computed. It was found that it was
1o' ID 2
ID significant at only one curve where a
superelevation of 0. 4 foot was provided.
PLAN A freeboard of one foot over the computed
water surface was provided throughout the
Figure 6. Stilling basin details. length of the chute.
A stilling basin of conventional design
was provided at the termination of the
chute. As shown in Figure 6, the basin
is 39 feet in length, 10 feet wide, and has two rows of baffle blocks and end sill of suf-
ficient height to create the proper depth of tailwater for the formation of a hydraulic
jump. Care was taken to locate the basin at the proper elevation to eliminate possible
erosion in the ditch section between the stilling basin outlet and Little West Fork Creek.
The design discharge for the stilling basin is 240 cfs. The velocity of the flow is re-
duced from 25 feet per second, at the entrance to the stilling basin, to 3. 5 feet per
second at the basin end sill.

TABLE 1
COMPARISON OF HYDROGRAPH DATA FOR STORMS OF VARIOUS FREQUENCIES

1- Year 10-Year 50-Year

Area Drainage
Area Max. Max. Max. Pond. Max . Max. Max. Pond. Max. Max . Max. Pond.
No. (acres) Inflow Outflow Pond Time Inflow Outflow Pond Time Inflow Outflow Pond Time
(cfs) (cfs) Elev. (hr) (cfs) (cfs) Elev. (hr) (cfs) (cfs) Elev. (hr)

1 198.6 63. 5 40.0 539. 0 6.5 103.5 63. 6 539. 9 12.5 137. 5 77.0 540. 7 13. 0
5a 372.0 165.0 18.7 536.4 30.0 270.0 22.3 538. 9 72.0 347.0 23. 8 540.0 96.0
7 38. 4 19.3 16.0 541. 8 4.5 31. 0 18.4 542.9 8.0 38. 9 19.6 543.5 10.5
8 31. 9 15. 3 6.1 539. 2 6.0 25.2 12 . 1 539. 8 10. 0 31. 6 14.8 540. 2 12.0
9 44 . 3 17.4 7. 4 543.2 6.0 28. 6 8.2 544.2 12.5 36 . 4 8.6 544.6 42 . 0
10 61.5 40.2 26 . 7 539. 2 4 . 5 64.2 32 . 9 540.0 9.0 79. 8 34 . 8 540.5 10.0
11 39.9 25.0 7.0 537. 9 6.5 40.2 7.8 538. 7 12. 0 49.8 8.0 539. 1 18.5
12 47.9 30. 4 12.7 529.8 6.0 49. 1 18.3 531. 0 10.5 61. 3 20.0 532. 0 11. 5
13b 244.7 180.0 19.6 521. 8 137. 0 270.0 32.0 525. 6 192.0 333,0 36.0 528. 2 219.0
14 100.0 40.8 12 . 5 539. 3 10. 0 66.3 20.6 540.4 17.5 85.0 23.0 540.8 21. 0
15 66.2 26.2 7.9 537. 9 6.5 42.6 9. 0 538. 6 18.5 54.6 9.0 539.4 25. 0
15c 19.3 14.2 14 . 2 22.9 22 . 9 28. 6 28. 6
17 87. 2 58.4 50. 0 531. 2 4. 5 93 . 5 62.0 534. 7 10. 0 116. 2 68.0 535. 1 10.0
18C 24 . 9 17.3 17.3 27. 8 27. 8 35 . 0 35 . 0
19 257.0 79.8 26.2 521. 0 13. 5 132. 5 37. 0 523.9 21. 0 172 . 9 41. 0 525 . 4 33.0
20 5.4 3.7 1. 9 520. 8 3.5 5.9 2. 6 521. 0 5.5 7.2 3.3 521. 5 8.5
21b 32.0 14.6 11. 7 516. 9 5.0 22.7 17. 4 517.8 9.0 29.8 18.4 519.0 10. 0
22° 32.7 :!:!.2 9.8 511. 1 10. 0 37. i lll. 9 512.2 13,U 49.7 22.5 513. 4 16.5
23 208. 0 87.6 26 . 2 512.1 18.5 144.7 39. 0 513.6 19 . 0 185.0 46.2 514.7 25. 0
24 54.6 30. 4 7.7 522.6 6.0 50.0 8.8 523.9 15 , 5 62.3 9.2 524.3 21. 0
25c 23 . 3 10.0 10. 0 16. 5 16. 5 20 . 8 20 . 8
a lncludes areas 2 thru 6 . brncludes di sc harge from upstream area . c No ponding in t he s e areas.
 7

To insure that the drainage system was adequate to handle storms of infrequent
occurrence, a 50-yr frequency flood was routed through the system. The computations
indicated that the system was adequate to provide for this extreme storm without flood-
ing of any facilities. A 1-yr frequency storm was also routed through the system to
determine the depth and duration of ponding that would be expected to occur more fre-
quently. Table 1 shows a comparison of ponding area hydrograph data for a 1-, a
10-, and a 50-yr frequency storm.

CONCLUSION
The Fort Campbell storm drainage system is, in essence, a hydraulically balanced
network of temporary ponding areas connected by short control pipes to a main trunk
sewer. The major portion of the runoff from the upstream third of the drainage basin
is retained for a sufficient length of time, in the two major ponds, to reduce drastically
peak downstream discharge rates. The large cost reduction that was accomplished by
the judicious use of temporary ponding made the project economically feasible. While
drainage projects on the scale of this one are unusual, a comparable percentage of
cost savings can be realized on smaller projects by a similar use of temporary ponding.
This project emphasizes that in this era of rising costs, the drainage engineer should
always be mindful of the potential for drainage cost reductions that are afforded by rela-
tively minor amounts of temporary ponding.

ACKNOWLEDGMENT
The authors, in the preparation of this paper, have made liberal use of reports,
studies, and correspondence prepared by various Corps of Engineers offices concerned
with the Fort Campbell project. Permission to use this material is gratefully acknowl-
edged.
Friction Factors for Hydraulic Design of
Corrugated Metal Pipe
JOHN L. GRACE, JR., U. S. Army Engineer Waterways Experiment Station

Results of model tests of two types of corrugated metal pipe

including friction factor-Reynolds number diagrams and mean
flow formulas developed from velocity distribution data are
reported. Calculated maximum values of the friction factor
due to the corrugations and the bolt nuts on the crests of the
structural plate corrugations for various sizes of each type
of pipe are compared with those of similar prototypes as re-
ported by other investigators. Recommended design values
of the friction factor for annular corrugated pipes with cor-
rugation depth-spacing ratios of 1:3 and 1: 5. 33 are related to
diameter, and simple empirical equations describing the re-
lations are developed.

•STRUCTURAL PLATE PIPE, widely used in drainage systems, is made of corrugated

metal sections bolted together in the field. These sections permit erection of pipe 5 ft
in diameter or larger (in increments of 0. 5 ft). Structural plate corrugations have a
depth of 2 in. and a pitch of 6 in. In standard corrugated metal pipe the depth of the
corrugations is only ½ in. and the pitch or spacing of the corrugations is 2% in. ,
crest-to-crest.
Tests to determine friction factors for standard corrugated metal pipe were made on
pipes 3, 5, and 7 ft in diameter at the U. S. Army Engineer Bonneville Hydraulic Lab-
oratory which published the res ults in 1955 (1, 8). Roughness coeffi cie nts determined
in these tests are used generally in culv er l design. However, extra polation of these
roughness coefficients to values applicable to structural plate pipe, which has corruga-
tions four times as deep and a depth-pitch ratio of 1:3 rather than 1:5. 33 was considered
unreliable. The HRB Committee on Surface Drainage of Highways has long recognized
the need for field or laboratory determination of hydraulic design coefficients for this
commonly used drainage material.
Anticipating that full-scale tests would have been costly, and that it would have been
feasible to test only the smaller sizes of structural plate pipe, the Bureau of Public
Roads and the Office, Chief of Engineers, initiated in 1958 a hydraulic model investi-
gation at the U. S. Army Engineer Waterways Experiment Station (WES) for the purpose
of determining friction factors for structural plate pipe. One model simulating a 5-ft
diameter standard corrugated pipe was tested to permit comparison of model and proto-
type results and to check the applicability of simulating corrugated metal pipes with
corrugated fiber glass conduits. The good agreement obtained between results of the
WES model and the Bonneville Hydraulic Laboratory prototype tests of 5-ft-diameter
standard corrugated metal pipe warranted the use of the fiber glass models.

iviODELS Alill TEST PROCEDlJRES

Four models were constructed: a 1:4-scale model of 5-ft-diameter standard corru-
gated pipe and three simulating structural plate pipes 5, 10, and 20 ft in diameter at
scales of 1:2. 2, 1:8, and 1:16, respectively . The diameter between crests of corruga-
tions of all models was 15 in. with the exception of the model simulating 5-ft-diameter

Paper sponsored by Committee on Surface Drainage of Highways .

8
 9

Figure 1. Sections of models representing (left to right) 5-, 10-, and 20-ft-diameter
structural plate pipes.

(o)

(b)
Figure 2. Structural plate pipe models of 40-diameter lengths; (a) 1:8-scale model of
10-ft-diameter pipe, and (b) 1:2.2-scale model of 5-ft-diameter pipe.
10

structural plate pipe which utilized a diam-

eter of 27. 27 in. The crests of corruga-
tions referred to throughout the paper are
those nearest the axis of the pipe and the
diameters quoted are the actual minimum
inside diameters except in the cases where
results .are related to nominal pipe diam-
eter. This unusual diameter (27. 27 in.)
and model scale (1:2. 2) was calculated to
be necessary to obtain flows with Reynolds
numbers representative of prototype con-
ditions using an available pumping system
with a rated capacity of 100 cfs under a
55-ft head. Fabricated sections of the
models simulating structural plate pipes
are shown in Figure 1. The sections were
assembled and tested in lengths ranging
from 22 to 100 times the respective pipe
diameter. Models of 5- and 10-ft-diam-
Figure 3. Piezome ter s and vcJ.ocity eter structural plate pipes are shown in
p r obes. Figure 2.
Water used in the operation of the models
was supplied by centrifugal pumps and
measured by means of either a calibrated
venturi meter or traverses of velocity
across the pipes. Piezometers located on
the crests of the corrugations (Fig. 3)
were used to observe the hydraulic gradi-
ents. Velocity probes and traversing
mechanisms (Fig. 4) were equipped with
total pressure and static pressure tubes
to obtain velocity and static pressure dis-
tribution data.
II Before beginning a test, a discharge
sufficient to remove air entrapped in the
corrugations at the top of the pipe was set
and instruments used to measure discharge,
F igure 4. Ve locity probes. pressure , and velocity were primed. The
test discharge was established, and all
data desired at that discharge were obtained
without interruption or modification of flow.
The hydraulic gradient was observed. Traverses of total and static pressures across
the pipe normal to the crest of a corrugation were obtained. The temperature of the
water was measured during each test. Flow with a Reynolds number of 5 x 10 6 in the
model simulating 5-ft-diameter structural plate pipe is illustrated in Figure 5.

Figm·e 5. Flow in model of 5- ft - di ameter p ipe, :l l + 5 X 106 •

 11

In determining the slope of the hydraulic gradient, pressure readings near the en-
trance and exit of the test sections were neglected to eliminate the respective effects of
boundary layer development and acceleration of flow. The ;werage velocities. V. the
slopes determined from the hydraulic gradients, S, and the actual diameter between
crests of the corrugations, D, were used to determine values of the friction factor, f,
by means of the Darcy-Weisbach equation. Values of the shear velocity. v, computed
1-
by means of the basic relation, v* = ,,_' %Sg, were used to determine values of a param-
eter termed wall Reynolds number, Rw = (v*k/v). The symbols k and v represent depth
of corrugation in feet and kinematic viscosity, respectively.

STANDARD CORRUGATED PIPE

Although the relative roughness, K/D, of the model of 5-ft-diameter standard cor-
rugated pipe was 0. 00936 rather than the expected value of 0. 0083, the resistance co-
efficient curve, f, versus wall Reynolds number, of the model was similar in shape to
that of the prototype reported by Webster and Metcalf (8) for wall Reynolds numbers
up to 1600 (Fig. 6). The maximum value of the resistance coefficient agreed most
favorably with that interpolated based on the results of the 3- and 5-ft-diameter standard
corrugated pipes. Thus, it was concluded that the material effect of fiber glass on the
resistance coefficient was essentially the same as that of metal and that geometrically
similar fiber glass models would adequately simulate corrugated metal pipes.
Analysis of the Bonneville Hydraulic Laboratory prototype test data indicated that
the maximum value of the resistance coefficient of standard corrugated pipes occurs
at flows with a common wall Reynolds number of 1300 (see Fig. 6). Therefore, appro-

0.14

f--

0 . 12
Oo O klD =0. 033(15"1

0.10
x:::.-~ 'l. o_....,,..- ~
1----

o.o~\~&
•\ -:.?
o ./
~--

oti l1~r-::
0

-- f-
,_ ->-

- --
~I,:!./ _/ ,/D a o.
-
--
0.0B
~ k/D = 0.014 (36"1

- .o.~ "
~-n
_j.--i--·
·-
-~(~ A' y
-
0.06
- A
r ; / D ;' 0.1!"8!
(60')
---- ---·-
~ r--T klD = 0,006 (84 •)
I r--
I I I I
~
0.04 - ---0- NEILL, C. R.

0.02
,---

--
-
---
-- --
STRAUB.LG .. ANO MORR15, H, M,
WE BSTER, M, J., ANO METCALF. L, R,
WES
PREDICTED f BASE D ON

+. :- 0, 188 1 5.50 (" r•

TI° k
1 3.SO;;
3
•10' s 6 1 e 9 l

5 6 7 8 9 I
10'
WALL REYNOLDS NUMBER - ffiw

F'igure 6. Re s istar,ce coefficients vs wa ll He yn olds n umber - standa rd corrugated met al

pipe, full pipe flow.
12

priale velocity dislribulion dala oI both Lhe WES model and the 5-ft- diameter prototype
w >1· s d lo d ve loJ) Lh following mean flow form ula which can I · ns d to r.ompute th e
maximum value of the resistance coefficient of any size of standard corrugated pipe.

Res ista nce coefficients computed by means of the mean flow formula agree most favor-
ably with the maximum values reported by the Bonneville (1) anct me ::samt Anthony Faiis
(2) Hydraulic Laboratories but are approximately seven percent less than the maximum
value reported by Neill (5) for 15-in.-diame ter pipe and that reported by Garde (4) and
Cha mberlain (3) for 12-in.-diameter standard corrugated pipe. Admittedly, the mean
fl ow formula for standard corrugated pipe was developed from limited velocity distri-
bution data (especially in the region of threshold velocities) due to practical considera-

0 , 13
. I ti
,, I I
'::
I
I -
- -- - - - - - -- -- .- - :
-
:
-
O,ll
-

0 "
:-\ \
- - -
:
-
--:
:
=
:
0 , 10
- \ -
::
-
\~
-
--
-=
\

\
I-

-:
I-
::
;: :
O 00
;: I\_ - --
::: '~ -
I-
I-
I =~ -
0 .07
t:
;:
,_ "< 0 0.-11
=
-
-
,_
~--- ........_

0 , 06
t
I-
'----- ---...... ......______
-
:
;: ,-....__ I ::
:
---- ---.'. r----.
I )
:::
I- :
0, 05
--
-
i:

::
:
:
0,04
-
h I ti I ,, I ii
' I Ill 1 11 1 1 11 I -
6
•
DIAM ETER, D IN FT

Q C OMPUT !!!:D ~ y M~ A.!~ FLO W F ORl"1U l A

NEGL EC TING THRESHOLD VELOC IT IE S
• GARDE AN D CHAMB ERLAIN
... NEILL
6, STR AUB AND MOR R IS
0 WEBSTER ANO METCALF

J<'igure 7 . f vs p ipe dirnnete r - s tando.r d corrugat e d pipe .

 13

f:! ' i' ' I '" .. . ,, n I I

I" "
I H ,, 11 I I C

:
'; --, - ,-

0.0256
-
~ -
0 0 256
-\ -
.:
.
- \ .
,- r- -
.
0 0 254
- -
0 0252
~

~
-
\ .
r - r-
- -

c - ,-
,_

-,- -
- e-

,- ,- , --
-
,-..

0 0250
~
\ :
.
:::
~ \ "
£&.ill -
::
-
0.024 8 -
- < 0 ao«
-
=
-
-
\ \ - ~- .
0 02<1 6 - I\
- -
\ - ~
- c-----:=
:
• r\ -
\ --
-
0 024 2
\ ~
- -

0 0240
I-
,::
r-
I"" ~ - :

~
:

"'-
:
- ~
- :.
!:
,_
0.023 8 ""-
I= I'-- .:-
r:::----- ~- -
J
ti ) I It I II"
"
0 0236 _j _j LU

DIAM E T E R, C IN FT

Fi gure S. Manni n g ' s n vs pipe diumete r - standard cotT u2:atc:d pipe .

tions and, therefore, the mathematical expression derived for the threshold velocities
is questionable. If the term 3. 50 (k/ r 0 ) is neglected, the modified mean flow formula
predicts maximum values of the resistance coefficients that agree favorably with those
reported by other investigators for standard corrugated metal pipes ranging from 1 to
7 ft in diameter as shown in Figure 7. This does not imply that the threshold velocities
do not exist in standard corrugated metal pipe but merely that the expression derived
is not adequate and this was expected in view of the lack of appropriate data near the
boundary of this type of pipe. Figure 7 indicates that the maximum or design value of
lhe 1·esistance coefficient of any size of standard corrugated pipe may be calculated by
means of the empirical equation. f "' 0. 124/n°· 42 , where D is pipe diameter in feet.
Values off weTe converted to Ma1ming' s n by means of basic relations and the relation
between n and pipe diamete r (Fig. 8) is satisfied by the empirical equation, n =
0 044
0. 0259/D " • These valu es of the resistance coefficient can be expected at flows with
wall Reynolds numbers near 1300 and are considered applicable for design since values
14

of Rw. encountered in field installations of 12-. 60-, and 96-in . -diameter standard
corrugated pipes flowing full with friction slopes of 0. 5 to 8. 0 percent and water tem-
peratures ranging from 45 to 75 F , range from 550 to 3400, 1250 to 7550 , and 1550 to
9550. respectively. There may be objections to the recommendation that the maximum
values of the resistance coeffici e nts observed in standard corrugated pipes be used as
a basis for selection of design values for all conditions since prototype tests (1. 3. and
4) indicate that the r es istance coefficients decrease with increasing wall Reyno lds num-
bers greater than 1300. Certainly this appears to be merit ed for the cases where the
Rw of flow in standard corrugated pipes is expected to be well above the value of 1300
(the range of Rw where a maximum value of the resistance coefficient is indicated). In
such cases, it is recommended that the results of the Bonneville Hydraulic Laboratory
prototype tests (1) as shown in Figure 6 be used in extrapolating the design values of the
resistance coefficient.

STRUCTURAL PLATE CORRUGATED PIPE

The resistance coefficient curve determined from tests of the model simulating 5-ft-
diameter structural plate pipe (Fig . 9) revealed that the resistance coefficient attained
a maximum value of 0. 111 at a Rw of about 8000 and that f remained constant for Rw
up to 22,000. Values of wall Reynolds numbers, expected in field installations of 5-,
10-. and 20-ft-diameter structural plate pipes flowing full with friction slopes of 0. 5
to 8. 0 percent and water temperatures ranging from 45 to 75 F, range from 5,000 to
30. 000, 7,000 to 43,000, and 10,000 to 60,000, respectively. Thus, the conditions
investigated with the model of 5-ft-diameter structural plate pipe simulate anticipated
field flow conditions adequately. Unfortunately , the limiting value of Rw (8000) was

0.14

0
n
0.12
p V Q 0
0 0
n 0 n )
--
0 / 'm 0
0
., / 0 0
n
0.10
0
0 ~--0 0 0 0
... ~ o.r
0

..,..,. 0 V
,-
~ ~o~Vo
--
Q

--- ----- --
R
0.08 I.ID~ 0.01~6

~
~[)..
0 Ii If" ~1A&
-
A
tJ.
tJ.
t..,, ~i - " "~f
.,.

"
l> A -
~i
A

- -- .,. _ ..- -
0.06
~ -;; ~
A
k/ D
0.00783

~
,__,,,..." R
.., Ill ":r " 'I:!' If
0.04

- I
LEGEND

0,02
- - - - - PREDICTED I BASS) ON
s
~ • 0.188 I ~.96
I~ I ) 1·•
t 1.56-
k
2 3
10•
4 6 7 8 9 1

v• \4 ,( J ,,,.

a I l I 4
I
5
1111 1
67891
I 3 4 5 6 7 8 !:j l
10'
WALL REYNOLDS NUMBER - :tlw

Fi3ure 9. Resistan ce coeff'i cient vs wall Reynolds number-struc tural pla t e pipe, full
pipe f'l ow .
 15

greater than that anticipated initially; and conseque ntly, flows with wall Reynolds num-
bers equal to or greater than 8000 were not possible with the selected models of 10-
and 20-ft-diameter structura l plate pipes and the a vailable water supply syste ms. How-
ever, results obta ined with the m odel of 10-ft-diameter structural plate pipe and wall
Reynolds numbers just below this limit agreed most favorably with that of the model of
5-ft-diameter structural pla t e pipe, and it was concluded tha t the resistance coefficient
of any size of this type of pipe approaches a maximum value and r emains constant for
flows with Rw equal to or greater than 8000. Since an analysis of the r esults of Webster
and Metcalf (8) indicate that the maximum value of the resistance coefficient of standard
corrugated pipes (3, 5, and 7 ft in diameter) occurred at flows with a common wall
Reynolds number, it seems quite reasonable that a similar relati on would exist for
structural plate pipes.
Velocity distribution data of the model simulating 5-ft-dia meter structural plate pipe
in the range of wall Reynolds numbers, where the resistance coefficient was at its max-
imum and constant value, were used to deve lop th e following mean flow formula.

V
v* = "f/8 = 0.188 + 4. 96
(ro)U
Zk
4
k
+ 1. 56 ro

Velocity distribution data of the model simulating 10-ft-diameter structural plate pipe
within the range of Rw near 8000 are satisfied by the m ean flow formula also. Thus,
it is concluded that the mean flow formula can b e used to compute the maximum value
of the resistance coefficient due to the corrugations of any size of structural plate pipe .

0.000

\
'
~ 0008

i
~
\:- -©
*~ 0.007
\
<
0
~
\~

\ ~ \.....--®
~
~
0
~

~ o.ooe
u
§
8
\ '\
\'-I"-.
~
u

~
z
~ \.
~ 0 .00!.
\ ' ~
~
0
f";:,..__
~ "-
~ P=:: r-----_ ~
~ 0.004

--~ t---- ~ f@
,.__
" r--=::::::
O.OOJ;
,o 12 13 14
NOMINAL PIPE. DIAMETtR - FT
·~
,. 17 . ,. 20 2)

Figure l O. Resistance f actor, 6f, attr ibutable to assembly bolt nuts -struc tural
plate pipe.
16
TABLE 1
Assembly bolt nuts which are located
BOLT-NUT RESISTANCE FACTOR, t,.f, STRUCTURAL
PLATE PIPE
on the crests of the corrugations in proto-

t,.f
(v r
CDNa
0. 785D'
types were not simulated in the models
and, therefore, the mean flow formula
does not reflect the added resistance they
would entail. However, H. G. Bossy of
CD= 1.1 a = 0. 0070 sq ft

No. of Pipe Diameter

the U. S. Bureau of Public Roads made a
Plates No. of detailed review of literature concerned
V
Nuts per ll.f
per Nominal Actual ni:::.mptf::.r v with the coefficient of drag of shapes sim-
!ting lm. J llt/
ilar to the bolt nuts and developed a method
4 60 4. 93 50 0. 649 0. 0085 to determine the increment of resistance
72 5. 94 63 0. 621 0. 0068
84 6. 97 77 0. 598 0. 0056
attributable to the assembly bolt nuts of
6 96 7.98 123 0.580 o. 0064 structural plate pipe. The results of
108 9. 00 143 0. 564 0. 0055
120 10. 02 164 0. 549 0. 0048
Bossy's analysis, presented in Table 1
8 132 11. 04 227 0. 537 o. 0053 and Figure 10, indicate that the increment
144 12.06 254 0. 525 0. 0047 of the resistance coefficient, Af , which
168 14.09 321 0.506 0. 0041
10 180 15.11 398 0. 498 0. 0042 can be attributed to the bolt nuts varies
192 16. 13 434 0. 490 0. 0039 with pipe diameter. and that a Af of 0. 0085
204 17.15 470 0. 483 0. 0037
12 216 18.17 575 0. 476 o. 0039 is reasonably applicable for the 5-ft-diam-
228 19.18 616 0. 469 0. 0036 eter structural plate pipe. Adding this in-
240 20.21 660 0. 464 0. 0034
252 21. 22 705 o. 459 0. 0032 crement to the f determined from the m e an
flow formula based on an actual diameter
b.f = increment of resistance coefficient attributable to bolt
nuts. between corrugation crests of 59. 1 in. ,
CD = coefficient of drag,
that recommended by the manufacturer,
N = number of objects (bolt nuts) on crest of corrugations
in a length of one pi:pe diameter. gives an f of 0. 12. The first and only re-
a = projected area of' object in a plane normal to direction ported prototype tests by Neill (5) of a 5-
of flow, sq ft.
D = actual diameter of' pipe between crests of corruga ft-diameter structural plate pipe (within
tions, ft.
v = local veolcity at raid.height of object, fps,
this range of wall Reynolds numbers) in-
V = mean velocity of flow, fps. dicate a maximum constant value of 0. 13
for the resistance coefficient based on a
diameter from crest to crest of corruga-
tions of 59 in. (7). Thus, the maximum value of the resistance coefficient predicted
from the WES model tests agrees favorably with that indicated by Neill's prototype
tests. Additional friction-loss data of'a small model of 5-ft-diameter structural plate
pipe presented by Kellerhals (6) confirm the data of the WES model of 5-ft-diameter
structural plate pipe in the lower range of central Reynolds number. VD/ v (2 to 5 :< 10 5 ).
Resistance coefficients due to the corrugations of structural plate pipes with nominal
diameters ranging from 5 to 20 ft were calculated by means of the mean flow formula
and the actual inside diameters between crests of corrugations as given by the manu-
facturers. The increment of the resistance coefficient attributable to the assembly
bolt nuts determined by Bossy (Fig. 10) was added to the value of the resistance coef-
ficient due to the corrugations to determine the total resistance coefficient of each of
the several sizes of structural plate pipe. The relation between total resistance coef-
ficient and diameter of pipe (Fig. 11) is satisfied by the empirical equations, f =
0. 258/D 0 ' 482 and fn = 0. 320/Dn°" 576 • It is not d that the equalion based on nominal pipe
diameter will yield a value of the resistance coefficient other than that determined by
the equation based on actual pipe diameter. This is required in order that the head
loss computed by the Darcy-Weisbach equation using the nominal diameter and a veloc-
ity based on the nominal diameter and design discharge will agree with that determined
using actual diameter and velocity, i.e. ,
2 5
L V L V~ (Dn)
h1 = f D 2g = fn Dn 2 g and fn = f D

The recommended design value of the total resistance coefficient obtained from the
foregoing equations of Figure 11 is that expected to occur at flows with wall Reynolds
numbers of 8000 or greater (the range of Rw in which f has attained a constant maxi-
mum value and also that to be expected in the field).
 17
0 . 13

o, 12

0, 11
= !,El!.
'· D~~,..

0. 10

_,
. 0. 09

0 00

0 07

0Jl6

DIAMETER IN FT

Figure 11. f and fn vs pipe diameter - structural plate pipe.

DIAMETER IN FT

Figure 12. n and nn vs pipe diameter-structura l plate pipe.

18

Values off were converted to Manning's n by means of basic relations . The relation
of re ·ommencled (k. ign vaht of Manninf s n to pipe diameter (Fig. 12) is satisfied by
lh e mpi r i a l e qu ations n = 0 . 037/ D0 ' 077 and n11 = O. 0416/ D 11°·
121

OTHER CORRUGATED PIPE

Since the depth-to-pitch ratio of corrugations 1 in. by 3 in. is the same as that of
structural plate corrugations , 2 in. by 6 in. , the mean flow formula for structural

0. 11
.J 1111 I I I 'I II II 11 1 1 ,,, , I I I I I I 11 ,,, I I I II L

I _,____ -, -- - -----
-1 ('..
- 1-

-
0. 10
--
--
-
-f- -
\ - -- - - - --
--
- --

'""~""- ----
0.09
I
- _,,..-- (=0 .1725
0 0..i1 1a - -- . ,_ - -
--- 1~ --
0.06
-
--
-
-- ~
"-. -
1 --
~ -
0.07
- -----.., --
- ,_ r---------
--- -- -- --....,...._
::; I I I I r
0,06
111 I
6 '' 8 '
DIAMETER , 0 , I N FT

F igure l]. f v s pipe di ar"eter - l - X 3-in . corrugat ions.

0 .030
µ
,.. I I 11 11 I 111 I 11 I 11 I II 1111 ,, ,, I 11 1111 II I I I I L
' -
-- -- - - - --
--
0,029

--
-
·-- ' I
~ ---
0 .026

,_ ' ~V
,- " : :i
0.0306

0
0 ,075

-
:
--
,_
-- l ~ ..........._ --
0 .027
,:
,...
----, ~ ---
I•
-
-
,.. ----- ----- r---.., ,.... --
0.026 -
,-
,.. -
-- --
--
---
c - - - 1• -- - - --- -- -
'7 I I I 11 11 i i It 11 1 1111 1111 I I I 1111 1111 1111 ,r
--
0.025
6 s
DIAMETER, D, IN FT

F ignrc l4 . Manning ' s n vs pipe diameter- l - X 3 -in . corrugat ions .

 19

plate pipe is considered applicable to corrugated pipe with annular 1-in. by 3 -in. cor-
rugations. Values off determined by means of the mean flow formula are related to
pipe diameter in Figure 13 which indicates that the resistance coefficient of any size
of this type of pipe can be calculated by the empirical equation, f = O. l 725/D 0 "478 •
Manning's n may be computed directly by the equation, n = 0. 0306/ D 0 " 075 (see Fig. 14).
Design values of Manning's n ranging from 0. 0282 to 0. 0262 are indicated for 3- to 8-
ft-diameter pipes with annular 1-in. by 3-in. corrugations.
The results reported herein are believed to be most adequate for determining design
values of the resistance coefficient for each type of corrugated pipe discussed. How-
ever, sufficient data are not available with which the effect of corrugation pitch or
spacing, >.., can be determined. In addition. little is known of the effects of helical
rather than annular corrugations on the resistance coefficient. It is believed that the
need for tests to determine the resistance coefficient of various configurations, includ-
ing both annular and helical , will arise in the near future and it is hcped that efforts
will be directed to determine the importance of these geometric properties on velocity
distribution in the range of maximum resistance, in orde r that a more complete under-
standing of the law of velocity distribution in corrugated pipe can be developed.

ACKNOWLEDGMENTS
The results reported herein are a summary of the research project sponsored jointly
by the Bureau of Public Roads and the Office, Chief of Engineers and conducted at the
U. S. Army Engineer Waterways Experiment Station for investigation of the hydraulic
resistance of structural plate corrugated metal pipe. The author is indebted to K. S.
Eff of the Office, Chief of Engineers, H. G. Bossy of the Bureau of Public Roads ,
T. E. Murphy of the Waterways Experiment Station, and G. H. Keulegan of the Bureau
of Standards (now an employee of th e Waterways Experiment Station) for many helpful
discussions of the test results and review of the analytical methods employed. Special
thanks are extended to Mr. Bossy for his analysis to determine the increase in the
resistance coefficient attributable to the assembly bolt nuts of structural plate corru-
gated metal pipe and for invaluable review of the paper.

REFERENCES
1. Webster, M. J., and Metcalf, L. R. Friction Loss es in Corrugated Metal Pipe.
U. S. Army Engineer Bonneville Hydraulic Laboratory, Rept. 40-1, Bonneville,
Oregon, July 1955.
2. Straub, L. G., and Morris, H. M. Hydraulic Data Comparison of Concrete and
Corrugated Metal Culvert Pipes. St. Anthony Falls Hydraulic Laboratory,
Univ. of Minnesota, Technical Paper 3B, Minneapolis, Minn .. 1950.
3. Chamberlain, A. R. Effect of Boundary Form on Fine Sand Transport in Twelve-
Inch Pipes. Colorado State Univ. Rept. CER No. 55. June 1955.
4. Garde, R. J. Sediment Transport Through Pipes. Colorado State Univ. Rept.
CER No. 56. Oct. 1956.
5. Neill, C. R. Hydraulic Roughness of Corrugated Pipes. Proc., ASCE, Vol. 88.
HY-3, New York, N. Y., pp . 23-44, May 1962.
6. Kellerhals, Rolf, and Bossy, H. G. Discussion of Hydraulic Roughness of Corru-
gated Pipes. Proc., ASCE, Vol. 89, HY-1 , New York, N. Y .. pp. 201-205.
Jan. 1963.
7. Neill, C. R. Closure of Discussion of Hydraulic Roughness of Corrugated Pipes .
Proc., ASCE, Vol. 89, HY-4, New York, N. Y., pp. 205-208, July 1963.
8. Webster, Morris J., and Metcalf. Lawrence R. Proc .. ASCE. Hydraulics Division.
Sept. 1959.
Camber Design Study for Concrete Pipe Culvert
ROBERT C. DEEN, Assistant Director of Research. Kentucky Department of Highways

When a pipe culvert is constructed on or near the natural ground surface

and covered by a highway fi 11 or embankment. the weight of the embank-
ment compresses and consolidates the foundation soil. settlement occurs,
and the culvert subsides and sags below the original grade line. Experi-
ence has shown that culverts which become clogged with silt and debris
become disjointed and faulted. leak, become undermined. and endanger
the stability of the embankment. These. and other damages attendant to
settlement. restrict the flow of water, prevent adequate inspection of the
structure. and may eventually require extensive maintenance or complete
replacement of the structure. Some of this damage may be avoided by
placing the culvert on cambered grades-that is, by installing the culvert
with its flow line somewhat above its normal or desired elevation along
the central portion of its length. This idea anticipates that settlement un-
der the load of the embankment will. in time. lower the flow line to the
desired straight grade.
The project reported in this paper was undertaken to develop a simpli-
fied criterion which would permit the inclusion of camber as a routine de-
sign feature in highway culvert installations. The work was based on the
theory of consolidation and consisted of consolidation tests and prediction
of settlement profiles under proposed embankments, the installation of
these culverts cambered according to the predicted settlement profiles,
and the observance of the settlements during and following the completion
of the embankments. Fairly close agreement between the predicted and
observed settlements invited serious speculation as to the possibility of
estimating camber, within reasonable limitations, from typical void ratio-
pressure curves obtained from typical or average soils.

•WHEN A pipe culvert is constructed on or near the natural ground surface and covered by
a highway fill or embankment, the weight of the embankment compresses and consoli-
dates the foundation soil, settlement occurs, and the culvert subsides or sags below the
original line as illustrated in Figure 1. The amount of settlement depends, of course,
on the fill height or load, the depth of foundation soil, and the susceptibility of the
foundation soil to consolidation. In addition, and because there may be movement of the
foundation soil outwardly and toward the toes of the embankment, the structure may
tend to lengthen. It may also lengthen slightly, however, simply because the distance
along the sag or settlement curve is greater than the straight grade distance. These
movements are damaging to the drainage structure and should be minimized or other-
wise compensated in design insofar as practicable.
Experience has shown that culverts which settle excessively below their original
straight grade frequently become clogged with silt and debris, become disjointed and
faulted, leak, become undermined, and endanger the stability of the embankment. These,
and other damages attendant to setilemenl, restd.ct the flow of water, prevent adequate
inspection of the structure, and may eventually require extensive maintenance or com-
plete replacement of the structure. Some of this damage may be avoided by placing
culverts on cambered grades-that is. by installing the culvert with its flow line some-
what above its normal or desired elevation along the central portion of its length (Fig. 2).

Fupcr s ponsore d b y Connni tte:c, on Culverts and Culve r t Pipe.

20
 21

Pic;urc 1 . Se tt lement of c ulve r t be l ow s t rai1:1ht grade.

--- --- ---

Desired Approximate Stroig; ;r~;-...=,r ~ - - - - __

Figu re 2 . Cumb ere d c ulvert and des ire d straight grade .

This idea anticipates that settlement under the load of the embankment will, in time,
lower the culvert to approximately the desired straight grade.
Some engineering specifications (1), handbooks (2) and treatises suggest the desir-
ability of cambering culvert pipe, but the literature which has been reviewed does not
s e em to offer any generally accepted criterion or formula for predicting even approxi-
mately the magnitude of the camber to be used. Spangler (3) suggests that the proper
amount of camber could be determined rather precisely in advance of construction by
application of some of the present knowledge of soil mechanics, such as the Terzaghi
theory of consolidation (4), but favors a more empirical approach to the problem. While
it is well recognized among soils engineers that extensive consolidation data and foun-
dation settlement analyses are necessary in the design of large and costly structures,
it would not be practical to require these analyses for each culvert installation on a
highway. To avoid such an expensive and time-consuming procedure, a short, fairly
accurate, simple method is desired, whether it be rational or empirical.
The ultimate objective of this investigation , therefore , was to develop a simplified
criterion which would permit the inclusion of camber as a routine design feature in
highway culvert installa tions. In reality, the work was founded on the theory of con-
solidation and consisted of consolidation tests and predictions of settlement profiles
under proposed embankments, the installation of culverts cambered according to the
predicted settlement profiles , and the observance of settlements during and following
the completion of the embankments. Fairly close agreement between the predicted and
observed settlements invited serious speculation as to the possibility of estimating
camber, within reasonable limitations, of course , from typical void ratio-pressure
curves obtained from typical or average soils.

PROJECT DESCRIPTION
Six locations on a section of I-64 near Simpsonville, Kentucky (Fig. 3), were selected
for study. Plans for the proposed highway were inspected, auger borings were made,
and the respective sites chosen on the basis of embankment heights and soil depths avail-
22

~ "'"'
0 0

~
f ¾1/
//4'f}98.M
.,. I
.
•
'
783.16
\ .
C>

"'
983+90 lAl

~ 1057 +35 IFJ

lS

-
To Louisville Sf ee.M, 742.0J
-
To Leain9ton
Scale : 1" = 300'

Figure 3 . Culvert l ocations.

TABLE 1
CULVERT DIMENSIONS AND INSTALLATION DATA

Embank-
Actual Number Foundation Max.
Culvert Diameter Slope ment
Station No . Length of Pipe Soil Depth Camberb
Designation (in.) (%) Heighta
(ft) Sections (ft) (ft)
(ft)

A 983 + 90
Interstate 18 227.25 56 1. 89 3-11 23 0.19
B 74 + 00
Veechdale Rd. 24 169.75 42 0.60 0-5½ 33 0.18
C 1000 + 50
Interstate 30 201.70 50 1. 90 0-6 13½ 0.14
D 70 + 00
Veechdale Rd. 18 150.05 37 4.39 0-5½ 27 0.23
E 10 _,_ 70
Ramp I 36 146.15 36 0.90 2-2½ 28½ 0.26
F 1057 + 35
Interstate 30 214.10 53 0.00 6-6½ 19 0. 13
"Repre sent s average of values measured at center of each pai r of lanes f or 4-lane divided highway
or value measured at cente r of roadway f or undiv ided highway . Includes pavement thickness .
bDid not necessarily o'cc ur at point whe r e embankment he i ght was measured.
 23

able. A summary of culvert dimensions and installation data is presented in Table 1.

All the pipe culverts on this section of highway consisted of reinforced concrete pipe.
Every effort was made to avoid interfe rence with the regular construction of the cul-
verts and embankments other than to establish the cambered grade line elevations.
Preliminary work began on the camber project in July 1958. Rough grading and em-
bankments were compl e ted in August 1959. The bituminous pavement on the undivided
roadway which crosses the interstate route and which overlies Pipes B and D was con-
structed in the fall of 1959 while th e mainline of 1-64 was paved in the fall of 1960.

METHODS AND PROCEDURES

Soil samples were obtained with soil augers at various intervals along the centerline
of each culvert site to establish soil profiles, depths to water table, and depths to bed-
rock . Undisturbed soil samples were obtained by the open-pit method near the center-
line of survey at each culvert site. The pits were de epened until the desired layer of
soil was encountered. In some cases, samples from different levels were obtained in
the same pit. Pit depths ranged from approximately 3 to 7 feet. When the desired
layer was reached, an undisturbed sample was carefully obtained and s ealed, marked
for identification, and transported to the laboratory for testing.
The specimens for consolidation testing were trimmed and fitted by hand directly
into the consolidation rings. Trimming was performed in a moist room to maintain the
original moisture contents as closely as possible. The finished spe cimens were 2. 5
inches in diameter and 1-in. thick. Pressures beginning at 1/~ tons per square foot were
applied in increments, using a load-increment ratio of one. The pressure on any par-
ticular sample was incr ased until it was greater than the unit pressur e to be applied
by the weight of the emba nlunent on the soil in the field. The maximum pressur e for
all tested samples was either 2 or 4 tons per square foot. The resulting void ratio-
pressure curve from each consolidation test was used in the camber computations.
The foundation soil profiles were supe rimposed on the pipe culvert section sheets
included in the highway plans. The depth of soil beneath the culvert flow line and the
height of embankment above the flow line were determined at 24-ft intervals along each
culvert site. This interval was selected because the construction crew chose to set
their batter boards every 24 fe e t, which is the length of six pipe sections.
Using the respective void ratio-pressure curves and Eqs. 1 and 2, the expected set-
tlement was calculated for each of the 24-ft intervals. All embankment material was
assumed to have a unit weight of 120 pcf. Often, in settlement calculations, the dis-
tribution of the vertical stress within the foundation produced by the weight of the em-
bankment is determined by use of influence charts, which are solutions of the Boussinesq,
Westergaard or similar equations (5). However, the depths of foundation soils encoun-
tered in this project were so shallow in relation to the widths of the embankments at the
bas e that stresses produced by the embankment weights diminished very little with depths
of foundation soils. For this reason, the midplanes of the foundation soils were as-
sumed to carry the full stresses produc ed by the embankment loads. Also, because
the foundation soils were relatively thin, the pressure produced on the midplane of the
foundation soil-due to its own weight-was neglected. Total settlements for Pipes A
and F were based on two dominating layers of compressible soil in the profile. For the
other pipes, the entire depth of soil beneath the flow line was assumed to be compres-
sible. The straight-grade elevations origina lly shown on the plans were corrected to
include the camber desired for each ins ta llalion.
As construction of the culverts progressed, elevations were obtained at the 24-ft
intervals within the culverts. Masonry nails were driven into the mortared joints in
the culvert inverts. Elevations were obtained on the nail heads to check the accuracy
to which the culverts were placed and also to provide initial readings before any settle-
ment occurred. Where the culvert flow lines were sufficiently flat to permit a hori-
zontal line of sight, elevations were determined with a level mounted on a special tri-
pod as shown in Figure 4. Readings were obtained on a short section of a standard
level rod as shown in Figure 5. A 6-v hunter's lantern served as means of illumination
within the culverts. Where the grades were too steep to use this technique, the straight
24

Figur e 4. Use o f l evel t o obt a in ele v a t ions within culve rt s laid on 1·el ativel y
f LOt grELdcs.

Figure 5 . Sect ion o f stw1dard leve l rod used in settlement meas ure ment s .
 25

Rod

- - - -- - ----- - -

Figure 6. Sketch illustrating use of transit in measuring settlement within culverts

laid on steep grades.

Figure 7. Short section of level rod used in conjunction with transit to measure cul-
vert settlement.

grade line of the culvert was extended and a hub was driven 2 f eet from each end of the
culvert so that its top was on the grade-line extension. By using a transit, a line of
sight could be obtained which was parallel to the straight grade line. A variation in a
rod reading within the culvert from the he ight of the instrument above the straight grade
line indicated the magnitude of camber or of settlement. This method is illustrated in
Figures 6 and 7 .

RESULTS AND DISCUSSION

From the 12 undisturbed samples obtained at the culvert sit es , 10 fixed-ring and six
floating-ring consolidation samples were trimmed and tested. It was not possible to
perform the floating-ring consolidation test on Pipe E and F samples because they were
26

TABLE 2
VOID RATIOS DETERMINED BY CONSOLIDATION TESTS

Void Ratio
Culvert Sample
Pressure (T/ sq ft)
Designation Number
0 ¼ ½ 1 2 4

A 1 fixed 1. 037 1. 028 1. 022 1. 005 0.968 0.918

1 floating 1. 045 1. 032 1. 022 0.998 0.959 0.900
.2 fixed 0.672 0.659 0.651 0.640 0.625 0. 510a
2 floating 0.608 0.585 0. 576 0.563 0.549 0.535a
B 1 fixed 0.722 0. 712 0.702 0.684 0. 653 0.620a
1 floating 0.765 0.739 0. 728 0.710 0. 671 0.623
2 fixed 0.680 0. 673 0.665 0. 651 0.629 0. 598
2 floating 0.720 0.708 0.697 0.679 0.650 0. 610
C 1 fixed 1. 058 1.009 0.985 0.932 0.864 0.799a
2 fixed 0.933 0.922 0.907 0.859 0.791 0. 727a
2 floating 0. 692 0.675 0.662 0.636 0.600 0.565a
D 2 floating 0.741 0. 717 0.710 0.689 0.648 0. 609a
E 1 fixed 0.783 0. 753 0.736 0.702 0.653 0 . 607
2 fixed 0.846 0.773 0.745 0.700 0.642 0. 583
F 1 fixed 1.107 1. 041 0.997 0.943 0.866 0.784a
2 fixed 0.803 0 . 790 0.777 0.757 0. 716 0.665

Average 0. 826 0.801 0.786 0.760 0. 718 0.672

aExtrapolated v alue s from voi d r atio-pressure curves .

too soft to support the weight of the ring. Averages of the fixed- and floating-ring test
values were used in settlement calculations when available for the same soil. Table 2
presents the void ratios and pressures obtained from each test.
To provide a simplified guide for estimating camber, a nomograph has been pre-
pared. First, an average void ratio-pressure curve was plotted from the average of
all consolidation data accumulated in this study. The void ratio scale was then con-
verted to a settlement scale by use of

{la)

S/D {lb)

where
n J._ _ ,L,...1 - - · - - ..... .. ~..J ,..,. ...... 1 ..... ..,,,,, ........ +
0 lULd.l. t::hpt:;t.,., l,c;U oc:;11,.11,.,1.e,.1..1.J.\..,.U.1.,

D thickness of compressible layer,

e1 initial void ratio, and
e2 final void ratio.

Because foundation soils at depths, the midplane in this case, are subjected to some
pressure due to their own weight, a value for the initial void ratio, e 1 , was arbitrarily
selected as that value corresponding to a pressure of 0. 18 ton/ sq ft, which is equivalent
 27
EXAMPLE
0•20 FT.
to an embankment height of approximately
H•!50FT.
S•l.29 FT.
3 feet. The pressure scale was converted
to a height-of-fill scale by determining the
heights of fill material, weighing 120 pcf,
corresponding to various pressures, or

H = 21 OOO p = 16. 67 p (2)

120
where
p pressure in tons/ sq ft and
H = height of fill in feet.

Because the settlement versus height-of-

. fill curve did include the simplifying as-
...0 .• sumption that average foundation soils
.
0:
were loaded equally prior to constructing
.
"'...
.:
;;. the embankment, a nomograph was pre-
pared as shown in Figure 8. The nomo-
...> ,o graph was prepared by determining the
"'
.
0
OI
• ...
0
,o
best equation for the average void ratio-
..J

.
.: •
..J w
0
0:
• . pressure curve and combining this equa-
tion with the more general equations pre-
0
...:c
~ ..."'
ii:
. viously given. This gave an equation in
which height of fill and depth of foundation
"':c •
i.i
~
i: ~
..J soil are necessarily known and settlement
is the value sought. Examples of camber
calculations are given in the Appendix.
The construction crew placed the cul-
verts so that most of the elevation points
were within a few hundredths of a foot of
the correct values. The maximum error
was a tenth of a foot for a very few scat-
tered points.
As indicated in Figure 9, the cambered
grade line for a pipe culvert placed be-
neath the 4-lane divided highway rose to
some maximum value beneath the embank-
Figure 8. Nomograph for pipe settlement ment for two lanes, dipped slightly due to
under fill.
the reduction in embankment height at the
median strip, and then rose beneath the
other two lanes before tapering to zero
camber at the culvert outlet. Cambered grade lines for culverts beneath the undivided
highways indicated the maximum values to be near the centers of the embankments and
zero values at the culvert ends. No settlement was predicted for the culvert ends be-
cause they would carry very little load. However, some settlement, possibly due to a
horizontal distribution of vertical stresses along the culvert or to disturbance caused
by headwall construction, did occur at the ends.

Cambered Culvert
------
OHired -~;;,i:.,~,; 51,;i;htG-;-od•t-=1- - - - - - - - - - ___________ _

Figure 9. Typical cambered flow line for culvert beneath 4-lane divided highway .
28

In discussing the accuracy of the camber predictions, each culvert will be considered
separately so that varying construction procedures and other factors which affected the
study might be more clearly explained. Except for Pipe B, all embankment cross-
sections shown in Figures 10 through 15 were obtained at the time of the last settle-
ment measurements. The settlement curves do not necessarily indicate the total num-
ber of measurements obtained for a particular culvert, because many of them would

30

;::
~
z Embankment
0
j:: ulverr
0
g
lJJ
_J Foundation Soil
lJJ 10
Bedrock

20

,----10 - 14-58
;:: .o~==:::;;;::::,-- - - - , - - - ---,- ----=',-----=;....;..'--'ir-- - - ,---,------,-- -----:;;,A
~
~ .I
lJJ
~
j .'2
I- •-Nomogroph
I-
)::/ _3L-_ __ J __ __ ~ : - - - -----::!:----4-.~:---..-± - - - . ---;ts,_o- - --;-:7~5- -- ,2~0;;:0.--------;2;-;:2~5
25 50 75 100 125 I I
LENGTH OF CULVERT MEASURED FROM INLET (FT)

Figure 10 . Actual and theoretical settlement curves for Pipe A.

4"'·----,-----....-------,--------.----.------,------r-----,-----,
~ - - - Bllumlnous Pavement
3
I-
LL
- 2
z Embankment
0

i
lJJ
_J
lJJ

·3 -=-o-----=2-=-
o- --....,4½0, - - --Go=----___,,a.,,__ __1.-1ao~- - -,2!,-o--- ---'
,4~0- -- -1.G
__
o__,
LENGTH OF CULVERT MEASURED FROM INLET (FT)

Figure 11. Actual and the oretic al s ettlement curves for Pipe B.
 29

almost coincide and would confuse the sketch. The settlement curve designated as
"Theoretical" in Figures 10 through 15 were obtained by using the void ratio-pressure
data for the soil s ampled at each pipe location and a pplying Eqs. 1 a nd 2. The settle-
ments marked "Nomograph" were obtained using Figure 8.

Embankment

Bedrock

t
1-
z
UJ
~ .11---~-"'r"
.J
I-
I-
UJ
Ill
· 2 0~ - - - --;t
,,.,..5- - -- 5-:fo= - -- --=.,..
= - -- -:-:!o:-::o,------- --'-- -- -.L.-- - - - ' - - -----l..l
<- ,., I 125 150 175 200
LENGTH OF CULVERT MEASURED FROM OUTLET (FT)

Figure 12. Actual and theoretical settlement curves for Pipe C.

3rr------.----..--- - - - . - - - ---r----..------,--- -- -,----,

Bl!umlnous Pavement

20----------L----~---~-------L----~---~-------L---'

I=' .0
IL

\z: ,I
UJ
:::ii
~ .2
I-
I-
~ ' 3 0=-- ---::
20
' ::-- - - " -- - - - ' - - - - - - - - L -- - - - ' - - --......J..-- ---'---'
40 60 80 100 120 140
LENGTH OF CULVERT MEASURED FROM INLET (FT)

Figure 13. Actual and theoretical settlement curves for Pipe D.

30

Pipe A
Curves illustrating the predicted ultimate settlement and observed settlements at
various time intervals are presented in Figure 10. It is noted that the maximum cam-
ber was required at a point near the shoulder of the highway over the outlet portion of
the culvert where the combination of embankment height and depth of foundation soil

2
f-
l>.
Embankment
z
0
f-
~
UI
....J
UI
Bedrock

10-4-58

f-
z
UI
:E
UI
....J
f-
f-
UI
(/)

20 40 60 80 100 120
LENGTH OF CULVERT MEASURED FROM OUTLET !FT)
Figure 14. Actual and theore tical settlement curves for Pipe E.

Embankment

Bedrock

9 -10'58
.o
.I
;:
l>.

f-
zUI
~ .3
UI
....J
f-
f-
UI .4
(/)

.5
0 25 50 75 100 125 150 175 200
LENGTH OF CULVERT MEASURED FROM OUTLET (FT)

Figure 15. Actual and theoretical settlement curves for Pipe F.

 31

was a maximum. Measurements taken on the 9-14-59 date coincided with the previous
values near the center of the embankment but showed further settlement toward the ends
of the culvert. This may be explained by the further addition of embankment near the
inlet and the completion of the embankment covering a haul road near the outlet. A
greater number of measurements was desired but could not be obtained within this 18-
in. culvert because any slight sedimentation within the culvert prevented access.

Pipe B
This 24-in. culvert was installed using a B1 bedding as called for by Kentucky High-
way Department Specifications. The construction of the B1 bedding is similar to that of
the "imperfect trench" method. Loose hay was used as the compressible material in
backfilling the trench. As shown in Figure 11, the measurements indicate a favorable
trend-that is, the settlement curve has approached the predicted curves.

Pipe C
This culvert is under a relatively low embankment and the foundation soil is rela-
tively shallow. It was included in the investigation because of its nearness to other
culverts studied. Figure 12 shows that the inlet portion was laid close to the solid
rock; camber and settlement data are shown for the outlet portion of the culvert. Sig-
nificant settlement was observed at the outlet and near the centerline of survey where
the culvert was close to rock. This is partially explained by the fact that earth-moving
equipment passed over the culvert before the pipe was covered adfquately.

Pipe D
Figure 13 reveals a good comparison between a.c tual and predicted settlement for this
18-in. culvert which was also constructed using a B1 bedding. It will be noted that ac-
tual settlement along the inlet portion of the culvert has already exceeded the predicted
ultimate value. Again, this may be attributed to the frequent pasl;lage of heavy equip-
ment along a haul road over the culvert immediately after construction of the backfill.

Pipe E
This culvert had the largest diameter , 36 inches, in the group and also required B 1
bedding. The foundation soil was rather shallow throughout the culvert site but was one
of the more compressible soils tested. The actual settlement curves (Fig. 14) conform
in a general way with the shape of the predicted settlement curve, but they do not yet
agree in magnitude.

Pipe F
This 30-in. culvert, the first one constructed, was placed on a foundation soil which
was rather uniform in depth. When construction was started, the resident engineer
decided to remove a portion of the undesirable foundation soil and to replace it with a
more suitable material. Settlement calculations were not corrected for this change,
and, of course, this accounts , in part, for the fact that actual settlements have not
been as great as the predicted values. This. fact is illustrated by the curves in Figure 15.

CONCLUSIONS
Insofar as the soils involved in this study might be considered to be typical of many
areas in Kentucky and perhaps elsewhere, it may be inferred that the camber and set-
tlement data offered herein would provide a reasonable approximation of the settlement
expected in many pipe culvert installations . In assuming the soils to be typical, it is
implied that the decreases in the void ratios for each increment of load determined for
these soils are more or less average. On this basis, then, the settlement of the mid-
plane of the foundation soil, which is also taken as the settlement of the culvert, is di-
rectly proportional to the decrease in void ratio occurring within the foundation soil.
A composite expression of the decrease in void ratio in terms of the fill height and depth
32

of foundation soil should provide the best generalization obtainable from the data avail-
able. Il is believed that such a generalization is satisfied by the camber guide, pre-
sented in the form of a nomograph, since it does take into account the initial void ratio
of a foundation soil produced by its own weight above its midplane and also the change
in the void ratio as a result of the additional load produced by the weight of fill. The
nomograph was prepared on the assumption that the foundation soil would have a sub-
merged unit weight of 65 pcf and that the embankment material would have a unit weight
of 120 pcf. More precisely, if the soils involved in this study are assumed to be typical,
the nomograph satisfactorily performs the same operations as the more general settle-
ment calculations with the exceptions that it does not allow for any stress distribution
through the foundation soil, nor does it apply to a compressible layer of soil at great
depths.
Of course, it is recognized that no truly a verage or typical soil exists and, therefore,
the nomograph will yield varying degrees of accuracy (as shown in Figs. 10 through 15)
depending on the variance from the so-called typical soil and its associated void ratio-
pressure curve. It should be remembered that the soils encountered in this study con-
sisted predominantly of silty clays and some clay silts and clays. Sands, gravels, and
nonplastic soils would have consolidation characteristics different from the soils studied
and would be obvious exceptions from the typical soil on which the nomograph is based.
It is implied, moreover, that the field engineer must determine the depth 01 t ounctauon
soil and height of fill expected at each culvert site and make a cursory appraisal of the
soil. Exceptional soils and exceptional depths of soils and fill heights may merit special
investigation. Thus, use of the nomograph should be tempered with judgment.
Although the culverts studied in this project consisted of reinforced concrete pipe,
it may be inferred that the guide developed therefrom would apply equally well to other
situations. The nomograph has been based on Terzaghi's theory of primary consolida-
tion, and the nomograph is thus applicable to those situations in which settlement is
likely to occur by this process. There is no reason to think that the nomographic guide
would not apply equally well to corrugated metal pipe culverts as well as box culverts.
It is suggested that this method of estimating settlement may find useful application
in other situations involving subsidence of embankments. The differential settlement
occurring between bridges and their approach embankments (see Fig . 16) is a serious
problem in highway maintenance (6, 7, 8). On modern roads, this defect has become
a hazard to high-speed traffic, and remedial work is expensive and causes considerable
inconvenience to road users. There are, as yet, no confirming data to show whether
or not the difficulty arises from consolidation within the foundation soil or to show that
it can be attributed largely to volume changes within the embankment material.
A typical example of such a situation is illustrated in Figure 1 7. It will be noted
that the abutment of the bridge is placed on piles which are bearing on firm rock at
significant depth. Generally, there is a considerable depth of relatively compressible
material between the rock level and the natural ground line. It is not unreasonable to
expect that the placement of significant embankment material over the foundation soil
will cause a differential settlement between the approach embankment and the bridge
deck since the embankment can settle as a result of consolidation occurring within the
original ground and the abutment cannot because it is founded on piles bearing on rock.
According to the nomograph presented in Figure 8, differential settlement of approxi-
mately one foot may be expected between the approach slab and the bridge deck. This
entire amount of settlement may not occur after the pavement has been completed and,
therefore, may not be manifestly apparent in the final grade because some of this set-
tlement will, of course, occur during the construction period as the embankment is
piaced. The diiieref1tial settlenierits -which ha,v·e been noted ~t bridge approaches in
Kentucky appear to be typically on the order of 4 to 6 inches. Although the possibility
of volume chiine/\R oc.c.urring within the embankment itself should not be overlooked,
it must be recognized that embankment loadings of as much as 15 or 20 feet on the
natural soil may induce significant settlement. The nomograph presented in this paper
might serve as a guide to estimate the order of magnitude of such settlements, and to
suggest the possible need for special provisions to account for or minimize these un-
wanted settlements.
 33

Figure l6. Settlement of bridge approach.

,,
/1
/1
\\\\
II
--
If \\ I
If \\

/J
,,
,, 1\
\\
\\ I
I
I
,, 1\ I I
IJ \\ r .l -
C::-::
.LJ-------
fl.. '1 \\
--- ___ /L__ __ --1 -- --;-Roc,u~ln,
OIM~
/
--

Figure l7. Example of conditions which might contribute to settlement of

bridge approac hes.
34

REFERENCES
1. Standard Specifications for Road and Bridge Construction. Kentucky Department
of Highways, 1956 (Section 5.11. 3).
2. Armco Drainage and Metal Products. Handbook of Drainage and Construction
Products. Pp. 244-245, 436, 1955.
3. Spangler, M. G. Influence of Compression and Shearing Strains in Soil Foundations
on Structures Under Earth Embankments. Highway Research Board Bull. 125,
pp. 170-177, 1956.
1. Tcrzaghi, Karl. Thecretical Soil Mechanics . .Jotm WilPy ::ind Sons; 1943.
5. Webber, Ray. Description of a Method of Predicting Fill Settlement Using Void
Ratio. Highway Research Board Bull. 173, pp. 80-93, 1958.
6. Jones, C. W. Smoother Bridge Approaches. Civil Engineering, June 1959.
7. Peck, R. B., and Ireland, H. 0. Backfill Guide. Journal of Structural Div.,
ASCE, Vol. 83, ST4, July 1957.
8. Margason, G. A. A Study of the Settlement of a Number of Bridge Approaches on
the Maidenhead By-Pass. Chart. Mun. Engr., Institution of Municipal Engi-
neers, England, Vol. 60, 1963.

Appendix
EXAMPLES OF CAMBER CALCULATIONS
Example 1. 2-Lane Highway

t
I
I
II
Straight Grade
Flow Line

902.82'

-------
900.00'
896.80'
0•20 fl. fDtt•111lntcl br Soundlft9)

Bedrock , Hordpon or Grovel

To Determine Expected Settlement:

Lay straight-edge from 20 feet on D line to 50 feet on H line and read settlement of
1. 29 feet on S line (Fig. 8).
 35

Note: In no case should camber be installed to the extent that a downstream eleva-
tion is higher than some upstream point of el vation. This problem may oc-
cur if a culvert bas a small difference in inlet a ncl outlet elevations. In such
a case, the maximum camber permitted by these limiting elevations should
be installed. Occasionally, the inlet portion of a culvert may have to be
placed on a straight horizontal grade line at an e levation equal to that of the
inlet.

Example 2. 4-Lane Divided Highway

<l.
I
I
I
Straight Grode
Flow Line H•21ft.
1

79184 794 30
789.00'
0~24 ft .

Pipe to bl in1toll1d to
Cambered Flow Line
I
789.0
Stralgh~rade'
Flow Line

To Determine Expected Settlement:

Of centerline of roadway over outlet portion of culvert-lay straight-edge from 24
feet on D line to 21 feet on H line and read settlement of 0. 81 feet on S line.
Of median-lay straight-edge from 18 feet on D line to 17 feet on H line and read
settlement of 0. 52 feet on S line.
Of centerline of roadway over inlet portion of culvert-lay straight-edge from 17
feet on D line to 19 feet on H line and read settlement of O. 54 feet on S line.
Field Verification of Ring Compression
Conduit Design
J. DEMMIN, Armco-Thyssen, Dinslaken, Germany

•IN July 1963, Armco-Thyssen, a joint venture of Armco Steel Corporation, Middle-
town, Ohio, and August Thyssen-Huette, Duisburg-Hamborn, Germany, carried through
live-load and loading-to-failure tests. The test structure was a 7-gage multi-plate
pipe arch of 20-ft 7-in. span and 13-ft 2-in. rise, Armco's largest structure of this
shape on record.
The live-load test was conducted to prove to the German Federal Railway that large
corrugated steel structures are safe for use as conduits and underpasses in railway
embankments. Therefore, the live-load test was to be conducted under the severest
possible loading conditions required by the German Federal Railway design crite1•ia,
considering a saiety 1acto1· oi J. The loading- t.o-iallun: t~::.i. wil.5 Cviiduct~d t .:, p • .:,..,idc
scie ntific data on the behavior of corrugated steel structures under loading conditions
especially to determine under what load the structure would finally collapse and how
this collapse developed. Both tests were conducted on the same test structure. Only
the cover height and the positioning of the load were varied according to the different
test purposes.
Size and gage of the structure were primarily designed for practical considerations
suggested by the test purposes. For general acceptance of corrugated steel structures
by the Federal Railway, it had to be proved that eve n the largest structure designed,
of the most unfavorable shape would satisfy performance requirements. Pipe arches,
in particular, were considered statically unfavorable. Therefore, Armco's largest
pipe arch was chosen as a test structure. Since the cover was low and the live load
was fairly small, the wall thickness was not determined by ring-compression methods,
but by empirical data applying to the structure during backfilling. Thel•efore, the wall
thickness was designed by the "flexibility factor. "
The suggested maximum flexibility .factor is 5. 0 x 105 ; FF = D2/ J. Since the periph-
ery of this pipe arch is 20 fl 7 in. x 13 ft 2 in. = 20711 (see Armco Catalog MP--1663 ),
for the pipe-arch structure D "' 207. In addition, the moment of inertia of multi-plate
wall for 7-gage thickness is given oy J = 0.1080 in. 1/m. and for 8-g~e thickness by
4
J = 0. 0961 in. /in. Therefore , the 7- gage flexibility factor FF= 2072/0. 1080 = 3. 97 x
10 (o. k.), and the 8-gage flexibility factor FF = 2072/ 0. 0961 = 4. 46 x 105 (o. k.). With
5

a special view to the loading-to-failure test and since the same structure was to be used
for both tests, a wall thickness of 7 gage was chosen.

TEST SETUP
Test Structure and Backfilling
The pipe-arch structure-20-ft 7-in. span and 13 - fl 2-in. rise-to which loads were
to be applied, consisted of two rings, each of 8-ft length, which could freely deflect
(Fig. 1). This 16-ft long test structure was completely within the pressure area of the
applied load under the selected cover heights. Additional pipe sections were attached
Lu Lhi::s cent1-=a.1 body. The section 3.t the cpen end ,.1.1 as ~Jso rn~<iP. up of two rings bolted
together, whereas only one ring section w,ls added to the rear which was closed by a
wooden cover and backed up with earth. The pipe sections adjacent to the central body
were only to serve for widening the upper grade surface, thus reducing the danger of
subgrade failure. They were separated from the center body by 4-in. wide gaps to
NOTE: In this pape r kp (kilopond) is equivale nt to kilograru (kg ).
Paper sponsore d b y Committee on Culvert s and Culvert Pipe .
36
 37

Figur e 1 . Test str ucture b efore backfi lling .

Figure 2 . Placement and compac tion of backfill.

permit independent deflection of the actual test structure. Only the lower corner plates
of a ll sections were firmly connected . To prevent soil seepage , the gaps between the
pipe se ctions were cove red with 10-gage corrugated metal strips of 1. 5-ft length.
Backfill material was placed in lifts of 8 in. , with each layer tamped separately
(Fig. 2). Gravel was used as backfilling material and surface vibrators were employed
for compaction. Tamping operations were continuously checked by drop-penetration
testing. A laboratory Proctor test showed a soil density of 107 percent of single Proc-
tor density (see Appendix) .
The test was carried out in the works area of the August Thyssen-Huette plant. An
excavated site that was to accommodate heavy column foundations served as a trench.
The test structure was installed between two strong concrete pillars .
38

Figure 3. .
Inside view of structure.

- wi
Par t i'al view -'th
-- .
measuring elements .
 39

Measuring Instruments
Strain measurements were taken with strain gage strips. Three gages were installed
at each of six measuring points (in the trough, and the crest of the corrugation and near
the axis through the center of gravity of the corrugated profile) in two sectional planes.
They were glued on with the special X-60 adhesive. To compensate for the influence of
thermal expansion, compensation strips were placed near the gage points. To accom-
plish this, gages were stuck into small test coupons of the pipe-arch material. These
were attached to the pipe arch so that they would undergo the same thermal expansion
as the test structure without suffering any strain through the imposed load. The actual

backfilling
backfilling height of cover 3.44 ft.

development determined
from readings
assumed development

Plane B

MaOSlab:

0- - ~- -~, Be~ing
in r/ p. in. Moment
"' "° 10 ,o ormal Force
F-igure 5. Development of normal forces and be nding moments from r eading taken.
40
i--- -- - -- -- 45.10 Ft.- - -- -- - -

cover

i.
A
.1 ~
A

Plan

1 3.44
Ft.

strip

Section B-B
8 I,+=: Ft.-------J~
I

i--- - - - -- - 40
._ !

h- - •-1 -l-,-
8 ' s ub gr ade cushion

- 16 ft. -

Figure 6. Setup for live-load-test.

 Symmetrical Loading Off-center Loading

Pmax = 151, 34 t Pmax = 151,34 t

--- -- - -- - - -- 13, 75

railroad ties

~,....
·11
--, -+-=~---, r- off center position
• ' I
\ ?-, /.. e = 3.44 ft.
\ ~ /~
\\\'=:6~~:::'!!Jf:-=-r'tfr.---....~WJ PmDk : 15l3" t

'2fJ'7" - - - - - - -
1
I--- - -- 23.85 - ------,

Section A-A
off center position

e • 6.89 ft.

Figure 6. Continued .
>I>-
,_.
42

strain was determined by establishing the difference between the measured value and a
base reading taken before loading (Figs. 3 and 4).
Deformation was measured photographically . Measuring lights, with a black dot in
the middle of each bulb, were installed next to and between the strain gage points.
Zeiss-Jena phototheodolites registered the displacements of the dots so that the mag-
nitude and direction of the displacements could subsequently be determined from the
photographs by a stereocomparator. This procedure permitted indication of the move-
ment of measuring points with an accuracy of 0. 02 in. To be able to determine pipe-
arch deformation on the spot at any time , additional gage pins were placed in the crest,
the invert and on the side walls. By means of a theodolite, the displacement of the
leveled points could then be read off immediately.

LlVE - LOAD TE ST
After installation of the instruments required for strain and deformation measure-
ments, backfilling and covering operations were begun on June 18, 1963. During back-
filling and earth tamping, considerable vertical deflection of the pipe arch was noted.
With 3. 44 ft of cover, the horizontal diameter had decreased by 2. 64 in. , and there
was an elongation of 3. 86 in. in the vertical diameter; i.e., the crest was pushed upby
3. 62 in. while the invert settled 0. 24 in. (zero reading: pipe free in trench). At the
same time, there was a considerable increase in the extreme fiber strains and, con-
sequently, the extreme fiber stresses.
Extreme fiber stresses due to backfilling and cover of 3. 44 ft over pipe center (Fig.
5) were in crest point IV 01 = +31, 931 psi, 03 = -39, 299 psi, and in crest point X o 1 =
+28, 759 psi, 03 = -30, 466 psi. To support the load, 8. 53-ft long railway ties were
placed side by side on the surface grade parallel to the pipe-arch axis , covering a

Figure 7. Slabs ready t o be p l ace d on s tructure .

 43

width of 3 x 3. 44 = 10. 33 ft, or about half the clear span of the pipe arch. Thus, the
supporting area was 8. 53 x 10. 33 ft = 88. 11 sq ft (Fig. 6).
Steel slabs from the August- Thyssen steel mill were used as a load (Fig. 7). For
the live-load test, the Munich Central Office of Federal Railways had determined that
50 tons was the most severe load a structure of similar span might have to carry. This
represents the load transmitted by a two-axle railway car, each axle weighing 25 tons.
Considering a safety factor of 3, the total load for the live-load test was to be 150 tons.
This load was to be applied by three independent slab piles placed axially on the pipe
arch and also on one side only, since for arched supporting structures, off-center load-
ing will often constitute the severest condition. For the loading-to-failure test the steel
slabs were also used as a load. As the actual carrying capacity was unknown, a maxi-
mum load of 1, 000 tons based on a computation with the ring compression formula was
planned to be applied for this test. With a supporting area of 88. 11 sq ft, this load
could be imposed only by piling the slabs crosswise.
On June 21, 1963, a cover height of 3. 44 ft, or one-sixth the span, was reached, so
that loading could begin. The steel slabs weighing between 5 and 10 tons, weighed in
advance, were positioned on the ties by a crane. Strain and deformation were mea-
sured at 25-ton load increments. These measurements showed that deflections and
strains resulting from the overhead load were small in comparison to those that had
resulted from backfilling and acted in the opposite direction. To start with, a load of
151. 32 tons was applied axially over the pipe arch (Fig. 8). Until then, no marked
changes in deflections and strains appeared. Results from application of this load
(Fig. 9) were as follows:

Plane 1-downward deflection in crest 0. 374 in.;

Plane 2-downward deflection in crest 0. 339 in.;

Figure 8. Live-load test, test structure with 151,32-ton axial load.

 .;,.
.;,.
Date of reading: 27. Juni 1!J(;3
6l!' Uhr
Time
load in tons -'151
Remarks
reading taken after
151 ton load had re-
..,. mained unchanged
Scale of profil 1:30 <:>
Scale of deflection f:1 for 6 days

measurements in-
dicated in milli- ~
meters

t
--· - - -
I/
~
~

· ~ - -~ . G I • -=--. - ---·
i~ i-4
.~ I

Figure 9. Live-load test, deformation measurement.

 45

Ii ve-load-te st
applied load P = 151, 32 t
readings 6 to 12

Normal Force

Plane A

development determined
from readings
assumed development

,____,.q-,--,,.o,,~q"'",_,,o,, in t/in. Moment

0

~..,,,.,--+.,---,,,,=-~...
10
Normal Foree
12, 2 t/ft.
Figure 10. Development of normal forces and bending moments from reading taken.

Changes in extreme fiber stresses (Fig. 10) in crest point IV 0'1 = -6, 088 psi, O's =
-626 psi; and in crest point X 0'1 = -7, 3 53 psi, O's = -2, 717 psi.

The load of 151. 32 tons was left in place for 6 days, and readings were taken each
day. Both the strain and deflection measurements varied at different times. During
the 6 days and, indeed, during loading operations, there was a shift in soil pressures
which, however, died away after a few days. Thus, practically no further change in
deflection could be noted on the third day. It was also observed that deflections and
strains were not symmetrical, although the gage points were located symmetrically and
46

Figure 11 . Test structure under load of 151.32 tons applied in 3.44-ft off-center
position.

Figure 12. Test st r u cture under l oad of 151. 32 t ons applie d in 6.89-ft off- c e nter
position.
 47

care had been taken to place the load as near as possible over the center. Apart from
inevitable off-center loadings, this development may be traced primarily to non-uniform
backfill material. The deflections caused by backfilling were only slightly diminished
under this load.
After 6 days the load was removed to one side by shifting the slabs (Fig. 11). First
one of the outer piles was moved to the other side, and after that the center pile. Load-
ing was then 6. 89 ft off-center (Fig. 12). Only very slight strains and deformations

live-load test
applied load P = 78, 61 t
readings 6 yo 9

Plane A

-- ----
----,-------
development determined
from readings
assumed development

-------
------"''- \
\
\
\
\
Plane B

Bending
o 0.' CV cµ q, in t/p. in. Momeni
,-....~,.-..,.,.-,..,~ , .
0
Normal force

12, 2 t/p. ft.

Figure l3. Development of normal forces and bending moments from reading taken.
48

were caused by this load shifting. The pipe-arch crest which had moved to the right by
0. 04 in. under the axial load, moved back 0. 12 in. to the left with the load in the off-
center position.

Results of Strain Measurements

Figures 5, 10, and 13 show the results of the strain measurements made in the
course of the live-load test. In some gage points several readings reveal that strain
development along the section height is not linear. This is not in agreement with Euler-
Benouilli 's hypothesis that sections will remain even, which generally is considered true
enough also in the plastic sphere. This strain pattern deviating from linearity may be
explained in that the pipe-arch wall of corrugated metal sheet represents a plane load-
bearing structure consisting of curved half-sections of a cylinder. Since the rigidity
of the pipe arch along the centerline is very small as compared with that across the
axis, the load will be primarily distributed along the ring, and the supporting structure
may be regarded as a curved beam with a corrugated cross-section. Under concentrated
pressures induced by rock in the backfilling material, however, the metal wall may in
places react as a plane load-carrying structure, thus developing localized strains op-
posed to the hypothesis of linearity of strains along the section height.

a st rain gages

Sand 0 -c 0. 16"

Sand 0 -c 0. 16 inch

c==----=- Sand O -c 0.16"

rock l. 2 inch supported again st sliding

Figure 14 .
 49
The same effect also became apparent in tests conducted at the Institute for Statics
and Steel Construction, for the purpose of clarifying this question. An Armco-Thyssen
corrugated metal sheet was submitted to bending stress in a manner shown in Figure 14.
These tests proved that the constantly acting lateral pressure, resulting from the cor-
rugated profile, cannot possibly be the reason for the nonlinear strain development
when using uniform granular material.
Although even localized pressures in the wave crest or the wave trough hardly af-
fected the linearity, lateral pressures resulting from the presence of rock in the back-
filling material would cause strain developments opposed to linearity.
For the determination of stresses and sectional forces from the strains, it was as-
sumed that all strains were within the range of elasticity. Due to the low bending
strength of the pipe arch, the acting bending moments will produce high extreme fiber
strains which may exceed the yield point. Particularly during the placement of fill,
considerable bending moments will be encountered in the absence of support by sur-
rounding soil. Since the instruments for strain measuring were not installed until
erection was completed, the yield development in the respective places could not be
registered. During backfilling and loading operations, stresses induced on the pipe
arch changed several times. Changes of this kind occurring in the plastic sphere· will
generate residual stresses that are superposed on the load stresses. It is not possible
to study the stress pattern accurately, since stresses during erection are unknown and,
furthermore, the stress curve will fluctuate as various loads are being applied or re-
moved. The best results are obtained when the stresses are derived independently
from the strains introduced at each individual load increment without considering initial
stresses. This procedure was followed when evaluating the measurements. Even if it
were possible to register all the influences affecting the strain measurements, a sum-
mation of strains or stresses would not provide much clarity inasmuch as the effects of
the individual load increments would be concealed.
The computed stresses and sectional forces shown in the tables as "stresses from
readings" and "sectional forces from readings" will, therefore, only approximately
represent the forces to which the pipe arch was subjected but will permit qualitative
conclusions as to the behavior of the structure under loading conditions.
In addition to the sectional forces resulting from backfilling and loading, which are
shown in the tables, a rough estimation may indicate the range of sectional forces de-
veloping by erection. The pipe arch was erected by attaching and bolting together pipe
elements of differing curvature, starting from the invert and continuing toward the
sides. Due to inevitable production tolerances when curving the plates, and as a result
of the weight of the structure, the rings consisting of individual sections can be closed
only by pulling the open ends together or by parting overlapping ends.
Since it is impossible to determine the necessary amount of adjustment after as-
sembly has been completed, the rough estimate of stresses during erection of the pipe
arch will be based on an empirical adjustment value of C2 = ±1. 64 ft. In the most un-
favorable instance, this adjustment and the effect of the pipe-arch weight will cause
the following bending moments to arrive at the points marked (Fig. 15):

Figure 15. Se ctional forces resulting from adjustment of ring ends.

 C11
0
Date of reading 1.!l Jvn; 1.!Jf;'3
Time 18!!!?
load in tons ~

--- Remarks Backfilling

and cover uy
Scale of Profile ~JO to about 3/4
rise
Scale of deflection 1 ~S

measurements indicated ~
in mi J limeters ,.,,r

-- ·- --

,_
~
Figure l6. Live-load test, deformation measurement.
 ;,ate of reading:7 21 Juni 1.J(;J
8gy
Time
.,,,,,,,- i load in tons: 0
"-- Remarks:
Base reading prior
for loading test
Scale of Profil 1:30
Scale of deflection f:S

measurements indicated
in millimeters

G ~ ~ . ---- ~
tt
Figure 17. Live-load test, deformation measurement . CJ1
....
 01
N
Date of reading cf Juni 1!JC3
Time 17fil9Uhr
load in tons 151
Remarks readings immediately
after application of
Scale of Profil: "f:.10 load
Scale of deflection: f:1
measurements indicated
in millimeters
1/ ~
0

\
\ v>

-- · - - -

·,
- --= C I - - .- ~ i ...
+~
Figure 18. Live-load test, deformation measurement.
 28. Jvn; 1.9(;3
Date of reading:
7gg Uhr
Time
load in tons -1S1
Remarks
Reading after 17 hours
off- center laoding
1:30
Scale of Profil °'
1-'1
Scale of deflection

measurements in- ~
dicated in milli-
meters

/
/
~ -~ - . ~
-- .-=----·
~

Figure 19. Live-load test, deformation measurement .

Cl
C,o)
 C11

Date of reading: ?8. Jun; 1.!Jr;J

""'
Time
18l..0 Uhr
load in tons
Remarks 0
Reading after
removal of load
Scale of profil -r.-.10
Scale of deflection f:1
_,/
measurements in-
dicated in milli- 1/'
meters

<.,.,

I
./
~
't'-- .--=:::: . --=:---. ---.;;;;;; . ~ =- .....
lo' !
,;-

Figure 20. Live-load test, deformation measurement.

 55

Measuring Lamp

Figure 21. Positioning of strain gage strips and measuring lamp.

Point a

Ma = ± 2,470 Jb-in./in.

Point b

Mb = ± 1,367 lb-in./in.

The stresses thus developed are as follows (the effect of normal force having been
neglected as insignificant):

Point a

min. 2 470
•
max. aa = ± 0.0989 = ± 24, 975 psi

Point b

max. 1,367 .
min. 17
b = ± 0. 0989 = ± 13 ' 822 psi

This rough estimate shows that the stresses in the load position "assembly" may be-
come so large that they must be taken into account together with the loading stresses
under the service load, when considering the stresses effective in the structure.
Deformation measurements are shown in Figure 9 and Figures 16 through 20. The
positioning of the strain gage strips and measuring lamp for this test is shown in
Figure 21.

LOADING-TO-FAILURE TEST
On June 28, 1963 preparations began for the loading-to-failure test. The slabs were
removed and the pipe arch uncovered to the crest. The unloading caused a slight ver-
tical rise of the crest of 3. 47 in. The upper layers were removed for the purpose of
conducting the crushing test with undisturbed and unpreloaded soil in the area of largest
soil pressures, i.e., directly underneath the applied load. Before the new material
was placed, three Heierli pressure cells were installed in backfill in a horizontal place
above the pipe arch (Fig. 22). The center cell was placed 4 in. above the crest under-
neath the center of the loaded area, and the other two were installed at distances of
56

... " .
.,;:-

Figure 22. Installing He ierli pre ssure cells .

Plan

Figure 23. Setup for loading-to-failure test .

 57

,·
I
- ·-t-·-7
. I
. I
I P,na,, = f07!}, 77 t
I
I
I
.

!' AlI
I -i

end co ,·t:r

,ins sect ion [0

keep out backfill

- - -16 h. -- - -8 h.- Section B~B

4•

1--r--1i P-,or9,17 t
1
I I !
I !
>---- - - - - - - - <>--- - A9,2 ft ~ - - t- - - - -- ---<
I
j / Slabs,
~ railway ties

Section A-A

i--- - -- 20'7"- - --
I--- -- - 23.85 ft,,-- - -

Figure 23. Continued.

6. 56 ft left and right of the crest. Measurements are made by pressure gage strips
incorporated in pressure cells. For the crushing test, the backfill was extended at the
shoulders as a further precaution against subgrade failure. This required the addition
of another ring section at the open end of the structure. After the cover height of 5. 15
ft for the crushing test was reached, loading was started on July 2, 1963. For higher
 01
co
Dace of reading : c, Jl./// 1..!J6'J
Time 8!!.• U/,r
.-·-v--
Load in cons 0
~
Pl ane 1 ~ "- Original deformation
prior to loading
Scale of Profile 1: 30

Scale of deformation 1:5

Measurements indicated
in millimeters

~ ·- -~.
\0')·1- ·
Fi gure 24. Loading-to- failure test , deformat i on measurement .
 Date of reading : J. Juli 'f.!16"2
00
Time J> UJ,r
Load in cons 26"0,SZ fo
Plane 1 Remarks : Original deformation
prior co loading
Scale of Profile 1:30
Scale of deformation 1: 1
Measurements indicated
in millimeters

,,')

-- · - - - . --- . ---- .
~
'\ /'
/
" ~ - ~
~t
Figure 25. Loading-to-fai lure test, deformation measurement.
01
CD
60

stability of the slab pile, slabs were placed crosswise for this test, using the same
supporting area of railway ties as in the live-load test. The setup for the loading-to-
failure test is shown in Figure 23.
At the end of the first day, a 260. 52-ton load had been applied. As was the case
during the live-load test, only slight deflections and strains were introduced by this
load. As compared to the conditions before the application of this load (Fig. 24) the
following values (Fig. 25) were noted for the most important deformations, stresses
and soil pressures at P = 260. 52 tons:

Plane 1-0. 26-in. vertical deflection in crest;

Plane 2-0. 27-in. vertical deflection in crest;

lo~<ling-to-failure test
applied load P = 260, 52 t
readings 24 to 28

Plane A

-..:,
---- --,;:------, -- --
- - develo;:iment frorn measured values
- - - assumed development

I~o 1• 1nal Force

(-)
X

/•/

Bending Moment

Plane B

~~"~ MaDslab :

0 OJ q; 4• •~ int/in. Bending-
'--~10,--~,0,--,,:':-0~.,,. 12, 2 t/ft. moment

Figure 26. Development of normal forces and bending moments from reading taken.
 61

Change of extreme fiber stresses (Fig. 26) in crest point IV = -6 , 159 psi = -1, 309
psi; in crest point X = -6, 841 psi = +28. 4 psi; and
Soil pressure at 4 in. above crest-()2 = 19. 34 - 5. 83 = 13. 51 psi.

The 260. 52-ton load was left unchanged overnight. The following morning, a reading
revealed the following slight changes under the same load:

Plane 1-0. 30-in. vertical deflection in crest;

Plane 2-0. 31-in. vertical deflection in crest;

loading-to-failure test
applied load P = 410, 5 t
readings 24 - 3 1 (-)

IV

/•I

Bending Moment

Plane A

/
--- -----
-....;:: --.......-..:::-..c
- - 1-------~---,___.,--
--
_.,...,

- - developm ent from measured values

- - -assumed development

-----,.,
(-)
Normal force

(,)

~ . .Jq-..,--:f:.,,--<\3=--::•.,
0
int/in. Bending -
12, 2 t/ft. mom ent
0- •,O NJ JO ..

Figure 27. Development of normal forces and bending moments from reading taken .
 C)
t,.j

Date of reading: ~- Jv/,' 1.!Jli.J

Time 1~ 2ll Uhr
Load in tons 56'1, 10 fo
Plane 1 Remarks Original deformation
prior to loading
Scale of Profile 1:30
Scale of deformation 1:5

Measurements indicated
in millimeters

,.p

I
,-
~-t I
Figure 213. Loading-to-failure test, deformation measurement.
 Date of reading : 4. Jvl,· 136"3
Time 13so Uhr
Load in tons 8c0 fo
Plane 1
Remarks: : Original deformation
prior to loading
Scale of Profile 1:30
Scale of deformation 1: 10 ---·
Measurements indicated
in millimeters
I
~
I

l
I
~

I
- - ·- --
1

' ~ ~ . ~ .-
I
~
Jt-
Figure 29 . Loading-to-failure test, deformation measurement.
0)
w
 0)

""'
Date of reading : S .Juli 1!16".J
Time 17'!§' Uhr
Load in tons -fO'J.!J. 77 lo
Plane 1 Remarks Crushing test was
stopped at chis point
Scale of Profile 1:30
Scale of deformation 1: 10

Measurements indicated
in millimeters ::!-----

- - ·- - - ' --- . - --- .

~
'
~ /
j_..

Figure 38- Loading-to-fail ure test, deformation measurement .

 65

4.8 2 ft.
gage point gage point gage point~
3 2 I
4"
~~ •
2

t57 m Over height

2

P= 52,66 lo
:;

. 2
7
- - P = 118,41 lo

-
7

2
- P = 175,85 lo

7
- P = 260,52 lo
2

P = 260,52 fo aft e r 13 hrs.

2

P= 294,6 lo
2
-
7
P=321,98 lo
2

7
P= 355,48/o
2 -
1
P= 410,50 lo

• f
2 i---_
-- P'= 410, 50 lo after 15, 5 hrs .

Figure 3l.
66

r
,.
p[kp/cm 2 J gage point gage point gage I point
3 2
- 4"

P=4t.4,80 to
2

P=503,40 to
2

P=527,40to
3

P =561,70 to
J

P=633,84 fo
3

P=689,54 fo
4

P=720,34 to

'
3

P =770,48 lo

Figure 32 .
 67

-..,,.

4.82 :fl:
pl kplcm 2J gage point gage point gage point
3 2 I il 4 11

'l

P=809,30lo

P=846,24 lo

P=875,44 lo

P:898,6010

P:929,7610

Fi gure 33 .
68

4. ~ :ff:
p [kp/crn2) gage point gage point gage point I
t----:::::::::::::t ===- - --,/ 14 11

T
6
5

'
3
2
P=953,47 lo

7
6
5
~
3
2
P=953,47 to after 74 hrs.

7
6
5

'
3
2

P=I000,75 to

7
6
5

3
2
'
P= 1055,59 to

·7
6
5

'
, ]
2

P:1079,77 to

Figure 34 .

Extreme fiber stresses in crest point IV == -5, 021 psi == +156 psi; in crest point X ==
-6, 600 psi == +484 psi; and
Soil pressure at 4 in. above crest-p2 == 18. 35 - 5. 83 == 12. 52 psi.
 69

These changes may be ascribed to consolidation of the soil. Although reduced soil
pressure was measured at the central gage point, pressures at the other point (p 1 and
p3) had increased.
On July 3, 1963, the load was increased to 410. 5 tons. Measurements showed the
following changes, as compared to the condition at P = 0:

Plane 1-0. 59-in. vertical deflection in crest;

Plane 2-0. 60-in. vertical deflection in crest;
Extreme fiber stresses (Fig. 27) in crest point IV= -10, 184 psi= -3, 001 psi; in
crest point X = -11, 734 psi = -2, 205 psi; and
Soil pressure at 4 in. above crest-p2 = 23. 90 - 5. 83 = 18. 70 psi.

The gage pins observed by the theodolite and the measurements of soil pressure
revealed a slight eccentricity of the load, which again had to be ascribed to inevitable
off-center loading and nonuniform soil. As the slab pile became higher (approximately
2. 46 ft/100 tons), the danger of inclination increased. Throughout the test, however,
direct deformation measurements and soil pressure readings evaluated on the spot per-
mitted an estimate on the amount of eccentricity, which could then be offset, as re -
quired, by stacking the slabs accordingly.
On July 4, 1963, the load was increased from 410. 5 to 953. 74 tons. From above
510 tons, deformations increased considerably (Figs. 28-30). Whereas a 0. 31-in.
deflection in the crest had been measured under a load of P = 260. 52 tons, the deflec-
tion increased to as much as 1. 12 in. under a 561. 70-ton load and to 3. 43 in. at 820
tons. Up to a 561. 70-ton load, soil pressures in the plane 4 in. above the crest showed
a larger increase at the outer measuring points 1 and 3 than at the central point 2
(Figs. 31 and 32). From 561. 70 to 929. 76 tons, soil pressure at the central gage point
increased faster than on the sides. Soil pressures at points 1 and 3 indicated and un-
stable behavior of the slab pile (Figs. 33 and 34). As it was expected that the pipe arch
would soon collapse and there was a danger of the high stack destroying the measuring
instruments when falling down, the strain gages were removed at P = 689. 54 tons, so
that after that no strain readings were taken.
With P = 689. 54 tons, readings were as follows:

Plane 1-2. 06-in. vertical deflection in crest;

Plane 2-3. 11-in. vertical deflection in crest;
Extreme fiber stresses (Fig. 35) in crest point IV= -18, 874 psi= -5, 291 psi; in
crest point X = -23, 084 psi = -7, 766 psi; and
Soil pressure at 4 in. above pipe-arch crest-p2 = 47. 22 - 5. 83 = 41. 39 psi.

Under a load of 850 tons, two inward bulges began to develop on each side of the
crest (Fig. 36). Atthat stage, the one on the right was about 11. 8 in. and the one on
the left 5. 9 in. deep, as measured radially. When darkness set in, loading had to be
interrupted at P = 953. 74 tons. Since a collapse seemed imminent on account of the
inward bulging, the pipe was watched throughout the night so that the development of a
possible collapse might be studied closely. The large increase in deformations noted
toward the evening, which caused the pipe arch to continue deflecting for a short while
even after loading had been stopped, came to a standstill in the course of the night.
On the next morning, it was noted that the first layer of slabs was resting firmly
against the soil as a result of settling of the ties and sagging of the slabs. Through
this, the loaded area had increased from 8. 53 x 10. 33 = 88. 11 sq ft to approximately
16. 4 x 9. 84 = 161. 4 sq ft. These and the earlier consolidations may be regarded as
the reason why settlements and deformations died down during the night after a period
of sharp rise. When loading was continued on July 5, 1963, the influence of the en-
larged loaded area was notable. Although the soil pressure at gage point 2 remained
unchanged under a load increase from 1,000.75 to 1,055.79 tons, it rose on both sides.
Under a load of P = 561. 70 tons, an irregular increase of pressures had already been
observed, particularly at the outer gage points. By the time 1,079.77 tons had been
applied, this development had reached such unfavorable effects that the soil pressure
70

loading-co-failure test
applied load P = 689,54 t Normal force
readings 24-37 (-)

IV

m ( •}

Bending Moment

\ Plane A
\ /
'' '
-::::::::::
-----=-- -=-.....1..---::::::....----
/
-- ----
- --development from
//
/

measured values
--- assumed development

Normal force

(-}

II

IX /IJ
I
I\I
( •J
Bending Moment / I
, I
V IJI I I
I I
\ \ Plane B
\.\ I I
,~ / /
~~~ -------
-_ - ___ VIL
__ _
_-_
✓/-
__..--,cMoOslob
--- :
✓
0
q, q, o,, q, in t/in. Bending-
'---',.~...c,o~,i,,,o----,,o 12,2 c/ft. moment

Figure 35. Development of normal forces and bending monents from reading.

at gage point 1 was nearly double that at point 3, which suggested a further loss of
symmetry. Deformation measurements, however, gave no indication of imminent
collapse. Even the bulge-shaped deformations did not increase much. Thus, there
was a risk that the slab pile, which had reached a height of approximately 28 ft and
was about 5. 25 ft above the surrounding terrain, would tumble down before the utmost
carrying capacity of the pipe arch could be reached. This would probably have dam-
aged the two cranes employed for stacking the slabs (Figs. 37 and 38). The applied
 71

Figure 36. Inside of pipe arch with bulge-shaped deformations on eiGher side of crest .
Center section of structure clearly deflected against adjacent rings.

load of Pmax = 1,079. 77 tons and measurements taken so far seemed to give ample
evidence; therefore, it was considered not necessary to continue loading until the pipe
arch collapsed, which would have been dangerous under the high load.
On July 6, 1963, the slab pile was removed by the cranes and on July 7, the un-
covered pipe arch was examined (Fig. 39). The bulge-shaped deformations observed
from 850 tons upward were of a plastic nature (Fig. 40), as was the deflection in the
crest line parallel to the axis.
Although the center section of the structure was free to move independently from
the outer parts and its length of 16 ft had been so selected that it should be completely
within the pressure area of the load, plastic deflection near the center was much larger
than toward the ends. The bulges always followed the longitudinal seams, even where
these were staggered in the two rings of the center section. Near these bulges the ring
sections were bent and the plates shifted against each other. The connecting bolts were
deformed to an extent that some had been sheared off.

Results of Strain Measurements

Figures 26, 27, 35, 41 and 42 show the normal forces and bending moments for the
various load increments as measured by the strain gages. As was done accordingly
when measuring deflection, the strains existing after backfilling were disregarded; in
other words, base readings of strains were taken as loading began.

Results of Deformation Measurements

Deflection readings have been shown separately for the structure after backfilling
and for the loading conditions, as was done for the live-load test. Figure 24 shows
 ~
·n Nl

\
\
\_\

Figure 37 - Loading-to-failure tes-~, application of Figure 38. Loading-to-failure tes t with P 1,000 tons .
load by magnetic crane.
 73

Figure 39. Test structw'e w1covcrcd after ma.ximwn loading of Prna.x 1,079.77 tons .

Figure 4o. Plastic deformations apparent in lillcovered structure.

74

Loading-to-failure test
applied load P = 175. 85 t
readings 24-27
(-)

IV

,Plane A

- development from measured values

--· assumed development

(-)
,:

(•/

Bending moment

,Plane R
I

_...,_,_"'=====~v~11.c.----::
· :::=;::~~
0,,:----•:!<~---;i~,
0'-----,,qc--,-:f: 'in t / in, Bending
30 ,o
12, 2 /ftmoment

Figure 41. Development of normal forces and bending moments from readings taken .

deflections during placement of fill and new cover up to a height of 5. 5 ft above center.
Figures 25, 28, 29 and 30 represent the newly introduced deformations for the various
load increments. As for the live-load test, these readings do not include the deflections
resulting from backfilling. The actual total of deflections from the beginning of backfill
placement becomes evident when superposing these deflection figures on Figure 24.

Results of Soil Pressure Measurements

Soil pressures were measured at three gage points on a plane 4 in. above the crest.
One of the gage points was located in the load center directly above the pipe-arch crest,
 75
_ _ _ _ ___,, Normal force

(-)
loading-failure test
applied load P = 561, 7 t
readings 24 • 35
IV

l Bending Moment

_ development from measured values

--- assumed development

_ _ _""-.'.No rma l force

-,,.q,-q,.,_,___.,q,c---1q, in t / in. Bending·

.......
0

,_..,,.,,---,-!::---:c::-----:,
0 0 30 0
12, 2 t/ft. moment

Figure 42. Development of normal forces and bending moments from reading.

and the others at a distance of 6. 56 ft on either side of the center. Soil pressure read-
ings are shown in Table 1 and have also been represented in a graph for further clarity.
The pattern of soil pressures at the outer gage points, which s hows higher values some-
times on the right and som etimes on the left sides, resulted from diffe1·e nt loading ac-
cording to the measured soil pressure. As soon as readings at one of the outer gage
points showed higher values, more load was applied on the other side to prevent in -
clination of the slab pile. Values shown are metric measures.
Computation of Average Distribution of Soil Pressures. -The soil pressure distri-
bution is assumed lin ear a long the height h = 4. 82 ft. From the determined values p0
and Pu the pressure distribution is given by:
76

TABLE 1 p
Po = F
SOIL PRESSURE
where
Soil Pressure
Applied Load (kg/sq cm) P applied ·load,
(t) F = loaded area 8. 53 x 10. 33 =
Point 1 Point 2 Point 3 88. 11 sq ft, and
Pu measured value.
1. 57 ma 0. 32 0.41 0.25
52.66 =P 0.45 0. 73 0.49 CONCLUSIONS
118.41 = P 0.65 0.97 0.63
The test described in this report con-
175. 85 = P 0.81 1. 15 0.78
ducted on an Armco-Thyssen multi-plate
260. 52 = P 1. 15 1. 36 1.07
260. 52 = pb
pipe-arch conduit of 20-ft 7-in. span,
1. 24 1. 29 1. 17
13-ft 2-in. rise and 7-gage wall thickness,
294. 60 = P 1. 36 1. 39 1. 27
showed the following results:
321. 98 =P 1. 48 1. 45 1. 37
355.48 = P 1. 68 1. 54 1. 46 1. With a cover height of one-sixth
410. 50 = P 1. 92 1. 68 1. 76
the span = 3. 44 ft and a loaded area 8. 53
410. 50 = pc 1. 97 1. 64 1. 85
ft wide and 10. 33 ft long = 88. 11 sq ft, the
410. 50 = pd 1. 98 1. 63 1. 95
pipe-arch-soil structure proved capable
444. 80 = P 2.12 1. 75 2.05
of carrying a load of P = 151. 32 tons ap-
503. 40 = P 2. 31 1. 98 2.24
plied both axia lly and off-center showing
527.40 = P 2.45 2.07 2.39
but slight deformation (0. 386 in. = 1/640
561. 70 = P 2.67 2.23 2.05
of span).
633. 84 = P 2.10 2. 73 2.80
2. With a cover height of one-fourth
689. 54 = P 1. 40 3.32 2.90
the span and the same axial loaded area
720. 34 = P 1. 23 3.68 3.00
a _load of 953. 75 tons was applied and,
770.48 = P 1. 48 4.17 2.64
with an enlarged loaded area of approxi-
809.30 = P 1. 75 4.41 3.37
mately 16. 4 x 9. 84 = 161. 4 sq ft resulting
846. 24 = P 2.15 4.68 3. 83
from settlement, a load of 1, 079. 77 tons
875. 44 = P 2.55 4. 80 4.07
could be reached in this test without the
898. 60 = P 2.83 4.98 4.00
pipe arch being crushed.
929. 76 = P 3.80 5.24 2.34
953. 47 = P 5.52 5. 58 2.64
953. 47 = pe
A comparison with the ring compres-
6.97 5. 58 3.63
sion method may seem of interest in this
1000. 75 = P 7.59 5.88 3.88 connection. ...4.... s is knO".V!l, t h P rlt1torn,i ni::l -
1055. 59 = P 8. 63 5.88 4.77
tion of load-carrying capacity by this
1079. 77 = P 9.29 5.92 5.34
theory is based alone on compression in
aCuver he:;lgll~ . a.~~--.
J-U..l,t::!.L
,r r
.l..J • .,) hT . the ring and the s eam strengths, as de-
bAfter 13 hr. eAfter 14 hr. rived from actual test data on bolted
CA:fter 4.5 hr . seams . For 7- gage multi -plate and 4
bolts/ ft the s e am s tr e ng U1 is 93, 000 lb/ ft
(see Armco Catalog MP-1663). The maxi-
mum load is determined as follows:

Table 2 shows the determination of average pressure distribution at the outer and
centrally located pressure cells. The pressure drop at the outer cells was 68 percent
that at the center cell 66 percent, the average being '

68 + s: ~ 68 = 67. 33 %.

On the basis of this load distribution the loaded area above the pipe-arch crest may
be determined. '
 77
M F1 = 10. 33 X 8. 53 88. 11 sq ft
~(l) 0
lf'>MLnlf'>OCNO>OOt-
COt-t-t-t-COLnlf'>Ln
0.
c.)
0.
cicicicicicicicici
<] Fl 88 . 11
F2 = 1 - 0 . 673 3 0. 3267
269. 70 sq ft.

Furthermore,
M CN
r£ F2 = (8i~3 + 2x) x (10. 33 + 2x) =
(l)
1:: . . . ... . . .
.,......,.....MOOMMOOO
'<!'COl:-Ln'<!'lf'>O>Ln'<I'
(l) I
c.) 0 .,.....CNM'<l'LnLC".llf'>COt- 269. 70 sq ft
0. 0.
<]

following
II M
M
(l)
.µ
0.
::l
. . .
Mt-Lnint-t-MCNOO
. . . .
coin'<!'.,.....LnO>COLn'<I'
. . x = 3. 51 ft at 4. 82-ft depth .
;J I
.,.....CNM'<!'inCOLnOOCO
0 0
0. 0.
<]
At crest level or 5. 15 ft below surface,

CNMinOOOMt-OOCN 1 3 51 3.75ft.
X = · X 5. 15
mcimci,....;o::ic-:ii:--=~ 4.82
.,......,.....CNCN.,.....s:t'CNCO

The total loaded length of the structure is

MM.,.....O>inLnCNO>CN
L = 8. 53 + (2 X 3 . 75) = 16. 03 ft.
mcimcrimi:--=,....;cim
.,......,..... ..... CNCNMCN'<t'

This shows that the test structure of 16-

ft length is completely within the loaded
area.
s:t<OOt-t-CNl:-OMt- According to the seam strength chart,
i:--:O'lNLnMNOOO~
,-f,-f(NM'<t's:t<in
the maximum load the structure can carry
will be 1,273 tons (metric tons), derived
as follows:
Pmax = 93,000 x 16 x 2 x 2,976 , 000lb;
less dead load of 20. 56 x 16 x 5. 15 x 100 =
.... . .. . .
,-fs;t<QQO.-;MOO,-f
LnOCOOOOO>s:t's:t'M 169,414 lb - leaving for the imposed
1""""4 1""""'I N 1""""'I ....-t M CO
load, 2,806,586 lb , or 1,273 metric
tons.

s
c.) LOO, 0 in in O O O 0
With 1, 079-ton loading , this ultimate
,....;mci,....;i:--=o::icric,;cri load was nearly reached in the test . The
0 Cl'
o. rn CN M Ln CO t- 00 O> ,-f CN
,-( ,-(
safety factor of 4 recommended for the
"p. determination of wall thickness by the
~ ring compression method is thus fully
insured for the safety of the structure
0 against collapse.
~ When 850 tons had been imposed, the
first signs of overloading appeared. Should
78
TABLE 3
AVERAGE VALUES FROM TENSION TEST

Wall Test Taken Yield Stress Tensile Stress

0
1Elongation
Thickness from ~F (lb/in.) B (lb/in.) (%)

Crest 54,447 61,302 17. 5

1 gage
Flank 44,694 53,252 29.5
Crest 52,228 58,443 23.5
5 gage
Flank 47,221 55, 115 35.6
Crest 55,442 64,360 21. 4
7 gage
Flank 45,870 58,600 29.7
Crest 51,460 58,785 22.2
8 gage
Flank 49,639 61,018 30.0

ARMCO MULTI-PLATE PROFIL NR. S 32

FOR COUNTRYSIDE ROADS
STANDARD CLEARANCE PROFILE
WIDTH OF CARRIAGEWAY= 16 1 5"

Scale 1 : 50 Metric System

Periphery 279 ~ = 22,68 m

27.58"

2x 18'Jt + 1x 15$
.68' _1 6 I 5" 1!l.6&'
7. B8" 7,PS'
23 I 5n

Figure 43.
 79

Figure 44. Special profile S 32 during construction .

these be eliminated, this would leave an actual safety factor of SF = 4 - 1, 273/850 =

4 - 1. 5 = 2. 5. Thus the loading-to-failure test proved again that the ring compression
method is well suited for designing corrugated steel pipe.
In consequence of this test result, a 213-ft long king-size multi-plate pipe arch of
23 . 42-ft span, 22. 30-ft rise and 279rr circumference could be successfully installed in
Germany under the Autobahn between Butzbach and Siegen. This is believed to be Europe's
largest corrugated pipe to date (Table 3, Figs. 43, 44).

ACKNOWLEDGMENTS
This test was conducted under the scientific direction of Professor Dr.-Ing. Dr.-lng.
h. c. Kloeppel, Darmstadt Technical University, Germany. This report is based on the
test report made by him. The computations and measuring results contained in this
paper were taken from that report. All strain measurements and tension tests were con-
ducted by the Institute of Statics and Steel Construction headed by Professor Kloeppel.
Deformation was measured by Dipl. -Ing. E . Jacobs, Essen Engineering College .
Measurements of soil pressures were made by the Weil/Rhein branch of Ernst-
Mach Institute.
Tests on backfilling material were made by the Institute of Soil Mechanics headed
by Professor Dr. -Ing. H. Breth, Darmstadt Technical University.
Operations were responsibly directed by Armco-Thyssen, Dinslaken.
The test setup was designed in conjunction with the German Federal Railway
Authorities.
80

Appendix
TESTING OF MATERIALS USED
Backfilling Material
Sandy gravel was used as backfilling material for the pipe arch. Its single Proctor
density at an optimum moisture content of 6. 8 percent was determined to be 120 pcf.
The results of the three axial pressure tests indicate a friction angle of 37. 5 deg for
the sandy gravel at this density.
During backfilling the compactness obtained at the 7 points was determined by the
calibrated sand method. This showed an average dry density of 128 pcf, which means
that by compaction of fill in 8-in. lifts with Losenhausen AT 200 surface vibrators, a
compactness of 107 percent of the single Proctor density was obtained. The results of
the drop-penetration test with 70 to 90 blows for 8 in. of penetration depth also indicate
the good compaction of the fill.

Tension Tests on Conduit

Test Specimen. -Corrugated multi-plate sheet of different gages as per the com-
pany's delivery program, but not curved vertical to the direction of corrugations.
Material. -MU St 34-2 steel plate, cold worked by pressing the rolled shape and
hot-dip galvanized consequently.
Tension Test. -Six proportional test bars from each specimen, i.e., four from the
corrugation crest and two from the flank.

Discussion
M. G. SPANGLER, Research Professor of Civil Engineering, Iowa State University ,
Ames-This is an excellent paper; a scholarly and well-written report on a well-con-
ceived and conducted full-scale experimental demonstration project in the field of loads
and supporting strengths of underground conduits. It is a particularly noteworthy con-
tribution in this field because it chronicles the change in shape of a pipe-arch structure
".lrotarl ...... .t"'.._, ...... hu
.....,...., ... ....,.....,_ 11nnn ,._,J ua-rtiro'll lno:1rlo
• ...., ......... ....,_ ...... ...,_...,....., <:inrl l".lto-ro:il
................................ .o.".l'Y"th
...., ............. ...., .................. n-ro.oC!11'Y"OC'.'
p ... .._,...,...,......... ........... 011o::1ntito:1Huo.
~
'l'Y"o
~".lt<:J .........
.... - ............................ ._, ..,.,_.,_ .._, n'Y".0.-
.t"' ... ..._,

sented which show that the deformation of a pipe arch under vertical load follows the
same general pattern as that of a circular flexible conduit; that is, the vertical dimen-
sion shortens and the horizontal dimension lengthens, thereby mobilizing the lateral
support of the side columns of soil. The writer has always assumed this to be true but
this is the first documentation of the facts which he has seen.
The author states that the live-load test was conducted under severest possible con-
ditions as regards the railroads' desires for loading on the structure and considering
a safety factor of 3. However, from the standpoint of structural performance of the
conduit, it is the writer's opinion that the installation was unusually favorable. It is
difficult to imagine an environment for a flexible conduit installation which could be
more favorable with respect to deformation of the pipe, the performance characteristic
most frequently in evidence when a structure of this kind gets into structural difficulty.
Flexible conduits, particularly those of larger radius, derive their ability to sustain
vertical load almost wholly from the restraining influence of the soil backfill at the
sides. The more strain-resistant the sidefill soil, the less will be the deflection of
the conduit and vice versa. To visualize this fact, imagine a structure of the type and
size used in these experiments, installed in such a way that there was no soil in contact
with the sides, and therefore no lateral pressures acting on the conduit (Fig. 45). Ob-
viously this imaginary structure could carry only the merest fraction of the vertical
load which the actual structure successfully carried.
 81

Figure 45. Imaginary pipe arch with no lateral pressure .

Now imagine further that the sidefill soil consisted of a highly compressible low-
density material such as a uniform grain-size silt of high moisture content. The de-
flection of the structure would be nearly as great and its ability to carry vertical load
nearly as limited as in the imaginary no-lateral-pressure case illustrated. These
imaginary situations are cited to emphasize the fact that the structural performance
of a flexible conduit is directly dependent on the strain-resistant quality of the sidefill
soil, and there is a tremendous range of soil quality between this very poor imaginary
material and the very excellent sandy gravel used in the experiments. The physical
properties of the conduit wall-that is, the gage of metal, depth and spacing of cor-
rugations, modulus of elasticity, etc. -are relatively minor contributors to resistance
to deformation and ability to carry vertical load. The structural performance of flex-
ible conduits cannot be predetermined without a reasonably precise statement concern-
ing the kind, quality and extent of the side columns of soil which play such an important
role in supporting the structure. It is not sufficient to say merely that the sidefill soil
should be "of good quality" or "thoroughly compacted" or some similarly vague de-
scription.
The quality of soil from the standpoint of its effectiveness in minimizing deformation
of flexible conduits can be expressed in terms of the "modulus of soil reaction" (3, 8),
whose units are lb/ sq in. It is somewhat similar to modulus of elasticity of elastic -
materials, except that it appears to involve a size-factor. Present knowledge, still
very imperfect, indicates the following relationship:

E' = er

in which
E' modulus of soil reaction, psi;
r radius of conduit wall, in. ; and
e modulus of passive resistance of soil, psi/in.

The modulus of passive resistance is a quantitative expression of the relationship

between strain of the soil and pressure exerted by a body pushing against it. This mod-
ulus is similar to Westergaard's (6) modulus of subgrade reaction, in his analysis of
stresses in concrete pavement slabs; and to Cummings' (2) modulus of foundation, in
his analysis of the stability of foundation piles against buckling under axial load.
The backfill soil used in Dr. Demmin's experiments was of extremely high quality
for the purpose of minimizing deformation of the conduit. It consisted of a sandy gravel
82

material which was placed in lifts of 8 in. and each layer compacted with surface vibra-
tors. Laboratory and field tests indicated an average dry density of 128 pcf or 107 per-
cent of single Proctor density. The angle of friction was 3 7. 50 deg; a very high-strength
material. It is apparent that this backfill material is closely comparable to that placed
at the sides of the classical Cullman County, Alabama (5) installation of 84-in. circular
metal pipes wherein the pipe deflection was negligible. It is a kind of material which is
completely unavailable in many areas, or if available, only at very high cost.
The modulus of reaction of the Cullman soil has been estimated to be in the neighbor-
hood of 7, 980 psi (4). In contrast, several installations of circular pipes have been
observed in which the estimated modulus of soil reaction was less than 300 psi (4). This
illustrates the wide range of sidefill soil restraint which may actually develop depending
on the quality of soil and the manner of its placement and compaction. There is also
evidence to indicate that even where high quality soil sidefills are provided, they must
extend laterally for a considerable distance to be fully effective. A number of situa-
tions have developed in which excessive deflection of circular flexible pipes could be
attributed to the fact that the side columns or berms of soil were very limited in lateral
extent. A rule of thumb in this regard relative to actual field installation is to provide
side columns of good quality, well-compacted soil for a distance on each side of the
structure equal to at least twice its horizontal dimension.
The wide range of possible values of the modulus of soil reaction encountered in
actual flexible conduit construction, accounts very largely for the wide range of per-
formance of these structures with reference to deflection under load. A survey of 239
corrugated steel culverts (4), conducted in 1943 by a leading manufacturer of this type
of structure, indicated a range in deflection from -5. 0 to +12. 1 percent of nominal di-
ameter. Other observers have noted similar results, though on a less extensive scale.
This characteristic of structural performance points up the need for research in this
area to evaluate and identify the strain-resistant characteristics of soil materials in
terms of determinable properties, such as mechanical analysis, Atterberg limits and
density. Watkins (9) has contributed a great deal to our knowledge in this area by his
work with the Modpares Device, but additional studies of the actual performance of
structures in relation to sidefill soil environment are sorely needed. It is suggested
that much value would accrue from an extensive detailed record of flexible conduit in-
stallations which would include not only the physical details of the conduits, but also
facts concerning their installation, such as the character of bedding, and the manner
of placement and lateral extent of the sidefills . The soil should be carefully identified
in each case and its density determined. Then accurate records of conduit deflections
over a period of several years would make it possible to determine empirically an ap-
propriate value of the modulus of soil reaction for a variety of soils within a practical
range of densities. The manufacturers of flexible metal pipes and pipe arches would
be ideal agencies for collecting such information because of their worldwide contacts
with installation of these kinds of structures.
An important phenomenon reported in the paper is the initial deformation of the
structure as the sidefill soil berms were built up and compacted. During this stage of
construction, the deflection of the pipe arch was opposite in direction to that caused by
vertical load in later phases of embankment construction and, in effect, was a "pre-
stressing" operation. The amount of reverse deflection was nominal in this instance
and well within that which the structure could tolerate. The relatively low magnitude
of this initial reverse deflection is thought to be associated with the very high strain-
resistant quality of the sandy gravel sidefills. If the material had been a compacted
clayey material, the reverse deflection probably would have been much greater. In-
stances are known in which it has been necessary to inhibit this initial reverse deflec-
tion by the installation of diagonally oriented tie rods inside the structure, or by piling
sand bags or loose soil on top as the sidefills were built up, to prevent reverse curva-
ture of the sides of the conduit and "barnroofing" of the top.
These experiments provide information which appears to conflict with the funda-
mental tenets of Whites' (7) Ring Compression Theory. This theoretical approach be-
gins with the assumption that all loads on a flexible underground conduit act normal to
the pipe wall and that the effective load system is similar to hydrostatic pressure acting
 83

p on the outside of a cylindrical vessel.

Therefore, it is postulated that the only
stresses of consequence in the pipe wall
are tangential compressive stresses;
hence the name Ring Compression Theory.
Figure 46 (1) illustrates this basic con-
cept. Bending moment and deflection
of the pipe are completely ignored in
the theory.
Dr. Dem min' s measurements clearly
5 indicate that there were bending moment
C=Px stresses of considerable magnitude in the
z experimenta l structure. During place-
ment and compaction of the sidefills , the
sides of the pipe arch were pushed inward
and the top moved upward. This caused
prestressing of the pipe wall in tension
on the inside face at the sides and bottom ,
and on the outside face at the top and at
the lower corners. At the completion of
3. 44 ft of cover, prestressing was reversed
to some extent, but there was a residual
moment which produced a maximum outer
fiber stress in the crown of nearly 40 , 000
Figure 46 . Basic conce pt of the r i ng com- psi. Graphs of the normal force and bend-
press ion theory . ing moment at 2 transverse planes through
the structure at this load are shown in
Figure 5 of the report.
As the live-load slabs were placed at the embankment surface, prestressing was
counteracted to the extent that the bending moment became essentially zero at an ap-
plied load of 78. 62 T, as shown in Figure 13. Then as further load was added up to
151. 32 T, the bending moment increased in the opposite sense as shown in Figure 10.
These bending moments, like the deflection, were probably much less in this installa-
tion than would have been the case if a more usual and less strain-resistant backfill
material had been used. That the bending moments keep on increasing as loads are
increased is shown by the moment diagrams in Figure 3 5 which were measured when
the applied load was at 689. 54 T. The failure to recognize bending moments and de-
flections and failure to relate these phenomena with the quality of the sidefill soil mate-
rial constitute serious shortcomings in the Ring Compression Theory, in this writer's
opinion.
In reference to the diagrams showing bending moments and normal forces around
the periphery of the pipe arch: Values of these functions developed from instrument
measurements are shown in solid lines, whereas dashed lines are used to indicate as-
sumed values in regions where the instruments apparently did not yield firm informa-
tion. It is noted that most of the diagrams shown assumed values in the bottom of the
structure between the corners and that these assumed values are consistently relatively
low.
This writer has never seen a pipe arch which has developed structural difficulty.
However, he has been told by some who have observed such phenomena that there is a
tendency for the bottom of the structure to bend upward near the longitudinal center-
line, which would seem to indicate a fairly high positive moment in this region. This
tendency is in evidence where measured values of bending moment are shown in Fig-
ures 5 and 10. However, most of the estimated values of moment are negative in direc-
tion and relatively low in magnitude.
Furthermore, the estimated normal forces on the bottom of the arch are very low
in magnitude , while the measured values on the top surface are relatively high. Since
action must equal reaction it is difficult to accept the estimated values as shown. At
least it is suggested that here is a fertile field of needed research to determine more
84

accurately the actual magnitude and distribution of normal forces on the bottom of an
arch and bending moment stresses in this regio11 and in the vicinity of the bottom
corners.
There is a great deal of value in demonstration projects such as this, but there are
dangers associated with them also. One danger is that readers may not fully realize
the favorable aspects of the demonstration and thus gain the impression that all such
structures will perform equally satisfactorily. This of course is far from true , as
evidenced by the fact that failures of underground conduits do occur. And all too often
such failed structures are merely replaced and potential lessons which might be learned
are not made available to the engineering profession.
It is this writer's contention that engineers can learn more from one failure situa-
tion, if it is thoroughly studied and the causes determined, than can be learned from a
dozen or more successful installations. One difficulty in the development of knowledge
in this manner is the reluc tance of owners and installers of conduits to permit publica-
tion of the facts when failures occur. Typical of attitudes in this regard is that of a
member of the staff of a certain state highway department. Knowing the writer's inter-
est in underground conduits, he told of a failure of a large-size highway culvert in his
state. It had been investigated and a report made to the chief engineer. When asked
for a copy of the report, including the photographs which accompanied it, he hesitated,
then agreed to send the report, but with the understanding that it be held confidential.
He remarked, "We are not very proud of this installation." In another state a series
of culverts under an interstate highway got into trouble and the writer was asked to
investigate the situation, but before even going on the job, was sworn to secrecy by
the chief engineer of the department. There is heartening evidence that this attitude
may be changing for the better, but it has been all too prevalent in the past.
Much of our knowledge in engineering practice has resulted from the study of failures
of structures and publication of the results. Early in this century the failure of the
great Quebec cantilever bridge stimulaJed research relative to the carrying capacity of
latticed steel columns, with the result that column design is now on a much more reli-
able basis than formerly. Later the failure of the Ft. Peck dam led to tremendous
advances in the art of foundation exploration and interpretation of sub-soil materials.
Still later, study of the failure of the Tacoma Narrows suspension span resulted in the
development of a vast body of knowledge of aerodynamic forces on suspension bridges,
and adequate design of this type of structure is much more sure than formerly.
In each of these instances , extensive and detailed studies of the causes of failure
were made by teams of experts, and the results of their studies were published so that
the whol e e ngineerin~ profession could read and profit thereby , Tt is this writer's plea
that the same type of high-level engineering statesmanship be applied in the culvert
industry so that structural distress and failures of this small, but important type of
structure may be reduced to a minimum.

References
1. Armco Steel Corporation, Drainage Products Division. Ring CompressionReport,
1964.
2. Cummings, A. E. The Stability of Foundation Piles Against Buckling. Proc.
Highway Research Board, Vol. 18, Pt. II, pp. 57-65, 1938.
3 . Spangler, M. G. The Structural Design of Flexible Pipe Culverts. Iowa Eng.
Exper. Sfa. Bulletin 153, Iowa State Univ., 1941.
4 . Spangler, M . G. Discussion of Structural Considerations and Development of
Aluminum Alloy Culvert, by A. H. Koepf. Highway Research Board Bull. 361,
pp. 55-64, 1962.
5. Timmers, John H. Load Study of Flexible Pipes Under High Fills. Highway Re-
search Board Bull. 125, pp. 10-11, 1956.
6 . Westergaard, H. M. Computation of Stresses in Concrete Roads. Proc. Highway
Research Board, Vol. 5, Pt. I, pp. 90-112, 1925.
7. White, H. L. , and Layer, J. P. The Corrugated Metal Conduit as a Compression
Ring. Proc. Highway Research Board, Vol. 39, pp. 389-397, 1960.
 85

8. Watkins, Reynold K., and Spangler , M. G. Some Cha r ..,l.lteristics of the Modulus
of Passive Resistance of Soil: A Study in Similitude. Proc. Highway Research
Board, Vol. 37, pp . 576-583 , 1958.
9. Watkins, R. K. Development and Use of the Modpares Device. Proc. ASCE , Vol.
90, PL 1, Jan. 1964.

J. DEMMIN, Closure-The writer is very happy that such a well-known expert on un-
derground conduits as M. G. Spangler was prepared to discuss the paper presented.
His comme nts are sincerely appreciated.
It certainly cannot be stressed too much that the structural performance of flexible
pipe to a great extent depends on the quality of the backfill material and the way it has
been compacted. It is also very true that from one failure situation one can learn more
than from a dozen successful installations. However, systematic examination of the
reasons for structural failure will be possible only if preceded by tests that were con-
ducted under known conditions. The test was to contribute to the task of collecting
fundamental theoretical data that might help to indentify the causes for structural
failure.
Professor Spangler mentioned in his discussion that the author has never seen a
pipe arch which had developed structural failure; this is true . But the author knows
more than 2, 000 structures installed in Germany which have never caused major trou-
bles so far.
Being an expert of great renown, Professor Spangler will be asked to investigate
all structural failure situations , and it may therefore seem understandable that, from
this point of view , the ability of the test pipe to sustain vertical loads should have been
qualified . In the meantime, however, the results of this experiment have been sub-
stantiated in the field, and it has become evident that structures will not collapse if
installed under similar conditions as was the test pipe. These conditions normally
are to be met quite easily.
Professor Spangler has indicated that the backfill soil was of extremely high quality
and that everything had been done thereby to minimize deformation. It is a fact that the
backfill material was selected by the Federal German Railways, and compacted in lifts
with commercial vibrators, as is recommended by our company in our installation in-
structions. For the test, a sandy gravel was used which had been taken from a gravel
pit without further processing. This material, naturally , will not be available on every
jobsite at an economically justifiable price. In case material of poorer quality is used,
greater deformation will develop, and the carrying capacity would be reduced accord-
ingly. As may be recalled, however, the test showed that a twentyfold load could be
applied when using good quality soil. There is ample reserve , therefore, to warrant
sufficient safety even where poorer quality backfill soil is used. By this, the writer
acknowledges that the quality of backfill soil must be regarded as a factor when pre-
determining the carrying capacity of flexible pipe. To express this quality in terms of
determinable factors, it will be necessary to know the "modulus of soil reaction. " This
modulus of soil reaction, together with an examination of the stability of a pipe section,
should provide reliable information on its structural performance. In Germany, Pro-
fessor Kloeppel is conducting research work in this field.
White's Ring Compression Theory has never claimed to be a scientific basis of
structural performance, and therefore a comparison between the ring compression
theory and the measured bending moments does not seem appropriate. However, the
ring compression theory at present provides the best approximation to the actual struc-
tural performance of flexible pipe. This is evidenced by the fact that hundreds of struc-
tures designed by this method are operating quite satisfactorily. As shown in the paper,
the author calculated a maximum load of 1,273 tons for the test structure on the basis
of the ring compression formula disregarding bending moments. The fact that the test
had to be stopped at 1, 079 tons without complete failure, shows that the ring compres-
sion formula gives astoundingly good approximations for determining load capacity.
86

It is certainly just ai. • propriate to ascribe too much value to the measured
bending moments, s ince ending moment str esses already dev eloping during as-
sembly and pr i or to backfilling are so high that they could cause the s teel to yield. It
must also be expected , tha t as the sidefill berms are built up to th e cr es t , bending
moment stresses might develop in other places, which might approach the yield point
of the steel. From a conventional point of view, therefore, the pipe has been "over-
loaded" several times even before the top cover is placed. Despite this, we know that
these bending moments have not much influence on the ability of a flexible structure to
carry loads. This fact will justify, disregarding the bending moments, as is the case
in the ring compression theory.
Even if the assumed values of bending moments and normal forces developed on
the bottom of the pipe are not based on strain gage readings, they were estimated with
good r e liability on the bas i s of deformation on the pipe invert. Unfortunately, the strain
gages installed on the bottom of the pipe arch were damaged beyond use. As deforma-
tions of the bottom of the pipe arch wer e very low in magnitude, the corresponding
bending moment would likewise be very low. The possibility of an inaccurate es tima te ,
as indicated by Spangler, would therefore seem unlike ly. Further, it was stated that
the small normal forces acting in the bottom area of the pipe arch, did not conform to
the relatively high values in the top of the structure. In the writer's opinion, this fact
may be explained by the great frictional forces acting around the pipe periphery, which
would bring about an equilibrium. ·
Finally, the writer would like to stress that this one large-scale experiment will
naturally not answer all the questions pertaining to the determination of the load-carry-
ing capa city of flexible pipe. Convincing evidence was provided, however , that when
using good qua lity backfill soil which was ca refully compacted a la r ge pipe a rch was
capable of carrying twenty times the load desired by the r ailroad aut horities . This
provides for a sufficient safety margin even in cases wher e lower quality soils are used.