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IMPROVING THE PERFORlMANCE
OF
SOLMETAL STRUCFiJRE:S
SUBJECTED TO LOSS OF SOIL SUPPORT
KARLOS MELGAR
A Thesis Submitted to the
College of Graduate Studies and Research thmugh the
Department of Civil and Environmentai Engineering in
Partid Fulfhent of the Requirements for the
Degree of Master of Applied Science in Civü Engineering at
The University of Windsor
Windsor, Ontario, Canada October, 1997
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The author reîains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiek may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.
O KARLOS MELGAR, 1997
1 hereby declare that 1 am the sole author o f this thesis. 1 authorise the University of
Windsor to lend this thesis to other institutions or individuals for the purpose of schoiarly
researc h.
KARLOS MELGAR
I M e r authonse the University of Windsor to reproduce this thesis by photocopying
or by other means, in total or in part, at the request o f other institutions or individuals for
the purpose of scholarly research.
KARLOS MELGAR
Years of dependable s e ~ c e and a multitude of wide ranging installations have led to
the comgated steel pipe industry to play a major role in modem engineering technology.
Flexible steel conduits play an important role in the fonn of culverts, storm m e r s ,
subdrains, spillways, underpasses, conveyor conduits and seNice tunnels; for highways,
railways, airports, municipalities, recreation areas, industrial parks, flood and consewation
projects, water pollution abatement and many other programs.
Ln recent years developments have been made which dlow engineers and contractors
the use of conventional comgated structural plates to design and build structures having
larger spans and increased permissible live and dead loads.
These structures are generaily used for conditions where the depth-of-cover is lùnited
to about 5 to 10 m and the design is constrained by a relatively low, wide-opening.
However, in ment years many accidents and sudden failures have been reported on
this type of structure. Such failures ofien originate fiom large soi1 senlements, poor soil
compacting practices, and frost-thaw cycles. As a result, many different mmhods have
been proposed to eliminate these problems. In this thesis the use of a Geogrid mesh to
reinforce the soil surrounding the comgated metal stnicture is proposed. It is the belief
of the author that this material (Geogrid), which is widely used in the design and
construction of retaining walls, d improve the strength and durability of soil-metal
structures.
The study canied out imrolved building and testllig pipe-arches under shallow depth-of
cover. The results obtained fiom these tests sewed to compare and document the
advantage of using reinforcd soil structures in contrast to non-reinforced soi1 stmctures.
FIRST AND FOREMOST TO GOD
TO M Y PARENTS AND SISTERS
vii
The author wishes to acknowledge Dr. J. B. Kennedy for his important suggestions
and encouragement. to him I say: thanks your invaluable advice wiil be remembered
always.
Also, the author iikes to thank the staff of the Technical Research Centre and Richard
Clark for their continuous help and support d h g this investigation.
Last but not least, the author kes to thank his parents and sisters for their conthuous
support and encouragement.
viii
LIST OF CONTENTS
.................................................................................................................... ABSTRACT v
... .......................................................................................... ACKNOWLEDGEMENTS VUI
.................................................................................................... LIST OF CONTENTS ix
.. LIST OF TABLES ........................................................................................................ mi
...................................................................................................... LIST OF FIGURES xiv
..................................................................................... CHAPTER 1: INTRODUCTION 1
................................................................................................................. 1.1 General 1
. . ............................................................................................. 1 -2 Objective and Scope - 3
CHAPTER U: Li'ïERATURE REVIEW ......................................................................... 7
2.1 Soil-Metal Structures ..................... ... .............................................................. 7
2.2 Reinforced Earth ............................. ., .................................................................. 1 1
2 . 3 Buckling of Conduit Waiis of Soil-Metal Stmctures Under Shallow Cover ........ -13
2 . 4 Meta1 Strips vs . Non-biodegradable Materials And Geogrids .............................. 17
2.4.1 Metal-Strips ................................................................................................... 18
2.4.2 Non-Biodegradable Fabncs And Geogrids .................................................. 19
2.4.2.1 Non-biodegradable fbrics ...................................................................... 19
2.4.2.2 Geugrids ................................................................................................ 22
2.4.2.3 Effects on the Load Bearing Capacity of Soils ........................................ 23
CHAPTER III: EXPERIMENTAL STWDY .................................................................. 26
3.1 Selection of Prototype Structure ......................................................................... 2 6
.................................................................. 3 -2 Development of the Mode1 Structure -26
............................................................................ 3 -3 Construction of the Pipe-Arch -28
.................................................................. 3 -4 Testing Equipment and Components -29
.......................................................................... 3.4.1 Properties of the Lake Sand 29
................................................................................................ 3.4.2 The Sand Box 30
...................................................................................... 3 .4.3 The Loading Device 3 1
.............................................................................................. 3 .4.4 Instrumentation 31
........................................................................... 3 .4.5 The Rubber Pressure Tubes -32
3 .4.6 The Reinforcement ......................................................................................... 33
3.4.7 The Pipe-Arch ............................................................................................... -35
3.5 Testing Procedure (Constniction and Set-up) ...................................................... 35
3 S.1 Preparation of Surroundhg Soi1 and BacW Operation .................................... 35
3.5.2 Testing of the Soil-Metal Structure ................................................................... 38
CHAPTER W : DISCUSSION OF RESULTS ............................................................... 68
4.1 Unreinforcecl-Soi1 Structure ................................................................................ 68
4.2 ReUiforced-Soi1 Structure (Failure of the Soii Surrounding Both Comer Plates) .. 7 1
4.3 Reinforceci-Soil Structure
(Faifure of the Soil Surroundhg One Corner Plate) ................................................... 73
4.4 Cornparison betweem Unreinforced-Soi1 and Reinforced-Soil Stnictures ............. -74
.............................................................................................. C W T E R V: DESIGN 124
CHAPTER VI : CONCLUSIONS AND RECOMMENDATIONS .............................. 137
....................................................................................................... 6.1 Conclusions 137
............................................................................................. 6.2 Recommendations 1 3 8
REFERENCES ............................................................................................................ 139
...................................................................................................... VITA AUCTORIS 145
LIST OF TABLES
............. Table 3.1 Sectional and Structurai Properties for Comgated Sheet and Plate 40
.................................... Table 3.2 Sand Cone Method Test Results on Lake Erie Sand 41
Table 3.3 Tende Test Resuits: Tensar Multinetting .................................................... 42
................................... Table 4.1 Pipe-Arch Deff d o n s (Unreinforcd Soii) - Stage 1 -76
........................ Table 4.2 Pipe-Arch Bendimg Moments (Unreinforceci Soil) - Stage 1 -77
.................................. Table 4.3 Pipe-Arch Axid Forces (Unreinforced Soil) - Stage 1 78
...... Table 4.4 Pipe-Arch Ddections (Unreinforced Soil) - Stage 2 ................... ..... 79
......................... Table 4.5 Pipe-Arch Bending Moments (Unreinfiorceci Soil) - Stage 2 80
Table 4.6 Pipe-Arch Axial Forces (Unreinforced Soil) - Stage 2 .................................. 81
Table 4.7 PipeArch Defiections (Unreinforced Soil) - Stage 3 .................................... 82
Table 4.8 Pipe-Arch Bendiog Moments (Unreidorced Soil) - Stage 3 ......................... 83
Table 4.9 Pipe-Arch h i a l Forces (Unreinforceci Soii) - Stage 3 .................................. 84
Table 4.10 Pipe-Arch Deflections (Reidorced Soil) - Stage 1 ........................................ 85
Table 4.1 1 Pipe-Arch Bending Moments (Reinforceci Soil) - Stage 1 ............................ 86
Table 4.12 Pipe-Arch Axial Forces (Reinforced Soil) - Stage 1 ..................................... 87
Table 4.13 Pipe-Arch Deflections (Reinforced Soii) - Stage 2 ...................................... 88
Table 4.14 Pipe-Arch Bending Moments (Reinforceci Soii) - Stage 2 ............................ 89
Table 4.1 5 PipaArch Axial Forces (Reinforcecl Soil) - Stage 2 .................................. -90
Table 4.16 Pipe-Arch Deflections (Reinforced Soil) - Stage 3 ....................................... 91
Table 4.17 Pipe-Arch Bencihg Moments (Relliforced Soil) - Stage 3 ............................ 92
. ..................................... Table 4.18 Pipe-Arch h i a i Forces (Reidorced Soil) Stage 3 93
......... . Table 4.1 9 Pipe-Arch Bending Moments (Reinforced Soil) Uneven Soil Fdure -94
.................. . Table 4.20 Pipe-Arch Axial Forces (Reinforced Soil) Unwen Soi1 Failure 95
.................... Table 4.2 1 Pipe-Arch Deflections (Reinforced Soil) . Uneven Soi1 Fdure 96
Table 5.1 Geogrïd Soil-Reinforcement . Spacing and Horizontal Length ................... 134
Table 5 -2 Length of Geogrid Layen ....................................................................... 135
LIST OF FIGURES
.................................................... ....................... Figure 1.1 Pipe-Arch Components ... 6
..................................... Figure 2.1 Basis of Sprangler's Derivation of the Iowa Formula 25
Figure 3.1 Structural Plate Shapes .............................................................................. 4 3
................................... Figure 3.2 Comgation Profile - Prototype Pipe-Arch (d in mm) 44
.................................. Figure 3.3 Prototype Pipe-Arch - Overall Dimensions (ail in mm) 45
........................................ Figure 3.4 Corrugation Profile - Mode1 Pipe-Arch (al1 in mm) 46
........................................ Figure 3.5 Mode1 Pipe-Arch Overail Dimensions (dl Ui mm) -47
Figure 3.6 Plywood Template - Side View ..................................................................... 48
.............................................................. Figure 3.7 Comgation Machine - Front View -49
Figure 3.8 Structural Sections - Haunches ........... ...... .......................................... 50
Figure 3.9 Finished Pipe-Arch ....................................................................................... - 5 1
Figure 3.10 Sand Box - Overall Dimensions (al1 in mm) .................................... .... .... 52
Figure 3.1 1 Loading Beam - Overail Dimensions (dl in mm) .......................................... 53
Figure 3.12 Location of Strain Gauges (aii in mm) ......................................................... 54
Figure 3.13 Arrangement of Strain Gauges .................................................................... 55
Figure 3.14 Location of Dia1 Gauges (ail in mm) ............................................................ 56
Figure 3.15 Arrangement of Dia1 Gauges ...................................................................... -57
Figure 3.16 Load Ceiis and Loaduig Device ................................................................... 58
Figure 3.17 Automatic Strain Indicator .......................................................................... 59
Figure 3.18 Components of Rubber Pressure Tubes ............................ .. .................. 6 0
.......................................................... Figure 3.19 Spachg of Reinforcement (ail in mm) 6 1
.................................................... Figure 3.20 Length of Reinforcing Layers (al1 in mm) 62
Figure 3.2 1 Tensife Test on Geogrid Sheets - Equipment Set-up (dl in mm) .................. 63
.................................................................... Figure 3.22 Geogrid Specimen (aii in mm) 6 4
Figure 3.23 Load vs . Elongation Curve for Geogrid Specimen ....................................... 65
.......................... ................... Figure 3.24 Fint Layer of Geogrid - At Haunch Level ... 66
.............................................. Figure 3.25 Sb& Layer of Geogrid - Below Crown Level 67
Figure 4.1 Umeinforced-Soi1 Pipe-Arch Stnichue .......................................................... 97
Figure 4.2 Unreuiforced-Soil Pipe-Arch - Deflected Shape ......................... ...... ......... 98
Figure 4.3 Unreinforceci-Soi1 Pipe-Arch - Bmding Moment Distribution ...................... -99
Figure 4.4 Unreinforced-Soil Pipe-Arch - Axial Load .................................................. 100
Figure 4.5 Failure of Soi1 at Invert and Haunches ......................................................... 101
Figure 4.6 Unreidorced-Soit Pipe-Arch - Yielding At Crown ..................................... 102
Figure 4.7 Catastrophic Failure of Unreinforced-Soil Pipe-Arch ................................... 103
Figure 4.8 Reinforceci-Soil Pipe-Arch - Ddected Shape .............................................. 104
Figure 4.9 Reinforcecl-Soil Pipe- Arch - Benduig Moment Distribution ......................... 105
Figure 4.10 RBnforced-Soi1 Pipe-Arch - h i a l Load ................................................. 106
Figure 4.1 1 Reinforced-Soi1 Pipe-Arch - At Fîrst Sign of Yielding ............................... 107
Figure 4.1 2 Beading Moment Diagram for Pipe- Arch - Uneven Soi1 Failure ................. 108
Figure 4.13 Axial Force Diagrarn for Pipe-Arch - Uneven Soii Failure .......................... 109
Figure 4.14 Deflected Shape for Pipe-Arch - Unwen Soil Faifure .............................. 110
Figure 4.15 Deflected Shape for Pipe-Arch - Soil Level at 970 mm fiom Invert ............ 111
Figure 4.16 Bending Moment Diagram for Pipe-Arch
................................................................................ Soi1 Level at 970 mm fiom hvert 112
Figure 4.17 Axial Force Diagnun for Pipe-Arch - Soi1 Level at 970 mm fiom Invert ..... 113
.... Figure 4.1 8 Deflected Shape for Pipe- Arch - Applied Load Range 6.9 kN to 7.1 kN 114
Figure 4.19 Ddected Shape for Pipe-Arch - Applied Load Range 8.7 kN to 9.4 kN .... 115
Figure 4.20 Axial Force Diagram for Pipe-Arch
................................. .................................... Applied Load Range 5 -6 kN to 5 -9 kN .... 116
Figure 4.21 Bending Moment Diagram for Pipe-Arch
Applied Load Range 6.9 kN to 7.1 kN ......................................................................... 117
Figure 4.22 Defiected Shape for Pipe-Arch - Applied Load Range 8.3 kN to 8.8 kN
Rubber Tubes Pressure of 1 -45 kN/rn2 ......................................................................... 118
Figure 4.23 Deflected Shape for Pipe-Arch .................................................................. 119
Figure 4.24 Bending Moment Diagnun for Pipe-Arch
Applied Load Range 8 -3 kN to 8 -8 kN - Rubber Tubes Pressure 1 -45 k ~ / m ~ .............. 120
Figure 4.25 Bending Moment Diagram for Pipe-Arch ................................................ 121
Figure 4.26 Axial Force Diagram for Pipe-Arch
Applied Load Range 8.3 kN to 8.8 kN - Rubber Tubes Pressure 1.45 kN/m2 .............. 122
Figure 4.27 Axial Force Moment Diagram for Pipe-Arch ......................................... 123
Figure 5.1 Overall Pipe-Arch Dimensions (all in mm) ................................................... 136
CHAPTER 1
INTRODZJCIlON
A culvert is usually, although not aiways, differentiated from a bridge by Wnie of the
fàct that the top of the culvert does not form a part of the travelled roadway. More
fiequentiy, culverts are differentiated from bridges on the basis of span length. Cuiverts
dso mer f?om bridges in that they are usually designed to flow niII under certain
conditions, whiie bridges are designed to pass floating debris or vessels.
There are two types of culverts; these are flexiile culverts and rigid dverts. Flexiile
adverts are eiuier thin-wded steel pipes or gaivanised corrugated metal pipes; they rely
onty partly on the strength of the pipe walls to resist the e x t d loads, and they are
designed to deflect under the ioads. When deflection takes place, the horizontal diameter
of the culvert increases and compresses the soi1 at the sides and in this marner the passive
resistance of the wil is triggered to help support the appiied loads. When fdure of a
flexible culvert does occur it is prllnarily because of excessive deflection. In contrast to
the flexible pipes, rigid culverts are composed of reinforcd concret+ cast iron or vitrified
clay and their load-carrying ability is primarily a hction of the stifmess of the walis of the
culverts. When fàilure does occur it is usuaily due to rupture of the walls of the dvert.
Comgated metal plate pipes can be divided generically into two categones, namely,
those that are manufactureci in closed pipe shapes and those that are assembled on site
â o m curved comgated plates. The structures in the former category are refmed to as
comgated steel pipe and are n o d y of smder diameter than those of the latter
category, whïch are usualiy rderred to as strucniral plate comgated aeel pipes.
New technology bas ailowed agineers and designers to use these structures for longer
spans and under relatively shallow soil cover conditions. However, under these conditions
the surromding soil may not provide enough suppon for the structure. This in twn allows
the structure to move more fieely and therefore increase Îts deformations. The lack of
sufncient support for the structure also gives rise to a considerable increase in the bending
moments in the structure as weli as in its susceptibility to sudden buckling failure.
Through the years many of these structures have fded because of hadequate support
provideci by the surrounding soil. Fdures of two structures were reporteci and
documented. The nrst fdure occurred in Ohio and the second one in Ontario [33]. What
is most unfortunate is that they both involved the loss of Lives due to their sudden faiures.
in 1986 Moore [33] inspecteci 14 1 soi1 steel structures in the county of Elgin, Ontario.
Moore found that 56 out of the 141 structures showed some sign of distress. Some of the
signs of distress found are:
1. Joint FaiIure.
2. Excessive deformation of the culvert's crown.
3. Lifting of the invert of the metal structure.
4. Crimp formation.
5. Excessive distortion in some culverts-
Several techniques have been suggested in trying to overcome the side effects of
building long span structures under shallow soil cover conditions. These difEerent
techniques can be grouped as follows [3]:
1. Techniques that reduce load effects, in partidar the thnist , in the conduit wd.
2. Techniques that increase the strength of the conduit wall by reinforcing it.
3. Techniques that increase the strength of the conduit wall by stiffening the soi1 and thus
enhrincing the stillhess of the radial support to the conduit wall.
The f h t two techniques make the structure stronger by means of adding Meners or
by introducing relieving slabs over the metallic structure [16]. This approach, although
widely u s e - proves to be d e r expensive and will lead to divert more external load to the
m d c structure and less load to the smmounding soil. This in tuni wiîi decrease the
number of load paîhs.
On the other band a l e s expensive and better rnethod is represented by the third
technique, accomplished by cementing the soi1 [IO], using h s t beams [12], or
reinforcing the soil by means of Rat bars [22]. Many studies have been conducted on sale
models that have proved the effectiveness of increasing the strength of the structure and
the load bearing capacÏty of the soil and thus reducing the probabiiity of
catastrophidsudden failure of soil-metal structures.
1.2 Objective and Scope
In generai, out of ail the different shapes of structural plate corrugated steel pipes that
are fàbricated, none requkes more care and attention than the Pipe-arch. Pipe-arches (see
Figure 1.1) are more prone to distress than other mil-steel bridges mainly because the
radius of w a t u r e of the haunch segments of the conduit Wall is sigdïcantiy d e r than
the radius of n w a w e of the invert segment, as well as the soi1 under the haunches is
usually very difncuh to compact properly. Nevertheless, Pipe-arches have becorne widely
used throughout North America in the construction of highway bridges and drainage
structures. W1th an increasing demand for using this type of structure a need for a more
reliable design method exists; one that prevents nidden and/or catastrophic f&e of the
structure. This study examines and compares the behaviour of reinforced-soi1 and
unreinforced-soil pipe-arches during the foilowing stages:
1. Construction and placement of the structure
2. Loading of structure (extemaîly applied loads)
3. Failure of the soil surroundhg the haunches of the structure
To accompli& this, experimental work was Cameci out to compare and analyse the
&ect of reinforcing the soil under the conditions mention4 above.
The objectives of this research are as follows:
1. To study the behaMour of unreidiorced-soii pipe-arches during the three stages
mentioned exdier.
2. To study the behaviour of reinforced-soi1 pipeaches during the three stages
mentioned earlier.
3. To compare and document the behaviour of meinforced-soi1 and reinforceci-soi1 pipe-
arches.
Figure 1.1 PipeArch Components
/ .' ,
/ / - Haunch ( Corner F l a te 1 Invert
This chapter reviews the previous research in the area of soil-metal structures,
reinforcexi earth and buckling of soil-metal structures. Also, previous research in the area
of non-biodegradable materials as an aitemative to metal strips for reinforcing the soil in
mil-metal structures is reviewed.
2.1 SoiElMeta1 Structures
Soil-metal structures have b& buiit for many yean. However, a great number of
confiicting theories concerning their analysis and design stdi rernain. Some of the
acceptable theories are presented in this section.
M. G. Sprangler (1941) [40] observed that the Martson theory [31] for calculating
loads on buried pipes was not adquate for flexible pipe design. Sprangier noted that
flexible pipes provided little inherent stiflhess in cornparison to rîgid pipes, yet they
perfonn remarlcably well when buried in soil. This si@cant ability of a flexible pipe to
support vertical soil loads is derived from (a) the redistribution of loads around the pipe,
and (b) the passive pressures induced as the sides of the pipe move outward against the
surrounding sol
Sprangier incorporated the &ects of the surrounding soil on the pipe's deflection.
This was accomplished by assuming that the loads applied would be d o r m l y distributeci
on the plane at the top of the pipe. He also assumed a d o m pressure over part of the
bottom, depending upon the bedding angle. On the sides, he assumed the horizontal
pressure on each side wodd be proportional to the deflection of the pipe into the soil.
The coostant of proportionabty was defined as shown in Figure 2.1 and was d e d the
modulus of passive resistance of the soil. The rnoddus would presumabiy be a constant
for a gR.m soii and could be measured in a simple laboratory test. Through analysis he
derived the foliowing Iowa formula:
w here,
9 = deflection lag faaor
K = bedding constant
WC = Martson's load per unit length of pipe, Ibfm
r = mean radius of the pipe, in
E = moddus of elasticity of pipe matenal, lb/in2
1 = moment of inertia of the pipe waîl per unit length, inafin
e = modulus of passive resistance of the side fiIl, 1b/(in2)(in)
AX = horizontal deflection or change in diameter, in
Reynold K. Watkins (1966) [45], investigated the modulus of passive resistance
through model studies and examineci the Iowa formula. As a r e d t of Watkins effort,
another soi1 parmeter was dehed. This was the modulus of soi1 reaction
Consequedy, a new formula called the modifieci Iowa f o d a was proposed.
Two obsewations f?om Watkins' work are of partidar note: (a) There is M e point in
evaluating E* by a model test and then using this modulus to predict ring ddection, since
the model gives ring deflection directiy. @) Ring deflection may not be the only
performance limit.
Work perforrned by White (1960) [47] showed that the deflection of underground
conduits does not govem the design , but wall strength does. He introduced the su-caiied
"ring compression theory", assuming that the tangentid compressive stress q in a conduit
wall is less than the yield stress of the w d material as show:
where,
W. = vertical load per unit length of the conduit
S = span or diameter of the conduit
A, = cross sectional area of the conduit walI
Fy = yield stress of the conduit wail material
The problem with this theory is that it negiects the bending moments in the conduit
walls which is reasonabiy correct under high fdls. Although such a condition is met
successfùily in many installations, it is not applicable if the soil cover is shallow or the
surrounding soii to the structure is loose.
A relationship between soii density and conduit deformations was proposed by
Watkins (1964) [46]. He found that when soil density exceeds a critical value. waü
strength and not the deflections. govem the design.
Brockenbrough (1964) [Il] suggested the following equations for a conduit's ultimate
design:
Fu = Fy for S / r < 24 (2-5)
F. = 40,000 - 0.081 (S / r )* for 294 < S / r < 500 (2-6)
where,
for S / r > 500 (2-7)
Fu = ultimate strength of the conduir walis, 1bf7Ïm2
Fy = yield stress of the conduit wail matenal, l b ~ i
S = diameter or span, in
r = radius of gyration of the conduit wali, in
Equations (2-5), (2-6), and (2-7) are anaiogous to the classical equatiom for column
design. Equation (2-5) specines the ultimate yield of the conduit wall material which
represents the wall m s h g zone. Interaction between yielding and buckling is
represented by equation (26). F ' d y , the zone of ring buckling is specrfied by equation
(2-7).
Lusher and Hoeg (1994) [29] studied the beneficial contributions of the backfiiî to the
performance of the soil-metal structures. They showed three very important
contributions: (a) pressure redistribution which activates the laterai earth pressure, (b)
deformation restrain which forces the conduit to buckle in a higher mode, and (c) arching
in which the vertical pressure on the conduit w d s is reduced as it deflects vertidy.
Despite aii the difîerent theories available and their Iimitations, one of the most
commonly used formulas for designing and analysing shallow cover soil-metal structures is
the Iowa formula dweloped by Sprangier. The Iowa formula has been widely used and
successfiilly applied, particulafly for circular conduits.
2.2 Reinforced Earth
Reinforced earth is a construction material comprishg soi1 that has been strengthened
by tende elernents aich as metal rods a d o r strips, non-biodegradable fabrics
(geotextiies), geogrids and the Wce. The fiindamentai idea of reinforcing the soi1 is not
new, in fàct, t goes back to biblical tirnes. However7 the present concept of systematic
adysis and design was developed by a French engineer, H. Vdal(1966) [43].
Viciai (1%6) [Ml, applied this concept to retaining w d s and showed that the cost was
below that of conventional A s . Schlosser and (1979) [38] suggested that soi1 with
rrinforcing sbips behaves as if it were isotropicaiiy cohesive. They considered the
reinforcement inside the soil as a substitute for a lateral restraining force enabhg the soil
to cany vertical stresses.
Juran et al. (1978) [19] tested sand samples reùiforced by ciradar plates made of
alumuiium discs. In generai, it was found that reinforcement stiffened the soil and also
increased failwe resistance.
Al-Hussaim (1978) [5] camied out a test on an insbumented reinforceci earth waii 4.88
m long and 3.66 m Iiigh. He found that the lateral earth pressure on the wall facing at the
end of the constniction could be reasonably approximated by the Rankine theory of earth
pressure. However7 the h e comecting the points of maximum tensiie stresses in the
reinforcing strips did not coincide with the theoretical Rankùie he.
Kennedy et al. (1980) [21] conducteci experùnental and theoretical work on a
reinforced earth retaining waii subjected to vertical surcharge load. Four differat
positions of the load were considered. They developed a simpHed patteni of distrîiution
for the t d e force dong the reinforcing strips.
Laba et al. (1984) [26] studied the &ect of horizontal as well as vertical surcharge
load on reinforced earth retalliing waiis. It was conchided that the location of the
maximum tende stresses dong the reinforcing strips and the potential M u r e plane can be
approrcimated by using Culmann's rnethod. It was also stated that the horizontal force
towards the wall facing wiIl increase the tensile stresses in the reinforcing strips and the
largest increase wili take place at a certain depth below the soil Surface.
Laba and Kennedy (1986) [25] proposed the stress &ér technique. It was found
that the over-stressed regions of the reinforcd earth wall trader stresses to the regions
where the reinforcing Nips have not yet reached their capacity. This transfer of stresses
was found to be influencecf by the surcharge load magnitude and its distance fiom the wail
fiKing.
More recent studies in the USA have revealed that the reinforcing material (metal
strips andior other materials) is capable of resisting fkost action effectively [33]. During
winter period the forces in the reinforcing material increased because they restricted the
ouiside movement of the wall fachg. Afier the s p ~ g thaw, these forces dropped back to
a level near the lower range of the previous fd.
In summary, some of the beneficial &ects for soil reinforcement are derived h m (a)
the soil's increased tende sîrength and (b) the shear resistance dweloped due to the
fiction a the soi1 reinforcement interfaces. Such reinforcement is comparable to that of
wncrete structures.
2.3 Buckiing of Conduit W& of Soü-Metai Strnetures Under Sbillow Cover
M e r investigators paid littie attention to buckling as a potential mode of fiilure of
the conduit w d . Sprangler (1941) [40] believed that the fdure of the conduit waU was
related either to wall cmshhg or to deformation of the pipe. Field performance of pipes
having diameters less than 3 m and under fairly large depths of soi1 cover has provideci
some support for this belid.
In recent years, a general increase in the sire of soil-metal stmctures has prompteci
f i d e r investigation on the phenomenon of Mure of the conduit wail. The research
performed on this phenomenon has brought to light the fact that buckling is a signincant
mode of failue, and that it cm take place even at small defonnations of the conduit. It is
now weii established that the stability d y s i s of the conduit w d is an indispensable
component of the design process, especially when the spans are large and the depth of soi1
cover is smail.
In determining the bucklirig stress-f., different approaches are studied. One approach
is derived fkom a modification of the buckling formula proposed by Timoshenko and Gere
(1961) [42].
w here,
E = modulus of elasticity of the conduit wail
R = radius of the conduit
r = radius of gyration of the conduit wd
This formula is subjected to the assumption that the soi1 in a mil-pipe system is non-
compressible and with an angle of fiction 9 tending to zero. In such a case the radial
pressure on the pipe is very neariy hydrostatic, and it can be descr i i by equation (2-8).
Watkins (1966) [45] M e r shidied this fonnuia and the e f f i of Sprangler's
assurnptions. He proposed thai, since the formula is based on the assumption that 9 = O, it
has the &kt of underestimating the buckling stress on the conduit d s . Watkins
developed a soi1 stiflhess parameter, K, to account for the Merence ôetween the actual
and assumed fluid mil. Watkins suggested that such a parameter could be taken as the
ratio of the horizontal to the vertical soi1 pressure. For cohesioniess =ils this factor is
qua1 to the active earth pressure K = 16. Thus the equation for buckling becomes:
Abdel-Sayed et al. (1994) [4] proposed that the parameter K should also depend upon
the relative Stïfhess of the soil with respect to the rigidity of the conduit wall and they
proposed the foflowing expression for K:
where,
E' = modulus of soi1 reaction, bfh2
1 = moment of inertia per unit Iength of column wail, in4
B = 1.22 for the sides and bottom of the conduit, and
= 1.22 ( 1 + 2 ( E 1 / E' R )Osz ) for the rest of the conduit
Furthemiore, the Ontario Highway Bridge Design Code OHBDC [36] adopted this
expression for the calculation of K.
A ciiffixent approach for studying buckling effects in conduit w d s was taken by Booy
(1957) [9]. He suggested that the buckling f o d a available for analyshg elasticdy
supportai curved beams could be used for evduating the buckling stress of the conduit
walls:
where,
A = cross-sectional area of the conduit wd per unit length
Lusher (1966) [28] deveioped the same buckling formula by studying the buckling of
cirdar beams under radial pressure and sumilating the soi1 ekct by springs of constant
modulus. He proposed that the modulus of soi1 reaction is dependent on the thickness of
the soi1 cover. He also developed an expression for calculating the effective modulus of
soi1 reaction E".
where,
v = Poisson's ratio for the soi1
fi = Thicicness of soi1 cover
r = radius of gyration of the conduit
R = Radius cr span of conduit
Subsequently, Meyerhof et al. ( 1968) [32] simplified this expression to the following
fonn:
The formula developed for curved beams represents a more accurate formula and it
was proved by Abdel-Sayed (1978) [2] that in the case of comgated sheets in plane strain
state of stress it cm be used without modiiïcation.
2. 4 Metal Strip vs. Non-biodegradable Matenais And Geogrids
2.4.1 MetriCstrips
Lee et al. (1973) [27] showed that with a consemtive design, 5mm thick gdvanised
steel stnps would be enough to hold a waii about 14 to 15m in height. The reinforcing
sîrips, which are thin and wide placed at regular intervais are often used in the design of
retaining wails and other reinforced soil structures.
Kennedy and Laba (1989) [22] proposed a concept of combining conventiond soil-
steel bridge design with the technique of reùiforcing the soil with stnps of steel. The steel
strips are laid at different lwels and tied to relatively thin facia panels.
In most instances galvanised metai strips have proved to be advantageous in providing
reinforcement for mil-steel structures. However, gdvanised steel is subjected to
corrosion. The rate of corrosion depends on severai environmental factors. Binquet and
Lee (1975) [8] suggested that the average rate of corrosion of gdvanised steel strips
varies between .O25 and -050 mm/yr. So, in the actuai design of reioforcement allowance
must be made for the rate of corrosion. This allowance is given by the following:
where,
tc = actual thickness of reinforcing strips to be used in construction
= thickne~~ of strip determined fiom design caldations
r = added thickness to compensate for corrosion
In recent years, new materials have been dweloped and studied. These materials are
not only resistant to environmental factors but aiso in some uistances they have been
found to be m g e r and less expensive.
2.4.2 Non-Biodegradable Fabrics And Geogrids
2.4.2.1 Non-biodegradable fabrics
Non-biodegradable fabrics are generaily referred to as geotextiles. Since 1970 the use
of geotextiles has increased tremendously around the world [14]. The fabrics are usually
made from petroleum produas, polyester, polyethylene, and polypropylene. They may
also be made fiom Fiberglas. Geotextiles may be woven, knitted, or non-woven.
Woven geotextiles are made of two sets of parallel filaments or strands of yam
systematically interlaced to form a pl- structure. Knitted geotextiles are formed by
interlockhg series of loops of one or more filaments or strands of yam to form a planar
structure. Non-woven geotextiles are fonned from filaments or strands of yarn to form a
planar stmcture. These filaments or short fibers are, in the be@nning arranged into a loose
web. They are then bonded by chernical, thermal a d o r mechanical means.
Geotextiles have been used extensiveIy in foundation engineering in many different
areas, and are of special inîerest in the construction and design of highways because of :
1. Separation: Geotextiies help keep various soi1 layers separate after construction and
d u ~ g the project s e ~ c e period of the structure. For example, in the constmction of
highways, a cclayed subgrade can be separated from a granuiar base subgrade.
2. Reinforcement: The tende strength of geofabrks increases the load-bearing capacity
of the soil.
Koemer (1990) [24] proposed a step by step procedure for designhg retaining walls
with geotextiie reinforcement. In this procedure the active pressure distribution on the
wd was caldateci by using Rankine's active pressure formulae:
w here,
IG = Rankine earth pressure coefficient
=ta1?(45 - 4 J 2 )
y1 = unit weight of granular backfill
z = vertical spacing of layers at any depth
4 1 = angle of interna1 friction of the soii
Koemer suggested that by determinhg the active pressure required the appropriate
geotextile fhric couid be selected baseci on the aiiowable strength of the fabric.
Furthermore, Koemer proposed thaî the length of each geotextile could be calcuiated
fiom:
where,
f, = ( H - ~ ) / t a n ( 4 5 + $ , / 2 )
f. = ( S a . [ F S p , l ) / ( h v b )
G~ = Rankine's active pressure
0" = y , + z
b- = £&ion angle at reinforcement (soil interface)
= angle of intemal fiction of the soil
S, = vertical spacing between layers of reinforcement
H = total depth of excavation
z = depth eom top of soil cover to the layer of reinforcement
FSp)= &or of s a f i against reinfiorcement puiiout
Koerner deterrnined that the magnitude of FSp, is generally between 1.3 and 1.5 and
that the fiction angle can be taken as 2/3 of Based on the published resuhs
presented by Martin et al. (1984) [30] this assurnption proved to be consavative.
Many studies have shown that the introduction of reinforcing geotextiie matends in
the construction of reidiorced earth structures has given excellent results. BiUard and Wu
(1991) [q tested a full-de g e o t d e reinforcd retaining wd, 1.5 m high. It was
desigrmi based on the assumption of Rankùie active pressure distribution and a factor of
safety equal to I for a surcharge, q, of 40.7 W/m2 on the surface of the bacldill. They
discovered that the wall actudy failed when the surcharge reached 127.5 kPJ/rn2. This
experimental findiog proved that the geotextile material had in fact increased the overall
load bearing capacity of the soil.
Geogrids are high-modulus polymer rnaterials, such as polypropylene and polyethylene
and are prepared by tende drawing. Netion Ltd. of the United Kingdom was the first
producer of geogrids. In 1982, the Tensar Corporation, presentiy Tensar Earth
Technologies, Inc., introduced geogrids in the United States [ 1 51.
The major hct ion of geogrids is reinforcement. Geogrids are relatively st i f f netlike
materials with large openings cded apertures. These apertures are large enough to ailow
interlockhg with the surrounding soi1 a d o r rock and perfonn the fiinction(s) of
reinforcement andor segregation.
In practice geogrids are found to be of two types: (a) biaxial geogrids and @) uniaxial
geogrids.
Uniaxial geogrids are manufactureci by stretching a punched sheet of exmided hi&-
density polyethylene in one direction under carefùiiy controlled conditions. This process
aligns the polymer's long chah of molecules in the direction of draw and results in a
produa with high one-directional tensile strength and modulus.
Biui.I geogrids are manufhccured by stretching the punched sheet of polypropylene
in two orthogonal directions. This process results in a product with high tensile strength
and different moduli in two perpendicuiar directions. The resulting grid apertures are
either square or rectangular.
Geogrids are manufàctured so that the open areas of the 8 d s are greater that 50% of
the total area. Currently, geogrids are manufàctureci in many shapes andor sues.
However grids used for soi1 reinforcement d y have apertures that are rectangular or
eilipticai in shape. Carroll (1988) [13] performed experimental test on geogrids used for
reinforcing soils and discovered that geogrids develop reinforcing sîrength at low strain
levels, such as 2%.
Geogrids, like geotsctiles, are also used as reinforcement in granular bacW for the
constniction of reidorced earth structures. The design procedure avaiiable for geogrïd
reinforceci soii construction is similar to the one used for geotextiie materials In 1990
Thamm et al. [4 11 tested a full-scale retaining waii reinfiorced with TENSAR SR2 geogrid.
Failure on the wd was caused by applying a load to a wncrete slab measuring 2.4 m x 0.9
m. The wall fded when the vertical load on the concrete slab reached 1065 kN. They
concludeci that the resistance of the wall had considerably increased when compared to a
rigid retaining wall.
2.4.23 EEeets on the Luad B d g Capacity of S O L
Guido et al. (1987) [la] performed tests to determine the load bearing capacity of
square foundations on laboratoxy models with sandy mils (relative density = 500h). Such
soiis were reinforceci with layers of non-woven heat-bonded geotextiies. For these tests
several parameters were varied (number of layers of geotsaile, strength of geotextile,
depth of cover , etc.). In generai, results showed that when the g e o t d e layers are
placed within a depth equal to the width of the foundation they increase the load beariag
capacity of the foundation.
Sakti and Das (1987) [39] reported some mode1 test results on the bearing capacity of
a strip foundation on saturated clay. They used a heat-bonded non-woven geotextile for
reinforcement. They concluded that in general the load bearing capacity of the foundation
was increased when using geotextiie material for reinforcing the soii, specially when the
first layer of geotsctile material was placed at a depth of O.XB (B = width of foundation).
Omar et al. (1993) [35] after extensive experimental investigation concluded that
geogrids can be used as soi1 reinforcement to increase the ultimate and allowable bearing
capacity of sMow foundations.
In general, the introduction of geogrids and non-biodegradable materials has irnproved
the load bearing capacity of soils. However, this becomes more advantageous when the
design involves a structure that will be placed under shallow soii cover conditions. This is
usually the case when designing pipe-arches and other soil-metal structures.
Figure 2.1 Basis of Sprangler's Derivation of the Iowa Formula
cxwPTxmnr
EXPERIMENTAL STUDY
3.1 Seleetion of Prototype Structure
It was noted eariier that soil-metal structures are fabncated in many different shapes
and sizes (Figure 3.1 ). The selection of any particular shape and size of a soil-metai
structure often depends on the constraints goveming the design. However, out of al1 the
shapes available none represents more risk for sudden failure than the pipe-arch.
Specidy, those pipe-arches that have large spans and are built under shdow soii cover
conditions.
The structure studied here is a sale mode1 of the larges avaiiable span of a pipe-arch
stmcture with a comgation profile of 152 x 51mm (Figure 3.2). Such a prototype
structure tends to fd suddenly because of yielding of the soi1 under the haunches of the
structure. The sectionai properties for the profile as well as the structural properties of the
pipe-arch were obtained fiom design tables prepared by the Amencan Iron and Steel
Institute [i l . These properties are s h o w in Table 3.1. and Figure 3 -3.
3.2 Development of the Modd Structure
In designing any soil-metal structure the three moa important factors to be considered
are (a) dead and live loads; (b) stiaiess of surrounding soi1 and soi1 cover. (c) waii
stirsiess of the metal structure. However, for structures under shallow soi1 cover
conditions deflection becornes the main constraint in the design. Thedore, the stnictural
components of the experùnental model were selected based on the relative deflection
ancilor deforrnation expected fiom the prototype structure. In order to accomplish this the
Sprangler's Iowa fomnla [40] was useci.
By applying the Iowa formula the horizontal deflection experienced by both the
prototype and the model can be related. From this relationship the stmctural components
of the model can be derived.
The resulting structure, d e r several iterations, was a metal pipe-arch made from flat
aluminium sheets Imm in thickness havhg a comgation profile as the one described in
Figure 3 -4 and overall dimensions as shown in Figure 3 -5.
The sectional properties for the experimental model were derived rnathematically.
These included the calculation of moment of inertia, 1; are* A; section modulus, S; and
radius of gyration, r. In calculating the properties, Wolford's formulas [SOI were used:
where-
1 = moment of inertia
S = section modulus
! = length of comgation
d = de@ of comgation
t = thickness of sheet
C5 = fhctor depending on shape or arc-and-tangent type comgation
Cs = factor dependhg on shape or arc-and-tangent type corrugation
3 3 Construction of the Pipe-Arch
Once the appropriate dimensions of the pipe-arch were determinecl (section 3.2)- the
next step was to build the structure.
The general procedure described by the American Society and Steel lndustry [ I l for
buildhg aaual structural steel plate structures, was adapted to the mode1 structure. Three
pipe-arches were buiit in the following manner:
First, two wooden templates were cut out of 19.0mm thick plywood. These templates
were cut according to the dimensions obtained in section 3.2 for the metal structure. The
two templates were then attached by using two pieces of 51 x 102m.m lumber having a
total length of 9 1 0mq as shown in Figures 3.6
The metal arch was made out of Imm thick galvanised aluminium sheets. Each
alwninium sheet had to be cut and comgated to the required length and comgation
profile. The metai was comgated by using a maoual comgation machine such as the one
show in Figure 3.7. This machine aiiows the user to set the re@ed comgation profile
by means of adjusting the levers located on the sides of the machine. Also, the required
c m t u r e of the metal arch c m be achieved by using the fiont and back levers.
After the aluminium sheets had been corrugated and cut, they were then manually
attached. This was accomplished by using 9.5mrn steel-aiumuiium rivets and an air rivet
gun. The rivets were placed dong the span of the structure. Each plate was secwed at
the crest and valley of the comgation profile. Typicsl examples of finished structural
plates are shown in Figure 3 -8.
Finally, afler the structurai plates were attached together, they were moulded to the
appropriate shape by using the wooden template shown previously in Figure 3.6. Figure
3.9 shows the f i shed pipe-arch structure.
3.4 Testing Equipmeot and Components
The equipment used during testhg consisted of seved reinforcement sheets of
geogriâ, a plywood-Plexiglas box, instntmentation and measuring devices, a loading
system, two nibber pressure tubes, Lake Erie sand, and three pipe-arches. The following
sections provide a detailed description of the properties of each piece of equipment.
3.4.1 Properties of the Lake Sand
The bacs used during construction of the structure was clean, fine. dry sand. Such
sand is obtained fiom Lake Erie and is available for commercial use. The properties of the
sand were investigated by applying the sand cone method and the direct shear test method.
B a d on the direct shear test method the angle of intemal fiction of the sand was
calculatecl to be $ = 40". The sand cone method revealed that the average d q compacted
unit weight of this particular batch of sand is y- = 16.8 kN / m3. with a saturation ratio S
= 92.7% and a moisture content o = 12.03%. A bief summary of these fidings is
provided in Table 3 -2.
3.4.2 The Sand Box
The pipe-arches were built inside a plywood-Plexiglas box. The box was made fiom
standard plywood sheets with a thickness of 2%nm and supported by 70 x 50 x 5mm steel
angles. One side of the box was made out of Plexiglas sheet with a thickness of 12.7m.m.
Two pain of steel angles of 60 x 60 x 6mm were used as vertical Meners and two pairs
of the same size angles were used as post stiffeners for the veriical sides. The overail
dimensions of the box are presented in Figure 3.10. The use of Plexiglas faciüated the
testing procedure specially regarding observation and control of the structure during
constmction.
A rectanpuiar hole was cut out fiom the fiont face of the box to facilitate placement of
the testing equipment. Also, four holes were cut out fiom the fiont face and back face of
the box to introduce two mbber pressure tubes used during testing.
3.43 The Loading Device
The pipe-arches were loaded by applyiug a stnp load. The footprht of the load ulas
equal to the inside width of the Plexiglas box, plus or minus a few millimetres to d o w for
fnaionless motion of a spreader beam during loading. The load was applied by using a 70
kN capacity hydraulic ram h e d vertically to the horizontal spreader beam of the loading
structural fiame. The load was transfèrred to the soil by a series of steps: first, the load
was hansferred fiom the hydraulic ram to the 950mm long spreader beam made out of
7 m thick steel plates. The beam then transfèrred the load to a piece of wood 950mm
long by 250mm wide and 38mm thick The wood rested over a rubber mat, 6mm thick, to
avoid local fdure in transferruig the load to the soil. Figure 3.1 1 shows the general
arrangement of the loading device and its overall dimensions.
3.4.4 Instrumentation
In order to meanire and record the desireci data, twenty electrk resistance strain
gauges per mode1 were installeci. A total of 10 different locations around the
cirderence of the pipe-arch were chosen for the gauge locations. Each location had
two main gauges installed, one on the crest of the comgation and a second one on the
valley of the same comgation profile. Figure 3.12 and 3.13 show these locations and the
generai arrangement of the snain gauges. The strain gauges with a gauge length equal to
lOmm were f&ricated by Showa Measuring Instruments. Ltd. The type of gauges used
were N 1 1 -FA- 10-350-23 gauges with a resistance of 349.8 R and a gauge factor of 2.1 1
k 1%.
The tangential strains detected during loading and backfiiling operation were recorded
with an Automatic Strain Indicator manufacturecl by Vishay Inter-Technology. The main
components of this machine are: The VIC-22 automatic primer, VIE-25 scan controller,
VIE-21 switch and balance unit, and eight digital strain indicators (Figure 3.17).
A total of eight mechanical did gauges were instaiied to measure and control the
deflection profile of the pipe-arches during the bacldilling operation and then loading of
the finished structure. The dial gauges were placed inside the structure as shom in
Figures 3.14 and 3.15.
Two universal flat load ceiis were also used during the loading of the structure in order
to monitor the applied load. Load ceil number 1 had a capacity of 25 kN and can be
identified by the serial nurnber equal to S N 06588-1. Load ce11 nurnber 2 was of the same
capacity as load ceii number 1 and its serial number was, S/N 012052-1. The load cells
and the beam are shown in Figure 3.16.
3-4.5 The Rubber fressure Tubes
In order to sirnulate loss of soil support due to fieeze-thaw cycle. A 7 m long piece
of flexible pressure hose was used to build two rubber pressure tubes each would hold air
inside to a maximum pressure of 2.98 kN/m2 . The flexible hose used had an inside
diameter qua1 to 130mm and was manufhctured by Checker Industrial. This type of
flemile hose is capable of holding pressure up to 7.25 k~/rn'. Each rubber tube built from
the flexible hose, had a span of 1 100mm.
In order to seai the ends of the tubes, four flanges having a diameter of 11Omm were
made out of stainless steel. These k g e s were placed one at each end of the tubes and
secureci with two 1 14mm clamps (see Figure 3.18). Once the clamps were secured and
tightened, a silicon paste was applied to the outer face of the flanges to seal any spaces
between the rubber tubes and the clamps. This last step was necessary to mnire that no
air would leak out f?om the rubber tubes during the backfilhg operation andor initial
loading of the structure.
Two holes lOmm in diameter were dnlled in each flange. One of the holes was used
to attach a 90" shut-off valve to regulate the amount of air pumped into the tubes. The
second hole serveci to instd a 14.5 kbJ/rn2 mechanicd dial gauge to monitor the air
pressure inside the tube.
3.4-6 The Reinforcement
Sheets of gm@d materiai were used for reinforcing the soil. Two out of the three
structures tested had reinforcing material attached to them by means of small aluminium
plates secured to the structure with 9Smm alUminium/steel rivets. The materid used for
reinforcement was fabricated by Tensar Polytechnologies, Inc. Such material is
commerciaily available under the name heavy duty hardware net. The size of the mesh
was 95 x 65mm. The width of the reinforcing sheet was 950mm (the width of the
reinforcement is equal to the span of the pipe-arch). The spacing between layers of
reinforcement was kept at approxïmately 1OOmm and a total of 8 layers of reinforcement
were used on each side of the structure (see Figure 3.19). The span of the reinforcing
mesh varieci in length dependhg on the location of any particular layer relative to the
metai structure. Figure 3.20 shows the length and general arrangement of the
reinforcement layers with respect to the metal structure.
In order to detemiine the strength of the materiai being used for reinforcement, a
simple test was developed. A test set-up similar to the one shown in Figure 3.21 was
employed. In this test small weights were added to an aiurninium rod clamped to a piece
of geogrid similar to the one shown in Figure 3.22. The piece of geogrid material being
tested was in tuni clamped to a steel beam by means of duminium plates and C-clamps.
As the weight was increased the elongation of the materiai was measured and recorded
until failure. A total of 30 tests were performed. Table 3.3 shows the average results of
the tests p e r f o d , also Figure 3.23 shows the load vernis elongation obtained for this
rnaterial. Fïnaily the data f?om the experirnental tests were checked against the nominal
values obtained fiom Tensar Polytechnologies Inc. The nominal values were somewhat
different f?om the magnitude of those obtained in the laboratory by about 3 to 4 %.
3.4.7 The PipeArch
A total of three pipe-arches were built as described in section 3.3. One of the three
pipe-arches was designed and built with no reinforcement material attached to it. The
other two structures were designed and built with geogrid rnaterial (used to reinforce the
s d ) aîtached to them.
3.5 Tating Procedure (Construction and Set-up)
In this section special attention is given to the testing procedure and the preparation of
the soi1 surrounding the structures tested. These two factors are critical since they
determine the stnictural behaviour of the structure and the reliabiiity of the results.
To ensure that each test provided the moa accurate results, the method outiined in this
section was ngorously foUowed and applied to each of the structures tested.
35.1 Preparation of Surrounding Soü and Backfiüi Operation
A good foundation for an underground pipe-arch will maintain the elevation and grade
of the invert to a planneci position (a) with the pipe-arch in the desired cross-sectionai
shape, and (b) without concentration of the foundation pressures that tend to produce
excessive stresses in the pipe-arch.
Buried pipe-arches rmist dways be relativeiy yielding compareci to the side fïii.
Thedore, preparing a hard bed for a buried pipe-arch would be equivalent to placing the
structure on an anvil for the load to strike. That is why softer foundations are desired.
When a load is appiied to a structure in a soft foundation, the load creates earth arching.
This results in reduction of the load on the structure as well as it provides a natual
cushioning effect on the structure.
In practice evaluation of the 508 is very important. When a soil contains undesirable
soil material such as muck or rock sledges, the soil in the site is excavated and replaced
with more desirable soil. For example large rocks or ledge rocks materials of poor or non-
uniform bearing capacity are often replaced with sand. Sand is accepted as a suitable fiii
because it provides uniform and relativeiy yielding support.
In the laboratory, Lake Erie sand was used as the fill material (see section 3.4.1). A
200mm thick layer (often referred as bedding) was compacted on the bottorn of the soi1
container. Then a 5ûmm thick layer of sand was pre-shaped to fit the invert radius of the
pipe-arch. The structure's beddiag was prepared wide enough to permit compacting the
rerninder of the backfiil under the haunches of the structure efficiently. As explainecl
earlier, this last layer (50mm thick) was lefi uncompaaed to allow relaxation of the
structure into the bedding.
Once the smicture was in place then the bacffiLl operation amed as follows:
For the unreinforced-soi1 structure:
Sand was placed in lOOmm thick layers and compacted on each side of the conduit.
Compacting was perfomed in an even rnanner starhg at a point closest to the
structure to the point W e s t away from the structure. This technique of compacting
the soi1 provided two advantages: an adequate strength of the compacted soil; and
second, it prevented pockets of uncompacteci soi1 fiom being placed next to structure.
Two rubber tubes located a few millimetres under the haunches of the structure were
fïiled with air to a constant pressure of 2.9 kN/m2 during the bacml operation.
Once the sand reached the top of the crown of the structure, two more layers, (one
lOOmm and a second one 75mm) were added and compacted on top of the structure.
For the hor&ont.lly reinforced-son structure:
The fïrst layer of reinforcing material atîached to the invert of the structure (geogrid)
was laid flat over the 200mm thick layer of compacted sand. This layer of geogrid was
placed undemeath the flexible hose fiUed with air.
A lOOmm layer of sand was placed on top of the first layer of geogrid and compacted
in the same mamer as it was done for the unreinforceci-soil structure (Figure 3.24).
For every lûûmm thick layer of well compacted sand, a layer of geogrid was unrolled
and laid f i t over the previous layer of sand. This process was repeated until the last
layer of reidorcement that was aîtached to the crown of the structure was covered
with sand (Figure 3 .Z).
4. Two more iayers of sand were placed over the last layer of geogrid. The first was a
100- thick layer of well compacted sand, and the second was a layer 75mm thick of
well compacted sand.
5. The rubber tubes were kept at a constant pressure of 2.9 kWm2 during the entire
process-
6. Each of the shens of geogrid was hefd in place and M y extended during the
b a c m g operation.
Experience and research have shown that the aitical density of bacW to be 85%
Standard Proctor density. Therefore, the backfili had to be compacted to a greater density
than the d c a l to assure good performance of the structure. A Standard Proctor densiîy
of 90% rninirnum was maintriinai during al1 of the test conducted, by means of a hand-held
tamper of 12 kg. in weight, such as the one shown in Figure 3.24.
3.52 Testhg of the SoBMetai Strucîure
The foliowing procedure appHes for both the unreinforced-soi1 and reinforceci-soi1
pipe-arches tested: During backfllhg, the structure was monitored by means of strain
gauge and dial gauges placed in the structure as describeci in section 3.4.4. Once the
Automatic Strain Indiaitor (see section 3.4.4) had been calibrated and set to zero,
readings for tangentid strain were taken after each layer of soi1 (100mm thick) had been
compacted. At the same time the deformation of the structure was monitored with 8 dial
gauges placed b ide the structure (see section 3 -4.4). This method was repeated until the
last layer of soi1 had been compacted. During the entire process of backfilling the pressure
in the flexible hoses located under the haunches was kept constant at 2.9 kWm2.
Mer compacting the soi1 on the top of the culvert, the loading device (described in
section 3.4.4) was set in place. With the aid of the hydraulic jack the load was applied to
the structure in equal uicrements. Mer each Uicrement readings for deflections, strains
and load magnitude were taken and recorded. During the application of the first few
increments of live load, the soi. surrounding the structure and specidly at the haunches
was kept undisturbed. The air pressure inside both of the rubber tubes was decreased
simultaneously and in small amounts for two of the three structures tested. Mer each
variation in pressure, readings for strains, deflections, and pressure inside the rubber tubes,
were taken and recorded.
A third horizontaliy reinforced-soil pipe-arch was tested in the sarne manner, except
that the pressure inside one of the two mbber tubes was kept constant at 2.9 kN/m2, while
the pressure inside the second rubber tube was decreased in s d amounts. Again, strains
and deflections were monitored and recorded for this structure.
Table 3.1
Sectional and Structural Properties for Corrugated Sheet an Plate Corrugation Profile: 152 x 51 mm
W al1 Area Tangent Taiigent Moment Section Radius Corrugation Thickness Lengt h Angle of Inertia Modulus of Gyration Radius
T A TL 1 S r CR mm mmA2 1 mm mm Degrees mmA4 / mm mmA3 / mm mm mm
i
Span Wse End Areri B Mt) R(c) R(b) mm mm mA2 mm mm mm mm
>
Table 3.2
Sand Cone Method Test Results ou Lake Erie Sand
Moisture Content
Dry weight of Sand Excavated (kg)
Volume of hole Excavated (mmA3 )
Dry unii weight of sand Compacted ( kN/mA3 )
ria fi Trial 2 Trial 3 Average
Table 3.3
Tensile Test Resufts: Teasar Multinetting
Force Gauge Length Elongation N (mm) ( % )
O 3 9.8 0.0 22.4 39-8 0.2 44.8 40.0 0.6 67.2 40.3 1.3 69.4 40.7 2.4 70.3 41.0 3 .O 71.7 41.6 4.5 76.2 41.7 4.9 78 -4 43.0 5.7 80.6 42.3 6.4 82.9 42.3 6.4 (fdure)
Figure 3.1 ' Structural Plate Shapes [3]
Figure 3.2 Corrugation Profile - Prototype PipeArch (ail in mm)
Figure 3.3 Prototype Pipe-Arch - Overall Dimensions (al1 in mm)
Figure 3.4 Corrugation Profile - Modei PipeArch (a11 in mm)
Figure 3.5 Mode1 Pipe-Arch Overall Dimensions (al1 in mm)
Figure 3.6 Plywood Template - Side View
Figure 3.7 Corrugation Machine - Front View
Figure 3.8 Structural Sections - Haunches
Figure 3.9 Finished Pipe-Arch
Figure 3.10 Sand Box - Overall Dimensions (ail in mm)
Figure 3.11 Loading Beam - Overall Dimensions (al1 in mm)
tcod n9 B e a ~ 4 p c ~ r l
Figure 3.12 Location of Strain Gauges (al1 in mm)
Figure 3.13 Arrangement of Strain Gauges
figure 3.14 Location of Dia1 Gauges (al1 in mm)
- ---L-- /
/
l - /
- . R O l o i Gouge
A' Nunber . ! Z I /
Figure 3.15 Arrangement of Dia1 Gauges
Figure 3.16 Load Cells and Loading Device
Figure 3.17 Automatic Strain Indicator
Figure 3.18 Components of Rubber Pressure Tubes
Figure 3.19 Spacing of Reinforcement (al1 in mm)
Figure 3.20 Length of Reinforcing Layers (al1 in mm)
Figure 331 Tende Test on Geogrid Sbeets - Equipment Set-up (ail in mm)
Figure 3.22 Geogrid Specimen (al1 in mm)
Figure 3.24 First Layer of Geogrid - At Haunch Level
Figure 3.25 Sixth Layer of Geogrid - Below Crown Level
CHAPTER IV
DISCUSSION OF RESULTS
4.1 Unreinforced-Soi1 Structure
The first experimentai mode1 built and tested was the unreidorced-soi1 pipe-arch
shown in Figure 4.1. &ring construction, readings for main and defieaion were taken
&er each layer of sand was compacted. The numerical results of the defonnations are
presented in Table 4.1. Here it can be observeci that the maximum deflection experienced
by the structure occurred at the crown and it was approximately equd to 4 7 m
(outwards). On the other h d , the invert of the structure deformed little in cornparison
with the rest of the structure having a total deflection of approxhately 2Smm (outwards).
The haunches of the structure, which are the most critical structural cornponents of the
pipe-arch, aiso experienced a maximum inward defomtion of 8mm.
The deformations experienced during construction were anticipateci basai on field
observations of pipe-arches and previous research available on this type of structures [23].
The strains recorded at this first stage served to calculate moments and &al forces
experienced by the structure during construction. These are shown in Tables 4.2 and 4.3.
From these tables, it can be obsexved that the maximum moment producing
compression at the inner fibers of the structure was qua1 to 79.6 N.m and it occuced at
the crown of the structure. The invert of the structure experienced a moment of 7.1 N.m.
in tension at the h e r fiben. F d y , the haunches' moments were 48 N.m in compression
at the inner fiben. Similar redts for axial force were obtained for the pipe-arch during
construction and are presented in Table 4.3.
The second stage of the test involved the application of a live load of a magnitude
equivalent to the standard live load required by the OHBDC [36] for these type of
structures.
During loading of the structure, the deftection, bending moment, and axial force varied
gradudy as the load increased. (note that during this stage the soi1 surrounding the metal
structure was kept undisturbed, by keeping the pressure inside the mbber tubes constant).
The ddection at the crown of the pipe-arch changed ftom approlrimately 4mm
(inward) for an applied load of 1.2 kN to 6 2 m (inward) for an applied load of 8.7 lcN.
(8.7 kN was the maximum load experienced by the structure before the soi1 surrounding
the structure failed). The haunches of the structure deformed little in cornparison to the
crown. They expenenced ddections ranghg tiom 0.OSrnm (outward) at a load of 1.2 kN
to 0.76mm (outward) at a load of 8.7 kN SUnilariy, the invert of the structure only
ddected 0.û9mm (inward) at a load of 8.7 kN (see figure 4.2). Table 4.4 shows the
deformation of the pipe-arch at different stages during loadiig.
The magnitude of the moment as weli as the axial force were also calculated at
different stages of loading. The moments at different loads are shown in Table 4.5 and the
axial force in Table 4.6. Table 4.5 shows that d u ~ g loading, the maximum bending
moment was 61 N.m producing tension at the inner fibers as shown in Figure 4.3. The
moment at the crown was equal to 38 N.m (tension at the inner fibers). Aiso, the moment
at the haunches and invert was determined to be 15 N.m (compression at the inner fibers)
and 4.5 N.m (tension at the inner fibers), respectively.
These moments were dl produced by an applied load of 8.7 kN, which was equal to
the maximum applied live load on the unreinforced-soi1 structure.
The axid force was also determined in the same manner as the bending moments and
ddections, Table 4.6 shows that the axial force at the cxown for the structure was 90.2
kN for the same load d e s c n i befiore. Also, results for the axial force at the haunches
and invert of the structure bave been included in this table. Figure 4.4 shows the axial
load at Merent stages of loading.
Once the applied load reached 8.7 kN, the next step was to study the effkct of
disturbing the soil around the haunches of the pipe-arch. This was accomplished by
reducing the pressure inside the rubber tubes. The pressure was reduced by letting air
flow out fiom the rubber tubes in a gradua1 rnanner. Tables 4.7 through 4.9 show the
variations in ddection, bending moment, axial force, nibber tube pressure, and applied
Ioad.
It can be readily observed from Table 4.7 and Figure 4.2 that the deflections at the
crown, haunches and invert increased to maximum value of 73mm (uiward), 3Smm
(outward) and 0.7mm (outward), respectiveiy. Also the applied live load of 8.7 kN had to
be reduced to a load of 6.8 kN, as a result of Mure of the soi1 surroundhg the structure.
Notice that this load was recorded once the pressure inside the rubber tubes had reached
zero.
S i a r results for bending moment and axial force for the pipe-arch are describecl in
Tables 4.8 and 4.9 and represented in Figures 4.3 and 4.4. The smcture was able to carry
the load successfully ody after small reductions in ihe pressure inside the rubber tubes had
occurred. However, once the soi1 completely lost its strength and the soi1 surrounding the
critical areas (haunches) of the pipe-arch had completely failed, the metal in various parts
of the structure starteci yielding, (see Tables 4.8 and 4.10) and the load carrying capacity
of the srnichue decreased. The pipe-arch structure eventuaily fded and was no longer
able to carry any load. A graphical history for the Mirent stages of the test conducted
on the meinforceci-soi1 structure is presented in Figures 4.5 through 4.7.
4.2 Reinfomd-Soü Structure (Flilure of the Soil Surrounding Both Corner Plates)
The experimental study of the horizontally reinforced-soi1 structure was conducted in a
similar manner as the one for the unreinforced-soil pipe-arch. The düference was that
geotextile material was used to horizontally reuiforce the soil surrounding the pipe-arch.
hiring construction the deformation, bending moment, and axial force were
monitored and measured. Tables 4.10 through 4.12 show the results obtained during
construction. The maximum defiection, during backfilling, occurred at the crown of the
structure and was equal to 25. lmm (outward), the haunches and the invert of the pipe-
arch defonned 4mm (inward) and 1.3mm (outward), respectively.
The bending moments obtained are given in Table 4.1 1. The maximum bending
moment recorded during construction was equal to 36.1 N-m (compression at the inner
fibers) and it was calculated f?om the readings of the strain gauges located at the crown of
the pipe-arch. The invert of the structure experienced a moment equal to 0.6 N.m
(compression at the innef fibers) and the corresponding moments at the haunches were
equal to 5.6 N.m (tension at the inner fibers). Likewise, results for the axial force are
given in Table 4.1 2.
At the loading stage, the horizontaily reinforced-soi1 pipe-arch was able to carry loads
of up to 11.2 W. The loading stage provided the following red ts (see Tables 4.13
through 4.15 and Figures 4.8 through 4.10): the deffection at the crown varïed fiom 2mm
(inward) at a initial applied load of 4.3 IrN to 12.8mm (inward) at a maximum applied load
of 11.2 kN. The conespondhg bencihg moment at these two stages were, 24.4 N.m
(tension at the inner fibers) at a load of 4.3 kN, and 1 5.9 N.m (tension at the inner fibers)
at a load of 11 -2 kN.
The haunches of the structure were aiso monitored and the r d t s obtained were as
follows: the deflection varied fiom 0.05mm (outward) at 4.3 kN to 0.23mm (outward) at a
load of 1 1.2 N.m. The corresponding moments were: 6.63 N.m (tension at the inner
fibers) at a load of 4.3 ldrl and 14.6 N.m (tension at the inner fibers) at a load of 1 1.2 M.
The invert of the pipe-arch produced the foilowing results: the deflection changed
form O.Omm at 4.3 kN. to 0 . 5 m (outward) at 1 1.2 kN. Also, the bending moment was
caldateci to be 0.6 N.m (tension at the inner fibers) at 4.3 kN and it varied to 0.89 N.m
(tension at the inner fiben) at a load of 1 1.2 kN.
The resuhs obtained for the axial force of the pipe-arc4 are presented in Table 4.15
and graphically shown in Figure 4.1 0.
Next, the finai stage of the experimentd test (Le.: when the soi1 is disturbed and the
pressure inside the rubber tubes is decreased) produced the results given in Tables 4.16
through 4.18 and are graphicaliy presented in Figures 4.8 through 4.1 O.
One important observation to notice fiom these results is that, small variations in the
pressure inside the rubber tubes had alrnost no effèct on the bending moment, deflection,
and axial force for the reinforceci-soil pipe-arch. Also, as the soil around the structure
started to fa the load ca-g capacity of the pipe-arch began to decrease, but it became
stable after a few seconds.
Finally, once the pressure ui the rubber tubes was reduced considerably, the load
canying capacity of the structure remaineci almoa unchangeci. This can be readily
obsefved fkom the renilts descnied in Tables 4.1 6 through 4.1 8. It is obvious fiom these
r&s that the reiaforcing material atîached to the structure was sàll carrying load even at
the 1st stage of testing, (Le.: when the soi1 surroundhg the stmcture had undergone a
considerable amount of M u e ) . The structure seems to recover its strength Ooad carrying
capacity) d e r the load surrounding the haunches had ftiiled (see Tables 4.16 through
4.18). Figures 4.1 1 shows the reinforcecl structure at yielding .
4.3 ReinforcebSoil Strncture (Faiiure of the Soi1 Surrouadiag One Corner Phte)
The study of a reinforceci-soil structure when uneven mil settlernents ocnir was also
carried out in the laboratory. The fkst two stages of testing ( b a c m g and loading
before distwbing the mil) gave similar resuits as to the ones obtained in the previous test.
The last stage of testing, when the pressure was reduced in one of the rubber tubes,
provided sirnilar resdts to the remforcecl-soi1 pipe-arch subjected to even soi1 settiements.
Again, the strength and beneficial e f f i s of the reinforcing material appear to be
praeut even d e r the load carxying capacity of the soi1 had decreased considerably. These
hdings are summarised in Tables 4.19 through 4.21 and shown in Figures 4.12 through
4.14.
4.4 Cornparison between Unninforced-Soil and Reinforced-Soü Structures
In cornparison, the total deflection at the crown for the meinforced-soi1 model,
after construction, was 48mm (outward) which is almost 25mm more that the one
experienced for the reinforced-soi1 pipe-arch, similar cornparisons can be made at the
haunches, invert and sides of the structure. This difference proves to be a direct result
fiom the introduction of the reinforcing sheets. Figures 4.1 5 through 4.1 7, compare the
benduig moment, deflection and axial force for both reinforced-soi1 and unreinforced-mil
stnictures during construction.
The introduction of reinforcing sheets of geotextile material laid transversefy to the
axis of the pipe-arch, proved to be bendicial in increasing the load carrying capacity of the
structure when temporary loads were applied to it. Since, this partida. pipe-arch was
under shaiiow soil cover conditions, temporary loads represent a great concem. The load
carrying capacity of the structure was increased by almost 400h when reinforcing sheets of
geotextile material were attached to the pipe-arch. The bending moments in the structure
were almost eliminated, and the axhi force and deflections g r d y reàuced. This can be
readily observed in Figures 4.1 8 through 4.2 1 .
As explained earlier, rubber tubes med with air, located near to the haunches of the
pipe-arch, were used to sirnulate the effect of fieeze-thaw cycles which occur often in cold
regions. Figures 4.22 and 4.23 show that the reinforceci-soi1 structure sders iittie
deformations when the pressure inside the pressure tubes was decreased. On the other
hand when no reinforcement was osed the soii surroundhg the structure move rapidly.
This rapid fdure of the soil surroundhg the structure, produceci a sudden and
catastrophic failure of the unreinforceci-soil structure, as shown in figure 4.7.
The axial forces and large bending moments accornpanied with this effect (fieezethaw
cycle) were also reduced when a rrinforced-soi1 system was used instead of an
unreinforced-soil system. This is show in Figures 4.24 through 4.27.
Table 4.3
Pipe-Arch Axial Force (Unreinforced-Soil) Stage 1 : Construction and Backfilling
(kN )
2 3 (Haunch)
4 5
6 (Cmwn) 7 8
9 (Haunch)
Soil Height From Invert (mm)
Strain Gaune Location 1 onvert)
1 02 204 306 4013 SI 0 61 2 97iJ
36.4 37.2 37.5 37.1 36.7 36.5 35.9
Table 4.4
Rubber Tuba - Pressure (kN/rnA2) Applied Load ( kN ) Diril Gauge Location O
1 (cmwn) 2
3 (Baunch) 4
S (Invert) 6
7(Haunch) 8
Pipe-Arch Deneetion (Unninforced-Soil) Stage 2: Application of an Externd Load
(mm) 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 1.2 1.7 2.4 4.0 5.7 7.0 8.4 8.7
Table 4.6
PipeArch Axial Force (Unreinforced-Soil) Stage 2: Appücation of an Extemal Load
(kN)
2 3 (Haunch)
4 5
6 (Crown) 7 8
9 (Haunch) 10
Rubber Tubes - Presaiure (kNlmA2) Applicd Load ( kN )
Strdn Caupre Location 1 (Invert)
2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 1 *2 1,7 2,4 , 4.0 5.7 7.0 8.4 8 3
35.5 35.4 35.2 35.0 34.9 34.8 34.7 34.6
Table 4.7
Rubber Tubes - Pressure (W/mA2) Applied Laad ( kN ) Dial Gauae Location
b-
1 (crown) 2
3 (Haunch) 4
S (Invert) 6
7(Haunch)
PipeArch Deflection (Unreinforced-Soil) Stage 3: Soi1 Fiilure
(mm) 2.61 2.32 1.74 2.61 2.03 1 .45 1.45 0.58 O
Table 4.9
Pipe-Arch Axial Force (Unreinforced-Soil) S t a ~ e 3: Soil Failure
(M) Rubber Tubes - Pressure ( k ~ l r n ~ 2 ) 1 2.6 1 2.32 1.74 0.58 2.M 1.45 0.58 O
Strain Cauee Location 1 (lnvert)
2 3 (Haunch)
4 5
6 (Crown) 7 8
9 (Haunch)
Table 4.1 0
PipeArch Deflection (Reinforced-Soi]) Stage 1: Construction and BackFüling
(mm) Soi1 Height From Invert
(mm) 1 02 204 306 408 51 O 61 2 970 Dial Cawe Location
1 (Crown) O. 2 -2.9 -6.9 -1 2.8 -1 7.4 -23.9 -25,1
Table 4.1 1
Soil Aeight From Invert (mm)
Strain Gauge Location 1 (lnvert)
2 3 (Haunch)
4 5
6(C row n)
PipeArch Bending Moment (Reinforced-Soi!) Stage 1: Construction aod Backfîlling
Table 4.1 2
PipoArc h Axial Force (Reinforced-Soil) Stage 1: Construction and Backfi~lling
Strain Gauae Location 1 (lnvert)
(kN)
2 3 (Haunch)
4 S
6(Crown) 7
Soil Height From Inverl (mm)
9 (Raunch)
102 2W 306 408 51 O 61 2 970
Table 4.14
Pipe-Arcb Bending Moment (Reinforced-Soil) Stage 2: Application of an External Load
Strain Gauee Location 1 (Invert)
( N.m )
2 3 (Haunch)
4
Rubber Tuber-Pmsaure (kNlmA2) Applied Load ( kN )
9 (Haunch)
2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 4.3 5.9 6.2 7.1 8.1 9.4 10.4 11.1 11.2
Table 4.16
PipeArch Deflcction (Reinforced-Soil) Stage 3: Soil Faüure
Diai Gauge Location 1 (Crown)
(mm)
7(H aunc h)
Rubber Tubes-Pressure (kN/mA2) Applied Lolid ( kN )
f
2.61 2.32 2.03 1.74 1.4s 0.58 1.45 1.45 O 9.8 9.8 9.8 9.8 9.8 9.8 8.8 9.2 1 0.7
Table 4.1 7
PipeArch Bending Moment (Reinforced-Soil) Stage 3: Soil Failure
( N.m )
2 3 (Htiunch)
4 S
6(Crown) 7 8
9 (Haunch) 10
Rubber Tu bes-Prensure (kNlmA2) Apptied Load ( kN )
Strain Gauge Location 1 (Invert)
2.61 2.32 2.03 1.74 1 .4S 0.58 1 .JS 1.43 O 9 8 9.8 9.8 9.8 9.8 9.8 8.8 9.2 10.7
0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1 .O
Table 4.1 9
Rubber Tube 1 - Pressure (kNlmA2) Rubber Tube 2 - Pressure (kNlmA2)
Applled Load ( kN ) Strain Gaune Location
1 (lnvert) 2
3 (Haunch) 4 5
6(Crown) 7 8
9 (Haunch) 10
Pipe-Arch Bending Moment (Reinforced-Soil) Uneven Soil Failure
Table 4.20
PipeArch Axial Force (ReinforceMoil) Uneven Soil Failure
Strain Cauge Location rl
1 (Invert) 22.8 22.9 22.8 22.8 22.8 22.7
(kN)
2 3 (Haunch)
4 S
6(Crown) 7 8
9 (Haunch)
Rubbcr Tube 1 - Pressure (kNlmA2) Rubber Tube 2 - Pressure (kNlmA2)
Applied Load ( kN )
2.9 2.9 2,9 2.9 2.9 2.9 2,03 1.45 0.58 O O O 10.7 10.7 10.7 10.7 12.0 12.7
Table 4,21
Pipe-Arch Deflection (Reinforced-Soil) Uneven Soil Failure
Dia1 Gauge Location 1 (Crown)
2 3 (Haunch)
4 5 (Invert)
6 7 (Haunch)
8
(mm) Rubber Tube 1 - Presnure (kNlmA2) Rubber Tube 2 - Pmssure (kNlmA2)
Applied Load ( kN )
2.9 2.9 2.9 2.9 2,9 2.9 2.03 1.45 O38 0 O O 10.7 10.7 1 0,7 10.7 12.0 12.7
Figure 4.1 Unreinforceci-Soi1 Pipe-Arch Structure
Figure 4.2 Unreinforced-Soi1 Pipe-Arch - Deflected Sbape
A. Reference shape B. Soi1 level at 510 mm from invert C. Soil level 175 mm above erown - Applied load 7 IrN - Rubber tube pressure
of 2.9 kN/m2 D. Soil level175 mm sbove crown - Appiied load 8.7 kN - Rubber tube
pressure of 1.74 kN/mz
Figure 4.3 Unreinforced-Soi1 Pipe-Areh - Bending Moment Distribution
A. Reference shape B. Soi1 levei 175 mm above crown - Applied load 7 kN - Rubber tube pressure
of 2.9 kN/m2 C. Soi1 level175 mm above crown - Applied load 8.7 kN - Rubber tube
pressure of 1.74 kN/m2
Fipre 4.4 Unreinforced-Soi1 PipeArch - Axial Load
A. Reference shape B. Soil level 175 mm above crown - Applied load 7 kN - Rubber tube pressure
of 2.9 w / m 2 C. Soil levei 175 mm above crown - Applied load 8.7 kN - Rubber tube
pressure of 1.74 kN/m2
Figure 4.5 Failure of Soi1 at Lnvert and Haunches
Figure 4.6 Unreinforced-Soi1 Pipe-Arch - Yielding At Crown
Figure 4.7 Catastrophic Failure of Unreinforced-Soi1 PipeArch
Figure 4.8 Reinforceci-Soi1 PipeArch - Deflected Shape
A. Reference shape B. Soi1 level at 510 mm from invert C. Soil level 175 mm above crown - Applied load 9.4 kN - Rubber tubes
pressure of 2.9 kN/m2 D. Soil level175 mm above crown - Applied load 9.8 kN - Rubber tubes
pressure of 1.45 kN/m2
Figure 4.9 Reinforced-Soi1 Pipe-Arch - Bending Moment Distribution
A. Reference shape B. Soil level175 mm above erown - Applied load 9.4 kN - Rubber tubes
pressure of 2.9 kN/m2 C. Soil level175 mm above crown - Applied load 9.8 IrN - Rubber tubes
pressure of 1.74 kN/m2
Figure 4.1 0 Reinforced-Soi1 Pipe-Arch - Axial Load
A. Reference shape Bo Soil fevel175 mm above crown - Applied load 9.4 W - Rubber tubes
pressure of 2.9 kN/m2 C. Soil level175 mm above crown - Applied load 9.8 kN - Rubber tubes
pressure of 1.74 kN/m2
Figure 4.11 Reinforced-Soi1 Pipe-Arch - At First Sign of Yielding
Figure 4.12 Bending Moment Diagram for Pipe-Arch - Uneven Soil Failure
A. Reference shape B. Soil levd 175 mm above crown - Applied load 10.7 kN - Rubber tubes
pressure of 2.9 kN/m2 and 2.03 kN/m2 C. Soil lwel175 mm above crown - Applied load 12.7 kN - Rubber tubes
pressure of 2.9 kN/m2 and O kN/m2
Figure 4.13 M a i Force Diagram for Pipe-Arch - Uneven Soi1 Failure
A Reference shape B. Soi1 level175 mm above crown - Applied load 10.7 IrN - Rubber tubes
pressure of 2.9 kN/m2 and 2.03 kN/rn2 C. Soi1 level 175 mm above crown - Appiied load 12.7 kN - Rubber tubes
pressure of 2.9 kN/m2 and O kN/m2
Figure 4.14 Deflected Shape for Pipe-Arch - Unweo Soil Fsilure
A Reference shape Bo Soil level 175 mm mbove crown - Apptied load 10.7 kN - Rubber tubes
pressure of 2.9 kN/m2 and 2.03 w/m2 C. Soil level175 mm above crown - Applied load 12.7 kN - Rubber tubes
pressure of 2.9 kN/m2 and O k.N/m2
Figure 4.15 Deflected Shape for PipeArch - Soi1 Level at 970 mm from Invert
A. Reference shape B. Reinforced-soi1 C. un reinforceci-soi1
I l l
Figure 4.16 Bending Moment Diagram for Pipe-Arch - Soi1 Level at 970 mm from Invert
A. Reference shape B. Reinforced-soit C. Unreinforced-soi1
Figure 4.17 Axial Force Diagram for PipeArch - Soi1 Level at 970 mm from Invert
A. Rderence shape B. Reinforced-soi1 C. Un reinfo rced-soi1
Figure 4.18 Ddected Shape for PipeArch - Applied Load Range 6.9 IrN to 7.1 IrN
A. Reference shape B. Reinforced-soi1 CI Unreinforceci-soi1
Figure 4.19 Deflected Shape for Pipe-Arch - Applied Load Range 8.7 kN to 9.4 kN
A Reference shape B. Reinfo rced-soi1 CI Unreinforced-soi1
Figure 420 Axial Force Diagram for PipeArch - Applied Load Range 5.6 kN to 5.9 kN
A. Reference shape B. Reinforced-soi1 C. Unreinforceci-soi1
Figure 4.21 Bending Moment Diagram for PipeArch - Applied Load Range 6.9 kN to 7.1 kN
A. Reference shape B. Unreinforced-soi1 C. Reinforced-soi1
Figure 4.22 Deflected Shape for Pipe-Arch - Applied Load Range 8.3 kN to 8.8 kN - Rubber Tubes Pressure of 1.45 kN/m2
Figure 4.23 Deflected Shape for Pipe-Arch
A Reference shape B. Reinforced-soi1 - Applied load 10.7 kN - Rubber tubes pressure O kN/m2 C. Unreinforced-soi1 - Applied load 6.8 kN - Rubber tubes pressure O kN/m2
Figure 424 Bending Moment Diagram for Pipe-Arch - Applied Load Range 8.3 kN to 8.8 W - Rubber Tubes Pressure 1.45 kNlm2
A. Reterence shape B. Reinfo rced-soi1 Ce Unreinforced-soi1
Figure 4.25 Bending Moment Diagram for PipeArch
A. Refereace sbape B. Reinforced-soi1 - Applied lord 10.7 icN - Rubber tubes pressure O kN/m2 C. Unreinforced-soi1 - Applied load 6.8 kN - Rubber tubes pressure O kN/rn2
Figure 4.26 Axial Force Diagram for Pipe-Arch - Applied Load Range 8.3 kN to 8.8 kN - Rubber Tubes Pressure 1.45 kNlm2
A. Refereuce shape B. Reinforced-soi1 C. Unreinforceci-soi1
Figure 4.27 Axial Force Moment Diagrnm for Pipe-Arch
A. Rderence shape B. Reinforced-soi1 - Applied load 6.8 kN - Rubber tubes pressure O kN/m2 C. Unreinforced-soi1 - Applied load 10.7 kN - Rubber tubes pressure O kN/m2
CaAPTER V
DESIGN
This chapter de& with the design of a reinforced-soi1 pipe-arch. The pipe-arch
designed in this chapter is sirnilar to the structure used as a prototype for obtaining the
models tested in the laboratory. The properties of the comgation profiie for this structure
as well as its overail dimensions are similar to the prototype structure described in chapîer
3. The material assumed for reinforcement is standard geogrid rnaterial commonly used in
practice.
Pro blem:
It is required to design a reinforced-soii pipe-arch that wiU cany a highway load equal
to 7.7 kPa. The structure is to have a span S = 6250m and a rise R = 3910mm. nie
suggested comgation profile of the metai is 152 x 5 1 mm (as described in chapter 3). The
comer plate of the structure has a radius R, = 840mm (see figure 5.1). The height of soil
cover is required to be H = 2m. The properties of the soil are as foiiows: angle of intemai
fiction éi = 40"; Weight of soi1 y = 19 kN/m3 . The rnaterial to be used to reinforce the
soil is BXlOO Tensar biaxial geogrid. Such materid is made out of polypropylene and has
the foilowing properties [14]: aperture size = 33mm; Open area = 70 % of total area;
Thickness = 2.286mm; Tende strength = 1 82 kN/m (minimum).
The elements required in the design are: the wail thickness of the metal structure, the
bolting requirements, the corner plate pressure and the length and spacing of the layers of
geogrid material.
The f h t step is to determine the bacm soi1 density required. For this case 85%
minimum soi1 den* is assumed.
Next, the design pressure [l] for this structure is obtained fiom:
where,
P, = total vertical applied load, kPa
DL = dead load, kPa
LL = h e load, kPa
H = height of cover, rn
S =span,m
K = soi1 density factor:
for S s H & Standard Proctor soi1 density 85% K = 0.86
for S 5 H & Standard Roctor soi1 density Wh K = 0.75
for S I H & Standard Proctor soi1 density 65% K = 0.65
for S > H & Any density K = 1.0
By applying equation (5-1) the design pressure for the conditions described above is
calculated as follows:
P,, = (1) ((19)(2) + (7.7)) = 45.7 kPa
From the ~g compression theory [48], the compressive thnist in the pipe-arch is
deterrnined by the foilowing relation:
where,
C = ring compression, kN/m
P, = design pressure? kPa
S =span,m
Therefore, ffom equation (5-2) the compressive t h s t in the conduit wali is
detennùied as follows:
The dowable wall stress, E, for this structure is determinecl by using the foiiowing
relationship :
where,
fc = design stress, MPa
fb = uitimate compressive wall stress, MPa
The ultimate compressive wall stress is cdculated by using equations (2-5), (2-61,
and/or (2-7). then by applying equation (5-3) the design waii stress is obtained and is @en
as:
& = 202 / 2 = 101 MPa for a 152 x 5 I m comgation
Next, the waiJ cross-sectional area, 4 = 1.415 mrn2/mm, can be determined fkom the
relationship between the compressive thrust and the aliowable wd stress [ 11, as foîiows:
w here,
C = ring compressio~ kN/m
fc = wd design stress, MPa
Equation (5-4). gives a value of 1.415 mm2/mm for the wall cross-sectional area.
From design tables provided by the American Iron and Steel Institute [l], a specified wall
thickness of 3 . h m provides a wall cross-sectional area of 3.522 mm2/m with a moment
of inertia I = 1057.25 mma/mm. Since 3 -522 mm2/mm > 1 -41 5 mm2/mm required, the
3mm thickness is acceptable for this design.
Next, the han- stiffiiess [l], FF, for the pipe-arch it is found by trial and error as
follows:
Iteration 1:
where,
S =spaq mm
E = Young modulus of elasticity for steel = 200 x (IO).', MPa
1 = moment of Inertia, m'/mm
From equation (5-5):
FF= ( (6250)* / (200x lo3)( (057.25) ) =0.185mmN
For a pipe-arch the maximum dowable flexible factor, FF', is given by [ I l :
FF' = 1.5 FF,
where,
FF. = recomrnended maximum flexible factor for o r d m installatios mmM
Values for FF. have been established through experience, based on minimum pipe
e e s s requirements for practical handling and installation without undue care or bracing.
These values are avaiiable through reference [ I l for Werent cornigaiion profles. From
these reference for a pipe-arch with a cormgation profile of 152 x 51mm, FFa is
determined to be 0.1 14 mm/N. Therefore the maximum aüowable flexible factor fkom (5-
6) is:
Since FF = 0.185 > FF' = 0.171 the design is not acceptable
Iteration 2:
By increasing the thichess of the metal to 4.0mm, then the moment of inertia becomes
1 = 1867.12 mm4/mm. Equation (5 -5 ) can be tried again for this new cross-section:
Therefore thû design is acceptable and 4.ûmm thick plates for construction can be
used*
Next, the corner bearing pressure on the soil must be determineci; this can be estimated
Iiom [il:
where,
P. = pressure acting on soi1 at corners, kPa
R, = radius at crown, mm
R, = radius of corner, mm
P, = design pressure, kPa
Therefore, the dowable comer bearing pressure on the soil must be at lest 170 kPa.
The reinforcement and its placement is designed by applying the equations formulated
in section 2.4.2.1. First, the minimum required tende strength of the geogrid must be
checked, this is accomplished as foilows 1141:
w here,
s = Rankine's active pressure per meter, kNlm
01 = angle of intemal fiction of the soi1
y, = Unit weight of soii, kN/m3
z = depth eom top of soil cover to the layer of reinforcement, m
H = total depth of excavation, rn
For a maximum depth of 6 m ( i-e.: at z = H ) equation (5-8), becomes identical to
equation (2- 15):
Such value is compared to the specified tensile modulus for the geogrid available for
design. The tensile areagth for BXlOO geogrid is oc = 182 W/m, which is much Iarger
than the minimum required. Therefore the strength of the geogrid mesh is adequate.
The spacing for the layers of the geogrid is determinecl as follows:
First Rankine's coefficient of active earth pressure is found Erom equation (2- 15):
Next the spacing ( S,) at different depths is fomd f?om the followllig equation [14]:
where,
QG = Allowable strength of geogrid per meter, kN/m
y1 = Unit weight of soii, kN/m3
K, = Rankine earth pressure coefficient
FSm, = Factor of safety against tie breaking
The results obtained form this equation at different levels are m a r i s e d in Table 5.1.
Next, the length for each layer of reinforcement is determined for the most critical
spacing between layers (i.e. 840mm). This is done by using equation (2-16).
The resufting lengths are as show in table 5.1. From these results the length for each
layer is chosen depending on the depth at which the geogrid is located.
For this p a m d a r structure a total of 7 layers per side are required. Table 5.2 shows
the lengths rounded for each layer and its correspondhg location with respect to the pipe-
arch.
Table 5.1
Geogrid Soil-Reinforcement - Spacing and Horizontal Length BXlOO - Tensar Multinetting
z S(v) L W b ) W.) WP) Factor Rankine Factor
Depth of Soi1 Spacing Length* of Safety Coelicient of Safety m m mm
1
* The length of reinforcement is based on the most critical spacing between layers ( Le. = 850 mm )
Table 5.2
Length of Geogrid Layers BXlOO - Tensar Multinetting
Location L Distance from Invert of Structure Length
m mm
* Continuous layer laid on top of the structure multiply distance times two.
Figure 5.1 Overall Pipe-Arch Dimensions (al1 in mm)
C-R VI
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
The following conclusions can be drawn nom this investigation:
1. Large moments, axial forces and deflections were observed during construction when
the unreinforced-soi1 structure was being backfded. On the other hand when the
horizontally reinforced-soi1 structures were bacwed, the moments, deflections and
lucial forces were reduced to a minimum. Thus, the shape of the structure was better
controlled.
2. The advmtage of the reinforcecl-soil systern are: first, aJ the defleaions that ocnu
during backfilling are kept evenly distributeci around the stnictare. Second, this system
not only proves to be beneficial when compaaing the so& but also later on when the
structure is being subjected to tanporary construction loads.
3. The load carrying capacity of the structure was greatly increased when the soii was
reinforceci with layers of geogrid material.
4. The haunches and invert of the reinforceci-soil pipe-arch experïenced iittle or no
defkctions, moments, andor axial forces when the surrounding soi1 first stW to fail.
5 . The fiction developed dong the mesh interfaces, made it possible to enhance the shear
resistance of the soil.
6. Sudden and catastrophic Mure, often found in unreinforced-soi1 pipe-arches can be
elimiiiated when using reinforcement. Reinforcing the soi1 surrounding the pipe-arch
changes the failure mode to a more predictable and progressive collapse.
6.2 Recommendations
Further research should be conducted. It is recommended that:
1. A study of the structural behaviour of a fûii scale mode1 be conduaed to fiuther
investigate the information obtamed fkom small scale models.
2. Testing of additional models should be conducted to detennine the beneficial effects of
adding more reinforcing maîerial to the critical components of the pipe-arch (invert and
haunches).
3. More research be performed to study the e f f i of using geogrid/geotextile materials
for other shapes of soil-metal structures.
4. A f i t e element analysis on the structural behaviour of full sale models should be
conducted. Such an andysis can be ver-ed by experimentai testing of fidi scale
rnodels.
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VITA AUCTORIS
The author was bom on March 3, 1972 in San Salvador, El Salvador. In 1989, the
author completed secondary school at the Externado San Jose secondary school in San
Salvador city. The author aniveci to Canada in 1989 and lived in Chatham, Ontario,
Canada for two years. In 1991, the author joined the Faculty of Engineering at the
University of Wmdsor, Wmdsor, Ontario, Canada. Then, in 1995 he graduated with a
Degree of Bachelor of Applied Science in Civil Enginee~g ("Second Chss Honours").
in 1996, he joined the Civil and Enwonmentai Engineering Department at the
University of Widsor as a Research and Teaching assistant. Findy, the author prepared
this thesis in partial fùWnent of requirements for the Degree of Master of Applied
Science in Civil Enginee~g
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