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CABLE-SUSPENDED PEDESTRIAN BRIDGE DESIGN
FOR RURAL CONSTRUCTION
by
AVERY LOUISE BANG
B.S. University of Iowa, 2007
B.A. University of Iowa, 2007
A project submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirement for the degree of
Master of Science
Department of Civil and Environmental Engineering
2009
2
Abstract
Lack of access to health care facilities, schools and markets is a great impediment.
For many communities in the developing world, alleviating rural isolation would help
break the cycle of poverty by providing access to educational opportunities, markets,
medical clinics and other basic services. The development of cable suspended
pedestrian bridges are one of the most economical and sustainable solutions to rural
isolation. This also presents a challenge for performing engineering analysis with
experimental material properties. A review of simple techniques for soil testing,
geotechnical models and designs for equivalent structures are reviewed. Soil
parameters are proven to have a minimal impact on the ultimate uplift capacity
required for anchor pull-out design. Recommendations are presented for design and
construction in the developing world. A case-study in Ethiopia provides a baseline
example as simplifying design assumptions are justified, and design process outlined.
Finally, lessons learned from simplifying design for development purposes and
general ethical considerations are discussed.
3
This report entitled:
Pedestrian Bridge Design Best Practices for Rural Construction
written by Avery Louise Bang
has been approved by the Department of Civil and Environmental Engineering
____________________________________________________ Professor Bernard Amadei (committee chair)
____________________________________________________ Asst Professor John McCartney
____________________________________________________ David Jubenville, P.E., Instructor
Date
The final copy of this paper has been examined by the signatories, and we find that both the content and the form meet the acceptable presentation standards
of scholarly work in the above mentioned discipline.
4
Table of Contents
Chapter 1: Introduction and Background .................................................................... 10
1.1 Cable-Suspended Pedestrian Bridges ............................................................... 10
1.1.1 Rural Transportation .................................................................................. 10
1.1.2 Pedestrian Bridges ..................................................................................... 10
1.1.3 Bridges to Prosperity.................................................................................. 13
1.1.4 Case Study: Sebara Dildi, Ethiopia ............................................................ 15
1.2 Research Objectives .......................................................................................... 19
1.3 Expected Research Contributions ..................................................................... 20
1.4 Organization of Report ..................................................................................... 20
Chapter 2: Typical Bridge Design Scenario ............................................................... 22
2.1 Model of Typical Bridge ................................................................................... 22
2.2 Structural Failure Parameters ............................................................................ 24
2.3 Geotechnical Failure Parameters ...................................................................... 26
Chapter 3: Structural Considerations .......................................................................... 28
3.1 Structural Analysis ............................................................................................ 28
3.1.1 Horizontal Tension ..................................................................................... 29
3.2 Pedestrian Bridge Loading ................................................................................ 31
3.2.1 Liveloads .................................................................................................... 31
5
3.2.2 Dead Loads ................................................................................................ 33
3.2.3 Wind Loads (Overturning) ......................................................................... 33
3.2.4 Load Combinations .................................................................................... 34
3.3 Structural Design .............................................................................................. 34
3.3.1 Suspenders ................................................................................................. 34
3.3.2 Main Cables ............................................................................................... 35
3.3.3 Decking ...................................................................................................... 38
Chapter 4: Geotechnical Considerations ..................................................................... 42
4.1 Fine-Grained Soils: Clays and Silts .................................................................. 42
4.1.1 Geotechnical Analysis & Anchor Capacity ............................................... 42
4.1.2 Recommended Parameters ......................................................................... 49
4.2 Coarse-Grained Soils: Sands, Gravels and Non-Plastic Silts ........................... 49
4.2.1 Geotechnical Analysis & Anchor Capacity ............................................... 49
4.2.2 Recommended Parameters ......................................................................... 53
4.3 Geotechnical Design ......................................................................................... 53
4.3.1 Design Process ........................................................................................... 53
4.3.2 Soil Classification & Testing ..................................................................... 55
4.4.3 Design Example: Sebara Dildi Case-Study ............................................... 65
Chapter 5: Quality Control Considerations ................................................................. 67
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5.1 Material Specifications ..................................................................................... 67
5.1.1 Concrete Mixture ....................................................................................... 67
5.1.2 Steel Cable ................................................................................................. 69
5.1.3 Cable Clamps ............................................................................................. 71
5.2 Construction Quality Control ............................................................................ 72
5.2.1 Cable Clamps ............................................................................................. 72
5.2.2 Backfill and Compaction ........................................................................... 74
Chapter 6: Conclusion and Discussion ....................................................................... 76
6.1 Summary ........................................................................................................... 76
6.2 Design for the Developing World ..................................................................... 77
6.2.1 Design Simplification ................................................................................ 77
6.2.2 Ethics of Accountability ............................................................................ 78
6.2.3 Transferring Best Practices to Developing Nations ................................... 80
6.3 Opportunities for Future Research .................................................................... 82
References ................................................................................................................... 84
Appendices .................................................................................................................. 88
Appendix 1: Soil Identification Table (Helvetas, 2001) ......................................... 88
Appendix 2: Computation of Simple Active & Passive Pressures ......................... 89
(DM-7 Section 7.2, Naval, 2009) ............................................................................ 89
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Appendix 3: Breaking Strength Properties of Cable ............................................... 90
Appendix 4: Specific Weight of Wood Specimen (CSG) ...................................... 91
Appendix 5: Explanation of Logan’s Pull-out tests for Footings in Sands ............. 92
Appendix 6: Abbreviated Unified Soil Classification System (Coduto, 2001) ...... 93
Appendix 7: Bjerrum Correction Factor for Vane Shear Test ................................ 94
8
Index of Figures
Figure 1 Suspension and Suspended Bridge Comparison .......................................... 12
Figure 2 Typical Suspended Footbridge, Las Vegas, Honduras ................................. 14
Figure 3 Map of Ethiopia & Sebara Dildi Bridge Site ................................................ 16
Figure 4 Sebara Dildi Bridge Rope Crossing ............................................................. 17
Figure 5 Typical Bridge Profile .................................................................................. 22
Figure 6 Typical Abutment Profile for Cable-Suspended Footbridges ...................... 23
Figure 7 Free Body Diagram of Anchor and Tower ................................................... 23
Figure 8 Typical Decking Cross-Section .................................................................... 25
Figure 9 Schematic to Derive Moment at Mid-Span .................................................. 29
Figure 10Typical Decking Detail Plan View .............................................................. 38
Figure 11 Typical Decking Cross-Section with Dimensions ...................................... 40
Figure 12 Variation of Fc' with H'/h Ratio (Adapted from Das, 1990) ...................... 44
Figure 13 Variation of β with Embedment Ratio for ψ=0 .......................................... 45
Figure 14 Net Ultimate Holding Capacity with Variation in Cohesion using Das
(1990) .......................................................................................................................... 47
Figure 15 Net Ultimate Holding Capacity with Soil Unit Weights using Das (1990) 48
Figure 16 Minimum Embedment with Friction Angles using Meyerhof and Adam
(1968) .......................................................................................................................... 51
Figure 17 Variation of Minimum Embedment with Soil Unit Weight using Meyerhof
and Adam (1968) ........................................................................................................ 52
Figure 18 Free Body Diagram Anchor (Adapted from DM-7, 2009) ......................... 54
9
Figure 19 Sieve Test (Adapted from Concrete, 2009) ................................................ 56
Figure 20 Typical Triaxial Testing Apparatus ............................................................ 58
Figure 21 Expected UU Triaxial Test Results for Cohesive Soil ............................... 59
Figure 22 Pocket Vane Shear Test .............................................................................. 62
Figure 23 Pocket Penetrometer ................................................................................... 62
Figure 24 Soil Classification and Testing Flow Chart ................................................ 64
Figure 25 Cable Uncoiling Procedure (Helvetas, 2001) ............................................. 70
Figure 26 Proper Cable Transport Technique ............................................................. 70
Figure 27 Failed Nepali bridge: Clamp Slippage ....................................................... 71
Figure 28 Proper Cable Clamp Installation ................................................................ 73
Figure 29 Reduction in Cable Cross-Section with Proper Torque ............................. 73
Figure 30 Proper Cable Clamp Installation and Torque Wrench ............................... 74
Figure 31 Hand Rammer ............................................................................................. 75
Index of Tables
Table 1 Liveload Schedule for 1.0-meter Deck Width ............................................... 32
Table 2 Assumed Dead Loading ................................................................................. 33
Table 3 LRFD Load Combination Alternatives .......................................................... 39
Table 4 Wood LRFD Resistance Factor Values ......................................................... 39
Table 5 Soil Property Assumptions Summary Table .................................................. 53
Table 6 Correlations for Coarse Grained Soils (Terzaghi, Peck & Mesri, 1996) ....... 63
Table 7 Concrete Ratios by Volume (Adapted Engineers, 2006) ............................... 69
10
Chapter 1: Introduction and Background
1.1 Cable-Suspended Pedestrian Bridges
1.1.1 Rural Transportation
It is estimated that about 900 million rural people in developing countries do not have
reliable year-round access to road networks, and 300 million are without motorized
access (Lebo, 2001). Aid dollars being invested into infrastructure improvements for
paved highways and major vehicular bridges are only serving those with a standard of
living appropriating vehicle use. The remaining 300 million rural citizens have
unreliable access to even the most basic services or opportunities.
Many governments lack the basic infrastructure capacity to link feeder roads and rural
footpaths, and the dilapidated state of the paved roads often is prioritized.
Investment in rural transportation improvements would help to reduce poverty
through improving access to markets, medical clinics and educational opportunities
not currently accessed. Accordingly, a country’s ability to maximize its economic
potential is closely linked to the efficiency of its transport system (Haynes, 2003).
1.1.2 Pedestrian Bridges
For nearly 50 percent of the world’s population living in rural isolation, the lack of
access reinforces the cycle of poverty (United Nations, 2005). Rural community
members spend a great deal of time and effort on transport activities to fulfill their
basic needs. Whether walking miles downriver to reach a river crossing en route to
11
school, or spending a full day to reach the weekend market, the worlds’ poorest
people are faced with the disadvantages of lack of direct access to the basic amenities
and adequate transport infrastructure necessary to reach them.
Rivers and streams isolate villagers of many communities, stranded from the feeder
roadways and pedestrian paths during annual floods. A development strategy that
gives priority to providing reliable, year-round access, to as much population as
possible has been proposed in several forms (Lebo, 2001: Blaikie, 1979). A main
proponent of these strategies is the need for pedestrian bridge crossings.
Affordability of an infrastructure project, pedestrian bridge or otherwise, is primarily
determined by a population's capacity to maintain its infrastructure over the long
term. In rural communities where motorized access is neither existent nor affordable,
improvements to the existing trail networks and the provision footbridges over river
crossing locations is one of the most cost-efficient investments to create the largest
impact. Many countries do not have a single pedestrian bridge in county and those
that do are most often over-sized, difficult to maintain and prohibitively expensive
structures. A simple footbridge design would provide a cost effective solution to be
built without foreign design assistance.
Pedestrian bridge technologies vary vastly in design, cost and function. Crossings
can be as simple as a fallen tree or as complex as a multi-million dollar work of art.
From a structural standpoint, pedestrian bridges have taken a number of forms, each
with the function of providing safe transport over an otherwise impassable crossing.
12
Arched bridges, simple beam bridges, truss bridges and cable-stayed bridges
constitute four main types of pedestrian bridges: a review of suspended cable-stayed
bridges follows. The difference between a cable-suspension bridge and a cable-
suspended bridge type is shown in Figure 1, where the blue cable indicates load-
bearing in both.
Figure 1 Suspension and Suspended Bridge Comparison
The development of cable-suspended pedestrian bridge construction has played an
interesting role in the history of human civilization (Gade, 1972). The first recorded
bridge with suspenders connecting handrail and walkway cables was built as early as
285 BC in the Province of Sichuan in China (Peters, 1987). Other known suspension
structures during a similar time period were documented in the Eastern Himalayas
and consisted of single woven cable, transversed by holding onto either two handrail
cables or in a movable basket. Perhaps in a parallel line of invention or speculatively
through early Chinese travelers, similar technical knowledge emerged in South
America (Peters, 1987). Ancient Incan civilization used rope bridges to span deep
gorges, connecting footpaths between villages. These bridges consisted of a pair of
13
stone anchors and massive woven grass cables and two additional woven cables for
guardrails. Consistent maintenance and annual replacement of the woven cables
made these bridges strong enough to carry the Spaniards while riding horses after
they arrived (Gade, 1972). Such primitive rope bridges led to the basic idea of
modern cable bridges.
The modern cable-suspended bridges constructed by Bridges to Prosperity do not
vary greatly from many of the historical bridges. The simple design, constructed
using manually-powered tools and only locally available materials are all the same
challenges faced by designers for rural developing world bridges today.
1.1.3 Bridges to Prosperity
Bridges to Prosperity (B2P) is a United States based non-profit organization that has
recognized the need for rural pedestrian bridges. Their work building and training a
specific cable suspended footbridge technology has connected rural communities with
access and opportunities in over a dozen countries around the world. The suspended
cable footbridge design used by B2P was first developed by the Swiss organization
Helvetas (2001). Helvetas took footbridge building practices from improvised
construction to a standardized bridge design manual while creating the world’s largest
trail bridge program in Nepal (Nepal, 2008). The suspended design relies on each
cable for load distribution and lacks the tall towers equated with suspension bridges.
An example of the Helvetas-type suspended bridge is shown in Figure 2.
14
Figure 2 Typical Suspended Footbridge, Las Vegas, Honduras
Helvetas successfully accomplished their goal of standardizing the design such that a
visual geotechnical evaluation and rudimentary topographic Abney level survey could
be used to produce entire construction drawings: only very basic geometry
calculations are required. Although the modulated design was appropriate for deep
gorge applications as found in Nepal, there is a desire to break-down the design
process to allow for easier design modifications more suitable for non-gorge
crossings. The author concluded that an example design process would allow a
designer to optimize the design to fit local capacity and material availability.
15
Many of the existing bridge design resources are specific to developed nations where
constructability and material availability may be considered a lower priority than cost
or time of construction (Bridges, 2009). Rural construction, particularly in the
developing world, creates a number of additional constraints and often present
challenges to engineers only experienced with developed-world design practices.
With the increase in humanitarian-aid engineering projects through organizations
such as Engineers Without Borders (EWB), there is an increased need for both final
modular designs as well as design process resources. B2P identified an
organizational goal to create a best-practices approach to rural footbridge design and
construction for general dissemination and internal reference (Bridges, 2009).
Bridges to Prosperity started in 2001 by using the Helvetas design manual as it was
the most comprehensive design reference available. Several design alterations and
modifications have taken B2P away from the original designs as many B2P crossings
have topographic situations not addressed in the Helvetas manual. All of these design
addendums and calculation assumptions have been posted on their internet site. This
document seeks to provide a more complete best-practice document to serve as a
resource for potential bridge-builders around the world through B2P’s online
database.
1.1.4 Case Study: Sebara Dildi, Ethiopia
On behalf of Bridges to Prosperity, the author will be constructing a 100 meter
suspended bridge in the Ethiopian state of Amhara in the summer of 2009. A site
16
visit and engineering survey were conducted in June of 2008. During the trip, the
need for a more complete design guide for soil testing and design was realized.
1.1.4.1 Background & Location
Approximately 40 kilometers from Lake Tana, a broken multi-arched bridge spans
the Blue Nile River gorge. The bridge links a major caravan route between two
trading regions: the Gonder region and the city of Debra Tabor to the north, and the
Gojjam region and the city of Debre Markos to the south. The bridge site is marked
in yellow in Figure 3 and the two aforementioned towns marked in red.
Figure 3 Map of Ethiopia & Sebara Dildi Bridge Site
"Sebara Dildi,” or broken bridge in the local Amharic dialect, was built in the mid-
1600’s of stone, sand, lime, and egg: an early version of an elastomeric adhesive
(Bridges, 2009). During World War II, the middle arch of the bridge was destroyed
by Ethiopian Patriots to impede Mussolini's Italian invasion force. During the effort
to cut away the arch, it collapsed and killed 40 men (Snailham, 1968) but succeeded
17
in slowing the Italian forces. After the Italian retreat, the bridge was never repaired.
The current method of crossing is both expensive and dangerous and requires one to
pay to be manually pulled across while holding to a knotted rope, as seen in Figure 4.
Figure 4 Sebara Dildi Bridge Rope Crossing
Approximately 450,000 people live directly on either side of the bridge and although
dangerous, traffic remains heavy at the crossing to avoid the additional 75 kilometer
trip required to use the next closest bridge (Bridges, 2009). Those who operate the
rope charge 3 Ethiopian Birr ($0.38) or approximately 20 percent of a person’s
average daily salary.
In 2002, Bridges to Prosperity attempted to fix the crossing by building a steel truss
bridge, set atop bridge remains. The bridge was swept away during the first rainy
18
season that followed, as water levels at the crossing point currently reach a higher
elevation than when the bridge was originally designed. This could be attributed to
high levels of deforestation in Ethiopia and in turn, higher levels of runoff (Nile,
2008). The failure of this bridge project led to the creation of the Bridges to
Prosperity organization, and although the first attempt to repair the bridge was
unsuccessful, Bridges to Prosperity plans to build a bridge with adequate freeboard
and clearance.
The crossing point is extremely remote. Flying from the capital city of Addis Ababa,
one must arrive by air in Bahir Dar: the closest city to the site. Approximately 3 hour
drive south is the township of Mota from which one must walk approximately 8 hours
through Ethiopian highlands into the Blue Nile Gorge at Sebara Dildi. The remote
nature of this site limits survey and testing equipment to what can be carried.
Construction materials will need to be brought in on mule thus designers must limit
the size and weight of any particular material or tool required for bridge construction.
1.1.4.2 Site Visit
The author visited the site in June 2008 with the intention to choose the best location
for a suspended bridge crossing. A site 200 meters downstream and up-trail from the
current crossing was selected based on a narrowing of the river and an avoidance of
several residuals landslides.
A rudimentary surveying approach using an Abney level and string was used to create
a topographic cross-section of the site. This process has been well documented:
19
reference the Helvetas Volume 1 Suspended Manual for further detail (Helvetas,
2001). The final span was found to be 100 meters, with a negligible height difference
between the abutments.
The suggested process for soil identification required only a visual identification by
which the surveyor classified the soil based on ability to ‘see’ more than fifty percent
of the grains (Appendix 1). Both abutments were excavated to one meter depth and a
soil sample was attained for visual classification. The soil visually classified as a
sand at both abutments. The author found it difficult to conclude on design
parameters from such a basic approach. A greater understanding of design
assumptions was required to conclude whether a more in-depth testing and
classification process was feasible or necessary.
1.2 Research Objectives
Extensive literature exists for equivalent structure behavior in the developed world,
but very limited documentation has been created that adequately addresses design for
development applications. Through a review of existing testing and modeling
approaches for comparable structures and parametric studies with pertinent
geotechnical models, a simplified design approach is desired. This includes
identifying viable geotechnical classification testing approaches, and offering
recommended soil parameter assumptions as needed. A design case-study, inclusive
of both structural and geotechnical design methods, will be included to improve
general understanding. The end result will allow future bridge designers to identify
20
the underlying assumptions in order to modify the design for sites where the Helvetas
standard does not apply.
1.3 Expected Research Contributions
Minimal research has been completed specifically on the geotechnical proprieties of
anchorages intended for rural pedestrian cable stay bridges. A review of cable
behavior and assumed failure mechanisms will be discussed. Structural design
process will be outlined, including a case-study example for a 100 meter span.
Furthermore, a literature review of models intended for similar structures commonly
used as foundation systems that require uplift or lateral resistance will be included.
By reviewing design and modeling of these well-understood structures, a design
approach for soil anchorages for small cable-stayed bridges will be proposed.
Furthermore, as testing equipment available in rural developing world applications
are often not available, conservative soil parameters will be proposed with respective
justification based on impact on geotechnical models. Existing documentation has a
greater emphasis on modulated design rather than design process. This document
will produce a design guide for soil classification and testing, structural and
geotechnical design and engineering quality control for pedestrian bridge design for
the developing world.
1.4 Organization of Report
The introduction chapter has given context for the cable-suspended bridge. The
following chapter will more precisely identify the technical challenge and parameters
21
through discussion of a typical cable-suspended bridge. Chapter 3 will detail the
structural design considerations including assumed cable behavior, cited codes and
standards, example loading calculations and a complete design process for the case-
study bridge. The main objective of the chapter is to demonstrate how to calculate
the anticipated loads being transferred from the structure into the anchorage system.
Chapter 4 discusses geotechnical design. Discussion into how to classify as soil as
either coarse or fine-grained followed by pertinent models for each. One specific
model is detailed for each soil type, from which assumptions are justified through
parametric studies. A simplified geotechnical model is proposed for design use for
cable-suspended bridges. Testing programs for both soil types are also discussed.
Chapter 5 introduces many of the quality control issues faced in footbridge
construction including both material property and construction quality assurance.
The final chapter concludes with a discussion of engineering design for the
developing world. Lessons learned from this report in design simplification are
presented and more general concepts on the topics of ethics of accountability are
discussed.
22
Chapter 2: Typical Bridge Design Scenario
2.1 Model of Typical Bridge
The primary objective of this report is to suggest an anchor design approach to resist
pull-out failure for footbridge deadman anchors, shown in Figure 5.
Figure 5 Typical Bridge Profile
Where:
L = span in meters
Lb = Backstay length
hsag = cable sag in meters
ho.b. = height overburden
Typical spans for consideration range from 40 to 120 meters, backstay lengths range
from 5 to 10 meters, cable sag range from 2 to 10 percent of the span and overburden
heights range from 1.5 to 3 meters. To limit the scope of this report, the
aforementioned characteristic dimensions will be considered the limits conditions for
each respective parameter.
The modulated Helvetas cable-suspended bridge design was developed with few
components and minimal connection points. The primary components of a cable-
23
suspended pedestrian bridge are: anchorage (1), ramped approaches (2), foundation
tiers and towers (3), handrail and walkway cables (4 & 5 respectively) and deck
walkway, as shown in Figure 6.
Figure 6 Typical Abutment Profile for Cable-Suspended Footbridges
A simplified free body diagram detailed in Figure 7 depicts the typical forces inflicted
upon the anchorage and tower. Chapter 3 will discuss the structural analysis process
needed to solve for forces in the tower and Chapter 4 will discuss geotechnical
analysis for the anchorage design based on those forces.
Figure 7 Free Body Diagram of Anchor and Tower
1 2
3
4
5
24
Where:
Pt = Cable tension =Force imposed on anchor
PV and PH = Respective components of the force.
Wt = Weight of Block + Weight Soil above Block = WB + WS
WB = X * Y * γB
Ws = X * h * γs
γs = unit weight of soil
γB = unit weight of reinforced concrete
c = cohesion intercept of the soil
ϕ = Angle of Friction of the soil
ψ = Angle of anchor cable
θ = Cable deflection angle
Pp = Passive force (Appendix 2).
Therefore, the geotechnical parameters of interest are the angle of friction (ϕ), the soil
unit weight (γs) and the cohesion (c). The only structural variable that influences the
final anchor design is the loading, (Pt).
2.2 Structural Failure Parameters
For cable to fail, the strands must elongate past the elastic range into the elastic-
plastic portion of the material’s stress-strain curve. As the deck live load increases,
the load to the walkway cables is increased proportionally until the added length due
to stretch forces the suspenders to transfer the load onto the handrail cables. Only
when both the handrail and walkway cables were fully loaded would cable have the
25
potential to go beyond the elastic state required for cable failure. The aforementioned
cable connection is shown in Figure 8.
Figure 8 Typical Decking Cross-Section
Steel cable is the primary load-bearing structural component, diverting the decking
loads between the towers and anchorage systems. The cable carrying the transverse
load results in a geometrical configuration where horizontal force at mid span is
inversely proportional to the sag. It follows that cable pulled infinitely horizontal is
unable to carry any transverse load as zero sag implies an infinitely large cable force
(Pugsley, 1957). Likewise, significant increase in cable sag would result in a greater
vertical reaction at the towers. Structural design optimization requires the designer to
designate a sag ratio that properly balances these two considerations.
The minimum safe working load of steel cable can be found by dividing the
manufacturers supplied breaking strength by the safety factor. The recommended
factor of safety for load-bearing steel cable is 3.5 (Bureau Reclamation, 2009). Cable
clamps are required to reach 80 percent efficiency rating, thus an accumulative factor
26
of safety of 2.8. As the material specifications are highly regulated and guaranteed
for a high level of precision, the result is a highly unlikely case for structural cable
failure. Discussions into the behavior of the cable and construction elements identify
other potential failure mechanisms.
Prior to the wide-spread use of computer modeling and finite element techniques,
cable typically was assumed to behave as a parabolic curve (Pugsley, 1957). This
simplified parabolic model allows a basic understanding of the fundamental
interdependence between stability, stiffness, and strength. The cable analysis
described in Chapter 3 is overly-simplified but included to provide a basic
understanding of cable behavior and to provide the framework for design
understanding.
2.3 Geotechnical Failure Parameters
The geotechnical failure mode of interest is anchor pull-out. As such, the ultimate
uplift capacity (Qu) of the soil must be found. Chapter 4 will outline an empirical
approach for calculating Qu for both fine and coarse-grained soils. The soil
parameters of interest in both models are soil unit weight (γ), friction angle (ϕ) and
cohesion (c).
The primary geotechnical failure mode of consideration is anchor pull-out. To
prevent pull-out failure, the anchor must be placed at an appropriate depth and
distance from the tower with consideration for soil strength parameters. The soil
parameters of interest are the soil unit weight (γ), cohesion (c), and the friction angle
27
(ϕ) of a soil. Separate design approaches for fine and coarse-grained soils is
recommended for calculating ultimate uplift capacity of anchors (Das, 1990). Smith
and Stalcup (1966) suggested that fine-grained cohesive soils attained up to 30%
increase in holding capacity as compared to coarse-grained, but 2 to 3 times the
horizontal displacement was required to activate the passive earth pressure. This
initial research indicated that further investigation was needed before assuming a
similar design model was appropriate for both fine and coarse grained soils.
Rock masses will not be considered herewith in as the following models are not
applicable to jointed rock masses where strength is controlled by joint orientation.
Furthermore, intermediate rock masses will not be considered as the anchor design
for excavatable rock mass is not based on the soil properties but rather the rock and
anchor’s ability to attach to surrounding material as a single mass. The designation
between intermediate rock mass and a soil will be defined as the later is able to be
excavated with man-powered shovels.
28
Chapter 3: Structural Considerations
Structural design requires few site-specific parameters and thus can be implemented
off-site. The best-practice approach to design requires identifying applicable codes
and regulations. Under most conditions, structural design codes applicable in the
United States or equivalent will be at least as comprehensive and well-proven as
those in the country of consideration. A designer must address the differences in
codes during his or her work, but may use a design methodology documented herein.
The international nature of this design further encourages a designer to consult local
codes and learn from the experience of comparison.
Redundancy in the modulated Helvetas design has resulted in only one documented
failure in over 2000 bridge constructions (Helvetas, 2001). The failure of this
particular bridge was due to insufficient torque on the clamps used to tie the cable
around the anchor. As this is a relevant material and construction quality control
item, quality control will be discussed in Chapter 5.
3.1 Structural Analysis
Assuming the cable is frictionless and a perfectly flexible material, the cable hangs in
a parabolic arc (Pugsley, 1957). The primary assumption is that the intensity of the
vertical distributed load is constant. The perfectly flexible cable is considered to
give no resistance to bending at any point and thus the resultant tensile force is
tangent to the curve at any point in the cable. Thus, to find the maximum tension in
29
the cable, it is necessary to know the relations involving tension, span, sag and the
length of cables (Meriam, 2007).
3.1.1 Horizontal Tension
Taking the moments about point A taken at mid-span and assuming that the supports
are at equivalent heights, one can solve for the horizontal tension in the cable per the
Figure 9.
Figure 9 Schematic to Derive Moment at Mid-Span
8
Where:
Wc = distributed load
Th = horizontal tension
L = span in meters
h = cable sag, in meters
Given the horizontal tension in the cable, solve for the slope of the cable at the towers
to acquire the maximum cable tension at the height of the towers.
30
The slope of the cable, the corresponding total tension in all cables and the tension in
each cable may be calculated from the following relationships:
4
Where:
θ = cable deflection angle
T’ = cable tension, in kN
N = number of cables
Tc = allowable tension per cable
One must chose the number of cables based on the availability of cable and its
respective breaking strength. Although each cable supplier must verify the breaking
strengths of the cable, Appendix 3 may be used for academic purposes. The sum of
the walkway and handrail cable design strengths must exceed the tension in the cable
after accounting for allowable stress design factors. Each cable takes a load
proportional to its’ cross sectional area and thus if cables of differing sizes are used,
each cable will take a proportional load to its cross-sectional area ratio.
In accordance with AASHTO (2003) standards, the following design approach and
assumptions were used throughout this report. To illustrate the design process, a
31
design example has been included through the text. By outlining pertinent
assumptions and processes, modifications to the standard design may be used. One
such scenario is a community’s request to widen the decking from 1.0 meter width to
1.5 meters to allow for animal-pulled carts or a decrease in deck-width for low traffic
crossings.
3.2 Pedestrian Bridge Loading
To find the tension in the cable, the load on the cable must be computed. The
following details the recommended design approach per American Association of
State Highway and Transportation Officials (AASHTO) article 3.16 and the
supplemental “Guide Specifications for Design of Pedestrian Bridges” document
(AASHTO, 1997). It is recommended that the reader reference applicable codes and
specifications in area of intended construction prior to design.
3.2.1 Liveloads
A liveload of 85 pounds per square foot is designated unless the walkway area is
greater than 400 square feet. Then the live load figure is slowly reduced between 400
square feet and 850 square feet, at which time the minimum standard of 65 pounds
per square foot is used. The 65 pounds per square foot minimum load limit is used to
provide a measure of strength consistency with the LRFD specifications, which
specify 85 pounds per square foot less a load factor indicated in the LRFD Design
specifications (AASHTO, 1997). The formula is as follows:
85 0.25 15/√
32
Where A is the total square feet of walkway surface area. Therefore, using a 1.0 -
meter walkway cross sectional area, the following live load schedule would apply:
Table 1 Liveload Schedule for 1.0-meter Deck Width
Span
(m)
English Unit Loading
(lbs/ft²)
Metric unit Loading
(kN/m²)
1-37 m 85 lbs/ft² 0.415 kN/m² 38-78 m proportional reduction,
from 85 to 65 lbs/ft² proportional reduction, from
0.415 - 0.317 kN/m² 79 + m 65 lbs/ft² 0.317 kN/m²
As noted in AASHTO (1997), the live load reduction for decking areas exceeding 400
square feet is consistent with ASCE 7-95, “Minimum Design Loads for Buildings and
Other Structures.” The reduction accounts for the reduced probability of the large
loading area of the structure being fully loaded at any given time. The likelihood of
the rural footbridge being fully loaded is somewhat unrealistic, but failure cases have
been reported during heavy traffic (Nepal, 2009). Furthermore, the likely case of
small motor-vehicles and animal-driven carts would require both distributed and
point-load analysis to find maximum loading case. As such, the conservative
assumption loading of 0.415 kN/m² (85 lb/ft²) is recommended.
Total LL = 0.415 kN/m, assuming 1.0 meter width
33
3.2.2 Dead Loads
Table 2 Assumed Dead Loading
Assumptions/Conversions Loading
Suspenders
8 mm diameter x 1.7 m steel rebar = 8.5e-5 m³ per rod Unit weight steel = 490 lb/ft³ = 7847.3 kg/m³
0.67 kg per suspender 0.0098 kN/kg
Suspender spacing 1 meter on center per side
0.0134 kN/ m
Cross beams
10 cm x 10 cm x 1.4 m Assume 600 kg/ m³ (Appendix 4)
Cross beams 1 meter on center
0.082 kN/m
Decking 5 cm x 20 cm x 2 m = 0.02 m³ per 2 meter member Assume 400 kg/ m³ (Appendix 4)
8 kg per decking panel 5 decking panels across
0.020 kN/m
Cable Assume 6x19 IWRC galvanized steel cable Assume 32 mm cable (1 ¼”) : 2.89 lb/ft
Assume 6 cables 1 lb/ft = 1.288 kg/m
0.219 kN/m
Total DL = 0.334 kN/m, assuming 1.0 meter width
3.2.3 Wind Loads (Overturning)
A wind load applied horizontally at right angles to the longitudinal axis of the bridge
shall be applied at 35 pounds per square foot (0.171 kN/m²), assuming that the wind
can readily pass through the bridge profile, per AASHTO specifications. The
specified wind pressures are for a base wind velocity of 100 miles per hour which in
such case a site has higher wind-velocity requirements: AASHTO Article 3.15 (1997)
may be referenced. Given the projected profile of the bridge is 1.1 meters in height:
the resulting wind overturn force is 0.183 kN/m.
Total WL = 0.183 kN/m, assuming 1.1 meter railing height
34
3.2.4 Load Combinations
The following load combinations will be used, extracted from Table 3.22.1A in
AASHTO (1997):
• Group I - (Dead + Live) at 100% of Allowable Stress (i.e., Load Combination Reduction Factor = 1.0).
• Group II - (Dead + Wind) /125% of Allowable Stress (i.e., Load Combination Reduction Factor = 1.25).
• Group III - (Dead + Live + 0.3 Wind) /125% of Allowable Stress (i.e., Load Combination Reduction Factor = 1.25).
Group I: 0.651 / directs
Group II: .
0.413 /
Group III: ..
0.565 /
Wc = 0.651 kN/m²
3.3 Structural Design
3.3.1 Suspenders
Suspenders transfer the loads from the deck to main cables, and are attached to
crossbeams at 1 meter intervals. Thus, with a 1 meter deck width, each suspender has
a tributary area of 0.5 m², and thus must be able to carry 0.325 kN of loading from the
0.651 kN/m loading. The minimum diameter of suspender can be calculated per the
following equation:
35
Where:
Fs = applied force in kN
Ps =allowable yield strength in kN/m²
Assuming ASTM A36 Grade 300 (ASTM) with a minimum yield strength of 24.5
kN/cm² (250 MPa) and a factor of safety of 1.5, and assuming a 1.0 meter deck width,
the minimum diameter of a suspender would be 1.6 mm. Due to the high surface area
to volume ratio of the suspender and thus increased likelihood of corrosion, a
minimum suspender diameter of 8 mm is recommended.
3.3.2 Main Cables
Assuming a 100 meter crossing, the design process is as follows for selection of the
primary cable. For further details on the mathematical derivation of the following
equations, see reference (Meriam, 2007).
0.361 / ²
Therefore:
8
0.651 100 ²
8 5 162.75
Where:
36
Th = horizontal tension, in kN.
L = Span in meters
hsag = cable sag, in meters
411.3°
Where:
θ = cable deflection angle
166
Where:
T’ = cable tension, in kN
Where:
N = number of cables
Tc = Allowable tension per cable
The sum of the walkway and handrail cable design strengths must exceed the tension
in the cable. In this example, 166 kN may be distributed either 4 cables (2 walkway
and 2 handrail) or 6 cables (4 walkway and 2 handrail) in order to support the load.
Using example design breaking strengths in Appendix 3 (including the factor of
safety of 3.5), the load can be split between 4 cables. Assuming each cable is to be
the same, each must have a minimum design strength equivalent to Tc. Thus, the
result is the minimum cable size of 16 mm, per Appendix 3. Each cable takes a load
proportional to its’ cross sectional area. The total design load imposed on the anchor
37
is equivalent to T’ or 166 kN in the case of a 100 meter bridge with a 1.0 meter
decking.
To calculate the amount of cable to order, one must first know the length of each
cable between towers:
183
For a 100 meter span and 5 percent sag, is equal to 100.67 meters per cable
between towers. To calculate the total length of cable required to purchase, one must
first decipher the length of the backstay which requires geotechnical design. For
practical purposes, a simplified equation would allow field supervisors to order cable
without an intimate understanding of the design process. As the length of the cable is
only increased by less than one percent when accounting for sag, neglecting this
added length and alternatively including a four percent contingency is practical. The
following is proposed:
1.04 14
The 14 meter addition allows for cable wrap-back, seven meters at either anchor,
approximate but standard on all crossings.
There are several design alterations that may be considered to reduce the length and
thus cost of cable, but while the length of the span may reduce to lessen this cost, the
tower height likely would increase thus increasing masonry costs.
38
3.3.3 Decking
There are two primary code sources used for bending stress problems in The United
States: Load and Resistance Factored Design (LRFD) and Allowable Stress Design
(ASD). LRFD will be discussed herein. A full design process is not detailed herein
as it is beyond the scope of this report, but the following provides context and
background for how the modular decking design alternatives currently in use by
Bridges to Prosperity were developed.
A typical decking plan view is shown in Figure 10. Note that the crossbeam spacing
is 1.0 meters. The deck width will be assumed 1.0 meters as well.
Figure 10Typical Decking Detail Plan View
3.3.3.1 LRFD Loadings
LRFD use slightly different nomenclature from the loading section at the beginning
of the chapter but for consistency, the following will continue to use similar
nomenclature.
39
Table 3 LRFD Load Combination Alternatives
LRFD Load combination alternatives: 1. 1.4DL 2. 1.2DL+1.6LL+.5(Lr or S or R) 3. 1.2DL+1.6(Lr or S or R)+(.5LL or .8WL) 4. 1.2DL+1.6WL+.5LL+.5(Lr or S or R) 5. 1.2DL+/- 1.0E+.5LL+.2S 6. 0.9DL +/- (1.6WL or 1.0E)
Table 3 lists the six fundamental factored load combinations from Minimum Design
Loads for Buildings and Other Structures (ANSI/ASCE 7-88) used for safety analysis
in LRFD. There will be assumed no roof (Lr), no snow (S) no rain (R), and no earth
(E) loadings. Therefore the LRFD design strength is 1.065 kN from load
combination 2. As the member is being design for compression, the required nominal
strength, assuming a resistance factor of 0.9 from Table 4, would be 1.183 kN.
Table 4 Wood LRFD Resistance Factor Values
Mode ϕ
Compression 0.90 Flexure 0.85 Tension 0.80 Shear 0.75
Structural design includes resistance to shear failure, flexure failure and for
serviceability, a maximum displacement must not occur. The crossbeams and
decking panels must be considered independently and for two load case scenarios:
fully loaded and point loaded in cross-section.
40
3.3.3.2 Cross beams
Crossbeams are the members that are spaced perpendicular to the length of the bridge.
There are three initial design choices: crossbeam spacing, and the width of the
decking.
Figure 11 Typical Decking Cross-Section with Dimensions
Figure 11 depicts a cross-section for a typical decking cross-section with a small
spacer board that is for constructability, but will not be considered in the following
calculations. The crossbeam bending calculations will be based off a cross beam
dimensioned (X+36 cm) by Y cm by Z cm (into the page). The additional 36 cm is
included for connection spacing on either side, as recommended from practical
experience.
3.3.3.3 Decking Planks
The length of the decking planks is recommended to be 3.0 meters, although 2.0
meter decking planks are also acceptable with a slight reduction in longitudinal
rigidity, as shown in the plan view of a typical decking in Figure 10. Design for
longitudinal beams should assume a multi-support, simple beam analysis. To identify
41
the maximum shear and applied moment, both point load and distributed load
scenarios should be considered.
For both cross-beam and decking plank design, one must state the material properties
and assume an initial member size. Material properties of interest are the material
yield strength, Fy, the ultimate flexural strength, Fu and the modulus of elasticity, E.
An initial member size is selected for the following parameters: cross-sectional area,
Ag, moment of inertia, I, the radius of gyration, r, and the corresponding slenderness
ratio, kL/r, the section modulus, S, and the maximum deflection (∆ = L/360).
As detailing every potential consideration and design alternative for decking design is
beyond the scope of this project, a modulated design is recommended for use.
Bridges to Prosperity has provided modular designs for both wood and steel decking
solutions: both provided with several size alternatives on their website (Bridges,
2009).
42
Chapter 4: Geotechnical Considerations
The main geotechnical design component of the bridge is the anchor block. The
primary purpose of these anchors is to transmit a tensile load from the cables to the
anchor and soil to prevent pull-out failure. Accordingly, it must have adequate
weight and placed at an appropriate depth and distance from the abutment to provide
adequate resistance (Das, 1990). Design models used to find the ultimate uplift
capacity of the anchor are separated for fine and coarse-grained soils due to their
difference in behavior. They behave differently due to the rate of pore water pressure
dissipation during loading. The following will discuss fine-grained-specific soil
analysis and recommendations, followed by coarse-grained-specific soil models and
recommendations. A recommended design process will summarize the findings from
these two proceeding sections.
4.1 Fine-Grained Soils: Clays and Silts
4.1.1 Geotechnical Analysis & Anchor Capacity
There are relatively few studies relating the holding capacity of inclined anchors
embedded in fine-grained materials under a tensile load (Das, 1990). One of the
most comprehensive studies of inclined plate anchors was completed by Das (1983).
The results showed that the net ultimate holding capacity of an inclined rectangular
anchor is related to an empirical breakout factor Fc’ as follows:
43
Where:
Fc’ = average breakout factor
Qu = net ultimate holding capacity
A = area of anchor plate = Bh
B = width of anchor plate
Cu = undrained cohsion of the clay soil (ϕ = 0 condition)
Ws = Weight of soil above anchor
ψ anchor inclination with respect to horizontal
H’ average depth of embedment
Therefore, for rectangular anchors, the breakout factor can be recalculated as follows:
The breakout factor Fc’ increases with the average embedment ratio H’/h to a
maximum value, at which point it asymptotically approaches a maximum value, as
depicted in Figure 12.
44
Figure 12 Variation of Fc' with H'/h Ratio (Adapted from Das, 1990)
The first step in solving for the ultimate holding capacity of the anchor is to calculate
the critical average embedment ratio (H’/h)cr for a rectangular anchor as follows:
0.73 0.27 1.55
Where:
0.107 2.5 7.0
Cu = undrained cohesion in kN/m²
If the design ratio H/h is greater than
, then it is considered a deep anchor and
the breakout factor assuming a zero degree anchor angle is as follows:
7.56 1.44
45
If the design ratio H/h is less than
, then it is considered a shallow anchor and
the breakout factor assuming a zero degree anchor angle is as follows:
7.56 1.44
Where β is found using Figure 13.
Figure 13 Variation of β with Embedment Ratio for ψ=0
The next step is to estimate the breakout factor for an anchor with a cable angle of 90
degrees. Although unrealistic, the process eventually correlates the actual backstay
angle to the ratio of the breakout factor at 0 degrees and 90 degrees.
0.5
0.5
0.9 0.1 1.31
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
β
α=(H'/h)/(H'/h)cr
46
Where:
0.0606 4.2 6.5
If the design ratio H/h is greater than
, it is considered to be a deep anchor and
the breakout factor assuming a zero degree anchor angle is as follows:
9 0.825 0.175
If the design ratio H/h is less than
, then it is considered a shallow anchor and
the breakout factor assuming a zero degree anchor angle is as follows:
0.41 0.59
Where :
0.5
0.5
Das details the process where Fc’ is determined through the following equation,
relating the variation of the average breakout factor as follows:
90 ²
47
With Das’ (1990) empirical procedure outlined above, a parametric study was
conducted with several assumed backstay cable inclinations, as shown in Figure 14.
Figure 14 Net Ultimate Holding Capacity with Variation in Cohesion using Das (1990)
Using Das’ approach for shallow-anchor design, Figure 14 summarizes the
dependency on cohesion for a load of 166 kN (which is representative for a 100 meter
span), assuming an anchor with a 1.2 m by 3.0 meter surface. A soil unit weight of
19 kN/m³ was assumed because the dependence on the unit weight is insignificant for
all ranges of loading types, as shown in Figure 15.
0
10
20
30
40
50
60
70
0 200 400 600 800 1000 1200
Minim
um Coh
esion to resist p
ull‐o
ut fa
ilure (k
N/m
²)
Net Ultimate Holding Capactiy (kN)
30 degrees 35 degrees40 degrees 45 degrees60 degrees Linear (30 degrees)Linear (35 degrees) Linear (40 degrees)Linear (45 degrees) Linear (60 degrees)
48
Figure 15 Net Ultimate Holding Capacity with Soil Unit Weights using Das (1990)
As the dimensions of interest are considered ‘shallow’ by Das’ (1990) definition, the
deep anchor scenario was not modeled. The assumed parameters for this model
included a surface length perpendicular to cable (h) of 1.2 m, an average embedment
depth (H’) of 1.2 meters, and an anchor width (B) of 3.0 meters. For typical loading,
detailed in the structural analysis in Chapter 3, the minimum cohesion values required
to resist pull-out failure for a 166 kN load are below realistic in-situ cohesion values
for fine-grained soils.
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
Minim
um Coh
esion to resist p
ull‐o
ut fa
ilure (k
N/m
²)
Net Ultimate Holding Capactiy (kN)
17 kN/m3 19 kN/m3 21 kN/m3 25 kN/m3
49
4.1.2 Recommended Parameters
The conclusion is that the soil unit weight and the minimum cohesion are fairly
insignificant soil properties within the pertinent parameters of interest. As detailed in
Chapter 2, the longest typical bridge of consideration is 120 meters. Accordingly,
even though the cohesion is important for high loads, these will not be observed in
these bridges.
Figure 14 proves the relative insignificance of soil parameters at given conditions of
interest. If no testing is available, a conservative cohesion of 20 kN/m² may be
assumed. Assuming that the structure is quickly loaded and the undrained strength
parameters direct, assuming a zero friction angle is also appropriate. Figure 15 shows
that the depth of embedment is relatively insensitive to the soil unit weight (19
kN/m³). Non-plastic silts will exhibit little or no cohesion and friction therefore they
are included with coarse grained soils.
4.2 Coarse-Grained Soils: Sands, Gravels and Non-Plastic Silts
4.2.1 Geotechnical Analysis & Anchor Capacity
Meyerhof and Adams (1968) proposed a semi-empirical relationship for estimating
the ultimate uplift capacity of strip, rectangular and circular anchors in coarse-grained
materials. It is one of few methods available for estimating the capacity of
rectangular anchors. Many alternative models are presented in literature for circular
or square anchor plates, but those will not be discussed as the shape of the anchor
requires a shape factor not included in other design models (Das, 1990). The
50
introduction of further empirically derived correction factors ideally would be
accompanied by experimental validation for use with anchorages similar in size and
use as footbridges. The Meyerhof and Adam’s model includes fewer assumed
assumptions than other models and thus will be discussed.
To find the ultimate uplift capacity per unit width of anchor, the following equation
may be used:
12
Where:
Qu’ = ultimate bearing capacity per unit width
Kb = Passive Pressure Coefficient
h = height of embedment
H = depth of bottom of anchor
H’ = average embedment of anchor
ψ = Angle of cable from anchor, from horizontal
γs = unit weight of soil
Several parametric studies were completed analyzing the impact of material
assumptions on the Meyerhof procedure for inclined anchors in a cohesionless soil
(Meyerhof, 1973). A study comparing the impact of backstay angles and minimum
embedment depth for a 166 kN load (from Chapter 3, structural loading for a 100
meter bridge) with various friction angles is summarized in Figure 16.
51
Figure 16 Minimum Embedment with Friction Angles using Meyerhof and Adam (1968)
As the backstay angle had a minimal impact on the embedment depth, a simplifying
conclusion specifying a minimum embedment of 2.0 meters may be suggested. As
this analysis is specific to a 100 meter bridge loading, these results may not be
extrapolated to all spans. The outlined analysis may be followed to produce similar
simplifying conclusions for any span of interest.
This particular study assumed a soil unit weight of 19 kN/m³, because the minimal
impact on the model for this parameter as shown in Figure 17.
0.00
0.50
1.00
1.50
2.00
2.50
20 30 40 50 60 70 80
Minim
um embe
dmen
t (m)
Backstay Angle (degrees from horizontal)
Phi = 25 degree Phi = 30 degrees Phi = 35 degrees Phi = 40 degrees
52
Figure 17 Variation of Minimum Embedment with Soil Unit Weight using Meyerhof and Adam (1968)
Varying the backstay angle of the anchor was found to have relatively minimal
impact on required friction angles within the range of feasible anchor angles from 20
to 60 degrees from the horizontal.
The variations of Kb for shallow strip anchors can be obtained from the earth pressure
coefficients of an inclined wall, and were summarized in a chart (Das, 1990). Each
anchor angle and assumed soil friction angle will have a unique empirical value.
Given the opportunity, pull-out tests on various sandy soils may provide further
insight and negate the need for conservative friction-angle assumptions. Logan
(Logan, 1976) completed an experimental series of pull-out tests for footings in sand.
Footings were loaded to failure and the failure mechanism was documented. Future
0.00
0.50
1.00
1.50
2.00
15 17 19 21 23 25 27
Minim
um Embe
dmen
t dep
th (m
)
Assumed Unit weight of soil (kN/m³)
Phi assumed 30 degrees, backstay assumed 45 degrees
53
work in this area could find his testing procedures and findings applicable. For
further details of Logan’s study and findings, reference Appendix 5.
4.2.2 Recommended Parameters
Figure 16 shows an increase in load when the friction angle is increased from 25 and
30 degrees. If no testing is available, it is recommended that a value of 26 degrees be
assumed for the value of friction angle. This is relatively low for quartz sands, as it is
the angle of repose. Figure 17 depicts a relative insensitivity for the assumed soil unit
weight thus 19 kN/m³ may be assumed. The most conservative strength for a coarse-
grained soil is when it is fully-drained in which case it will have a zero cohesion
intercept. Table 5 is a summary of recommended soil assumptions.
Table 5 Soil Property Assumptions Summary Table
Fine-grained soilγsoil 19 kN/m³ϕ 0 Degreesc 20 kN/m²
Coarse-grained soilγsoil 19 kN/m³ϕ 26 Degreesc 0
4.3 Geotechnical Design
4.3.1 Design Process
Sections 4.1 and 4.2 detailed two distinct analysis approaches for anchors in fine and
course grained soils respectively to identify design simplifications. The following is
54
modified DM-7 design approach (2009) that may be used for design of anchors in
fine or coarse-grained soils. Soil parameter assumptions justified in the
aforementioned sections may be used, or further testing approaches detailed later in
the chapter may be used to reduce material uncertainty.
Where:
Pt = Force (can be found from the Structural Considerations section)
PV and PH = Respective components of the force.
Wt = Weight of Block + Weight Soil above Block = WB + WS
WB = X * Y * 2300 kg/m³ (unit weight concrete)
WB = X * h * γ
γ = unit weight of Soil
c = cohesion
ϕ = Angle of Friction
Pp = Passive pressure (Appendix 2).
Figure 18 Free Body Diagram Anchor (Adapted from DM-7, 2009)
55
The design process is very straight forward and only requires verification that the
anchor of interest is able to resist the vertical force and the horizontal force with
independent calculations.
1) Step 1: Check resistance to vertical force:
1.5
2) Step 2: Check resistance to horizontal force :
1.5
4.3.2 Soil Classification & Testing
4.3.2.1 Soil Classification
The geotechnical component of the design for rural bridges involves an estimate of
the resistance to pull-out of an anchor. The parameters governing the mechanical
response of the soil to such loadings as well as the recommended testing approaches
are dependent on the rate of loading and the drainage characteristics of the soil. The
main parameters needed are the shear strength, usually represented by the Mohr-
Coulomb failure envelope where the strength is sensitive to the water content and
density:
tan
For the case of short-span pedestrian footbridge design, the anchorage systems have
been proven in Sections 4.1 and 4.2 to be relatively insensitive to input soil
parameters. As such, it is recommended by the author that the soil at a minimum be
classified with the objective to choose between the two modeling alternatives. If no
56
further testing is possible, use of the conservative soil parameters are suggested for
these groups.
The Unified Soil Classification System (USCS) groups soils using their grain-size
distribution and plasticity characteristics, in order to separate them by their expected
engineering behavior (Appendix 6). The USCS assigns a group symbol to the soil,
along with standardized descriptions appropriate for that group name which is useful
for selection of design strategies. The USCS begins by separating the soil into either
coarse-grained or fine-grained, depending if greater that 50 percent of the material is
larger or smaller than a 200 sieve, with the exception of highly organic soil. Highly
organic soils often will smell have fibers and are typically dark in color. If found on
site, organic soil should be excavated and discarded due to their poor properties and
thus will not be discussed herein.
Figure 19 Sieve Test (Adapted from Concrete, 2009)
57
USCS further differentiates between the coarse-grain into ‘gravels and sands’ and
fine-grain into ‘silts and clays’. This second classification step requires further
sieving for coarse-grained soils and laboratory work including the Atterberg limit
tests for fine-grained soils.
For on-site feasibility, the use of a 0.074 mm screen, equivalent to sieve size #200
should be used. If the in-situ soil is clumped, the soil must be washed prior to using
the sieve. To collect the soil sample, the site investigator shall dig a small trench and
sieve one 5-gallon bucket of material onto a standard 75 micrometer mesh
(Wovenwire, 2009). The action of digging a test-pit also gives one a better
understanding of soil variability and an increased awareness of drainage issues to
better identify where the soil may present excavation difficulties.
A second required classification step is to administer the dilatancy test detailed in
Section 4.4.2.2. Given the results of the sieve and dilatancy test, respective field
testing approaches should be completed for soils classified with greater than 50
percent passing the 0.074 mm sieve. The test requires a sample with a soft putty
consistency. Observe the reaction during shaking, followed by squeezing the soil in
ones hand with vigorous tapping. During the test, if the soil behaves as a fine-grained
soil, the vibration would densify the soil and water would appear on the surface. In a
clay sample, no change occurs and thus may be classified as fine-grained (Field,
2009). Silt has a tendency for dilatancy so excess water would disappear from the
surface.
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58
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Therefore, th
ideal testing
l test would
in the triaxi
the structura
dge traffic.
l departures
ed soil along
UU triaxial t
Test Results for
may be carr
n the entire
or stress (σ1-
he shear stren
and laborat
d simulate a
al cell with
al loading
Sudden bri
. During th
g the banks o
ests in a labo
Cohesive Soil
ried out eithe
sample, the
- σ3), from
ngth corresp
tory accessib
a similar loa
the drain v
condition w
idge loading
he rainy seas
of a river. F
oratory.
er on undistu
axial pressu
which the m59
ponds
bility,
ading
valves
would
gs are
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Figure
urbed
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60
principle stress is determined. Several tests should be completed to create a similar
plot to that detailed in Figure 21. In this case, (σ1- σ3) is not sensitive to σ3 as the
increase in total stress is carried completely by the pore water. The input parameter
from the test to use in the design models is su which is related to the maximum
principal stress difference (σ1- σ3), by the following relationship.
2
The VST is often used in-situ to obtain approximations of shear strength of saturated
cohesive soils, specifically where undisturbed samples of acceptable quality are
difficult to obtain (Terzaghi, Peck & Mesri, 1996). The VST consists of a metal
vane which is inserted into the ground and torque is applied until the soil fails in
shear, when the test is completed according to ASTM D2573. It is pertinent to note
that the rate of vane rotation is intended to ensure undrained conditions at failure. As
such, it is very beneficial to sample the soil either before or after testing, to
understand the drainage conditions of the soil tested because the presence of a silt or
coarse-grained soil will not produce usable results (ASTM D2573, 2008).
Furthermore, as the soil must be saturated prior to testing, it is advised to take a
sample near the stream bed rather than in the intended area of excavation, assuming
homogeneity between the two sites.
The undrained shear strength of a fine grained soil is correlated to the torque required
for failure, the vane dimensions and the plasticity index per the following equation:
61
67
Where:
su = undrained shear strength
Tf = torque at failure
d = diameter of vane
= Bjerrum correction factor
To properly identify the Bjerrum correction factor (Appendix 7), the plasticity index,
Ip, must be found. The Plasticity Index of a soil is the numerical difference between
the liquid limit and the plastic limit, (LL-PL) (Coduto, 2001). The water content is
one of the parameters which is very difficult to ascertain in the field without access to
an oven.
The pocket vane shear tester is a more portable and inexpensive version of the VST.
The pocket VST test should be completed according to ASTM D 4648 which
designates the rotation of a 12.7-mm high x 12.7-mm diameter vane at approximately
90 degrees per minute (Geotest, 2009). The vane may be advanced to depths of
interest by first excavating a small pit, to 1.5 to 2.0 meters in depth, or to a depth
more closely correspond to the soil properties at the depth of the anchor.
62
Figure 22 Pocket Vane Shear Test
The pocket penetrometer is another method to obtain the undrained shear strength of
a saturated soil. By pushing the small probe into a fine-grained soil, the measured
unconfined compressive strength measured can be converted to shear strength by
diving by 2 (Coduto, 2006). Figure 24 shows a picture of a typical pocket
penetrometer.
Figure 23 Pocket Penetrometer
The spring operated pocket penetrometer is a small and transportable device that
measures the undrained compressive strength by pushing a 0.25” (6.4 mm) diameter
loading piston into the material of interest, to the depth of a calibration groove
machined on the piston 0.25 cm from the end. The strength in kN per square cm is
obtained by noting the position of the indicating ring on the scale, which is retained
63
until reset (Professional, 2009). Both of these testing devices are highly mobile and
inexpensive thus providing a viable testing solution for rural applications.
4.3.2.3 Strength of Coarse-Grained or Cohesionless Soils
If the soil is classified as coarse-grained, obtaining undisturbed samples is nearly
impossible, especially in rural areas. Accordingly, it is difficult to quantify strength
without field tests like the Standard Penetration Test (SPT) or the Cone Penetration
Test (CPT). However, these tests require specialized equipment unavailable in the
field. Accordingly, it is recommended to use correlations. Correlations involve an
estimate of the soil density. Efforts should be made to estimate the density in the
field and use correlations such as those presented in Table 6.
Table 6 Correlations for Coarse Grained Soils (Terzaghi, Peck & Mesri, 1996)
If advanced testing is not available, conservative soil strength parameters are given in
Figure 24. These were developed based on the findings of the analyses in Sections
4.1 and 4.2. For every soil type, the first step is to sieve with a 0.074 screen. The
second step is the dilatancy test, outlined in Section 4.3.2. If the soil shows properties
of dilatant silts, it will be modeled as a coarse-grained soil.
64
Based on the classification of the soil, either tests or correlations should be used to
identify soil strength properties. If adequate testing is devices are not available, the
analyses suggest that conservative values can be used.
Figure 24 Soil Classification and Testing Flow Chart
65
4.3.3 Design Example: Sebara Dildi Case-Study
100 meter span results in 166 kN load onto the anchor, as detailed in the Structural
Design section. Soil classification resulted in a coarse-grained soil on either
abutment. Using the Meyerhof method detailed in Section 4.2.1, and Figure 16, an
initial embedment depth of 1.7 meters was chosen, and similar anchor geometries
were chosen: block X, Y, L = 1 meter x 1 meter x 3 meter wide at a depth of 1.7
meters.
Assumptions γ_soil 19 kN/m³ϕ 26 Degreesc 0 ψ 30 Degreesh 1.7 m B 3 m Qu(total) 166 kN Qu (g) 55.3 kN/m
Pt = 166 kN
PV = Pt * sin(ψ) = 83 kN/m = 83/3 = 27.67 kN
PH = Pt * cos(ψ) = 143.76 kN/m = 47.92 kN
WB = X * Y * 25 kN/m³ (unit weight reinforced concrete) = 1 x 1 x 25 = 25 kN
Ws = X * h * γ = 1 x 1.7 x 19 kN/m³ = 32.3 kN
Wt = 25 kN + 28.5 kN = 57.3 kN
Pp = Passive pressure (Appendix 2 for Granular Soil)
tan 45 tan 45 19 . = 74.04 kN
66
1) Check
1.5
57.3 27.6 2.07 1.5
2) Check
1.5
74.04 47.9 1.55 1.5—
In conclusion, the 1 meter by 1 meter by 3 meter anchor at a depth of 1.7 meters is
acceptable for a 100 meter span with coarse-grained soil conditions. As detailed in
Chapter 4, further design iterations could increase the depth of embedment with the
objective to reduce the size of the anchor depending on priorities for optimization.
67
Chapter 5: Quality Control Considerations
Although engineers and project designers intend for designs to be constructed exactly
per specification, as-built drawings even in the developed world often vary greatly
from the original designs. Design factor of safety and the in-situ factor of safety are
rarely the same. Due to inadequacies in workmanship, material quality, quality
control, etc., the capacity of the completed bridge is not actually known, thus the
design factor of safety must be liberal to account for those conditions.
Designers must include added factors of safety in design to account for the probable
occurrence of inadequate craftsmanship and material specifications. The following
will detail a few of the critical quality control issues that a field supervisor must
account for, but further research is needed to adequately address quality control
measures.
5.1 Material Specifications
5.1.1 Concrete Mixture
Concrete is one of civilization’s oldest building materials and most often is a material
already widely used in most rural communities. Teaching the local laborers the
importance of proper mixing techniques and mixture types will improve the quality of
all concrete construction and thus may be one of a project’s primary successes
(Ruskulis, 1996).
68
Concrete is produced by mixing water, Portland cement and sand and gravel. To
produce a good concrete block, care needs to be taken in the quality of the sands and
gravels used in the mixture. Construction quality control of the sand and gravel
materials often requires preparatory work as natural conditions rarely leave well-
graded deposits. The fine aggregate with a diameter less than 5 mm, more commonly
referred to as sand, is often available on rural construction sites. No silt or clay
passing a #200 sieve or about 0.074 mm may be used. Similar to the process for soil
classification, if sand is sourced locally out of a riverbed, a mesh screen must be used
to ensure proper grain-size. Sands need to be washed and sifted through a screen with
5 mm openings. Coarse aggregate or gravel is a mixture of rock with a range of 6-20
mm diameter which may be found in-situ or created by crushing larger locally
available rock. The gravels and sands should have regular grain-size grading without
one specific size dominating the size distribution: with sand, particularly too many
fines (Ruskulis, 1996).
Water content controls the workability of the mixture and chemically reacts with the
cement to bond the resulting concrete. One of the critical components of quality
control is to ensure that the proper ratio is maintained during construction for
increased portions of water will improve workability but decrease material strength
(Engineer, 2002). For hand-mixing, a water to cement ratio of about 0.55 produces a
workable and durable concrete (Davis, 2002) but for more specific cement ratios,
Table 7 may be referenced.
69
Table 7 Concrete Ratios by Volume (Adapted Engineers, 2006)
Mixing technique is another aspect of quality concern. Many rural laborers are
familiar with mixing concrete but local methods of mixing are often inferior as there
is a lack of quality control standards. Common is the volcano approach, in which
aggregates and cement are mixed by hand, forming a pile. A hole dug out of the top
provides a bowl-form for the water to be poured and mixed. Although common, this
approach is not appropriate as it is difficult to attain an even mixture. Alternatively,
to hand-mix concrete, one must specify that the water is to be splashed into the
mixture in lifts while being manually mixed using a shovel.
Once set, the fresh concrete must be kept wet during the curing period. Concrete will
set in three days but reaches workable strength after seven days (Hazeltine,2003).
For greater detail on appropriate methods for concrete mixtures, reference Engineers
Without Borders, Concrete Mixes Guidelines (Engineers, 2006).
5.1.2 Steel Cable
Steel cable has two types of elongation: elastic stretch that fluctuates with the applied
load and the permanent stretch that corresponds with the cable strands rearranging
Mix Ratio by Volume (Cement:Sand:Gravel:Water)
Typical Use on Bridges
Approximate Yield (m³)
1 : 3 : 6 : 1.6 Tower Foundations, Block Anchors
0.24
1 : 2.5 : 5 : 1.6 Tower Foundations on poor soil
0.21
1 : 2 : 4 : 1.6 Non-structural Approach walls
0.17
1 : 2.5 : 3.5 : 1.6 Structural Column in Tower
0.17
70
and tightening in cross-section. The type of cable purchased dictates the amount of
hoisting sag. Cable may be purchased as either non-prestretched or prestretched, the
latter which will be considered herein. It is pertinent to not that if non- prestretched
cable is used, the design engineer must increase the anticipated sag onset from
loading which would have a greater impact on the hoisting sag set.
Cable handling is of paramount importance. It is critical not to unwind the cable
incorrectly, as this may cause kinks in the cable which result in weak points in the set
cable and thus potential failure points. Figure 26 shows the proper way to unwind the
cable.
Figure 25 Cable Uncoiling Procedure (Helvetas, 2001)
Cable transport from the drop point to the bridge site is also critical. Figure 27 shows
the proper way to transport cable.
Figure 26 Proper Cable Transport Technique
71
5.1.3 Cable Clamps
U-bolt clamps, often referred to as bull-dog clamps, are used to tie the cable around
the anchors. The singularity of the clamping method is one of the few design aspects
that does not include redundancy. As such, the material properties of the steel used to
create the clamps and the process used to attach the clamps is critical for the quality
assurance a bridge project.
The structural integrity of the clamps used to connect the steel cable is an area of
concern, as clamp failure is the source of the only known bridge failure to date
(Nepal, 2008) as shown in Figure 28.
Figure 27 Failed Nepali bridge: Clamp Slippage
Malleable steel clamps are most common but are inadequate for continuous load-
bearing design (Crosby, 2009) such as in the case of cable-suspended bridges. Drop-
72
forged are of superior quality for bridge-type loadings but are often difficult to locate
in developing countries.
The difference between the two is the process used to create the clamp. As with all
steel, the principal mechanical properties of interest to designers are strength,
ductility and hardness all of which are dependent on the process used to create the
clamp. In the casting process to create malleable clamps, the mold has the shape of
the desired component and the liquid metal flows into the desired shape. Malleable
clamps are able to attain the same efficiency ratings based on breaking strength of
wire rope, but are apt to continuously loosen with continued load and thus reduce
their ‘grip’ on the cable. With forged steel, the original shape is an ingot that is
forged into shapes by presses. The resulting product has a greater material strength
and lower ductility. As such, the torque specified to reach maximum efficiency rating
is greater than a malleable clamp of comparable diameter but once torque, the clamp
is far less likely to slip. It is the engineering field supervisor’s responsibility to
ensure that the clamps used on-site are per specification.
5.2 Construction Quality Control
5.2.1 Cable Clamps
Proper installation of cable clamps is one of the most critical components of
construction quality control. Correct installation is shown in Figure 29 and shows
both ropes are arrayed parallel and in contact with the bow clamp screws twisted on
from the
‘live end’
To attain
minimum
torqued, t
approxim
side of the c
of the cable
maximum
m torque requ
the cross-se
mately 25% a
Figur
carrying rope
e, as shown.
Figure 28
efficiency r
uired. It is t
ectional area
s shown in F
re 29 Reduction
e. It is essen
8 Proper Cable
rating of the
the author’s
a of the dea
Figure 30.
n in Cable Cros
ntial that the
Clamp Installa
e clamp, the
experience t
ad-end of th
s-Section with P
e clamp sadd
ation
e manufactu
that for the c
he cable wil
Proper Torque
dle surround
urer designa
clamp to be
ll be reduce
73
ds the
ates a
fully
ed by
74
To attain the required torque, one must reference manufactures standards. As the
installation of cable clamps occurs within a short span (a 26 mm cable requires 7
clamps, each spaced at 15 cm on center), it is very difficult to exert excess force.
Based on the 26 mm diameter of the cable, the required torque is approximately 300
ft-lbs. Assuming a typical laborer may be able to exert 80 to 100 pounds of force, a
3-foot wrench barely achieves full torque. It is unreasonable to require a torque-
wrench to measure actual torque applied at rural construction sites, thus one clamp in
addition to manufacturer’s specifications is recommended for each cable. Figure 31
shows a completed clamp installation in with the wrench used for cable installation.
Figure 30 Proper Cable Clamp Installation and Torque Wrench
5.2.2 Backfill and Compaction
Care must be taken when backfilling the approaches. Soil should be placed in layers
no greater than 15 cm thick. In the case of clays or silt backfill, a hand-rammer
should be used to compact the soil, shown in Figure 32.
75
Figure 31 Hand Rammer
Alternatively, community members or livestock walking thoroughly atop each layer
will ensure proper compaction. With soil placed in lifts the weight of the soil above
the anchor relied on in the design can be achieved. Furthermore, compaction of the
backfill ensures excessive settlement will not damage the approach ramp concrete.
Several other quality control items are critical to ensure the safety of the pedestrian
footbridges. The inclusion of these few is intended to encourage bridge designers and
field supervisors to consult the Helvetas manual (2001) for a more complete
coverage. Further research and publication in this area would also be extremely
beneficial for those working with rural footbridge technologies.
76
Chapter 6: Conclusion and Discussion
6.1 Summary
Pedestrian bridges ensure access to education and health, commerce and opportunity.
Rural pedestrian bridges contribute towards the improvement of living conditions for
some of the world’s most economically and socially disadvantaged. The simplicity of
the technology and the availability of a design example will ensure many more
bridges are built.
A review of pertinent structural design codes and geotechnical models were reviewed.
Parameter assumptions were justified through parametric models, and a simple design
approach adapted from DM-7 (Naval, 2009) was proposed for design use for both
fine and coarse grained soil types.
The loading assumptions and structural design approach was presented in Chapter 3,
including a case-study based on a 100 meter span and 1.0 meter decking. Chapter 4
detailed pertinent academic approaches to anchor design for fine and coarse grained
soils. Separate consideration for either soil type was given and soil parameter
assumptions concluded upon. A recommended soil testing and classification flow
chart was provided to acquire soil parameters for use in the DM-7 anchor design
process. Structural loading assumptions and codes are provided in the context of a
case-study example. The final product found that the 100 meter Ethiopia bridge case
study with a sandy-soil at either abutment must resist 166 kN of loading. One anchor
design solution is detailed. Several of the key quality control measures were outlined
77
in Chapter 5, with the intention to introduce the reader to the importance of material
and construction quality control for footbridge projects.
6.2 Design for the Developing World
The spectrum of potential benefits for infrastructure projects in developing countries
ranges from improved beneficiary access, for example improved educational standard
allowed from year-round access to schools, to the introduction of construction
technology transfer. Despite the benefits of any type of international aid work,
ethical dilemmas of accountability and safe practice are pertinent. The process of
design simplification presents a number of technical and logistical challenges.
Furthermore, professional ethics must be considered when detailing the operations,
maintenance and project lifespan accountability. A general discussion of transferring
a technology from the developed to developing world is also considered from a
lessons-learned context.
6.2.1 Design Simplification
Great care must be taken not to reduce the quality of a design when simplifying.
Many technologies needed in the developing world have well-documented design
approaches for use in developed countries. To make these technologies appropriate
for rural applications, modifications for material availability, low cost and limited
tools and equipment must be accounted for. The process of simplification requires
the engineer to make many of the same design decisions as in an industrialized
context, but with a varying hierarchy of priorities. For example, in the case of
78
infrastructure projects, a designer in The United States may be willing to sacrifice an
increase in budget to reduce the construction time. In the developing world, most
often time and labor are least expensive and thus lowering the cost of a project would
be prioritized. Finding the balance between cost, and construction time is of
paramount importance.
Standardizing designs and design processes specifically for development work
provides a greater level of comfort in a design, reducing this likelihood of project
design failure. But, modulated designs require a number of assumptions: a design
code to be followed, material availability and project objectives by the beneficiaries.
Local engineering design codes and community usage requests must be taken when
simplifying a design from the original context in the developed world to that of the
developing. As such, even a simplified and modulated design must have the
flexibility to be modified. Design manuals are often created for use in the developing
world as was the case of the Helvetas manual. It is the suggestion of the author that
development projects may have the greatest impact when a modulated design also is
supplied with a detailed explanation of the design process and assumptions used.
This allows for a more general use of the work as secondary contributors are able to
modify to better suit their local community and national standards.
6.2.2 Ethics of Accountability
Accountability for humanitarian-aid projects requires one to consider the professional
ethical codes for practice in a country other than where one is licensed. In typical
79
industry work, the engineering profession has a very high level of professional
accountability but design codes and regulations allow an engineer a level of
confidence in his or her work. Abroad, the same codes and regulations are
applicable, but the designs often are impractical and thus additional individual
consideration must be given to each project. Furthermore, as developing world
construction techniques and quality control are often inferior to those considered
standard in the developed world, making standardized quality assurance and control
documents for each type of project further ensures project reliability and safety.
The inadequacy of the legal framework in many developing countries measures
reduces the liability of contractors to ensure quality control by their own measures
(Leisninger, 2009). If a developing country has no regulation or has one but does not
enforce it, it is likely that additional margin of safety should be included in the design
as well. A complete best-practice design guide includes the assumed factors of
safety, but an additional document improving the quality control would allow a
designer to fully understand the areas of concern and more assign appropriate factors
of safety considering local capacity for local accountability.
Additionally, project engineers and implementing organizations need to take the
initiative to be personally accountable for each project. A plan of how to avoid
failure as well as what happens in the case of failure is essential. Insurance
companies in the developed world play an essential role in the guarantee of an
engineered project: the developing world projects deserve a similar level of project
80
assurance. Attention in all humanitarian projects should address the issue of ethical
responsibility and how to address a failure situation.
Bridges to Prosperity takes great lengths to ensure quality control throughout each
project. A document is currently being created that would be inclusive of all critical
quality control and maintenance issues. Ultimately, it is the engineer’s responsibility
to take personal accountability for a project’s enduring success and thus operation and
maintenance instructions and training should be included as a required component of
every project. Returning to assist with maintenance also helps to reduce the risk of a
failure.
6.2.3 Transferring Best Practices to Developing Nations
Many lessons were learned in the attempt to transfer a technology fairly well-
understood under typical engineering conditions into a setting for development work.
Perhaps the greatest lesson learned was not attempt to reinvent the wheel. Many
military and emergency engineering documents exist. An academic understanding of
the design issue is necessary but the most pertinent and useful reference materials are
those which consider the lack complexity in simple design.
In the case of footbridge design, the first step was to identify the intended audience
for the report. Ideally a document would be produced that could be used as a field
manual in the developing world. This particular document targeted a more academic
audience. With the vocabulary of choice more technical, further steps were taken to
identify the specific engineering problem and pertinent parameters. When the
81
number of input parameters exceeded the feasible ability of in-situ testing, the model
was used for parametric studies to compare possible material assumptions. As the
intended audience was identified as having a working knowledge of geotechnical
engineering, a greater focus was placed on justifying assumptions. Documents with a
more general intended audience may chose to include technical assumptions and
models in an appendix.
Constructability is another critical issue. Many of the design references for soil
anchors for power-lines assumed that changing the depth of embankment would be
the easiest control variable. In the case of rural construction, each meter of added
excavation could add weeks to a project as only man-powered excavation is possible.
This additional construction time may be preferred over additional cost, but the
balance between design cost and time is vastly different from the original design
intent outlined in academic sources. A considerable amount of effort should be taken
to consider both the theoretical and practical sides of a testing program or design.
Designers interested in creating a best-practices guide to design for developing
applications are suggested to limit the amount of theoretical information gathered and
to focus on what is already being done. This report is primarily concerned with
existing academic literature applicable to a somewhat specific product. In future
research and publication, a lesser focus would be placed on academia and a greater
emphasis would be placed on constructability and cost issues, as these are of
paramount importance to application in developing world applications.
82
6.3 Opportunities for Future Research
Future experimental research is needed to verify the correlation between assumed soil
parameters and the ultimate uplift capacity of rectangular dead-man anchors.
Although research pertinent to equivalent structures were reviewed, the lack of
studies with similar loading and geometrical scenarios was disappointing. Further
research could address one of the following: comparison between increases in anchor
width versus burying the anchor to a greater depth, correlation between rudimentary
field tests and laboratory tested friction angles and changes in ultimate pull-out
capacity for various coarse-grained and fine-grained soils. From experimental data, a
more complete database and design assumption matrix may be created. Furthermore,
the need for an improved testing approach would need to be developed or a testing
device, such as those detailed in Chapter 4, would need to be correlated to the
empirical findings to calibrate the devices.
A Best Practice Guide for Construction Quality Assurance and Quality Control,
including Safety precautions also would be an excellent contribution to the field of
pedestrian bridge design. Chapter 5 briefly addressed a few of the key quality control
components, but a document properly addressing this topic was beyond the scope of
this report. Included in any effective construction document should be the design
process used and the assumed quality of each component. For example, a structural
engineer in The United States must specify A50 steel if he or she assumed 50 ksi
yield stress in their design. Without this declaration of material standard and without
the proper system of quality control, an unknowing contractor may choose to use a
83
less expensive and more readily available A36 steel with inferior yield strength. In
the developing world, this component of construction and material quality control
must be documented very clearly.
84
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Appendices
Appendix 1: Soil Identification Table (Helvetas, 2001)
The above table is provided for reference only but is not implicitly recommended
through inclusion. The table is used in Helvetas’ design manual (2001).
Appendix
(DM-7 Se
x 2: Compu
ection 7.2, N
utation of Si
Naval, 2009)
imple Activee & Passive Pressures
89
90
Appendix 3: Breaking Strength Properties of Cable
Typical IWRC 6x19 Cable Properties: Assumed tensile strength of 1770 MPa) Verify with Supplier
Nominal Diameter Weight Breaking strength
Breaking strength
Design Breaking strength (FS = 3.5)
Inches mm lbs/ft kg/m tons kg kN kN
1/4 6.4 0.116 0.17 2.94 2667.12 26.16 7.47
5/16 7.9 0.18 0.27 4.58 4154.91 40.75 11.64
3/8 9.5 0.26 0.39 6.56 5951.13 58.36 16.67
7/16 11.1 0.35 0.52 8.89 8064.87 79.09 22.20
1/2 12.7 0.46 0.68 11.5 10432.62 102.31 29.23
9/16 14.3 0.59 0.88 14.5 13154.18 129.00 36.86
5/8 15.9 0.72 1.07 17.9 16238.61 159.25 45.50
3/4 19.1 1.04 1.55 25.6 23223.93 227.75 65.07
7/8 22.2 1.42 2.11 34.6 31388.59 307.82 87.95
1 25.4 1.85 2.75 44.9 40732.59 399.45 114.13
1 1/8 28.6 2.34 3.48 56.5 51255.94 502.65 143.61
1 1/4 31.8 2.89 4.30 69.4 62958.62 617.41 176.40
1 3/8 34.9 3.5 5.21 83.5 75749.93 742.85 212.24
1 1/2 38.1 4.16 6.19 98.9 89720.57 879.86 251.39
.
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Appendix 4: Specific Weight of Wood Specimen (CSG)
Wood - dried kg/m³
Afromosia 705 Apple 660 - 830 Ash, black 540 Ash, white 670 Aspen 420 Balsa 170 Bamboo 300 - 400 Birch (British) 670 Cedar, red 380 Cypress 510 Douglas Fir 530 Ebony 960 - 1120 Elm ( English ) 600 Elm ( Wych ) 690 Elm ( Rock ) 815 Iroko 655 Larch 1280 - 590 Lignum Vitae 1370 Mahogany ( Honduras) 545 Mahogany ( African ) 495 - 850 Maple 755 Oak 590 - 930 Pine ( Oregon ) 530 Pine ( Parana ) 560 Pine ( Canadian ) 350 - 560 Pine ( Red ) 370 - 660 Redwood ( American ) 450 Redwood ( European ) 510 Spruce ( Canadian ) 450 Spruce ( Sitka ) 450 Sycamore 590 Teak 630 - 720 Willow 420
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Appendix 5: Explanation of Logan’s Pull-out tests for Footings in Sands
Logan (1976) completed a series of pull-out tests for pad and stem footings in sand
which appear appropriate to the footbridge anchors due to similarities in geometry
and loadings. The test method described a series of instruments installed around each
tests footing to evaluate the uplift movement of the surrounding ground due to pull-
out, taken to failure.
During the tests, movement was negligible up to 30 kips (133 kN) of load with
geometries within reasonable footbridge anchor sizes. As detailed in Chapter 3, this
loading is within 15% of expected tensile loads incurred on an anchorage for a 100
meter bridge. The tests found that upward movement of the ground was confined to
the effective volume of soil included within a slope of 30 degrees from the top corner
of the anchor pad (Logan, 1976, pg 72). It should be noted that Logan’s tests were
conducted by pulling the footing at a slope 78.9 degrees which is significantly greater
than found in footbridge applications. Thus, although the experimental objective was
to model failure patterns, the study provided insight into the true behavior of anchors
in coarse-material under tensile loadings.
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Appendix 6: Abbreviated Unified Soil Classification System (Coduto, 2001)
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Appendix 7: Bjerrum Correction Factor for Vane Shear Test
Bjerrum’s Correction Factor for use in the Vane Shear Test is for use with saturated,
normally consolidated clays. Ip is the plasticity Index of a soil is the numerical
difference between the liquid limit and the plastic limit, LL-PL, presented in a percent
form (Coduto, 2001).
