STONE ARCH BRIDGES:
AN UNDERUTILIZED TECHNOLOGY IN
THE MODERN UNITED STATES
by
Nicholas R. DiNardo
A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Civil Engineering
2019 Summer
© 2019 Nicholas R. DiNardo All Rights Reserved
STONE ARCH BRIDGES:
AN UNDERUTILIZED TECHNOLOGY IN
THE MODERN UNITED STATES
by
Nicholas R. DiNardo
Approved: ______Michael J. Chajes, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee
Approved: ______Sue McNeil, Ph.D, Chair of the Department of Civil and Environmental Engineering
Approved: ______Levi T. Thompson, Ph.D. Dean of the College of Engineering
Approved: ______Douglas J. Doren, Ph.D. Interim Vice Provost for Graduate & Professional Education and Dean of the Graduate College
ACKNOWLEDGMENTS
I would like to take the time to thank all of my friends and family. Without their support, this paper may not have made it to the table or screen in front of you. Who are we without the ones we love? I’d also like to thank all of the professionals in the field whom I contacted for information, the many researches whose work I cited, and especially all the great professors at the University of Delaware who have taught and guided me to the finish line. Special shout-out to Dr. Chajes for believing in me and helping me throughout my graduate career. Finally, there is one more person I’d like to thank. Thank you, David, for being one of the greatest friends that I have ever had. You helped me sustain my creativity, was there for me through my struggles, and were always a pleasure to spend time with. May your soul rest in peace.
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TABLE OF CONTENTS
LIST OF TABLES ...... viii LIST OF FIGURES ...... x ABSTRACT ...... xii
Chapter
1 PRESSING ISSUES IN OUR DAY AND AGE ...... 1
Structural Deficiency of Bridges in the U.S. National Highway System ...... 1 Climate Change ...... 5
The Green House Effect ...... 5 Advanced Lifestyle ...... 6 The Effects of Climate Change ...... 7
Solutions? ...... 9
2 HISTORY OF THE STONE ARCH BRIDGE ...... 11
Discovering the Stone Arch and Ancient Bridge Building ...... 12
Roman Stone Arch Bridges ...... 13 Ancient Chinese Stone Arch Bridges ...... 16
Revival of the Stone Arch via the Industrial Revolution ...... 17
Masonry Arch Bridges in the European Railway System ...... 18 The American Rail System: Statistically Hidden but Physically There .... 22
The Carrolton Viaduct ...... 23 The Canton Viaduct ...... 23 The Rockville Stone Arch Bridge ...... 24
Impact of Railway Masonry Arch Bridges ...... 25
When and Why Did We Stop Using the Stone Arch? ...... 26
The Traditional Method of Masonry Construction ...... 27 Engineering and Design Before the 20th Century ...... 29
iv
Constructability of Steel and Concrete ...... 30
Masonry Bridges Still a Solution in Some Nations ...... 30 Chapter Conclusion ...... 32
3 THE DURABILITY OF THE STONE AND ARCH COMBINATION ...... 33
Earth, Rocks and Geological Processes ...... 34
Igneous Rocks ...... 35 Sedimentary Stones ...... 37 Metamorphic Rocks ...... 39
Strength and Durability ...... 40
Deterioration Mechanisms of Stone, Concrete and Steel ...... 40
Stable Stone ...... 40
Salt Crystallization ...... 41 Aqueous Dissolution ...... 41 Freeze-Thaw ...... 42 Thermal Expansion ...... 43
Porous Concrete ...... 44
Corrosion Damage to Reinforcing Steel ...... 44 Alkali-Aggregate Reaction ...... 45 Chemical Attack ...... 46
Corrosive Steel ...... 47
Tarnishing ...... 47 Atmospheric Corrosion or Uniform Deterioration ...... 48 Galvanic Corrosion ...... 48 Crevice Corrosion ...... 49 Pitting Corrosion ...... 49
Identifying Stone Types Commonly Used for Construction ...... 50 Comparing Durability ...... 53
Structural Mechanics of the Double Hinged Arch ...... 54
Schematic and Terminology of the Arch ...... 55 Experiment to Explain Load Path of the Arch ...... 56
v
Structural Analysis of the Arch Shape ...... 57
Free Body Diagram and Section ...... 57 Solving for the Vertical Reactions ...... 57 Solving for the Horizontal Reactions ...... 58
Limit States and Modes of Failure ...... 61
Limit States ...... 61 Loading ...... 62 Modes of Failure for Block-Arches ...... 63
Chapter Conclusion ...... 64
4 ECONOMIC VIABILITY OF STONE ARCH BRIDGES ...... 65
Life Cycle Cost Analysis ...... 65
Steps of the LCCA ...... 66 The Time Value of Money ...... 66
LCCA for Concrete and Steel Girder Bridges in Pennsylvania ...... 68
Average Deterioration Rates and Estimating Bridge Service Life ...... 70 Dr. Barker’s LCCA Results ...... 73 Estimates for Bridge Construction on the National Highway System (NHS) by the Federal Highway Administration ...... 76
The Economic Value of Durability ...... 77
Estimating the Service Life of a Stone Arch Bridge ...... 77 Maximum Initial Cost of Stone Arch Bridge ...... 79 Equivalent Uniform Annual Costs (EUAC) ...... 86 Maintenance ...... 89 Salvage Value ...... 91
Applicability of the Stone Arch Solution ...... 92
Limitations from Design and Construction ...... 92
Accelerating Construction ...... 93 Cost of Stone ...... 95
Conditions at Possible Sites of Interest ...... 96
vi
Chapter Conclusion ...... 97
5 PREVENTING FUTURE CARBON EMISSIONS ...... 98
Emissions from Steel Production ...... 98 Emissions from Cement Production ...... 100 Emissions from Producing Dimensional Stone ...... 100 Emissions from Bridge Building ...... 102 Chapter Conclusion ...... 107
6 THESIS CONCLUSION AND FUTURE WORK ...... 108
REFERENCES ...... 110
vii
LIST OF TABLES
List of Roman bridges used for modern traffic (O'Connor, 1993), (Barow & Ragette, 2013) Notes: ~ = approximately, LxWxH= Span Length by Arch Barrel Width by Arch Height ...... 15
Number of Stone Arch Bridges in Various Railways as Reported by the UIC (Orban, 2004) * Estimated Number ...... 19
Estimation of stone arch bridges (no culverts) in the European Railway Systems (Proske & van Gelder, 2009) ...... 21
The manifestation of reinforcement corrosion (Heckroodt, 2002) ...... 45
List of stone types traditionally used for bridge construction (Proske & van Gelder, 2009) ...... 51
List of stone types suitable for building construction (Hugues, 2005) .... 52
General durability of each classification of stone (Heckroodt, 2002) ..... 53
FHWA condition ratings (FHWA, 1995) ...... 71
Deterioration rates of concrete and steel girder bridges (Barker, 2016) . 72
Average service life concrete and steel girder bridges (Barker, 2016) ... 73
Life Cycle Cost results of total database (Barker, 2016) ...... 73
Life Cycle Cost of simple span bridges (Barker, 2016) ...... 74
Life Cycle Cost of two-span bridges (Barker, 2016) ...... 75
Life Cycle Cost results for brides with a maximum span of 140 feet (Barker, 2016) ...... 75
FHWA’s estimated bridge construction cost paired with Dr. Barker’s results in 2017 dollars ...... 76
Average deterioration rates of stone arch bridges compared to steel and concrete girder bridges ...... 78
viii
Average service life of stone arch bridges compared to concrete and steel girder bridges ...... 79
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 11 as the overall limit (overall database) ...... 82
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 12 as the overall limit (single span bridges) ...... 82
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 13 as the overall limit (two span bridges) ...... 83
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 14 as the overall limit (bridges <140 feet) ...... 83
Maximum cost for a stone arch bridge using the FHWA estimates from Table 15 as the overall limit ...... 84
Impact on the increased budget column when the comparable bridge’s service life varies ...... 85
Table used to express the short comings of presenting the results in present value costs by varying the stone arch bridge’s service life ...... 86
EUAC using calculated using concrete and steel girder initial costs from Table 14 and the average maximum stone arch cost from Table 21 ...... 88
Appraisal Descriptions of Condition Ratings (FHWA, Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges, 1995) ...... 96
Details of the five projects evaluated by Hoeckman & Nelis (Hoeckman & Nelis, 2012) ...... 104
Sources of emissions in each project and their respective percentages of contribution to the total amount of emissions (Hoeckman & Nelis, 2012) ...... 105
Calculation of emission prevention from using stone arch bridges ...... 106
ix
LIST OF FIGURES
Figure 1 Rising Life Expectancy of Particular Nations through the 20th century (Kangas, 2010) ...... 7
Figure 2 Progression of the false vault (arch) (Proske & van Gelder, 2009) ...... 12
Figure 3 Roman semi-circular stone arch bridge in Spain (Stellez, n.d.) ...... 14
Figure 4 Zhaozhou Bridge: 1,400-year-old segmented stone arch bridge with open spandrel walls that reduce lateral flood loads. (Morgan, 2007) ..... 16
Figure 5 The Carrolton Viaduct over Gwynn’s Falls (ASCE, n.d.) ...... 23
Figure 6 Canton Viaduct (Boucher, 1968) ...... 24
Figure 7 The Rockville Stone Arch Bridge carrying modern train Rockville, Pennsylvania (American-Rails.com, 2007) ...... 25
Figure 8 Construction of a stone arch barrel using traditional methods (Minnesota Department of Transportation , n.d.) ...... 28
Figure 9 The Danhe Bridge (HighestBridges.com, 2017) ...... 31
Figure 10 Visualization of the creation of Earth through the accretion theory (Bliss) ...... 35
Figure 11 Left- Image of a Conglomerate Rock (Mark, 2015) Right- Sandstone (Khattak, 2018) ...... 39
Figure 12 Limestone cavern produced by aqueous dissolution (ScienceStruck, 2018) ...... 42
Figure 13 Schematic of a single span stone arch bridge (Proske & van Gelder, 2009) ...... 55
Figure 14 Freebody diagram and internal reactions of an arch ...... 58
Figure 15 Placing force, F, on structure and releasing the horizontal reaction at B 60
Figure 16 General depiction of the condition rating of any structure, element, or component over time (FHWA, Life Cycle Costs Primer, 2002) ...... 71
x
Figure 17 Installation of a precast concrete segmented arch by crane (Ball, 2015) 94
xi
ABSTRACT
In the United States today, our highway infrastructure system as a whole is need of repair. This is a major issue as the American people are highly dependent upon our highway infrastructure system to keep society functioning. In 2015, the U.S. Federal Highway Administration (FHWA) reported that of America’s 614,387 bridges, 20% are either structurally deficient or functionally obsolete. Also, approximately 39% of America’s bridges are 50 years old and approaching the end of their design lives (ASCE, 2017). This indicates that in the coming decades, an even larger number of bridges will be demanding attention. To make matters worse, our entire race is endangered by climate change. The International Panel on Climate Change (IPCC) is reporting that our planet is heating up due to greenhouse gas emissions from human activities. Current predictions estimate that increases in average global temperatures will likely result in frequent flooding of coastal cities, the inundation of entire islands, frequent and intense hurricanes and other alarming consequences. This may result in the loss of lives and livelihoods. The production of steel and concrete is a major contributor to these issues as they account for ten percent of global emissions annually.
So not only are concrete and steel bridges short-term solutions for long-term needs, but their production is magnifying our planet’s most dangerous threat.
Together, these problems combine to create one very extreme issue. Many bridges will soon need to be rebuilt and doing so sustainably is vital. These new bridges must be economical in life cycle costs and environmentally friendly. Finding a solution to solve these issues simultaneously may seem impossible but when there is a will, there is always a way, and that way could be stone arches. Stone arch bridges around the world are averaging well over 100 years of serviceable life. This thesis was written to
xii prove that stone arch bridges can be the most economically viable and environmentally sustainable structure type for bridges that need to span 100 feet or less.
xiii
Chapter 1
PRESSING ISSUES IN OUR DAY AND AGE
“Every civilization, including this one, faces an endless cycle of challenge and response; no civilization is ordained to be forever preeminent. Wealth and leadership in the world must be earned by doing the right thing in response to grave challenges.” (Pinkerton, 2015)
Structural Deficiency of Bridges in the U.S. National Highway System In the modern United States, our highway infrastructure system is an important cog in the machine that is our functioning civilization. Every day, hundreds of millions of Americans use and depend on the National Highway System (NHS) to get to work, to bus students to school, to ship goods to homes and businesses, to perform services, or to simply travel from one place to another. Quality, safe, efficient, and durable transportation infrastructure is imperative to sustaining the United States. Annually, American drivers travel 3 trillion miles on the 614,387 bridges and 4,109,418 miles of paved roadways that compose the NHS
(ASCE, 2017). Every American is highly dependent upon transportation infrastructure and there is no doubt it plays a significant role in the success of the nation’s economy. Though maintaining this system is crucial to the progression of the American people, the last several decades have proven that this is a very difficult task to fiscally accomplish. Over the past 60 years, federal funding for building and maintaining infrastructure in general has significantly decreased. From the period of 1960 to 2007,
1 overall funding for transportation infrastructure fell from 3% of the nation’s GDP to about 1.1% (Pinkerton, 2015). Due to lack of funding, a large percentage of our local, state and interstate highways are in disrepair and/or functionally inadequate. James P. Pinkerton, a journalist, drives this point home:
“In its ‘report card,’ the American Society of Civil Engineers (ASCE) awarded the U.S. aviation system a grade D; the rail system, a C+; public transit, D; bridges, C+; and the highway system, D. Its cumulative GPA for all infrastructure and its effects, including solid and hazardous waste, drinking water, power grids, levees, waterways, and ports, was D+. This overall near failing grade has remained largely the same in every report card since 1989, a pattern the civil engineers believe is ‘due to delayed maintenance and underinvestment across most [infrastructure] categories.’” (Pinkerton, 2015) The Federal Highway Administration estimated that the unmet capital investment need for the NHS in 2012 was $836 billion. For NHS bridges alone, deferred maintenance has led to a backlog of $123 billion (FHWA, 2015). This value of unmet investments is validated by the ASCE’s current bridge report card, which summarizes the condition of all the NHS’s bridge stock. As of 2016, 9.1% of bridges were reported to be structurally deficient1, with an estimated
188 million trips made over these bridges daily (ASCE, 2017). To make matters worse, the number of structurally deficient bridges is expected to rise significantly in the coming years. The ASCE reports that “the average bridge in the U.S. is 43 years old. Most of the country’s bridges were designed for a lifespan of 50 years, so an increasing number of bridges will soon need major rehabilitation or retirement”
1 A bridge is considered structurally deficient when it is in need of significant rehabilitation or replacement.
2 (ASCE, 2017). Clearly then, in order to keep our roadways safe and functional, many bridges will need to be repaired or replaced in the near future. Another classification of bridges concerning to the ASCE are those considered to be “functionally obsolete.” Functionally obsolete bridges are prevalent throughout the NHS and are defined by their inadequacy in either satisfying updated code requirements or serving current traffic demand. For example, a bridge may be functionally obsolete if it has too few of lanes to satisfy its current average daily traffic or having too narrow of lanes and shoulders. Many bridges with these issues cause congestion, and, therefore, drivers are subject to longer travel times and a higher probability of being involved in accidents. Of the nation’s 614,387 bridges, 13.6% were considered functionally obsolete in 2016. (ASCE, 2017)
Together, structurally deficient and functionally obsolete bridges account for almost 23% of all bridges. So, what do we do about this problem? The ASCE makes several recommendations to raise the grade of the U.S.’s infrastructure report card (ASCE, 2017). Specifically: • “Increase funding from all levels of government in order to continue reducing the number of structurally deficient bridges, decrease the
maintenance backlog, and address the large number of bridges that have passed or are approaching the end of their design life;” (ASCE,
2017) • “Bridge owners should consider the costs across a bridge’s entire lifecycle to make smart design decisions and prioritize maintenance and rehabilitation;” (ASCE, 2017)
• “Fix the federal Highway Trust Fund by raising the federal motor fuels tax. To ensure long-term, sustainable funding for the federal surface
3 transportation program, the current user fee (18.4 cents per gallon on gasoline and 24.4 cents per gallon on diesel) should be raised and tied to inflation to restore its purchasing power, fill the funding deficit, and ensure reliable funding for the future;” (ASCE, 2017) • “States should ensure their funding mechanisms (motor fuels taxes or
other means) are sufficient to fund needed investment in bridges;” (ASCE, 2017) and • “States and the federal government should consider long-term funding solutions for transportation infrastructure and potential alternatives to the motor fuel taxes, including further study and piloting of mileage- based user fees.” (ASCE, 2017)
Though these suggestions seem rather simple, achieving such tasks will be difficult as most are dependent upon passing increased budgets through state and federal legislatures. Political support for the transportation infrastructure system was significantly diverted in the 1970’s due to the environmental “green” movement and has not returned since. Building such a large infrastructure system has had major impacts on the environment in many locations, and they did not go unnoticed. As a result, financial support for building/maintaining new and existing bridges has dwindled.
Fast-forwarding to today, both major political parties consistently falls short of passing budgets that are adequate to simply maintain what we currently have built, let alone go beyond mere maintenance in order to sustain the system. With the growing concerns over climate change, the case against transportation infrastructure is even stronger. Engineers are left with only their creativity to solve this issue.
4 Climate Change
The Green House Effect Venus, Earth’s so called “sister planet,” was once a mystery to humanity. Before the modern age, one may have speculated that there was life on the surface beneath its opaque skies. Today, we now know there is almost zero probability of life on Venus. By using satellites, space landing craft and spectrometers, scientists have determined that Venus is uninhabitable for all familiar forms of life. One significant reason for this is that its surface is scorching at a temperature of 462°C, which by the way, is hotter than Mercury’s surface, which reaches temperatures as high as 426°C. Wait, what? Venus’s distance from the sun is almost double that of Mercury, and the sun is the primary heat source for all the planetary surfaces in our solar system. How could Venus be hotter than Mercury? This occurs in large part because of the greenhouse effect. The greenhouse effect is a natural process on any given planet with an atmosphere. Essentially, an atmosphere is layers of gas. Some types of gas cause the sun’s radiation to reflect heat back to the planet’s surface. Essentially, heat is insulated by these gases and the process results in the increase of surface temperature. Such gases labeled as
“greenhouse gases” include carbon dioxide, methane, water vapor, and nitrous oxide. Using spectrometry, it was determined Venus’s atmosphere is composed of 97.5% carbon dioxide. Mercury lacks an atmosphere. Therefore, Venus’s surface is hotter because of its ability to retain more heat than Mercury. So why am I talking about Venus? For the past two centuries, many nations across the planet have been participating in the alteration of Earth’s natural carbon cycle by producing massive amounts of carbon dioxide and emitting this gas into the
5 atmosphere. As a result, humanity is accelerating the greenhouse effect causing atmospheric temperatures to increase and climates to change across the planet.
Advanced Lifestyle The combination of the Industrial Revolution and the continued era of academic enlightenment bred new knowledge and technologies which have changed humanity forever. During this time, people realized that the combustion of fossil fuels, like coal and oil, could be exploited. Doing so created the electrified and fast-paced world seen today. The use of fossil fuels to produce electrical and mechanical energy was, and is, extremely dependable. Machines enabling mass production and quick transportation were developed; homes were heated in the harshest of winters; global trade was facilitated; the rate of consumption of Earth’s resources exploded. Wealth and higher standards of living poured into the nations that industrialized with fossil fuels. The shackles of the natural world were broken, and a new style of life was born. In the last century, life expectancy in almost every nation across the planet has increased (see Figure 1). The growth rate of the global population during this time period is unprecedented. The world population blew-up, growing from 1.65 billion in 1900 to 7.4 billion in 2015 (Roser, Ritchie, & Ortiz-Ospina, 2019). This growth was largely due to advancement in engineering, healthcare, women’s rights, civil rights, transportation, computer technology, college-educated populations, and numerous other fields which have flourished with new knowledge and efficient practice. Major growth is still projected in the 21st century as the population is expected to increase to 9.8 billion by 2050 (UN, 2017).
6
Figure 1 Rising Life Expectancy of Particular Nations through the 20th century (Kangas, 2010)
Together, population growth and advanced lifestyle have come at great environmental cost. Humanity’s search for a more stable, comfortable, and long-lived life has placed tremendous stress on our planet. Earth’s natural resources are being consumed at unprecedented rates and this is negatively affecting her ecosystems and natural processes. Now, we may have unknowingly started a fire with the potential to burn down humanity’s greatest civilizations.
The Effects of Climate Change The Intergovernmental Panel on Climate Change (IPCC) deemed it is “high- likely” that human activities are responsible for a steady increase in the average atmospheric temperatures of the planet. Such human activities include the burning of fossil fuels, deforestation, advanced wars, and many more destructive practices. With
7 the major population growth discussed earlier, humanity has significantly increased its demand and use of natural resources. In their 2013 report, the IPCC concluded: • “[Atmospheric] carbon dioxide concentrations have increased by 40% since pre-industrial times, primarily from fossil fuel emissions and secondarily from net land use change emissions,” (IPCC, 2013); • The average temperature of the planet has risen 0.85°C over the period of 1880 to 2012 (IPCC, 2013); • “Warming of the climate system is unequivocal, and since the 1950s, many of the observed changes are unprecedented over decades to millennia. The atmosphere and ocean have warmed, the amounts of snow and ice have diminished, sea level has risen, and the
concentrations of greenhouse gases have increased” (IPCC, 2013). With every action there is reaction, and in this case, it is the alteration of the planet’s natural processes. The latest predictions say that sea level rise will inundate entire islands and many coastal areas, including those of the United States. These effects will lead to significant damages in our coastal cities. Not only is land expected to be covered by the oceans, but warmer water temperatures could increase the frequency and intensity of hurricanes. At this point, a realistic estimation of the potential loss of life and economic damages due to climate change is impossible.
So how does this relate to our infrastructure systems? In 2010, the world production of cement and steel accounted for 5.5% and 5%, respectively, of the world’s global carbon dioxide emissions (Climate Action Tracker, 2017). These are sizable amounts of annually occurring emissions. If we were to rebuild a great number of bridges as required, the amount of carbon emissions resulting from this task
8 would be considerable because of the use of cement and steel (this is further discussed in Chapter 5).
Solutions? Maintaining an efficient highway system is necessary to sustain and grow the United States’ economy. Failing to keep our bridges and the highway system working efficiently will negatively affect the mechanics of all business in America. If a significant number of bridges were deemed “unsafe,” the speed and efficiency at which America works will be hindered. Solving the problem of how to replace/repair inadequate bridges in a way that will limit carbon emissions while also being economical requires out-of-the-box thinking. Regarding the economic issue, budgets for transportation are not likely to increase to the amount needed. Life Cycle Cost Analysis (LCCA) are often considered when choosing the most economical bridge designs. Selecting the most economically sustainable structure will ensure that taxpayers get the most out of their money, but how effective is this when concrete and steel structures fall in the same range of serviceability? New materials and construction methods are needed to achieve higher levels of economic viability. Generally, cutting overall costs and lengthening the design life of bridges is absolutely necessary to solve this catastrophic level of infrastructure deterioration. Simultaneously, carbon dioxide emissions are leading humanity down a path to self-destruction. The impacts of climate change, like sea-level rise and frequent, intense hurricanes, are threatening human lives and livelihoods. So, how do we rebuild the transportation infrastructure needed for our nation’s success while minimizing
9 environmental impact? Perhaps the answer is to look to our past for an answer to our future. This paper explores how the ancient technology of stone arch bridges, may be used to address these issues. The stone arch bridge is the most durable bridge-type known to man as some of the oldest are over two millennia in age and service life. In
Chapter 2, the history of the stone arch bridge and its use throughout time is discussed, along with its progression in design. Most importantly, Chapter 2 establishes the stone arch bridge’s physical ability to last for centuries to multi-millenniums. In Chapter 3, the properties of stone and structural mechanics of the arch become the focus to show why such bridges have performed so well. Then in Chapters 4 & 5, the sustainability of the structure type, both economically and environmentally, is studied in comparison to typical concrete and steel girder bridges with lengths of 100 feet or less. Finally, Chapter 6 concludes the thesis and makes recommendations for future work.
10 Chapter 2
HISTORY OF THE STONE ARCH BRIDGE
The stone arch structure has played a significant role in the prosperity of history’s greatest civilizations. Their use goes back to the dawn of civilization as they were used to construct tombs, underground caverns, passageways, and windows. Later, stone arches became a key factor in enabling large scale civilization and essential to developing many of the modern nations that we know today. They were used to build essential infrastructure for stable land-based trade routes, transport potable water via aqueducts, and even provide the sacred space for art in the domes of temples. It would not be an overstatement to rank the discovery of the stone arch among fire and the wheel in importance to humanity. In terms of bridges, their application has extended into modern times as the strength of the stone arch went unmatched until the development of concrete and steel. Some researchers estimate that around one million stone arch bridges stand worldwide (MelBourne, 2007). Since the 1800s, railroads have built and utilized stone arch bridges and it’s likely that an overwhelming majority of these bridges are still in operation today. This chapter explores how stone arches were discovered, studies the progression of their architecture, and discusses their use during particular periods of time.
11 Discovering the Stone Arch and Ancient Bridge Building During pre-historic times, ancient builders discovered stone was capable of bridging a gap. Thick and fairly straight monolithic boulders were used as columns and beams to create structures. Eventually, people discovered smaller rocks could be stacked to make walls, and that they could also lean straight, beam-like stones upon one another to create the triangular “false arch.” The false arch provided enough space for windows, doors ways and tunnels. Around the Mesopotamian era, man realized that small stones could also be stacked into the shape of an arch to span a distance. This was significant for ancient people as small stones are easier to move and place. A visualization of the progression of the stone arch is shown in Figure 2:
Figure 2 Progression of the false vault (arch) (Proske & van Gelder, 2009)
Some of the oldest known stone arches are found in the burial tombs of ancient Ur in the Middle East. The structures are called “vaults” and span 3 feet. It is estimated they were constructed somewhere around the year 4,000 B.C. making them approximately 6,000 years old. Other civilizations, like the Sumerians and Ancient
Egyptians, also used vaults. (Proske & van Gelder, 2009)
12 The first civilization to use stone arches bridges was the Etruscan civilization, located in what is now Italy. Though the Greeks also used wedged-shaped stones, the Etruscans were responsible for the development of utilizing wedged-shaped stones for the purpose of bridge-building (Proske & van Gelder, 2009). The Roman civilization, also founded in Italy, continued to develop the art and went on to build stone arch bridges for at least 400 years (O'Connor, 1993).
Roman Stone Arch Bridges The Romans were masterful bridge builders. Many of their works still stand today. The longevity of Roman construction is due to two extremely important advancements. First, they found that pentagonal shapes could be used to better lock in blocks of the arch. The Roman’s level of craftsmanship in shaping blocks allowed for a tight fit between units. Second, they invented mortar. Mortar is very useful in both arch and wall construction. It can be used as the connector of irregularly shaped rocks and transfer load between them efficiently. Also, it gave more resistance to the sliding of the spandrel walls (Proske & van Gelder, 2009). Approximately 400 bridges of Roman descent exist in either complete or partial condition. They are predominately found in Italy but are also scattered across the European continent and areas around the Mediterranean (Barow & Ragette, 2013).
A significant proportion of these structures have been cared for over the years and are still in great condition. It is also of interest to point out that almost all of their bridges utilized semi-circular arches.
13
Figure 3 Roman semi-circular stone arch bridge in Spain (Stellez, n.d.)
Often, these structures are still in service as pedestrian bridges. However, some have been integrated into the modern transportation systems of various nations. Table 1 is a non-exhaustive list of Roman bridges used for vehicular traffic today. They have been identified in two ways, in books by O’Connor or Borrow who stated that they carried modern vehicular traffic, and by locating pictures that showed vehicles on them. The fact that there are multiple 2000-year-old structures that are still at work and resisting modern loads is remarkable. An even greater number of bridges would still be in use, but as O’Connor stated, many Roman bridges were destroyed in various wars over the last two millenniums. However, evidence of their work still exists today as Roman foundations have often been reused to build new structures upon.
14
List of Roman bridges used for modern traffic (O'Connor, 1993), (Barow & Ragette, 2013) Notes: ~ = approximately, LxWxH= Span Length by Arch Barrel Width by Arch Height
Dimensions Year of Name Location Spans Material (LxWxH) Completion 135 m x 10.95 m x Aelius Pons Italy 3 Travertino 136 BC 15 m Tuff, 68.8 m x 8.9 m x Cestius Pons Italy 3 Travertino, 46 BC 15 m Gambino Ponte di Tre 31.6m x 12.5 m x Large Tuff Italy 5 ~200 AD Ponte 5m Blocks Ponte di Porta 62 m x 6.32 m x Italy 1 Travertine ~100 BC Cappucina 22.2 m 241 m x 5.45 m x Pont Vieux France 10 Limestone ~1200 AD Variable 38 m x 7.45 m x Brodalo Bridge Spain 4 - - 5.5 m 71.9 m x – x 15.8 Ponte di Nona Italy 9 Gabine ~100 BC m Ponte d’Augusto Italy 62.6 m x 8.6 m x – 5 - 20 AD at Rimini 22.2 m x 26 m x 6 Ponte Romano Italy 1 Travertine ~25 BC m Ponte Pusterla Italy - 3 - ~100 AD 85 m x 5.5 m x 3.4 Pont Julien France 3 Limestone ~200 AD m Puente Romano Spain 274 m x – x – 16 - ~0 AD de Cordoba Puente Romano 721 m x ~5m x Spain 57 Granite ~25 BC de Merida ~8m Puente de 125 m x 7.9 m x Spain 4 Granite - Albarregas 6.7 m Villa Formosa Portugal ~85 m x 6.7 m x – 6 - - Bridge over the 75 m x 7.1 m x 23 Portugal 3 Granite ~100 AD Bibey m Roman Bridge at 116.6 m x 6.9 m x Portugal 12 Granite ~100 AD Chaves 8.9 m
15 Ancient Chinese Stone Arch Bridges The Romans were not the only prolific ancient stone arch bridge builders. The Ancient Chinese possessed the knowledge and capability to build high-quality stone arch bridges as well. They made a substantial contribution to their design and architecture through the discovery of segmented arches. The segmented arch was an extremely important advancement in masonry arch design because, in the most frequent site conditions, they significantly decrease the amount of materials and labor required to construct the bridge. This optimization eliminates the need for large ramps which would otherwise be required for a deep, semi-circular arch. Information on this design would eventually travel along the silk trail and make its way to the western world.
Figure 4 Zhaozhou Bridge: 1,400 year-old segmented stone arch bridge with open spandrel walls that reduce lateral flood loads. (Morgan, 2007)
16 Figure 4 shows the world-famous 1,400 year-old, 37 m spanned, limestone Zhaozhou Bridge (Morgan, 2007). This is one of the first masonry bridges to feature open spandrels, the second most important contribution of the Ancient Chinese to masonry bridges. Open-spandrel walls optimize bridge performance in two ways: by decreasing the dead weight of the structure, and by decreasing horizontal loading from floodwaters. With less dead load, abutments can be smaller because they have to resist less force both vertically and laterally. Flood loads are decreased by allowing water to flow through the bridge, effectively allowing the bridge to take on larger floods with a higher probability of survival. The Zhaozhou Bridge has proven to be durable under extreme events. It has survived at least eight wars, ten major floods, and numerous earthquakes, including a 7.6 magnitude earthquake recorded in 1966. (Zhou, Zhang,
An, Zhang, & Li, 2016)
Revival of the Stone Arch via the Industrial Revolution In the 19th century, stone arches again played a significant role in advancing civilization. During the Industrial Revolution, improved scientific theories pushed technology farther into the future and industry boomed. New machines enabled mass production of goods, and trade among industrializing nations flourished. As a result, the demand for quick transportation of materials, products, and people dramatically increased. Trains became a critical solution for meeting this demand and massive networks of railway systems were constructed around the world. However, there was one major issue for rail owners and the engineers who designed the systems. At the time, trains were the heaviest live load known to structural engineers. Many wooden bridges were initially built but proved insufficient for sustaining the load cycle demand over extended periods of time. In the early
17 1800s, study and experimentation with concrete & iron had merely begun and was not yet a viable answer. Engineers needed a solution and stone arch bridges again found their time to shine. They were the only known structure type capable of supporting such heavy loads while being expected to last. Hundreds of thousands of stone arch bridges were constructed by railroad organizations around the world. Most have proven to be invaluable investments as many are still in use today. The next few sections focus on the stone arches in the United States and European railway systems and detail the reasons associated with their longevity.
Masonry Arch Bridges in the European Railway System Masonry arch bridges, which include brick as a material, comprise a significant proportion of many European railway systems. Technological advancements in rail systems and increased demand for larger trains capable of hauling more weight have required structural health and strength assessments for all bridges in their systems. As a result, stone arch bridges have become a subject of study and investigation by numerous researchers and rail organizations. One organization, the International Union of Railways (UIC), studies and publishes reports on various subjects concerning the rail systems of their members.
They launched a research project in the early 2000s to aid the assessment, inspection, and maintenance of masonry arch bridges for their 14 members. Combined, these rail systems were found to possess over 200,000 masonry arch bridges and culverts. This number equates to about 60% of their total bridge stock (Orban, 2007). These numbers were published by the UIC in a report from 2004 by Z. Orban. A summary of the results is found in Table 2.
18
Number of Stone Arch Bridges in Various Railways as Reported by the UIC (Orban, 2004) * Estimated Number
Number of Number Ratio of stone Ratio of stone Railway stone arch of stone arch bridges on arch bridges on Organization bridges and arch all bridges and all bridges culverts bridges culverts without culverts French 78000* 18060 76.8 43.5 (SNCF) Italian (RFI) 56888 N/A 94.5 N/A British (NR) 17867 16500 46.9 N/A Portuguese 11746 874 89.8 39.6 (REFER) German 35000* 8653 38.9 27.5 (DB) Spanish N/A 3144 N/A 49.3 (RENFE) Czech (CD) 4858 2391 18.9 35.8
The report also included other statistics of interest related to size, age, and condition of these bridges (Orban, 2004):
• Short spanned bridges and culverts comprise a majority of the structures. Approximately 60% of the bridge spans are under 6.5 feet and about 80% are under 16.5 feet. Only 8.5% of arches exceed a 33-foot span (8.5% equates to around 17,000 bridges).
• Approximately 85% of the masonry arch bridges are single-span structures.
• Approximately 70% of the bridges are between 100 and 150 years old. About 12% (24,000 bridges) are more than 150 years old.
19 • The shapes of masonry arches were not reported by many of the railway administrations. The only conclusion that could be made was that semi-circular deep arches are the most common type.
• “The vast majority of masonry arch bridges are in good and medium condition (approximately 85%) but there is a significant proportion in a poor or very poor condition.” (Orban, 2004)
• “The organizations included in their report were the MAV /Hungary, DB /Germany/, SNCF /France/, NR /UK/, ÖBB /Austria/, SBB /Switzerland/, JBV /Norway/, CD /Czech Republic/, REFER /Portugal/, RENFE /Spain/, RFI /Italy/, BS /Denmark/, JapanRail-RTRI /Japan/, PKP /Poland/.” (Orban, 2004) Another study by WK Weber in 1999, cited by Proske & van Gelder, also estimated the number of masonry railway bridges within various rail organizations throughout Europe. The results, which do not include culverts, are reported in Table 3. Note that there are discrepancies between the two data tables for overlapping rail organizations. This may be due to differences in their processes for labeling a bridge as a culvert, or the exact information available to each of the researchers at their respective points in time. So, what exactly does all this information mean? Generally, it confirms that the masonry arch bridge has performed very well for the European rail industry. Orban reported that 85% of stone arch bridges studied were in either good or very good condition. At the same time, 70% of these bridges were between 100-150 years old and 12% were greater than 150 years old. It seems the durability and adaptability of stone arch bridges are well proven by this research.
20
Estimation of stone arch bridges (no culverts) in the European Railway Systems (Proske & van Gelder, 2009)
Overall Number Number Oldest Railway of of Ratio in Arch Railway Organization Distance Railway Masonry Percent Bridge in Km Bridges Bridges From Belgium 3432 3400 600 18 1845 (SNCB/NMBS) British (BR) 16528 26240 13000 50 1825 Bulgarian (BDŽ) 4299 982 62 6 1867 Danish (DSB) 2344 1500 135 9 1853 German (DB) 4087 32017 9146 29 1837 Finnish (VR) 5874 1905 60 3 1861 French (SNCF) 32731 28259 13167 47 1840 Greek (CH, OSE) 2484 2100 710 34 1883 Italian (FS) 16112 59473 37400 63 1850 Irish (CIE) 1944 2752 1484 54 1839 Yugoslavian (JŽ) 2770 619 22 1874 Luxemburg (CFL) 275 282 149 53 1859 Dutch (NL) 2753 2790 50 2 1842 Norwegian (NSB) 4027 2700 311 12 1888 Austrain (ÖBB) 5605 5048 1200 24 1838 Polish (PKP) 25254 8500 1020 12 1842 Portuguese (CP) 3054 1928 883 46 1875 Rhaetian (RhB) 375 489 931 1888 Rumanian (CFR) 11430 4067 240 6 1859 Swedish (SJ) 9846 3500 100 3 1857 Swiss (SBB) 2985 5267 914 17 1847 Spanish (RENFE) 13041 6371 3205 50 1860 Czechoslovakia (ČSD) 13100 9411 3213 34 1845 Hungarian (MAV) 7605 2375 278 12 1845 Total: 189185 214126 88877 42% 1825
21 The American Rail System: Statistically Hidden but Physically There In the rail systems of the United States, masonry bridges have played a similar role. In the early 19th century, American railway engineers were faced with the same issues of bridge durability which resulted from the immense load of freight trains. Stone arches were again found to be the best solution, and many were constructed by various private rail organizations around the country. In an overview of stone arch bridges in the United States, author Thomas Boothby stated, “America’s most active period of masonry arch bridge construction coincided with an expansive period of railroad development.” (Boothby & Roise, 1995). The boom in the rail industries meant they had enough capital to construct many stone arch bridges. Also, Boothby stated that most of these structures have been
“scrupulously” maintained. This seems likely given the high percentage of European masonry arch bridges found to be in good condition in the previous section. The exact percentage of masonry bridges in the American railway bridge stock is not currently known. Specific information on the quantity and condition of rail bridges are unknown because “as private property, they are not subject to governmental oversight. As a result, information about railroad bridges is much more difficult to obtain” (Boothby & Roise, 1995). In the absence of the overall assessment of stone arch bridges in the American Rail system, information regarding specific bridges that are classified as historical landmarks is the only thing that can be located. The American Society of Civil Engineers (ASCE) preserves the stories of civil engineering achievements throughout history on their website. To establish more context on stone arch bridges in the United States, a few examples of landmark masonry arch railroad bridges are provided in the next subsections.
22 The Carrolton Viaduct The Carrollton Viaduct was the first masonry railroad bridge built in the United States (see Figure 5). The bridge, whose construction was completed in 1829, is located in Baltimore, Maryland. “This structure proved the feasibility of using a viaduct to transport railway vehicles across a wide and deep valley,” (ASCE, n.d.). Three engineers from the U.S. Army Corps of Engineers traveled to England to observe the construction of masonry bridges for British Railways. They brought home the techniques employed to build this arch which spans 80 feet in length and 51 feet in height. The bridge is still in use today by CSX Transportation.
Figure 5 The Carrolton Viaduct over Gwynn’s Falls (ASCE, n.d.)
The Canton Viaduct The Canton Viaduct is another notable stone arch bridge that has proven to be durable and capable for use in modern times (see Figure 5). Built-in 1834, this granite arch bridge which utilizes 42 deck arches is 70 feet tall, 22 feet wide, and 615 feet long. It was originally constructed with a single track and used to provide rail services between Boston and New York. The live loading of the bridge increased when a
23 second track was added in 1860. In 1990, the bridge was rehabilitated to be used in the modern high-speed rail system (150 mph+) connecting Boston and Washington, D.C. (ASCE, n.d.). This structure is a prominent example of the strength, endurance, and adaptability of stone arch bridges.
Figure 6 Canton Viaduct (Boucher, 1968)
The Rockville Stone Arch Bridge
Another notable masonry structure within the American Railway bridge stock is the Rockville Stone Arch Bridge (see Figure 7). Completed in 1902, the bridge is 3820 feet long (48 spans of 70 feet) and 52 feet wide. It carries four sets of railroad tracks and is the longest and widest stone-arch railroad bridge in the world (ASCE, n.d.). It was built to be a long-lasting replacement for two bridges, one wooden, and one iron, which had previously been used to cross the Susquehanna River. The
Rockville Stone Arch Bridge has been tested by record-setting floods and by
24 substantial increases in load weights, yet it is still used today by both freight trains and Amtrak. (ASCE, n.d.)
Figure 7 The Rockville Stone Arch Bridge carrying modern train Rockville, Pennsylvania (American-Rails.com, 2007)
Impact of Railway Masonry Arch Bridges When assessing the economic value of stone arch railway bridges, gauging their impact is a difficult task. The UIC states on their website that stone arch bridges have an “inestimable asset value” (UIC, n.d.). If one were to calculate an actual value, several factors require consideration. First, over time, how many bridges would have been built using alternative materials instead of a single masonry arch bridge? The answer would probably be 2 to 3 if you simply look at the average service life for modern bridges, which is 50-80 years. The majority of masonry arch bridges are likely to reach 200 years (this value is estimated in Chapter 4).
Second, how long would train traffic to be detoured while construction took place for these bridges? Time is money, and the faster a train reaches its destination,
25 the quicker everyone involved with the shipment is paid. Realistically, any bridge could take up to several months to construct. If the rail organizations wish to construct the bridge as quickly as possible, the cost of the bridge will rise significantly because contractors will charge overtime rates for laborers. Needless to say, shutting-down rail lines could become very costly.
Third, what are the impacts of inflation and the discounting of the value of the dollar over the service of life of the bridge? The average economist will tell you that your money is worth more today than it is tomorrow because the cost for labor and goods are constantly rising. The investment made in masonry bridges was one that returned on its initial cost many years ago and has been an asset for earning profits. (The economic value for a single stone arch bridge will be investigated in Chapter 4.)
When and Why Did We Stop Using the Stone Arch? Although history proves that an adequately designed and properly constructed stone arch bridge has the potential to last for hundreds of years, new stone arch bridges have rarely been built over the past century. Why? There are several reasons, but it is primarily due to the upfront cost and the inefficient use of time involved with constructing stone arch bridges using traditional methods.
When concrete and iron first emerged in the 19th century, few structures were built using these relatively new materials. As time progressed, so did both materials. It was found early on that these materials had significant potential. By the early 1900s, ductile steel replaced brittle iron and the benefits of reinforcing concrete with steel were discovered. Over the years, vast amounts of resources have been expended on research to improve their physical properties and the accuracy of our ability to predict their behavior. As these materials established themselves, masonry took a backseat.
26 There are several reasons why concrete and steel were preferred over masonry in the 20th century. The next subsections detail each reason that made concrete and steel the preference over masonry in bridge construction.
The Traditional Method of Masonry Construction In the past, building a stone arch bridge represented a daunting task. The foremost reason for masonry bridges being left behind is the amount of effort required to construct a stone bridge. It takes significantly more time and materials to construct a masonry bridge than a comparable concrete or steel bridge. A stone arch bridge is comprised of either sculpted stone blocks or irregularly shaped stones fitted with mortar. These blocks, or “units,” are used to build walls and arches. Shaping the units took a lot of time and effort to properly do so. The first step in masonry bridge construction is to build the stone foundation which is often made of large stone blocks and wooden piles. Next, heavy stone block units, usually dressed with mortar, were stacked one by one with the aid of pulley systems to build abutment walls and infilled with soil. Building stone abutments wasn’t all too much of an issue in terms of time and effort. The real problem was building the bridge’s superstructure, which is extremely intensive. Wooden forms called “centering” are needed to stack blocks on and create the barrel. These forms are often intricate and require this wooden arch to be precisely built, perfectly symmetrical and to the engineer’s specifications. Highly skilled carpenters are needed to construct such formwork. Also, multiple forms are often needed, as seen in Figure 8. Because of this, the formwork significantly affected the cost of the project, adding time, labor and materials.
27
Figure 8 Construction of a stone arch barrel using traditional methods (Minnesota Department of Transportation , n.d.)
The process of building the superstructure is also very slow. To build the arch barrel, heavy stone blocks that were carefully sculpted into specific shapes, are dressed with mortar and stacked one by one radially along the form. When both sides of the centering covered with blocks and the keystone is put in place at the top of the arch, effectively locking the units in position by means of their own weight. Placing the keystone completes the member and allows the arch to stand by itself. The centering is then taken down completely or moved to another location to be used to build another barrel. In the case of multi-spanned arch bridges, the spans would have to be constructed in unison to ensure the stability of the piers from lateral loading. Lateral loads from the dead weight of the arch span are usually balanced by the adjacent span or by an abutment.
28 After completing the barrel, the spandrel walls are constructed by dressing stone blocks and stacking them. Again, this is another cumbersome and laborious task as stone is heavy and needs to be carefully placed to ensure the balance and stability of the wall and the barrel. The combination of the barrel, spandrel walls and abutments creates a shell that can be filled with sand, rubble, a combination of the two, or even concrete. Doing so completes the superstructure. The spandrel walls often serve as the parapets. The deck is then constructed on the fill, and the bridge is complete. With the limited technology available for construction and preparing the blocks themselves, building a stone arch was a laborious task.
Engineering and Design Before the 20th Century Before the modern age of design and construction, there were not as many tools for analysis. For engineers especially, there was a lack of theoretical knowledge in certain areas that would not be discovered until after masonry arches were phased out. Designing a stone arch was dictated by empirical formulas of span to height ratios that were found to work by trial and error over two millennia. As a result, engineers could not feel absolutely certain about their work until they saw the bridge perform with their own eyes. To ensure safety, and with no real analytical methods available, designers tended to keep designs the same from bridge to bridge. Few would take risks in order to advance the practice. Given the standard of today, it is easy to comprehend why yesterday’s engineers desired to move away from such feelings of ambiguity and vulnerability.
29 Constructability of Steel and Concrete From the time they were established, concrete and steel bridges have been considerably faster to construct than masonry bridges. Long steel beams are put into place using cranes, and, as such, they are faster to erect and connect than dressing and stacking blocks. Concrete, even though its construction process also requires formwork, was poured into place and did not require highly skilled craftsmen to sculpt blocks. The speed of construction became a significant economic factor in the capital cost of bridge construction during the 20th century. The cost of labor has steadily risen over the past 120 years. Between wages and benefits, the average laborer’s per capita wage was $15/hour more in 1999 than in 1909 (Fisk, 2003). Wages rose for several reasons, including the formation of labor unions and “technology, capital, demography, immigration, education, and government intervention,” (Fisk, 2003). With these factors, stone became the most expensive option of the three. As a result, masonry was phased out as a viable building material for both railway and highway bridges. Stone arches were seldom built in the latter half of the 20th century. (Proske & van Gelder, 2009)
Masonry Bridges Still a Solution in Some Nations Though masonry arches have taken a backseat in almost every industrialized nation, they are still being constructed in some areas around the world. These locations are often within underdeveloped nations and places with low labor costs. For example, a stone arch bridge design manual was created for local governments in Uganda by BTC, a Belgian development company. The main goal was to “pilot stone arch culverts and bridges in rural areas, where low labor costs and high
30 cost of industrial building materials favor this technology.” (BTC, 2019) Essentially, the manual to tabulates stone arch bridge designs and gives instruction on their construction to permit low skill or inexperienced laborers to build reliable bridges. This will ultimately help the Ugandan people establish a safe and stable network of road infrastructure.
Furthermore, the world’s most impressive example of a stone arch bridge is the product of the modern area. The Danhe Bridge in Jincheng, China was constructed in 2001 and took four and a half years to complete (see Figure 8). The total length of the bridge is approximately 1360 feet, which is comprised of eight spans (seven spans of 100 feet) and one span of 480 feet. The combined width of the piers composes the remaining length. The height of the main span is 106 feet. With a width of 80 feet, the bridge was designed to carry a modern four-lane expressway. While the arch and spandrels are constructed of stone, the fill and deck are concrete. China is one of the only nations still producing stone arch bridges because of their low labor costs. (HighestBridges.com, 2017)
Figure 9 The Danhe Bridge (HighestBridges.com, 2017)
31 Chapter Conclusion This chapter touched upon various points in time and many places around the world. As explained, stone arches were often a major factor in the development and success of many of humanity’s greatest civilizations. Some ancient bridges have survived and are still in use today, lending wonder about the dollar value of their durability. This prompts a question: why are new stone arch bridges rarely built today?
The answer: the intense amount of work involved with constructing a stone arch bridge using traditional methods and the high labor cost of the modern era. However, it seems that where the costs of bridge construction are low, new stone arches may be found. Looking forward, this paper will explore how the issue of construction can be addressed, along with the life-cycle economic benefit provided by their proven service-life capacity. But before this, it is important to establish what physically causes the stone arch to perform so well. Enter Chapter 3, Durability of the Stone and Arch Combination.
32 Chapter 3
THE DURABILITY OF THE STONE AND ARCH COMBINATION
Through human eyes, stone arch bridges have probably been looked at as
“permanent” by most of the people who have ever seen them. There are many examples of ancient bridges in use that were built by the Romans, Chinese, and other ancient civilizations. Their continued existence is proof that the stone arch can stand for thousands of years given the proper design and construction. The key to the combination’s durability is that stone is strong in compression and durable even when exposed to the harsh outdoor environment. At the same time, the types of stone used to build structural systems are some of the most chemically stable materials that are naturally occurring. When combining these material traits with the geometry of the arch, a perfect match is formed. Stone in the shape of the arch keeps the member in compression and minimizes tensile forces. This produces a high-quality structural component capable of spanning short to medium distances. This chapter explains why the stone arch has such tremendous potential when it comes to service life. The factors that will be investigated in this section will be the material properties of stone, its deterioration mechanisms, which types are suitable for bridge construction, and the structural mechanics of the two-hinged arch. The failure mechanisms of a masonry bridge are also discussed. For good measure, the factors affecting the deterioration of steel and concrete are detailed to allow for comparison between the three materials.
33 Earth, Rocks and Geological Processes To learn about the durability of stone, we must first travel back to the birth of the solar system. Essentially, Earth is a sphere predominately made of stone which is molten in the mantle and lithified at the crust. An unimaginable amount of heat energy was needed to produce this material and all of its variety. For the past 4.5 billion years, the Earth has essentially been a continuously running stone factory. More than five thousand individual types of stone have been identified to date, and collectively, they are the most abundant resource that this planet has to offer. Each of these stone types can be grouped into one of three categories: igneous, sedimentary, or metamorphic. The three categories are defined by the three unique processes of stone formation. In short, igneous rocks are produced by the crystallization of magma or lavas, sedimentary rocks are formed by the lithification of sediments, and metamorphic rocks developed from natural deformations of molecular arrangements forced by immense amounts of heat and pressure over a geologic scale of time. Many of these rock types may appear to be very similar, but in fact, are unique due to slight differences in chemical formula or atomic structure. Hugues states, “differentiation within these rock groups is sometimes due only to minor variations in the chemical composition or the pressure or temperature conditions.” (Hugues, 2005)
In this section, each of the three rock categories is detailed to provide knowledge of the forces behind the production of stone. Understanding where stone comes from answers why it is a high-quality material. The amount of time and energy expended on the production of stone is unmatched by any man-made material.
34 Igneous Rocks Believe it or not, the overarching story (pun intended) of our planet and the life it beholds is highly dependent upon igneous rocks. Igneous rocks form the crust of the Earth and the continental land upon which we live. For billions of years, primordial heat has been escaping the planet and bleeding into space. It was created by the friction of colliding planetesimals and planetoids that formed Earth.
Figure 10 Visualization of the creation of Earth through the accretion theory (Bliss)
It is believed that the Earth was formed through “accretion.” This theory states that the accumulation matter revolving around the sun created the solar system. Essentially, the accumulation of dust produced planetesimals (imagine asteroids) that then collided with each other to create planetoids (See Figure 10). Eventually, planetoids traveling in parallel rings around the sun at different speeds would collide. Collisions occurred until the collective group of massive rocks, for which we now know as the planets of our solar system, ate up all the matter in their respective
35 gravitational zones. The massive forces of these collisions created an unimaginable amount of heat. Much of this heat still exists in the mantle today, but over time, it has escaped into space causing the solidification of magmas and lavas, ultimately thickening the crust. Simultaneously, the laws of physics have been at work sinking the heavier elements, to the core like iron, nickel and magnesium. In turn, the uppermost crust of the planet has become rich with lighter elements like silica, hydrogen, and oxygen. The natural differentiation between lighter and heavier elements led to the creation of two major types of magma with unique chemical compositions. Basically, there are two types of crust with two different densities; basaltic and rhyolitic. Basaltic magma is mainly composed of silica but is very high in its concentration of iron and generally contains traces of magnesium. Cooled basaltic flows have created the solid tectonic plates that lie under the ocean. Basaltic lavas are predominately found at the seafloor because they flow at divergent fault lines, which are places where lava seeps out directly from the mantle. Basaltic flows are not commonly seen above-ground but can be found in special places like Iceland, where an above ground divergent fault is located, or in shield volcanoes, like those of
Hawaii. The lighter rhyolitic magmas are also composed predominately of silica and iron, but they have much higher concentrations of dissolved gases, like water and carbon dioxide. The presence of these gases makes rhyolitic magma volatile and is the reason why some volcanos explode. Cooled rhyolitic flows created the continental land upon which we live. Because rhyolitic magma has high silica and low iron concentrations and contains volatile gases, its density is lower than that of basaltic
36 magma. This enabled rhyolitic magma to build upon the heavier (and stronger) basaltic plates and create the “continental shelf.” Igneous rocks are subdivided into three categories: plutonic, hypabyssal, and extrusive. Plutonic rocks are formed when magma rising from the mantle to Earth’s surface slowly solidifies deep within the crust. Millions of years are needed to fully crystallize the minerals and become solid plutonic rocks. Hypabyssal rocks are formed when relatively smaller amounts of magma quickly solidify within volcanic vents or chambers. Extrusive rocks are formed through volcanic eruptions at the Earth’s surface. Extrusive rocks are formed when lava2 solidifies. Extrusive rocks can be very dense, or very weak and porous depending on its chemical composition and the manner in which it cooled.
Sedimentary Stones Various types of sedimentary stones are useful in construction. When researching the multitude of examples of masonry bridges, finding arches constructed of limestone, sandstone, and other sedimentary stones is commonplace. Though durable, the strongest sedimentary stones are often considerably weaker than most igneous rocks as completely different processes form this rock type.
Sedimentary stones are not directly the result of cooled lavas. Instead, they are formed by the sediments of existing igneous, metamorphic and other sedimentary rocks. Any substance exposed to nature’s elements will be subjected to wear and tear by both mechanical and chemical means. Such mechanisms include combinations of freeze-thaw, erosion, and/or chemical reactions which are further discussed later in
2 Magma becomes lava when exposed to the surface.
37 this chapter. With tremendous amounts of time, these sediments will eventually accumulate and be covered by layers of other sediments. Eventually, they will lithify by means of compression from the weight of the layers above and/or by cementation by naturally occurring binders. These binders are either calcareous, argillaceous, dolomitic, siliceous, limonitic, or ferruginous. (Hugues, 2005)
The processes which form the sediments are used to classify sedimentary rocks. Clastic sedimentary rocks made from sediments that are, “deposits of rock fragments and particles that have been formed, transported and consolidated by mechanical means only,” (Hugues, 2005). Clastic rocks are further categorized into three groups, conglomerates, sandstones, and siltstones, which are defined by their grain size, which are >2 mm, 2 to 0.02 mm, and < 0.02 mm, respectively. Chemical sediments are the other classification. These sediments form as a result of chemical reactions and Hugues states that chemical sediments come from “molecules that have separated out from solutions” (Hugues, 2005). Some sedimentary rocks are basically natural concrete. Concrete is essentially a mixture of rocks having that vary in size and a binder. The same can be said for many sedimentary rocks. The difference is that nature has no prejudice when it comes to the picking the constituent aggregates of its concrete. Therefore, there is a large variety of sedimentary rocks and some are more useful than others. The images in
Figure 11 give a comparison of two very different sedimentary rocks.
38
Figure 11 Left- Image of a Conglomerate Rock (Mark, 2015) Right- Sandstone (Khattak, 2018)
Because sedimentary rocks do not have a coherent structure, their properties, including strength, will vary. A sandstone, like that shown in Figure 11 on the right, is more appropriate to use for load-bearing structures, rather than the conglomerate rock shown in the left of Figure 11. The molecular structure of sandstone is like mortar; very fine sands that have been compressed and cemented together. Rocks with coherent microstructure are generally strong and have constant properties throughout their cross-section. This makes their reaction to load more predictable and therefore safer.
Metamorphic Rocks Metamorphic rocks are the final rock classification and are formed through multiple complex processes. Hugues explains, “metamorphic rocks are formed by the transformation of igneous, sedimentary or older metamorphic rocks as a result of changing physical and chemical condition over periods lasting millions of years,”
(Hugues, 2005). Such transformations to microstructure are caused by varying
39 temperatures, pressures or tectonic movements, and usually a combination of these forces. Generally, the conditions for these forces are found deep within the Earth’s crust. (Hugues, 2005) Metamorphic rocks are further classified by the original rock materials that transformed.
Strength and Durability
The relationship between strength and durability of stone are highly correlated. That is because the density of the rock affects both parameters. Stones that are dense will be both strong in compression as well as resistant to deterioration mechanisms (which are described more detail in the following section).
Deterioration Mechanisms of Stone, Concrete and Steel
As seen in the previous chapter, various examples of ancient masonry bridges made from igneous, sedimentary, and metamorphic stones have been in use for centuries, and some for thousands of years. Of course, these bridges have been cared for, but the material properties of stone are certainly the major factor for their incredible service life. This section of the thesis focus on how exactly stone deteriorates and makes a comparison to the deterioration mechanisms of steel and concrete.
Stable Stone Stone, the material which this planet is predominately composed of, was made to last. As stated earlier, there is a large variety of stone with differing chemical compositions and properties and each will decay at differing rates and circumstances. Generally, moisture on the surface of a given rock initiates deterioration. The main deterioration mechanisms of stone and its variety are listed next.
40 Salt Crystallization Salt crystallization is often regarded as the primary cause of stone deterioration. Salt crystallization refers to the expansion of salts deposited into the pores of a rock. Expansion of salt crystals will increase the internal stress experienced by the rock and can cause cracking. Additionally, thermal expansion and contraction of crystalized salts also increases stress (Clifton, 1980). The presence of salts within the pores of the stone will also attract moisture from humid air and will accelerate deterioration. (National Materials Advisory Board, 1982) Generally, this type of deterioration occurs when common soluble salts, like sodium chloride or sodium sulfate, are absorbed by water and later deposited into the pores of a rock’s surface. The water eventually evaporates, and the residual salts are left to crystallize. Upon crystallization, the salts expand, and this cycle will repeat over time. The cycles of leaching and drying “cause the outer layers of the materials to disintegrate slowly” (Heckroodt, 2002). The surface of the stone will spall, and more pores will be exposed. The rate at which the mechanism will deteriorate a stone’s condition is dependent upon its pore size distribution and pore interconnectivity. The rate of deterioration decreases as the average pore size decreases. These properties differ within every rock classification and type. Common sources of soluble salts are mortar, seawater, de-icing agents used for roadways, brackish groundwater, and from acid rain (Heckroodt, 2002).
Aqueous Dissolution Stone types classified as “carbonates,” like limestone and dolostone, can be dissolved by rain or groundwater. These two sources of water can be acidic if they
41 contain carbon dioxide, sulfur dioxide or nitrogen oxides, which lowers pH levels. The rainwaters of urban areas in both the US and Europe are sufficient in acidic level to accelerate the weathering of carbonate stone structures (Clifton, 1980). Rainwater is apparently not much of a problem where pollutants are low in concentration. In the natural world, beautiful caves, like the one seen in Figure 12, are produced by this kind of deterioration.
Figure 12 Limestone cavern produced by aqueous dissolution (ScienceStruck, 2018)
Freeze-Thaw Freeze-thaw aids the breakdown of porous masonry materials over long periods of time. When water is deposited into the pores of a rock and crystalizes under freezing temperatures, the volume of the water will increase by 9%. This adds stress
42 on the pores of the rock. Cycles of freeze-thaw lead to flaking on the surface layer of a given rock. Eventually, the material may crumble. (Heckroodt, 2002) The rate of damage ultimately depends upon pore size distribution within the rock, along with the interconnectivity of the system. Water in large pores will freeze when reaching 32ºF, but this is not the case for water in pores smaller than 0.5 µm. In an interconnected system of pores, the smaller pores will feed the larger ones and add to the pressure within the large pores. When the tensile strength of the material is reached, spalling occurs. (Heckroodt, 2002) The risk of frost damage to a particular rock can be estimated by determining the value of its saturation coefficient (Heckroodt, 2002). The saturation coefficient is the ratio of a material’s natural absorption3 to its total absorption4. High saturation coefficients can mean that the material is at risk of frost damage.
Thermal Expansion When it comes to stone structures, thermal expansion will generally not play a major role in its deterioration. Heckroodt states that “thermal gradients will generate stresses in materials. However, diurnal temperature fluctuations… are rarely sufficient to result in spalling,” (Heckroodt, 2002). Therefore, thermal expansion is the least amount of concern for stone.
3 Natural absorption is defined as the amount of water absorbed by the material specimen when immersed in cold water for 24 hours
4 Total absorption is defined as the amount of water absorbed when the specimen is completely inundated in boiling water for 5 hours.
43 Porous Concrete In today’s world, concrete is a material that is widely used and extremely useful for producing strong and stable structures. The main cause of failure in a concrete structure is due to the corrosion of reinforcing steel. There are also several other mechanisms related to concrete deterioration that are less common but can be just as critical in effect. These mechanisms are listed and detailed in the succeeding subsections.
Corrosion Damage to Reinforcing Steel Generally, concrete members are composites. Concrete is only effective in resisting compressive forces, so steel is needed to deal with any significant tensile forces. Steel in the form of rebar, wire, and/or cable is usually placed in the regions where members are expected to experience tension. Together, these two materials have proven themselves to work well and are utilized often in modern engineering and construction. However, there is a trade-off, and that is steel’s vulnerability to corrosion. When the correct environmental conditions are present, steel will corrode because of anodic and cathodic processes. In anodic dissolution, iron atoms are turned into ferrous ions. The cathodic process involves the overall amount of oxygen decreasing and causes a reaction to occur between the steel and water to form hydroxyl ions. Ultimately, this causes the reinforcing steel to rust. (Stuart, 2013) Rusting increases the rebar’s physical size and this corrosion product can reach up to ten times its original volume (Heckroodt, 2002). Also, the strength of the rebar will be weakened as the expansion causes internal tensile forces to occur on the
44 microstructure of the concrete. As a result, the concrete will crack, spall, and reduce the overall cross-sectional area of the structural member. Before corrosion starts, either chlorides or carbon dioxide must reach the depth of the embedded reinforcing steel in potent concentration. Several factors can lead to the corrosion of rebar. Heckroodt tabulated such factors and their influence as shown in Table 4.
The manifestation of reinforcement corrosion (Heckroodt, 2002)
Factor Influence Geometry of the Large-diameter bars at low covers allow easy spalling element Deep cover may prevent full oxidation of corrosion Cover Depth product Moisture Conductive electrolytes encourage well-defined macro- Condition cells Age of Structure Rust stains progress to cracking and spalling Rebar Spacing Closely spaced bars encourage delamination Crack Cracks may provide low resistance paths to the Distribution reinforcement Service Stresses Corrosion may be accelerated in highly stressed zones Quality of Severity of damage depends on the concrete quality Concrete
The resistivity to and rate of corrosion depends on the amount of moisture within the concrete and the concentration of ionic elements within that moisture. The moisture content within the pores of the concrete is controlled by the permeability and interconnectivity of the pore structure. (Heckroodt, 2002)
Alkali-Aggregate Reaction
Another type of damage that concrete is susceptible to alkali-aggregate reaction. This mechanism occurs due to reactions between aggregates and cement
45 (Stuart, 2013). Alkaline pore solutions react with internal moisture and particular types of aggregate to form an expansive gel within the concrete member. With a few years worth of time, the reaction will produce an expansive gel which can cause cracking and shorten the member’s life expectancy (Heckroodt, 2002). There are several types of alkali-aggregate reactions. Alkali-silica reaction
(ASR) is the most common alkali-aggregate reaction. In this type of reaction, free silica within the aggregate reacts with water to produce the gel. The other kind of reaction, which is less common, is alkali-carbonate rock reaction. This occurs when alkaline pore solutions react with a carbonate aggregate. No gel is formed but instead, expansion is caused by the swelling of the aggregate crystals, along with any clay minerals that may have been present within the aggregate. (Heckroodt, 2002)
Chemical Attack The deterioration of concrete can be initiated by multiple naturally occurring chemicals solutions. According to Heckroodt, “all liquids with a pH below 12.5 will attack concrete, but the attack will be slow if the pH is above about 6, and increases rapidly with increasing acidic conditions,” (Heckroodt, 2002). The reaction rate of concrete to solutions depends on temperature, flow rate, solubility of the reaction products, mobility of the ions, and permeability of the concrete.
There are various types of chemical attacks. One such attack that is a common concern for large concrete structures designed for carrying flowing water occurs because of “soft water.” This solution is defined by its deficiency in dissolved calcium and magnesium ions, giving it a pH of 5. Cement will be dissolved, exposing aggregates within the concrete and eventually creating leakage paths. “Sulfate attack” when a solution contains sulfates.
46 Corrosive Steel Strong, ductile, constructible, and predictable are all qualities that steel possesses. Since arriving on the scene in the 19th century, its popularity among structural engineers has grown to become a staple in the modern world. It can deliver a solution for almost any need in structural engineering. Though mechanical performance may suggest that steel is the perfect material for any civil engineering application, it does have an Achilles heel. Steel is corrosive and is destined to deteriorate if not properly taken care of, even in dry conditions. Heckroodt states that:
The fundamental cause of corrosion is the inherent instability of metals in the metallic form. The tendency is for metals (except the noble metals) to revert to more stable forms, such as oxides or sulphides. The driving force for this reversion to more stable forms differs from metal to metal and is expressed as the electrode potential of that metal under defined conditions. (Heckroodt, 2002) Specifically, structural steel has fair resistance to corrosion, but it is still the main cause of its failure. As stated earlier in the concrete deterioration section regarding the corrosion of reinforcement, steel will corrode due to anodic and cathodic processes in the presence of moisture. Ferrous atoms chemically react with the moisture to form hydrated oxides, which can swell up to ten times of their original volume. Rust is produced and the effective cross-section of the member is reduced. (Heckroodt, 2002) The next subsections detail the various types of deterioration for any given metal.
Tarnishing Tarnishing occurs when a metal is exposed to and oxidized by a dry, corrosive gas or a liquid. The rate at which metal will tarnish depends on the characteristics of the oxidized layer. This layer will either be porous and non-adherent to the metal’s
47 surface or the exact opposite. If the oxide layer follows the first case, oxygen is given constant access to the metal’s surface via open pores and it will quickly deteriorate. If instead the layer is non-porous and adherent, it will act as a protective agent working against deterioration. This is because the rate of deterioration will be slow down as oxygen will have a hard time reaching the undeteriorated surface. Using protective coating systems that work in this manner is actually common practice in the field. (Heckroodt, 2002)
Atmospheric Corrosion or Uniform Deterioration Atmospheric corrosion, or uniform deterioration, refers to the uniform rusting of a metal’s exposed surface in the presence of moisture. This type of corrosion is common and predictable. The initial design of a structure accounts for such deterioration by utilizing protective coatings like paints or anticipating the loss of cross-sectional area (Stuart, Metal Deterioration, 2013). The rate of deterioration is generally slow but high humidity and ambient temperatures, along with the accumulation of salts and pollutants on the metal’s surface and can increase the rate of atmospheric corrosion (Heckroodt, 2002).
Galvanic Corrosion Galvanic Corrosion is the product of two dissimilar metals, or alloys, with different chemical compositions, which are in contact with one another while in the presence of moisture or a corrosive solution. The difference in conductive potential between the two metals becomes a driving force towards deterioration (Stuart, Metal Deterioration, 2013). While in contact, the more reactive metal will deteriorate quicker than it would by itself as it will protect the inert metal. This occurs because the
48 reactive metal will act as the anode, and the inert metal as the cathode (Heckroodt, 2002). Galvanic deterioration is not common but can be very destructive. However, galvanic deterioration can be effectively avoided through proper design (Stuart, Metal Deterioration, 2013).
Crevice Corrosion
Crevice corrosion involves moisture, or a solution, becoming stagnant on the surface of a metal. Crevices or locations of connections can provide the proper conditions to allow for stagnation and deterioration. Oxygen differential cell corrosion is the most common form of crevice deterioration. This occurs when moisture is entrapped within a crevice and has a lower oxygen content than what it would be if it were exposed on the surface of the metal. The lower oxygen content in the crevice forms an anode and the metal becomes the cathode. “This anodic imbalance can in turn lead to the creation of highly corrosive localized condition in the crevice, which results in deterioration of the surrounding metal,” (Stuart, Metal Deterioration, 2013). Crevice deterioration can also lead to pack rust. When crevice corrosion occurs within a metal connection, rust is formed but is not free to fall. Instead, it is caught between the two metal members that are connected and left with nowhere to go. As a result, the rust accumulates and adds internal pressures to the members and can distort their positioning.
Pitting Corrosion “Pitting is the deterioration of a metal surface, confined to a point or small area, which results in the formation of a cavity or hole in the material,” (Stuart, Metal
Deterioration, 2013). Such a cavity or grouping of cavities can potentially fail an
49 entire structure. Generally, pitting corrosion is caused by chloride ions that, under the right conditions, attack weak spots in the metal. Low dissolved oxygen concentrations, localized chemical or mechanical damage to the surface, or damage to the protective coating system can also cause pitting. This type of corrosion can be very difficult to detect, therefore making it very dangerous. (Heckroodt, 2002)
Identifying Stone Types Commonly Used for Construction When evaluating the suitability of a material for construction, engineers must look at several material properties. Strength, ductility, and durability are ones that are commonly evaluated. The following two tables (Table 5 and Table 6) are from separate sources and both designate stone types commonly used for load-bearing masonry structures. The first list is from Dirk Proske and his book, “The Safety of Historical Stone Arch Bridges,” which specifically addresses the types of stone commonly used to build historical stone arch bridges. The second list is from Theodor Hugues and his work, “Dressed Stone,” which details the types of stone used for constructing facades, walls, and other purposes. Hugues list was shortened to be more pertinent for constructing bridges. For both lists, units were converted from metric to U.S. customary units.
In general, most types of stone suitable for bridge construction have a compressive strength that is greater than that of high strength concrete and some of which are even stronger than steel. Stone is extremely durable when compared to these two modern materials, but its major disadvantage is that it is a brittle material.
50 List of stone types traditionally used for bridge construction (Proske & van Gelder, 2009)
Thermal Unit Flexural Compressive Expansion Name Weight Bending Strength (Psi) Coefficient (lb/ft^3) Strength (Psi) (in/µin/F) Granite, Syenite 180 23000 - 35000 1500 - 3000 0.44 Diorite, Gabbro 193 25500 - 43500 1500 - 3200 0.49 Siliceous Porphyry 180 26000 - 43500 2200 - 3000 - (Rhyolite) Basalt Lava 154 11500 - 22000 1200 - 1750 - Diabase 186 26000 - 36000 2200 - 3600 0.42 Quartzite, 173 22000 - 43500 1750 - 3000 - Grewacke Siliceous 173 17500 - 29000 435 - 2200 - Sandstone Dense Lime and 180 11500 - 26000 870 - 2200 0.42 Dolomite Other 180 3000 - 13000 725 - 1200 - Limestones Travertine 167 3000 - 8500 600 - 1500 0.38 Volcanic Tuff 128 - 300 - 900 - Gneiss 193 23000- 40500 1500 - 2200 -
51
List of stone types suitable for building construction (Hugues, 2005)
Tensile Unit Rock Compressive Bending Name Type Weight Classification Strength (Psi) Strength (lb/ft^3) (Psi) Granite Plutonic 162 - 175 19000 - 39000 725 - 2600 Syenite Plutonic 162 - 175 23000 - 35000 725 - 2600 Diorite Plutonic 175 - 187 25000 - 43000 870 - 3200 Gabbro Plutonic 175 - 187 25000 - 43000 870 - 3200 1450 - Igneous Rhyolite Extrusive 156 - 175 26000 - 43000 2900 2180 - Trachyte Extrusive 156 - 181 26000 - 43000 2900 1890 - Basalt Extrusive 181 - 187 35000 - 43000 3630 Conglom. Clastic 144 3000 - 23000 300 - 2180 Sandstone Clastic 125 - 169 4000 - 21000 - Limestone Chemical 162 - 181 11000 - 35000 435 - 2760 Shelly Chemical 162 - 181 12000 - 26000 870 - 2900 Sedimentary Limestone Travertine Chemical 150 - 156 3000 - 8500 300 - 1900 Tuffaceous Chemical 106 - 137 4000 - 7000 - Limestone Dolomite Chemical 162 - 181 11000 - 35000 435 - 2900 Orthogneiss 162 - 187 14500 - 29000 - Paragneiss 162 - 187 14500 - 29000 - 1890 - Quartzite 162 - 169 22000 -43000 Metamorphic - 2900 Serpentinite 162 - 175 20000 - 36000 - Marble 162 - 181 11000 - 35000 435 - 2900 Migmatite 167 22500 3000
52
Comparing Durability The overall durability of a stone type is dependent upon pore size distribution and pore interconnectivity (National Materials Advisory Board, 1982). The crystalline structure of various stone types is extremely fine and can be considered impermeable.
To explain the general durability of each classification of stone, Table 7, which was created by Heckroodt, is provided. This table generally explains the durability of rocks based on their classification. It shows that extremely durable types of stone can be found in each category. There are many types of stone that are highly resistant to mechanical and chemical wear.
General durability of each classification of stone (Heckroodt, 2002)
Rock Group Durability Classification Examples Highly durable Hard: slow surface wear Granite, Impermeable: highly resistant to environmental Igneous Dolerite, deterioration Basalt Surface Discoloration by pollution, weathering, and organic growth Very durable Low to Zero Porosity: Generally, very suitable for Metamorphic Marble exposure to severe environmental conditions Good Resistance to surface wear Variable durability Generally porous with a relatively rough surface and Sandstone, Sedimentary variable resistance to salt and frost attack Limestone Deterioration mainly caused by atmospheric pollution (through acid rain)
53 Let us now compare the properties of concrete, steel and stone. In some cases, the compressive strength of particular types of stone may be stronger than steel while also being more stable when exposed to the elements. At the same time, many stone types have much higher strength in tension than conventional, unreinforced concrete. Concrete is much easier to crack because of its lower tensile strength. With this, and the fact that concrete is much more permeable than stone, meaning its deterioration is quicker. When it comes to comparing the durability of stone and steel, stone has the advantage because it is not nearly as chemically reactive as steel. Oxidation and moisture eat away at any steel structure exposed to weather, unless maintained rigorously. If equally sized blocks of concrete, steel, and stone were placed side by side in any random location, it is reasonable to expect the stone block to last the longest.
Structural Mechanics of the Double Hinged Arch The mechanical properties of the arched geometry allow for stone to be efficiently used in bridge building. The principle strength of stone is its ability to withstand high compressive forces. When using this material to span any distance, it is most effective to do so in the form of an arch. Because of its shape, compression is the main stress exerted upon the block units which make the arch. With the chemical/mechanical stability of stone and the compressive reaction of the arch together, a perfect match is created and yield extraordinary performance. However, in practice stone arches will experience flexure and shear forces and can ultimately lead to failure. They occur because of the specifics of the geometry (semi-circular versus segmented), the form of its construction, the nature of the
54 loading, or movement of abutments. The next few subsections will focus on the arch’s reaction to load and the limit-states which produce modes of failure for the arch barrel.
Schematic and Terminology of the Arch To be able to sufficiently explain the mechanics and analysis of the arch, it is important to note some import arch terminology (see Figure 13):
Figure 13 Schematic of a single span stone arch bridge (Proske & van Gelder, 2009)
• Crown- The point at which the of the arch is maximum
• Voussoir- A trapezoidal shaped block unit used in the arch
• Extrados- The curvilinear line that is formed from the top of the arch cross-section
55 • Intrados- The curvilinear line that is formed from the bottom of the arch cross-section
• Abutment- In the case of the two hinged arch, the abutments are hinges that keep the arch from displacing in the vertical and horizontal directions
• Springline-The interface between the cross-section of the arch and the abutment
• Centerline rise- The height of the centerline of the arch
Experiment to Explain Load Path of the Arch
Instead of starting with an in-depth technical explanation of arch mechanics, let us first do an experiment. Think of a leather banded watch, or if you may have one, grab it. A watch can be used to sufficiently explain the structural mechanics of a continuous arch.
First, place the watch on a flat surface in the shape of an arch. The face of the watch will be at the crown. With no restrictions at either end, you will see that once you let go of the watch, the crown falls, and the leather bands push outwards at either side so that the arch can flatten. Now, put the watch back into the shape of an arch and hold the bands at their ends, essentially pinning them with your thumbs and middle fingers. You will see that the arch is now stable and can stand. If you push down on the watch face with your index fingers, the bands will not move outward, but instead, the watch face dips down and the bands bend. This is because the bands are rather flexible and the lateral displacement is restricted by your fingers, effectively keeping the ends in the same position. A stone arch, which is composed of individual voussoirs, or units, reacts similarly. The abutments of the bridge will effectively prohibit the units, and overall arch, from translating laterally, just as your fingers did to the watch. The prevention of
56 this movement induces stress in the arch. This stress will predominately be compression but can also include shear and flexure.
Structural Analysis of the Arch Shape
Free Body Diagram and Section
So now, with that experiment in mind, we can get technical. A double-hinged arch is a statically indeterminate structure to the first degree. It has four total reactions, two in the horizontal direction and two in the vertical directions. Internally, the pinned arch will experience an internal shear force (V), moment (M), and axial thrust (N). At any cross-section taken from the arch, the shear will be perpendicular, the axial thrust will be tangent, and the moment will be about the z-axis. In the case of a bridge, a uniform load for the dead weight and point loads which represent the live load, will be applied in the negative y-direction (see Figure 14 on the next page).
Solving for the Vertical Reactions Solving for the y-reactions is quite simple as the equations of static equilibrium are sufficient. Summing the forces in the y-direction and a taking a moment about either hinge will reveal their values as there are only two unknowns total and two unique equations available. Notice that under symmetric loading, the y-reactions shall be equal to one another.
57
Figure 14 Freebody diagram and internal reactions of an arch
Solving for the Horizontal Reactions The work for this kind of problem comes from solving for the value of the horizontal reactions. In the analysis, external horizontal forces, such as centrifugal and braking forces caused by vehicles, are neglected. With these assumptions, the arch experiences load purely in the vertical direction. First, we turn to the equation of equilibrium for the x-direction and find that the horizontal reactions at both hinges are equal:
∑ 퐹푋 = 0 = 퐴푥 − 퐵푥 → 퐴푥 = 퐵푥
From here, another equation that is compatible with the model must be found. This new equation should not introduce any new unknown variables but must include the horizontal reaction. With these constraints, Castigliano’s theorem on strain-energy displacement can provide an appropriate solution. Using the principle of the
58 conservation of energy, this theorem correlates the amount of strain with the displacement (Δ) of a structure at a specified location. This deflection/strain will be in the direction of a selected force occurring on a determinate structure. Castigliano’s theorem is written as:
푠 푁 ∗ 휕푁 푠 푀 ∗ 휕푀 푠 푘푉 ∗ 휕푉 Δ = ∫ 푑푠 + ∫ 푑푠 + ∫ 푑푠 0 퐴퐸 ∗ 휕푄 0 퐸퐼 ∗ 휕푄 0 퐺퐴 ∗ 휕푄 As stated earlier, N, M, and V are the internal thrust, moment, and shear forces. The variables A and I are the cross-sectional area and moment of inertia. E and
G are the elastic and shear moduli. K is a constant related to the cross-sectional geometry, and s is the curvilinear length of the arch. For this analysis, the deflections from the internal shear and axial forces in the arch are neglected as they are insignificant when compared to the value of the moment deflection.
To solve for the unknown forces using this equation, we need to manipulate our model to achieve the desired results because the structure must be determinant in order to use Castigliano’s theorem. To achieve this, one hinge is changed to a roller and the horizontal reaction is replaced by a redundant force, Q. For the sake of explanation, let’s place a load F on the structure:
59
Figure 15 Placing force, F, on structure and releasing the horizontal reaction at B
The force, F, will induce deflection along the x-axis at B, just like in our watch experiment. In the real model, a pin exists and limits this deflection, Δ, to 0. That means some value of force, Q, will completely prevent deflection. With Castigliano’s theorem, we can solve for Q (i.e. the horizontal reaction) by taking the derivative of the total strain energy with respect to Q. The internal moment, M, will be solved for in both the redundant system and can be done so by visualizing the arch as a straight beam.
Completing this calculation will reveal the value of the horizontal reaction. With all reactions known, approximated internal stresses may be calculated. However, for precise analysis, it is recommended that finite element methods are used. These methods can account for rotation and translation of individual blocks.
60 Limit States and Modes of Failure When it comes to stone arch bridges, assessing their performance can be pretty complicated. As mentioned earlier, a lack of theoretical knowledge and valid ways to estimate capacity was a major reason for the engineers of the 20th century to turn from the stone arch bridge and pursue more predictable materials. The geometry of the arch was rather difficult in itself and being discontinuous added a cherry the on top.
However, this has changed. Because there are so many stone arch bridges in use today, there has been an academic following and progression towards understanding their behavior. Computer programing has also made the arched geometry easier to work with and models far more accurate. In the next subsections, the limit states and modes of failure for masonry arches are detailed.
Limit States When designing any bridge, its associated limit states must be considered to ensure it performs properly. Limit states seek to define the events in which the structure can fail. An individual bridge will be unique in its modes of failure, but the ‘states’ which press a bridge to its ‘limit’ can be transcendent across bridge types. According to AASHTO, “[all] bridges shall be designed for specified limit states to achieve the objectives of constructability, safety, and serviceability, with due regard to issues of inspectability, economy, and aesthetics,” (AASHTO, 2017). These limit states include (AASHTO, 2017):
1. The Service Limit State - restrictions on stress, deformation, and crack width under regular service conditions.
2. The Fatigue and Fracture Limit State- restrictions on stress range as a result of a single design load occurring at the number of expected stress range cycles.
61 3. The Strength Limit State- ensures that strength and stability, both local and global, are provided to resist the specified statistically significant load combinations that a bridge is expected to experience in its design life.
4. The Extreme Event Limit States- ensures the structural survival of a bridge during a major earthquake or flood, or when collided with a vessel, vehicle, or ice floe, possibly under scoured conditions. They are then used to find every situation, or mode, for which a bridge may collapse. Bridge owners expect to know their bridge is one, safe, and two, that they can be confident it will perform as expected to be worth their investment. In each failure mode, an expected capacity or resistance to failure must be explored and clearly defined. The strength limit state of stone arch bridges is well understood today, but a clear and concise understanding for the capacities of the other limit states has not been achieved. As a result assessing a stone-arch bridge’s performance must include an approach which considers “the form of construction, materials, loading, etc.” (Melbourne, 2007) Together, the service, fatigue and fracture limits states must be combined to create a Permissible Limit state that defines the maximum allowable regular service load for which the bridge can carry. (Melbourne, 2007)
Loading The loading of a masonry arch is an extremely important factor in its performance. First, it is important to point out that continuous arches, like that of steel or concrete structures, have different modes of failure than that of stone arches. The disconnect in cross-section located at joints enables sliding and rotation of the units when loaded. Also, the capacity of blocked arches can increase directly because of higher dead load, which is not intuitive. This occurs for two reasons:
62 1. The funicular shape (the shape for which external forces will only stress the member in compression) for distributed loads is the semi- circular arch.
2. Increased weight on the structure increases axial compression on the blocks. This results in increased resistive friction that works against the sliding and rotation of the units. Because of this, heavier dead loads increases the stability of the arch and therefore increases the load-carrying capacity bridge. Another important thing to note is that the granular fill is essentially a continuous layer between the roadway and arch barrel. Depending on the depth and type of material, live loads will distribute over the arch. Classical geotechnical methods describing the load dispersion of soil can be used to find the distributed load experienced by the arch. Generally, the location of a point load which will most likely result in collapse is at the quarter span of the arch. (MelBourne, 2007)
Modes of Failure for Block-Arches There are several ways in which a masonry arch will fail. The first two modes of failure have been sufficiently studied and considered to be well understood. The first mode is a mechanism where the loading on the bridge causes multiple hinges to form. If a particular number of hinges form, the bridge can collapse and fail. The second mechanism is a punching shear or ‘snap-through’ failure that can occur when there is not enough axial compression in the units. These two failures represent the ultimate limit stress and are predetermined by the bridge’s geometry, loading, material, and form of construction. Some other forms of failure can occur from the sliding units, sliding of abutments, local crushing from excessive compressive forces, backfill failure, or foundation failures. “Currently it is
63 assumed that the ‘safe’ capacity for masonry is around 50% of the ultimate load carrying capacity.” (Melbourne, 2007)
Chapter Conclusion The stone and arch combination creates a bridge type that may not be topped by any alternative in terms of service life. The perseverance of this structure type is largely due to the fact that stone is the by-product of natural processes, which can take millions of years to complete. Produced in these processes are materials with very low porosity and low pore interconnectivity, making it very difficult to deteriorate by natural means. At the same time, this dense microstructure yields extremely high compressive strength. These traits together with the mechanics of the two hinged arch create a level of durability that is currently unmatched. With this fact understood, the focus of this paper now turns to how this durability equates to economic potential, which may be greater than that of the steel and reinforced concrete girder bridges commonly used today.
64 Chapter 4
ECONOMIC VIABILITY OF STONE ARCH BRIDGES
In the prior two chapters, the stone arch bridge was established as the most durable bridge-type known to mankind. It is apparent that a properly designed and constructed stone arch bridge can reach hundreds of years of serviceable life. In this chapter, the economic value of their durability is investigated to gauge whether or not stone arch bridges might actually be an economically viable alternative to concrete and steel girder bridges in the United States. Using Life Cycle Cost Analysis, academic research, and information from practitioners in the field, an economic comparison is made between comparably sized concrete, steel and stone arch bridges.
Life Cycle Cost Analysis In the current age of bridge building, budgets are tight, and funds are not likely to increase enough to solve the bridge infrastructure problems discussed in Chapter 1. As a result, various transportation authorities across the U.S. have turned to tools like Life Cycle Cost Analysis (LCCA) to deliver the most cost-effective bridges.
LCCA is a method used to evaluate the economic viability of a bridge design over its entire service life. LCCAs supply bridge owners with estimates on how much money they can expect to spend and when they will spend it throughout the life of the structure. Cost estimates are created for each proposed design so that all alternatives can be compared. The total cost is defined in an LCCA by summing all the costs of construction over the structure’s life. This includes initial cost, maintenance cost with respect to timing, and its expected service life.
65 The timing of costs is extremely important in LCCA. Future costs must be calculated with respect to the time value of money, which accounts for inflation and the opportunity cost of investing the funds elsewhere. So-called “user costs” to drivers and maintenance activities throughout a bridge’s life could also be considered but are not in this analysis.
Steps of the LCCA Performing a LCCA is a five-step process. First, all design alternatives must be produced (e.g. concrete girder bridge, steel girder bridge, and stone arch bridge). Second, the timing of regular maintenance as well as major rehabilitation for each alternative must be established. The third step is to then estimate the cost of these repairs with respect to the time value of money. Next, these values are combined and divided by the total amount of deck area to give a dollar per square foot unit cost. If the bridge alternatives have a differing expected service life, extra steps should be taken to compute perpetual present value costs so that the results are directly comparable. The final step is to analyze the results. (FHWA, Life Cycle Costs Primer, 2002)
The Time Value of Money One of the fundamental principles of economics is the time value of money. This basically means that a dollar today is worth more than a dollar tomorrow and this occurs for two reasons: inflation and the opportunity cost of using the funds. Inflation is, “a quantitative measure of the rate at which the average price level of a basket of selected goods and services in an economy increases over a period of time,”
(Investopedia, 2019). Inflation naturally increases the prices for goods and services
66 over time in all industries. The opportunity cost of the money used is the value at which these funds could have returned if they were used somewhere else, like an investment that guarantees an economic return (e.g. interest on a bond). In LCCA, an effective discount rate (DR) is established to account for opportunity costs. Essentially it is used to convert costs into present value dollars so that overall costs for each alternative can be determined. The DR removes the general effect of inflation and only accounts for the opportunity cost of the funds. It is expressed as a percentage and represents the value at which money’s buying power will decrease annually. (Barker, 2016) Using the DR, future cash flows are discounted to an equivalent present value which represents what the task would cost using today’s money. In this report, this value will be called the Present Value Cost (PVC). “The PVC represents a present amount that, at a given DR, will be enough to pay the initial cost of the bridge and all future costs,” (Barker, 2016). The PVC of a future cost occurring at year N with the effective discount rate of DR is expressed as:
푃푉퐶 = 퐹푢푡푢푟푒 퐶표푠푡 (1 + 퐷푅)−푁 For example, this equation could be used to estimate the cost of building a bridge of known present value in the future. If a two-lane concrete girder bridge spanning 100 feet cost $1,460,000 right now and one wanted to know what it would cost in 80 years with the assumed discount rate of 2.3 %, the calculation would go as follows:
퐹푢푡푢푟푒 퐶표푠푡 = $1,460,000(1 + .023)80 = $9,000,000 While PVCs can effectively estimate the amount of money that the bridge owner would need to invest, PVCs can only be used for direct comparison with design
67 alternatives that share equal service lives. To compare bridges of differing service lives, Perpetual Present Value Costs (PPVCs) or Equivalent Uniform Annual Costs (EUACs) must be calculated. The “Perpetual Present Value Cost (PPVC) is determined by assuming that at the end of the bridge’s life, it is replaced by an identical bridge into perpetuity,” (Barker, 2016). EUAC develops the life cycle cost amount annualized over the entire life of the bridge and reports a cumulative dollar amount. Both are equal in terms of the results. The calculation for PPVC is as follows:
(1+퐷푅)푠푒푟푣푖푐푒 푙푖푓푒 푃푃푉퐶 = 푃푉퐶[ ] (1+퐷푅)푠푒푟푣푖푐푒 푙푖푓푒−1
LCCA for Concrete and Steel Girder Bridges in Pennsylvania Dr. Michael Barker, Ph. D., PE, and professor of Civil and Architectural
Engineering at the University of Wyoming performed a mass LCCA using the State of Pennsylvania’s bridge stock and reported the results in his paper, “Historical Life Cycle Costs of Steel and Concrete Girder Bridges” (Barker, 2016). The purpose of this report was to examine the life cycle costs of “typical” concrete and steel girder bridges and reveal whether or not tangible cost advantages exist between one another. To answer this question, the entire history of each bridge including initial costs, maintenance, rehabilitation and bridge life was gathered. PennDOT supplied Dr.
Barker with all of their condition ratings, construction, and maintenance logs for some 25,403 bridges. Of these bridges, he looked at 8,466 structures. Specifically, he aimed to evaluate the information given for five bridge types:
1. Steel Rolled I-Beam
2. Steel Plate I-Girder
3. Concrete Prestressed Box- Adjacent
68 4. Concrete Prestressed Box- Spread
5. Concrete Prestressed I-Girder Of the 8,466 bridges, a majority were excluded as only 1,186 bridges, or 14%, were eligible to be included in the final analysis. The bridges were required to meet a set of criteria to ensure that the results expressed the life cycle costs for the average or “typical” girder bridge. The criterion used is listed below:
• Bridges built between 1960 and 2010
• Bridges with complete and accurate department maintenance records
• Bridges with known initial costs
• Bridges with complete and accurate external contractor maintenance and rehabilitation records
• Range limitation for initial cost to fall between $100/SF and $500/SF Most exclusions came from not meeting the age range criterion, not having complete initial costs records, or having inaccurate maintenance records which excluded the maintenance timing. Because of this, Dr. Barker noted that:
“There were many bridges that had maintenance and external contracts but without known dates or costs. These bridges were removed from the database. Therefore, the database is biased towards bridges that did not have maintenance or external contracts since these would not have been removed as long as they had initial costs.” All in all, he ended up excluding the bridges with incomplete history and developed a life cycle cost database detailing the perpetual present value costs for the five bridge types.
69 Average Deterioration Rates and Estimating Bridge Service Life At the tie of Dr. Barker’s study, most of the bridges included in this life cycle cost database were still in service. To complete the analysis, estimating the remaining life of these structures was required. This was achieved by computing an average deterioration rate for all the bridge types of interest. For more accurate results, bridges excluded from the LCCA for reasons related to the cost criterion were still included in the calculation to derive the deterioration rate. To calculate this average deterioration rate, PennDOT’s bridge condition database was used. The conditions of each element (superstructure, substructure, and deck) of every bridge are individually listed within this file on a scale from one to nine, where nine is perfect condition and one is extremely poor. The FHWA actually uses the same system for condition ratings and the list as follows:
Since this information was gathered in 2014, the 2014 condition rating for the superstructure was used. The superstructure condition rating is used for all calculations rather than choosing the overall lowest grade for the three bridge components because the report was specifically focused on girder LCCA. The average deterioration rate is calculated using this equation:
(2014 푆푢푝푒푟푠푡푟푢푐푡푢푟푒 퐶표푛푑푖푡푖표푛 푅푎푡푖푛푔) − 9 퐷푒푡푒푟푖표푟푎푡푖표푛 푅푎푡푒 = 2014 − (푌푒푎푟 퐵푢푖푙푡) There are a few disadvantages associated with using this method to measure the deterioration rate because, realistically, they are not linear. Over a bridge’s service life rehabilitations will raise condition ratings in a discontinuous and sporadic manner. Figure 16 shows a general depiction of how a structure’s condition decreases overtime, and how rehabilitation can improve its rating.
70 FHWA condition ratings (FHWA, 1995)
Code Description N Not Applicable 9 Excellent Condition 8 Very Good Condition- no problems noted 7 Good Condition- some minor problems 6 Satisfactory Condition- structural elements show some minor deterioration 5 Fair Condition- all primary structural elements are sound but may have minor section loss, cracking, spalling or scour 4 Poor Condition- advanced section loss deterioration, spalling, or scour 3 Serious Condition-loss of section, deterioration, spalling or scour have seriously affected primary structural components. Local failures are possible. Fatigue cracks in steel or shear cracks in concrete may be present. 2 Critical Condition- advanced deterioration of primary structural elements. Fatigue cracks in steel or shear cracks in concrete may be present or scour may have removed substructure support. Unless closely monitored it may be necessary to close the bridge until corrective action is taken. 1 Imminent Failure Condition- major deterioration or section loss present in critical structural components or obvious vertical or horizontal movement affecting structure stability. Bridge is closed to traffic, but corrective action may put back in light service. 0 Failed Condition- out of service - beyond corrective action.
Figure 16 General depiction of the condition rating of any structure, element, or component over time (FHWA, Life Cycle Costs Primer, 2002)
71 Also, there is no consideration for average daily traffic and regular maintenance. To check the results, Dr. Barker consulted with PennDOT engineers and found that their models for deterioration rates garnered similar results. Dr. Barker’s results are tabulated below:
Deterioration rates of concrete and steel girder bridges (Barker, 2016)
Number of Deterioration Rate Coefficient of Bridge Type Bridges 1960- (Condition Rating Variation (St. 2010 Loss/Year) Deviation/Mean) Steel I-Beam 550 -0.07114 54.7% Steel I-Girder 1017 -0.08144 57.4% P/S Box- Adjacent 1440 -0.08125 50.9% P/S Box- Spread 2196 -0.07988 70.9% P/S I-Beam 1384 -0.08383 63.3%
These values were then used to estimate the remaining life of each bridge structure that was used in the final LCC database. This was done assuming that the bridge will be replaced when the superstructure condition rating reaches the value of three. The calculation to do this is listed below:
3 − (2014 푆푢푝푒푟푠푡푟푢푐푡푢푟푒 퐶표푛푑푖푡푖표푛 푅푎푡푖푛푔) 푅푒푚푎푖푛푖푛푔 퐿푖푓푒 = (퐴푣푒푟푎푔푒 퐷푒푡푒푟푖표푟푎푡푖표푛 푅푎푡푒) Using this estimate, the total service life for each structure could be estimated:
푆푒푟푣푖푐푒 퐿푖푓푒 = 2014 − (푌푒푎푟 퐵푢푖푙푡) + 푅푒푚푎푖푛푖푛푔 퐿푖푓푒 Dr. Barker’s results found that each of the girder types are very close in expected bridge life. They are reported in Table 10 for each bridge type.
72 Average service life concrete and steel girder bridges (Barker, 2016)
Number of Bridges in Average Year Average Bridge Bridge Type Final LCC Database Built Life (years) Steel I-Beam 82 1981 81.3 Steel I-Girder 230 1977 79.2 P/S Box- Adjacent 400 1985 74.0 P/S Box- Spread 581 1984 79.9 P/S I-Beam 412 1984 74.5
Dr. Barker’s LCCA Results Using all cost information, estimated bridge life, and the discount rate provided by PennDOT, the life cycle costs for each bridge type was calculated. Table 11 gives the averages for perpetual present value costs, initial costs, and future costs in present value for each bridge type. These costs are reported in a dollar per square foot unit.
Averages that detail the age, expected bridge life, number of spans, and length are also reported in the table, along with the number of bridges included in the analysis.
Life Cycle Cost results of total database (Barker, 2016)
Initial Future Avg # Avg Bridge # of PPVC Avg Avg Cost Costs of Year Type Bridges (2014) Length Life (2014) (2014) Spans Built Steel I- 54 $232.78 $194.78 $0.42 166 2.19 1980 82 Beam Steel I- 144 $273.71 $226.10 $0.21 406 4.07 1976 80 Girder P/S Box- 282 $278.30 $223.74 $0.96 89 1.31 1987 74 Adjacent P/S Box- 397 $256.11 $210.65 $2.06 89 1.56 1986 79 Spread P/S I- 309 $217.50 $174.10 $0.20 212 2.43 1985 73 Beam
73 Dr. Barker presented his results in various other manners to explore which bridge types were the most cost-effective for specific situations. Tables 12, 13, and 14 limit the data by fixing the number of spans or the total length to a set number. These tables will be used later to calculate the economic value of the durability for which the stone arch provides.
Summarizing Dr. Barker’s results, each bridge is of similar scale in cost efficiency for any given situation. The rank of the bridge types can flip-flop from worst to first given the situation. Because of this, Dr. Barker concluded that “all the types of bridges are fairly competitive in both initial costs (present value) and perpetual present value costs,” meaning that there was not a significant difference between the life cycle cost of concrete and steel girder bridges.
Life Cycle Cost of simple span bridges (Barker, 2016)
Initial Future Avg # Avg Bridge # of PPVC Avg Avg Cost Costs of Year Type Bridges (2014) Length Life (2014) (2014) Spans Built Steel I- 22 $302.38 $253.90 $0.13 90 1.00 1981 84 Beam Steel I- 21 $318.73 $263.02 $0.25 128 1.00 1979 81 Girder P/S Box- 215 $300.74 $241.81 $1.00 65 1.00 1987 74 Adjacent P/S Box- 245 $294.67 $245.40 $1.06 54 1.00 1988 81 Spread P/S I- 105 $287.24 $234.67 $0.04 108 1.00 1989 76 Beam
74 Life Cycle Cost of two-span bridges (Barker, 2016)
Initial Future Avg Bridge # of PPVC Avg Avg # Avg Cost Costs Year Type Bridges (2014) Length Spans Life (2014) (2014) Built Steel I- 16 $234.04 $193.99 $0.05 198 2.00 1988 81 Beam Steel I- 24 $210.49 $175.04 $0.24 243 2.00 1976 81 Girder P/S Box- 32 $242.74 $191.74 $1.53 155 2.00 1987 72 Adjacent P/S Box- 59 $226.78 $183.55 $0.08 127 2.00 1989 74 Spread P/S I- 53 $230.78 $183.02 $0.18 209 2.00 1985 71 Beam
Life Cycle Cost results for brides with a maximum span of 140 feet (Barker, 2016)
Initial Future Avg Bridge # of PPVC Avg Avg # Avg Cost Costs Year Type Bridges (2014) Length Spans Life (2014) (2014) Built Steel I- 27 $266.24 $222.08 $0.16 84 1.26 1978 82 Beam Steel I- 18 $311.26 $257.19 $0.29 119 1.00 1977 81 Girder P/S Box- 240 $292.38 $235.03 $0.95 69 1.09 1987 74 Adjacent P/S Box- 325 $272.20 $225.14 $2.16 64 1.23 1986 81 Spread P/S I- 98 $281.64 $231.20 $0.05 104 1.08 1987 77 Beam
75 Estimates for Bridge Construction on the National Highway System (NHS) by the Federal Highway Administration On an annual basis, the Federal Highway Administration (FHWA) publishes estimates for both NHS and non-NHS bridge construction. Such information is provided for each state in terms of a dollar per square foot of deck space unit cost. Table 15 reports this value for various states along the east coast. These values can be used to gauge whether or not Dr. Barker’s estimates were on-point and to see how a general estimate compares with his specified estimates for one and two-span bridges. To include Dr. Barker’s results in this table, they were averaged across all bridge types and converted to 2017 dollars using the FHWA’s National Highway Construction Cost Index (NHCCI). The value reported in the index for March 2014 is equal to 1.6278 and the value for December 2017 is equal to 1.6619. (FHWA, 2017)
FHWA’s estimated bridge construction cost paired with Dr. Barker’s results in 2017 dollars
Dr. Barker’s non-NHS Dr. Barker’s NHS estimated result for State estimated cost result for one cost ($/SF) two spans ($/SF) span ($/SF) ($/SF) New Jersey $462.00 $489.00 - - Massachusetts $460.00 $417.00 - - Rhode Island $441.00 $269.00 - - Vermont $409.00 $334.00 - - Connecticut $368.00 $443.00 - - Pennsylvania $301.00 $325.00 $252.95 $189.35 New Hampshire $299.00 $320.00 - - New York $296.00 $301.00 - - Maryland $292.00 $384.00 - - Virginia $290.00 $221.00 - -
76 The Economic Value of Durability
Estimating the Service Life of a Stone Arch Bridge The most important factors that influence the life cycle cost of a bridge are the initial cost and its expected service life. In Chapter 2, stone arch bridges around the world were presented and many were found to have been functioning for centuries to millenniums. It is likely that no engineer has ever estimated that their bridge design would last for a thousand years, and I do not plan to be the first. Within that amount of time, anything can happen. Instead, a more practical estimate of their life is needed in order to produce a reasonable life cycle cost analysis. To do this, the estimated service life for a stone arch bridge was found using Dr. Barker’s method for calculating an average deterioration rate, the National Bridge Inventory (NBI), and a similar bridge condition database created by PennDOT. The NBI is a database provided by the FHWA which details information regarding every bridge in the National Highway System (NHS). Such details include bridge type, bridge dimensions, age, and condition ratings by bridge element. PennDOT provides a similar bridge database detailing their bridge stock.
In the NBI, 1,599 masonry bridges were found to exist and are carrying vehicular traffic on the NHS. They are rated using the same 1 to 9 condition rating method described earlier in Table 8. Of these 1,599 bridges in the NBI, 558 are culverts. Since Dr. Barker’s analysis only took place in Pennsylvania, it made sense to check out their bridge condition database. That database included 280 masonry arches bridges, 5 of which are culverts.
77 The average deterioration rates of these bridges are reported in Table 16. Dr. Barker’s results are also listed so that a clear comparison of durability can be made between stone arches and modern girders. To provide an apple to apples comparison, the condition rating for the superstructure was used to garner these results, just as Dr. Barker had done.
Average deterioration rates of stone arch bridges compared to steel and concrete girder bridges
Number of Deterioration Rate Coefficient of Bridge Type Bridges Included (Condition Rating Variation (St. in Analysis Loss/Year) Deviation/Mean) Stone Arch- NBI 1599 -0.04113 56.5% Stone Arch- Penn 280 -0.03600 40.0% Steel I-Beam 550 -0.07114 54.7% Steel I-Girder 1017 -0.08144 57.4% P/S Box- Adjacent 1440 -0.08125 50.9% P/S Box- Spread 2196 -0.07988 70.9% P/S I-Beam 1384 -0.08383 63.3%
These results show that the stone arch deteriorates at a rate which is approximately half of each of the modern girder types. It is also worth noting that the stone arch has the second-largest sample size and has a similar coefficient of variation to the rest of the results. The coefficient of variation is large meaning that the condition data is spread. It can be inferred that there are some bridges that are rated quite low (poor condition) while others were probably rehabilitated and are listed to be in very good condition. This is why Dr. Barker pointed out that average deterioration rates are not completely accurate as the method does not consider maintenance and rehabilitation.
78 Next, the calculated deterioration rates were then used to estimate the residual life of every masonry bridge in the two databases. For an individual bridge, the residual life was then combined with its current age to find the estimated service life. This calculation was made for every bridge in the database and then averaged across the databases, respectively. The average service lives calculated using both databases are found in Table 17, along with Dr. Barker’s results.
Average service life of stone arch bridges compared to concrete and steel girder bridges
Number of Bridges Average Service Life Bridge Type Included in Analysis (years) Stone Arch- NBI 1,599 210.1 Stone Arch- Penn 280 203.6 Steel I-Beam 550 81.3 Steel I-Girder 1,017 79.2 P/S Box- Adjacent 1,440 74.0 P/S Box- Spread 2,196 79.9 P/S I-Beam 1,384 74.5
From these results, it seems appropriate to say that a stone arch bridge has a service life of approximately 200 years. Also, stone arch bridges are at least 2 to 2 and
1/3rd times more durable than concrete and steel girder bridges.
Maximum Initial Cost of Stone Arch Bridge For this study, comparing actual construction costs of stone arch bridges with that of modern concrete and steel bridges is not possible. Stone arch bridges have not been built in the recent past, therefore, a limited amount of information is available to build a direct comparison. To address this issue, the theoretical maximum initial cost is found. This value expresses the initial cost for which a stone arch bridge will break
79 even (in terms of life cycle costs) with building several concrete or steel bridges over the course of a 200-year life span. Essentially, the difference in initial cost found between stone arches and girder bridges will be used to illustrate the economic value of their durability. To find this value, the PPVC equation was back solved using the results found by Dr. Barker for concrete and steel girder bridges and the 200-year service life assumption for a stone arch bridge. Again, the PPVC is the “perpetual present value cost” that can fund the bridge type of interest and replace that same design into infinity. Back solving the PPVC equation sets Dr. Barker’s results as the limit so that the PPVC of a stone arch bridge will match the value of the concrete or steel bridge for which it is being compared to. A differing value of initial costs is found because the value of a stone arch’s service life is used in the equation. Note that the same discount rate from by Dr. Barker’s LCCA is used to ensure it does not influence the outcome. For this analysis, maintenance, rehabilitation, salvage, and demolition costs were neglected due to a lack of cost information. The back solved equation is written as follows:
(1 + 퐷푅)푠푒푟푣푖푐푒 푙푖푓푒 − 1 푀푎푥푖푚푢푚 퐼푛푖푡푖푎푙 퐶표푠푡 = 푃푉퐶퐶[ ] (1 + 퐷푅)푠푒푟푣푖푐푒 푙푖푓푒 However, before back solving the PPVC costs, several steps must be taken. First, Dr. Barker’s results for the initial cost of the girder bridges must be converted to 2018 dollars using the NHCCI. This construction cost index tracks the price for tasks related to highway construction and measures their average change overtime. Their current index only reaches to the year 2018. The equation for converting a dollar value to present value can be seen below:
80 퐶퐶퐼 2018 2018 퐷표푙푙푎푟푠 = ∗ 2014 퐷표푙푙푎푟푠 퐶퐶퐼 2014 Next, the PPVC for just the initial cost must be calculated since this analysis will not consider future costs:
(1 + 퐷푅)푠푒푟푣푖푐푒 푙푖푓푒 푃푃푉퐶 = 퐼푛푖푡푖푎푙 퐶표푠푡[ ] (1 + 퐷푅)푠푒푟푣푖푐푒 푙푖푓푒 − 1 For example, if Dr. Barker’s results for a steel I-beam bridge from Table 11 was used, the calculation would occur as follows:
1.8727 2019 퐼푛푖푡푖푎푙 퐶표푠푡 = $194.78 ∗ = $218.43 1.6699 (1 + 0.023)82 푃푃푉퐶 = $218.43 = $258.48 (1 + 0.023)82 − 1
(1 + 0.023)200 − 1 푀푎푥 퐼푛푖푡푖푎푙 퐶표푠푡 = $258.48 [ ] = $255.75 (1 + 0.023)200
This calculation was performed to create the following tables, which uses Dr. Barker’s results tabulated in Table 11 through to Table 14. This was also done using the estimated construction costs provided by the FHWA in Table 15. It is important to note that the FHWA did not list an expected life span to go along with these estimates. In the absence of this information, the average life span of the 5 girder types Dr.
Barker evaluated was used, which equated to 76.6 years. All costs are reported in 2018 dollars per square foot of deck space.
81 Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 11 as the overall limit (overall database)
Max Initial Stone Avg PPVC Stone Increased Bridge Type Cost DR Arch Life (2018) Arch Budget (2018) Life Cost Steel I-Beam 82 $224.68 $265.88 2.3% 200 $263.06 17% Steel I- 80 $260.81 $311.28 2.3% 200 $307.99 18% Girder P/S Box- Adjacent 74 $258.08 $317.00 2.3% 200 $313.65 22% P/S Box- 79 $242.98 $291.31 2.3% 200 $288.22 19% Spread P/S I-Beam 73 $200.82 $247.97 2.3% 200 $245.35 22% Average: $283.65 19%
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 12 as the overall limit (single span bridges)
Max Initial Stone Avg PPVC Stone Increased Bridge Type Cost DR Arch Life (2018) Arch Budget (2018) Life Cost Steel I- Beam 84 $292.87 $343.77 2.3% 200 $340.13 16% Steel I- Girder 81 $303.39 $360.54 2.3% 200 $356.73 18% P/S Box- Adjacent 74 $278.93 $342.61 2.3% 200 $338.98 22% P/S Box- Spread 81 $283.07 $336.39 2.3% 200 $332.83 18% P/S I-Beam 76 $270.69 $329.15 2.3% 200 $325.66 20% Average: $338.87 19%
82 Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 13 as the overall limit (two span bridges)
Max Initial Stone Avg PPVC Stone Increased Bridge Type Cost DR Arch Life (2018) Arch Budget (2018) Life Cost Steel I- 81 $223.77 $265.92 2.3% 200 $263.10 18% Beam Steel I- 81 $201.91 $239.94 2.3% 200 $237.40 18% Girder P/S Box- 72 $221.17 $274.58 2.3% 200 $271.67 23% Adjacent P/S Box- 74 $211.72 $260.06 2.3% 200 $257.31 22% Spread
P/S I-Beam 71 $211.11 $263.56 2.3% 200 $260.77 24% Average: $258.05 21%
Maximum cost for a stone arch bridge using the PPVC of just initial costs from Table 14 as the overall limit (bridges <140 feet)
Max Initial Stone Avg PPVC Stone Increased Bridge Type Cost DR Arch Life (2019) Arch Budget (2019) Life Cost Steel I-Beam 82 $256.17 $303.14 2.3% 200 $299.93 17%
Steel I-Girder 81 $296.67 $352.55 2.3% 200 $348.82 18% P/S Box- 74 $271.11 $333.00 2.3% 200 $329.47 22% Adjacent P/S Box- 81 $259.70 $308.62 2.3% 200 $305.35 18% Spread P/S I-Beam 77 $266.69 $322.71 2.3% 200 $319.30 20% Average: $320.57 19%
83 Maximum cost for a stone arch bridge using the FHWA estimates from Table 15 as the overall limit
NHS Max NHS Stone Avg Estimated Stone Inc. State PPVC DR Arch Life Cost Arch Budget (2018) Life (2018) Cost New Jersey 76.6 $520.60 $631.18 2.3% 200 $624.50 20% Massachusetts 76.6 $518.35 $628.45 2.3% 200 $621.80 20% Rhode Island 76.6 $496.94 $602.49 2.3% 200 $596.11 20% Vermont 76.6 $460.88 $558.77 2.3% 200 $552.86 20% Connecticut 76.6 $414.68 $502.76 2.3% 200 $497.44 20% Pennsylvania 76.6 $339.18 $411.23 2.3% 200 $406.87 20% New 76.6 $336.93 $408.49 2.3% 200 $404.17 20% Hampshire New York 76.6 $333.55 $404.39 2.3% 200 $400.11 20% Maryland 76.6 $329.04 $398.93 2.3% 200 $394.70 20% Virginia 76.6 $326.78 $396.20 2.3% 200 $392.00 20% Average: $489.06 20%
Judging by the consistency of the results, the value of the durability of a stone arch bridge is about 20% of the initial costs for a comparable concrete or steel bridge. However, the factor which influences this calculation the most is the average life span of the girder bridge for which it is being compared. That being said, a 10- to 20-year difference in service life for a girder bridge can have an exponential impact on the result of the “increased budget.” Table 22 shows just how big of a difference this can make.
84 Impact on the increased budget column when the comparable bridge’s service life varies
Stone Bridge Avg Initial Discount Max Stone Increased Arch Design Life Cost PPVC Rate Arch Cost Budget Life 1 50 $250.00 $368.07 2.3% 200 $364.18 46% 2 55 $250.00 $350.29 2.3% 200 $346.58 39% 3 65 $250.00 $323.87 2.3% 200 $320.44 28% 4 75 $250.00 $305.51 2.3% 200 $302.27 21% 5 100 $250.00 $278.68 2.3% 200 $275.73 10%
All in all, the durability of stone arch bridges has significant economic value. This is especially true if location or site conditions make it likely for a concrete or steel bridge to underperform. On the flip side, it seems that even if concrete and steel technologies are pushed to service lives of 100 years, the stone arch will still have increased value over girder bridges. However, there is a major disadvantage at looking at the economics in present values. This perspective of economics does not express all the benefits. A problem is revealed by varying the service life of the stone arch bridge, which shows that little difference is made in the increased budget column if its life span is pushed to extreme values. Table 24 was made to visualize how this approach fails to show the complete benefits.
For bridge design 5 of Table 24, the stone arch life was extended to 1,000 years. This design would obviously prevent the construction of many concrete or steel girder bridges, so how can the benefit be consistent with a bridge that only lasts 200 years? This is because the PPVC calculation assumes that additional funds are investing at the time of the original bridge construction. These funds are assumed to grow at an interest rate that equals the discount rate. These funds will grow with time
85 so that at the end of the bridge’s service life there will be enough money to replace the bridge. Some funds are leftover that are again assumed to grow so that the bridge can be replaced into perpetuity.
Table used to express the shortcomings of presenting the results in present value costs by varying the stone arch bridge’s service life
Bridge Avg Initial Discount Stone Max Stone Increased PPVC Type Life Cost Rate Arch Life Arch Cost Budget 1 76.6 $250.00 $303.10 2.3% 150 $293.10 17% 2 76.6 $250.00 $303.10 2.3% 200 $299.89 20% 3 76.6 $250.00 $303.10 2.3% 250 $302.07 21% 4 76.6 $250.00 $303.10 2.3% 300 $302.77 21% 5 76.6 $250.00 $303.10 2.3% 1000 $303.10 21% Average: $300.19 20%
So what this means is that if the PPVC for a bridge which is expected to last for 300 years is $303.10 per square foot, only one additional dollar per square foot is needed to be invested at an interest rate of 2.3% in order to replace the bridge in 300 years. This is an unrealistic assumption as it is not common practice among bridge owners to invest more than the initial cost of the structure. To see the full benefits of the durability of a stone arch bridge, the equivalent uniform annual costs (EUAC) are explored in the following section.
Equivalent Uniform Annual Costs (EUAC) In the previous section, costs were evaluated from the perspective of present value costs. While it is useful to look at economics in this manner, the full benefits of the durability of the stone arch bridge are not fully expressed. Essentially, all the
86 bridges in the NHS are owned by government entities which are funded by American taxpayers. They are a common good for which we all agree are necessary to have and for which legislators decided how much money should be spent on them. Simultaneously, everyone would probably like to see less of their expenses in state and federal budgets. So how exactly can stone arch bridges solve this issue?
Looking at the costs from an annual perspective, the result of utilizing stone arch bridges often and wherever appropriate has the potential to achieve significant savings for state and federal budgets. The EUAC style of presentation basically produces the yearly costs of a bridge design over the analysis period (service life of the bridge). EUAC is equal to that of present value costs, but it gives a better sense to bridge owners of the total amount of money they will need to spend on a bridge and when they will need to spend it. In the FHWA’s “Life Cycle Cost Analysis Primer”, they stated that “when decision-makers are accustomed to using annualized costs, EUAC may be a more useful form for the analysis results” (FHWA, Life Cycle Costs Primer, 2002). The EUAC is calculated by switching around PVC equation to solve for future costs:
퐹푢푡푢푟푒 퐶표푠푡 = PVC (1 + 퐷푅)푁 To create the EUAC provided in Table 25, the size of the bridge must be established. A model deck was provided for each bridge type, which are all equal deck in area. The deck is non-skewed, has four, 12-foot lanes with sidewalks and barriers. The width in total is 60 linear feet and the length of the bridge is 100 linear feet, which multiply to give a deck area of 6,000 SF. Also, the DR is still 2.3%, and the costs values are from Dr. Barker’s results in Table 14 converted to 2018 dollars and the average maximum cost for a stone arch bridge in Table 21.
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P/S Box- P/S Box- Bridge Type Steel I-Beam Steel I-Girder P/S I-Beam Stone Arch Adjacent Spread Initial Cost $256.17 $296.67 $271.11 $259.70 $266.69 $320.57 ($/SF) Bridge Life (years) 82 81 74 81 77 200 Analysis Period (years) 200 200 200 200 200 200 Deck Space (SF) 6000 6000 6000 6000 6000 6000 Cost
88 $1,537,020.00 $1,780,020.00 $1,626,660.00 $1,558,200.00 $1,600,140.00 $1,923,420.00
Cost of 1st Replacement $9,919,310.46 $11,229,261.94 $8,751,725.39 $9,829,909.75 $9,216,834.25 $0.00 Cost of 2nd Replacement $64,015,250.23 $70,839,835.39 $47,085,867.57 $62,012,017.57 $53,089,125.73 $0.00 Total Costs $75,471,580.69 $83,849,117.34 $57,464,252.96 $73,400,127.32 $63,906,099.98 $1,923,420.00
EUAC using calculated using concrete and steel girder initial costs from Table 14 and the average maximum stone arch cost from Table 21
The results from performing LCCA using EUAC show that building a stone arch bridge rather than the typical girder bridge could potentially save a large number of taxpayer dollars. Because the stone arch bridge is projected to last 200 years, two girder bridges are prevented from being built. The amount of budgeted dollars which are avoided from being spent is likely to be somewhere between $50-80 million over the course of a stone arch bridge’s life. If the stone arch bridge can be in the same price range as typical concrete and steel girder bridges and utilized on a large scale, significant amounts of budgeted dollars could be saved.
Maintenance When it comes to maintenance cost information of stone arch bridges, very little data is publicly available. Since many of these masonry structures were built in the 1800s and early 20th century, finding the complete maintenance records with accurate timing and cost required of LCCA would be a long shot. Keeping organized and accurate maintenance logs was not a common practice before the modern era. Overall, not having maintenance costs included in the LCCA is not too big of a deal from the perspective present values. In Dr. Barker’s work, he explained that “the impact on the averages [of LCCAs] will be relatively small since future discounted maintenance costs are small compared to initial costs.” (Barker, 2016) This occurs because of the time value of money. The present value of future cash flows inevitably decreases due to the opportunity-cost of time passing. However, PennDOT does provide some information related to the maintenance of their historic stone arch bridges. Pennsylvania is one of the earliest states to develop and is rich in its history as one of the original colonies of the United States. Many structures throughout the state are regarded as landmarks due to having some sort of
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historical significance, which includes many stone arch bridges. The counties of and around Philadelphia have some of the densest concentrations of stone arch bridges in the entire nation. As a result, PennDOT prepared both a management plan and maintenance manual specifically for stone arch bridges. Apparently working on historic structures require their own definitions for
“repair” and “rehabilitation.” PennDOT’s “Stone Arch Bridge Management Plan” defines repairs and rehabilitations as:
• “Repair refers to a corrective measure or corrective measures or task(s) intended to return a specific defect or deterioration to a functional or near original condition or state.” (PennDOT, 2018)
• “Rehabilitation is defined as ‘the process of returning a property to a state of utility, through repair or alteration, which makes possible an efficient contemporary use while preserving those portions and features of the property that are significant to its historic, architectural, and cultural values.’” (PennDOT, 2018)
Some common repairs to historic stone arch bridges include rebuilding wing walls and parapets damaged due to traffic impacts. Common rehabilitations include major rebuilding of bulging spandrel walls and rebuilding arch rings and arch barrels. PennDOT mentions that routine maintenance can extend the service life of a stone arch bridge for “a relatively small amount of money when compared to the cost of repair and rehabilitation.” (PennDOT, 2007) In their management plan, they also express that repairing these bridges is often worth the investment. Apparently, repair can be very costly but almost all the funds on a repair project go directly to the repair itself as “relatively little funding is needed for decision-making or planning.” (PennDOT, 2018)
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Salvage Value For any bridge project, some materials are considered salvageable and can be sold to either be recycled or reused. The economic benefit gained from salvaging the stone from masonry bridges has considerably more potential than that of steel or concrete bridges because there are far more ways to either recycle or reuse stone. Its foremost value comes from being able to be directly reused to build the same bridge over again. Through meetings with a local contractor in Pennsylvania which works on stone arch bridges for PennDOT, I found that stone units can be directly reused to build the same bridge. This is actually common practice in Pennsylvania as many of their stone arch bridges are regarded as landmarks and there is a concerted effort to ensure their historic integrity. In PennDOT’s Stone Arch Bridge Management Plan, it is stated that
“If voussoirs and arch barrel stones are cut and precisely gauged, they should be numbered and photographed prior to beginning rehabilitation work; where possible, they should be replaced as originally constructed,” and, “If possible, use the existing stones to repair/rehabilitate/restore the arch.” (PennDOT, 2018) This means that the bridge can be reconstructed using the original materials, which are often are found in good condition. If a significant proportion of the stone can be reused, this could potentially cut the overall cost for the next bridge as there will be fewer materials to purchase and transport to the site. For the units which are not in good shape and will not be used to rebuild the bridge, they can be crushed for use as aggregates. Crushed stone is needed in almost every highway construction project today as they are needed to make concrete, asphalt, and the subbase of roadways. Crushed stone could even be sold to landscapers
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if nothing else. Whatever it may be used for, there is surely someone that would be willing to purchase these units to use if the quantity is great enough. If a situation were to occur where a bridge was not going to be replaced by another masonry arch bridge, it is likely that the stone would still hold high value. I once interned for a restoration company that did masonry repairs. On a specific project, we were restoring a historic house that was made from stone and were required to maintain a similar definition of integrity as described above for historic masonry bridges. On this job, many dilapidated stones were replaced by “reclaimed” stone that was purchased from a stone distributer. This reclaimed stone came from another old structure that had been demolished. Basically, it seems that whatever the scenario may be at the end of a stone arch bridge’s life, there will definitely be a way to make money back from the material. So again, stone gains value because of its durability and from the many ways it can be reused.
Applicability of the Stone Arch Solution
Limitations from Design and Construction
This section is started not with the positives but with the negatives, and for great purpose. The reader should understand that the stone arch may not be economically viable for some of the most common site conditions and for particular locations throughout the United States. There are several economic limitations for stone arch bridges, and they list as follows: 1. Accelerating the speed of masonry arch construction is a necessity. The
traditional manner of construction is too slow and will not work with
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today’s labor rates. Also, building more than two spans may not be possible using the accelerated construction method discussed later. 2. Depending on location, the type of stone, and available quarry services, material costs can be expensive due to the preparation of the blocks and their delivery.
3. Clearance issues from the arch geometry may limit whether or not it is an appropriate design for crossing over roadways. 4. Stone arch bridges are heavy and may not be compatible with all soil conditions. 5. High degrees of skew should be avoided. With that being said, the limitations of this structure type enable one to find where a stone arch will be the best choice. But first, the first two limitations will be detailed because they are complicated.
Accelerating Construction Though it seems that there is tremendous value in the durability of stone arch bridges, this value will never be realized if only traditional construction methods are available. As explained in Chapter 2, constructing bridges in the traditional manner is very laborious and time-consuming. This means that they will probably exceed the maximum cost outlined previously. However, there are certainly ways to address this concern using modern technology. A company named Macrete, working with Belfast University, may have already found the solution for cutting construction costs with their precast arch system called the Flexi-Arch. With this system, concrete voussoirs are connected to create a single member and the arch as a whole is hoisted into place using a crane. This enables
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much faster construction as their arch barrel can be built within a single day. With some of the same creativity, a way to utilize an analogous methodology to construct a stone arch can certainly be found.
Figure 17 Installation of a precast concrete segmented arch by crane (Ball, 2015)
However, using this style of construction may not work for building more than two spans. To make the piers of an arch bridge as thin as possible, the horizontal thrust of adjacent spans must be utilized to balance lateral forces. To do this in the past, spans would be constructed in unison, requiring multiple forms. Building a multi- spanned arch bridge by crane will require some sort of way to balance the thrust during construction while the structure is still incomplete.
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Cost of Stone Depending on where the project is located and the types of stone available, stone can be very expensive. There are several reasons for this, but it is primarily due to the effort and cost associated with producing the needed “dimensional” blocks. First, the blocks must be cut in bulk quantity from a quarry and then cut again into specific shapes and sizes. Diamond tipped blades cooled by water and other heavy machinery are required to get the job done quickly. Furthermore, dimensional stone accounts for only 3.1% of the overall stone mining industry, meaning demand is low compared to other stone products (IBISWorld, 2018). Also, transport associated with stone products can be expensive due to their weight. As a result, stone is generally not shipped long distances. “Therefore, the industry has a geographically dispersed structure and comprises many small-scale operations servicing narrow geographic markets.” (IBISWorld, 2018) As a result, some regions will have higher costs than others. To get an idea of what stone may cost on the East Coast, several quarries were contacted. Each had different types of stone, locations and prices. Several quotes were obtained via telephone and in-person meetings. They ranged from $100 to $120 per cubic foot, which including delivery. Sedimentary stones were cheaper than granite.
This makes sense given that the demand for sedimentary blocks is higher than for granite blocks as “an estimated 54.0% of the volume of dimension stone sold is limestone; 21.0% is granite; 14.0% is sandstone” (IBISWorld, 2018). With high material pricing, it is likely that material costs may account for 50-75% of the construction cost of stone arch bridges.
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Conditions at Possible Sites of Interest To gauge the applicability of the stone arch bridge, the NBI can again provide valuable information. According to the National Bridge Inventory (NBI), 62.9% of bridges on the National Highway System (NHS) are 100 feet or less in length. To be exact, there are 386,883 bridges falling within this range of length, and they seem to be following the same trend of structural deficiency as reported in Chapter 1. This can be seen by the values shown in Table 26. The percentage of these short bridges which have received an appraisal rating of 5 or less in the NBI is detailed and their combined total is 32.3%.
Appraisal Descriptions of Condition Ratings (FHWA, Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges, 1995)
Condition Number of # Appraisal Description % Rate Bridges Somewhat better than minimum adequacy 5 Fair 17.8% 69,040 to tolerate being left in place as is Meets minimum standards if left on its 4 Poor 8.63% 33,403 own Intolerable requiring high priority of 3 Serious 2.07% 8,004 “corrective action” Intolerable condition and requires high 2 Critical 3.21% 12,408 priority of replacement Imminent This value of rating code is not used 1 - - Failure 0 Failed Bridge closed 0.63% 2,435
Currently, over 5% of bridges that are 100 feet and less require either major rehabilitation or complete replacement (ratings of 3 or lower). With another 8.63% rated in poor condition, disrepair among bridges which are this size is common.
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Seeing that almost 18% of bridges are not too far from needing attention (rating of 5) is also not encouraging. These values indicate that a market for stone arch bridges currently exists.
Chapter Conclusion In my lifetime, significant action from the entire nation will be required to repair our transportation infrastructure. If the choice were made to rebuild the National Highway System, stone arch bridges should certainly be considered as a viable option for single and two-span bridges. With revolutionizing their construction methods, their durability can certainly lead to long-term cost savings for governments and taxpayers. Assuming this new method of construction produces a stone arch bridge that falls in a similar range of cost as concrete and steel girder bridges, using stone arch bridges on a large scale could derive significant economic value through the elimination of the need to build many short-lived girder bridges.
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Chapter 5
PREVENTING FUTURE CARBON EMISSIONS
Climate change is currently humanity’s foremost issue. As described in
Chapter 1, this global phenomenon may have disastrous consequences if current practices that contribute significant amounts of greenhouse gas emissions go unchanged. Addressing this issue will take major reform across all industries, including within the construction of transportation infrastructure. Given the state of disrepair in the National Highway System, producing more emissions will be necessary for a rebuild. However, stone arch bridges may be used to minimize emissions as we rebuild our nation’s infrastructure. To prove it, this chapter will lay out the production processes of steel, cement, and dimensional stone to describe the manners in which emissions are created and to compare their differences. Emissions related to bridge building are also described and used to show the environmental value of the durable and long-lasting stone arch.
Emissions from Steel Production Globally, the production of steel is a major contributor of greenhouse gas emissions. More than 1.3 billion metric tonnes of steel are produced every year and the demand is expected to increase to 3 billion metric tonnes by 2050 (Brown, Gambhir, Florin, & Fennell, 2012). In 2015, the production of steel was responsible for five percent of the world’s total greenhouse gas emissions (Climate Action
Tracker, 2017). These emissions are mainly produced by the consumption of electricity and fuel.
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There are two manners in which steel is produced and both are energy intensive. The first method is referred to as, “primary steel production” and it is defined by its use of raw materials and their conversion into new steel. The other method is referred to as “secondary steel production,” and it utilizes recycled steel to create new steel. Both processes require furnaces which consume large amounts of energy to supply extreme levels of heat needed to melt materials. (Brown, Gambhir, Florin, & Fennell, 2012) Required temperatures may reach up to 1200ºC. (World Coal Association, 2019) For primary steel production, emissions are mainly created from the quarrying of raw materials, their transportation to the steel production plant, and the mass consumption of electricity used for the heating of materials within furnaces. At a production plant, the first step is to convert iron ore and coking coal into ‘pig’ iron by melting these materials in a blast furnace. Next, steel is created by removing the impurities of pig iron and lowering its carbon content. This is done by placing pig iron in a Basic Oxygen Furnace (BOF). In the BOF, “high purity oxygen at high temperature is used to remove carbon and other impurities from the pig iron, forming steel of the required carbon content.” (Brown, Gambhir, Florin, & Fennell, 2012)
Again, significant amounts of energy are consumed to heat these furnaces to the appropriate temperatures. In the secondary steel production process, used steel is transported to a facility and recycled through melting the materials in an Electric Arc Furnace (EAF). Melting iron ore and coke are not needed to produce secondary steel, so the materials only need to be heated once. As a result, the secondary process emits fewer greenhouse gases but still requires significant amounts of energy to do so.
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Additionally, extra greenhouse gases will be emitted from both processes as the steel will need to be shaped and cut as required for its intended purpose. Both fossil fuels and electrically powered machinery will be needed to do so. With all of these factors combined, steel production consumes a lot of energy and emits large volumes of environmentally impactful gases.
Emissions from Cement Production Cement is the binder used to combine sand with aggregates and produce solid concrete. Worldwide, annual cement production is currently at 3.3 billion metric tonnes and is expected to increase to 4.5 billion metric tonnes by 2050 (Brown, Gambhir, Florin, & Fennell, 2012). In 2010, cement production contributed 5.5 percent of the world’s greenhouse gas emissions. (Climate Action Tracker, 2017)
The emissions from cement production are largely due to the need to heat raw materials to 2000ºC in a kiln for an extended period of time. Other sources for emissions include quarrying for limestone and other raw materials, mechanical crushing of such materials, and the transportation of the raw materials to the cement plant and moving the finished product to concrete plants. Additional emissions will be created by the use of concrete mixing machinery as cement needs to be combined with water, sand and aggregates to ultimately produce concrete.
Emissions from Producing Dimensional Stone Currently, emissions from producing dimensional stone are not well documented. With a lack of information, a true comparison between the production of steel, cement, and stone cannot be made. However, deductive reasoning can be used to
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illustrate the environmental advantages of utilizing dimensional stone rather than concrete or steel. The first thing to point out is that the production of each of these three materials starts at a quarry. Though each material type may be able to utilize different processes for extraction (e.g. blasting with explosives versus cutting out blocks), all will require the clearing of natural vegetation, thus changing land-use. Net land-use change is a major factor in climate change and results in emissions. The logic behind this relates to the fact that clearing of vegetation will reduce nature’s capacity for converting carbon dioxide to oxygen. Also, each quarrying method will require the use of heavy machinery to extract and prepare the materials. Without an in-depth study, it may be safe to assume that emissions from quarrying the three material types are of similar magnitude. For perspective, the process for removing raw material to produce dimensional stone is described. First, vegetation is cleared to expose the face of the desired stone. Next, large blocks are cut out from the ground. Generally, this is done by quarrying in “benches,” which can be up to 8 to 12 feet wide by 20 feet in length depending on the landscape and rock type. Holes must be drilled along the perimeter of the bench.
Blocks are then extracted by either cutting with saws equipped with diamond wire, or by splitting the stone using hydraulic splitters or small explosive charges. After freeing the stone blocks, they are transported to either an inhouse facility or purchased by another company. (University of Tennessee-Center for Clean Products, 2008) The next step is where dimensional stone gains an advantage over steel and concrete. After the raw material is extracted, there are significantly fewer steps involved with finishing the product. The blocks extracted from the quarry must be cut
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again into specific shapes and sizes by either a circular blade or a diamond wire saw. (University of Tennessee-Center for Clean Products, 2008) For the purpose of bridge building, they are ready to be used and transported to the site after this step. This sets dimensional stone apart in terms of emissions because there is no need for furnaces or kilns. This step was essentially provided by the natural processes which produced the stone. Without the need for massive amounts of energy for heating, the emissions related to the production of dimensional stone can be expected to be far less than those from the production of cement and steel.
Emissions from Bridge Building Material production is not the only source of greenhouse gas emissions that occur when building a bridge. In fact, there are at least three more significant sources of emissions for any given bridge construction project. Listed below are the main sources of emissions (Hoeckman & Nelis, 2012):
1. Fabrication- emissions from the production of materials required for the project
2. Transportation- emissions from the use of vehicles to transport materials to the site
3. Construction- emissions related to the machinery and equipment used to construct the bridge
4. Overhead- emissions from the consumption of electricity and fuel at offices and workshops Depending on the material type, there may be emissions due to additional factors. For instance, steel corrosion protection (coatings) is a significant factor in emissions of a steel bridge project, so it can be singled out from the construction category.
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To gauge what material production looks like as percent of the total emissions on a given bridge project, a study, “Environmental Implications of Steel Bridge Construction,” is used. In this study by Wim Hoeckman and Olivia Nelis, the total emissions of five individual steel bridge projects located in Europe were estimated. Each project was completed in either 2010 or 2011 and differed in size, structure type, and erection methods. (Hoeckman & Nelis, 2012) Details of the five projects follow in Table 27.
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Details of the five projects evaluated by Hoeckman & Nelis (Hoeckman & Nelis, 2012)
Mitre gates Bridge Bridge Bridge Duffel Bridge Nantes Kattendijk Grobbendonk Luxemburg lock Steel Bridge: 254 t 573 t 2,280 t 1,954 t 2,527 t consumption Doors: 417 t Bridge: L = 69 m L = 109 m L = 110 m L = 122 m L = 210.5 m B = 13 m Dimensions B = 18 m B = 13 m B = 18.5 m B = 27.4 m H = 5.4 m H = 15.5 m H = 20 m H = 20.5 m H = 57 m (pylon) Doors: 104 B = 14 m
H = 9 - 12.5 m Bridge: Truss; Bowstring; Fully Bowstring; Fully Bowstring; Bolted Cable stayed; Fully Fully welded welded; Concrete deck welded; cross girders; welded; Orthotropic Description Gates: Fully on steel cross girders Orthotropic deck Concrete deck deck welded Fabrication hours 25.3 h/t 22.0 h/t 10.4 h/t 23.5 h/t 35.7 h/t Zinc spray + 2 Bridge: 4 layers Zinc spray + 2 3 layers (230 µm); Corrosion 3 layers layers (140 µm) or (340 µm) layers (150 µm to interior of pylon: 1 (240 µm) 3 layers (arch) (200 Doors: 2 layers protection system 240 µm) layer (40 µm) µm) (500 µm) Distance 100 km 100 km 300 km 1,200 km 100 km workshop to site Ship (doors) and Barge (over canals) Truck Truck Barge (over sea) Transport to site barge (bridge) Fully completed Float in Launching In situ Float in direct placing Erection method in situ Erection hours 6.2 h/t 9.9 h/t 6.2 h/t 5.4 h/t 2.4 h/t
Though these bridges are all larger than the average girder bridge, they may still give insight into the percentages for which each factor contributes emissions for bridge construction. Using available information, the emissions for each project were calculated. They expressed their results as a value normalized by the total steel tonnage of the project so that they could be directly compared. They are found in Table 28.
Sources of emissions in each project and their respective percentages of contribution to the total amount of emissions (Hoeckman & Nelis, 2012)
Mitre gates Bridge Bridge Bridge Bridge Duffel Kattendijk Grobbendonk Luxemburg Nantes lock
kg kg kg kg Percent kg Percent Percent Percent Percent C02 C02 C02 C02 of C02 of of Total of Total of Total /ton /ton /ton /ton Total /ton Total Fabrication 150 30.2% 133 28.3% 88 28.9% 129 21.6% 194 34.3% Corrosion 139 28.0% 137 29.1% 70 23.0% 96 16.1% 172 30.4% protection Transport 47 9.5% 17 3.6% 31 10.2% 204 34.2% 51 9.0% Construction 51 10.3% 77 16.4% 57 18.7% 63 10.6% 16 2.8% Overhead 109 22.0% 106 22.6% 59 19.3% 104 17.4% 132 23.4% TOTAL 496 - 470 - 305 - 596 - 565 -
For large bridges, it seems that fabrication (or material production) consistently averages around 30% of the total project emissions. Other than overhead emissions, fabrication seems to be the most consistent value throughout the five projects. However, these percentages differ from project to project and may not linearly correlate with 100-foot bridges. Instead, what may be safe to say is that the other
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sources of emissions of bridge construction combined are likely to out-weigh the emissions from production. To evaluate the environmental advantages of stone, let’s say that for small bridge construction, fabrication of materials causes 30 to 50 percent of the total emissions. For simplicity, let’s also assume that the emissions of constructing a stone arch bridge are similar to that of a comparably sized concrete or steel girder bridge (see Table 29). If this were the case, a stone arch bridge with the life expectancy of 200 years is likely to offset at least 170 percent of the emissions that would have been otherwise caused if concrete or steel was used instead. If the emissions from the production of dimensional stone are less than that of concrete and steel, the number of emissions prevented will grow even larger. The value grows even larger if the succeeding stone arch bridge can be built using a majority of the same materials from the retiring bridge.
Calculation of emission prevention from using stone arch bridges
Stone Concrete/Steel Fabrication 50% 50% Construction 35% 35% Overhead 15% 15% Life (years) 200 75 Bridges Needed 1 2 2/3 Total Emissions 100% 267% Emissions Prevented 167% -
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Chapter Conclusion Though a true estimate is currently unavailable, it is likely that the utilization of stone arch bridges in place of concrete and steel girder bridges could prevent significant amounts of greenhouse gas emissions from occurring. Due to the fact that raw materials must be quarried to produce all three materials and the fabrication of dimensional stone does not require the use of furnaces or kilns, significantly less energy is needed to produce stone (i.e. less CO2 emissions result). Even more meaningful, the extended service life of stone arch bridges and their ability to be rebuilt using the same materials can significantly cut emissions from future infrastructure needs. With these factors combined, the stone arch bridge is very likely to possess much higher environmental value, but cannot be said definitively without future study.
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Chapter 6
THESIS CONCLUSION AND FUTURE WORK
In the modern world, transportation is a vital part of life and we need it to survive. However, we also need healthy ecosystems and natural processes of the planet uninterrupted. Making great changes in the ways we build is necessary. With the major issues of a delipidated infrastructure system and climate change, serious consequences will derive from inaction. Both problems are in no way mutually exclusive and current bridge designs can exacerbate the combined issue as they are short term solutions for long term needs.
Another issue that was not mentioned at all in this paper until now is the fact new solutions rarely come along in the civil engineering world. Civil engineering structures, such as bridges, carry a great deal of risk and investment with them. Bridge owners need to be absolutely sure of what they are buying, so time is needed to experiment, accept and implement new technologies. What this means is that new materials and solutions may not arrive fast enough to impact these issues. It seems that right now is the time to act on climate and the time to replace vast amounts of infrastructure is quickly approaching. At this moment, the only solution ready to plug and play may very well be the stone arch bridge. The stone arch bridge has a lengthy track record of success around the world. This ancient technology has tied itself to many of humanity’s greatest civilizations and has been essential to our development. It is known that hundreds of thousands of these bridges stand as fruitful investments world-wide. The stone arch bridge needs not to
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prove its performance to become a viable bridge again, but only to find a new method of construction. Due to their estimated service life of 200 years, one stone arch bridge is likely to outlast two to three concrete or steel girder bridges. Significant economic and environmental value is yielded from this durability as both future expenditures and future greenhouse gas emissions can effectively be avoided. With the capabilities and creativity held in the modern era of construction, stone arch bridges can certainly become a sustainable alternative for one and two-span girder bridges. Though it seems there is certainly potential in bringing back stone arch bridges, there are needs for future studies with varying directions. First off, the construction process for the placement of arches must be reinvented. Modeling and experimentation will be required. The second thing would be estimating the total construction cost of a stone arch bridge using this new method. Given that the materials and labor pricing fluctuate based on location, stone arches are probably not economically viable everywhere. The third and final thing would be to figure out exactly what quantity future emissions can be prevented by utilizing stone arches. Chapter 5 made conclusions from deductive reasoning and putting a more accurate number on emissions will definitively prove the environmental value of stone arch bridges.
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REFERENCES
AASHTO. (2017). AASHTO LRFD Bridge Design Specifications. Washington, DC. ASCE. (2017). 2017 Infrastructure Report Card. American Society of Civil Engineers. ASCE. (n.d.). Canton Viaduct. Retrieved January 2, 2019, from ASCE: https://www.asce.org/project/canton-viaduct/ ASCE. (n.d.). Carrollton Viaduct. Retrieved January 2019, from ASCE: https://www.asce.org/project/carrollton-viaduct/ ASCE. (n.d.). Rockville Stone Arch Bridge. Retrieved from ASCE: https://www.asce.org/project/rockville-stone-arch-bridge/ Ball, M. (2015, January 16). Engineers Develop the Longest Flat-Pack Arch Bridge. Retrieved from Informed Infrastructure: http://informedinfrastructure.com/12696/engineers-develop-the-longest-flat- pack-arch-bridge/ Barker, M. G. (2016). Historical Life Cycle Costs of Steel & Concrete Girder Bridges. University of Wyoming, Civil & Architectural Engineering. Barow, H., & Ragette, F. (2013). Roads and Bridges of the Roman Empire. Fellbach: Edition Axel Menges. Bliss, R. (n.d.). Accretion. DigitalBlasphemy.com. Boothby, T. E., & Roise, C. K. (1995). An Overview of Masonry Arch Bridges in the USA. the First International Conference on Arch Bridges, (pp. 11-20). Bolton. Boucher, J. E. (1968). Northeast Railroad Corridor, Amtrak Route between RI/MA State Line & South Station, Boston, Suffolk County, MA. Retrieved from Library of Congress: https://www.loc.gov/pictures/item/ma1240.photos.076610p/ Brown, T., Gambhir, A., Florin, N., & Fennell, P. (2012). Reducing CO2 emissions from heavy industry: a review of technologies and considerations for policy makers. London: Imperial College. BTC. (2019, June). Stone arch bridges - A practical manual for local governments. Retrieved from Enabel: https://www.enabel.be/publication/stone-arch-bridges- practical-manual-local-governments Clifton, J. R. (1980). Stone Consolodating Materials: A Status Report. Retrieved from Cool Conservation OnLine: http://cool.conservation- us.org/byauth/clifton/stone/
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Climate Action Tracker. (2017, October). Decarbonising the global steel and cement sectors requires more than zero carbon fuels: analysis. Retrieved from Climate Action Tracker: https://climateactiontracker.org/publications/blog- decarbonising-global-steel-and-cement-sectors-requires-more-zero-carbon- fuels-now/ Climate Action Tracker. (2017, October). MANUFACTURING A LOW-CARBON SOCIETY: HOW CAN WE REDUCE EMMISSIONS FROM CEMENT AND STEEL. Retrieved from Climatetracker.org: https://climateactiontracker.org/documents/60/CAT_2017-10- 18_DecarbIndustry_CATAnalysis.pdf FHWA. (2002). Life Cycle Costs Primer. Office of Asset Management. Federal Highway Administration. Retrieved from https://www.fhwa.dot.gov/asset/lcca/010621.pdf FHWA. (2015). Status of the Nation's Highways, Bridges, and Transit: Conditions & Performance. Washington, D.C.: U.S. Department of Transportation. FHWA. (2017, November 14). National Highway Construction Cost Index (NHCCI). Retrieved from Federal Highway Administration: https://www.fhwa.dot.gov/policy/otps/nhcci/ FWHA. (1995). Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges. Washington D.C.: U.S. Department of Transportation. Fisk, D. M. (2003). American Labor in the 20th Century. U.S. Bureau of Labor Statistics. Heckroodt, R. O. (2002). Guide to Deterioration and Failure of Building Materials. London: Thomas Telford Publishing. HighestBridges.com. (2017, February 10). Danhe Bridge. Retrieved from HighestBridges.com: http://www.highestbridges.com/wiki/index.php?title=Danhe_Bridge Hoeckman, W., & Nelis, O. (2012). ENVIRONMENTAL IMPLICATIONS OF STEEL BRIDGE CONSTRUCTION. Victor Buyck Steel Construction. Hugues, T. (2005). Dressed Stone. Walter de Gruyter GmbH. IBISWorld. (2018, May). Stone Mining in the US. Retrieved from IBISWorld: https://clients1-ibisworld- com.udel.idm.oclc.org/reports/us/industry/default.aspx?entid=124 Investopedia. (2019, March 26). Inflation. Retrieved from Investopedia: https://www.investopedia.com/terms/i/inflation.asp IPCC. (2013). Summary for Policymakers. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. New York: Cambridge University Press. John, J. S. (2015, March 13). Oolitic Limestone 1. Retrieved from Flickr: https://www.flickr.com/photos/jsjgeology/16797398092
111
Kangas, O. (2010). One Hundred Years of Money, Welfare and Death: Mortality, Economic Growth and the Development of the Welfare State in 17 OECF Countries 1900-2000. International Journal of Social Welfare, 19, S42-S59. Khattak, O. (2018, December). Sandstone. Retrieved from Geologylearn.com: https://geologylearn.blogspot.com/2015/03/sandstone.html Mark. (2015, July). Gemstone Forum Archive. Retrieved from lapidaryforum.net: http://lapidaryforum.net/gemstone/index.php?topic=17815.0 MelBourne, C. (2007). A new masonry arch bridge assessment strategy (SMART) . ARCH’07 – 5th International Conference on Arch Bridges . Minnesota Department of Transportation . (n.d.). Stone Arch Bridge. Retrieved from John Marvig Railroad Bridge Photography: http://www.johnmarvigbridges.org/Stone%20Arch%20Bridge.html Morgan, T. (2007, November 30). ZhaozhouBridge4. Zhaoxia, China: AsiaVtour.com. National Materials Advisory Board. (1982). Conservation of Historic Stone Buildings and Monuments. Washington, D.C.: National Academy Press. O'Connor, C. (1993). Roman Bridges. New York: Cambridge University Press. Orban, Z. (2004). ASSESSMENT, RELIABILITY AND MAINTENANCE OF MASONRY ARCH RAILWAY BRIDGES IN EUROPE. Barcelona: CIMNE. Orban, Z. (2007). UIC Project on assessment, inspection and maintenance of Masonry Arch Bridges. ARCH’07 – 5th International Conference on Arch Bridges. PennDOT. (2007). PENNDOT STONE ARCH BRIDGE MAINTENANCE MANUAL . October. PennDOT. (2018). Stone Arch Bridge Management Plan. State of Pennsylvania, Department of Transportation. Pinkerton, J. P. (2015). A VISION OF AMERICAN STRENGTH: HOW TRANSPORTATION INFRASTRUCTURE BUILT THE UNITED STATES. American Road & Transportation Builders Association. Proske, D., & van Gelder, P. (2009). Safety of Historical Stone Arch Bridges. New York: Springer. Roser, M., Ritchie, H., & Ortiz-Ospina, E. (2019). World Population Growth. OurWorldInData.org. Retrieved from https://ourworldindata.org/world- population-growth ScienceStruck. (2018, May 8). An Explanation of How Limestone Caves are Formed at Every Stage. Retrieved from ScienceStruck: https://sciencestruck.com/how- are-limestone-caves-formed Stellez, E. (n.d.). Puente romano de Alcantara. Retrieved from Flickr: https://www.flickr.com/photos/eduardocagney/8424383079/ Stuart, M. (2013). Concrete Deterioration. Retrieved from PDH Onlinw: https://pdhonline.com/courses/s155/s155content.pdf Stuart, M. (2013). Metal Deterioration. Retrieved from PDHonline: https://pdhonline.com/courses/s174/s174content.pdf
112
UIC. (n.d.). Assessment of Masonry Arch Bridges. Retrieved from Union Inter Des Chemins: https://uic.org/com/uic-e-news/593/article/masonry-arch-bridges- workshop-to-be-held-from-7-8-june-in-madrid-and-from-18- 19?page=iframe_enews UN. (2017, June 21). World population projected to reach 9.8 billion in 2050, and 11.2 billion in 2100. Retrieved from United Nation Department of Economic and Social Affairs: https://www.un.org/development/desa/en/news/population/world-population- prospects-2017.html University of Tennessee-Center for Clean Products. (2008, August). Granite Dimensional Stone Quarrying and Processing: A Life-Cycle Inventory. Retrieved from National Stone Council: https://naturalstonecouncil.org/life- cycle-inventory/granite-life-cycle-inventory USGS. (2019, February). National Minerals Information Survey- Mineral Commodity Summaries. Retrieved from United States Gelogical Survey: https://www.usgs.gov/centers/nmic/dimension-stone-statistics-and-information World Coal Association. (2019). How is Steel Produced? Retrieved from World Coal Association: https://www.worldcoal.org/coal/uses-coal/how-steel-produced Zhou, M., Zhang, J., An, L., Zhang, X., & Li, T. (2016). Spanning over 1400 years: China’s remarkable Zhaozhou Bridge. Proceedings of the Institution of Civil Engineers (pp. 113-119). Institution of Civil Engineers.
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