This chapter addresses the introduction of engineering concepts in grades K-12 and the content of the module, fracture and dams. The literature shows that there is a call for engineering design and skills in the K-12 classroom. The technical, societal, and personal impacts of fracture and dams make these subjects appropriate to provide a well-rounded introduction to engineering. A basic study of fracture mechanics shows the user real-world applications of his or her skills in math and science, providing some purpose for learning these skills. A study of dams also provides an interdisciplinary, real-life application of math and science. In addition, the societal nature of dams reveals the consequences of engineering design on living things. Thus, the study of the fracture of dams incorporates math and science as well as social studies, providing an opportunity to bridge the gap between the technical and non-technical subjects. Bridging this gap may help to attract more students to engineering and give students a more well-rounded view of engineering.

This chapter presents the background and review of the literature pertaining to engineering skills in the K-12 classroom and the subjects of fracture mechanics and dams. The introduction of engineering to K-12 is first reviewed. Fracture simulation and its applicability to concrete dams is discussed to establish the motivation for use of these subjects for a SimScience module. The fracture analysis program FRANC2D is described with respect to its incorporation in the module. The wide range of the impacts of dams is presented, showing the current nature of dam debates and the personal relevancy of these impacts. The use of case histories to describe applications of fracture mechanics to dams is reviewed. Finally, the fracture mechanics of dams is connected to K-12 curricula.

The Regents of the University of the State of New York published the Learning Standards for Mathematics, Science, and Technology (Regents, 1996). These standards address the need for integration of new ways to learn and integrate math, science and technology in K-12:

These standards explicitly recognize the importance of engineering design at pre-college levels. In itself, the introduction of engineering reaches many of the other standards, such as appropriate use of technology, use of mathematics and scientific theories, evaluation of solution alternatives, connection to ethics and history, and practical application of math, science, and technology. These standards provide substantial motivation for the development of a website on fracture and dams that incorporates so many aspects included in the standards.

A number of authors have addressed the introduction of engineering to K-12. Crawford et al (1994) found that teaching engineering design in elementary schools can provide a more profound understanding of math and science, attract a greater number of more diverse students to engineering, connect technical concepts to daily life, and develop teamwork skills. The earlier engineering is introduced to students, the more time and different ways students then have to think about engineering. In addition, an interdisciplinary introduction of engineering to young students helps make engineering a more appealing subject for university study for a larger, more diverse group of students. Basic engineering demonstrations and hands-on activities for K-5 help develop the building blocks of engineering skills (Wilson et al, 1995). "Engineering Concepts for High School Classrooms," an introductory engineering program for high schools, teaches critical thinking, communication, and teamwork; again, this program was found to improve understanding of math and science and their applications (Muller et al, 1995). Finally, McKenna and Agogino’s (1998) high school Introduction to Engineering class elicited positive feedback and high quality work from the students. The students were found to be highly motivated and able to learn the fundamentals of engineering problem solving. Successful introduction of engineering to K-12 classes by these researchers indicates that students are receptive to engineering concepts and could benefit from the Cracking Dams module.

Fracture mechanics, the study of crack initiation and propagation, is an interdisciplinary field currently dominated by computer simulation, making it an ideal module topic for SimScience. It is widely applicable to materials science, civil and environmental engineering, and mechanical and aerospace engineering. The strength approach to analyzing structures discounts any section that has become fractured. The use of fracture mechanics provides a viable and often more appropriate alternative to the strength approach in recreating a fracture event or predicting the damage tolerance of a structure. Fracture continues to be a problem in different type of structures; fractures have plagued the Boeing 737 (Reuters, 4/26/99) and the prototype of a new Japanese jet fighter (Associated Press, 6/6/99). Fracture of dams was aptly addressed at the Fifteenth International Congress on Large Dams (ICOLD) in 1985 under the heading, "Concrete dams, an old problem always present: cracking" and again at several International Conferences on Dam Fracture. The propagation of a crack in concrete can be quick and catastrophic as evidenced by the disastrous failures of dams like St. Francis Dam in California in 1928 and Malpasset Dam in France in 1959 (Angelton et al, no year; Leonards, 1985). Thus, analysis of the crack and attempts to remedy the situation must be swift.

Fracture mechanics finds many applications in numerical analysis and computer simulation. As a result of the 15^th ICOLD, concrete dams have often been the subjects of fracture simulation. The Cornell Fracture Group continues to develop FRANC2D and FRANC3D, fracture simulation software using finite element analysis in two and three dimensions. Development has even progressed to a version of two-dimensional fracture simulation for the web, making it available for student use.

Computer simulation of fracture in dams was one of the first applications of the finite element method; the Norfork Dam in Arkansas was the subject (Sims, 1964). Fracture analysis has been used to determine both the history of a fracture event and the prediction of crack growth. The Fontana and Kolnbrein dams, in North Carolina and Austria, respectively, were analyzed in two and three dimensions to determine possible causes of crack propagation. Both investigations provided reasonable results on probable fracture mechanisms (Chappell and Ingraffea, 1981; Lin, 1988; Linsbauer et al, 1989 (2)). Critical fracturing of the El Atazar dam in Spain was analyzed to determine possible effects on the structure (Martha et al, 1990, 1991).

Fracture mechanics may be linear elastic or non-linear elastic; linear fracture mechanics (LEFM) is the simpler of the two. LEFM is applied to structures with elasticity or slight inelasticity at the crack tip. Linsbauer (1990) looked at two characteristics of large concrete structures such as dams and determined that LEFM is applicable to large concrete dams. Linsbauer et al (1989) deemed LEFM applicable for the analysis of Kolnbrein Dam in Austria due to the small size of the process zone (area of inelasticity around the crack tip) relative to dam thickness and the large size of the crack relative to the aggregate size. Chappell and Ingraffea (1981) also used LEFM in their modeling of the Fontana Dam and they found reasonably accurate predictions of crack trajectory and stability.

Another issue in the modeling of the fracture of dams is the inclusion of water pressure in cracks on the upstream side of a dam. Experiments by Bruhwiler and Saouma (1995) showed that hydrostatic pressure inside a crack shortens the process zone size and decreases both K_Ic and G_F, but that the tensile strength is not affected (K_Ic is the fracture toughness, a measure of material resistance to cracking; G_F is the fracture energy, the amount of energy sufficient to overcome the resistance of the material to crack growth). This leads to the conclusion that a strength-based approach cannot account for the presence of water pressure, which may preclude its use in analyzing cracked structures which may experience such pressure. Bhattacharjee and Leger (1995) found the combination of reduced structural resistance and process zone size to lead to a brittle fracture of the upper block of the Koyna Dam (India) in a simulation. Linsbauer et al (1989) did note that water pressure was included in the cracks in their models of the Kolnbrein Dam (Austria). These examples demonstrate the recognized importance of including water pressure in the simulation of cracking in dams.

As shown in the literature, the fracture of dams may be simulated using linear elastic fracture mechanics due to the comparative sizes and nature of the fracture and the dam. Linear elastic simulation is considerably less complicated than non-linear analysis; thus, simulation of dams can be simple enough for beginners. Although additional simplifications must be made for the beginner, he or she can still get a good understanding of when to use a simulation, how to perform a simulation, and how to begin to understand the results.

The web version of FRANC2D, which is referred to as web-FRANC2D from here on, allows the user to do a linear-elastic fracture analysis using some of the tools of the original FRANC2D. The original FRANC2D was written by Dr. Paul Wawrzynek, as were most of the modifications to create the web version. Dr. Bruce Carter contributed to the fine-tuning of web-FRANC2D. The web version is limited in nature, providing the inexperienced user with several decisions to make about their simulation but not so many choices as to be overwhelming. The interface between the web-FRANC2D program and the World Wide Web, namely a Java applet and CGI-scripts, is discussed in Chapter Four.

Dams are unnoticed by many people most of the time, although they provide fundamental services everyday. It is not until a catastrophic failure that most people take notice of dams. There are groups of people who debate the other everyday problems of dams, present even when they are not failing, taking lives, or destroying property. A dam’s impact on society, ecologically and personally, demands analysis, both socially and scientifically, providing a solid connection between engineering and its effects on society. The controversy that surrounds both the construction and failure of dams remains a current topic that can motivate learning of fracture mechanics and social impacts of engineering. Thus fracture mechanics and dams are exciting topics for a SimScience module.

Construction, maintenance, repair, and analysis of dams occurs everyday; failures occur infrequently but devastatingly. There are 355 dams being constructed all over the world this year alone (International Journal on Hydropower & Dams World Atlas, 1999). In the United States, there are almost 75,000 dams that require monitoring, maintenance, and repairs (National Inventory of Dams, 1998-9). Of these dams, 2,737 produce hydroelectricity; 9,267 provide irrigation; 13,942 provide flood control; 8,907 provide water supply; 33,251 provide recreation; 14,735 provide fire protection (National Inventory of Dams, 1998-9). The large majority of the nation’s dams provide more than one service.

Privately owned hydroelectric dams are subject to renewal by the Federal Energy Regulatory Commission (FERC) every 30 to 50 years (Federal Energy Regulatory Commissions, 1999). More than 220 dams will come up for renewal in the next ten years. Renewal requires structural, economical, geological, social, and environmental analysis of each dam. For the first time in history, FERC denied renewal to a dam, the Edwards Dam on Maine’s Kennebec River, in 1998. The dam is being removed during the course of 1999 as a result (Adams, 1999).

The current importance of dams can also be seen in the number of organizations who are concerned with the safety of dams: United States Committee on Large Dams, International Commission on Large Dams, World Commission on Dams, and the Association of State Dam Safety Officials to name a few. Unfortunately, dams are still failing, although the number of failures has decreased significantly over the years. As recently as 1998, a dam that held back mining waste in Spain failed, releasing millions of gallons of water and waste. In 1995, Folsom dam in California failed when one of its gates collapsed. In 1976, Teton Dam in Idaho failed, killing 14 people.

The current nature of dams is apparent in continued computer simulations of dams. A need for analytical simulation of dams continues in the effort to maintain and repair dams, renew licenses, and avoid failure. USCOLD has just concluded the next iteration of reporting on the Numerical Analysis of dams in early June of 1999, proving that the computer simulation of dams continues to be a topic of pressing national interest (USCOLD, 1999). The 1985 report by the US Commission on Large Dams (USCOLD), detailing the analytical practices of dams by industry and government, shows that a majority of the analyses are done using computer simulations (Yeh, 1985). One-third of the report participants use the Finite Element method because it gives a more realistic stress distribution and more flexibility with regards to geometry and boundary conditions than other methods, such as the trial-load method. For two-dimensional analyses, half of the companies reported using plane stress and half plane strain. Most organizations reported that they include part of the foundation in their model. A fixed base and special base elements were also reported as being used.

Numbers of existing dams and dams to be constructed are significant. The design and maintenance of dams is well served by the efficient, cost-effective nature of computer simulation. As a result, the computer simulation of cracking in dams remains a necessity. This compelling nature of cracking in dams is conveyed to the student on the website.

3.3.2 Controversy over dams

Dams provide many services to people everyday, but they also impact the environment everyday. This creates controversy over dams, which keeps it a current topic in the news. Environmental and social organizations are fighting for the breach of dams such as the four Lower Snake River dams in the Western US and the Three Gorges Dam in China, which has not yet been completed.

Dams such as these are endangering species of wildlife, causing relocation of millions of people, inundating acres of historical artifacts, and imposing change on the lives of content people. Several species of salmonoids are endangered as a result of the dams on the Colorado and Snake Rivers. Several species of mollusks are endangered as a result of dams on the Ohio, Cumberland, and Tennessee rivers (Associated Press, 6/2/99). 78,000 people had to be relocated for the Volta Dam in Ghana; 120,000 for the Aswan High Dam in Egypt (Goldsmith and Hildyard, 1984). Often relocation of these peoples was unsuccessful: not enough land was available, families were split up, houses were too small, conflicting Indian tribes were placed together. Historical artifacts have been covered by the dam reservoirs on the Colorado river and the soon-to-be reservoir on the Yangtze river in China. These controversies are also communicated to the user in the module. The WebQuests for the module encourage students to consider these societal impacts as well as perform technical simulations of dams.

The relevance of fracture mechanics to concrete dams becomes apparent in the four case histories that are presented on the website: El Atazar, Fontana, Kolnbrein, and Malpasset dams. There is a long history of precedence for the use of case studies to learn about engineering in the professional and academic research world. The 1999 USCOLD Benchmark Workshop on Numerical Analysis of Dams focused on the case of the Schlegeis Dam in Austria to discuss problems with arch dams (USCOLD, 1999). In fact, most published conference proceedings are, in essence, a compilation of cases, meant to teach researchers and professionals about problems and solutions in their fields. Numerous researchers have championed the use of case studies and case-based reasoning to teach engineering both at the K-12 and university level (Billington and Mark, 1983; Fitzgerald, 1995; Hsi and Agogino, 1994; Jarz et al, 1997; Petroski, 1994; Sansalone, 1990; Valenzuela, 1993; Vesper, 1964). Students can benefit from this technique as much as researchers or professionals.

In general, case histories provide a full view of what actually happened; this serves to motivate students by presenting problems that really needed to be solved (Vesper, 1964). In Cracking Dams’ Case Histories, the engineering thought process from the realization of a crack in the dam through the iterative remedy process to the current status of the dam is revealed. Tabak (1997) notes that case-based learning makes an expert’s implicit strategies explicit for learners. There is no glorification of engineering, and if the solution that was implemented did not work, let students learn from that. This is also a chance for the user to see what an engineer might do on a daily basis, analytically, experimentally, or in the field. All in all, one of the most important things in engineering is developing an intuition and what better way is there to do this than studying the past. An applied understanding of engineering is developed with case-based reasoning. The histories exhibit the use of engineering skills (teamwork, iterative design, and problem solving) and computer simulation to resolve the fracture issues in each case.

3.4.1 On El Atazar Dam, Spain

Although not very much is known about this case history, it has some important points to make. El Atazar Dam was constructed in Spain beginning in 1968. This doubly curved concrete arch dam could provide hydroelectric power, but authorities have chosen to use it only for the regulation of water supply to Madrid and its province (Urbistondo and Yges, 1985). This decision reflects a weighing of options by the engineers; it was more important to supply water than provide power.

During the filling of the reservoir, it was noticed that the left bank blocks were moving slightly more than the right bank blocks (Urbistondo and Yges, 1985). Movement was due to thermal and hydrostatic head variations. The left abutment was a hillside, more deformable than the abutment on the right side, leading to the asymmetric movement. After study of data on the dam, engineers decided to build a support, which lessened the movement. But this movement in the dam lead to both cracking in the dam and in the foundation.

A crack was found in one of the most dangerous parts for a crack to be in an arch dam – at the center of the upstream side near the foundation (Martha et al, 1990). Some Spanish authorities decided outside consultation on El Atazar’s crack was necessary; analyses of the dam with FRANC3D were performed at Cornell in 1990. Three-dimensional analysis requires powerful graphics interface and numerical tools to simulate fracture; FRANC3D accomplished this. El Atazar was one of the first applications of three-dimensional fracture analysis.

Just before the analyses were being performed, the dam made the front page headline of a Spanish newspaper – the dam is not cracked (No author, 1985). A Spanish politician up for reelection did not want to be associated with the stigma of acracked dam under his authority and so ordered the news story. Thus the public was led to believe their source of drinking water, irrigation, and flood control was functioning flawlessly in order to get a politician reelected.

The crack grew significantly following heavy rains. The movement of the dam fractured the foundation. The extent of the known current status of the dam is that the crack was repaired in 1979 and the foundation was to be reconsolidated (Urbistondo and Yges, 1985).

This case history is a testament to a dam as a societal structure – one with enough power to get an official reelected. It also serves to show that the Spanish engineers were able to look above the politics and consult on the future of the crack – and avoid endangering people’s lives. Technically, the three-dimensional study of El Atazar revealed the need for further development of three-dimensional fracture mechanics for arch dams (Martha et al, 1991). The El Atazar case history exemplifies the social and political importance of a dam and the responsibility the engineers took to place the society’s safety first.

The Fontana case history is comprised of numerous examples of deductive reasoning, teamwork, iterative design, use of computer analyses, and engineering decision making. Construction on the Fontana Dam in North Carolina began in 1942. The Tennessee Valley Authority (TVA), the owners of the dam, saw first traces of cracking in 1949 and then pronounced cracking in 1972. Deductive reasoning and teamwork lead them to develop two hypotheses for the cracking. Computer simulations of the dam’s behavior were performed and compared to data from monitoring of the dam to determine validity of the results. The TVA was then able to decide the cause of cracking. Next they needed to design a remedy, certainly an iterative process. Having determined not one, but three causes of cracking, a combination of remedies was necessary. Of the four case histories, Fontana’s combination of causes of cracking is unique.

As part of the most powerful hydro station in Austria, the Kolnbrein Dam has a huge societal impact (Geologe et al, 1991). Kolnbrein Dam construction began in 1973. The case history of this dam evidences this impact as well as deductive reasoning, iterative design, teamwork, use of computer simulation, and engineering decision-making. The dam site chosen for Kolnbrein Dam was U-shaped, instead of the traditional V-shape for arch dams; it has been determined that this decision lead to cracking (Baustadter and Widmann, 1985). The reservoir was partially filled at two different times. The first time, in 1978, the structure initially acted normally. At the second partial filling in 1979, increases in uplift and joint water pressures were noticed; engineers attempted to remedy this with additional drainage. But this was not sufficient to enable the dam to hold a full reservoir.

Deemed necessary to improve the tourist area and provide drinking water and irrigation supply, the construction of Malpasset Dam was anxiously anticipated but devastatingly received (Dargeou, 1955). The story begins with the engineering decision to build the dam at the site called Malpasset in 1955 although unsuitabilities of the site were noted (Goldsmith and Hildyard, 1984). This case history ends in tragedy, the failure of the dam in 1959, killing possibly 500 people. In addition to this terrifying societal impact, the history also displays the ability of engineers to learn from the failure. With foresight the engineers at Fontana did not have, the Malpasset engineers tested for the possibility of the chemical reaction which affected the concrete in the Fontana dam; this was not a potential problem in Malpasset dam. Five years of monitoring of the site’s geology prior to construction of the dam showed it to be a favorable site for a thin doubly curved arch dam (Dargeou, 1955). Cracking was seen near the toe of the dam just a few weeks before failure, but it was not investigated. Failure was sudden and catastrophic, the dam opening like a gate to release a torrent of water and then a large part of itself.

Experts are still in disagreement as to the initial cause of the failure but are certain the geology of the foundation played a large part (Leonards, 1985). Being the first dam of its type to have failed, Malpasset proves that no dam type should be assumed to be 100% reliable. Numerous other lessons were learned; some good did come of the tragedy. Three-dimensional computer stability analyses were developed to study the cause of the failure; these types of analyses are now used to design new arches under new standards. The emergence of testing the foundation for different traits and the development of rock mechanics also resulted. The importance of safety monitoring was realized; could failure have been avoided if the cracking had been investigated?

Malpasset dam was not rebuilt; its remains standing as a remembrance of the devastating social impact of this dam. The case history proves that sometimes problems cannot be forseen even with five years of monitoring and that there are many lessons to be learned from a tragedy.

Each of these cases is detailed at the three levels of complexity in the module. From the cases the user can see that the initial design for a solution to cracking in the dams is not perfect; iterative design is required. Students also see the teamwork and problem solving involved in each case as well as the use of simulation. The section of the website detailing these stories provides a source for case-based reasoning by the students, particularly encouraged in the Advanced level WebQuest. The precedence for using case-based reasoning, especially in engineering, is very strong.

Engineering applications to the curriculum appear even in K-4. Simple concepts of evidence, models, and explanation; properties of materials; and shapes and sizes are introduced at this level (National Research Council, 1996). Mathematics attention in K-4 ranges from measuring to pattern recognition, use of computers to estimation; decreased emphasis is being placed on rote memorization and simplified word problems (Vos, 1996). Fracture and dams provide a vehicle for learning about shapes and sizes as well as models and computer use in engineering.

Energy, forces, motion, and work, all important factors of fracture mechanics, are first introduced as early as middle school science classes (Regents, 1992). Connections between mathematics (and other subjects) and the outside world become an emphasis in grades 5-8 (Vos, 1996). A Perspective on Reform in Mathematics and Science Education, by the National Council of Teachers of Mathematics, suggest that open-ended problems should be addressed by students at this level as well (Vos, 1996). Algebra is introduced in terms of variables, expressions, and equations. Simple concepts introduced in K-4 are built on in grades 5-8 to describe weight, density, area, forces, and so on. These science and math skills are applied in the description of dams and simple fracture equations.

Trigonometry, physics, and calculus provide 9^th -12^th graders with further tools to determine pressures, more complex geometries, and free body diagrams. Even chemistry has a connection to dams in the creation of concrete – a chemical reaction; incompatibilities in concrete components lead to further chemical reactions that cause cracking in dams. High school math and science subjects become the building blocks for college-level engineering subjects. Seeing applications of math and science to engineering during high school may provide more motivation to learn these subjects and draw more students to the field of engineering.

Motivation is also provided by the non-technical connections to math and science that are seen in the study of dams. The study of dams reveals the impacts of engineered structures on the environment, the land and animals, and the people.

This chapter has reviewed research in the areas of fracture mechanics and its applications to dams. The subjects are for a SimScience module due to their extensive use of computer simulation and their controversial nature. Computer simulation of fracture is a major part of the module and it provides an opportunity for critical thinking and a hands-on experience. The controversial nature of dams provides motivation for students to learn about dams. Some background on both fracture and dams provides a more complete understanding of both of these subjects in the module. Four case histories of fractured dams were presented as examples that are included in the module; they provide a historical basis from which students can learn about real-world applications of fracture mechanics to dams. Finally, the introduction of engineering to K-12 was reviewed. Several studies have indicated that K-12 students are receptive to engineering concepts. In particular, there are numerous connections between the existing curricula and fracture mechanics and dams, making the introduction of these engineering topics to K-12 easier.