This is an edited excerpt from Rex’s Memoirs. I will be adding more of these through time, starting with some related to his work.
One of My Formative and Favorite Projects
Fontana dam was a 487-ft. high structure built in a very narrow deeply incised gorge. Since it was a World War II project, completion in the minimum possible time was a high priority. To achieve this two by-pass tunnels were blasted through the left bank to allow the river water to bypass the actual dam site and the construction area to be completely dewatered. These tunnels could them be used for the lower portions of the final spillway system. At the correct point in the construction schedule, the entrance to each tunnel was concreted shut, and 45 degree inclined tunnels were drilled to the mountain surface. A spillway entrance structure equipped with two radial [tainter] gates was built on each tunnel. Since tunnel costs are high, it was essential that the tunnel cross-section be kept as small as possible. To accommodate the larger gates, a much wider structure than the main tunnel was required, dictating a funnel shape be designed to connect the tunnel segments.
Just prior to the construction of Fontana Dam, the Hoover Dam spillway tunnels had developed major erosion during their first use. The cause of the problem was in much dispute. We believed that cavitation was the cause, and since cavitation was only partially understood at that time, we spent much time researching it, and how it might affect the very similar proposed Fontana tunnel spillways.
Cavitation is now well understood to be a condition that occurs when the pressure within a liquid is reduced to the point that the liquid at the point of the low pressure turns to gas. This event is harmful if the gas bubble or cavity, as it is termed, enters a region of higher pressure, where it collapses rapidly in the form of an implosion. The collapse is so rapid that it generates a local pinpoint pressure in excess of 250,000 pounds per square inch (psi). If multiple bubbles form and collapse next to a solid surface, it is the same as subjecting that surface to multiple pinpoint 250,000 psi blows. The hardest materials cannot stand up to this and concrete can be damaged quite quickly. Any offset or even a fairly slight curvature of a conduit wall can cause cavitation if the velocity of the fluid is fairly high.
Dr. George Harold Hickox, the Director of the TVA Hydraulics lab at the time, assigned me the day by day spillway studies for the Fontana spillway tunnels. This was the start to my career of researching poorly understood hydraulic problems.
It was the consensus of all involved with the tunnel designs, that at the highest flows, the tunnels should not flow full. There are always unpredictable and usually undesirable flow problems during the shift from partial to full flow in a pipe system. To ensure that full flow would not occur, entrance flow conditions needed to be developed that prevented standing or traveling waves from filling the tunnels. We also knew the water velocity inside the main tunnels would be high enough to produce cavitation if the surfaces were incorrectly shaped. To assist in design development, we constructed a 1:51 scale model. (The 51 scale was chosen since we could buy standard Plexiglas pipe of a diameter that produced this scale for the proposed 32-foot diameter tunnel.) One of the lead engineers, Sim Cox, in the Knoxville Civil Design group, developed the 1st layout and sent it to the Lab. I was given this design to model and on laying it out, I found it could not be built the way he had designed it. But with relative minor modifications, the new Elder/Cox design achieved the desired flow capacity without having to increase the tunnel cross-section. Al Peterka and I were the lead engineers for this model.
The first task I was assigned was to get velocity estimates for various reaches of the tunnel and the outlets. We had no computers and this was an iterative type calculation, i.e. you estimated both the coefficients involved in the computation for a stretch of tunnel and obtained an answer, and then back calculated to see if the known variables would give that answer. If they did not give the answer you estimated a new answer. You kept at this until you made the calculated and estimated answer agree. It was figuratively, a back breaking job not only because of the sheer number of calculations required, but also because at that time we had very poor information on the resistance values for large diameter concrete pipes. In fact, I probably spent more time researching the resistance values than the actual calculations. The final computations indicated that the velocity would be about 100 miles per hour (145 ft/sec) at the bottom of the 45 degree inclined sections and 70-mph (105 ft/sec) at the outlet. These velocities were definitely much higher than those needed to cause cavitation.
The photographs that we had of the area around the Hoover tunnel damage indicated a hump in the tunnel lining just above the damaged area. Since the heads at Hoover Dam were higher than those calculated for Fontana, our study plus the Hoover photos convinced us that cavitation was the cause of the Hoover damage. Furthermore, we were convinced that the high velocities expected in the Fontana tunnels required that the tunnel linings be carefully designed and, just as importantly, carefully constructed. We convinced Oren Reed, the Construction Engineer that the tunnel lining had to be built as perfectly as was possible.
Dr. Hickox and I developed a series of tests that gave us the probable critical velocity above which cavitation would occur at humps or depressions of various sizes. Carefully developed tests in later years showed our values to be conservative but not greatly so. We used these values as criteria for the allowable deviations and changes in alignment. During most of the tunnel lining construction I was the inspector and made almost weekly trips to overview the construction. We also convinced Oren to use high strength concrete and to be very careful with the wall alignment. As a result the two spillway tunnels have operated for thousands of hours with minimal damage.
The shaping of the outlets of these tunnels was another project turned over to me. By that time I had an estimate of the velocity at the outlets. With velocities of 70-mph at the outlet we obviously needed to protect the riverbed below the outlets. After considering various designs, we decided on what was then called a “ski jump” outlet. This is normally a structure with a curved bottom that throws the water into the air. It is a viable option if the downstream rock is relatively hard and if there are no structures or lands in the area that will be eroded by the falling water. At Fontana we felt this was the case, but if we allowed the water to be thrown directly downstream it would set up a strong clockwise eddy that could erode the right bank. Also, the water landing in the riverbed would eroded the bottom and form a bar downstream. We wanted to minimize the amount of erosion since the bar would need to be excavated to maintain the maximum head available for the turbines.
A 1:100 scale model was decided upon to develop a design. I was assigned model design and operation. My objective was to develop “ski jump” shapes that would prevent the eddy from forming, at all possible discharges, and that would minimize the amount of river bed and bank erosion. An erodible sand bed was placed immediately downstream from the powerhouse and the tunnel outlets. This was molded to the shape of the proposed final river bed and bank lines. I then started carving blocks of plaster-of-paris into various shapes in an attempt to find a shape that would create the desired erosion pattern. Only a few modifications could be made to a given plaster block before too much material was removed and the resulting erosion pattern was unacceptable. It was easier to start with a new block than to try to build up an existing one. I kept notes on the performance of each block, and after 46 tries I developed the two required outlet shapes. (My only try at sculpture!) Since the tunnels were 100 feet apart, the shape of the right hand outlet had to be drastically different from the left hand one. The left-hand outlet had to throw water in sort of left hand direction all the way to the right bank, while limiting the flow on the left to the edge of the left bank. The right-hand outlet had to expand the throw in both directions but not as much left as right.