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San José State University
Department of Economics |
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applet-magic.com Thayer Watkins Silicon Valley & Tornado Alley USA |
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in China in August 1975 |
Civil engineers when designing a dam must establish the capacity of the dam and the rate at which water can be passed through the dam by means of flood gates. Flood gates are an expensive component of a dam's construction so engineers must consider a trade-off between the cost of the dam and the security it will provide.
The dam design determines the probability that a storm will cause the dam to overflow and possibly destroy the structure. If this probability is 0.01 then the dam is said to be able to handle any thing up to a 100 year flood; i.e., a flood that occurs on average once in a hundred years. This terminology is misleading because it implies that severe storm occurrences are independent random events whereas this is not the case. The random events may be the weather conditions. The weather conditions that produces one severe storm may persist and produce another severe storm not long afterwards. Hurricanes and other tropical cyclones tend to be spawned in sets so one severe hurricane may be followed by others in a short period of time.
The policy of operation for the dam is a factor in determining the probability of catastrophic failure. If a dam is held empty it has the greatest capacity for control of severe floods. But such a policy would destroy the usefulness of the dam for storing water for providing irrigation water. And if the dam reservoir is being kept empty then the small flood are not being controlled. On the other hand if the dam does not retain some unutilized capacity it will be useless for controlling flood dangers. The dam authorities must decide the proper excess capacity to maintain based on the trade-off they see between the value of stored water versus the value of flood control. Note that in the matter of using dams for flood control it is a question of reducing the cost of small floods at the expense of increasing the damage from the floods which bring about the catastrophic failure of the dam because the water stored behind the dam will be added virtually instantly to the flood. The failure of one dam will quite likely lead to the failure of other dams down stream. The effect will be cumulative.
Some simple algebra shows the nature of the problem. Let the storage capacity of a dam be C and let G be the rate at which water can be passed through the dam based upon the number and size of the flood gates built into the dam. Let the unutilized capacity of the dam be E and the normal stored water be A. Thus A+E=C. A storm may be characterized by the magnitude of the flow at the dam site F and the duration of the flow D.
The rate at which the dam fills up is given (F-G). The time it takes the flood to fill up the unutilized capacity is E/(F-G). If this is greater than the duration of the storm then the flood is contained but if E/(F-G)<D then there is a catastrophic failure. The flood flow down stream jumps suddenly from G to (F + C/T) where T is the length of time it takes for the failed dam to empty. The dam authorities have to consider the effect of design and operating policy choices on an objective function of the form
where f(A) is the value of having stored water of amount A, is the probability of a dam failure and is the downstream cost of the failure. The probability of a dam failure is a matter of the probability of the combination of F and D and .
China has been plagued with severe floods from time immemorial. The area where the weather systems from the north (from North Central Asia) meet the weather systems from the south (from the South China Sea) is particularly hard hit. This is the region of the Huai River. In 1950, shortly after an episode of severe flooding in Huai River Basin, the government of the People's Republic of China announced a long term program to control Huai River system. It was called, "Harness the Huai River." The name captured the dual purpose of the program: 1. to control the river and prevent flooding, 2. utilize the water captured for irrigation and to generate electricity.
Under this program there were built two major dams, the Banqiao Dam on the Ru River and Shimantan Dam on the Hong River. The Ru and Hong Rivers are not tributaries of the Huai River but are part of the same river system as the Huai River; i.e., the Huang He (Yellow River) system. There were numerous smaller dams built as well.
The Bangiao Dam was originally designed to pass about 1742 cubic meters of water per second through sluice gates and a spillway. The capacity storage capacity was set at 492 million cubic meters with 375 million cubic meters of this capacity reserved for flood storage. The height of the dam was at little over 116 meters.
There were some flaws in the design and construction of Banqiao Dam, including cracks in the dam and sluice gates. With advice provided by Soviet engineers the Banqiao Dam and the Shimantan Dam were reinforced and expanded. The Soviet design was called an iron dam, a dam that could not be broken.
The pass-through of the Banqiao Dam was to protect against a 1000 year flood, which was estimated to be one from a storm that would drop 0.53 meters of rain over a three day period. The Shimantan Dam was to protect against a 500 year flood, one from a storm that drops 0.48 meters of rain over a three day period.
The Shimantan Dam had a capacity of 94.4 million cubic meters with 70.4 million cubic meters for flood storage.
Once the Banqiao and Shimantan Dams were completed many, many smaller dams were built. Initially the smaller dams were built in the mountains, but in 1958 Vice Premier Tan Zhenlin decreed that the dam building should be extended into the plains of China. The Vice Premier also asserted that primacy should be given to water accumulation for irrigation. A hydrologist named Chen Xing objected to this policy on the basis that it would lead to water logging and alkalinization of farm land due to a high water table produced by the dams. Not only were the warnings of Chen Xing ignored but political officials changed his design for the largest reservoir on the plains. Chen Xing, on the basis of his expertise as a hydrologist, recommended twelve sluice gates but this was reduced to five by critics who said Chen was being too conservative. There were other projects where the number of sluice gates was arbitrarily reduced significantly. Chen Xing was sent to Xinyang.
When problems with the water system developed in 1961 a new Party official in Henan brought Chen Xing back to help solve the problems. But Chen Xing criticized elements of the Great Leap Forward and was purged as a "right-wing opportunist."
At the beginning of August in 1975 an unusual weather pattern led to a typhoon (Pacific hurricane, the name is based up the Chinese words for big wind, da feng) passing through Fujian Province on the coast of South China continuing north to Henan Province, (the name means "South of the (Yellow) River.") The rain storm that occurred when the warm, humid air of the typhoon met the cooler air of the north. This led to a set of storms which dropped a meter of water in three days. The first storm, on August 5 dropped 0.448 meters. This alone was 40 percent greater than the previous record. But this record-busting storm was followed by a second downpour on August 6 that lasted 16 hours. On August 7 the third downpour lasted 13 hours. Remember the Banqiao and Shimantan Dams were designed handle a maximum of about 0.5 meters over a three day period.
By August 8 the Banqiao and Shimantan Dam reservoirs had filled to capacity because the runoff so far exceeded the rate at which water could be expelled through their sluice gates. Shortly after midnight (12:30 AM) the water in the Shimantan Dam reservoir on the Hong River rose 40 centimeters above the crest of the dam and the dam collapsed. The reservoir emptied its 120 million cubic meters of water within five hours.
About a half hour later, shortly after 1 AM, the Banqiao Dam on the Ru River was crested. Some brave souls worked in waist-deep water amidst the thunderstorm trying to save the embankment. As the dam began to disintegrate one of these brave souls, an older woman, shouted "Chu Jiaozi" (The river dragon has come!)
The crumbling of the dam created a moving wall of water 6 meters high and 12 kilometers wide. Behind this moving wall of water was 600 million cubic meters of more water.
Altogether 62 dams broke. Downstream the dikes and flood diversion projects could not resist such a deluge. They broke as well and the flood spread over more than a million hectares (2.5 million acres) of farm land throughout 29 counties and municipalities. One can imagine the terrible predicament of the city of Huaibin where the waters from the Hong and Ru Rivers came together. Eleven million people throughout the region were severely affected. Over 85 thousand died as a result of the dam failures. There was little or no time for warnings. The wall of water was traveling at about 50 kilometers per hour or about 14 meters per second. The authorities were hampered by the fact that telephone communication was knocked out almost immediately and that they did not expect any of the "iron dams" to fail.
People in the flooded areas who survived had to face an equally harrowing ordeal. They were trapped and without food for many days. Many were sick from the contaminated water.
The hydrologist Chen Xing, who had criticized the dam-building program, was rehabilitated and taken with the high Party officials on an aerial tour of the devastated area. Chen was sent to Beijing to urge the use of explosives to clear channels for the flood waters to drain.
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