APPLICATIONS OF OVERTOPPING RISK ANALYSIS FOR THE EARTH DAM OF FLOOD CONTROL RESERVOIR

Beijing Postgraduates School, North China Inst. of Water Resources & Hydropower,

Abstract: It should be ensured that the dam is safe during flood period. Among the dam failures around the world, the failures of earth dam are in the majority, whereas the majority of earth dam failures are initiated from overtopping and thereby dam break. The research on applying overtopping risk analysis technique to the safety evaluation against overtopping and increasing the benefits of flood-control reservoirs is described in this paper. Considering thoroughly the uncertainties of flood, wind, reservoir storage and discharge capacity, the authors developed the theory of overtopping risk against the design series of flood and wind simultaneously. A risk criterion or an acceptable risk of overtopping was also recommended by the authors. In the paper, particular emphasis was paid on the applications of the overtopping risk theory to Douhe Reservoir, Qinghe Reservoir, Yuecheng Reservoir and Zhuzhuang Reservoir as well as the increasing of their economic benefits as the meanwhile the dams are safe during flood with their reliability against overtopping of 99.999% or more. Wide spread of the technique of overtopping risk analysis will bring us remarkable economic and social benefits.

1 INTRODUCTION

Along with the development of industry and agriculture as well as the growth of population, the deficit in water resources has increasingly arisen in some regions, particularly the North China, and it will restrict the further development of economy if the problem be not solved properly. On the other hand, the annual distribution of rainfall is very non-uniform, such as in North China the rainfall is concentrated in July, August and September. Therefore, the problem of flood control is serious. It is traditional practice that the reservoir level, during flood period, should be limited to such a specified elevation that the actual water level in the reservoir before the next flood coming into the reservoir is equal to or lower than the specified one. So the specified elevation is defined as “limiting reservoir level before coming flood” or simply “limiting level before flood”(LLBF). The limiting level before flood is frequently set at such a lower elevation that the water stored in the reservoir after flood period did not reach the normal high-water level or only a small volume of water is stored, which means the reservoir did not do what it should do, although the dam did be safe surely. So, if we can solve the contradictory between dam safety and reservoir storage benefits, the reservoir will make its most of water conservancy works and the water resources in a river basin will be utilized more fully to support the economic development, which is an important subject confronting the hydraulic scientists. Among the dam failures around the world, the failures of earth dam are in the majority, whereas the majority of earth dam failures are initiated from overtopping and thereby dam break. In view of the facts mentioned above, considering thoroughly the uncertainties of flood, wind, reservoir storage volume and discharge capacity, the authors developed the theory of overtopping risk against the design series of flood and wind simultaneously^[1][3~9]. A risk criterion or an acceptable risk of the order of magnitude of

is also recommended by the authors^[1][3~9]. So the safety evaluations against overtopping for small and intermediate-scale reservoir may be made on the basis of established theory of overtopping risk and a reliability against overtopping taken as 99.999% or more. As for the large reservoir, the possibility of raising the limiting level before flood specified by designer in order to increase the storage benefits may be investigated during the safety evaluation process by means of overtopping risk analysis. In this paper, particular emphasis was paid on the applications of the overtopping risk theory to Douhe Reservoir, Qinghe Reservoir, Yuecheng Reservoir and Zhuzhuang Reservoir, which will show us the remarkable economic benefits from these applications. It is expected that all of these applications, as earlier practices, will be beneficial to the lay down of reliability standards and specifications for hydraulic engineering.

2 UNCERTAINTIES[1]

For earth dams the overtopping is strictly forbade unless it is previously permitted during designing. Once overtopping of earth dam occurs, the dam should be considered as beginning of dam break which may result in a catastrophe. For a reservoir already constructed, there are four factors, i.e. flood, wind, reservoir storage volume and discharge capacity, are the main sources of uncertainty^[1]. They are discussed individually as follows:

2.1 Inflow flood

Inflow flood, either the design one or forecasted or measured one, is considered in the traditional reservoir design as a random process. For the design flood, its uncertainties are initiated from the stochastic characteristics of the statistics of historical hydrological data(storm rainfall, peak flow of flood, etc.), of typical flood hydrograph, of loss of rainfall, and of unit hydrograph. For the forecasted flood, its uncertainties are initiated from the stochastic characteristics of the rainfall distribution in both space and time, and of the forecast model used and parameter values taken. For the measured flood, its uncertainties are initiated from its stochastic characteristics of measuring in space and time, and of the measuring errors.

2.2 Discharge capacity

In the reservoir design, it is traditionally to consider the discharge capacity as a deterministic quantity, but strictly speaking, it is a random quantity whose uncertainties are initiated from many sources, such as the schematization of 3D flow to 1D flow, the value of roughness coefficient, the scale effect of model test and various tolerance in geometrical sizes during construction. All of these uncertainties that influence the discharge capacity are treated by taking the discharge coefficients of both spillway and outlet works as random variables with limited variation respectively.

2.3 Reservoir area and storage volume

Although the reservoir area and storage volume were traditionally considered as deterministic quantities, they are actually random variables. The contour lines plotted by different surveyors for a given reservoir topography may be different. With the same contours, the calculated reservoir area and storage volume at a given level may be different due to variety of computation philosophy and the instruments used. Moreover, the sediment transportation during and after flood may change the underwater topography and thereby the reservoir area and storage volume unless the underwater contours be surveyed after each flood immediately, whereas the finance and manpower may restrict to do so.

2.4 Wind

It is well known also that wind of any magnitude from any direction is a random event too. As for the overtopping risk of an earth dam, the wind toward the dam during flood period is major concern and is defined as “effective wind for overtopping” by us. Strictly speaking, the statistics of wind series should take the data of wind corresponding each flood. Unfortunately, such data is difficult to obtain in present time, and therefore we take the series data of maximum wind during flood period, which will bring the results of risk analysis on the safe side. Therefore, the effective wind series used in the overtopping risk analysis for earth dam should be the series of maximum wind toward the dam during flood period.

3 OVERTOPPING RISK MODEL

3.1 Definition of overtopping risk

Overtopping refers the case that reservoir water level rises above the top elevation,

, of the dam or the parapet and overflow occurs. Let

be the initial water level in reservoir. Then, the condition that overtopping occurs is

, where

is water rise up caused by overtopping load L while L is time dependent and is also a random variable. So,

expresses as a random process

. Overtopping risk

is the probability of reservoir water level over the top elevation of the dam or the parapet during the specific period T for analysis, and may be expressed as

It can be seen from equation(1) that the key problem for risk computation is to study the stochastic characteristics of

is a periodic random process with a period of C (such as annual hydrological cycle), the risk within time interval T may be derived from that during only one period C as follows:

As mentioned above,

is a period random process with a period of one year and the risk within time interval T may be derived from that during one year, and therefore the study of annual overtopping risk becomes the basic of research on overtopping risk.

Engineering practices demonstrate that a common flood or gentle breeze along with tiny rain, can not cause an overtopping event but only serious load can. It was used to simplify the load series

as a series of annual maximum random events

and when it is multiple loads take it as the sum of individual series of each maximum random load. The above simplification brings obviously some approximations, but it is simple and practical while the approximations make the results of risk analysis both with satisfactory accuracy and on the safe side. Therefore, the simplification of

may be done assuredly. It should be noted that among the factors influencing the reservoir water level, the limiting level before flood and reservoir regulation are also important and they introduce an artificial subjective randomness which is not periodic. Therefore, it is necessary to divide

into two parts, one is

which is water level rise caused by reservoir regulation and water level before flood, and the other is

which is water level rise caused by the periodic random process itself. We shall take this model of division in our study.

3.2 Overtopping risk model for single inflow flood

For single inflow flood, the key problem in overtopping risk is to determine

in equation (1), which may be solved by reservoir routing. Now, the routing process is a random process and both storage volume

and reservoir water level

are Markov processes and independently increasing processes. Then, the stochastic differential equation of reservoir routing may be expressed as follow:

where

is the mean value of reservoir water level,

is the initial condition of

is reservoir water level before flood,

is flood process,

is the mean value of outflow discharge which is a function of reservoir water level

and hydraulic parameter C expressing the effect of the type and size as well as discharge coefficient of the spillway and outlet works,

is the mean value of reservoir area and

is Wiener process with a standard error

as follows:

where

is the random variable of storage volume,

is probability density of storage volume itself,

is the random variable of storage volume caused by the randomness of inflow and outflow processes, and

is probability density of

It can be proven that equation (3) satisfies Lipschitz condition and the transfer probability density satisfies Forkker-Planck equation.

Solution of above equations gave us the sum of mean value and standard error of reservoir level,

, and then the overtopping risk for single inflow flood may be determined as

3.3 Overtopping risk model against the simultaneous actions of annual maximum flood series and effective wind series

As mentioned previously, we should take the effective wind series, i.e. series of maximum wind toward the dam during flood period. The wind causes setup,

, of reservoir water level and wave runup,

, along the upstream slope of the earth dam. Both

and

can be computed with the formulas in literatures, such as [2]. It should be noted that wind causes a series of random wave, and wave heights follow Rayleigh distribution. As for wave runup on the dam slope, they follow also Rayleigh distribution because the coefficient of correlation between wave runup and wave height is 1. On the other hand, the probability distribution of maximum wind velocity during a time interval is extreme type Ⅰ distribution. Therefore, the runup caused by effective wind series is composite random variable, and its distribution function

may be expressed as follow:

where

is probability density of maximum wind during flood period, and

is probability density of runup under certain wind velocity.

When the overtopping risk against flood and wind actions simultaneously is discussed, it should be noted that the

in risk formula

is composed of two parts, one is

due to flood, and the other is

due to wind, and they are random processes. We should take

, but

may not concurred with

and

. This difficulty may be solved by taking simply

, which simplifies the computation and makes the results on the safe side.

Therefore, the total overtopping risk against flood and wind series simultaneously is given by

where

is the probability of occurrence of flood peak

within interval

is the probability of occurrence of wind velocity within interval

, and

is the probability of overtopping under these two conditions.

4 OVERTOPPING RISK CRITERION

Based on the investigations on the data of dam overtopping and dam break around the world, it was concluded that the probability of overtopping for earth dam is

per year per dam. Once overtopping and dam break occur, their consequences are very serious and therefore we should take overtopping risk of the order of magnitude

as an acceptable risk. Before the publication of national standard, we use

as a risk criterion temporarily.

According to equation (3), when

is taken as an acceptable risk, the safety reliability of the dam against simultaneous actions of flood and wind series is 99.999% and it is believed that with such a reliability, there exists sufficient sense of security for any decision maker.

5 ENGINEERING APPLICATIONS

The successful applications for Douhe, Qinghe, Yuecheng and Zhuzhuang Reservoirs are summarized in Table 1. The results of risk

and

under two critical modes are shown in Table 1 respectively. The first mode is taking the dam crest elevation as critical without consideration of runup

while the second mode taking the parapet top elevation as critical with consideration of

Reservoir Name	Douhe	Qinghe	Yuecheng	Zhuzhuang
Type of main dam	Earth	Earth	Earth	Masonry-Concrete
Max. height of dam(m)	25	39.6	55.5	95
Total volume of water storage( )
Dam crest elev.(m)	44	138.1	159.5	261.5
Parapet top elev.(m)	45.3	139.25	161.3	262.7
Frequency of design flood	0.1%	0.1%	0.1%	1%
Frequency of extreme flood	PMF	0.01%	0.01%	0.05%
Existence of auxiliary dam	yes	no	yes	no
Spillway and outlet works	spillway & sluice	spillway & tunnel	spillway & tunnel	spillway & outlet
Limited Level Before Flood(LLBF) designed and corresponding overtopping risk
LLBF suggested and corresponding overtopping risk
Safety reliability for overtopping under suggested LLBF	>99.9999%	>99.999%	>99.999%	>99.999%
Increase of LLBF and corresponding increment of water storage
Organization responsible for appraisal	Water Resources Dept., Hebei Province, PRC	Water Resources Dept., Liaoning Province, PRC	Haihe Water Conservancy Commission, PRC	Water Resources Dept., Hebei Province, PRC
Approval and implementation	approved and implemented	approved and implemented	not implemented until 1999, due to the reinforcing and rehabilitation of auxiliary dam being undergone	approved and implemented
Remarks		(1)		(2)

(1) A final alternative for simultaneous regulation of Qinghe with other 3 reservoirs was optimized and then analyzed.
(2) For the masonry-concrete type of dam, no worry about overtopping, but only for increasing the water storage.

6 CONCLUSIONS

Considering thoroughly the uncertainties of flood, wind, reservoir volume and discharge capacity, the overtopping risk theory has been established and applied successfully to several large reservoirs in China. Safety reliabilities against overtopping for all of these dams have been evaluated and pertinent suggestion about reservoir regulation for each reservoir has been presented, which ensures the dam be safely against flood for flood control while make the storage of water as much as possible in order to raise the reservoir benefits and utilize the valuable water resources sufficiently. This is important for the region of water defecit, particularly for the North China.

The increment of water storage to be got with overtopping risk analysis may be seen from engineering applications summarized in Table 1. It can be concluded that the overtopping risk analysis is a valuable non-structural measure for flood control.

As for the small and intermediate-scale reservoir, their safety evaluations may be made through overtopping risk analysis and then some scientific basis for the better regulation of reservoirs may be presented to the leading body and pertinent management department.

It is believed that once the technique of overtopping risk analysis be spread to all of the large reservoirs with strong dam as well as to a great number of small and intermediate-scale reservoirs will bring us huge economic benefits and valuable social benefits.

[1] CHEN Zhaohe, LI Qijun, SUN Ying, et.la, Research Report-Overtopping Risk for Earth Dams and Risk Criterion, Postgraduates School, Beijing Administrator’s Inst. of Resources & Hydropower, Dec. 1996(in Chinese).

[2] Ministry of Water Resources & Electric Power, Design Specifications for rolled embankment dam, Water Resources & Electric Power Publ., June 1985(in Chinese).

[3] CHEN Zhaohe, ZHOU Baolian, LI Qijun et.la, Research Report-Increasing the economic benefits of Douhe Reservoir through overtopping risk analysis, Postgraduates School, Beijing Inst. of Economic Management for Water Resources & Electric Power(EMWREP), March, 1991(in Chinese).

[4] LI Qijun, YE Shouzhong, CHEN Zhaohe, Application of Risk Analysis in Management of Water Resources for a Large Reservoir, Advances in Hydro-Science and –Engineering, vol.Ⅱ, 1995.

[5] CHEN Zhaohe, LI Qijun, et.la, Research Report-Increasing the economic benefits of Qinghe Reservoir through overtopping risk analysis, Postgraduates School, Beijing Inst. of EMWREP, 1993(in Chinese).

[6] LI Qijun, CHEN Zhaohe, LIU Lisha, Overtopping risk analysis for the earth dam of Qinghe Reservoir, IAHR. Stochastic Hydraulics ’96, Australia, July, 1996.

[7] CHEN Zhaohe, LI Qijun, et.la, Research Report-Increasing the economic benefits of Yuecheng Reservoir through overtopping risk analysis, Postgraduates School, Beijing Inst. of EMWREP. March, 1993(in Chinese).

[8] CHEN Zhaohe, LI Qijun, et.la, Research Report-Increasing the economic benefits of Zhuzhuang Reservoir through overtopping risk analysis, Postgraduates School, Beijing Inst. of EMWREP. March, 1993(in Chinese).

[9] Ying SUN, Zhaohe CHEN and Qijun LI, Overtopping Risk Analysis as a Non-structural Measure, Proc. of ’99 Intern. Symp. on Flood Control, Beijing, China, 1999.