INCREASING THE ECONOMIC BENEFITS
OF TAIHE RESERVOIR BY MEANS OF
OVERTOPPING RISK ANALYSIS

Sun Ying      Chen Zhaohe

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

Beijing, China, (86)-010-63286960

Li Qijun

Beijing Institute of Hydraulic Research, Beijing, China, (86)-010-68460474

Abstract: Overtopping risk analysis against simultaneous actions of flood and effective wind series was applied to the management of water resources for a large reservoir — Taihe Reservoir located in Shandong Province, China. The maximum storage capacity of the reservoir is 1.833 . It has an earth dam. In the analysis, the flood, wind, volume of reservoir and discharge capacity are all considered as random variables. Then a stochastic differential equation and a risk model are established for the earth dam to analyze its risk of overtopping against the design series of flood events accompanied with the runup generated by wind wave during flood period. On the basis of risk analysis, it was recommended that its limiting reservoir level before coming flood originally suggested by Taihe Reservoir Administration, say 226.0 may be raised to an elevation of 230.5 much more on the safe side which corresponds to a risk of the order of (or a safety of 99.99999%) against overtopping under concurrence of flood and wind events during flood period. The increase of volume of storage corresponding to the suggested increment of limiting level, 4.5 , will be 2.511 , which may bring a remarkable economic benefit to Taihe Reservoir Administration.

Keywords: risk analysis, overtopping, risk model, flood series

1  INTRODUCTION

In order to improve the management of Taihe Reservoir, Shandong Province, China, a risk model is developed for its earth dam to analyze its risk of overtopping against the design series of flood events accompanied with the runup generated by wind wave during flood period. Taking  as acceptable risk, or 99.999% as acceptable safety reliability, the risk analysis shows that the earth dam is very reliable against the simultaneous actions of design flood and effective wind events. On the basis of risk analysis, we recommended that its overtopping limiting level before flood, say elevation 226.0 , may be safely raised to an elevation of 230.5 . The correspondent increase in water volume of storage should bring a remarkable economic benefit to Taihe Reservoir Administration along with a great deal of social benefits.

2  RESERVOIR CHARACTERISTICS

Taihe Reservoir located in Zichuan District, Zibo City, Shandong Province, China. It controls a catchment area of 780 . The maximum storage capacity of the reservoir is 1.833 . It has an earth dam. The maximum height of the dam is 48 . Crest length of the dam is 1182 and crest elevation is 242 . Top elevation of the parapet on the dam crest is 243.5 . The west spillway is consisted of five spans, each gate 10 8.5 (width height) with weir crest at elevation 226.0 . The maximum discharge capacity of west spillway is 5720 . The east spillway is also consisted of five spans, each gate 12 7.5 with weir crest at elevation 228.0 . The maximum discharge capacity of east spillway is 5590 . The outlet work is a circular conduit of 3.0 diameter with maximum length of 519.1 .

3  HYDROLOGICAL CHARACTERISTICS

In the design of the reservoir, its design flood has a frequency of 1% and the extreme flood has a frequency of 0.05%. The design hydrograph is established as follows: at first, ascertain the designed 24hr maximum net rainfall from the designed 24hr maximum rainstorm; secondly, distribute the net rainfall according to the 24hr distribution for the design type of rainfall, and finally, the design hydrograph be calculated by use of the unit hydrograph of Taihe Reservoir.

4  UNCERTAINTIES

In our study, the flood, wind, volume of reservoir and discharge capacity are all considered as random variables.

4.1  Flood

It is well known that flood of any frequency is random event. Generally, it follows P–Ⅲ type of distribution, which is very familiar with us. For Taihe Reservoir, the probability density function for the maximum 24hr rainfall may be expressed as follows:

                      (1)

4.2  Wind

It is well known also that wind of any magnitude from any direction is a random event. The wind setup, wave height and runup generated by wind are then random too. As for the overtopping risk of the earth dam, the wind toward the dam during flood period is major concern and is defined as “effective wind for overtopping” by us. For Taihe dam, the effective directions of wind are S, N, NE and SE. The maximum wind velocities during 1965~1999 were collected from Bureau of Meteorology, Zibo City, and the pertinent effective wind as well as their maximum velocities at the water surface were determined. It was shown that the maximum velocities of effective winds in our case follow the extreme TypeⅠdistribution. Its distribution function may be expressed as follows:

                                 (2)

The mean value is  and the standard error .

4.3  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. Under the same contours, the calculated reservoir area and storage volume at a given water level may be different due to variety of computation philosophy and the instruments used. Moreover, the sediment transport 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.

Relationship between water level and reservoir area  is shown in literature [4].

A normal distribution is assumed for it with a standard error .

4.4  Discharge capacities

The discharge capacities of Taihe Reservoir are consisted of two parts: west and east spillways. The uncertainties of each part arise from many sources, such as the simplification of 3-D flow to 1-D flow model, measurement errors and roughness estimate. We may consider the random nature of discharge follows approximately the normal distribution. We take the relationship between reservoir water level and the discharge of west and east spillways as mean value curve respectively. Their standard error are taken as  where  is the mean value of discharge.

5  RISK MODEL

The risk model of overtopping was developed and may be expressed as follows:

                                (3)

where = risk against simultaneous actions of a series of flood and effective wind events; = initial reservoir level; = reservoir level increase due to flood; = wind setup; = wave runup on upstream slope of the dam; = predetermined critical elevation, such as the dam crest elevation or top elevation of parapet.

In the case of concurrence of flood event [ , ] and wind event [ , ], the risk  is

                                  (4)

Then, the total risk may be expressed as follows:

                                  (5)

In the above equations, the mean value of wind setup may be calculated by the following equation:

                                       (6)

where = velocity of wind at 10 above reservoir level ( ); = fetch length ( ); = the average depth of the reservoir along the fetch length; = a coefficient, its value varied in the range of (1.5~5.0) ; = angle between the wind direction and water body fetched, and may be taken as  on the safe side. Because variables  follow extreme TypeⅠdistribution, the variables  do so too. The standard error for  may be determined as

                                        (7)

where = standard error of the variable .

It was well known that wind velocities follow Rayleigh distribution, and wave heights do so too. Its distribution function and probability density function are:

   for    and      for                  (8)

Mean value M(x) and standard error (x) are related with distribution parameter  as follows:

   and                                (9)

As for wave runups on the dam slope, they follow Rayleigh distribution because the coefficient of correlation between wave runup and wave height is 1. The mean value of wave runups may be computed by the following equations:

                  (10)

where = coefficient considering the roughness and permeability of dam slope; = empirical coefficient as a function of dimensionless parameter ;  and = slope angle; = average wave height ( ); = average wave length ( ); = wind velocity ( ); = fetch ( ); g=gravitational acceleration.

Because wind events are stochastic, the variables  are composite random variables. It may be shown that the probability  of occurrence of  when the wind velocity is within the interval [ , ] is

                                 (11)

where  is the probability density function of Rayleigh distribution for the interval [ , ]. Therefore, the distribution function of  may be expressed as

                        (12)

In order to compute , it is necessary to normalize at  due to Rayleigh distribution of  and do iteration by means of the AFOSM method.

 is a function of flood flow , reservoir area  and discharge capacity  and may be determined through flood routing. A stochastic differential equation for flood routing may be established as follows:

                            (13)

Because the variable  did not expressed as analytic function, we have to solve eq.(5) numerically by means of Integration―AFOSM method.

6  CRITICAL MODE

Two modes were analyzed. The first taking the crest elevation of the earth dam, i.e. in Taihe case 242.0 as the critical elevation . The second, taking the top elevation of parapet, i.e. 243.5 as .

The performance formulas for the first and second modes are

    and                         (14)

7  RESERVOIR REGULATION

The regulation of Taihe reservoir taking 230.0m as limiting reservoir level before coming flood, or simply limiting level before flood (LLBF), is shown in Table 1. Similarly, other six regulations taking 230.5, 231.0, 231.5, 232.0, 234.0 and 234.5m as LLBF respectively, are also given by Taihe Reservoir Administration and omitted herein due to space limitation.

           Table 1  The regulation of Taihe Reservoir

8  RESULTS OF RISK ANALYSES

We take the crest elevation of the earth dam , say 242.0 as the first critical elevation for flood and wind setup, the computed risk is designated as ; while take the top elevation of parapet, say 243.5 as the second critical elevation for flood, wind setup and wave runup, the computed risk is designated as . The results of risk analysis are shown in Table 2.

If we take a risk of order of magnitude of  as an acceptable risk, it can be seen from Table 2 that the limiting reservoir level before coming flood 226.0 may be safely raised to elevation 234.5 .

9  RECOMMENDATIONS AND CONCLUSIONS

On the basis of risk analysis against overtopping for Taihe dam, it was recommended that its limiting reservoir level before coming flood originally suggested by Taihe Reservoir Administration, say 226.0 may be raised to an elevation of 230.5 much more on the safe side which corresponds to a risk of the order of (or a safety of 99.99999%) against overtopping under concurrence of flood and wind events during flood period. The increase of volume of storage corresponding to the suggested increment of limiting level, 4.5 , will be 2.511 , which may bring a remarkable economic benefit to Taihe Reservoir Administration. Besides the direct economic benefit, a great deal of social benefit will be gained due to the corresponding reduction of the possibility of damage caused by waterlogging in the farm land downstream of the reservoir, as well as the improvement of reservoir water quality and aquatic environment.

                         Table 2  Overtopping risk under the 1^st and 2^nd critical modes

Here, we should point out that although limiting reservoir level before coming flood may be raised to an elevation 234.5 , which is also on the safe side corresponding to a risk of the order of magnitude of , we recommend that it be raised to 230.5 only, because the following two conditions were considered: 1. The Taihe dam hasn’t experienced any larger flood after its reinforcing; 2. Under concurrence of flood and wind events during flood period, the Taihe dam should be much more safe.

The risk analysis presented herein may be applied to similar cases where the earth or rockfill dam should never be overtopped. Besides, it may be applied to serve scientific quantitative data for management of reservoir. During the enlargement or strengthening of existing dam, the risk analysis presented herein may be applied to provide pertinent guidelines.

References

[1]  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.

[2]  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.

[3]  Taihe Reservoir Administration, The regulation of Taihe Reservoir in flood season, 1999.