Risk analysis for earth dam overtopping

Water Science and Engineering, Jun. 2008, Vol. 1, No.2,76 -87ISSN 1674 -2370, htp://kkb.hhu.edu.cn, e-mail: wse@hhu.edu.cnRisk analysis for earth dam overtoppingMo Chongxun*, Liu Fanggui, Yu Mei?, Ma Rongyong', Sun Guikail1. College ofCivil and Architectural Engineering, Guangxi University, Narning 530004, P. R. China;2. Instiute of Soil Science, Chinese Academy of Sciences, Nanjing 210008, P: R. ChinaAbstract: In this paper, a model of overtopping risk under the joint effects of floods and wind waves, which isbased on risk analysis theory and takes into account the uncertainties of floods, wind waves, reservoir capacityand discharge capacity of the spillway, is proposed and applied to the Chengbihe Reservoir in Baise City inGuangxi Zhuang Autonomous Region. The simulated results indicate that the flood control limiting level can beraised by 0.40 m under the condition that the reservoir overtopping risk is controlled within a mean variance of5x10*. As a result, the reservoir storage will increase to 16 million m' and electrical energy generation andother functions of the reservoir will also increase greatly.Key words: overopping risk analysis; earth dam; flood; wind wave; risk standardDOI: 10.3882/j. issn. 1674-2370.2008.02.0081 IntroductionMore than 86 000 reservoirs have been constructed in China, with a total storagecapacity of over 4500 tillion m'. This is a greater number of reservoirs than in any othercountry in the world. They play an essential role in controlling and harvesting benefits fromfloods throughout China. However, for historical reasons, more than 90% of the dams areembankment dams. Accidents are potential threats to people's lives and property downstream,due to overtopping and dam breaches caused by insufficient information, inadequate surveyand design, poor construction quality or improper management. From the 1950s to the 1990s,1 147 dams suffered from overtopping during floods, accounting for 46.6% of the total numberof dam failures in China during that period (Zhang and Wen 1992). About one -third of theworld's dam failures have been caused by flood overtopping, which indicates that floodovertopping is an important factor affecting reservoir projects' safety. Moreover, because of apoor understanding on the randomness of floods, reservoir water levels during flood seasonsare often lowered arificially in order to avoid overtopping and protect the lives and propertyof downstream residents. Excessive flood discharge during flood seasons leads to insufficientreservoir storage after the flood season, making the reservoir incapable of providing theexpected benefits of its design. If things go on like this, not only are valuable hydropowerresources wasted and the reservoir project's profit lowered, but a lot of construction capital is中国煤化工This work was supported by the National Natural Science F50609005), theScience Foundation of Guangxi Education Department;YHC NM H Gd the ScienceFoundation of Guangxi University (Grant No. X071096).*Corresponding author (e-mail: mochongxun gxu@ 163.com)Received Apr. 15, 2008; accepted May 30, 2008also stagnant and water enterprises are trapped in a poor economic condition in which theycannot survive and develop soundly. Therefore, the solution of the conflicts between aproject's safety and its profit is a permanently important and complex problem.Reservoir overtopping risk analysis technique is the key to solving this problem. Threedifferent computing methods emerging from current analysis and research on reservoirovertopping risk can be summarized as follows:(1) The method based on an observed water level sequence estimates the risk of damovertopping by analyzing the frequency of the highest annual frontal water level. TheNonparametric Hypothesis Testing Method is used to determine the distribution of the highestfrontal water level. Then, the overtopping risk can be computed according to the chosen leveldistribution U(z). If the overtopping risk is P =P(z>Z), then P=1- P(c≤Z) =1-U(Z),where z is the highest frontal water level and Z is the elevation of the dam crest. The highestfrontal water level is the factor with the most direct influence on dam safety, so studying itsvariability is useful for overtopping risk analysis. However, it is a non-natural sequenceaffected by human factors, and the feasibility of this method is still under discussion.(2) In the method based on the design flood, the flood control limiting level is taken as theinitial flood-regulating level, the regulation model is built according to the reservoir's operationrules, reservoir routing is conducted by analyzing design floods of different frequencies, andthe corresponding highest frontal water levels are calculated. Consequently, a relationshipbetween the highest annual frontal water levels and their probabilities is established. Thus,overtopping risk can be calculated through the dam crest elevation. The obvious defect of thismethod lies in the assumption that the design flood frequency is equal to the frequency of thehighest frontal water level, which means that the randomness of the initial flood-regulatinglevel is ignored, as are the wind and wave factors. Therefore, this method does not correspondto the actual circumstances of the project.(3) In the method based on random flood simulation, the annual maximum reservoirinflow flood process sequence, which comprehensively represents the statistical characteristicsof the observed reservoir inflow flood, is simulated using the reservoir inflow floodrandomness model, according to which the sequence of the highest frontal water level can beobtained to calculate the overtopping risk. The difficulty of this method lies in building a modelreflecting the general features of the flood, so that the probability can be reliably estimated anda comprehensive analysis can be conducted. In order to meet computation accuracy needs, thesimulation is very complex. Therefore, this method is limited in its practical applicability.In this paper, a model of overtopping risk under the joint effects of floods and wind wavesis established based on previous research of overtopping. In the model, the uncertainties offloods, wind waves, storage capacity of the reservoir and discharge capacity of spillways arecomprehensively considered. A corresponding computer program has been developed tocalculate the risk of overtopping, considering the join[中国煤化工ns on the floodMYHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol. 1, No.2,76 -8777control and scheduling plan of the proposed reservoir. The reservoir water level can be adjustedto improve the reservoir's profit on the condition that the dam overtopping risk is within thestandard values.2 Earth dam overtopping risk model considering the joint effectsof floods and wind waves2.1 Overtopping risk modelDam overtopping is defined as the situation in which water flows over the dam crestbecause the frontal water level is higher than the elevation of the dam crest. Ifz(u)≥Z(1)where Z is the elevation of the dam crest and z(t) is the frontal water level at time t, thendam overtopping occurs.Overtopping risk (R(T)) refers to the probability of the frontal water level being higherthan the elevation of the dam crest during the analytical period T (usually one year), whichcan be expressed asR(T)=P(z(t)≥z) 0≤t≤T(2)The dam overtopping risk model that considers the joint effects of floods and windwaves can be written asR(T)=P(z(t)≥Z)=P(mx +e+h≥Z) .(3)where Zmax is the highest frontal water level caused by floods, e is the backwater heightcaused by wind and h is the swash height of wave.2.2 Uncertainty analysis2.2.1 ZmaxThe uncertainty of Zmax is derived from the flood, water discharge and reservoircapacity, etc. For a given reservoir dispatching regime, Zmx is determined from flooddischarge Q (1), reservoir area F(z) and water discharge s(z), through the followingrelationship:Q(t)-S(z)= dv/dt = F(z)dz/dt= F(z)f(z,t)(4)where f(z,t) is the probability density function of water level z at time t and e(t),s(z) and F(2z) are stochastic functions. The reservoir water level z(t) at time t iscomputed using Eq. (4). However, Eq. (4) is a stochastic differential equation, and obviouslyz() cannot be expressed as an analytical function of Q(t)， S(z) andF(z). Thus, Eq. (4)must be transformed into a linear equation through difference methods. For an unsolvedfunction like Eq. (4), the stochastic differential equation for flood regulation can be obtainedthrough the Runge-Kutta method, and, consequently, a four- order formula with higheraccuracy is formed:中国煤化工(.)=z()+h(K, +2(K2YHCNMHG(5)78Mo Chongxun et al. Water Science and Engineering, Jun.2008, Vol. 1, No.2, 76 -87whereK =(Q()- s()) F(z(t))K2 =(+n2)- s(z(t)+ 0.5hK, ))F(r(t)+ 0.5hK})K; = (4+1n)- s(z(t )+ 0.5hK, )yF(z(1)+ 0.5hK,)K, = (Q(.)- s(z(t)+ hkK,))F(z(t)+ hK;)in which z( ) represents the reservoir water level at time t in m, 0() is the reservoirinf]ow in m'/s, s(z(t;)) is the reservoir outflow in m/s, F(z(t)) is the reservoir surfaceareainm2andhistimestepins.The mean variance of z(i+) at time t is calculated using a superposed secondmoment method, namely(.))= D()+ (h236)(0(K)+ 4(D(K,)+ D(,)+ D(K.))(6)D(K)=f 0(t)- s(z(t)]()[ D()]+F2(z())[ Q()- s(z())D[F(<()]+D(s(z())F"())~]F2 (z(t))D(K2)=「(t41n )- s(z(t)+ 0.5hK)]'F (e(t)+ 0.5hK)[D(e(t)+ 0.25h2D(K)]+:F2(<(t)+ 0.5hK.)「(oun)- s(z()+ 0.5hK,)]1D(s(z(t)+ 0.5hK,))F*(z(t)+ 0.5hK.)]D(K,)=[(wn)- s(<()+0.5hK,)]印(<()+ 05K>)[D(<()+ 0.25h2D(<.)]+F"(z(t)+0.5hK2)[ (Q(un)- s(z()+ 0.5hK,)]1D(S(z(t)+ 0.5hK))F(C)+0.5hK)“| D[F (C()+0.5hK2)J+-户(z()+0.5hK2)D(K.)=「(..)-S(z()+ hK,)]fr(<(;)+ hx,)D())+h'D(Ks)]+F(eC)+hK)广][ ((.)- s(z(t)+ hK,)]D[f(;)+05hK,]+-D(s(z(t)+ hK,))F"(z()+hK)F2 (zt)+ hK,)in which E(z)= dF(z)/dz. When discharge in the spillway is S= MB、2g(z(t)- z.)'(M is a discharge coefficient, B is the overflow width of the weir, z(t, ) is the reservoirwater level and Z。is the elevation of the weir crest), then())=(3(28(e()- zs)”)(M())t($Mw 2018 )-7 ])D())中国煤化工'TYHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol. 1, No.2,76 -87()+95K))(&xE(t)+0.5hK, -z.)") D(M()+05K))+(151B2g()+ 05hK, - ()(2()+(251h*D(K)])(<(<(t)+ 0.K.)=(](2(<()+.01h,-z,)") D(M()+05K,)+(151B]2g()+ oShK, - ()[()+ 025'D(K2)]()+051K)=(v8)()+0.5hK, -z.)*) ()+5(5K,)+(.5B2()+.hK, -z)[D())+ 025h D(s)]where the values of z(x)，S(x)， F(x) and F(x) are all obtained from their own meanvalues.2.2.2 e and hpGenerally, the rise of the water level caused by wind waves will not result inovertopping. Only when a flood raises the water level to a certain height, can the wind wavescause overtopping. Therefore, the precondition to calculating the wind speed series is theoccurrence of a flood. As for the overtopping risk, only the wind blowing towards the dambody will cause overtopping, which will not happen in non-flood seasons or if the wind isblowing away from the dam body, however strong the wind is. Thus, the effective wind shouldbe defined as wind that blows towards the dam body during a flood.The wind-related factors causing overtopping include the backwater height caused bythe wind e and the wave swash height市. Due to the randomness of wind blowing fromdifferent directions and at different speeds, the backwater height and the wave swash heightare random as well.According to the Rolled-Earth Dam Design Standard (MWRPI 1985) the backwaterheight caused by the wind can be computed as follows:e= (Kw'D/(2gH))cosβ(7)where K is a comprehensive friction coefficient whose value ranges from 1.5x105 to 5.0x10*,and is usually 3.6x10*; W is the wind speed at 10 m above the water surface in m/s; D is thefetch length of the reservoir in m; H is the average water depth of the reservoir in m;and βis the included angle between wind direction and the fetch length, which in general is β =0°.Thus, the mean value and mean variance of e can be calculated using the first-ordersecond-moment method:e= KW D1(2gH)(8)σ.=(KWD/(gH))xσw(9)where W is mean wind speed and σw is the meaneries.中国煤化工The mean value of the swash height can be compmmended byIYHCNMHG80Mo Chongxun et al. Water Science and Enginering, Jun. 2008, Vol. 1, No.2, 76 87the Rolled-Earth Dam Design Standard (MWRPI 1985):h =(K.Kw 1N1+m2 )vh(10)whereh=h/1.71h= 0.0166Ws/4Dl'Sa=0.389WD"Sand in which K。is the roughness permeability cofficient of the slope; Kw is an empiricalcoefficient determined by the non-dimensional value W /√VgH , cormposed of wind speed W.average water depth of the water area H and gravity acceleration g; m is a gradientcoefficient; h and h are, respectively, wave height and its mean value (m); and h is meanwave length (m).The mean variance of h can be converted through following formula:M(x)=√0.5rμ .(11)[σ(x)= J0.<(4-π)μwhere M(x) and σ(x) are the mean value function and mean variance function,respectively, and μ is a wave height distribution coefficient.2.3 Solution for overtopping risk modelA dam's overtopping risk is calculated using the Integration-JC method based on Eq. (3).The central task of this method is the numerical integration of the discharge series Q ,whichis divided into several intervals, [, Q ]. The probability of Q within these intervals isP=f(Q)dQ, which can be used to calculate f(Q). Q; can be seen as a fixed valuewithin a certain interval that is small enough. If described by a graph, Q(t) can be seen as adefinite flood hydrograph. For Q (1), the mean value and the mean variance, D(zmx ), ofthe highest frontal water level z, n大，are calculated using Eq. (5) and Eq. (6), respectively. Asfor wind speed, W , the mean value and mean variance of e are calculated according to themaximum effective wind speed using Eq. (8) and Eq. (9), while the mean value and meanvariance of h are calculated with Eqs. (10) and (11). As such, the dam overtopping risk, P,caused by the joint efects of [Q-. Q}] and the maximum effective wind speed isP=P(z1 +e+h≥z)(12)in which Z and Zmx|have a normal distribution, e has an extremum I distribution andh has a Rayleigh distribution. Because normal and abnormal variables exist in Eq. (12), P .is computed using the JC method (Wu 1990). The P of each interval for the discharge seriesQ and wind speed series W is calculated and superposed. Then the overtopping risk isobtained as follows:=之rf(Q)P中国煤化工(13):YHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol. 1, No.2, 76 87813 Discussion of earth dam overtopping risk criteriaCalculation of earth dam overtopping risk aims at judging whether the risk is acceptableor not. Therefore, an overtopping risk evaluation standard is needed. When the risk assessmentmethod was originally introduced in the dam safety field, it was based purely on economic riskcriteria, including casualties estimated using an economic value index. At present, this methodhas basically been abandoned. The value of risk criteria should be determined on the basis ofthe risk levels widely accepted by the society, as the ability to bear different risks varies acrosscountries and industries. With changes in social, economic and environmental states as well aspeople's psychological conditions, the allowable risk criteria change correspondingly.Different countries and organizations will propose allowable risk criteria in accordance withtheir own circumstances (Salmon and Hartford 1995; Krenzer 2000; Rettemeier et al. 2000.According to data from the Australian Bureau of Statistics, the maximum morality rateof the Australian population is approximately 1.0x10* per year, on the basis of which theAustralian Risk Assessment Guidance (ANCOLD 2003) proposed that individual risk above1.0x107 per year was intolerable for operating dams, and individual risk above 1.0x10-5per year was intolerable for newly-constructed dams and extension projects of operating dams.In 1983, David E. Langseth pointed out in his thesis concermning spillway flood design criteriathat, in order to guarantee dam safety, the failure risk should be at a level of 10- , whereas theovertopping risk caused by inadequate flood discharge should be at a level of 10~ (Zhu et al.2003). In addition, according to the statistics, 1 105 serious dam damage accidents hadhappened abroad by the end of 1975, including 145 accidents caused by flood overtopping. Ifthe dam failure risk is 10+ , then the dam overtopping failure riskis 10- .From 1954 to 2001, the mean annual dam breach rate in China was 8.79x10+ peryear, about 4 times higher than the worldwide rate (2.0x10 per year). Since 1980, China'smean annual dam breach rate has gradually declined due to the reinforcement of dam safetymanagement. From 1981 to 2001, the rate was 5.54x10+ per year, still higher than theworldwide rate, with 1.1x10- per year for medium reservoirs (0.01-0.1 billion m),2.8x10* per year for mini ( I ) reservoirs (1.0 -10 million m) and the relatively high rate of6.4x10- per year for mini (Il) reservoirs (0.1-1.0 million m3) (Xie et al. 2007). Generallyspeaking, China's mean annual dam breach rate is approaching that of Westem developedcountries, and many Chinese scholars have conducted significant studies on the value of damovertopping risk criteria (Sun and Huang 2005; Zhu et al. 2003; Hao et al. 2003; Sheng andPeng 2003). However, in the absence of national and professional overtopping risk standards,an overtopping risk level of 10° may be acceptable. This is equal to the risk level of anearthquake, which means that the acceptable safety reliability of overtopping exceeds99.999%.In summary, a dam breach risk level of 10~-3中国煤化工10* levelispreferred in China. The lower the dam breach risk levTYHCNMHG11 be accepted.82Mo Chongxun et al. Water Science and Engineering, Jun. 2008, VoL. 1, No. 2, 76 -87If individual risk reaches the level of 10*, people no longer have to worry about damovertopping risk, which is a reason for China to identify this value. At present, this level ofdam overtopping risk is still difficult to achieve in China. There is a large difference betweenthe economy, technology and public awareness of risks in China and those in Westerndeveloped countries; a level of 10~ is not consistent with actual situation in China. Besidesfloods and wind waves, there are many other factors that can lead to dam overtopping: (1) theabatement of the gate lifting device can cause the gate to fail to open on time; (2) a flood fromthe watershed area of the reservoir can be underestimated, so that the flood exceeds thedefensive capability of the reservoir; (3) the inflow flood caused by an upstream dam breachcan exceed design flood results in a chain reaction; and (4) the reservoir can be inappropriatelyoperated. According to statistics, dam overtoppings caused by floods and wind waves accountfor half of the total. Therefore, at present, it is appropriate to consider 5.0x10* the limit ofdam overtopping risk caused by the joint effects of floods, wind and waves. In this study, thisvalue was applied to a case of dam project risk research.4 Case studyThe Chengbihe Reservoir in Guangxi Province was used as a case study to compute andanalyze the dam overtopping risk.4.1 Introduction of the Chengbihe ReservoirThe Chengbihe Reservoir, located 7 km north of Baise City in Guangxi ZhuangAutonomous Region, lies on the Chengbi River, a tributary of the Youjiang River. It is part ofthe large- scale reservoir of grade I project (ABCR 1998) and has a storage capacity of 1.15billion m'. It is a carryover storage multi-function reservoir, not only for power generation, butalso for water supply, flood control, irmigation, fisheries and reservoir tours. The dam is anearth-rock dam with a maximum height of 70.40 m whose seepage prevention measure is aconcrete core wall. A power station with a total capacity of 30000 kW and an average annualenergy output of 123.73 million kW/h is at the dam toe. The flood control limiting level of thereservoir coincides with its normal high-water level, 185.00 m.The Chengbihe Reservoir uses a gate dam to discharge the flood. While the flood controllimiting level of the reservoir is 185.00 m, the crest elevation of the spillway is 176.00 m. Theflood control operation rule is that the opening gates will be used to keep the water level of thereservoir at 185.00 m when the reservoir inflow is less than the reservoir outflowcorresponding to the flood control limiting water level; when the reservoir inflow is largerthan the reservoir outflow corresponding to the flood control limiting level, the flood will bedischarged through the gates.4.2 Computation of wind regimeAccording to the maximum wind speed series中国煤化工flood seasonsMYHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol, 1, No.2, 76 -87.83from 1970 to 2005, the mean value and mean variance of the maximum omni -directional windspeed in the flood season are calculated as W. =5.40 m/s and σ= 1.46 m/s, respectively;the mean value and mean variance of effective wind obtained through conversion areW, =5.01 m/s and σ, =1.57 m/s, respectively.The wind speed values above must be converted into wind speed at 10 m above thereservoir surface, which means the wind elevation is 200.40 m. According to The HydraulicDesign Manual (MWRPI 1984), the wind speed can be converted from 205 m (anemoscopeelevation) to 200.40 m with a conversion coefficient of K =0.96. Then the mean value andmean variance of the wind speed (m/s) at 10 m above the reservoir surface areW1o = KW = 0.96x5.40=5.18σT10= Kσ = 0.96X1.46=1.40Next, the wind speed at 10 m above the reservoir surface is converted into wind speedon the reservoir surface. On the basis of The Hydraulic Design Mamual (MWRPI 1984), theconcealed coefficient of the anemoscope is K|=1.4 and its topographic coefficient isK2 =0.9. According to W。and the product value K=K xK, =1.3, the wind speed on thereservoir surface,W,=6.70 m/s, andimeanvariance,σ2= W2lWo. Tro .= 6.70/5.18x1.40=1.81 m/s, are obtained from The Hydraulic Design Manual (Volume IV),Table 17-4-2 on pages 4-13 (MWRPI 1984).As a matter of fact, only the wind blowing towards the dam body will cause theovertopping. Thus, the omni-directional wind must be converted into effective wind, whosespeed conversion coefficient isKw =W, /W = 5.01/5.40=0.93K。=σ,/σ =1.57/1.46=1.08The mean value and the mean variance of the maximum effective wind speed on the reservoirsurface in the flood season are, respectively:W =KyW, = 0.93x6.70=6.23σ=Kgσ2=1.08x1.81=1.954.3 Handling of various uncertain factors(1) When the flood series satisfies P-II ditribution, its distribution density functioncan be calculated asf(Q)= 0.0372(Q - 475.50) Q.05 exp(-0.00062(Q - 475.50))(14)(2) The uncertainty of the flood discharging capacity can be expressed by the dischargecoefficient M, which has a normal distribution, and its mean value M, which can bedetermined from Wu (1994). Experimental data generated by the spillway flow model indicatethat the difference in flow coefficients after stabilization is 10% and the mean variance of Mis 0.10M. .(3) The reservoir area function F(z) shows中国煤化工the observedYHCNMHG84Mo Chongxun et al. Water Science and Engineering, Jun.2008, Vol.1, No. 2, 76 -87value as its mean value F and 0.05F as its mean variance. According to statistics, thesimulated risk is apt to be safe as long as the relative error of the observed length is controlledto less than 0.1% and the mean variance is 0.05F.(4) The uncertainties of the initial flood-regulating level and dam crest elevation causedby reservoir operation, management, survey and construction errors are relatively low. Themean values of uncertainties can be design values, while both of their mean variances are0.01 m .4.4 Results analysisThe wind height and wave swash height are calculated according to the mean value,6.23 m/s, and mean variance, 1.95 m/s, of the maximum effective wind speed during the floodseason. As the wind height and wave swash height are less than the depth of the reservoir, theirmean value and mean variance hardly vary with changes in the initial flood-regulating level,so it is assumed that they don't vary with changes in the flood control limiting level. Afternormalization, the mean value and mean variance of the wind height are 0.069 m and 0.007 m,respectively, while the mean value and mean variance of wave swash height are 0.365 m and0.165 m, respectively. The risk values of the Chengbihe Reservoir dam overtopping withdifferent flood control limiting levels in flood seasons are calculated using Eq. (13) and listedin Table I.Table 1 Calculated Chengbihe Reservoir overtopping risksFlood controlFrontal level (m)Overtopping riskslimiting level (m)Mean valueMean varianceNo consideration of wave wall___ In consideration of wave wall185.00188.570.03001.918X 10*<10*185.20188.63 .0.02963.065X 10*185.40188.75 .0.02904.768X 10*<10* .185.60188.820.02867.151X 10*< 10*Table 1 shows that if the flood meets the dam at the original flood control limiting levelof 185.00 m, the overtopping risk without consideration of the wave wall is 1.918x10%，smaller than the allowable risk of 5.0x10°, while the overtopping risk that considers theimpervious wall is lower than 10*, much smaller, ilustrating that the dam overtopping risk tothe Chengbihe Reservoir is apt to be minimal when the dam is operating at the original floodcontrol limiting level of 185.00 m during flood seasons. With the continuous rise of the floodcontrol limiting level, the overtopping risk becomes greater. When the flood control limitinglevel rises from 185.00 m to 185.40 m, the overtopping risk is 4.768x10* without regard to therole of the wave wall, smaller than the allowable risk of 5.0x 10*. The overtopping risk is stilllower than 10-8 when the wave wall function is taken into consideration. But when the floodcontrol limiting level rises to 185.60 m, the overtopping risk is 7.151x10*, greater than theallowable risk. Thus, the overtopping risk to the Chengbihe Reservoir is acceptable when theflood control limiting level fluctuates between 185.中国煤化工ghout the floodYHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol. 1, No. 2, 76-8785season.Based on the analysis above, a water level of 185.40 m during floods is recommended.Because the flood control limiting level of the Chengbihe Reservoir is equal to its normalstorage level, the iacrease of 0.40 m when the reservoir level rises from 185.00 m to 185.40 mcauses a storage increase of 16 million m' and a corresponding mean annual direct economicprofit of about 100 million CNY.5 ConclusionsIn this paper, the basic theory and computation method for determining the risk of earthdam overtopping under the joint effects of floods and wind waves, in consideration of theuncertainties of floods, wind waves, storage capacity of the reservoir and discharge capacity,are proposed and applied to the Chengbihe Reservoir using reliability mathematics, stochastichydraulics, stochastic hydrology and other related knowledge. The results indicate thatincreasing the reservoir level by 0.40 m can increase storage by 16 million m' and lead to acorresponding mean annual direct economic profit of about 100 million CNY while at thesame time protecting the reservoir dam from overtopping. The authors have analyzed theovertopping risk of the Chengbihe Reservoir in a previous paper (Mo et al. 2003), in which the“simplified calculation method", which only takes into account a thousand-year frequencydesign flood and the maximum effective wind in flood seasons, was used to calculate theovertopping risk. The overtopping risk standard, with consideration of economic loss in a dambreach, was selected as 7.120x10~. As a result, the flood control limiting level increase was1.60 m and the storage increase was 64 million m'. As opposed to the method used in Mo et al.(2003), the method presented in this paper considers the interval probability combination offloods and wind waves. Thus, the computation accuracy is higher and the results are safer. Inaddition, as 5.0x10% is chosen as the overtopping risk limit, taking no account of economicloss factors, its result is more reasonable than that of the simplifed calculation method.Consequently, the results can provide some decision-making support for the reservoirmanagement department, and the overtopping risk analysis method proposed by the authorscan be applied to other operating earth dams as well.ReferencesAdministrative Bureau of the Chengbihe Reservoir (ABCR). 1998. Introduction for the Chengbihe Reservoir.Baise: ABCR. (in Chinese)Australian National Committee on Large Dams (ANCOLD). 2003. Guidelines on Risk Assessment. Australia:ANCOLD.Hao, B. Y., Wang, H. S., Zhang, Q. F, and Gu, J. F. 2003. Application of dam overtopping risk analysis in theDongwushi Reservoir. Hebei Water Resources and Hydropower Engineering, (2), 40 41. (in Chinese)Krenzer, H.2000. The use of risk analysis to support dam safety decision and management. The Proceedingsof 2Ith Intermational Congress on Large Dams. Bijing: The International Commission on Large Dams,799- 801.中国煤化工Ministry of Water Resources & Power Industry (MWRP).YHCNMHGal (Volume IV),86Mo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol.1, No.2, 76-87Beijing: Water Resources and Electric Power Press. (in Chinese)Ministry of Water Resources & Power Industry (MWRPI). 1985. Rolled earth dam design standard. Beijing:Water Resources and Electric Power Press. (in Chinese)Mo, C. x,, Liao, x. T, and Ma, R. Y. 2003. The risk analysis of dam overtopping to the project of ChengbiheReservoir. Journal of Guangxi University (Natural Science Edition), 28(2), 151-154. (in Chinese)Rettemeier, K., Falkenhagen, B., and Kongeter, J 2000. Risk assessment - new trends in Germany. TheProceedings of 2lth Intermational Congress on Large Dams. Beijing: the Intermational Commission onLarge Dams, 625- 641.Salmon, G M., and Harford, D. N. D. 1995. Risk analysis for dam safety. Intermnational Water Power andDam Construction, 47(3), 42- 47.Sheng, J. B., and Peng, X. H. 2003. Study on risk standard of Chinese reservoirs. The Proceedings of FirstYouth Science & Technology Forum. Beijing: Chinese Hydraulic Engineering Society. (in Chinese)Sun, Y., and Huang, W. J. 2005. Risk analysis on overtopping for operation management of reservoir. JourmalofHydraulic Engineering, 36(10), 1153-1157. (in Chinese)Wu, C. G 1994. Hydraulics. Beiing: Higher Education Press. (in Chinese)Wu, s. W.1990. Analysis of Structural Reliability. Beijing: China Communications Press. (in Chinese)Xie, H. L., Liu, J. J.. and Zhang, S. D. 2007. Introduction of evaluating method for dam safety and riskanalysis. Journal of Water Resources and Water Engineering, 18(5), 93- -95, 99. (in Chinese)Zhang, X. L, and Wen, M. X. 1992. Statistical analysis of China's reservoir failure and discussion on itssecurity stratcgy. The Proceedings of Water Management. Beijing: Water Management Department ofMinistry of Water Resources. (in Chinese)Zhu, H. L, Chen, Z. H, and Zhou, z. H.2003. Risk analysis on dam overtopping of Taihe Reservoir. Damand Safery, (4), 11-14. (in Chinese)中国煤化工MHCNMHGMo Chongxun et al. Water Science and Engineering, Jun. 2008, Vol.1, No.2, 76 8787