Overtopping Probability Research Articles

Risk and uncertainty analysis for dam overtopping – Case study: The Doroudzan Dam, Iran

There is a growing tendency to assess the safety levels of existing dams by using mathematical and statistical methods. In this study, the application of risk and uncertainty analysis to dam overtopping is presented for Doroudzan Reservoir located at the south part of Iran. The main objective of the overtopping analysis of dams is estimating the height of water in the reservoir under various inflows and comparing the computed results with the dam crest elevation. Hence, the main steps of this study include univariate flood frequency analysis of annual maximum inflows to estimate the peak flows in various return periods, generate inflow hydrographs based on the estimated peak flows, and route the hydrographs through the reservoir to compute the maximum height of the water in reservoir. In this study, the spillway discharge coefficient, quantile of peak flows, and initial water surface level are subject to uncertainty, and the Monte-Carlo simulation (MCS) and Latin hypercube sampling (LHS) are applied to perform the uncertainty analysis. In addition to inflows, the effect of different wind speeds on the probability of overtopping has been considered. The results demonstrated that both increasing water level and wind speed have significant impact on the risk of overflowing.

Dam overtopping risk using probabilistic concepts – Case study: The Meijaran Dam, Iran

Hydrologic risk assessment and uncertainty analysis by mathematical and statistical methods provide useful information for decision makers. This study presents the application of risk and uncertainty analysis to dam overtopping due to various inflows and wind speeds for the Meijaran Dam in the north of Iran. The procedure includes univariate flood and wind speed frequency analyses, reservoir routing, and integration of wind set-up and run-up to calculate the reservoir water elevation. Afterwards, the probability of overtopping was assessed by applying two uncertainty analysis methods (Monte Carlo simulation and Latin hypercube sampling), and considering the quantile of flood peak discharge, initial depth of water in the reservoir, and spillway discharge coefficient as uncertain variables. The results revealed that rising water level in the reservoir is the most important factor in overtopping risk analysis and that wind speed also has a considerable impact on reservoirs that are placed in windy areas.

Modeling parametric uncertainty in optimal open channel design using FORM-PGSL coupled approach

Optimal design of artificial open channels is essential for the planning and management of irrigation projects. In this paper a modified formulation is presented for the comprehensive design of open channels considering the seepage loss, evaporation loss and land acquisition cost along with the lining and excavation cost. The resulting formulation is solved using a recent meta-heuristic optimization technique namely probabilistic global search Lausanne (PGSL). The uncertainty associated with channel design parameter may lead to the failure of canals (channels). The parametric uncertainty in open channel design is modeled using first order reliability method (FORM). A bi-objective optimization model is presented in the study which minimizes the cost and minimizes the probability of overtopping considering a probabilistic cost function as the objective function. A new approach is proposed to solve the model in a meta-heuristic environment following PGSL as the solution method. Also a chance constrained optimization model which considers overtopping probability constraint and channel capacity constraint simultaneously along with the objective of minimization of cost is propounded and solved using PGSL. The solutions obtained using coupled FORM-PGSL approach is encouraging and the method can be used for optimal and reliable design of artificial open channels.

Overtopping Risk Analysis Using MC-LHS Method

Based on the theory of risk analysis, this study develops a LHS –MC method to evaluate dam overtopping probability that accounts for the uncertainties arising from wind speed and peak flood. LHS method is used to generate samples of peak flow rate and wind speed especially for rare events. One example of dam overtopping risk analysis is presented to demonstrate the validity and capability of the proposed method. By means of numerical example, it is shown that LHS method is efficient which tends to convergence within a few simulation times. Reservoir routing, which incorporates operation rules, wind setup, and run-up, is used to evaluate dam overtopping probability.

Formation and Stablity of the Sky Pond Landslide Dam, China

The Sky Pond landslide dam is located in Muchang valley, a branch of the Yellow River branches. From this point it is about 6Km to the mouth of the valley from where the Yellow River flows 0.8Km downwards to the planned Jishi gorge hydropower station. The Sky Pond landslide dam is actually formed by two landslides from both the left and right bank slopes and completely blocks the seasonal river channel. The volume of the landslide dam is about 14 millions m3 with 2.37 millions m3 water stored in the dammed lake under the condition of perennial mean water level. Because (1) the dam body is large in width and thickness; (2) the dammed lake water is small both in volume and weight compared to the landslide dam; (3) recharge to the dammed lake is basically the same as the discharge every year; and (4) there is a natural spillway in the dam body, the landslide dam is present at least 750 years after its formation. Although landslide dams which have existed for several hundreds to thousands of years are generally considered as stable, there are remains which may fail catastrophically. In order to analyze the stability of the Sky Pond landslide dam and provide justification for the future engineering decisions, this paper describes the engineering geological conditions near the landslide dam and the characteristics of the dam body, and a detailed discussion of the formation mechanism of the landslide. Based on engineering geology investigation, a qualitative assessment of the stability of the dam and an analysis of the probability of dam overtopping and piping is carried out. Limit equilibrium analysis has been used to calculate the stability of the dam slope under various operational conditions. Results of the stability analyses indicate that the Sky Pond landslide dam should remain stable and does not present a potential theat to the planned hydropower station.

Probability of Flood-Induced Overtopping of Barriers in Watershed-Reservoir-Dam Systems

An engineering methodology is developed to build hazard curves to evaluate the probability of flood-induced overtopping of barriers in watershed-reservoir-dam systems. The probable maximum precipitation in the watershed under consideration and its distribution in time during the acting storm is estimated. Considering the effects of the local geology, soil, topography, and land use, a random representation of the storm hourly rain is translated into effective runoff, including losses due to evaporation, interception, and surface retention. The uncertainty in the hydrological characteristics of the drainage basin is captured by a random time to concentration. Random hourly unit graphs are constructed analytically for a convex watershed and convoluted with the storm time-history to result in the random hydrograph for the inflow flood into the reservoir of the dam system. Flood routing through the reservoir is then computed with or without noise in the model. The deterministic path leads to a hydrograph for t...

Risk analysis for flood-control structure under consideration of uncertainties in design flood

This study presents a risk analysis model to evaluate the failure risk for the flood-control structures in the Keelung River due to the uncertainties in the hydrological and hydraulic analysis, including hydrologic, hydraulic, and geomorphologic uncertainty factors. This study defines failure risk as the overtopping probability of the maximum water level exceeding the levee crown, and the proposed risk analysis model integrates with the advanced first-order and second-moment (AFOSM) method to calculate the overtopping probability of levee system. The proposed model is used to evaluate the effects of the freeboard and flood-diversion channel on the flood-control ability of the levees in the Keelung River, which were designed based on the 3-day, 200-year design rainfall event. The numerical experiments indicate that the hydrologic uncertainty factors have more effect on the estimated maximum water level than hydraulic and geomorphologic uncertainty factors. In addition, the freeboard and the flood-diversion channel can effectively reduce the overtopping probability so as to significantly enhance the flood-control capacity of the levee system in the Keelung River. Eventually, the proposed risk analysis successfully quantifies the overtopping risk of the levee system under a scenario, the increase in the average 200-year rainfall amount due to climate change, and the results could be useful when planning to upgrade the existing levee system.

Theory and application of loss of life risk analysis for dam break

The loss of life risk evaluation model for dam break is built in this paper. By using an improved Monte Carlo method, the overtopping probability induced by concurrent flood and wind is calculated, and the Latin Hypercube Sampling is used to generate random numbers. The Graham method is used to calculate the loss of life resulting from dam failure. With Dongwushi reservoir located at Hebei Province taken as an example, the overtopping probability induced by concurrent flood and wind is calculated as 4.77×10−6. Loss of life is 24 220 when the warning time is 0.25–1 h and flood severity understanding is vague, which indicates that the risk is intolerable. The losses of life under three other conditions are tolerable: warning time 0.25–1 h, and precise flood severity understanding; warning time more than 1 h, and vague flood severity understanding; warning time more than 1 h, and precise flood severity understanding.

Evaluation of dam overtopping probability induced by flood and wind

This study develops a probability-based methodology to evaluate dam overtopping probability that accounts for the uncertainties arising from wind speed and peak flood. A wind speed frequency model and flood frequency analysis, including various distribution types and uncertainties in their parameters, are presented. Furthermore, dam overtopping probabilities based on monthly maximum (MMax) series models are compared with those of the annual maximum (AMax) series models. An efficient sampling scheme, which is a combination of importance sampling (IS) and Latin Hypercube sampling (LHS) methods, is proposed to generate samples of peak flow rate and wind speed especially for rare events. Reservoir routing, which incorporates operation rules, wind setup, and run-up, is used to evaluate dam overtopping probability.

Overtopping Probability Constrained Optimal Design of Composite Channels Using Swarm Intelligence Technique

In this paper swarm intelligence based methodology is proposed for optimal and reliable design of irrigation channels. The input parameters involved in channel design are prone to uncertainty and the solution of deterministic model may result in flooding risk and affect the stability of the channel. To provide reliability in the design, an overtopping probability constrained design is presented in this study. The deterministic equivalent of the probabilistic constraint is derived by following the principle of first order uncertainty analysis. In order to account for the uncertainty of design parameters in the objective function, a modified cost function is proposed. A methodology is propounded to solve it in a metaheuristic environment and solved it using elitist-mutated particle swarm optimization (EMPSO) method. The EMPSO based solutions are found to be quite successful and better than the classical optimization methods. Finally, it is concluded that the proposed methodology has a good potential for reliable design of composite channels for designer specified reliability values.

Water Resources Policy and Practice Issues Exposed by Katrina

Water Resources Policy and Practice Issues Exposed by Katrina

Irregular Wave Seepage and Overtopping of Permeable Slopes

Experiments were conducted in a wave flume to investigate wave seepage and overtopping of permeable stone slopes with wide crests. The numerical model based on the time-averaged continuity, momentum, and energy equations is extended to include the landward water flux due to wave seepage and overtopping. The measured wave runup distributions are fitted to the Weibull distribution whose shape parameter increases with the increase of the wave overtopping probability. The wave overtopping rate normalized by the wave-induced water flux at the still water shoreline is shown to depend on the wave overtopping probability and the horizontal number of stones above the maximum wave setup. A simple formula for the seepage rate is proposed by analyzing the seepage flow driven by the wave setup on the seaward slope. The extended numerical model is shown to be in agreement with the measurements of the free surface elevation, cross-shore velocity, wave runup, and seepage and overtopping rates but will need to be evaluated using more extensive data sets.

Improvement of overtopping risk evaluations using probabilistic concepts for existing dams

Hydrologic risk analysis for dam safety relies on a series of probabilistic analyses of rainfall-runoff and flow routing models, and their associated inputs. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated in order to evaluate the probability of dam overtopping. Typically, parametric density estimation methods have been applied in this setting, and the exhaustive Monte Carlo simulation (MCS) of models is used to derive some of the distributions. Often, the distributions used to model some of the random variables are inappropriate relative to the expected behaviour of these variables, and as a result, simulations of the system can lead to unrealistic values of extreme rainfall or water surface levels and hence of the probability of dam overtopping. In this paper, three major innovations are introduced to address this situation. The first is the use of nonparametric probability density estimation methods for selected variables, the second is the use of Latin Hypercube sampling to improve the efficiency of MCS driven by the multiple random variables, and the third is the use of Bootstrap resampling to determine initial water surface level. An application to the Soyang Dam in South Korea illustrates how the traditional parametric approach can lead to potentially unrealistic estimates of dam safety, while the proposed approach provides rather reasonable estimates and an assessment of their sensitivity to key parameters.

Quantitative flood risk assessment for Polders

In the Netherlands, the design of dikes and other water retaining structures is based on an acceptable probability (frequency) of overtopping. In 1993 a new safety concept was introduced based on total flood risk. Risk was defined as the product of probability and consequences. In recent years advanced tools have become available to calculate the actual flood risk of a polder. This paper describes the application of these tools to an existing lowland river area. The complete chain of calculations necessary to estimate the risk of flooding of a polder (or dike ring) is presented. The difficulties in applying the present day tools and the largest uncertainties in the calculations are shown.

Statistical Modeling of Overtopping for Extreme Waves on Fixed Deck

A statistical model is developed to predict wave overtopping of extreme waves on a fixed deck. The probability density function for the volume of overtopping water is based on the truncated Weibull distribution with the assumption of a local sinusoidal wave profile. The sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data for the instantaneous free surface elevation measured in front of a fixed deck and the instantaneous free surface elevation and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. Conditional sampling of the crest heights seaward of the deck gave a normalized probability distribution similar to that of the maximum water level measured on the deck for each overtopping event. The model prediction of the exceedance probability of deck overtopping gave very good agreement for large overtopping values.

Dynamic properties of green water event in the overtopping of extreme waves on a fixed dock

A statistical model is developed to predict wave overtopping volume and rate of extreme waves on a fixed deck. The probability density function for the volume and rate of overtopping water are formulated based on the truncated Weibull distribution with the assumption of local sinusoidal profile for small amplitude waves. Sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data of the instantaneous free surface elevation measured in front of a fixed deck, and overtopping volume and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. The model prediction of the exceedance probability of deck overtopping gave qualitatively good agreement for large overtopping values.

Irregular Wave Overtopping of Revetments in Surf Zones

Twelve test runs were conducted to examine the overtopping processes of normally incident irregular waves over a revetment of a 1:2 rough impermeable slope fronted by a gentle, smooth slope and situated well inside the surf zone. The measured overtopping probability and average overtopping rate are affected noticeably by the spectral shape and wave grouping of the incident irregular waves measured immediately outside the surf zone. The empirical procedure for estimating these overtopping quantities is found to yield only order‐of‐magnitude estimates for this experiment. The measurements made for the 12 runs are used to calibrate and evaluate the existing one‐dimensional, time‐dependent numerical model, which is modified slightly to allow the spatial variation of the bottom friction factor. The calibrated numerical model is shown to be fairly capable of predicting the average overtopping rate and the depth of overtopping flow on the crest of the revetment. The measured and predicted time series and spectra of the flow depth including entrained air show the grouped nature of irregular wave overtopping events.

STOCHASTIC ASPECTS OF DAM SAFETY ANALYSIS

A stochastic analysis is presented of the probability of overtopping of a dam. The discussion is based on the case of a dam for a small water storage reservoir which has recently been constructed in the Saar district in the FRG. The problem is first solved by means of a simulation method. However, it is possible to describe the result of the simulation method by means of a much simpler model which is based on a solution of the failure integral of Freudenthal for uncorrelated resistances and loads. It is shown that the actual safety of this dam against overtopping is extremely sensitive to both the operation rule for the reservoir, and the freeboard allowance. Some general conclusions are derived from this study for assisting in the ongoing discussion of dam safety.