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OCR for page 91
91 Predicted Hydrograph (75year) Predicted Scour Depth Vs. Time 18000 12 15000 10 Streamflow (m 3 /s) Scour Depth (m) 12000 8 9000 6 6000 4 3000 2 0 0 0 15 30 45 60 75 0 15 30 45 60 75 Time (Year) Time (Year) (a) Hydrograph (b) Scour Depth vs. Time Figure 11.3. Predicted hydrograph and scour depth versus time curve near Woodrow Wilson Bridge site (Project time = 75 years). ability that the design conditions are exceeded in the course of show whether the scour depth is sensitive to the temporal the life of the structure. Thus, from the probability distribution structure of stream-flow sequences and will indicate the level of d (Figure 11.4) it is possible to determine the cumulative of detail that is necessary to include in the hydrologic stochas- distribution function (CDF) of d (Figure 11.5). The risk is then tic model. estimated as the probability of exceedance (Figure 11.5). Table 11.1 reports the risk level associated with different proj- ect lives and design values of d. It is observed that R is a non- 11.4 OBSERVATIONS ON linear function of d and Lt. This analysis provides a statistical CURRENT RISK LEVELS framework that can be used in a costbenefit study of bridge foundation design. A direct comparison between the risk results obtained here Commonly accepted methods of scour analysis in cohe- with the SRICOS Method (Table 11.1) and traditional sionless soils refer to a single peak-flow value selected on the approaches based on single peak-flow values is not easy. basis of its return period, Tr, as well as to the associated level Nevertheless, an example is provided here. The peak-flow of risk. Such an approach does not account for the contribution value associated with a given return period can be deter- to bridge scour due to smaller (and more frequent) floods. The mined through a flood-frequency analysis (e.g., Chow et al., SRICOS-EFA Method can be used to include the effect of the 1988; pp. 375378). Figure 11.6 shows the result of such an entire hydrograph. The Monte Carlo procedure outlined in this analysis for the Woodrow Wilson Bridge measured hydro- section represents a possible new probabilistic approach to graph. As can be seen on that figure, the 100-year flood has scour analysis. Ongoing research is developing an extended a discharge of 12,600 m3/s and the 500-year flood has a version of this approach using different stochastic hydrologic value of 16,600 m3/s. If the design life of the bridge is Lt, the models able to account for the daily flow distribution and for the autocorrelation of the stream-flow series. This study will Lt=50year 100 Lt=75year Lt=50year Lt=100year 0.5 10 Lt=75year Lt=150year R(d) (%) 0.4 Lt=100year 1 0.3 Lt=150year p(d) 0.2 0.1 0.1 0.01 0 5 7.5 10 12.5 15 5 7.5 10 12.5 15 d (m) d (m) Figure 11.5. Risk associated with different design values Figure 11.4. Probability distribution of scour depth, d, of the final scour depth, d, and different lengths of the for different lengths of the project life, Lt. project life, Lt.
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92 TABLE 11.1 Risk of failure associated with different design values of scour depth and project lives Design value of Project Life Scour depth (m) 50 yrs 75 yrs 100 yrs 150 yrs 6.5 42% 74% 91% 99.8% 7.0 25% 48% 70% 93% 7.5 14% 27% 40% 65% probability of exceedance or risk R for a flood having a return other disciplines within civil engineering. For example, struc- period Tr is given by the following: tural engineers have based their codes on a risk level of about 0.1%. Geotechnical engineers probably operate at about 1%. R = 1 - (1 - 1 Tr ) Lt (11.3) Scour engineers seem to operate at a much higher risk level. This is particularly worrisome since there is no safety factor on If the design life of the bridge is 75 years, the probabil- the depth of scour passed on from the scour engineer to the ity that the flood with a return period of 100 years will be geotechnical engineer from which the pile length is calculated. exceeded during the 75-year design life is 53% (or about One useful approach in this respect is to conduct a sensitiv- one chance out of two) according to Equation 11.3. For the ity analysis by varying the input parameters and monitoring 500-year flood and for the same 75-year design life, the risk the impact of the parameter variation on the final scour depth. is 14% (or about one chance in seven). This would help in realizing how important each parameter is Even if a bridge designed for a 100- or 500-year flood and give a range of scour depth values. Note that the proposed experiences a 1,000-year flood, this bridge may not collapse. method is a prediction method, not a design method. Indeed, Indeed, collapse of the bridge is based on a different criterion the equations were derived from a number of best-fit regres- than just exceedance of the design flood. There are numerous sions against the experimental data. The proposed method inherent redundancies in the design of a bridge and many becomes a design method when a factor of safety is added. The design parameters have to be exceeded before collapse occurs. recommended factor of safety is 1.5. In other words, the pre- Nevertheless, the risk level associated with the floods used in dicted final depth of scour should be multiplied by 1.5 before everyday design appears very high compared to risk levels in it becomes a design scour depth. Flood-frequency curve based on Original Hydrograph (1931-1999) 20000 y = -2 491. 6L n(x) + 12629 2 R = 0. 9563 Streamflow (m3/sec) 15000 10000 100 year flood: 12629m 3 /s 5000 3 500 year flood: 16639m /s 0 100 10 1 0. 1 Percent probability of exceedance in X years Figure 11.6. Flood-frequency curve for the Potomac River at the Woodrow Wilson Bridge.