National Academies Press: OpenBook

Pier and Contraction Scour in Cohesive Soils (2004)

Chapter: Chapter 11 - Future Hydrographs and Scour Risk Analysis

« Previous: Chapter 10 - Verification of the SRICOS-EFA Method
Page 89
Suggested Citation:"Chapter 11 - Future Hydrographs and Scour Risk Analysis." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
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Page 89
Page 90
Suggested Citation:"Chapter 11 - Future Hydrographs and Scour Risk Analysis." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
Page 90
Page 91
Suggested Citation:"Chapter 11 - Future Hydrographs and Scour Risk Analysis." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
Page 91
Page 92
Suggested Citation:"Chapter 11 - Future Hydrographs and Scour Risk Analysis." National Academies of Sciences, Engineering, and Medicine. 2004. Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press. doi: 10.17226/13774.
×
Page 92

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89 CHAPTER 11 FUTURE HYDROGRAPHS AND SCOUR RISK ANALYSIS 11.1 BACKGROUND Since the SRICOS-EFA Method predicts the scour depth as a function of time, one of the inputs is the velocity versus time curve, or hydrograph, at the foundation location. This hydro- graph should cover the period over which the scour depth must be predicted. A typical bridge is designed for 75 years. There- fore, the design for a new bridge requires the knowledge of the hydrograph from the year of construction until 75 years later. The question is: how can one obtain the future hydrograph covering that long period of time? This requires predicting the future over a 75-year period. One solution is to use a hydrograph recorded at a nearby gage station over the last 75 years and assume that the future hydrograph will be equal to the past hydrograph. If the gage is not at the future bridge location, the discharge can be mul- tiplied by the ratio of the drainage area at the bridge site over the drainage area at the gage site. If the record at the gage sta- tion is not 75 years long, one can simply repeat the recorded hydrograph until it covers the 75-year period. If the recorded hydrograph does not include the design flood (100-year flood or 500-year flood), one can spike the hydrograph with one or more of those floods before running the SRICOS program (Figure 11.1). Another solution is to use the new technique that is pre- sented here. This technique consists of using a past hydro- graph, preparing the frequency distribution plot for the floods within that hydrograph, sampling the distribution randomly and preparing a future hydrograph for the required period that has the same mean and standard deviation as the mea- sured hydrograph. This process is repeated 10,000 times and, for each hydrograph, a final scour depth (the depth reached after 75 years of flow) is generated. These 10,000 final depths of scour are organized in a frequency distribution plot with a mean and standard deviation. That plot can be used to quote a scour depth with a corresponding probability of occurrence, or better, to choose a risk level and quote the corresponding final depth of scour. 11.2 PREPARATION OF THE FUTURE HYDROGRAPHS The SRICOS-EFA Method determines the scour depth at the end of the bridge life as a progressive process driven by a given sequence of daily stream-flow values throughout the life, Lt, of the structure. The randomness of the hydrologic forcing suggests combining the scour model with some hydro- logical and statistical analyses. If the stream-flow sequence (or hydrograph) is modeled as a stochastic process, it is possible to set up a Monte Carlo procedure that samples different real- izations of the hydrograph (of length Lt) from that process and estimates (using the SRICOS-EFA Method) the scour depth, d, at the end of the bridge life for each of them. Thus, d is regarded as a random variable and its statistics can be studied in detail to determine the risk of failure associated with differ- ent choices of the design value of the scour depth. The modeling of daily stream-flow, Q, can be tackled using different approaches (e.g., Bras and Rodriguez-Iturbe, 1986; Montanari et al., 1997; 2000) corresponding to different levels of complexity. A first simple analysis suggested here consid- ers Q as a random, uncorrelated variable. A suitable distribu- tion is fit to the data and the hydrographs are then generated as a series of values sampled from such a distribution. Ongoing research also is applying other stochastic models to account for both the autocorrelation and the memory of the process and is assessing whether the temporal structure (i.e., both autocorre- lation and memory) of the stream-flow sequences is able to affect the statistical properties of the scour-depth probability distribution. The theoretical distribution used to model daily stream-flow observations needs to be defined only for positive values of Q, to have a positive skew, and to be able to provide an accurate representation of the extreme values (i.e., good fit at the upper tail of the distribution). As expected, the extreme values are found to greatly affect the scour depth estimates and an impre- cise modeling of stream-flow maxima could easily lead to unrealistic estimations of the scour depth statistics. Logarith- mic transformations are frequently used to study stream-flow extremes (e.g., Chow et al., 1988; Benjamin and Cornell, 1970); therefore, a log-normal distribution can be a good can- didate for modeling the daily stream-flows. The method of moments is used to determine the parameters of the distribu- tion. As such, Q is expressed as the exponential of a normally distributed random variable, y, with mean µ µ σ µ y Q Q Q = +         1 2 1 11 1 2 2Log ( . )

and standard deviation with µQ and σQ being the mean and the standard deviation of daily stream-flow, respectively. In the case of the Woodrow Wilson Bridge, stream-flow data is available at the Little Falls Station (USGS #01646500) on the Potomac River, approximately 13 km upstream from the bridge. Correction of the measured stream flow is applied by multiplying the values by the drainage area ratio. The cor- rection is on the order of 3%. Figure 11.2 shows the original hydrograph and the corresponding prediction of scour depth history using the SRICOS-EFA Method. The mean and stan- dard deviation of Q in the period of record 1931–2000 are µQ=327 m3s−1, and σQ=467 m3s−1, respectively, while the max- imum discharge in the 70-year-long record was 12,056 m3s−1. Synthetic hydrographs of the same length generated by sam- pling from a log-normal distribution of mean µQ and standard σ σ µy Q Q = +      Log 1 11 2 2 ( . ) 90 deviation σQ have, on average, a maximum value of about 12,000 m3s−1, which suggests that such a distribution gives an adequate representation of the extrema. Figure 11.3 shows an example of a generated future hydrograph and the associated scour depth history as predicted by the SRICOS-EFA Method. 11.3 RISK APPROACH TO SCOUR PREDICTIONS Many equally possible future hydrographs such as the one in Figure 11.3 are generated by the random sampling process. For each hydrograph, the SRICOS program generates a scour depth history, including a final depth of scour, d, at the end of the project life. These values of the final depth of scour can be organized in a frequency distribution. Figure 11.4 shows the probability distributions obtained for the example of the Woodrow Wilson Bridge at the end of a chosen bridge life, Lt. This analysis can be used to estimate the level of risk, R, associated with the choice of different design values of scour depth and project lives. By definition, the risk level is the prob- Hydrograph (Add 500year flood) 0 3000 6000 9000 12000 15000 18000 1960 1970 1980 1990 2000 Time (Year) St re am flo w (m 3 /s ) Scour Depth Vs. Time (Add 500year flood) 0 2 4 6 8 10 12 1960 1970 1980 1990 2000 Time (Year) Sc ou r D ep th (m ) (b) Scour Depth Vs. Time Curve (a) Hydrograph Original Hydrograph 0 3000 6000 9000 12000 15000 18000 1930 1940 1950 1960 1970 1980 1990 2000 Time (Year) St re am flo w (m 3 /s ) Original Scour Depth vs. Time 0 2 4 6 8 10 12 1930 1940 1950 1960 1970 1980 1990 2000 Time (Year) Sc ou r D ep th (m ) (b) Scour Depth vs. Time (a) Hydrograph Figure 11.1. Woodrow Wilson measured hydrograph spiked with a 500-year flood. Figure 11.2. Original hydrograph and scour depth versus time near Woodrow Wilson Bridge site.

ability that the design conditions are exceeded in the course of the life of the structure. Thus, from the probability distribution of d (Figure 11.4) it is possible to determine the cumulative distribution function (CDF) of d (Figure 11.5). The risk is then 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- linear function of d and Lt. This analysis provides a statistical framework that can be used in a cost–benefit study of bridge foundation design. Commonly accepted methods of scour analysis in cohe- sionless soils refer to a single peak-flow value selected on the basis of its return period, Tr, as well as to the associated level of risk. Such an approach does not account for the contribution to bridge scour due to smaller (and more frequent) floods. The SRICOS-EFA Method can be used to include the effect of the entire hydrograph. The Monte Carlo procedure outlined in this section represents a possible new probabilistic approach to scour analysis. Ongoing research is developing an extended version of this approach using different stochastic hydrologic models able to account for the daily flow distribution and for the autocorrelation of the stream-flow series. This study will 91 show whether the scour depth is sensitive to the temporal structure of stream-flow sequences and will indicate the level of detail that is necessary to include in the hydrologic stochas- tic model. 11.4 OBSERVATIONS ON CURRENT RISK LEVELS A direct comparison between the risk results obtained here with the SRICOS Method (Table 11.1) and traditional approaches based on single peak-flow values is not easy. Nevertheless, an example is provided here. The peak-flow value associated with a given return period can be deter- mined through a flood-frequency analysis (e.g., Chow et al., 1988; pp. 375–378). Figure 11.6 shows the result of such an analysis for the Woodrow Wilson Bridge measured hydro- graph. As can be seen on that figure, the 100-year flood has a discharge of 12,600 m3/s and the 500-year flood has a value of 16,600 m3/s. If the design life of the bridge is Lt, the Predicted Hydrograph (75year) 0 3000 6000 9000 12000 15000 18000 Time (Year) St re am flo w (m 3 /s ) Predicted Scour Depth Vs. Time 0 2 4 6 8 10 12 0 15 30 45 60 750 15 30 45 60 75 Time (Year) Sc ou r D ep th (m ) (b) Scour Depth vs. Time (a) Hydrograph 0 0.1 0.2 0.3 0.4 0.5 5 7.5 10 12.5 15 d (m) p(d ) Lt=50year Lt=75year Lt=100year Lt=150year 0.01 0.1 1 10 100 5 7.5 10 12.5 15 d (m) R (d) (% ) Lt=50year Lt=75year Lt=100year Lt=150year Figure 11.3. Predicted hydrograph and scour depth versus time curve near Woodrow Wilson Bridge site (Project time = 75 years). Figure 11.4. Probability distribution of scour depth, d, for different lengths of the project life, Lt. Figure 11.5. Risk associated with different design values of the final scour depth, d, and different lengths of the project life, Lt.

probability of exceedance or risk R for a flood having a return period Tr is given by the following: If the design life of the bridge is 75 years, the probabil- ity that the flood with a return period of 100 years will be exceeded during the 75-year design life is 53% (or about one chance out of two) according to Equation 11.3. For the 500-year flood and for the same 75-year design life, the risk is 14% (or about one chance in seven). Even if a bridge designed for a 100- or 500-year flood experiences a 1,000-year flood, this bridge may not collapse. Indeed, collapse of the bridge is based on a different criterion than just exceedance of the design flood. There are numerous inherent redundancies in the design of a bridge and many design parameters have to be exceeded before collapse occurs. Nevertheless, the risk level associated with the floods used in everyday design appears very high compared to risk levels in R Tr Lt= − −( )1 1 1 11 3( . ) 92 other disciplines within civil engineering. For example, struc- tural engineers have based their codes on a risk level of about 0.1%. Geotechnical engineers probably operate at about 1%. Scour engineers seem to operate at a much higher risk level. This is particularly worrisome since there is no safety factor on the depth of scour passed on from the scour engineer to the geotechnical engineer from which the pile length is calculated. One useful approach in this respect is to conduct a sensitiv- ity analysis by varying the input parameters and monitoring the impact of the parameter variation on the final scour depth. This would help in realizing how important each parameter is and give a range of scour depth values. Note that the proposed method is a prediction method, not a design method. Indeed, the equations were derived from a number of best-fit regres- sions against the experimental data. The proposed method becomes a design method when a factor of safety is added. The recommended factor of safety is 1.5. In other words, the pre- dicted final depth of scour should be multiplied by 1.5 before it becomes a design scour depth. Flood-frequency curve based on Original Hydrograph (1931-1999) y = -2 491. 6Ln(x) + 12629 R2 = 0.9563 0 5000 10000 15000 20000 0.1110100 Percent probability of exceedance in X years St re am flo w (m 3 /s ec ) 100 year flood: 12629m 3/s 500 year flood: 16639m 3/s 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% TABLE 11.1 Risk of failure associated with different design values of scour depth and project lives Figure 11.6. Flood-frequency curve for the Potomac River at the Woodrow Wilson Bridge.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 516: Pier and Contraction Scour in Cohesive Soils examines methods for predicting the extent of complex pier and contraction scour in cohesive soils.

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