diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/02-hydrologic-risk-analysis.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/02-hydrologic-risk-analysis.mdx index 0453d30a4..3c8a6ef28 100644 --- a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/02-hydrologic-risk-analysis.mdx +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/02-hydrologic-risk-analysis.mdx @@ -21,14 +21,18 @@ This risk analysis includes the evaluation of an earthen embankment dam with a c shown in . The following examples generally build upon each other, and the risk analyses will progress from simple to more complex. - +{/*Table 1*/} + diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/03-example-1.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/03-example-1.mdx index 34dc86f45..e221198a1 100644 --- a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/03-example-1.mdx +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/03-example-1.mdx @@ -2,15 +2,18 @@ title: Example 1 - Single Failure Mode --- -import NavContainer from "@site/src/components/NavContainer"; -import VersionSelector from "@site/src/components/VersionSelector"; import Link from "@docusaurus/Link"; import addBaseUrl from "@docusaurus/useBaseUrl"; -import TableVertical from "@site/src/components/TableVertical"; -import TableReference from "@site/src/components/TableReference" -import FigureInline from "@site/src/components/FigureInline"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; import Figure from "@site/src/components/Figure"; -import FigureReference from "@site/src/components/FigureReference"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; th percentile, 50th percentile, and 95th percentile annual exceedance probabilities (AEP) were provided for each stage. To begin building the -model, add a tabular hazard function as demonstrated in the following steps and in . - -1. Right-click on the **Hazards** folder in - the Project Explorer window and select - **Add Tabular Hazard...** Name the hazard function in the prompt (e.g., Stage Frequency) and press **OK**. - -2. The hazard for the stage frequency curve is stage and is measured in feet. In the **Tabular Hazard Properties** section of the Properties - window, (a), select _Stage_ for **Hazard Type** and _ft_ for **Hazard Units**. - -3. The stage frequency curve is generally plotted on a normal probability-linear scale (i.e., AEP plotted on the x-axis on a normal probability scale - and stage plotted on the y-axis on a linear scale). In the **Interpolation Transforms** section of the Properties window, the **Hazard** is set to - _None_ (linear interpolation), and the **Probability** is set to _Normal Z-variate_, (b). - -4. The stage frequency data contains fixed stages and uncertainty for the AEP values. Since uncertainty is defined for the probabilities in the stage - frequency relationship and not the hazard, the **Uncertain Value** drop-down menu is set to _Probability_. Select an appropriate input distribution that - best defines the stage frequency dataset and enter the data into the hazard function. Uncertainty in the AEP is defined by 5th, 50th, - and 95th percentile values. _PERT-Percentile Z_ is selected from the **Distribution** drop-down menu as is typical for this type of analysis. - Enter the hazard function from by copying and pating into the table as indicated - in (c). - -. + + + Right-click on the Hazards folder in + the Project Explorer window and select + Add Tabular Hazard... Name the hazard function in the prompt (e.g., Stage Frequency) and press OK. + + ), + }, + //Step 2 + { + title: ( + <> + The hazard for the stage frequency curve is stage and is measured in feet. In the Tabular Hazard Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. The + stage frequency data contains fixed stages and uncertainty for the AEP values. Since uncertainty is defined for the probabilities in the stage frequency relationship and not + the hazard, uncheck the Hazard is Uncertain check box. + + ) + }, + //Step 3 + { + title: ( + <> + The stage frequency curve is generally plotted on a normal probability-linear scale (i.e., AEP plotted on the x-axis on a normal probability scale + and stage plotted on the y-axis on a linear scale). In the Interpolation Transforms section of the Properties window, the Hazard is set to  + None (linear interpolation), and the Probability is set to Normal Z-variate, (b). + + ) + }, + //Step 4 + { + title: ( + <> + Select an appropriate input distribution that best defines the stage frequency dataset and enter the data into the hazard function. Uncertainty in the AEP is defined by 5th, 50th, + and 95th percentile values. PERT-Percentile Z is selected from the Distribution drop-down menu as is typical for this type of analysis. + Enter the hazard function from by copying and pating into the table as indicated + in (c). + + ) + } + ]} /> -
+{/*Figure 1*/} +
+ +{/*Table 2*/} +th Percentile AEP' }, + { value: '50th Percentile AEP' }, + { value: '95th Percentile AEP' } + ] + ]} + columns={[ + [ + 640.35, 640.89, 641.16, 641.28, 641.62, 641.86, 642.77, 642.93, 643.12, '643.30', + 643.58, 643.72, 643.86, '644.00', 644.14, 644.16, 644.26, 644.51, 644.53, 644.56, + 644.58, 644.71, 644.78, 644.87, 644.95, 645.04, 645.13, 645.29, 645.87, 646.64, + 648.14, 650.65, 650.93, 652.01, 652.37, 652.77, 653.14, 653.78, 653.96, '654.10' + ], + [ + "9.33E-01", "7.49E-01", "5.56E-01", "4.68E-01", "2.73E-01", "1.92E-01", "9.32E-02", "8.43E-02", "7.50E-02", "6.49E-02", + "4.59E-02", "3.60E-02", "2.70E-02", "1.75E-02", "8.28E-03", "6.99E-03", "2.56E-03", "1.04E-03", "9.48E-04", "7.93E-04", + "6.99E-04", "1.63E-04", "1.00E-04", "8.68E-05", "7.52E-05", "6.21E-05", "5.00E-05", "4.58E-05", "3.32E-05", "2.52E-05", + "1.60E-05", "7.33E-06", "6.54E-06", "3.48E-06", "2.71E-06", "2.01E-06", "1.33E-06", "6.00E-07", "4.81E-07", "3.95E-07" + ], + [ + "9.48E-01", "7.88E-01", "5.92E-01", "4.93E-01", "3.12E-01", "2.20E-01", "1.20E-01", "1.08E-01", "9.60E-02", "8.52E-02", + "6.45E-02", "5.37E-02", "4.17E-02", "2.79E-02", "1.43E-02", "1.24E-02", "6.18E-03", "3.00E-03", "2.75E-03", "2.40E-03", + "2.19E-03", "6.92E-04", "6.41E-04", "5.77E-04", "5.20E-04", "4.58E-04", "4.00E-04", "3.75E-04", "2.99E-04", "2.52E-04", + "1.83E-04", "1.13E-04", "1.07E-04", "7.37E-05", "6.31E-05", "5.16E-05", "4.03E-05", "2.49E-05", "2.14E-05", "1.90E-05" + ], + [ + "9.66E-01", "8.22E-01", "6.32E-01", "5.39E-01", "3.49E-01", "2.68E-01", "1.45E-01", "1.33E-01", "1.19E-01", "1.06E-01", + "8.49E-02", "7.32E-02", "5.74E-02", "4.00E-02", "2.34E-02", "2.11E-02", "1.40E-02", "6.23E-03", "5.78E-03", "5.18E-03", + "4.72E-03", "2.45E-03", "1.98E-03", "1.91E-03", "1.84E-03", "1.76E-03", "1.68E-03", "1.59E-03", "1.23E-03", "9.50E-04", + "7.68E-04", "5.39E-04", "5.17E-04", "3.92E-04", "3.49E-04", "3.07E-04", "2.56E-04", "1.78E-04", "1.58E-04", "1.43E-04" + ] + ]} +/> ## Transforms @@ -103,306 +139,823 @@ for this analysis. The system response probabilities for the backward erosion piping potential failure mode were obtained from team elicitation using the event tree method. The elicited system response probabilities are shown in , and the corresponding failure mode event tree is shown -in . - - - Node 1
- Continuous Pathway
- Distribution: Triangular +in . + +{/*Table 3*/} + + Node 1
+ Continuous Pathway
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2
+ Unfiltered Exit Downstream
+ Distribution: Deterministic + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3
+ Initiation
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4
+ Progression (Mechanical)
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 5
+ Progression (Hydraulic)
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 6
+ Unsuccessful Intervention
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 7
+ Breach
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { value: ( + <> + Mean SRP w/ Intervention + + ), + colSpan: 2 + }, + { value: ( + <> + Mean SRP w/o Intervention + + ), + colSpan: 2 + } + ], + //Stage (ft) + [ + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", + null, null + ], + //641.00 + [ + '0.030', 0.095, '0.450', 0.192, + { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format + 0.999, + { value: "---", colSpan: 6 }, + 0.999, + '0.000', '0.000', '0.000', '0.000', + '0.500', '0.750', 0.999, '0.750', + '0.000', '0.000', '0.000', '0.000', + 0.005, '0.050', '0.050', 0.035, + '0.000', '0.000', '0.000', '0.000', + "0.00E+00", + "0.00E+00" + ], + //642.50 + [ + '0.030', 0.095, '0.450', 0.192, + { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format + 0.999, + { value: "---", colSpan: 6 }, + 0.999, + '0.010', '0.050', '0.100', 0.053, + '0.500', '0.750', 0.999, '0.750', + 0.002, '0.010', '0.100', 0.037, + '0.010', '0.070', '0.100', '0.060', + 0.015, 0.075, '0.200', 0.097, + "1.66E-06", + "2.76E-05" + ], + //644.00 + [ + '0.030', 0.095, '0.450', 0.192, + { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format + 0.999, + { value: "---", colSpan: 6 }, + 0.999, + '0.050', 0.075, '0.250', 0.125, + '0.500', '0.750', 0.999, '0.750', + 0.005, '0.040', '0.200', 0.082, + '0.010', '0.070', '0.100', '0.060', + '0.100', '0.200', '0.500', 0.267, + "2.34E-05", + "3.91E-04" + ], + //645.50 + [ + '0.030', 0.095, '0.450', 0.192, + null, 0.999, null, 0.999, + '0.090', '0.300', '0.500', 0.297, + '0.500', '0.750', 0.999, '0.750', + '0.010', 0.075, '0.300', 0.128, + '0.050', '0.200', '0.600', 0.283, + '0.200', '0.600', '0.900', 0.567, + "8.77E-04", + "3.10E-03" + ], + //647.50 + [ + '0.030', 0.095, '0.450', 0.192, + null, 0.999, null, 0.999, + '0.200', '0.600', '0.850', '0.550', + '0.500', '0.750', 0.999, '0.750', + 0.015, '0.090', '0.350', 0.152, + '0.900', '0.990', 0.999, 0.963, + '0.800', '0.950', 0.999, 0.916, + "1.06E-02", + "1.10E-02" + ], + //649.65 + [ + '0.030', 0.095, '0.450', 0.192, + null, 0.999, null, 0.999, + '0.500', '0.750', '0.900', 0.717, + '0.500', '0.750', 0.999, '0.750', + '0.020', 0.095, '0.400', 0.188, + '0.900', '0.990', 0.999, 0.963, + '0.900', '0.990', 0.999, 0.963, + "1.64E-02", + "1.70E-02" + ] + ]} + /> + +{/*Figure 2*/} +
+ +To build the event tree system response function for the BEP PFM, use the following procedure: + + + Right-click on the System Response folder in + the Project Explorer window and select + Add Event Tree Response... Name the system response function in the prompt (e.g., Backward Erosion Piping with Intervention). RMC-TotalRisk contains + a database of event trees for common potential failure modes that can be used for system response functions. For BEP, select Flood from the Category drop-down + menu and select Backward Erosion Piping from the Template drop-down menu and press OK. + + ) + }, + { //Step 2 + title: ( + <> + The hazard for the system response function is stage and is measured in feet. In the Event Tree Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. - ), - rowSpan: 4 - }, - null, null, null, - { - value: ( + ) + }, + { //Step 3 + title: ( + <> + In the Interpolation Transforms section of the Properties window, select interpolation methods that are best suited for the hazard and system response + probability. For this PFM, the Hazard is set to None (linear interpolation), and the Probability is set to Logarithmic, (b). + + ) + }, + { //Step 4 + title: ( + <> + Assign the hazard levels that define the system response curve to the event tree by clicking on the + Hazard node + symbol, (c), and entering the hazard levels into the Hazard Levels section + of the Properties window, (d). Alternatively, hazard levels can be assigned + by hovering over the Initiating Hazard node name, clicking the Branch Properties + symbol, and entering the hazard levels into the Hazard Levels section of the pop-up box that appears. The BEP PFM uses six hazard levels to define the + system response curve as shown in . Click the add + row symbol to add a new row to the bottom of the + hazard level table. + + ), + freeform: ( <> - Node 2
- Unfiltered Exit Downstream
- Distribution: Deterministic + {/*Figure 3*/} +
), - rowSpan: 4 }, - null, null, null, - { - value: ( - <> - Node 3
- Initiation
- Distribution: Triangular + { //Step 5 + title: ( + <> + Ensure the structure of the event tree, including the number, name, and description of each node, matches the potential failure mode being evaluated. To + add a branch to the event tree or delete a branch from the event tree, click on the symbol + and perform one of the following options: + + ), + child: [ + //Step 5a + { + title: ( + <> + Click the Add new branch button (to add a + branch) or the Delete all branches from this node + button (to delete branches) in the node toolbar, (a). + + ) + }, + //Step 5b + { + title: ( + <> + Click the Add Branch Node button (to add a + branch) or the Delete Branch button (to + delete branches) in the Sub-Branches section of the Properties window, (b). + + ) + } + ] + }, + { //Step 6 + title: ( + <> + The Name and Description of the node can be changed in the Select Branch Properties section of the Properties window, (c), + or by clicking the Branch Properties symbol. - ), - rowSpan: 4 + ), + freeform: ( + <> + {/*Figure 4*/} +
+ + ), }, - null, null, null, - { - value: ( - <> - Node 4
- Progression (Mechanical)
- Distribution: Triangular + { //Step 7 + title: ( + <> + Edit the nodal properties and enter system response probabilities for each node from into + the event tree. Select an event tree node by clicking on the event tree node symbol or name, (a). + Assign system response probabilities using the options located in the System Response section of the Properties window, (b). + The Source and Distribution options for the system response probabilities should be assigned to fit the probabilities estimated by the risk assessment team. + Node 1 in the BEP PFM is a stage-independent node, indicating that the probabilities do not change with stage, and was estimated with a minimum or lowest + reasonable value (LRV), most likely value (MLV), and a maximum or highest reasonable value (HRV). The Source for Node 1 is set to Single Value  + and the Distribution is set to Triangular. + ), + freeform: ( + <> + {/*Figure 5*/} +
+ ), - rowSpan: 4 + }, + { //Step 8 + title: ( + <> + The system response probabilities for Node 2 in the BEP PFM event tree are stage-independent but are only represented by a most likely value wthout a probability + distribution. To assign system response probabilities for Node 2, the Source is set to Single Value and the Distribution is set + to Deterministic, . The system response probabilities for Node 3 are stage-dependent + (i.e., the probabilities change with stage) and are represented by a LRV, MLV, and HRV. For Node 3, the Source is set to Multi Value and the + Distribution is set to Triangular, . Assign the system response probabilities for the remaining nodes + of the event tree using the same procedure. + + ), + + freeform: ( <> +
+ ), }, - null, null, null, - { - value: ( - <> - Node 5
- Progression (Hydraulic)
- Distribution: Triangular + { //Step 9 + title: ( + <> + Once the event tree has been completed, click on the Response tab within the event tree window to view a graph of the system response curve plotted against + stage. The mean system response curve is plotted with a blue dashed line, (a), and the + 90% confidence bounds are shaded in light blue, (b). This curve can be compared against + the system response probability input data to ensure accuracy. To change the graph axis extents, axis type, or axis properties, right click on the axis of + interest and click Format Axis: [Axis Name Here], (c). The Axis Type can be + set to Linear, Logarithmic, Normal Probability, or Gumbel Probability in the Axis Type drop-down menu within + the Properties window, (d), along with other axis customizations. - ), - rowSpan: 4 + ), + freeform: ( + <> +
+ + ) }, - null, null, null, - { - value: ( + ]} +/> + +## Consequences + +### Life Loss Function + +For this example, daytime and nighttime life loss estimates were developed for a range of reservoir stages for both non-breach and breach scenarios. The daytime +exposure scenario rate was assumed to be 45% while the nighttime exposure rate was assumed to be 55%. Three consequence functions are created in RMC-TotalRisk: +Day, Night, and Composite. The composite curves are created using the day and night scenarios weighted by their respective exposure rates. + + + Right-click on the + Consequences folder in the Project Explorer window and select + Add Tabular Consequence… Name the consequence function in the prompt (e.g., Non-Breach_Day) and press OK. + + ) + }, + { //Step 2 + title: ( <> - Node 6
- Unsuccessful Intervention
- Distribution: Triangular + For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, select Life Loss and Lives, (a). + + ) + }, + { //Step 3 + title: ( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). + + ) + }, + { //Step 4 + title: ( + <> + Select an appropriate input distribution and enter the life loss data into the consequence function. Uncertainty in the life loss values for this project is + defined by minimum, most likely, and maximum values for both the daytime and nighttime scenario, . For this dataset, a PERT distribution is selected from + the Distribution drop-down. Enter the stage and daytime life loss values from by copying and pasting into the table as + indicated in (c). + + ), + freeform: ( + <> + {/*Table 4*/} + + {/*Figure 8*/} +
+ + ) + }, + { //Step 5 + title: ( + <> + Repeat the same process to create a non-breach life loss consequence function for the nighttime scenario. Enter the stage and nighttime life loss values + from by copying and pasting into the table as indicated in . + + ), + freeform: ( + <> +
- ), - rowSpan: 4 - }, - null, null, null, - { - value: ( + ) + }, + { //Step 6 + title: ( + <> + Right-click on the Consequences folder in the Project Explorer window and select Add Composite Consequence… Name the consequence function + in the prompt (e.g., Non-Breach) and press OK. + + ) + }, + { //Step 7 + title: ( + <> + For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, select Life Loss and Lives, (a). + + ) + }, + { //Step 8 + title: ( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). + + ) + }, + { //Step 9 + title: ( + <> + Since pre-defined weights will be used to combine the daytime and nighttime scenarios, the Composite Type within the Consequence Functions section of the + Properties window is set to Mixture. To add consequence functions to the composite consequence function, click the Add row(s) to the bottom of the table button. + The Non-Breach_Day and Non-Breach_Night functions are selected from the drop-down menu, and the appropriate weights are assigned to each function to create the + composite, (c). + + ) + }, + { //Step 10 + title: ( <> - Node 7
- Breach
- Distribution: Triangular + To keep the Project Explorer window organized, multiple functions of the same type can be grouped together. Select the Non-Breach_Day, Non-Breach_Night, + and Non-Breach consequence functions by holding down the Shift key and selecting them. Right-click and + select Group. + Name or rename the group as desired, (d). + + ), + freeform: ( + <> +
- ), - rowSpan: 4 - }, - null, null, null, - { value: "Mean SRP w/ Intervention", colSpan: 2 }, - { value: "Mean SRP w/o Intervention", colSpan: 2 } - ], - [ // Second column - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - "LRV", "MLV", "HRV", "EV", - null, - null - ], - [ // 641.00 - "0.030", "0.095", "0.450", "0.192", - { value: "0.030", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format - { value: "0.095", colSpan: 6 }, - { value: "0.450", colSpan: 6 }, - { value: "0.192", colSpan: 6 }, - { value: "---", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format - { value: "0.999", colSpan: 6 }, - { value: "---", colSpan: 6 }, - { value: "0.999", colSpan: 6 }, - "0.000", "0.000", "0.000", "0.000", - { value: "0.500", colSpan: 6 }, // Expanding across the remaining columns in a "merged" format - { value: "0.750", colSpan: 6 }, - { value: "0.999", colSpan: 6 }, - { value: "0.750", colSpan: 6 }, - "0.000", "0.000", "0.000", "0.000", - "0.005", "0.05", "0.05", "0.035", - "0.000", "0.000", "0.000", "0.000", - "0.00E+00", - "0.00E+00" - ], - [ // 642.50 - { value: "Same as 641.00 (Pool Independent)", colSpan: 5, rowSpan: 4 }, null, null, null, // Expanding across the remaining columns in a "merged" format - null, null, null, null, - "0.010", "0.050", "0.100", "0.053", - null, null, null, null, - "0.002", "0.010", "0.100", "0.037", - "0.01", "0.07", "0.100", "0.06", - "0.015", "0.075", "0.2", "0.097", - "1.66E-06", - "2.76E-05" - ], - [ // 644.00 - null, null, null, null, - null, null, null, null, - "0.050", "0.075", "0.250", "0.125", - null, null, null, null, - "0.005", "0.0450", "0.200", "0.082", - "0.01", "0.07", "0.1", "0.06", - "0.1", "0.2", "0.5", "0.267", - "2.34E-05", - "3.91E-04" - ], - [ // 645.50 - null, null, null, null, - null, null, null, null, - "0.090", "0.300", "0.500", "0.297", - null, null, null, null, - "0.010", "0.075", "0.300", "0.128", - "0.05", "0.2", "0.6", "0.283", - "0.2", "0.6", "0.9", "0.567", - "8.77E-04", - "3.10E-03" - ], - [ // 647.50 - null, null, null, null, - null, null, null, null, - "0.200", "0.600", "0.850", "0.550", - null, null, null, null, - "0.015", "0.090", "0.350", "0.152", - "0.9", "0.99", "0.999", "0.963", - "0.8", "0.95", "0.999", "0.916", - "1.06E-02", - "1.10E-02" - ], - [ // 649.65 - null, null, null, null, - null, null, null, null, - "0.500", "0.750", "0.900", "0.717", - null, null, null, null, - "0.020", "0.095", "0.400", "0.188", - "0.9", "0.99", "0.999", "0.963", - "0.9", "0.99", "0.999", "0.963", - "1.64E-02", - "1.70E-02" - ] -]} -alt="Backward erosion piping system response probabilities." -caption="Backward erosion piping system response probabilities." + ) + }, + { //Step 11 + title: ( + <> + Follow the same procedure outlined in Steps 1 through 10 to create the consequence functions for an internal erosion breach using the data in . + BEP is an internal erosion mechanism, and internal erosion failure modes were assumed to have the same consequences in this example. The internal erosion + breach composite function is shown in . + + ), + freeform: ( + <> + {/*Table 5*/} + + {/*Figure 11*/} +
+ + ) + } + ]} /> -
+### Economic Cost -To build the event tree system response function for the BEP PFM, use the following procedure: +To create an economic cost consequence function, the procedure is the same as documented in [Life Loss Function](#life-loss-function). In step 2 and step 7, +the **Consequence** and **Consequence Unit** should be set to _Economic Cost_ and _$_, respectively. No economic costs were modeled for this example. -1. Right-click on the **System Response** folder in - the Project Explorer window and select - **Add Event Tree Response...** Name the system response function in the prompt (e.g., Backward Erosion Piping with Intervention). RMC-TotalRisk contains - a database of event trees for common potential failure modes that can be used for system response functions. For BEP, select _Flood_ from the **Category** - drop-down menu and select _Backward Erosion Piping_ from the **Template** drop-down menu and press **OK**. - -2. The hazard for the system response function is stage and is measured in feet. In the **Event Tree Properties** section of the Properties - window, (a), select _Stage_ for **Hazard Type** and _ft_ for **Hazard Units**. - -3. In the **Interpolation Transforms section of the Properties window, select interpolation methods that are best suited for teh hazard and system response - probability. For this PFM, the **Hazard** is set to _None_ (linear interpolation), and the **Probability\*\* is set to _Logarithmic_, (b). - -4. Assign the hazard levels that define the system response curve to the event tree by clicking on the Initiating - Hazard - symbol, (c), and entering the hazard levels into the **Hazard Levels** section - of the Properties window, (d). Alternatively, hazard levels can be assigned - by hovering over the Initiating Hazard node name, clicking the Branch Properties - symbol, and entering the hazard levels into the **Hazard Levels** section of the pop-up box that appears. The BEP PFM uses six hazard levels to define the - system response curve as shown in . Click the add - row symbol to add a new row to the bottom of the - hazard level table. - -
- -5. Ensure the structure of the event tree, including the number, name, and description of each node, matches the potential failure mode being evaluated. To - add a branch to the event tree or delete a branch from the event tree, click on the symbol - and perform one of the following options: - - - Click the **Add new branch** button (to add a - branch) or the **Delete all branches from this node** - button (to delete branches) in the node toolbar, (a). - - - Click the **Add Branch Node** button (to add a - branch) or the **Delete Branch** button (to - delete branches) in the **Sub-Branches** section of the Properties window, (b). - -6. The **Name** and **Description** of the node can be changed in the **Select Branch Properties** section of the Properties window, (c), - or by clicking the Branch Properties symbol. - -
- -7. Edit the nodal properties and enter system response probabilities for each node from - into the event tree. Select an event tree node by clicking on the event tree node symbol or name, (a). - Assign system response probabilities using the options located in the **System Response** section of the Properties window, (b). - The **Source** and **Distribution** options for the system response probabilities should be assigned to fit the probabilities estimated by the risk assessment team. - Node 1 in the BEP PFM is a stage-independent node, indicating that the probabilities do not change with stage, and was estimated with a minimum or lowest - reasonable value (LRV), most likely value (MLV), and a maximum or highest reasonable value (HRV). The **Source** for Node 1 is set to _Single Value_ - and the **Distribution** is set to _Triangular_. - -
- -8. The system response probabilities for Node 2 in the BEP PFM event tree are stage-independent but are only represented by a most likely value wthout a probability - distribution. To assign system response probabilities for Node 2, the **Source** is set to _Single Value_ and the **Distribution** is set to - _Deterministic_, . The system response probabilities for Node 3 are stage-dependent - (i.e., the probabilities change with stage) and are represented by a LRV, MLV, and HRV. For Node 3, the **Source** is set to _Multi Value_ and the **Distribution** - is set to _Triangular_, . Assign the system response probabilities for the remaining nodes - of the event tree using the same procedure. - -
- -9. Once the event tree has been completed, click on the **Response** tab within the event tree window to view a graph of the system response curve plotted against - stage. The mean system response curve is plotted with a blue dashed line, (a), and the - 90% confidence bounds are shaded in light blue, (b). This curve can be compared against - the system response probability input data to ensure accuracy. To change the graph axis extents, axis type, or axis properties, right click on the axis of - interest and click _Format Axis: [Axis Name Here]_, (c). The **Axis Type** can be - set to _Linear_, _Logarithmic_, _Normal Probability_, or _Gumbel Probability_ in the **Axis Type** drop-down menu within the **Properties** - window, (d), along with other axis customizations. - -
+## Risk Analyses -## Consequences +Once all necessary components have been added, a risk analysis is created using the following procedure. For this example, there is +only one risk analysis required to compute the life safety risk associated with the BEP failure mode. Had economic costs been modeled, +a separate risk analysis would have been necessary to compute the economic risk for the failure mode. -### Life Loss function + + Right-click the Risk Analyses folder and select Add Risk Analysis… Name the risk analysis in the prompt (e.g., Backward Erosion Piping + with Intervention) and press OK. + + ) + }, + { //Step 2 + title: ( + <> + For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, select Life Loss and Lives, (a). + + ) + }, + { //Step 3 + title: ( + <> + For this risk analysis one hazard function, one system response function, and two consequence functions are required, (b). Add + components to the risk analysis Diagram by clicking the green plus sign, clicking on a node output connector, or right-clicking anywhere in the diagram. + + ), + child: [ + { //Step 3a + title: ( + <> + First, add a hazard node to + the diagram. Select the hazard function (e.g., Stage Frequency) from the blank drop-down box in the hazard node. + + ) + }, + { //Step 3b + title: ( + <> + Next, add the non-breach condition by clicking on the hazard node output connector and adding a + consequence node and selecting + the composite non-breach life loss function (e.g., Non-Breach) from the drop-down box. + + ) + }, + { //Step 3c + title: ( + <> + Finally, add the backward erosion piping potential failure mode and the associated breach condition. + + ), + child: [ + { //Step 3c.i + title: ( + <> + Add a response node by clicking on the hazard node output connector and select the appropriate system response function + (e.g., Backward Erosion Piping with Intervention) from the drop-down box. + + ) + }, + { //Step 3c.ii + title: ( + <> + Add the breach condition by clicking on the response node output connector and adding a consequence node + and selecting the composite breach life loss function (e.g., Internal Erosion) from the drop-down box. + + ) + } + ] + }, + { //Step 3d + title: ( + <> + Re-arrange the nodes (click and hold, then drag) as desired to personalize the diagram. + + ) + } + ] + }, + { //Step 4 + title: ( + <> + When running a risk analysis with uncertainty, the simulation options can be adjusted within the Options tab of the Properties window. + + ), + child: [ + { //Step 4a + title:( + <> + Within the Simulation Options section, the Confidence Interval is set to 90% and Realizations is set + to 10,000, (a). + + ) + }, + { //Step 4b + title:( + <> + The Integration Options, System Component Options, System Options, and Risk Measure Options are + set to their default values, (b). + + ) + } + ] + }, + { //Step 5 + title: ( + <> + To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and + click Estimate, (c). To run the risk analysis with uncertainty, select Simulate Risk with Full Uncertainty. + + ), + freeform: ( + <> + {/*Figure 12*/} +
+ {/*Figure 13*/} +
+ + ) + } + ]} +/> -For this example, daytime and nighttime life loss estimates were developed for a range of reservoir stages for both non-breach and breach scenarios. The daytime -exposure scenario rate was assumed to be 45% while the nighttime exposure rate was assumed to be 55%. Three consequence functions are created in RMC-TotalRisk: -Day, Night, and Composite. The composite curves are created using the day and night scenarios weighted by their respective exposure rates. +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. The **Risk Types** reported +in RMC-TotalRisk are Incremental, Background, Total, Failure, and Non-Failure. For this example, the incremental _Mean, E[N]_ (also referred to +as the average annual life loss, AALL), of 1.11E-03 and an _Exceedance Probability, α_ (also referred to as annual probability of failure, APF) +of 7.02E-06 were calculated for BEP with intervention. + +The F-N Plot is viewed by clicking on the **F-N Plot** tab within the risk analysis window. The F-N Plot displays the probability distribution of +life loss from all potential failure modes and all population exposure scenarios for each inundation scenario. Incremental, background (non-breach), +and total (residual) risk can be portrayed on this plot as shown in **Error! Reference source not found.** The F-N Plot can also portray uncertainty + in the risk analysis results. shows the incremental risk F-N plot for this example with uncertainty. + +The α-ƞ Plot (also commonly referred to as the f-N̅ Plot) is viewed by clicking on the **α-ƞ Plot** tab within the risk analysis window. +The α-ƞ Plot displays the annual probability of failure and weighted average life loss with uncertainty, . + +{/*Figure 14*/} +
+{/*Figure 15*/} +
+{/*Figure 16*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/04-example-2.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/04-example-2.mdx new file mode 100644 index 000000000..d3afd975d --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/04-example-2.mdx @@ -0,0 +1,188 @@ +--- +title: Example 2 - Single Failure Mode, No Intervention +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 2 - Single Failure Mode, No Intervention + +This example starts with the completed risk analysis from [Example 1](./03-example-1.mdx) and adds the without intervention scenario. +The hazard, transform, and consequence functions will remain unchanged from [Example 1](./03-example-1.mdx). New RMC-TotalRisk concepts +covered by this example include copying an event tree and plotting the results of multiple risk analyses on the same plot. + +## Hazards + +The hydrologic hazard for this example is the same as [Example 1](./03-example-1.mdx). Reference procedure in [Hazards](./03-example-1.mdx#hazards) +from Example 1 to create the hazard function for this risk analysis. + +## Transforms + +The stage frequency, system response, and consequence data for this risk analysis are all a function of stage (ft). Therefore, a transform function is + not required for this analysis. + +## System Responses + +To build the event tree for the BEP PFM without the consideration of intervention, copy and paste the event tree completed in +[System Responses](./03-example-1.mdx#system-responses) +from Example 1 for BEP PFM with intervention and set the probability of no intervention in the event tree to 1.0 for all hazard levels. + + + Right-click on the Backward Erosion Piping with Intervention event tree in the System Responses folder in the + Project Explorer window and click Copy… Name the copied system response function in the prompt (e.g., Backward Erosion + Piping without Intervention) and press OK. + + ), + }, + { //Step 2 + title: ( + <> + Select the Backward Erosion Piping with Intervention event tree in the System Responses folder in the + Project Explorer window. + + ) + }, + { //Step 3 + title: ( + <> + Click on the “No Intervention” branch of the event tree. Set the Source to Single Value, set the Distribution to Deterministic, and input a value of 1, . + + ), + freeform: ( + <> + {/*Figure 17*/} +
+ + ) + }, + { //Step 4 + title: ( + <> + Click on the Response tab within the event tree window to view a graph of the system response curve plotted against stage, . + + ), + freeform: ( + <> + {/*Figure 18*/} +
+ + ) + } + ]} +/> + +## Consequences + +The consequence functions for this example are the same as [Example 1](./03-example-1.mdx). +Reference the procedure in [Consequences](./03-example-1.mdx#consequences) from Example 1 to create the consequence functions for this risk analysis. + +## Risk Analyses + +Create and simulate a new risk analysis for BEP without intervention. + + + Right-click on the Backward Erosion Piping with Intervention risk analysis in + the Risk Analyses folder in the Project Explorer window and click Copy… Name the copied risk analysis in the + prompt (e.g., Backward Erosion Piping without Intervention) and press OK. + + ) + }, + { //Step 2 + title: ( + <> + For the response node , use the drop-down box to change the response from “Backward Erosion Piping with Intervention” + to “Backward Erosion Piping without Intervention”, . + + ), + freeform: ( + <> + {/*Figure 19*/} +
+ + ) + }, + { //Step 3 + title: ( + <> + Use the procedure described in steps 4 and 5 of Risk Analyses from Example 1 to run the simulation. + + ) + } + ]} +/> + +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. In the Alternatives filter menu, +select “BEP without Intervention” to display the results in the same table as “BEP with Intervention” as shown in . This table shows the +incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 6.34E-03 without intervention and 1.09E-03 with intervention and an +_Exceedance Probability, α_ (also referred to as annual probability of failure, APF) of 3.71E-05 without intervention and 6.89E-06 with intervention. + +The incremental F-N Plot with uncertainty is shown in and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 20*/} +
+{/*Figure 21*/} +
+{/*Figure 22*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/05-example-3.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/05-example-3.mdx new file mode 100644 index 000000000..0af06b3d6 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/05-example-3.mdx @@ -0,0 +1,1281 @@ +--- +title: Example 3 - Multiple Failure Modes +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 3 - Multiple Failure Modes + +This example starts with the completed risk analysis from [Example 2](./04-example-2.mdx) and adds three additional PFMs: overtopping erosion (OT), +internal migration (IM) of embankment soils into the underlying rock foundation, and concrete lined spillway erosion (CLSE). +Each failure mode is evaluated with and without intervention. New RMC-TotalRisk concepts covered by this example include the use +of transform functions and system component options to combine multiple failure modes. + +## Hazards + +The hydrologic hazard for this example is the same as [Example 1](./03-example-1.mdx). Reference procedure in [Hazards](./03-example-1.mdx#hazards) +from Example 1 to create the hazard function for this risk analysis. + +## Transforms + +The hydrologic hazard has a **Hazard** of _Stage_ and **Hazard Units** of _ft_. The BEP, IM, and OT system response relationships are functions of stage; +however, the CLSE system response is a function of spillway discharge. Therefore, a transform function is required to convert the original hazard +of stage to spillway discharge for that PFM. + + + Right-click on the Transforms folder in + the Project Explorer window and select Add Tabular Transform… Name the transform function in the + prompt (e.g., Stage to Spillway Discharge) and press OK. + + ) + }, + { //Step 2 + title: ( + <> + The stage frequency hazard is stage and is measured in feet. The hazard for the concrete lined spillway erosion is spillway discharge and is measured + in cubic feet per second (cfs). In the Tabular Transform Properties section of the Properties window, (a), select Stage for Hazard Type, ft for Hazard Units, Flow for Transformed Hazard, and cfs for Transformed Units. + + ) + }, + { //Step 3 + title: ( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Transformed Hazard, (b). + + ) + }, + { //Step 4 + title: ( + <> + The relationship between stage and spillway discharge is defined by the dataset in . There is no uncertainty for the hazard or the transformed hazard, + so the Distribution drop-down menu is set to Deterministic, (c). Copy and paste the stage and spillway discharge + data from into the table, (d). + + ), + freeform: ( + <> + {/*Figure 23*/} +
+ {/*Table 6*/} + + + ) + }, + { //Step 5 + title: ( + <> + The consequence relationship for CLSE is a function of stage. Therefore, a transform function is also required to convert from spillway discharge back to stage. + Create a new transform by repeating steps 1 through 4, but with Flow for Hazard Type, cfs for Hazard Units, Stage for Transformed Hazard, and ft for Transformed Units. + Copy and paste the spillway discharge and stage data into the appropriate column of the table, . Flow will + be in the X column and Stage will be in the Value column. + + ), + freeform: ( + <> + {/*Figure 24*/} +
+ + ) + } + ]} +/> + +## System Responses + +The system response probabilities for each PFM were obtained from team elicitation using the event tree method. The elicited system response probabilities and the corresponding +failure mode event tree added to the analysis in this example are provided in the following tables and figures. + +The procedure for building the event trees for the PFMs in this example follows the same steps described in [System Responses](./03-example-1.mdx#system-responses) +from Example 1 for with intervention and from [Example 2](./04-example-2.mdx#system-responses) for without intervention. The **Hazard Type**, **Hazard Units**, and **Interpolation Transforms**, however, will be different for the CLSE failure mode. + compares the inputs of the PFMs added for Example 3 to the inputs for the BEP PFM that was created in Examples 1 and 2. + +{/*Table 7*/} + + Node 1
+ Unsuccessful Intervention
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Node 2 + value: ( + <> + Node 2
+ Slope Protection Failure
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Node 3 + value: ( + <> + Node 3
+ Initiation
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Node 4 + value: ( + <> + Node 4
+ Continuation
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Node 5 + value: ( + <> + Node 5
+ Breach
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Mean SRP w/ Intervention + value: ( + <> + Mean SRP w/ Intervention + + ), + colSpan: 2 + }, + { //Mean SRP w/o Intervention + value: ( + <> + Mean SRP w/o Intervention + + ), + colSpan: 2 + } + ], + [ // Stage (ft) + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", null, null + ], + [ //649.65 + '0.000', '0.000', '0.000', '0.000', '0.000', '0.000', '0.000', '0.000', + '0.500', '0.000', '0.000', '0.000', '0.000', '0.000', '0.000', '0.000', + '0.000', '0.000', '0.000', '0.000', "0.00E+00", "0.00E+00" + ], + [ // 650.15 + 0.003, 0.075, 0.225, 0.101, 0.001, 0.008, '0.060', 0.023, + '0.050', '0.350', '0.600', 0.333, 0.002, '0.010', '0.100', 0.037, + '0.000', '0.000', 0.001, '0.000', "4.82E-09", "4.77E-08" + ], + [ // 651.15 + '0.500', 0.775, '0.900', 0.725,'0.450', '0.680', '0.900', 0.677, + 0.055, '0.500', '0.850', 0.468, '0.050', '0.100', '0.580', 0.243, + '0.020', '0.300', '0.500', 0.273, "1.53E-02", "2.11E-02" + ], + [ // 652.15 + '0.850', 0.945, 0.999, 0.931,'0.750', '0.900', 0.999, 0.883, + '0.500', '0.750', '0.900', 0.717,'0.450', '0.780', '0.990', '0.740', + '0.500', '0.680', '0.900', 0.693, "3.02E-01", "3.25E-01" + ], + [ // 654.15 + 0.945, 0.995, 0.999, '0.980', '0.850', '0.900', 0.999, 0.916, + '0.750', '0.900', '0.990', '0.880', '0.900', '0.990', 0.999, 0.963, + '0.580', '0.750', '0.950', '0.760', "5.78E-01", "5.90E-01" + ], + [ // 656.60 + 0.995, 0.999, 0.999, 0.998, '0.990', 0.999, 0.999, 0.996, + 0.995, 0.999, 0.999, 0.998, '0.990', 0.999, 0.999, 0.996, + '0.700', '0.900', '0.990', 0.863, "8.52E-01", "8.54E-01" + ] + ]} +/> +{/*Figure 25*/} +
+{/*Figure 26*/} +
+{/*Figure 27*/} +
+{/*Figure 28*/} +
+{/*Table 8*/} + + Node 1
+ Open Defects
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2
+ Ineffective Treatment
+ Distribution: Deterministic + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3
+ Initiation
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4
+ Downstream Transport
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 5
+ Continuation
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 6
+ Progession (No Clogging)
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 7
+ Unsuccessful Intervention
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 8
+ Breach
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Mean SRP w/ Intervention + value: ( + <> + Mean SRP w/ Intervention + + ), + colSpan: 2 + }, + { //Mean SRP w/o Intervention + value: ( + <> + Mean SRP w/o Intervention + + ), + colSpan: 2 + } + ], + [ //Stage (ft) + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + null, null + ], + [ //641.00 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + '0.800', 0.895, 0.999, 0.898, 0.075, 0.225, '0.500', 0.267, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + 0.008, 0.045, '0.200', 0.084, 0.001, 0.002, 0.008, 0.004, + "5.96E-08", "7.07E-07" + ], + [ //642.50 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + 0.825, 0.945, 0.999, 0.923, '0.100', 0.238, '0.500', 0.279, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + 0.018, '0.050', '0.250', 0.106, 0.001, 0.004, '0.010', 0.005, + "1.10E-07", "1.04E-06" + ], + [ //644.00 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + 0.825, 0.945, 0.999, 0.923, 0.125, 0.275, 0.563, 0.321, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + 0.025, 0.075, '0.250', 0.117, 0.003, '0.010', 0.035, 0.016, + "4.45E-07", "3.81E-06" + ], + [ //645.50 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + 0.825, 0.945, 0.999, 0.923, 0.138, 0.313, 0.625, 0.359, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + '0.050', '0.100', '0.300', '0.150', 0.006, 0.025, 0.075, 0.035, + "1.41E-06", "9.41E-06" + ], + [ //647.50 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + '0.850', '0.960', 0.999, 0.936, '0.150', '0.400', '0.700', 0.417, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + '0.100', '0.250', '0.500', 0.283, '0.020', '0.080', '0.250', 0.117, + "1.04E-05", "3.66E-05" + ], + [ //649.65 + '0.040', '0.150', '0.450', 0.213, '0.100', '0.450', '0.750', 0.433, + 0.875, '0.970', 0.999, 0.948, 0.213, '0.450', 0.775, 0.479, + 0.003, 0.008, 0.075, 0.029, 0.068, 0.162, 0.681, 0.304, + 0.845, '0.900', 0.999, 0.915, '0.100', '0.250', 0.825, 0.392, + "1.31E-04", "1.43E-04" + ] + ]} +/> +{/*Figure 29*/} +
+{/*Figure 30*/} +
+{/*Figure 31*/} +
+{/*Figure 32*/} +
+{/*Table 9*/} + + Node 1
+ Uplift
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2a
+ Stagnation Pressure
+ Distribution: Deterministic + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2b
+ Stagnation Pressure
+ Distribution: Deterministic + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3a
+ Scour Initiates
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3b
+ Scour Initiates
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4a
+ Unsuccessful Intervention
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4b
+ Unsuccessful Intervention
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 5a
+ Scour Depth
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 5b
+ Scour Depth
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 6a
+ Undermining
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 6b
+ Undermining
+ Distribution: Deterministic + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 7a
+ Scour Width
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 7b
+ Scour Width
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 8a
+ Breach
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null,{ + value: ( + <> + Node 8b
+ Breach
+ Distribution: Triangular + + ), + rowSpan: 4 + }, + null, null, null, + { //Mean SRP w/ Intervention + value: ( + <> + Mean SRP w/ Intervention + + ), + colSpan: 2 + }, + { //Mean SRP w/o Intervention + value: ( + <> + Mean SRP w/o Intervention + + ), + colSpan: 2 + } + ], + [ //Stage (ft) + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + "LRV", "MLV", "HRV", "EV", "LRV", "MLV", "HRV", "EV", + null, null + ], + [ //25,000 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000',0.001,0.001,0.005,0.002, + 0.001,0.001,0.005,0.002, 0.001, 0.001,0.006,0.003, + 0.001,0.001,0.006,0.003, '0.900','0.950','0.990',0.947, + '0.900','0.950','0.990',0.947,'0.100','0.250','0.600',0.317, + '0.100','0.250','0.600',0.317,'0.050','0.100','0.400',0.183, + '0.050','0.100','0.400',0.183,'0.010','0.050','0.100',0.053, + '0.010','0.050','0.100',0.053,"0.00E+00","0.00E+00" + ], + [ //40,000 + '0.000','0.000',0.001,'0.000',0.006,'0.030','0.150',0.062, + '0.000','0.000','0.000','0.000',0.001,0.005,'0.010',0.005, + 0.001,0.005,'0.010',0.005,0.003,'0.030','0.100',0.044, + 0.003,'0.030','0.100',0.044,'0.990','0.990',0.999,0.993, + '0.990','0.990',0.999,0.993,'0.250','0.500','0.850',0.533, + '0.250','0.500','0.850',0.533,'0.080','0.150','0.450',0.227, + '0.080','0.150','0.450',0.227,0.025,0.075,'0.150',0.083, + 0.025,0.075,'0.150',0.083,"4.89E-11","1.10E-09" + ], + [ //90,000 + 0.001,0.001,0.003,0.002,0.035,'0.100',0.275,0.137, + '0.000',0.001,0.003,0.001,0.004,0.075,0.182,0.087, + 0.004,0.075,0.182,0.087,'0.150','0.500',0.825,0.492, + '0.150','0.500',0.825,0.492,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,'0.400','0.750','0.900',0.683, + '0.400','0.750','0.900',0.683,'0.090','0.200','0.550','0.280', + '0.090','0.200','0.550','0.280','0.050','0.090','0.250','0.130', + '0.050','0.090','0.250','0.130',"1.66E-06","3.37E-06" + ], + [ //180,000 + '0.010',0.075,0.175,0.087,'0.250','0.600','0.800','0.550', + 0.006,0.035,'0.200','0.080','0.100','0.350',0.696,0.382, + '0.100','0.350',0.696,0.382,0.775,0.925,0.995,0.898, + 0.775,0.925,0.995,0.898,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,'0.650','0.900','0.990',0.847, + '0.650','0.900','0.990',0.847,'0.100','0.450','0.750',0.433, + '0.100','0.450','0.750',0.433,'0.080','0.100','0.400',0.193, + '0.080','0.100','0.400',0.193,"2.94E-03","3.28E-03" + ], + [ //235,000 + '0.100','0.600',0.825,0.508,'0.550','0.800',0.945,0.765, + '0.010',0.075,0.325,0.137,0.325,0.688,0.878,'0.630', + 0.325,0.688,0.878,'0.630','0.900','0.970',0.999,0.956, + '0.900','0.970',0.999,0.956,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,'0.800','0.900','0.990',0.897, + '0.800','0.900','0.990',0.897,'0.250','0.700','0.900',0.617, + '0.250','0.700','0.900',0.617,'0.090','0.150','0.500',0.247, + '0.090','0.150','0.500',0.247,"3.75E-02","3.92E-02" + ] + ]} +/> +{/*Figure 33*/} +
+{/*Figure 34*/} +
+{/*Figure 35*/} +
+{/*Figure 36*/} +
+{/*Table 10*/} + + Step(s) from Example 1,
+ System Responses + + }, + { value: 'Backward Erosion
Piping' }, + { value: 'Overtopping Erosion' }, + { value: 'Internal Migration' }, + { value: 'Concrete Lined
Spillway Erosion' } + ] + ] + } + columns={[ + [ //Input + "Event Tree Category", "Event Tree Template", "Hazard Type", "Hazard Units", "Hazard Interpolation
Transform", "Probability Interpolation
Transform", + "Hazard Levels", "System Response
Probabilities" + ], + [ //Step(s) from Example 1, System Responses + "Step 1", "Step 1", "Step 2", "Step 2", "Step 3", "Step 3", "Step 4", "Step 7" + ], + [ //Backward Erosion Piping + "Flood", "Backward Erosion
Piping", "Stage", "ft", "None (linear)", "Logarithmic", + { value: <> 6
(See & ) }, + { value: <> See } + ], + [ //Overtopping Erosion + "Flood", "Embankment Overtopping
Erosion", "Stage", "ft", "None (linear)", "None (linear)", { value: <>6
(See & ) }, + { value: <>See } + ], + [ //Internal Migration + "Flood", "Internal Migration of
Embankment into
the Foundation", "Stage", "ft", "None (linear)", "Logarithmic", + { value: <>6
(See & ) }, + { value: <>See } + ], + [ //Concrete Lined Spillway Erosion + "Flood", "Concrete Lined
Spillway Erosion", "Flow", "cfs", "None (linear)", "Logarithmic", + { value: <>5
(See & ) }, + { value: <>See } + ] + ]} +/> + +## Consequences + +For this example, daytime and nighttime life loss estimates were developed for a range of reservoir stages for non-breach +() and the following breach scenarios: +internal erosion breach (, applies to BEP and IM PFM), overtopping breach (, applies to OT PFM) and concrete lined spillway erosion breach (, +applies to CLSE PMF). The daytime exposure scenario rate was assumed to be 45% while the nighttime exposure rate was assumed to be 55%. No economic costs were modeled +for this example. The procedure for creating a tabular life loss consequence function is detailed in [Life Loss Function](./03-example-1.mdx#life-loss-function) +from Example 1 and each input is accompanied by its procedural step. +A comparison of inputs between the life loss consequence functions is provided in . + +{/*Table 11*/} + +{/*Table 12*/} + +{/*Figure 37*/} +
+{/*Figure 38*/} +
+{/*Table 13*/} + + Step(s) from Example 1,
+ Life Loss Function + + }, + { value: 'Backward Erosion
Piping' }, + { value: 'Overtopping Erosion' }, + { value: 'Internal Migration' }, + { value: 'Concrete Lined
Spillway Erosion' } + ] + ] + } + columns={[ + [//Input + "Hazard Type", "Hazard Units", "Hazard Interpolation
Transform", "Probability Interpolation
Transform", + "Distribution", "Life Loss", "Composite Type" + ], + [//Step(s) from Example 1, Life Loss Function + "Step 2", "Steps 2 & 7", "Steps 3 & 8", "Steps 3 & 8", "Step 4", "Steps 4 & 5", "Step 9" + ], + [//Backward Erosion Piping + "Stage", "ft", "None (linear)", "None (linear)", "PERT", { value: <>See Table 5} + , "Mixture" + ], + [//Overtopping Erosion + "Stage", "ft", "None (linear)", "None (linear)", "PERT", { value: <>See }, "Mixture" + ], + [//Internal Migration + "Stage", "ft", "None (linear)", "None (linear)", "PERT", + { value: <>See Table 5}, + "Mixture" + ], + [//Concrete Lined Spillway Erosion + "Stage", "ft", "None (linear)", "None (linear)", "PERT", { value: <>See }, "Mixture" + ] + ]} +/> + +## Risk Analyses + +Once all necessary components have been added, a risk analysis is created using the following procedure. To evaluate the risk without and with +the consideration of intervention, two risk analyses will be needed: one with intervention and one without intervention. + + + Right-click on BEP with Intervention... + Rename the risk analysis in the prompt (e.g., Total Risk with Intervention) and press OK. + + ) + }, + { //Step 2 + title: ( + <> + Right-click on BEP without Intervention... + Rename the risk analysis in the prompt (e.g., Total Risk with Intervention) and press OK. + + ) + }, + { //Step 3 + title: ( + <> + For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, select Life Loss and Lives. + + ) + }, + { //Step 4 + title: ( + <> + For this risk analysis one hazard function, four system response functions, and five consequence functions are required. Add components to the risk analysis Diagram by + clicking the green plus sign, clicking on a node output connector, or right-clicking anywhere in the diagram. + + ), + child: [ + { //Step 4a + title: ( + <> + Add the overtopping erosion and internal migration potential failure modes and their associated breach conditions (backward erosion piping should + already be present). These PFMs have the same hazard (stage) as the hazard function and can be added to the risk analysis without a transform function. + + ), + child: [ + { //Step 4a.i + title: ( + <> + For each new PFM, add a response node by clicking + on the hazard node output connector and select the appropriate system response function from the drop-down box. + + ) + }, + { //Step 4a.ii + title: ( + <> + Add the breach condition to each response function by clicking on the response node output connector and adding a consequence node + and selecting the corresponding composite breach life loss function from the drop-down box. + + ) + }, + ] + }, + { //Step 4b + title: ( + <> + Add the concrete lined spillway erosion potential failure mode and its associated breach condition. Since this PFM is a function of spillway discharge (flow) + and the hazard and consequences are functions of stage, transform functions are required. + + ), + child: [ + { //Step 4b.i + title : ( + <> + Add a transform node by clicking on the hazard node + output connector and select the Stage to Spillway Discharge function from the drop-down box. + This transforms the hazard from the hazard function (stage) to the hazard of the CLSE PFM (spillway discharge). + + ) + }, + { //Step 4b.ii + title : ( + <> + Add a response node by clicking on the Stage to Spillway Discharge transform node output connector and select the appropriate + system response function (e.g., CLSE with Intervention) from the drop-down box. + + ) + }, + { //Step 4b.iii + title: + ( + <> + Add a transform node by clicking on the + CLSE response node output connector and select the Spillway Discharge to Stage function from the drop-down box. This transforms the hazard from the + system response function (spillway discharge) to the hazard of the CLSE consequences (stage). + + ) + }, + { //Step 4b.iv + title: + ( + <> + Add the CLSE breach condition by clicking on the Spillway Discharge to Stage node output connector and adding a consequence node + and selecting + the composite breach life loss function (e.g., CLSE Breach) from the drop-down box. + + ) + } + ] + }, + { //Step 4c + title: ( + <> + Re-arrange the nodes (click and hold, then drag) as desired to personalize the diagram. The final risk analysis diagram is shown in . + + ) + } + ], + freeform: ( + <> + {/*Figure 39*/} +
+ + ) + }, + { //Step 5 + title: ( + <> + Before running a risk analysis, the simulation options can be adjusted within the Options tab of the Properties window. + + ), + child: [ + { //Step 5a + title: ( + <> + Within the System Component Options section, set the Failure Mode Method to Joint Failures and set the Joint Consequences to Maximum, (a). + Additional options for Failure Mode Method include Common Cause Failures and Competing Failures (the Joint Consequences option will not be displayed if + either Common Cause Failures or Competing Failures is selected). + + ) + }, + { //Step 5b + title: ( + <> + Within the Simulation Options section, set the Confidence Interval to 90% and set + the Realizations to 10,000, (b). + + ) + }, + { //Step 5c + title: ( + <> + The Integration Options, (c), System Options, (d), + and Risk Measure Options, (e), are set to their default values. + + ) + } + ], + freeform: ( + <> + {/*Figure 40*/} +
+ + ) + }, + { //Step 6 + title: ( + <> + To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and click + Estimate. + To run the risk analysis with uncertainty, select Simulate Risk with Full Uncertainty and click Estimate. + + ) + }, + { //Step 7 + title: ( + <> + Follow the same procedure outlined in Steps 1 through 6 to create and run a second risk analysis for the without intervention scenario. The hazard and consequence + functions for this risk analysis are identical, while the responses are changed to the corresponding “without intervention” functions. + + ) + } + ]} +/> + +# Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. In the Alternatives filter menu, +select “Total Risk without Intervention” to display the results in the same table as “Total Risk with Intervention” as +shown in . This table shows the incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of +1.02E-02 without intervention and 4.75E-03 with intervention and an _Exceedance Probability, α_ (also referred to as annual +probability of failure, APF) of 9.63E-05 without intervention and 6.34E-05 with intervention. + +{/*Figure 41*/} +
+ +The incremental F-N Plot with uncertainty is shown in , the mean α-ƞ Plot is shown in +, and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 42*/} +
+ +{/*Figure 43*/} +
+ +{/*Figure 44*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/06-example-4.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/06-example-4.mdx new file mode 100644 index 000000000..125ffb910 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/06-example-4.mdx @@ -0,0 +1,664 @@ +--- +title: Example 4 - Spillway Gate Inoperability +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 4 - Spillway Gate Inoperability + +This example starts with the completed risk analysis from [Example 3](./05-example-3.mdx) and adds spillway gate inoperability. New RMC-TotalRisk concepts covered by this +example include weighting stage frequency relationships and the development of composite hazard curves. + +## Hazards + +In this example, the dam has three spillway Tainter gates. Inoperability of the Tainter gates impacts the hazard and introduces the following scenarios to the +risk analysis: 0 gates inoperable, 1 gate inoperable, 2 gates inoperable, and 3 gates inoperable. Based on a fault tree analysis, each gate was assumed to have the +same 0.48 probability of being inoperable. Binomial theorem was used to calculate the probability of each gate inoperability scenario, and the probabilities are shown in . + +{/*Table 14*/} + + +First, create a hazard function for each gate inoperability scenario using the stage frequency relationships in through and the procedure in [Hazards](./03-example-1.mdx#hazards) from Example 1. + +To build a composite stage frequency curve, the stage frequency curves either need to extend to the same maximum stage or the stage frequency curves need to be bounded +at their maximum stage. In this example, because the stage frequency curves stop at different maximum stages, each curve needs to be bounded using the following procedure. +Once bounded, the stage frequency curve will become horizontal at the maximum elevation. + +{/*Table 15*/} +th Percentile AEP' }, + {value: '50th Percentile AEP'}, + {value: '95th Percentile AEP'} + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.89,641.16,641.28,641.62,641.86,642.77,642.93, + 643.12,'643.30',643.58,643.72,643.86,'644.00',644.14,644.16, + 644.26,644.51,644.53,644.56,644.58,644.71,644.78,644.87, + 644.95,645.04,645.13,645.29,645.87,646.64,648.14,650.65, + 650.93,652.01,652.37,652.77,653.14,653.78,653.96,'654.10' + ], + [//5th Percentile AEP + "9.33E-01","7.49E-01","5.56E-01","4.68E-01","2.73E-01","1.92E-01","9.32E-02","8.43E-02", + "7.50E-02","6.49E-02","4.59E-02","3.60E-02","2.70E-02","1.75E-02","8.28E-03","6.99E-03", + "2.56E-03","1.04E-03","9.48E-04","7.93E-04","6.99E-04","1.63E-04","1.00E-04","8.68E-05", + "7.52E-05","6.21E-05","5.00E-05","4.58E-05","3.32E-05","2.52E-05","1.60E-05","7.33E-06", + "6.54E-06","3.48E-06","2.71E-06","2.01E-06","1.33E-06","6.00E-07","4.81E-07","3.95E-07" + ], + [//50th Percentile AEP + "9.48E-01","7.88E-01","5.92E-01","4.93E-01","3.12E-01","2.20E-01","1.20E-01","1.08E-01", + "9.60E-02","8.52E-02","6.45E-02","5.37E-02","4.17E-02","2.79E-02","1.43E-02","1.24E-02", + "6.18E-03","3.00E-03","2.75E-03","2.40E-03","2.19E-03","6.92E-04","6.41E-04","5.77E-04", + "5.20E-04","4.58E-04","4.00E-04","3.75E-04","2.99E-04","2.52E-04","1.83E-04","1.13E-04", + "1.07E-04","7.37E-05","6.31E-05","5.16E-05","4.03E-05","2.49E-05","2.14E-05","1.90E-05" + ], + [//(5th Percentile AEP) + "9.66E-01","8.22E-01","6.32E-01","5.39E-01","3.49E-01","2.68E-01","1.45E-01","1.33E-01", + "1.19E-01","1.06E-01","8.49E-02","7.32E-02","5.74E-02","4.00E-02","2.34E-02","2.11E-02", + "1.40E-02","6.23E-03","5.78E-03","5.18E-03","4.72E-03","2.45E-03","1.98E-03","1.91E-03", + "1.84E-03","1.76E-03","1.68E-03","1.59E-03","1.23E-03","9.50E-04","7.68E-04","5.39E-04", + "5.17E-04","3.92E-04","3.49E-04","3.07E-04","2.56E-04","1.78E-04","1.58E-04","1.43E-04" + ] + ]} +/> +{/*Table 16*/} +th Percentile AEP' }, + {value: '50th Percentile AEP'}, + {value: '95th Percentile AEP'} + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.67,641.31,641.63,642.27,642.59,642.90,643.22, + 643.54,643.86,'644.50',644.82,645.14,645.46,645.78,'646.10', + 646.42,646.74,647.06,647.38,647.69,648.01,648.33,648.65, + 648.97,649.29,649.61,649.93,650.25,650.57,650.89,651.21, + 651.53,651.85,652.16,652.48,'652.80',653.12,653.76,'654.40' + ], + [//5th Percentile AEP + "9.33E-01","8.60E-01","4.51E-01","2.70E-01","1.41E-01","1.08E-01","8.56E-02","7.03E-02", + "5.09E-02","2.98E-02","1.79E-03","2.61E-04","1.75E-04","1.30E-04","9.83E-05","8.62E-05", + "7.72E-05","6.93E-05","6.31E-05","5.74E-05","5.22E-05","4.75E-05","4.33E-05","3.95E-05", + "3.59E-05","3.27E-05","2.98E-05","2.73E-05","2.50E-05","2.29E-05","2.09E-05","1.81E-05", + "1.47E-05","1.19E-05","9.50E-06","7.50E-06","5.76E-06","4.07E-06","1.77E-06","6.81E-07" + ], + [//50th Percentile AEP + "9.48E-01","8.79E-01","4.73E-01","3.09E-01","1.65E-01","1.36E-01","1.10E-01","9.03E-02", + "6.89E-02","4.32E-02","4.53E-03","1.39E-03","7.95E-04","6.79E-04","6.18E-04","5.70E-04", + "5.28E-04","4.92E-04","4.62E-04","4.34E-04","4.08E-04","3.84E-04","3.62E-04","3.41E-04", + "3.22E-04","3.03E-04","2.84E-04","2.65E-04","2.47E-04","2.31E-04","2.16E-04","2.01E-04", + "1.76E-04","1.53E-04","1.34E-04","1.16E-04","1.01E-04","8.04E-05","4.72E-05","2.65E-05" + ], + [//95th Percentile AEP + "9.64E-01","8.97E-01","5.17E-01","3.45E-01","1.91E-01","1.62E-01","1.35E-01","1.12E-01", + "8.89E-02","5.97E-02","8.70E-03","3.20E-03","2.56E-03","2.12E-03","1.93E-03","1.84E-03", + "1.75E-03","1.67E-03","1.59E-03","1.51E-03","1.44E-03","1.37E-03","1.30E-03","1.24E-03", + "1.18E-03","1.12E-03","1.06E-03","1.01E-03","9.66E-04","9.25E-04","8.79E-04","8.22E-04", + "7.48E-04","6.73E-04","6.10E-04","5.51E-04","4.94E-04","4.15E-04","2.84E-04","1.84E-04" + ] + ]} +/> +{/*Table 17*/} +th Percentile AEP' }, + {value: '50th Percentile AEP'}, + {value: '95th Percentile AEP'} + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.69,641.37,641.71,642.39,642.73,643.07,643.41, + 643.75,644.09,644.77,645.11,645.45,645.79,646.13,646.47, + 646.81,647.15,647.49,647.82,648.16,'648.50',648.84,649.18, + 649.52,649.86,'650.20',650.54,650.88,651.22,651.56,'651.90', + 652.24,652.58,652.92,653.26,'653.60',653.94,654.62,'655.30' + ], + [//5th Percentile AEP + "9.33E-01","8.51E-01","4.12E-01","2.38E-01","1.28E-01","9.60E-02","7.74E-02","5.95E-02", + "3.91E-02","1.75E-02","1.45E-03","7.25E-04","5.90E-04","4.95E-04","4.47E-04","4.03E-04", + "3.64E-04","3.28E-04","2.96E-04","2.72E-04","2.51E-04","2.30E-04","2.12E-04","1.93E-04", + "1.73E-04","1.56E-04","1.40E-04","1.25E-04","1.12E-04","1.01E-04","8.17E-05","6.43E-05", + "4.96E-05","3.85E-05","2.96E-05","2.00E-05","1.19E-05","7.32E-06","2.43E-06","6.67E-07" + ], + [//50th Percentile AEP + "9.48E-01","8.72E-01","4.31E-01","2.77E-01","1.53E-01","1.24E-01","9.90E-02","7.94E-02", + "5.69E-02","2.74E-02","3.65E-03","2.71E-03","2.22E-03","1.94E-03","1.81E-03","1.69E-03", + "1.58E-03","1.48E-03","1.38E-03","1.29E-03","1.20E-03","1.12E-03","1.04E-03","9.71E-04", + "9.04E-04","8.52E-04","8.04E-04","7.53E-04","7.04E-04","6.31E-04","5.52E-04","4.73E-04", + "4.00E-04","3.36E-04","2.72E-04","2.06E-04","1.53E-04","1.13E-04","5.62E-05","2.56E-05" + ], + [//95th Percentile AEP + "9.65E-01","8.92E-01","4.78E-01","3.09E-01","1.80E-01","1.50E-01","1.24E-01","1.01E-01", + "7.51E-02","4.02E-02","7.50E-03","5.79E-03","4.94E-03","4.61E-03","4.30E-03","4.00E-03", + "3.81E-03","3.62E-03","3.45E-03","3.28E-03","3.12E-03","2.96E-03","2.82E-03","2.68E-03", + "2.55E-03","2.43E-03","2.31E-03","2.20E-03","2.09E-03","1.96E-03","1.73E-03","1.52E-03", + "1.34E-03","1.17E-03","1.03E-03","8.36E-04","6.64E-04","5.24E-04","3.19E-04","1.80E-04" + ] + ]} +/> +{/*Table 18*/} +th Percentile AEP' }, + {value: '50th Percentile AEP'}, + {value: '95th Percentile AEP'} + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.72,641.45,641.82,642.55,642.92,643.29,643.65, + 644.02,644.39,645.12,645.49,645.86,646.22,646.59,646.96, + 647.32,647.69,648.06,648.42,648.79,649.16,649.53,649.89, + 650.26,650.63,650.99,651.36,651.73,'652.10',652.46,652.83, + '653.20',653.56,653.93,'654.30',654.66,655.03,655.77,'656.50' + ], + [//5th Percentile AEP + "9.33E-01","8.39E-01","3.63E-01","1.99E-01","1.11E-01","8.48E-02","6.74E-02","5.21E-02", + "3.53E-02","2.25E-02","1.09E-02","9.06E-03","8.10E-03","7.25E-03","6.61E-03","6.08E-03", + "5.59E-03","5.13E-03","4.72E-03","4.35E-03","4.01E-03","3.68E-03","3.39E-03","3.11E-03", + "2.81E-03","2.51E-03","2.23E-03","1.97E-03","1.55E-03","1.21E-03","9.36E-04","6.83E-04", + "4.34E-04","2.56E-04","1.39E-04","7.64E-05","4.06E-05","1.99E-05","3.74E-06","7.26E-07" + ], + [//50th Percentile AEP + "9.49E-01","8.63E-01","3.82E-01","2.35E-01","1.38E-01","1.09E-01","8.76E-02","7.03E-02", + "5.15E-02","3.50E-02","1.98E-02","1.83E-02","1.69E-02","1.56E-02","1.44E-02","1.32E-02", + "1.22E-02","1.12E-02","1.03E-02","9.57E-03","8.96E-03","8.42E-03","7.92E-03","7.49E-03", + "7.08E-03","6.55E-03","6.03E-03","5.26E-03","4.48E-03","3.74E-03","3.06E-03","2.36E-03", + "1.71E-03","1.15E-03","7.81E-04","5.07E-04","3.26E-04","2.02E-04","7.39E-05","2.82E-05" + ], + [//95th Percentile AEP + "9.64E-01","8.83E-01","4.32E-01","2.81E-01","1.66E-01","1.37E-01","1.11E-01","9.03E-02", + "6.87E-02","4.92E-02","2.98E-02","2.77E-02","2.57E-02","2.39E-02","2.21E-02","2.05E-02", + "1.92E-02","1.82E-02","1.72E-02","1.62E-02","1.53E-02","1.45E-02","1.36E-02","1.28E-02", + "1.21E-02","1.14E-02","1.07E-02","1.01E-02","8.99E-03","7.80E-03","6.63E-03","5.45E-03", + "4.17E-03","3.07E-03","2.24E-03","1.62E-03","1.16E-03","8.06E-04","3.87E-04","1.94E-04" + ] + ]} +/> + +To build a composite stage frequency curve, the stage frequency curves either need to extend to the same maximum stage +or the stage frequency curves need to be bounded at their maximum stage. In this example, because the stage frequency +curves stop at different maximum stages, each curve needs to be bounded using the following procedure. Once bounded, +the stage frequency curve will become horizontal at the maximum elevation. + + + Click the add row symbol to add a new row to the bottom of the hazard function table. + + ) + }, + {//Step 2 + title: ( + <> + Input a stage minimally higher than maximum stage in the relationship (e.g. maximum stage plus 0.001), (a). + + ) + }, + {//Step 3 + title: ( + <> + Assign an exceedance probability of 1E-16 for the 5th percentile, the 50th percentile, and the 95th percentile values, (b). + + ), + freeform: ( + <> + {/*Figure 45*/} +
+ + ) + } + ]} +/> + +Next, build the composite hazard function. + + + Right-click on the Hazards folder + in the Project Explorer window and select + Add Composite Hazard… Name the hazard function in the prompt (e.g., Composite Hazard) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + The hazard for the composite stage frequency curve is stage and is measured in feet. In the Composite Hazard Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title: ( + <> + The stage frequency curve is generally plotted on a normal probability-linear scale (i.e., AEP plotted on the x-axis on a normal probability scale and stage + plotted on the y-axis on a linear scale). In the Interpolation Transforms section of the Properties window, the Hazard is set to None +   (linear interpolation), and the Probability is set to Normal Z-variate, (b). + + ) + }, + {//Step 4 + title: ( + <> + In the Hazard Functions section of the Properties window, check the box for Is Mixture, then click the add + row symbol to add rows to hazard function table. + Add a row for each gate inoperability scenario. Use the drop-down menu under Hazard Function in each row to select a gate inoperability scenario and input + the probability of that scenario under Weight, (c). + + ), + freeform: ( + <> + {/*Figure 46*/} +
+ + ) + } + ]} +/> + +## Transforms + +The addition of gate inoperability requires three transform functions: composite stage to spillway discharge, spillway discharge to composite stage, +and composite stage to the stage associated with 100% gate reliability. + +The composite hydrologic hazard has a **Hazard** of _Stage_ and **Hazard Units** of _ft_. The BEP, IM, and OT system response relationships are functions of stage; +however, the CLSE system response is a function of spillway discharge. Therefore, a transform function is required to convert the composite stage to +spillway discharge accounting for gate inoperability. The data for this transform is provided in . [Example 3](./05-example-3.mdx) already includes transform functions for +stage to spillway discharge and spillway discharge to stage, but these relationships are for 100% gate reliability. To update these relations to account for +gate inoperability, copy the data from and paste it into the transform table. For the stage to spillway discharge transform function, paste stage +into the **X** column and paste flow into the **Value** column . For the spillway discharge to stage transform function, paste the flow into the **X** column +and paste stage into the **Value** column, . + +{/*Table 19*/} + +{/*Figure 47*/} +
+{/*Figure 48*/} +
+ +Non-breach life loss is a function of stage for 0 gates inoperable or 100% gate reliability. A transform function is necessary to move from the composite or average +stage across all gate inoperability scenarios to the stage associated with 100% gate reliability. The data for this transform is provided in . + +{/*Table 20*/} + + + + Right-click on the Transforms folder in the Project Explorer + window and select Add Tabular Transform… Name the + transform function in the prompt (e.g., Composite Stage to 100% Reliable Stage) and press OK. + + ) + }, + {//Step 2 + title:( + <> + In the Tabular Transform Properties section of the Properties window, (a), select Stage for Hazard Type, + ft for Hazard Units, Stage for Transformed Hazard, and ft for Transformed Units. + + ) + }, + {//Step 3 + title:( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Transformed Hazard, (b). + + ) + }, + {//Step 4 + title:( + <> + There is no uncertainty for the hazard or transformed hazard, so the Distribution drop-down menu is set to Deterministic, (c). Copy and paste + the data from into the table, (d). + + ), + freeform: ( + <> + {/*Figure 49*/} +
+ + ) + } + ]} +/> + +## System Responses + +:::note +Add paragraph to discuss how overtopping and concrete lined spillway erosion system response probabilities could change + when using composite hazard. Composite hazard will affect durations of overtopping and spillway flow compared to example 3. + Best practice is to add multiple branches to the PFM sub-event tree for each operational performance scenario and assign the + operational performance probabilities to those branches. From there, the remainder of the event tree would be evaluated for + each scenario discretely to obtain the system response probability. + ::: + + The system response functions for this example are the same as those in [Example 3](./05-example-3.mdx#system-responses). + Reference the procedure in System Responses from [Example 1](./03-example-1.mdx#system-responses), [Example 2](./04-example-2.mdx#system-responses), and [Example 3](./05-example-3.mdx#system-responses) + to create the system response functions for this risk analysis. + +## Consequences + + The consequence functions for this example are the same as those in [Example 3](./05-example-3.mdx#consequences). + Reference the procedure in Consequences from [Example 1](./03-example-1.mdx#consequences), [Example 2](./04-example-2.mdx#consequences), and [Example 3](./05-example-3.mdx#consequences) + to create the system response functions for this risk analysis. + + ## Risk Analyses + + The risk analyses for Example 4 are setup in a similar fashion to those [Example 3](./05-example-3.mdx#risk-analyses), but the hazard function will now reference _Composite Hazard_ + and the _Composite Stage to 100% Reliable Stage_ transform is required between the hazard and the non-breach consequences. + + + Delete the existing non-breach consequence function at the top of the diagram by clicking the “x” in the top left corner of the box. + + ) + }, + {//Step 2 + title:( + <> + Add a transform node by clicking on the hazard node + output connector and select the Composite Stage to 100% Reliable Stage function from the drop-down box. + + ) + }, + {//Step 3 + title:( + <> + Add the non-breach condition by clicking on the transform function output connector and adding a + consequence node and selecting the composite + non-breach life loss function (e.g., Non-Breach) from the drop-down box to complete the diagram, . + + ), + freeform: ( + <> + {/*Figure 50*/} +
+ + ) + }, + {//Step 4 + title:( + <> + To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and + click Estimate. To run the risk analysis with + uncertainty, select Simulate Risk with Full Uncertainty and click Estimate. + + ) + }, + {//Step 5 + title:( + <> + Follow the same procedure outlined in Steps 1 through 4 to create and run a second risk analysis for the without intervention scenario. + The hazard, transform, and consequence functions for this risk analysis are identical, while the responses are changed to the corresponding + “without intervention” functions, . + + ), + freeform:( + <> + {/*Figure 51*/} +
+ + ) + } + ]} + /> + +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. In the Alternatives filter menu, +select “Total Risk without Intervention” to display the results in the same table as “Total Risk with Intervention” as shown in . +This table shows the incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 6.53E-02 without intervention and 5.67E-02 with +intervention and an _Exceedance Probability, α_ (also referred to as annual probability of failure, APF) of 4.68E-04 without intervention and 4.15E-04 with intervention. + +{/*Figure 52*/} +
+ +The incremental F-N Plot with uncertainty is shown in , the mean α-ƞ Plot is shown +in , and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 53*/} +
+{/*Figure 54*/} +
+{/*Figure 55*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/07-example-5.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/07-example-5.mdx new file mode 100644 index 000000000..6770096b7 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/07-example-5.mdx @@ -0,0 +1,776 @@ +--- +title: Example 5 - Debris Blockage +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 5 - Debris Blockage + +This example starts with the completed risk analysis from [Example 3](./05-example-3.mdx) and adds debris blockage. +A new RMC-TotalRisk concept covered by this example is calculating weights from cumulative density functions. These weights are used to develop a composite hazard curve. + +## Hazards + +Debris blockage of the Tainter gates reduces the outflow capacity of the gates and impacts the hazard. In this example, the following debris blockage scenarios were evaluated + in the risk analysis: 0% blockage, 10% blockage, 25% blockage, and 50% blockage. Cumulative density functions were estimated for each debris blockage scenario using team + elicitation and are summarized in . + +{/*Table 21*/} + + +First, create a hazard function for each debris blockage scenario using the stage frequency relationships in through and the procedure in [Hazards](./03-example-1.mdx#hazards) from Example 1. + +{/*Table 22*/} +th Percentile AEP' }, + { value: '50th Percentile AEP' }, + { value: '95th Percentile AEP' } + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.89,641.16,641.28,641.62,641.86,642.77,642.93, + 643.12,'643.30',643.58,643.72,643.86,'644.00',644.14,644.16, + 644.26,644.51,644.53,644.56,644.58,644.71,644.78,644.87, + 644.95,645.04,645.13,645.29,645.87,646.64,648.14,650.65, + 650.93,652.01,652.37,652.77,653.14,653.78,653.96,'654.10' + ], + [//5th Percentile AEP + "9.33E-01","7.49E-01","5.56E-01","4.68E-01","2.73E-01","1.92E-01","9.32E-02","8.43E-02", + "7.50E-02","6.49E-02","4.59E-02","3.60E-02","2.70E-02","1.75E-02","8.28E-03","6.99E-03", + "2.56E-03","1.04E-03","9.48E-04","7.93E-04","6.99E-04","1.63E-04","1.00E-04","8.68E-05", + "7.52E-05","6.21E-05","5.00E-05","4.58E-05","3.32E-05","2.52E-05","1.60E-05","7.33E-06", + "6.54E-06","3.48E-06","2.71E-06","2.01E-06","1.33E-06","6.00E-07","4.81E-07","3.95E-07" + ], + [//50th Percentile AEP + "9.48E-01","7.88E-01","5.92E-01","4.93E-01","3.12E-01","2.20E-01","1.20E-01","1.08E-01", + "9.60E-02","8.52E-02","6.45E-02","5.37E-02","4.17E-02","2.79E-02","1.43E-02","1.24E-02", + "6.18E-03","3.00E-03","2.75E-03","2.40E-03","2.19E-03","6.92E-04","6.41E-04","5.77E-04", + "5.20E-04","4.58E-04","4.00E-04","3.75E-04","2.99E-04","2.52E-04","1.83E-04","1.13E-04", + "1.07E-04","7.37E-05","6.31E-05","5.16E-05","4.03E-05","2.49E-05","2.14E-05","1.90E-05" + ], + [//95th Percentile AEP + "9.66E-01","8.22E-01","6.32E-01","5.39E-01","3.49E-01","2.68E-01","1.45E-01","1.33E-01", + "1.19E-01","1.06E-01","8.49E-02","7.32E-02","5.74E-02","4.00E-02","2.34E-02","2.11E-02", + "1.40E-02","6.23E-03","5.78E-03","5.18E-03","4.72E-03","2.45E-03","1.98E-03","1.91E-03", + "1.84E-03","1.76E-03","1.68E-03","1.59E-03","1.23E-03","9.50E-04","7.68E-04","5.39E-04", + "5.17E-04","3.92E-04","3.49E-04","3.07E-04","2.56E-04","1.78E-04","1.58E-04","1.43E-04" + ] + ]} +/> + +{/*Table 23*/} +th Percentile AEP' }, + { value: '50th Percentile AEP' }, + { value: '95th Percentile AEP' } + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.67,641.31,641.63,642.27,642.59,'642.90',643.22, + 643.54,643.86,'644.50',644.82,645.14,645.46,645.78,'646.10', + 646.42,646.74,647.06,647.38,647.69,648.01,648.33,648.65,648.97, + 649.29,649.61,649.93,650.25,650.57,650.89,651.21,651.53,651.85, + 652.16,652.48,'652.80',653.12,653.76,'654.40' + ], + [//5th Percentile AEP + "9.33E-01","8.60E-01","4.51E-01","2.70E-01","1.41E-01","1.08E-01","8.56E-02","7.03E-02", + "5.09E-02","2.98E-02","1.79E-03","2.61E-04","1.75E-04","1.30E-04","9.83E-05","8.62E-05", + "7.72E-05","6.93E-05","6.31E-05","5.74E-05","5.22E-05","4.75E-05","4.33E-05","3.95E-05", + "3.59E-05","3.27E-05","2.98E-05","2.73E-05","2.50E-05","2.29E-05","2.09E-05","1.81E-05", + "1.47E-05","1.19E-05","9.50E-06","7.50E-06","5.76E-06","4.07E-06","1.77E-06","6.81E-07" + ], + [//50th Percentile AEP + "9.48E-01","8.79E-01","4.73E-01","3.09E-01","1.65E-01","1.36E-01","1.10E-01","9.03E-02", + "6.89E-02","4.32E-02","4.53E-03","1.39E-03","7.95E-04","6.79E-04","6.18E-04","5.70E-04", + "5.28E-04","4.92E-04","4.62E-04","4.34E-04","4.08E-04","3.84E-04","3.62E-04","3.41E-04", + "3.22E-04","3.03E-04","2.84E-04","2.65E-04","2.47E-04","2.31E-04","2.16E-04","2.01E-04", + "1.76E-04","1.53E-04","1.34E-04","1.16E-04","1.01E-04","8.04E-05","4.72E-05","2.65E-05" + ], + [//95th Percentile AEP + "9.64E-01","8.97E-01","5.17E-01","3.45E-01","1.91E-01","1.62E-01","1.35E-01","1.12E-01", + "8.89E-02","5.97E-02","8.70E-03","3.20E-03","2.56E-03","2.12E-03","1.93E-03","1.84E-03", + "1.75E-03","1.67E-03","1.59E-03","1.51E-03","1.44E-03","1.37E-03","1.30E-03","1.24E-03", + "1.18E-03","1.12E-03","1.06E-03","1.01E-03","9.66E-04","9.25E-04","8.79E-04","8.22E-04", + "7.48E-04","6.73E-04","6.10E-04","5.51E-04","4.94E-04","4.15E-04","2.84E-04","1.84E-04" + ] + ]} + /> + +{/*Table 24*/} +th Percentile AEP' }, + { value: '50th Percentile AEP' }, + { value: '95th Percentile AEP' } + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.69,641.37,641.71,642.39,642.73,643.07,643.41, + 643.75,644.09,644.77,645.11,645.45,645.79,646.13,646.47, + 646.81,647.15,647.49,647.82,648.16,'648.50',648.84,649.18, + 649.52,649.86,'650.20',650.54,650.88,651.22,651.56,'651.90', + 652.24,652.58,652.92,653.26,'653.60',653.94,654.62,'655.30' + ], + [//5th Percentile AEP + "9.33E-01","8.51E-01","4.12E-01","2.38E-01","1.28E-01","9.60E-02","7.74E-02","5.95E-02", + "3.91E-02","1.75E-02","1.45E-03","7.25E-04","5.90E-04","4.95E-04","4.47E-04","4.03E-04", + "3.64E-04","3.28E-04","2.96E-04","2.72E-04","2.51E-04","2.30E-04","2.12E-04","1.93E-04", + "1.73E-04","1.56E-04","1.40E-04","1.25E-04","1.12E-04","1.01E-04","8.17E-05","6.43E-05", + "4.96E-05","3.85E-05","2.96E-05","2.00E-05","1.19E-05","7.32E-06","2.43E-06","6.67E-07" + ], + [//50th Percentile AEP + "9.48E-01","8.72E-01","4.31E-01","2.77E-01","1.53E-01","1.24E-01","9.90E-02","7.94E-02", + "5.69E-02","2.74E-02","3.65E-03","2.71E-03","2.22E-03","1.94E-03","1.81E-03","1.69E-03", + "1.58E-03","1.48E-03","1.38E-03","1.29E-03","1.20E-03","1.12E-03","1.04E-03","9.71E-04", + "9.04E-04","8.52E-04","8.04E-04","7.53E-04","7.04E-04","6.31E-04","5.52E-04","4.73E-04", + "4.00E-04","3.36E-04","2.72E-04","2.06E-04","1.53E-04","1.13E-04","5.62E-05","2.56E-05" + ], + [//95th Percentile AEP + "9.65E-01","8.92E-01","4.78E-01","3.09E-01","1.80E-01","1.50E-01","1.24E-01","1.01E-01", + "7.51E-02","4.02E-02","7.50E-03","5.79E-03","4.94E-03","4.61E-03","4.30E-03","4.00E-03", + "3.81E-03","3.62E-03","3.45E-03","3.28E-03","3.12E-03","2.96E-03","2.82E-03","2.68E-03", + "2.55E-03","2.43E-03","2.31E-03","2.20E-03","2.09E-03","1.96E-03","1.73E-03","1.52E-03", + "1.34E-03","1.17E-03","1.03E-03","8.36E-04","6.64E-04","5.24E-04","3.19E-04","1.80E-04" + ] + ]} + /> + +{/*Table 25*/} +th Percentile AEP' }, + { value: '50th Percentile AEP' }, + { value: '95th Percentile AEP' } + ] + ] + } + columns={[ + [//Stage (ft) + 640.35,640.72,641.45,641.82,642.55,642.92,643.29,643.65, + 644.02,644.39,645.12,645.49,645.86,646.22,646.59,646.96, + 647.32,647.69,648.06,648.42,648.79,649.16,649.53,649.89, + 650.26,650.63,650.99,651.36,651.73,'652.10',652.46,652.83, + '653.20',653.56,653.93,'654.30',654.66,655.03,655.77,'656.50' + ], + [//5th Percentile AEP + "9.33E-01","8.39E-01","3.63E-01","1.99E-01","1.11E-01","8.48E-02","6.74E-02","5.21E-02", + "3.53E-02","2.25E-02","1.09E-02","9.06E-03","8.10E-03","7.25E-03","6.61E-03","6.08E-03", + "5.59E-03","5.13E-03","4.72E-03","4.35E-03","4.01E-03","3.68E-03","3.39E-03","3.11E-03", + "2.81E-03","2.51E-03","2.23E-03","1.97E-03","1.55E-03","1.21E-03","9.36E-04","6.83E-04", + "4.34E-04","2.56E-04","1.39E-04","7.64E-05","4.06E-05","1.99E-05","3.74E-06","7.26E-07" + ], + [//50th Percentile AEP + "9.49E-01","8.63E-01","3.82E-01","2.35E-01","1.38E-01","1.09E-01","8.76E-02","7.03E-02", + "5.15E-02","3.50E-02","1.98E-02","1.83E-02","1.69E-02","1.56E-02","1.44E-02","1.32E-02", + "1.22E-02","1.12E-02","1.03E-02","9.57E-03","8.96E-03","8.42E-03","7.92E-03","7.49E-03", + "7.08E-03","6.55E-03","6.03E-03","5.26E-03","4.48E-03","3.74E-03","3.06E-03","2.36E-03", + "1.71E-03","1.15E-03","7.81E-04","5.07E-04","3.26E-04","2.02E-04","7.39E-05","2.82E-05" + ], + [//95th Percentile AEP + "9.64E-01","8.83E-01","4.32E-01","2.81E-01","1.66E-01","1.37E-01","1.11E-01","9.03E-02", + "6.87E-02","4.92E-02","2.98E-02","2.77E-02","2.57E-02","2.39E-02","2.21E-02","2.05E-02", + "1.92E-02","1.82E-02","1.72E-02","1.62E-02","1.53E-02","1.45E-02","1.36E-02","1.28E-02", + "1.21E-02","1.14E-02","1.07E-02","1.01E-02","8.99E-03","7.80E-03","6.63E-03","5.45E-03", + "4.17E-03","3.07E-03","2.24E-03","1.62E-03","1.16E-03","8.06E-04","3.87E-04","1.94E-04" + ] + ]} + /> + +Next, build a composite stage frequency curve. To build a composite stage frequency curve, the stage frequency curves either need to extend to the same +maximum stage or the stage frequency curves need to be bounded at their maximum stage. In this example, because the stage frequency curves stop at different +maximum stages, each curve needs to be bounded using the following procedure. Once bounded, the stage frequency curve will be horizontal once it reaches +the maximum elevation. + + + Click the add row symbol to add a new row to the bottom of the hazard function table. + + ) + }, + {//Step 2 + title: ( + <> + Input a stage minimally higher than maximum stage in the relationship (e.g. maximum stage plus 0.001), (a). + + ) + }, + {//Step 3 + title: ( + <> + Assign an exceedance probability of 1E-16 for the 5th percentile, the 50th percentile, and the 95th percentile values, (b). + + ), + freeform: ( + <> + {/*Figure 56*/} +
+ + ) + } + ]} +/> + +Calculate the probabilities for the debris blockage scenarios from the cumulative density functions. + + + Calculate the average probability of debris blockage across all stages for each debris blockage scenario. + The average probabilities are shown in . + + ), + freeform: ( + <> + {/*Table 26*/} + + + ) + }, + {//Step 2 + title: ( + <> + Calculate the average probability for mid-point blockage scenarios (5% blockage, 17.5% blockage, and 37.5% blockage) as shown in . + + ), + freeform: ( + <> + {/*Table 27*/} + + + ) + }, + {//Step 3 + title: ( + <> + Partition the debris blockage scenarios using the mid-point debris blockage scenarios and calculate the probability of blockage as shown in . + + ), + freeform: ( + <> + {/*Table 28*/} + + + ) + } + ]} +/> + +Next, build the composite hazard function. + + + Right-click on the Hazards folder + in the Project Explorer window and select + Add Composite Hazard… Name the hazard function in the prompt (e.g., Composite Hazard) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + The hazard for the composite stage frequency curve is stage and is measured in feet. In the Composite Hazard Properties section of + the Properties window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title: ( + <> + The stage frequency curve is generally plotted on a normal probability-linear scale (i.e., AEP plotted on the x-axis on a normal probability scale and + stage plotted on the y-axis on a linear scale). In the Interpolation Transforms section of the Properties window, the Hazard is + set to None (linear interpolation), and the Probability is set to Normal Z-variate, (b). + + ) + }, + {//Step 4 + title: ( + <> + In the Hazard Functions section of the Properties window, check the box for Is Mixture, then click the add row +  symbol to add rows to hazard function table. Add a row for each debris blockage scenario. Use the drop-down menu under Hazard Function in + each row to select a debris blockage scenario and input the probability of that scenario under Weight, (c). + + ), + freeform: ( + <> + {/*Figure 57*/} +
+ + ) + } + ]} +/> + +## Transforms + +The addition of debris blockage requires three transform functions: composite stage to spillway discharge, spillway discharge to composite stage, and +composite stage to the stage associated with 0% blockage. + +The composite hydrologic hazard has a **Hazard** of _Stage_ and **Hazard Units** of _ft_. The BEP, IM, and OT system response relationships are functions +of stage; however, the CLSE system response is a function of spillway discharge. Therefore, a transform function is required to convert the +composite stage to spillway discharge accounting for gate inoperability. The data for this transform is provided in . +[Example 3](./05-example-3.mdx) already includes transform functions for stage to spillway discharge and spillway discharge to stage, but these relationships are for 0% blockage. +To update these relations to account for gate inoperability, copy the data from and paste it into the transform table. For the +stage to spillway discharge transform function, pasted stage into the **X** column and paste flow into the **Value** column . For +the spillway discharge to stage transform function, paste the flow into the **X** column and paste stage into the **Value** column, . + +{/*Table 29*/} + +{/*Figure 58*/} +
+{/*Figure 59*/} +
+ +Non-breach life loss is a function of stage for the 0% blockage scenario. A transform function is necessary to move +from the composite or average stage across all debris blockage scenarios to the stage associated with 0% blockage. +The data for this transform is provided in . + +{/*Table 30*/} + + + + Right-click on the Transforms folder + in the Project Explorer window and select + Add Tabular Transform… Name the transform function in the prompt (e.g., Composite Stage to 0% Blockage Stage) and press OK. + + ) + }, + {//Step 2 + title:( + <> + In the Tabular Transform Properties section of the Properties window, (a), + select Stage for Hazard Type, ft for Hazard Units, Stage for Transformed Hazard, and ft for Transformed Units. + + ) + }, + {//Step 3 + title:( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Transformed Hazard, (b). + + ) + }, + {//Step 4 + title:( + <> + There is no uncertainty for the hazard or transformed hazard, so the Distribution drop-down menu is set to Deterministic, (c). + Copy and paste the data from into the table, (d). + + ), + freeform: ( + <> + {/*Figure 60*/} +
+ + ) + } + ]} +/> + +## System Responses + +The system response functions for this example are the same as those in [Example 3](./05-example-3.mdx). Reference the procedure in System Responses +from [Example 1](./03-example-1.mdx#system-responses), [Example 2](./04-example-2.mdx#system-responses), and [Example 3](./05-example-3.mdx#system-responses) +to create the system response functions for this risk analysis. + +## Consequences + +The consequence functions for this example are the same as those in [Example 3](./05-example-3.mdx). Reference the procedure in Consequences from +[Example 1](./03-example-1.mdx#consequences), [Example 2](./04-example-2.mdx#consequences), and [Example 3](./05-example-3.mdx#consequences) to create the +consequence functions for this risk analysis. + +## Risk Analyses + +The risk analyses for Example 5 are set up in a similar fashion to those in [Example 3](./05-example-3.mdx), but the hazard function will now reference +_Composite Hazard_ and the _Composite Stage to 0% Blockage Stage_ transform is required between the hazard and the non-breach consequences. + + + Delete the existing non-breach consequence function at the top of the diagram by clicking the “x” in the top left corner of the box. + + ) + }, + {//Step 2 + title:( + <> + Add a transform node by clicking on + the hazard node output connector and select the Composite Stage to 0% Blockage Stage function from the drop-down box. + + ) + }, + {//Step 3 + title:( + <> + Add the non-breach condition by clicking on the transform function output connector and adding a consequence node and + selecting the composite non-breach life loss function (e.g., Non-Breach) from the drop-down box to complete the diagram, . + + ), + freeform: ( + <> + {/*Figure 61*/} +
+ + ) + }, + {//Step 4 + title:( + <> + To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and + click Estimate. To run the + risk analysis with uncertainty, select Simulate Risk with Full Uncertainty and click Estimate. + + ) + }, + {//Step 5 + title:( + <> + Follow the same procedure outlined in Steps 1 through 4 to create and run a second risk analysis for the without intervention scenario. The hazard, + transform, and consequence functions for this risk analysis are identical, while the responses are changed to the corresponding “without intervention” + functions, . + + ), + freeform:( + <> + {/*Figure 62*/} +
+ + ) + } + ]} +/> + +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. In the Alternatives filter menu, select +“Total Risk without Intervention” to display the results in the same table as “Total Risk with Intervention” as shown in . This table shows the +incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 1.29E-01 without intervention and 1.17E-01 with intervention and an +_Exceedance Probability, α_ (also referred to as annual probability of failure, APF) of 9.29E-04 without intervention and 8.53E-04 with intervention. + +{/*Figure 63*/} +
+ +The incremental F-N Plot with uncertainty is shown in , the mean α-ƞ Plot is shown +in , and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 64*/} +
+{/*Figure 65*/} +
+{/*Figure 66*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/08-seismic-risk-analysis.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/08-seismic-risk-analysis.mdx new file mode 100644 index 000000000..62fd5a965 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/08-seismic-risk-analysis.mdx @@ -0,0 +1,19 @@ +--- +title: Seismic Risk Analysis +--- + +import NavContainer from "@site/src/components/NavContainer"; +import VersionSelector from "@site/src/components/VersionSelector"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import TableVertical from "@site/src/components/TableVertical"; +import TableReference from "@site/src/components/TableReference"; + + + +This risk analysis includes the evaluation of the same earthen embankment dam with a concrete gated spillway +as in the prior chapter, but for seismic failure modes instead of hydrologic failure modes. \ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/09-example-6.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/09-example-6.mdx new file mode 100644 index 000000000..cc24b85d9 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/09-example-6.mdx @@ -0,0 +1,1092 @@ +--- +title: Example 6 - Seismic Embankment Failure +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 6 - Seismic Embankment Failure + +This example steps through the evaluation of seismic crest deformation that leads to overtopping. New RMC-TotalRisk concepts covered +by this example include the development of an event tree with primary and secondary hazards and how to calculate the weights for the secondary hazard. + +## Hazards + +Two hazards are required for this risk analysis. The non-breach risk is a function of stage and is computed using the same stage frequency curve as in [Example 1](./03-example-1.mdx). +Reference the hazard function development in [Hazards](./03-example-1.mdx#hazards) from Example 1 to create the hazard for non-breach risk. + +The seismic failure mode and incremental risk in this example is a function of both PGA and stage. To model this in RMC-TotalRisk, stage duration will be the primary hazard +and PGA will be the secondary hazard. + +The primary hazard (stage duration) is developed first. + + + Right-click on the Hazards folder in the Project Explorer + window and select Add Tabular Hazard… Name + the hazard function in the prompt (e.g., Stage Duration) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + The hazard for the stage duration curve is stage and is measured in feet. In the Tabular Hazard Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title: ( + <> + Uncheck the Hazard is Uncertain check box. + + ) + }, + {//Step 4 + title: ( + <> + The stage duration curve is generally plotted on a linear scale. In the Interpolation Transforms section of the Properties window, the Hazard is set + to None (linear interpolation), and the Probability is set to None (linear interpolation), (b). + + ) + }, + {//Step 5 + title: ( + <> + Select an appropriate input distribution that best defines the stage frequency dataset and enter the data into the hazard function. + Because uncertainty was not considered in the development of this stage duration curve, Deterministic is selected from the Distribution drop-down + menu. Enter the hazard function from by copying and pasting into the table as + indicated in (c). + + ), + freeform: ( + <> + {/*Table 31*/} + + + {/*Figure 67*/} +
+ + ) + } + ]} +/> + +Development of the secondary hazard (PGA frequency) occurs in the system response event tree for each failure mode. The PGAs that define the system response +of the failure mode each get a branch in the event tree immediately after the stage duration hazard function as shown in . +Using the seismic hazard curve data in , weights are calculated for each PGA of the event tree. + +{/*Figure 68*/} +
+{/*Table 32*/} + + + + Identify the PGA values used to evaluate the system response (0.05g, 0.2g, 0.45g, and 0.68g), . Note that the first PGA must be equal to the + threshold for the system response (SRP equal to 0). + + ), + freeform: ( + <> + {/*Table 33*/} + + + ) + }, + {//Step 2 + title: ( + <> + Partition the seismic hazard function using the PGA threshold value, the mid-points between the PGAs that define the system response (), and the highest + PGA evaluated for the system response, . + + ), + freeform: ( + <> + {/*Table 34*/} + + + {/*Table 35*/} + + + ) + }, + {//Step 3 + title: ( + <> + Calculate the probability of having a PGA hazard within the partition by subtracting the AEP of the highest PGA of the partition from the AEP of the lowest PGA of + the partition, . + + ) + } + ]} +/> + +Building an event tree for a failure mode and applying these probabilities to the event tree will be covered in [System Responses](./09-example-6.mdx#system-responses). + +## Transforms + +The primary hazard (stage duration), system response, and consequence data for this risk analysis are all a function of stage (ft). Therefore, a transform function is not required. + +## System Responses + +The system response probabilities for embankment crest deformation were obtained from team elicitation using the event tree method. The elicited system response +probabilities are shown in and the corresponding failure mode event tree is shown in . When using RMC-TotalRisk to evaluate a failure mode that +is driven by a seismic hazard, the seismic hazard must be partitioned by assigning weights to each representative seismic ground motion evaluated for system response. + +{/*Table 36*/} + + Node 1
+ Liquefaction or
Cyclic Softening + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2a
+ More Deformation
than freeboard + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 2b
+ More Deformation
than freeboard + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3a
+ Intervention + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 3b
+ Intervention + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4a
+ Breach + + ), + rowSpan: 4 + }, + null, null, null, + { + value: ( + <> + Node 4b
+ Breach + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage + '641.00','642.50','644.00',649.63,'641.00','642.50','644.00',649.63, + '641.00','642.50','644.00',649.63,'641.00','642.50','644.00',649.63, + '641.00','642.50','644.00',649.63,'641.00','642.50','644.00',649.63, + '641.00','642.50','644.00',649.63 + ], + [//0.050 LRV + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.100','0.250','0.650',0.999, + 0.085,0.213,0.553,'0.900' + ], + [//0.050 MLV + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.450','0.650','0.900',0.999,0.383,0.553, + 0.765,'0.900' + ], + [//0.050 HRV + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.900',0.999,0.999,0.999,0.765, + '0.900','0.990',0.999 + ], + [//0.200 LRV + '0.150','0.150','0.150','0.150','0.000',0.009,'0.040','0.500', + '0.000',0.001,0.002,0.005,'0.000','0.050','0.080','0.650', + '0.000',0.001,'0.010',0.325,'0.350','0.500','0.850',0.999, + 0.298,0.425,0.723,'0.900' + ], + [//0.200 MLV + '0.500','0.500','0.500','0.500','0.000',0.085,'0.380','0.900', + '0.000',0.002,'0.010','0.020','0.000',0.075,'0.200','0.850', + '0.000',0.038,'0.100',0.425,'0.650','0.850','0.950',0.999, + 0.553,0.723,0.808,'0.900' + ], + [//0.200 HRV + '0.850','0.850','0.850','0.850','0.000','0.400','0.700',0.999, + '0.000','0.010','0.030','0.100','0.000','0.100','0.500','0.900', + '0.000','0.090','0.250','0.450','0.990',0.999,0.999,0.999,0.842, + '0.900','0.990',0.999 + ], + [//0.450 LRV + '0.250','0.250','0.250','0.250','0.000','0.020','0.100','0.740', + '0.000',0.002,0.004,'0.010','0.000',0.075,'0.100','0.750', + '0.000',0.001,0.002,0.375,'0.500','0.800','0.900',0.999, + 0.425,'0.680',0.765,'0.900' + ], + [//0.450 MLV + '0.650','0.650','0.650','0.650','0.000','0.250','0.680','0.990', + '0.000','0.010','0.020',0.071,'0.000','0.100','0.400','0.900', + '0.000',0.002,'0.200','0.450','0.850','0.900','0.990',0.999, + 0.723,0.765,0.842,'0.900' + ], + [//0.450 HRV + '0.900','0.900','0.900','0.900','0.000','0.600','0.900',0.999, + '0.000','0.030','0.080',0.114,'0.000','0.250','0.700','0.990', + '0.000',0.125,'0.350',0.495,0.999,0.999,0.999,0.999, + 0.849,'0.990',0.999,0.999 + ], + [//0.680 LRV + '0.400','0.400','0.400','0.400','0.000',0.065,'0.580','0.990', + '0.000',0.005,'0.010',0.015,'0.000','0.100','0.250','0.900', + '0.000',0.002,0.004,'0.450','0.750','0.900','0.990',0.999, + 0.638,0.765,0.842,'0.900' + ], + [//0.680 MLV + '0.750','0.750','0.750','0.750','0.000','0.470','0.900',0.999, + '0.000',0.014,'0.070',0.094,'0.000','0.300','0.650','0.990', + '0.000','0.150',0.325,0.495,'0.900','0.990',0.999,0.999, + 0.765,0.842,0.849,'0.900' + ], + [//0.680 HRV + '0.990','0.990','0.990','0.990','0.000','0.850',0.999,0.999, + '0.000','0.040',0.086,0.141,'0.000','0.400','0.900',0.999, + '0.000','0.200','0.450','0.500',0.999,0.999,0.999,0.999, + 0.849,'0.990',0.999,0.999 + ] + ]} +/> + +:::note +Figure 69 is missing. Add image. Placeholder below uses Figure 70's image. +::: + +{/*Figure 69*/} +
+{/*Figure 70*/} +
+ + + Right-click on the System Responses folder in the + Project Explorer window and select + Add Event Tree Response… Name the system response + function in the prompt (e.g. Crest Deformation). RMC-TotalRisk contains a database of event trees for common potential failure modes that can be used for system response + functions. Select Seismic from the Category drop-down menu and select the Crest Deformation failure mode from the Template drop-down menu and press OK. + + ) + }, + {//Step 2 + title:( + <> + The hazard for the system response function is stage and is measured in feet. In the Event Tree Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title:( + <> + In the Interpolation Transforms section of the Properties window, select interpolation methods that are best suited for the hazard and system response probability. + For this PFM, the Hazard is set to None (linear interpolation), and the Probability is set to Logarithmic, (b). + + ) + }, + {//Step 4 + title:( + <> + Assign the hazard levels that define the system response curve to the event tree by clicking on the Hazard + node symbol, (c) and entering the stage duration hazard levels into the Hazard Levels section of the Properties + window, (d). Alternatively, hazard levels can be assigned by hovering over the Hazard node name, clicking + the Branch Properties symbol, and entering the + hazard levels into the Hazard Levels section of the pop-up box that appears. The embankment deformation PFM uses four hazard levels to define the system + response curve as shown in . Click the remove row + symbol to remove a row from the middle of the hazard + level table before pasting or inputting data. + + ) + }, + {//Step 5 + title:( + <> + Hover over the Hazard node symbol and click + the Add new branch button (to add a branch). Repeat + until there five total branches (four seismic hazard branches and one no hazard branch). Rename the first four branches in this level of the event tree with the + PGA levels that define the system response and rename the final branch “remainder”, (e). + + ), + freeform: ( + <> + {/*Figure 71*/} +
+ + ) + }, + {//Step 6 + title:( + <> + Hover over the first system response node at the top of the tree and click copy all branches to + clipboard . Hover over the next node down in the event + tree and click paste copied branches to this node . Except + for the remainder node, repeat for the remaining nodes in this level of the event tree to complete the rest of the tree. + + ) + }, + {//Step 7 + title:( + <> + Ensure the structure of the event tree, including the number, name, and description of each node, matches the potential failure mode being evaluated. + + ) + }, + {//Step 8 + title:( + <> + The Name and Description of the node can be changed in the Selected Branch Properties section of the Properties window, or by clicking the Branch + Properties symbol. + + ) + }, + {//Step 9 + title:( + <> + Edit the nodal properties and enter the seismic weights into the tree (deterministic single value source) followed by the system response probabilities + from for each node in the event tree. Select an event tree node by clicking on the event tree node + symbol or name, (a). + Assign system response probabilities using the options located in the System Response section of the Properties + window (b). The Source and Distribution options for the system response probabilities should be assigned to fit the probabilities estimated by the + risk assessment team. + + ), + freeform: ( + <> + {/*Figure 72*/} +
+ + ) + } + ]} +/> + +{/*Figure 73*/} +
+{/*Figure 74*/} +
+ +## Consequences + +For this example, daytime and nighttime life loss estimates were developed for a range of reservoir stages for both non-breach and seismic embankment breach +scenarios. The daytime exposure scenario rate was assumed to be 45% while the nighttime exposure rate was assumed to be 55%. Three non-breach consequence functions +are created in RMC-TotalRisk: Day, Night, and Composite. The composite curves are created using the day and night scenarios weighted by their respective exposure rates. + + + Right-click on the Consequences folder in the Project Explorer window and + select Add Tabular Consequence… Name the + consequence function in the prompt (e.g., Non-Breach_Day) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, select Life Loss and Lives, (a). + + ) + }, + {//Step 3 + title: ( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). + + ) + }, + {//Step 4 + title: ( + <> + Select an appropriate input distribution and enter the life loss data into the consequence function. Uncertainty in the life loss values for this project is defined by + minimum, most likely, and maximum values for both the daytime and nighttime scenario, . For this dataset, + a PERT distribution is selected from the Distribution drop-down. Enter the stage and daytime life loss values from by copying and pasting into the table as indicated in (c). + + ), + freeform: ( + <> + {/*Table 37*/} + + {/*Figure 75*/} +
+ + ) + }, + {//Step 5 + title: ( + <> + Repeat the same process to create a non-breach life loss consequence function for the nighttime scenario. Enter the stage and nighttime life loss values + from by copying and pasting into the consequence table as indicated in . + + ), + freeform: ( + <> + {/*Figure 76*/} +
+ + ) + }, + {//Step 6 + title: ( + <> + Right-click on the Consequences folder in the Project + Explorer window and select + Add Composite Consequence… Name the consequence function in the prompt (e.g., Non-Breach) and press OK. + + ) + }, + {//Step 7 + title: ( + <> + For Hazard Type and Hazard Units, select Stage and ft. For Consequence and Consequence Unit, + select Life Loss and Lives, (a). + + ) + }, + {//Step 8 + title: ( + <> + The Interpolation Transforms are set to None (linear interpolation) for both the Hazard and Consequences, (b). + + ) + }, + {//Step 9 + title: ( + <> + Since pre-defined weights will be used to combine the daytime and nighttime scenarios, the Composite Type within the Consequence Functions section of the + Properties window is set to Mixture. To add consequence functions to the composite consequence function, click + the Add row(s) to the bottom of the table button. The + Non-Breach_Day and Non-Breach_Night functions are selected from the drop-down menu and the appropriate weights are assigned to each function to create the + composite, (c). + + ) + }, + {//Step 10 + title: ( + <> + To keep the Project Explorer window organized, multiple functions of the same type can be grouped together. Select the Non-Breach_Day, Non-Breach_Night, and + Non-Breach consequence functions by holding down the Shift key and selecting them. + Right-click and select Group. Name or rename the + group as necessary, (d). + + ), + freeform: ( + <> + {/*Figure 77*/} +
+ + ) + }, + {//Step 11 + title: ( + <> + Follow the same procedure outlined in Steps 1 through 10 to create the consequence functions for a seismic embankment breach using the + data in . The seismic embankment breach composite function is shown in . + + ), + freeform: ( + <> + {/*Table 38*/} + + {/*Figure 78*/} +
+ + ) + } + ]} +/> + +## Risk Analyses + +Once all necessary components have been added, a risk analysis is added using the following procedure. For this example, there are only two risk analyses required to +compute the life safety risk associated with the seismic crest deformation failure mode: one with intervention and one without intervention. + +:::note +Replace figure 79 with correct non-breach risk +::: + +:::note +Replace figure 80 with correct non-breach risk +::: + +:::note +Replace figure 81 with correct non-breach risk +::: + + + Right-click the Risk Analyses folder and + select Add Risk Analysis… Name the + risk analysis in the prompt (e.g., Crest Deformation without Intervention) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, + select Life Loss and Lives, (a). + + ) + }, + {//Step 3 + title: ( + <> + For this risk analysis two hazard functions, one system response function, and two consequence functions are + required, (b). Add components to the risk analysis Diagram by clicking + the green plus sign, clicking on a node + output connector, or right-clicking anywhere in the diagram. + + ), + child: [ + {//Step 3a + title: ( + <> + First, add a hazard node to the diagram. + Select the hazard function (e.g., Stage Frequency) for the non-breach risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3b + title: ( + <> + Next, add the non-breach condition by clicking on the non-breach risk hazard node output connector and adding a consequence + node and selecting the composite non-breach + life loss function (e.g., Non-Breach) from the drop-down box. + + ) + }, + {//Step 3c + title: ( + <> + Add a second hazard node to the diagram. + Select the hazard function (e.g., Stage Duration) for the incremental risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3d + title: ( + <> + Finally, add the crest deformation potential failure mode and the associated breach condition to the incremental risk hazard node. + + ), + child: [ + {//Step 3d.i + title: ( + <> + Add a response node by clicking on the + incremental risk hazard node output connector and select the appropriate system response function (e.g., Crest Deformation with Intervention) from the drop-down box. + + ) + }, + {//Step 3d.ii + title: ( + <> + Add the breach condition by clicking on the response node output connector and adding a consequence + node and selecting the + composite breach life loss function (e.g., Seismic Embankment Breach) from the drop-down box. + + ) + } + ], + }, + {//Step 3e + title: ( + <> + Re-arrange the nodes (click and hold, then drag) as desired to personalize the diagram. + + ) + } + ], + freeform: ( + <> + {/*Figure 79*/} +
+ + ), + }, + {//Step 4 + title: ( + <> + When running a risk analysis with uncertainty, the simulation options can be adjusted within the Options tab of the Properties window. + + ), + child: [ + {//Step 4a + title: ( + <> + Within the Simulation Options section, the Confidence Interval is set to 90% and Realizations is set to 10,000, (a). + + ) + }, + {//Step 4b + title: ( + <> + The Integration Options, System Component Options, System Options, and Risk Measure Options are set to their default values, (b). + + ) + } + ] + }, + {//Step 5 + title: ( + <> + To run the risk analysis without uncertainty, select Simulate Mean Risk Only in the Simulation section of the Properties window and + click Estimate, (c). To + run the risk analysis with uncertainty, select Simulate Risk with Full Uncertainty. + + ), + freeform: ( + <> + {/*Figure 80*/} +
+ + ) + }, + {//Step 6 + title: ( + <> + Follow the same procedure outlined in steps 1 through 5 to create and run a second risk analysis for the without intervention scenario. The hazard, transform, + and consequence functions for this risk analysis are identical, while the responses are changed to the corresponding “without intervention” + functions, . + + ), + freeform: ( + <> + {/*Figure 81*/} +
+ + ) + } + ]} +/> + +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results. In the Alternatives filter menu, select +“Total Risk without Intervention” to display the results in the same table as “Total Risk with Intervention” as shown in . This +table shows the incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 9.78E-05 without intervention and 6.00E-06 with intervention +and an _Exceedance Probability, α_ (also referred to as annual probability of failure, APF) of 2.95E-08 without intervention and 1.77E-08 with intervention. + +The incremental F-N Plot with uncertainty is shown in , and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 82*/} +
+{/*Figure 83*/} +
+{/*Figure 84*/} +
+ + diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/10-example-7.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/10-example-7.mdx new file mode 100644 index 000000000..92b664b86 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/10-example-7.mdx @@ -0,0 +1,1157 @@ +--- +title: Example 7 – Seismic Gated Spillway (Single Failure Mode) +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; + + + +# Example 7 – Seismic Gated Spillway (Single Failure Mode) + +In this example, components of a concrete gated spillway are subject to failure when exposed to shaking during an earthquake. The spillway consists of three Tainter gates, +two piers, two middle anchorages, and two end anchorages, . For this risk analysis, only failure of the Tainter gates is evaluated. + +{/*Figure 85*/} +
+ +Because failure of a single component can result in several different breach sizes (typically given by number of gate or concrete monolith failures), calculating the total +risk for failure modes associated with the components of a concrete gated spillway differs from calculating the total risk for hydrologic and seismic embankment failure modes. +Failure of a single component can result in several different breach scenarios (e.g., gate failure for a 3-gate spillway can result in a breach of 1 gate, 2 gates, or 3 gates +depending on the failure combination). Therefore, the method for calculating the total risk includes either the use of combinatorics or extensive event trees that account for +the probability of failure (or non-failure) of multiple concrete gated spillway components. To accurately calculate the total risk due to gate failure, all possible failure +combinations must be accounted for. A gate failure can occur due to any possible failure/non-failure combination of the three gates within the spillway, with the eight unique +combinations listed in . + +{/*Table 39*/} +1,2,3,4,5,6,7,8 + ], + [//Gate 1 + "Non-Fail","Fail","Non-Fail","Non-Fail","Fail","Fail","Non-Fail","Fail" + ], + [//Gate 2 + "Non-Fail","Non-Fail","Fail","Non-Fail","Fail","Non-Fail","Fail","Fail" + ], + [//Gate 3 + "Non-Fail","Non-Fail","Non-Fail","Fail","Non-Fail","Fail","Fail","Fail" + ], + [//# of Gates Breached + 0,1,1,1,2,2,2,3 + ] + ]} + fullWidth={false} + alt="Gate failure combinations." + caption="Gate failure combinations." +/> + +The annual probability of failure is calculated using several steps. First, an event tree is created that represents the probability of seismic gate failure for a single +spillway gate. Next, a second event tree is constructed to represent all possible failure combinations for gate failure as shown +in . The annual probability of failure is equal to the sum of all branches in the event tree that result in one or +more gate failures. The branches in the event tree that display the breach sizes (e.g., 1 gate breach, 2 gate breach, etc.) are included to demonstrate the resulting breach +size and are assigned a probability of one. Each branch of the event tree is matched with the appropriate life loss consequence scenario to calculate the average annual life +loss. The average annual life loss is equal to the sum of the products of the annual probability of failure and life loss consequences for each branch that results in one or +more gate failures. + +{/*Figure 86*/} +
+ +RMC-TotalRisk does not allow the user to assign life loss consequences to discrete branches within an event tree; therefore, an alternative method is used to calculate the annual +probability of failure and average annual life loss. The event tree in is duplicated for each possible breach size scenario +(e.g., 1 gate breach, 2 gate breach, etc.). Dummy probabilities are created using tabular system response functions to represent probabilities of zero and one, and these dummy +probabilities are assigned to the end branches of the event tree – the end branches that result in the number of gate failures of interest are assigned a probability of one, and the +end branches that do not are assigned a probability of zero. This results in event trees that are used to calculate the annual probability of failure for each discrete breach +scenario. Consequence functions for each breach scenario are created and the total risk is calculated by combining the discrete breach scenario event trees and their +corresponding consequences using the joint risk model. + +## Hazards + +The primary hazard for this risk analysis is the same as in [Example 6](./09-example-6.mdx). Reference the hazard function development procedure +in [Hazards](./09-example-6.mdx#hazards) from Example 6 to create the primary hazard for this risk analysis. + +## Transforms + +The primary hazard (stage duration), system response, and consequence data for this risk analysis are all a function of stage (ft). Therefore, a transform function is not required. + +## System Responses + +### Seismic Gate Failure + +The single risk-driving PFM for the dam is seismic failure of the spillway Tainter gates. The system response probabilities for the potential failure mode were obtained from team +elicitation using the event tree method. When using RMC-TotalRisk to evaluate a PFM that is driven by a seismic hazard, the seismic hazard must be partitioned by assigning +weights to each representative seismic ground motion evaluated for system response. The procedure for calculating seismic weights is shown in [Hazards](./09-example-6.mdx#hazards) from Example 6. +For the seismic gate failure PFM, the seismic ground motions evaluated for system response and their respective weights for event tree analysis are provided in . + +{/*Table 40*/} + + +For this PFM, a PGA of 0.05g is assigned as the threshold for non-zero system response (i.e., all ground motions less than 0.05g have a system response probability of zero). +Therefore, the first seismic hazard partition does not include the non-exceedance probability for peak ground accelerations less than 0.05g. Instead, the non-exceedance +probability is included in the remainder partition and will not contribute to the annual probability of failure. + +The event tree for the seismic gate failure PFM is shown in and the elicited system response probabilities are shown +in . As the failure is due to a sudden seismic event, intervention to prevent breach is not considered possible; +therefore, only a “without intervention” scenario is evaluated. + +{/*Figure 87*/} +
+{/*Table 41*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV", + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV" + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.075,'0.150','0.450',0.225, + 0.095,0.275,'0.600',0.323,'0.150','0.350','0.800',0.433 + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.090','0.250','0.550',0.297, + 0.125,0.325,0.675,0.375,0.225,'0.500','0.900',0.542 + ], + [//640.00 + '0.000','0.000','0.000','0.000','0.100','0.300','0.700',0.367, + '0.200','0.450',0.825,0.492,'0.400','0.650','0.950',0.667 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.150','0.400','0.750',0.433, + 0.225,'0.550',0.875,'0.550','0.450','0.700','0.990',0.713 + ] + ]} +/> + +The procedure for the creating the seismic gate failure PFM event tree is the same as the procedure used to create the seismic crest deformation PFM event tree detailed +in [System Responses](./09-example-6.mdx#system-responses) from Example 6. + +{/*Table 42*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV", + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV" + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.001,'0.050','0.270',0.107, + '0.010','0.200','0.550',0.253,0.042,'0.350','0.850',0.414 + ], + [//633.00 + '0.000','0.000','0.000','0.000',0.001,0.075,'0.380',0.152, + 0.015,'0.250','0.650',0.305,0.093,'0.460','0.900',0.484 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.002,0.175,'0.450',0.209, + '0.050','0.430','0.750','0.410','0.170','0.550','0.970',0.563 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.010','0.200','0.500',0.237, + '0.100','0.500','0.850',0.483,'0.200','0.650','0.990',0.613 + ] + ]} +/> +{/*Figure 88*/} +
+{/*Figure 89*/} +
+ +### Breach Scenarios + +As stated previously, RMC-TotalRisk requires that gate failure combination event trees for each breach scenario (as shown in ) be +constructed along with dummy probabilities to correctly calculate the total risk. First, dummy probabilities are created using tabular response functions, followed by the creation +of the gate failure combination event trees. + +The procedure for creating the dummy probabilities is as follows: + + + Right-click on the System Responses folder in the + Project Explorer window and + select Add Tabular Response… Name the + system response function in the prompt (e.g., Breach_0) and press OK. + + ) + }, + {//Step 2 + title:( + <> + The hazard for the system response function is stage and is measured in feet. In the Tabular Response Properties section of the + Properties window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title:( + <> + Since this response function is a dummy probability that is equal to zero, the interpolation method will not affect the response function or event tree where the + function is used. In the Interpolation Transforms section of the Properties window, the Hazard and Probability interpolation transforms are left on the + default settings of None (linear interpolation), (b). + + ) + }, + {//Step 4 + title:( + <> + Assign a distribution, stages, and response probabilities to the tabular response function. The Distribution for the response function is set + to Deterministic, (c). The tabular response function will use two stages to assign a uniform probability; click + on Add row(s) to the bottom of the table to add a + second row. The stages assigned in the function should encompass the entire range of stages within the stage-duration hazard curve, and the probabilities should + be set equal to zero for all stages within the function. For this function, stages of 600 feet and 660 feet are used, (d). + + ), + freeform: ( + <> + {/*Figure 90*/} +
+ + ) + }, + {//Step 5 + title:( + <> + Follow the same procedure to create a second dummy probability with a probability of one. In Step 1, name the system response function “Breach_1” and assign + probabilities of 1.0 to the function in Step 4. + + ) + } + ]} +/> + +Once the dummy probability tabular system response functions have been created, use the following procedure to create event tree responses for the discrete breach scenarios. + + + Right-click on the System Responses folder in + the Project Explorer window and select + Add Event Tree Response… Name the system response function in the prompt (e.g., 1 Gate Breach). RMC-TotalRisk contains a database of event trees for + common potential failure modes that can be used for system response functions. For the 1 Gate Breach event tree, select Generic from the Category drop-down + menu and select Basic from the Template drop-down menu and press OK. + + ) + }, + {//Step 2 + title:( + <> + The hazard for the system response function is stage and is measured in feet. In the Event Tree Properties section of the Properties + window, (a), select Stage for Hazard Type and ft for Hazard Units. + + ) + }, + {//Step 3 + title:( + <> + In the Interpolation Transforms section of the Properties window, select interpolation methods that are best suited for the hazard and system response + probability. For this PFM, the Hazard is set to None (linear interpolation), and the Probability is set to Logarithmic, (b). + + ) + }, + {//Step 4 + title:( + <> + Assign the hazard levels that define the system response curve to the event tree by clicking on the Hazard + node symbol, (c), and + entering the hazard levels into the Hazard Levels section of the Properties window, (d). Alternatively, hazard levels can be assigned by hovering over the + Hazard node name, clicking the Branch Properties symbol, and + entering the hazard levels into the Hazard Levels section of the pop-up box that appears. The hazard levels for the breach scenario event tree are identical to those used + in the seismic gate failure PFM event tree from Seismic Gate Failure. + + ), + freeform:( + <> + {/*Figure 91*/} +
+ + ) + }, + {//Step 5 + title:( + <> + Ensure the structure of the event tree, including the number, name, and description of each node, matches the event tree + in . To add a branch to the event tree or delete a branch from the event tree, click on the node + symbol or remainder node + symbol and perform one of the following options: + + ), + child:[ + {//Step 5a + title: ( + <> + Click the Add new branch button + (to add a branch) or the Delete all branches from this node + button (to delete branches) in the node toolbar, (a). + + ) + }, + {//Step 5b + title: ( + <> + Click the Add Branch Node button (to add a branch) or + the Delete Branch button (to delete branches) in + the Sub-Branches section of the Properties window, (b). + + ) + } + ] + }, + {//Step 6 + title:( + <> + The Name and Description of the node can be changed in the Selected Branch Properties section of the Properties + window, (c), or by clicking + the Branch Properties symbol. To + allow for system response probabilities to be applied more easily to each node in the event tree, a different naming convention is used for the events along the + top branch of the event tree. The phrase “(P)” is added to the node names along this branch to signify that these are “parent” nodes which will be used as a + reference for system response probabilities in a later step, (d). + + ), + freeform: ( + <> + {/*Figure 92*/} +
+ + ) + }, + {//Step 7 + title:( + <> + The nodes corresponding to gate failure in the 1 Gate Breach event tree (i.e., nodes named “Gate 1 Fail”, “Gate 2 Fail”, and “Gate 3 Fail”) represent the + probability that seismic gate failure will occur. The nodal probabilities for each node in the tree are assigned by setting them equal to the system response + probabilities of the seismic gate failure event tree function created in Seismic Gate Failure. However, the system + response probability between the spillway gates is not perfectly correlated (i.e., a high system response probability for gate 1 does not correspond to a + high system response probability for gate 2 and gate 3). Therefore, each gate will be sampled independently of the seismic gate failure event tree function. At + the same time, the responses of the same gate within the event tree should be perfectly correlated (i.e., the system response probability for “Gate 2 Fail (P)” + emanating from the “Gate 1 Fail (P)” branch of node 1 should be the same as the system response probability for “Gate 2 Fail” emanating from the “Gate 1 Non-Fail” + branch of node 1). To account for this, the system response probabilities for each individual gate will be set equal throughout the event tree. + + ), + child:[ + {//Step 7a + title: ( + <> + Select the event tree node symbol or name + for “Gate 1 Fail (P)”, (a). Assign system response probabilities using the options located in + the System Response section of the Properties window, (b). As the nodal probability for this node will + reference a separate system response function within the model, the Source is set to Response Function. Once this option is selected the event + tree chance node symbol is replaced with + a reference node symbol ,  + (c). The Response Function for this node in the event tree is set to Seismic Gate Failure. + The Sample Independently box for this node is checked to account for the independence of Gate 1. + + ), + freeform: ( + <> + {/*Figure 93*/} +
+ + ) + }, + {//Step 7b + title: ( + <> + Repeat Step (a) to assign nodal probabilities to the “Gate 2 Fail (P)” and “Gate 3 Fail (P)” nodes along the top branch of the event tree. + + ) + }, + {//Step 7c + title: ( + <> + Select the event tree node symbol or name + for “Gate 2 Fail” from the “Gate 1 Non-Fail” branch of node 1, (a). The nodal probability for + this node will reference the “Gate 2 Fail (P)” system response probability from the top branch of the event tree. Set the Source to Event Node; once + this option is selected the event tree chance node + symbol is replaced with a reference node + symbol ,  + (b). The Event Nodes is set to Gate 2 Fail (P). Since the system response probability + for this node is assumed to be the same as the “parent” node to which it is referenced, the Sample Independently box is left + unchecked, (c). + + ), + freeform: ( + <> + {/*Figure 94*/} +
+ + ) + }, + {//Step 7d + title: ( + <> + Repeat Step (c) to assign nodal probabilities to the remaining “Gate 3 Fail” nodes in the event tree. Ensure the Event Nodes is set + to Gate 3 Fail (P) for these nodes. + + ) + } + ] + }, + {//Step 8 + title: ( + <> + To capture the probability of failure correctly, only the branches in the event tree that result in the desired number of gate failures should be captured. + The tabular response functions “Breach_0” and “Breach_1” are used to capture the branches that are desired and “zero out” branches that are not. As in Step 7, + reference response functions are used for the event tree end nodes. For the 1 Gate Breach event tree, the Response Function is set to Breach_1 for end + nodes that result in a 1 gate breach, , and is set to Breach_0 for end nodes that result in a + 0 gate breach, 2 gate breach, or 3 gate breach, . + + ), + freeform: ( + <> + {/*Figure 95*/} +
+ {/*Figure 96*/} +
+ + ) + }, + {//Step 9 + title: ( + <> + Once the event tree has been completed, click on the Response tab within the event tree window to view a graph of the system response curve plotted against + stage. The mean system response curve is plotted with a blue dashed line, (a), and the 90% confidence + bounds are shaded in light blue, (b). This curve can be compared against the system response probability + input data to ensure accuracy. To change the graph axis extents, axis type, or axis properties, right click on the axis of interest and + click Format Axis: [Axis Name Here], (c). The axis type can be set to Linear, Logarithmic, Normal Probability, Basic, + or Gumbel Probability in the Axis Type drop-down menu within the Properties window, (d), along with + many other axis customizations. + + ), + freeform: ( + <> + {/*Figure 97*/} +
+ + ) + }, + {//Step 10 + title: ( + <> + Repeat this procedure twice more to create event trees for a 2 Gate Breach and 3 Gate Breach. All steps are identical except for Step 8. For the 2 Gate Breach + event tree, end nodes that result in a 2 gate breach should be assigned a Response Function of Breach_1 while end nodes that result in a 0 gate + breach, 1 gate breach, or 3 gate breach should be assigned a Response Function of Breach_0. For the 3 Gate Breach event tree, end nodes that + result in a 3 gate breach should be assigned a Response Function of Breach_1 while end nodes that result in a 0 gate breach, 1 gate breach, or 2 + gate breach should be assigned a Response Function of Breach_0. The system response curve for the 2 Gate Breach event tree is shown + in and the system response curve for the 3 Gate Breach event tree is shown in . + + ), + freeform: ( + <> + {/*Figure 98*/} +
+ {/*Figure 99*/} +
+ + ) + } + ]} +/> + +In the Project Explorer, functions can be grouped into collapsible and expandable lists. Since the dummy probability tabular functions are used within the breach scenario event +trees, these items can be grouped by holding Ctrl + clicking on the items in the Project Explorer window. Once the desired items are selected, right click and +select **Group**, . Once +the group has been created, RMC-TotalRisk will prompt the user to name the group (i.e., Breach Scenarios). The group can be named at any time by double clicking on the group +name. The items can also be ungrouped by right clicking on the group name and clicking **Ungroup**, +. + + +{/*Figure 100*/} +
+{/*Figure 101*/} +
+ +## Consequences + +As detailed above, seismic failure of the concrete gated spillway gates can result in a 1 gate breach, 2 gate breach, or 3 gate breach. Consequence models for each scenario, +along with the non-breach condition, have been run for the analysis. No economic costs have been modeled for this scenario. + +Life loss estimates have been developed for a range of reservoir stages for the following scenarios: Non-breach, 1 gate breach, 2 gate breach, and 3 gate breach. The life loss +scenarios have been developed for daytime and nighttime conditions. The daytime exposure scenario rate is assumed to be 45% while the nighttime exposure rate is assumed to be +55%. A total of twelve consequence functions will be created for the risk analysis. The procedure for creating a tabular life loss consequence function is detailed +in [Consequences](./09-example-6.mdx#consequences) from Example 6. Composite life loss consequence functions in RMC-TotalRisk for non-breach, 1 gate breach, 2 gate breach, +and 3 gate breach scenarios are shown in , , +, and , respectively. + +{/*Figure 102*/} +
+{/*Figure 103*/} +
+{/*Figure 104*/} +
+{/*Figure 105*/} +
+{/*Table 43*/} + +{/*Table 44*/} + +{/*Table 45*/} + +{/*Table 46*/} + + +## Risk Analyses + +To calculate the total risk for seismic gate failure, all breach scenarios must be combined into a single analysis so that all failure combinations are accounted for. + +:::note +Replace figure 106 with correct non-breach risk +::: + +:::note +Replace figure 107 with correct non-breach risk +::: + + + Right-click the Risk Analyses folder and + selecting Add Risk Analysis… Name + the risk analysis in the prompt (e.g., Seismic Gate Failure) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, select Life Loss and Lives. + + ) + }, + {//Step 3 + title: ( + <> + For this risk analysis two hazard functions, three system response functions, and four consequence functions are required. Add components to the risk + analysis Diagram by clicking the green plus sign, + clicking on a node output connector, or right-clicking anywhere in the diagram. + + ), + child: [ + {//Step 3a + title: ( + <> + First, add a hazard node to the diagram. + Select the hazard function (e.g., Stage Frequency) for the non-breach risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3b + title: ( + <> + Next, add the non-breach condition by clicking on the non-breach risk hazard node output connector and adding a consequence + node and selecting the + composite non-breach life loss function (e.g., Non-Breach) from the drop-down box. + + ) + }, + {//Step 3c + title: ( + <> + Add a second hazard node to the diagram. Select + the hazard function (e.g., Stage Duration) for the incremental risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3d + title: ( + <> + Next, add the 1 Gate Breach, 2 Gate Breach, and 3 Gate Breach system response functions and their associated breach life loss consequence functions + to the incremental risk hazard node. These PFMs have the same hazard (stage) as the incremental risk hazard function and can be added to the risk + analysis without a transform function. + + ), + child: [ + {//Step 3d.i + title: ( + <> + Add a response node by + clicking on the incremental risk hazard node output connector and select the appropriate system response function (e.g., 1 Gate Breach) + from the drop-down box. + + ) + }, + {//Step 3d.ii + title: ( + <> + Add the breach condition by clicking on the response node output connector and adding a consequence + node and selecting the + composite breach life loss function (e.g., 1 Gate Breach) from the drop-down box. + + ) + }, + {//Step 3d.iii + title: ( + <> + Repeat steps c.(1) and c.(2) for the 2 Gate Breach and 3 Gate Breach system response functions and their associated consequence functions. + + ) + } + ] + }, + {//Step 3e + title: ( + <> + Re-arrange the nodes (click and hold, then drag) to personalize the diagram. The final risk analysis diagram is shown in . + + ), + freeform: ( + <> + {/*Figure 106*/} +
+ + ) + } + ] + }, + {//Step 4 + title: ( + <> + When running a risk analysis, the simulation options can be adjusted within the Options tab of the Properties window. + + ), + child: [ + {//Step 4a + title: ( + <> + Within the System Component Options section, the Failure Mode Method is set to Joint Failures and the Joint Consequences are set to Maximum, (a). Additional options for Failure Mode Method include Common Cause Failures and Competing Failures. The Joint Consequences option will not be displayed if either Common Cause Failure or Competing Failures is used. + + ) + }, + {//Step 4b + title: ( + <> + Within the Simulation Options section, the Confidence Interval is set to 90% and Realizations is set to 10,000, (b). + + ) + }, + {//Step 4c + title: ( + <> + The Integration Options, (c), System Options, (d), and Risk Measure Options, (e), are set to their default values. + + ), + freeform: ( + <> + {/*Figure 107*/} +
+ + ) + } + ] + }, + {//Step 5 + title: ( + <> + To run the risk analysis without uncertainty, click on the General tab in the Properties window, select Simulate Mean Risk Only in the Simulation section, and click Estimate. To run the risk analysis with uncertainty, select Simulate Risk with Full Uncertainty and click Estimate. + + ) + } + ]} +/> + +## Results + +Once the risk analysis model has been simulated, the **Summary Statistics** tab provides a table of summary results, . This table shows the incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 8.50E-04 and an _Exceedance Probability, α_ (also referred to as annual probability of failure, APF) of 1.26E-04. + +{/*Figure 108*/} +
+ +The incremental F-N Plot with uncertainty is shown in , and the α-ƞ Plot with uncertainty is shown in . + +{/*Figure 109*/} +
+{/*Figure 110*/} +
\ No newline at end of file diff --git a/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/11-example-8.mdx b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/11-example-8.mdx new file mode 100644 index 000000000..0f9bb7f82 --- /dev/null +++ b/docs/desktop-applications/rmc-totalrisk/applications-guide/v1.0/11-example-8.mdx @@ -0,0 +1,2944 @@ +--- +title: Example 8 – Seismic Gated Spillway (Multiple Failure Modes) +--- + +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import Figure from "@site/src/components/Figure"; +import FigureInline from "@site/src/components/FigureInline"; +import FigReference from "@site/src/components/FigureReference"; +import NavContainer from "@site/src/components/NavContainer"; +import ProcessList from "@site/src/components/ProcessList"; +import TableReference from "@site/src/components/TableReference"; +import TableVertical from "@site/src/components/TableVertical"; +import VersionSelector from "@site/src/components/VersionSelector"; +import Tabs from '@theme/Tabs'; +import TabItem from '@theme/TabItem'; +import TableVerticalNoRef from '@site/src/components/TableVerticalNoRef'; + + + +# Example 8 – Seismic Gated Spillway (Multiple Failure Modes) + +The components of the concrete gated spillway are subject to failure when exposed to seismic ground shaking. The spillway consists of three Tainter gates, two piers, two middle +anchorages, and two end anchorages, . For this risk analysis, failure of all components is evaluated, resulting in four risk-driving PFMs: seismic pier failure, +seismic gate failure, seismic middle anchorage failure, and seismic end anchorage failure. + +{/*Figure 111*/} +
+ +Calculating the total risk for potential failure modes related to the components of a concrete gated spillway differs from the evaluation of hydrologic potential failure modes or +seismic embankment potential failure modes. The reason is that the failure of the spillway components can result in several different breach sizes (typically given by number of +gate or concrete monolith failures). This can become complicated because the failure of a single component can result in several different breach scenarios (e.g., gate failure +for a 3-gate spillway can result in a breach of 1 gate, 2 gates, or 3 gates depending on the failure combination). Therefore, the method for calculating the total risk includes +either the use of combinatorics or extensive event trees that account for the probability of failure (or non-failure) of multiple concrete gated spillway +components. lists the resultant gate breaches that occur due to failure of the spillway components. For this +spillway, the failure of a single pier or middle anchorage always results in a two-gate breach, while the failure of a single gate or end anchorage always results in a one +gate breach. + +{/*Table 47*/} +Pier 1,Pier 2,Gate 1,Gate 2, + Gate 3,Middle Anchorage (MA) 1,Middle Anchorage (MA) 2, + End Anchorage (EA) 1,End Anchorage (EA) 2 + ], + [ + 'F','-','F','-', + '-','F','-','F','-' + ], + [ + 'F','F','-','F', + '-','F','F','-','-' + ], + [ + '-','F','-','-', + 'F','-','F','-','F' + ] + ]} + footnotes={["NOTE: “F” represents a component failure; “-“ represents a component non-failure."]} +/> + +To accurately calculate the total risk due to spillway component failure, all possible failure combinations must be accounted for. A breach of a spillway gate can occur due +to any possible failure/non-failure combination of the spillway components. There are 512 unique combinations as listed in +(click below to open collapsible panel). + +{/*Table 48*/} +
+ Table 48: Spillway component failure combinations + + {/*1-50*/} + + + + {/*51-100*/} + + + + {/*101-150*/} + + + + {/*151-200*/} + + + + {/*201-250*/} + + + + {/*251-300*/} + + + + {/*301-350*/} + + + + {/*351-400*/} + + + + {/*401-450*/} + + + + {/*451-500*/} + + + + {/*501-512*/} + + + + +
+ +The annual probability of failure is calculated using several steps. First, event trees are created to represent the probability of seismic gated spillway component failure +for each component (pier, gate, middle anchorage, end anchorage). Next, secondary event trees are created to represent the failure combinations for each component of the +spillway as shown in through . Finally, an event tree is +constructed to represent all possible failure combinations for the gated spillway – this event tree contains the secondary event trees for each component of the spillway in +series and is very large. The final event tree has been simplified in . The annual probability of failure is equal +to the sum of all branches in the event tree that result in one or more gate failures. The event tree also contains branches that display the breach size (e.g., 1 gate breach, +2 gate breach, etc.) to demonstrate the resulting breach size for each branch and are assigned a probability of 1.0. The simplified event tree denotes these branches +as “X Gate Breaches” as each branch contains multiple component failure/non-failure combinations. + +{/*Figure 112*/} +
+ +{/*Figure 113*/} +
+ +{/*Figure 114*/} +
+ +{/*Figure 115*/} +
+ +{/*Figure 116*/} +
+ +To calculate the average annual life loss, each branch of the event tree is matched with the appropriate life loss consequence scenario as shown in . +The average annual life loss is equal to the sum of the products of the annual probability of failure and life loss consequences for each branch that results in one or more +gate failures. + +{/*Figure 117*/} +
+ +Instead of using this time- and labor-intensive procedure, the user can leverage the joint risk model in RMC-TotalRisk to simplify the calculation. The event trees +in through are duplicated for each possible breach +scenario (e.g., 1 gate breach, 2 gate breach, etc.). This results in a total of 12 event trees – three event trees for each spillway component (e.g., 1 Gate Breach_Pier, +2 Gate Breach_Pier, 3 Gate Breach_Pier, 1 Gate Breach_Gate, etc.). Dummy probabilities are created using tabular system response functions to represent probabilities of +zero and one, and these dummy probabilities are assigned to the end branches of the event trees – the end branches that result in the number of gate failures of interest +are assigned a probability of one, and the end branches that do not are assigned a probability of zero. Consequence functions for each breach scenario are created and the +total risk is calculated by combining the discrete breach scenario event trees for each spillway component with their corresponding consequences using the joint risk model. + +## Hazards + +The primary hazard for this risk analysis is the same as in [Example 6](./09-example-6.mdx). Reference the hazard function development procedure +in [Hazards](./09-example-6.mdx#hazards) from Example 6 to create the primary hazard for this risk analysis. + +## Transforms + +The primary hazard (stage duration), system response, and consequence data for this risk analysis are all a function of stage (ft). Therefore, a transform function is not required. + +## System Responses + +### Seismic Loading Weights + +The four risk-driving PFMs for the dam are seismic pier failure, seismic gate failure, seismic middle anchorage failure, and seismic end anchorage failure. When using +RMC-TotalRisk to evaluate PFMs that are driven by a seismic hazard, the seismic hazard must be partitioned by assigning weights to each representative seismic ground +motion evaluated for system response. The procedure for calculating seismic weights is shown in [Hazards](./09-example-6.mdx#hazards) from Example 6. For the PFMs +in this risk analysis, the seismic ground motions evaluated for system response and their respective weights for event tree analysis are provided in . + +{/*Table 49*/} + + +For all four PFMs, a PGA of 0.05g is assigned as the threshold for non-zero system response (i.e., all ground motions less than 0.05g have a system response probability of zero). +Therefore, the first seismic hazard partition does not include the non-exceedance probability for peak ground accelerations less than 0.05g. Instead, the non-exceedance probability +is included in the remainder partition and will not contribute to the annual probability of failure. + +### Seismic Gate Failure + +The event tree for the seismic gate failure PFM is shown in and the elicited system response probabilities are +shown in and . As the failure is due to a sudden +seismic event, intervention to prevent breach is not considered possible; therefore, only a “without intervention” scenario is evaluated. + +{/*Figure 118*/} +
+ +The procedure for the creating the seismic gate failure PFM event tree is the same as the procedure used to create the seismic crest deformation PFM event tree +detailed in [System Responses](./09-example-6.mdx#system-responses) from Example 6. + +{/*Table 50*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV", + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV" + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.075,"0.150","0.450",0.225, + 0.095,0.275,"0.600",0.323,"0.150","0.350","0.800",0.433 + ], + [//633.00 + '0.000','0.000','0.000','0.000',"0.090","0.250","0.550",0.297, + 0.125,0.325,0.675,0.375,0.225,"0.500","0.900",0.542 + ], + [//640.00 + '0.000','0.000','0.000','0.000',"0.100","0.300","0.700",0.367, + "0.200","0.450",0.825,0.492,"0.400","0.650","0.950",0.667 + ], + [//644.00 + '0.000','0.000','0.000','0.000',"0.150","0.400","0.750",0.433, + 0.225,"0.550",0.875,"0.550","0.450","0.700","0.990",0.713 + ] + ]} +/> +{/*Table 51*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV", + "LRV","MLV","HRV","EV","LRV","MLV","HRV","EV" + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.001,"0.050","0.270",0.107, + "0.010","0.200","0.550",0.253,0.042,"0.350","0.850",0.414 + ], + [//633.00 + '0.000','0.000','0.000','0.000',0.001,0.075,"0.380",0.152, + 0.015,"0.250","0.650",0.305,0.093,"0.460","0.900",0.484 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.002,0.175,"0.450",0.209, + "0.050","0.430","0.750","0.410","0.170","0.550","0.970",0.563 + ], + [//644.00 + '0.000','0.000','0.000','0.000',"0.010","0.200","0.500",0.237, + "0.100","0.500","0.850",0.483,"0.200","0.650","0.990",0.613 + ] + ]} +/> +{/*Figure 119*/} +
+{/*Figure 120*/} +
+ +### Seismic Pier Failure + +The event tree for the seismic pier failure PFM is shown in Figure and the elicited system response probabilities are +shown in , , +, and . As the failure is due to a sudden seismic +event, intervention to prevent breach is not considered possible; therefore, only a “without intervention” scenario is evaluated. + +{/*Figure 121*/} +
+ +The procedure for the creating the seismic pier failure PFM event tree is the same as the procedure used to create the seismic crest deformation PFM event tree +detailed in [System Responses](./09-example-6.mdx#system-responses) from Example 6. + +{/*Table 52*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.15 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000','0.000','0.000',0.001,'0.000', + '0.000','0.000',0.001,0,0.001,0.006,0.065,0.024 + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.000','0.000',0.001,'0.000', + '0.000',0.001,'0.010',0.004,0.011,'0.100','0.200',0.104 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.001,0.002,0.003,0.002, + 0.003,0.013,'0.100',0.039,0.015,'0.150','0.300',0.155 + ], + [//644.00 + '0.000','0.000','0.000','0.000',0.001,0.004,'0.010',0.005, + 0.025,'0.100','0.200',0.108,0.033,'0.200','0.400',0.211 + ] + ]} +/> +{/*Table 53*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.15 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.051,0.387,0.677,0.372, + '0.300',0.677,0.919,0.632,'0.500','0.900','0.990',0.797 + ], + [//633.00 + '0.000','0.000','0.000','0.000',0.071,0.393,0.688,0.384, + '0.300',0.688,0.934,0.641,'0.500','0.900','0.990',0.797 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.094,0.396,0.693,0.394, + '0.350',0.693,0.941,0.661,0.532,'0.900',0.997,'0.810' + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.100','0.400','0.700','0.400', + '0.350','0.700','0.950','0.667','0.672','0.950','0.999','0.874' + ] + ]} +/> +{/*Table 54*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.15 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000','0.010','0.100','0.250','0.120', + 0.066,'0.150','0.350',0.189,0.441,'0.900','0.990',0.777 + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.040','0.200','0.300','0.180', + 0.106,'0.250','0.400',0.252,'0.450','0.900','0.990','0.780' + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.097,'0.300','0.500',0.299, + 0.159,'0.310','0.500',0.323,'0.450','0.950',0.999,'0.800' + ], + [//644.00 + '0.000','0.000','0.000','0.000',0.286,'0.600','0.750',0.545, + 0.398,'0.700','0.950',0.683,'0.600','0.990',0.999,0.863 + ] + ]} +/> +{/*Table 55*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.15 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.026,'0.150','0.350',0.175, + '0.150','0.400',0.774,0.441,'0.250',0.585,'0.900',0.578 + ], + [//633.00 + '0.000','0.000','0.000','0.000',0.036,'0.150','0.350',0.179, + '0.150','0.400',0.786,0.445,'0.250',0.585,'0.900',0.578 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.047,'0.150','0.350',0.182, + '0.150','0.400',0.793,0.448,'0.250',0.585,'0.900',0.578 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.050','0.150','0.350',0.183, + '0.150','0.400','0.800','0.450','0.250',0.618,'0.900',0.589 + ] + ]} +/> +{/*Figure 122*/} +
+{/*Figure 123*/} +
+ +### Seismic Middle Anchorage Failure + +The event tree for the seismic middle anchorage failure PFM is shown in and the elicited system response probabilities +are shown in , , and +. As the failure is due to a sudden seismic event, intervention to prevent breach is not considered +possible; therefore, only a “without intervention” scenario is evaluated. + +{/*Figure 124*/} +
+ +The procedure for the creating the seismic middle anchorage failure PFM event tree is the same as the procedure used to create the seismic crest deformation PFM event +tree detailed in [System Responses](./09-example-6.mdx#system-responses) from Example 6. + +{/*Table 56*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000',0.002,0.002,0.001,0.002,'0.020',0.038,'0.020' + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.000','0.000',0.002,0.001, + 0.002,0.008,0.012,0.007,'0.010','0.150','0.200','0.120' + ], + [//640.00 + '0.000','0.000','0.000','0.000','0.000',0.002,0.004,0.002, + 0.002,0.016,'0.030',0.016,'0.100',0.304,'0.500',0.301 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.000',0.008,'0.010',0.006, + '0.010',0.118,'0.200',0.109,'0.200',0.534,0.802,0.512 + ] + ]} +/> +{/*Table 57*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//623.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//633.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//640.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//644.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ] + ]} +/> +{/*Table 58*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000',0.001,0.004,'0.010',0.005, + 0.003,'0.010','0.050',0.021,'0.010','0.050','0.100',0.053 + ], + [//633.00 + '0.000','0.000','0.000','0.000',0.001,0.022,'0.050',0.024, + '0.010',0.075,'0.300',0.128,'0.050','0.200','0.500','0.250' + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.007,0.075,'0.150',0.077, + 0.015,'0.200','0.500',0.238,'0.100',0.274,0.693,0.356 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.010',0.274,'0.500',0.261, + 0.057,0.382,'0.680',0.373,'0.150','0.500',0.842,0.497 + ] + ]} +/> +{/*Figure 125*/} +
+{/*Figure 126*/} +
+ +### Seismic End Anchorage Failure + +The event tree for the seismic end anchorage failure PFM is shown in and the elicited system response probabilities +are shown in , , and +. As the failure is due to a sudden seismic event, intervention to prevent breach is not +considered possible; therefore, only a “without intervention” scenario is evaluated. + +{/*Figure 127*/} +
+ +The procedure for the creating the seismic end anchorage failure PFM event tree is the same as the procedure used to create the seismic crest deformation PFM event tree +detailed in [System Responses](./09-example-6.mdx#system-responses) from Example 6. + +{/*Table 59*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000',0.004,0.007,0.004,0.001,0.025,0.048,0.025 + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.000','0.000',0.004,0.001, + 0.001,0.007,0.009,0.006,0.005,'0.090',0.138,0.078 + ], + [//640.00 + '0.000','0.000','0.000','0.000','0.000',0.003,0.008,0.004, + 0.001,'0.010',0.034,0.015,'0.050',0.267,'0.500',0.272 + ], + [//644.00 + '0.000','0.000','0.000','0.000','0.000',0.008,'0.010',0.006, + 0.005,'0.040','0.090',0.045,'0.100',0.485,'0.670',0.418 + ] + ]} +/> +{/*Table 60*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//623.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//633.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//640.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ], + [//644.00 + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999, + 0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999 + ] + ]} +/> +{/*Table 61*/} + + 0.05 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.015 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.40 + + ), + rowSpan: 4 + }, + null,null,null, + { + value: ( + <> + 0.68 + + ), + rowSpan: 4 + }, + null,null,null + ], + [//Stage (ft) + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV', + 'LRV','MLV','HRV','EV','LRV','MLV','HRV','EV' + ], + [//622.90 + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000', + '0.000','0.000','0.000','0.000','0.000','0.000','0.000','0.000' + ], + [//623.00 + '0.000','0.000','0.000','0.000','0.000','0.000',0.001,0.001, + '0.000',0.002,0.008,0.003,0.001,0.008,0.018,0.009 + ], + [//633.00 + '0.000','0.000','0.000','0.000','0.000',0.003,0.007,0.003, + 0.001,0.011,0.045,0.019,0.007,0.032,0.087,0.042 + ], + [//640.00 + '0.000','0.000','0.000','0.000',0.001,0.009,0.018,0.009, + 0.002,0.034,0.084,'0.040',0.019,0.058,0.151,0.076 + ], + [//644.00 + '0.000','0.000','0.000','0.000',0.001,0.042,0.073,0.039, + 0.012,0.084,0.148,0.081,0.034,0.129,0.224,0.129 + ] + ]} +/> +{/*Figure 128*/} +
+{/*Figure 129*/} +
+ +### Breach Scenarios + +Breach scenario event trees need to be created for each spillway component for a total of 12 event trees. The procedure for creating the breach scenario event trees is the +same as the procedure used to create the seismic gate failure breach scenario event trees detailed in [Breach Scenarios](./10-example-7.mdx#breach-scenarios) from Example 7. + +## Consequences + +As detailed above, seismic failure of the concrete gated spillway components can result in a 1 gate breach, 2 gate breach, or 3 gate breach. Consequence models for each +scenario, along with the non-breach condition, have been run for the analysis. The consequence functions for this risk analysis are identical to those detailed +in [Consequences](./10-example-7.mdx#consequences) from Example 7. + +## Risk Analyses + +To calculate the total seismic risk for the concrete gated spillway, all breach scenarios must be combined into a single analysis so that all failure combinations are accounted for. + +:::note +Replace Figure 130 with a figure that can actually be seen. +Replace Figure 130 with correct non-breach risk. +::: + +:::note +Add figure to show simulation options as consistent with other examples. +::: + + + Right-click the Risk Analyses folder and + selecting Add Risk Analysis… Name + the risk analysis in the prompt (e.g., Total Seismic Risk) and press OK. + + ) + }, + {//Step 2 + title: ( + <> + For Consequence and Consequence Unit in the Risk Analysis Properties section of the Properties window, select Life Loss and Lives. + + ) + }, + {//Step 3 + title: ( + <> + For this risk analysis two hazard functions, twelve system response functions, and thirteen consequence functions are required. Add components to the risk + analysis Diagram by clicking the green plus + sign, clicking on a node output connector, or right-clicking anywhere in the diagram. + + ), + child: [ + {//Step 3a + title: ( + <> + First, add a hazard node to the diagram. Select the + hazard function (e.g., Stage Frequency) for the non-breach risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3b + title: ( + <> + Next, add the non-breach condition by clicking on the non-breach risk hazard node output connector and adding a consequence + node and selecting the composite + non-breach life loss function (e.g., Non-Breach) from the drop-down box. + + ) + }, + {//Step 3c + title: ( + <> + Add a second hazard node to the diagram. + Select the hazard function (e.g., Stage Duration) for the incremental risk from the blank drop-down box in the hazard node. + + ) + }, + {//Step 3d + title: ( + <> + Next, add the 1 Gate Breach, 2 Gate Breach, and 3 Gate Breach system response functions for each spillway component and their associated breach life + loss consequence functions to the incremental risk hazard node. These PFMs have the same hazard (stage) as the hazard function and can be added to the + risk analysis without a transform function. + + ), + child: [ + {//Step 3d.i + title: ( + <> + Add a response node by clicking + on the incremental risk hazard node output connector and select the appropriate system response function (e.g., 1 Gate Breach_Pier, etc.) from + the drop-down box. + + ) + }, + {//Step 3d.ii + title: ( + <> + Add the breach condition by clicking on the response node output connector and adding a consequence + node and selecting the + composite breach life loss function (e.g., 1 Gate Breach) from the drop-down box. + + ) + }, + {//Step 3d.iii + title: ( + <> + Repeat steps c.(1) and c.(2) for the remaining system response functions and their associated consequence functions. + + ) + } + ] + }, + {//Step 3e + title: ( + <> + Re-arrange the nodes (click and hold, then drag) to personalize the diagram. The final risk analysis diagram is shown in . + + ), + freeform: ( + <> + {/*Figure 130*/} +
+ + ) + } + ] + }, + {//Step 4 + title: ( + <> + When running a risk analysis, the simulation options can be adjusted within the Options tab of the Properties window. + + ), + child: [ + {//Step 4a + title: ( + <> + Within the System Component Options section, the Failure Mode Method is set to Joint Failures and the Joint Consequences are set + to Maximum, Figure X(a). Additional options for Failure Mode Method include Common Cause Failures and Competing Failures. The Joint Consequences option will not be displayed if either Common Cause Failure or Competing Failures is used. + + ) + }, + {//Step 4b + title: ( + <> + Within the Simulation Options section, the Confidence Interval is set to 90% and Realizations is set to 10,000, Figure X(b). + + ) + }, + {//Step 4c + title: ( + <> + The Integration Options, Figure X(c), System Options, Figure X(d), and Risk Measure Options, Figure X(e), are set to their default values. + + ) + } + ] + }, + {//Step 5 + title: ( + <> + To run the risk analysis without uncertainty, click on the General tab in the Properties window, select Simulate Mean Risk Only in the Simulation section, and + click Estimate. To run the risk analysis with + uncertainty, select Simulate Risk with Full Uncertainty and + click Estimate. + + ) + } + ]} +/> + +## Results + +Once the risk analysis model has been simulated, the Summary Statistics tab provides a table of summary results, . +This table shows the incremental _Mean, E[N]_ (also referred to as the average annual life loss, AALL), of 8.50E-04 and an _Exceedance Probability, α_ (also referred to as +annual probability of failure, APF) of 1.26E-04. + +The incremental F-N Plot with uncertainty is shown in , and the α-ƞ Plot with uncertainty is shown +in . + +{/*Figure 131*/} +
+{/*Figure 132*/} +
+{/*Figure 133*/} +
diff --git a/scripts/generateSidebars.js b/scripts/generateSidebars.js index cd2d3b297..08a03cb1e 100644 --- a/scripts/generateSidebars.js +++ b/scripts/generateSidebars.js @@ -228,7 +228,9 @@ function generateSidebarForRmcTotalRiskApplicationsGuide(versionPath, relativePa const documentInfoDocs = []; let prefaceDoc = null; let hydrologicDoc = null; - const exampleDocs = []; + const hydroExampleDocs = []; + let seismicDoc = null; + const seismicExampleDocs = []; files.forEach((file) => { const fileBase = file.replace('.mdx', '').replace(/^\d+-/, ''); @@ -242,8 +244,13 @@ function generateSidebarForRmcTotalRiskApplicationsGuide(versionPath, relativePa prefaceDoc = { type: 'doc', id, label }; } else if (file === '02-hydrologic-risk-analysis.mdx') { hydrologicDoc = { id, label }; - } else if (file.startsWith('03-')) { - exampleDocs.push({ type: 'doc', id, label }); + //TODO: find a better way to do this + } else if (file.startsWith('03-') || file.startsWith('04-') || file.startsWith('05-') || file.startsWith('06-') || file.startsWith('07-')){ + hydroExampleDocs.push({ type: 'doc', id, label }); + } else if (file === '08-seismic-risk-analysis.mdx') { + seismicDoc = { id, label }; + } else if (file.startsWith('09-') || file.startsWith('10-') || file.startsWith('11-')) { + seismicExampleDocs.push({ type: 'doc', id, label }); } }); @@ -268,7 +275,18 @@ function generateSidebarForRmcTotalRiskApplicationsGuide(versionPath, relativePa link: { type: 'doc', id: hydrologicDoc.id }, collapsible: true, collapsed: false, - items: exampleDocs, + items: hydroExampleDocs, + }); + } + + if (seismicDoc) { + customStructure.push({ + type: 'category', + label: seismicDoc.label || 'Seismic Risk Analysis', + link: { type: 'doc', id: seismicDoc.id }, + collapsible: true, + collapsed: false, + items: seismicExampleDocs, }); } diff --git a/src/components/TableVerticalNoRef.js b/src/components/TableVerticalNoRef.js index 4261911bb..d29269ffb 100644 --- a/src/components/TableVerticalNoRef.js +++ b/src/components/TableVerticalNoRef.js @@ -1,8 +1,18 @@ -import React from "react"; import "../css/custom.css"; import "../css/tables.css"; -const TableVerticalNoRef = ({ headers = [], columns = [], fullWidth = true, alt, colWidths, colAlign, widthMode = "full" }) => { +const TableVerticalNoRef = ({ + alt, + headers = [], + columns = [], + colWidths, // e.g., [14, "20ch", "minmax(16ch, 1fr)"] + colAlign, // e.g., ["left","center","right"] + headerAlign, // e.g., ["center","center","right"] (optional) + colVAlign, // e.g., ["top","middle","bottom"] for body cells + headerVAlign, // e.g., ["middle","bottom","middle"] (optional) + widthMode = "full", // "full" | "intrinsic" + footnotes, // Array + }) => { const renderHTML = (content) => ({ __html: content }); const colCount = columns.length ?? 0; @@ -21,91 +31,152 @@ const TableVerticalNoRef = ({ headers = [], columns = [], fullWidth = true, alt, styleVars[`--a${i + 1}`] = colAlign[i]; } } + if (Array.isArray(headerAlign)) { + for (let i = 0; i < Math.min(headerAlign.length, colCount); i++) { + styleVars[`--ha${i + 1}`] = headerAlign[i]; // header horizontal + } + } + if (Array.isArray(colVAlign)) { + for (let i = 0; i < Math.min(colVAlign.length, colCount); i++) { + styleVars[`--v${i + 1}`] = colVAlign[i]; // body vertical + } + } + if (Array.isArray(headerVAlign)) { + for (let i = 0; i < Math.min(headerVAlign.length, colCount); i++) { + styleVars[`--hv${i + 1}`] = headerVAlign[i]; // header vertical + } + } if (widthMode === "intrinsic") { styleVars["--table-width"] = "max-content"; styleVars["--table-display"] = "inline-table"; } - // For header alignment with colSpan: use the alignment of the first covered column - const headerCellAlign = (startColIndex /* 0-based */) => `var(--a${startColIndex + 1}, left)`; + // Header alignment helpers for colSpan + const headerTextAlignAt = (zeroBasedCol) => + `var(--ha${zeroBasedCol + 1}, var(--a${zeroBasedCol + 1}, left))`; + const headerVertAlignAt = (zeroBasedCol) => `var(--hv${zeroBasedCol + 1}, middle)`; // default header vertical const skipBodyCells = new Set(); return ( -
- - {/* Widths via CSS vars (one per data column) */} - - {Array.from({ length: colCount }).map((_, i) => ( - - ))} - +
+ {/* If you use a scroller wrapper elsewhere, you can place the footnotes inside it too */} +
+
+ + {Array.from({ length: colCount }).map((_, i) => ( + + ))} + - - {headers.map((headerRow, rowIndex) => { - let cursor = 0; // 0-based column index tracker across this header row - return ( - - {headerRow.map((cell, colIndex) => { - if (!cell) return null; - const { value, colSpan = 1, rowSpan = 1 } = cell; - const style = { textAlign: headerCellAlign(cursor) }; - const th = ( - - ); - cursor += colSpan; // advance by the span - return th; - })} - - ); - })} - + + {headers.map((headerRow, rowIndex) => { + let cursor = 0; + return ( + + {headerRow.map((cell, colIndex) => { + if (!cell) return null; + const { value, colSpan = 1, rowSpan = 1 } = cell; + const thStyle = { + textAlign: headerTextAlignAt(cursor), + verticalAlign: headerVertAlignAt(cursor), + }; + const node = ( + + ); + cursor += colSpan; + return node; + })} + + ); + })} + - - {Array.from({ length: rowCount }).map((_, rowIndex) => ( - - {columns.map((col, colIndex) => { - const cellKey = `${colIndex}-${rowIndex}`; - if (skipBodyCells.has(cellKey)) return null; + + {Array.from({ length: rowCount }).map((_, rowIndex) => ( + + {columns.map((col, colIndex) => { + const cellKey = `${colIndex}-${rowIndex}`; + if (skipBodyCells.has(cellKey)) return null; - const raw = col[rowIndex]; - if (raw && typeof raw === "object" && "value" in raw) { - const { value, rowSpan = 1, colSpan = 1 } = raw; + const raw = col?.[rowIndex]; - // register covered cells to skip (rowSpan/colSpan) - for (let r = 0; r < rowSpan; r++) { - for (let c = 0; c < colSpan; c++) { - if (r !== 0 || c !== 0) { - skipBodyCells.add(`${colIndex + c}-${rowIndex + r}`); + if (raw && typeof raw === 'object' && 'value' in raw) { + const { value, rowSpan = 1, colSpan = 1 } = raw; + for (let r = 0; r < rowSpan; r++) { + for (let c = 0; c < colSpan; c++) { + if (r !== 0 || c !== 0) { + skipBodyCells.add(`${colIndex + c}-${rowIndex + r}`); + } } } + return ( + + ); } return ( ); - } + })} + + ))} + +
1 ? colSpan : undefined} rowSpan={rowSpan > 1 ? rowSpan : undefined} className="table-header" style={style}> - {value} -
1 ? colSpan : undefined} + rowSpan={rowSpan > 1 ? rowSpan : undefined} + className="table-header" + style={thStyle} + dangerouslySetInnerHTML={ + typeof value === 'string' ? renderHTML(value) : undefined + } + > + {typeof value === 'string' ? undefined : value} +
1 ? rowSpan : undefined} + colSpan={colSpan > 1 ? colSpan : undefined} + className="table-body-cell" + style={{ + textAlign: `var(--a${colIndex + 1}, left)`, + verticalAlign: `var(--v${colIndex + 1}, middle)`, + }} + > + {value} + 1 ? rowSpan : undefined} - colSpan={colSpan > 1 ? colSpan : undefined} className="table-body-cell" - style={{ textAlign: `var(--a${colIndex + 1}, left)` }} + style={{ + textAlign: `var(--a${colIndex + 1}, left)`, + verticalAlign: `var(--v${colIndex + 1}, middle)`, + }} + dangerouslySetInnerHTML={ + typeof raw === 'string' ? renderHTML(raw) : undefined + } > - {value} + {typeof raw === 'string' ? undefined : raw}
- return ( - - {typeof raw === "string" ? undefined : raw} - - ); - })} - - ))} - - + {/* Footnotes block (only if provided and non-empty) */} + {Array.isArray(footnotes) && footnotes.length > 0 && ( +
+
    + {footnotes.map((note, idx) => ( +
  1. + + {typeof note === 'string' ? ( + + ) : ( + note + )} + +
    2. + ))} +
+
+ )} +
); }; diff --git a/src/pages/desktop-applications/rmc-totalrisk.js b/src/pages/desktop-applications/rmc-totalrisk.js index dfbcb127b..fb4ab1eef 100644 --- a/src/pages/desktop-applications/rmc-totalrisk.js +++ b/src/pages/desktop-applications/rmc-totalrisk.js @@ -18,7 +18,7 @@ const totalRiskData = [ icon: 'img/TotalRisk.png', doc_location: 'desktop-applications/rmc-totalrisk/applications-guide', doc_name: 'RMC TotalRisk Applications Guide', - active: false, + active: true, draft: true, }, { diff --git a/src/theme/Layout/buildNavLinks.js b/src/theme/Layout/buildNavLinks.js index 914fb1733..e54a0c957 100644 --- a/src/theme/Layout/buildNavLinks.js +++ b/src/theme/Layout/buildNavLinks.js @@ -155,6 +155,7 @@ export default function buildNavLinks(useBaseUrl, latestVersions = {}) { href: totalRiskHref, children: [ { id: 'tr-users-guide', text: "RMC-TotalRisk User's Guide", href: trUserGuideHref }, + { id: 'tr-apps-guide', text: "RMC-TotalRisk Applications Guide", href: trAppHref }, // Optionally add trAppHref/trVerifHref if needed in the menu ], }, diff --git a/static/figures/desktop-applications/rmc-totalrisk/applications-guide/figure4.png b/static/figures/desktop-applications/rmc-totalrisk/applications-guide/figure4.png deleted file mode 100644 index 6aa2a1af9..000000000 Binary files a/static/figures/desktop-applications/rmc-totalrisk/applications-guide/figure4.png and /dev/null differ diff --git a/static/figures/desktop-applications/rmc-totalrisk/applications-guide/icons/branchproperties.png b/static/figures/desktop-applications/rmc-totalrisk/applications-guide/icons/branchproperties.png deleted file mode 100644 index d38af2f54..000000000 Binary files a/static/figures/desktop-applications/rmc-totalrisk/applications-guide/icons/branchproperties.png and /dev/null differ diff --git a/static/figures/desktop-applications/rmc-totalrisk/applications-guide/icons/newbranch.png b/static/figures/desktop-applications/rmc-totalrisk/applications-guide/icons/newbranch.png 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