This section uses tests performed by hand or by means of an Excel spreadsheet.
3.1 Test of all possible trajectories of the Global check and the Overall result
Description
This benchmark tests all possible trajectories according to the Global check and all possible combinations between the Global and the Detailed checks:
| Case | Step 1a | Step 1c | Step 1d | Step 1e Average slope | Step 1e Breach flow | Step 1e | Global check | Detailed check | Overall result | Warning message | Information message |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A | No | Pass | Pass | Warning | D50 < 200 μm in the Detailed check, Advanced check needed | ||||||
| B | Yes | Yes | Fail | Fail | Fail | Artificial foreland, Advanced check needed | |||||
| C | Yes | No | Yes | Fail | Fail | Fail | Criteria on "steepest slope over 5 m" met, Advanced check needed | ||||
| D | Yes | No | No | Yes | No | Yes | Fail | Pass | Pass | ||
| E | Yes | No | No | Yes | Yes | Yes | Fail | Pass | Pass | ||
| F | Yes | No | No | No | Yes | Yes | Fail | Fail | Fail | ||
| G | Yes | No | No | No | No | No | Pass | Pass | Pass | ||
| H | Yes | No | No | No | No | No | Pass | Fail | Warning | Global passes but Detailed fails, check input |
For case A, the same input as benchmark 1-1 (see group 1) is used except for the surface line (the length of the foreland is increased to 160 m instead of 60 m) and a "Distance influence zone" of 10 m is used.
For case B, the same input as benchmark 1-1 (see group 1) is used except for the foreland: an artificial instead of a natural foreland is assumed.
For case C, the same input as benchmark 1-1 (see group 1) is used except for the position of the characteristic point "Insert river channel" which is lowered to get a slope channel of 1 : 7,1.
For case D, the same input as benchmark 1-1 (see group 1) is used.
For case E, the same input as benchmark 1-1 (see group 1) is used except for the state parameter which is equal to -0.06 instead of -0.03.
For case F, the same input as benchmark 1-1 (see group 1) is used except for the state parameter which is equal to -0.06 instead of -0.03, except for the diameters D50 and D15 which are equal to 250 μm and 150 μm resp. for sand layers and except for the channel slope which is 1 : 2 instead of 1 : 6.
For case G, the same input as benchmark 1-1 (see group 1) is used except for the state parameter which is equal to -0.06 instead of -0.03 and except for the diameters D50 and D15 which are equal to 250 μm and 150 μm resp. for sand layers.For the Detailed check, the required probability of failure is 1 per 40000 years instead of 1 per 4000 years and the migration velocity is 0.5m/year instead of 10 mm /year.
Benchmarks results
For each cases, the Global and Detailed checks are worked out in an Excel spreadsheet.
Hereafter, the main results are given per case,
NOTE: For the Detailed check, the reliability index (β) can't be easily calculated by an analytical solution, as the four stochastics (cotan(β), cotan(γ), D/H and c) have a LogNormal distribution. Therefore, the value of the reliability index (β) calculated by D-Flow Slide (using a FORM analysis, invoked from a probabilistic library largely tested) is used in the spreadsheet.
Case A:
Global check - Step 1:
Channel depth: H = 15 m
Thickness of the sensitive layer: Hvw = 25 m
Marge = 2 Hvw + 1.5 (H - Hvw) = 35 m
Slope of the observation profile: 1:15
Assessment level: Z = -10 m
XSsign = 85 m
XSzv = 30 m
XSsign > XSzv => Flow slide would not lead to damage on levee => Global check passes.
Detailed check: (see table below for intermediary results) Probability of flood damage by liquefaction (= 0.00) < Allowable probability of failure (2.50 × 10-6) => Detailed check passes.
Overall check: as Global and Detailed check pass, the Overall check passes.
Case B:
Global check - Step 1: Same results as benchmark 1-1 (flow slide would lead to damage on levee) => Go to step 3.
Global check - Step 3: The foreland is artificial => Global and Detailed check fail, an Advanced check is needed.
Detailed check: (see table below for intermediary results) Probability of flood damage by liquefaction < Allowable probability of failure => Detailed check passes.
Overall check: as step 3 of Global check fails, the Overall check fails whatever the Detailed check result.
Case C:
Global check - Step 1: Same results as benchmark 1-1 (flow slide would lead to damage on levee) => Go to step 3.
Global check - Step 3: The foreland is natural => Go to step 4.
Global check - Step 4: The slope channel is 1:7,1 so softer than 1:7 => Flow slide is not possible based on geometry => Global check passes.
Detailed check: The determination of the reliability index for the Detailed check is not possible using the spreadsheet because the formula implemented in the spreadsheet applies only for horizontal foreland, which is not the case here.
Overall check: As the Detailed check result is not known, the Overall result can't be deduced.
Case D:
Results are identical to benchmark 1-1 and can be found in Group 1.
Case E:
Global check - Step 1: Same results as benchmark 1-1 (flow slide would lead to damage on levee) => Go to step 3.
Global check - Step 3: The foreland is natural => Go to step 4.
Global check - Step 4: The slope channel is 1:6 so steeper than 1:7 => Flow slide is possible based on geometry => Go to step 5.
Global check - Step 5: The state parameter is -0.06 so less than -0.05 => Liquefaction is not possible based on the state parameter => Go to step 6.
Global check - Step 6: The average diameters over a thickness of 5m are D50 = 180 μm and D15 = 130 μm. So layers are present with D50 < 200 μm and D15 < 100 μm => Global check fails and Detailed check needed.
Detailed check: (see table below for intermediary results) Probability of flood damage by liquefaction < Allowable probability of failure => Detailed check passes.
Overall check: as Detailed check passes, the Overall check passes.
Case F:
Global check - Step 1: Same results as benchmark 1-1 (flow slide would lead to damage on levee) => Go to step 3.
Global check - Step 3: The foreland is natural => Go to step 4.
Global check - Step 4: The slope channel is 1:6 so steeper than 1:7 => Flow slide is possible based on geometry => Go to step 5.
Global check - Step 5: The state parameter is -0.06 so less than -0.05 => Liquefaction is not possible based on the state parameter => Go to step 6.
Global check - Step 6: The average diameters over a thickness of 5m are D50 = 250 μm and D15 = 150 μm. So no layers are present with D50 < 200 μm and D15 < 100 μm => Go to step 7.
Global check - Step 7: The slope channel is 1:2, so the slope is steeper than the critical (local) slope from the CUR table => Global check fails and Detailed check needed.
Detailed check: (see table below for intermediary results) Probability of flood damage by liquefaction > Allowable probability of failure => Detailed check fails.
Overall check: Global and Detailed checks fail, so the Overall check fails.
Case G:
Global check - Step 1: Same results as benchmark 1-1 (flow slide would lead to damage on levee) => Go to step 3.
Global check - Step 3: The foreland is natural => Go to step 4.
Global check - Step 4: The slope channel is 1:6 so steeper than 1:7 => Flow slide is possible based on geometry => Go to step 5.
Global check - Step 5: The state parameter is -0.06 so less than -0.05 => Liquefaction is not possible based on the state parameter => Go to step 6.
Global check - Step 6: The average diameters over a thickness of 5m are D50 = 250 μm and D15 = 150 μm. So no layers are present with D50 < 200 μm and D15 < 100 μm => Go to step 7.
Global check - Step 7: The slope channel is 1:6, so the slope is softer than the critical (local) slope from the CUR table => Global check passes.
Detailed check: (see table below for intermediary results) Probability of flood damage by liquefaction > Allowable probability of failure => Detailed check fails.
Overall check: Global passes and Detailed checks fails, that's not logical, so a warning message is displayed in the Overall check.
D-Flow Slide results
D-FLOW SLIDE results are in accordance with the results by hand as show in the tables below.
Results of benchmark 3-1 for case A
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 35.000 | 35.000 | 0.00 % |
| Slope [1:xxx] | 15.000 | 15.000 | 0.00 % |
Assessment level | -10.000 | -10.000 | 0.00 % |
Step 1: Would flow slide lead to damage on levee? | No | No | OK |
Result of the Global check | Pass | Pass | OK |
| Fictive channel depth Hr [m] | 19.087 | 19.087 | 0.00 % |
| Fictive slope cotan αr [-] | 23.000 | 23.000 | 0.00 % |
| Max. allowable retrogression length Lallowable [m] | 150.000 | 150.000 | 0.00% |
| Probability of occurence P(ZV) [/km/year] | 9.14 × 10-7 | 9.14 × 10-7 | 0.00 % |
| Reliability index critical length β | - | 39.999 | - |
| Probability P(L > Lallowable) | 0.00 | 0.00 | 0.00 % |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | 0.00 | 0.00 | 0.00 % |
| Allowable probability of failure [/year] | 2.50 × 10-6 | 2.50 × 10-6 | 0.00 % |
Result of the Detailed check | Pass | Pass | OK |
| Overall result | Pass | Pass | OK |
Results of benchmark 3-1 for case B
The overall result is not correctly determined in D-Flow Slide if the foreshore is artificial: D-Flow Slide uses the Detailed check result but it should directly conclude that the Overall check fails.
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 35.000 | 35.000 | 0.00 % |
| Slope [1:xxx] | 15.000 | 15.000 | 0.00 % |
Assessment level | -10.000 | -10.000 | 0.00 % |
Step 1: Is liquefaction damaging on basis of geometry? | Yes | Yes | OK |
Step 3: Artificially underwater installed and non-compacted sandy foreshore? | Yes | Yes | OK |
Result of the Global check | Fail | Fail | OK |
| Fictive channel depth Hr [m] | 21.571 | 21.571 | 0.00 % |
| Fictive slope cotan αr | 10.5 | 10.5 | 0.00 % |
| Max. allowable retrogression length Lallowable [m] | 60 | 60 | 0.00 % |
| Probability of preventing a liquefaction P(ZV) [/km/year] | 1.24 × 10-6 | 1.24 × 10-6 | 0.00 % |
| Reliability index β | - | 1.712253127713 | - |
| P(L > Lallowable) | 4.34 × 10-2 | 4.34 × 10-2 | 0.23 % |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | 5.38 × 10-8 | 5.38 × 10-8 | 0.00 % |
| Allowable probability of failure [/year] | 2.50 × 10-6 | 2.50 × 10-6 | 0.00 % |
Result of the Detailed check | Pass | Pass | OK |
| Overall result | Fail | Fail | OK |
Results of benchmark 3-1 for case C
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 31.514 | 31.514 | 0.00 % |
| Slope [1:xxx] | 15.000 | 15.000 | 0.00 % |
Assessment level | -10.775 | -10.775 | 0.00 % |
Step 1: Is liquefaction damaging on basis of geometry? | Yes | Yes | OK |
Step 3: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
| Step 4: Flow slide possible based on geometry only? | No | No | OK |
Result of the Global check | Pass | Pass | OK |
| Fictive channel depth Hr [m] | 17.762 | 17.762 | 0.00 % |
| Fictive slope cotan αr | 10.5 | 10.5 | 0.00 % |
| Probability of preventing a liquefaction P(ZV) [/km/year] | 3.29 × 10-7 | 3.29 × 10-7 | 0.00 % |
| Reliability index β | Not available | 3.749 | |
| P(L > Lallowable) | Not available | 8.88 × 10-5 | |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | Not available | 1.10 × 10-10 | |
| Allowable probability of failure [/year] | 2.50 × 10-6 | 2.50 × 10-6 | 0.00 % |
Result of the Detailed check | Not available | Pass | - |
| Overall result | Not available | Pass | - |
Results of benchmark 3-1 for case D
See results of benchmark 1-1 in Group 1.
Results of benchmark 3-1 for case E
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 35 | 35 | 0.00 % |
| Slope [1:xxx] | 15 | 15 | 0.00 % |
Assessment level | -10 | -10 | 0.00 % |
Step 1: Is liquefaction damaging on basis of geometry? | Yes | Yes | OK |
Step 3: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
| Step 4: Flow slide possible based on geometry only? | Yes | Yes | OK |
| Step 5: Is liquefaction possible based on state parameter? | No | No | OK |
| Step 6: Layers present with a thickness of minimal 5m, in which D50<200 μm or D15<100 μm ? | Yes | Yes | OK |
Result of the Global check | Fail | Fail | OK |
| Fictive channel depth Hr [m] | 21.571 | 21.571 | 0.00 % |
| Fictive slope cotan αr | 10.5 | 10.5 | 0.00 % |
| Probability of preventing a liquefaction P(ZV) [/km/year] | 6.24 × 10-7 | 6.24 × 10-7 | 0.00 % |
| Reliability index β | 3.749 | 3.749 | 0.00 % |
| P(L > Lallowable) | 8.86 × 10-5 | 8.88 × 10-5 | 0.23 % |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | 5.53 × 10-11 | 5.54 × 10-11 | 0.18 % |
| Allowable probability of failure [/year] | 2.50 × 10-6 | 2.50 × 10-6 | 0.00 % |
Result of the Detailed check | Pass | Pass | OK |
| Overall result | Pass | Pass | OK |
Results of benchmark 3-1 for case F
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 35 | 35 | 0.00 % |
| Slope [1:xxx] | 15 | 15 | 0.00 % |
Assessment level | -10 | -10 | 0.00 % |
Step 1: Is liquefaction damaging on basis of geometry? | Yes | Yes | OK |
Step 3: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
| Step 4: Flow slide possible based on geometry only? | Yes | Yes | OK |
| Step 5: Is liquefaction possible based on state parameter? | No | No | OK |
| Step 6: Layers present with a thickness of minimal 5m, in which D50<200 μm or D15<100 μm ? | No | No | OK |
| Step 7: Is breaching possible? | Yes | Yes | OK |
Result of the Global check | Fail | Fail | OK |
| Fictive channel depth Hr [m] | 18.524 | 18.524 | 0.00 % |
| Fictive slope cotan αr | 10.5 | 10.5 | 0.00 % |
| Probability of preventing a liquefaction P(ZV) [/km/year] | 1.03 × 10-4 | 1.03 × 10-4 | 0.00 % |
| Reliability index β | 1.289 | 1.289 | 0.00 % |
| P(L > Lallowable) | 9.88 × 10-2 | 9.87 × 10-2 | 0.10 % |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | 1.02 × 10-5 | 1.02 × 10-5 | 0.00 % |
| Allowable probability of failure [/year] | 2.50 × 10-6 | 2.50 × 10-6 | 0.00 % |
Result of the Detailed check | Fail | Fail | OK |
| Overall result | Fail | Fail | OK |
Results of benchmark 3-1 for case G
| Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|
Marge | 35 | 35 | 0.00 % |
| Slope [1:xxx] | 15 | 15 | 0.00 % |
Assessment level | -10 | -10 | 0.00 % |
Step 1: Is liquefaction damaging on basis of geometry? | Yes | Yes | OK |
Step 3: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
| Step 4: Flow slide possible based on geometry only? | Yes | Yes | OK |
| Step 5: Is liquefaction possible based on state parameter? | No | No | OK |
| Step 6: Layers present with a thickness of minimal 5m, in which D50<200 μm or D15<100 μm ? | No | No | OK |
| Step 7: Is breaching possible? | No | No | OK |
Result of the Global check | Pass | Pass | OK |
| Fictive channel depth Hr [m] | 21.571 | 21.571 | 0.00 % |
| Fictive slope cotan αr | 10.5 | 10.5 | 0.00 % |
| Probability of preventing a liquefaction P(ZV) [/km/year] | 3.09 × 10-3 | 3.09 × 10-3 | 0.00 % |
| Reliability index β | 3.749 | 3.749 | 0.00 % |
| P(L > Lallowable) | 8.86 × 10-5 | 8.88 × 10-5 | 0.23 % |
| Probability of flood damage by liquefaction P(falen|ZV) [/year] | 2.74 × 10-7 | 2.75 × 10-7 | 0.36 % |
| Allowable probability of failure [/year] | 2.50 × 10-7 | 2.50 × 10-7 | 0.00 % |
Result of the Detailed check | Fail | Fail | OK |
| Overall result | Warning | Warning | OK |
