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 | Fail | Fail | ||
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 distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the surface line (the length of the foreland is increased to 160 m instead of 60 m)
- 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 distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- 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 distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- 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 except:
- for the distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the grain diameters:
- for Calais sand : D50 = 230 μm (instead of 180) and D15 = 130 μm (unchanged)
- for Compacted sand : D50 = 210 μm (instead of 160) and D15 = 110 μm (unchanged)
For case E, the same input as benchmark 1-1 (see group 1) is used except:
- for the distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the grain diameters:
- for Calais sand : D50 = 230 μm (instead of 180) and D15 = 130 μm (unchanged)
- for Compacted sand : D50 = 210 μm (instead of 160) and D15 = 110 μm (unchanged)
- for the channel slope which is 1 : 2 instead of 1 : 6
For case F, the same input as benchmark 1-1 (see group 1) is used except:
- for the distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the channel slope which is 1 : 7.1 instead of 1 : 6.
For case G, the same input as benchmark 1-1 (see group 1) is used except:
- for the distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the channel slope which is 1 : 7.1 instead of 1 : 6.
- for the grain diameters:
- for Calais sand : D50 = 230 μm (instead of 180) and D15 = 130 μm (unchanged)
- for Compacted sand : D50 = 210 μm (instead of 160) and D15 = 110 μm (unchanged)
For case H, the same input as benchmark 1-1 (see group 1) is used except:
- for the distribution of the stochastic parameters of the Detailed check (LogNormal instead of Deterministic/Normal)
- for the state parameter which is equal to -0.06 instead of -0.03
- for the grain diameters:
- for Calais sand : D50 = 230 μm (instead of 180) and D15 = 130 μm (unchanged)
- for Compacted sand : D50 = 210 μm (instead of 160) and D15 = 110 μm (unchanged)
- 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
Marge = 2 H = 30 m
Slope of the observation profile: 1:15
Assessment level: Z = -10 m
XSsign = 80 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 gives a Warning message because D50 < 200 μm , an Advanced check is therefore needed.
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 |
---|---|---|---|
Step 1a: Would flow slide lead to damage on levee? Marge [m] Slope [1:xxx] Assessment level [m + NAP] |
No 30.000 15.000 -10.000 |
No 30.000 15.000 -10.000 |
OK 0.00 % 0.00 % 0.00 % |
Step 1c: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
Step 1d: Flow slide possible based on criteria "steepest slope aver 5m" ? Average slope over a height of at least 5 m [1:xxx] |
No 6 |
No 6 |
OK 0.00 % |
Step 1e: Flow slide possible based on average geometry only? Total inclination of the channel slope [1:xxx] Is breaching possible? |
Yes 6 Yes |
Yes 6 Yes |
OK 0.00 % 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] | 2.92 × 10-7 | 2.92 × 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 | Warning | Warning | OK |
Results of benchmark 3-1 for case B:
| Benchmark | D-FLOW SLIDE | Relative error |
---|---|---|---|
Step 1a: Would flow slide lead to damage on levee? Marge [m] Slope [1:xxx] Assessment level [m + NAP] |
Yes 30.000 15.000 -10.000 |
Yes 30.000 15.000 -10.000 |
OK 0.00 % 0.00 % 0.00 % |
Step 1c: Artificially underwater installed and non-compacted sandy foreshore? | Yes | Yes | OK |
Step 1d: Flow slide possible based on criteria "steepest slope aver 5m" ? Average slope over a height of at least 5 m [1:xxx] |
No 6 |
No 6 |
OK 0.00 % |
Step 1e: Flow slide possible based on average geometry only? Total inclination of the channel slope [1:xxx] Is breaching possible? |
Yes 6 Yes |
Yes 6 Yes |
OK 0.00 % 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] | 3.95 × 10-7 | 3.95 × 10-7 | 0.00 % |
Reliability index β | - | 1.712 | - |
P(L > Lallowable) | 4.34 × 10-2 | 4.34 × 10-2 | 0.23 % |
Probability of flood damage by liquefaction P(falen|ZV) [/year] | 1.72× 10-8 | 1.72 × 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 |
---|---|---|---|
Step 1a: Would flow slide lead to damage on levee? Marge [m] Slope [1:xxx] Assessment level [m + NAP] |
Yes 28.016 15.000 -10.331 |
Yes 28.016 15.000 -10.331 |
OK 0.00 % 0.00 % 0.00 % |
Step 1c: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
Step 1d: Flow slide possible based on criteria "steepest slope aver 5m" ? Average slope over a height of at least 5 m [1:xxx] |
Yes 3.901 |
Yes 3.901 |
OK 0.00 % |
Step 1e: Flow slide possible based on average geometry only? Total inclination of the channel slope [1:xxx] Is breaching possible? |
Yes 7.395 Yes |
Yes 7.395 Yes |
OK 0.00 % OK |
Result of the Global check | Fail | Fail | OK |
Fictive channel depth Hr [m] | 23.791 | 23.791 | 0.00 % |
Fictive slope cotan αr | 8.413 | 8.413 | 0.00 % |
Max. allowable retrogression length Lallowable [m] | 60 | 60 | 0.00 % |
Probability of preventing a liquefaction P(ZV) [/km/year] | 5.63 × 10-8 | 5.63 × 10-8 | 0.00 % |
Reliability index β | - | -1.334 | - |
P(L > Lallowable) | 9.09 × 10-1 | 9.09 × 10-1 | 0.00 % |
Probability of flood damage by liquefaction P(falen|ZV) [/year] | 5.12 × 10-8 | 5.12 × 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 D:
| Benchmark | D-FLOW SLIDE | Relative error |
---|---|---|---|
Step 1a: Would flow slide lead to damage on levee? Marge [m] Slope [1:xxx] Assessment level [m + NAP] |
Yes 30.000 15.000 -10.000 |
Yes 30.000 15.000 -10.000 |
OK 0.00 % 0.00 % 0.00 % |
Step 1c: Artificially underwater installed and non-compacted sandy foreshore? | No | No | OK |
Step 1d: Flow slide possible based on criteria "steepest slope aver 5m" ? Average slope over a height of at least 5 m [1:xxx] |
No 6 |
No 6 |
OK 0.00 % |
Step 1e: Flow slide possible based on average geometry only? Total inclination of the channel slope [1:xxx] Is breaching possible? |
Yes 6 No |
Yes 6 No |
OK 0.00 % OK |
Result of the Global check | Fail | Fail | OK |
Fictive channel depth Hr [m] | 21.571 | 25.571 | 0.00 % |
Fictive slope cotan αr | 10.500 | 10.500 | 0.00 % |
Max. allowable retrogression length Lallowable [m] | 60 | 60 | 0.00 % |
Probability of preventing a liquefaction P(ZV) [/km/year] | 3.92 × 10-7 | 3.92 × 10-7 | 0.00 % |
Reliability index β | - | 1.712 | - |
P(L > Lallowable) | 4.34 × 10-2 | 4.34 × 10-2 | 0.00 % |
Probability of flood damage by liquefaction P(falen|ZV) [/year] | 1.70 × 10-8 | 1.70 × 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 | Pass | Pass | OK |
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 |