Group 1: Benchmarks from literature (exact solution)
This section describes a number of benchmarks for which an exact analytical solution can be found in the literature.
1.1. Study Case described in "Technisch Rapport Voorland Zettingsvloeiing"
Description
The example given in "Annex A - Case Study" of the Deltares report 1200503-001-GEO-0004 "Concept Technisch Rapport Voorland Zettingsvloeiing" of G.A. van den Ham & Co is used.
In this example, both global and detailed checks are completed on the basis of a (fictitious) dike section, which with regard to geometry and soil structure is typical of the Southwest Delta.
The dike has a height of NAP+5 m, a crest width of 3 m and a slope of 1:3.
The foreshore begins to imaginary toe of the dike at an elevation of NAP and is 60 m wide. The toe of the trench is NAP-15 m and has a slope of 1:6. The dike section is 800 m long. The phreatic level is at NAP-2 m.
The soil profile is as follows:
- from NAP+3.5 m to NAP+1 m: peat
- from NAP+1 m to NAP-5 m: silty clay
- from NAP-5 m to NAP-18 m: moderately to loosely compacted sand (Calais)
- from NAP-18 m to NAP-30 m: densely compacted sand
Benchmarks results
The details of the calculation can be found in annex A of the report. The main results are given in the table below. The global check fails but the detailed check passes.
D-Flow Slide results
Results of benchmark 1-1 for the Global Check
|
Benchmark |
D-FLOW SLIDE |
Relative error |
|---|---|---|---|
Marge |
xxx |
xxx |
xxx |
X coordinate of the observation profile (Xsign) |
xxx |
xxx |
xxx |
X coordinate of the liquefaction point (XZV) |
xxx |
xxx |
xxx |
Step 1: Is liquefaction damaging on basis of geometry? |
Yes |
Yes |
|
Step 2: Artificially underwater installed and non-compacted sandy foreshore? |
No |
No |
|
Step 4: Is liquefaction possible on the basis of the geometry? |
Yes |
Yes |
|
Step 5: Are there any sensitive to liquefaction layers present? |
Yes |
Yes |
|
Result of the Global Check |
Failed |
Failed |
|
Results of benchmark 1-1 for the Detailed Check
|
Unit |
Benchmark |
D-FLOW SLIDE |
Relative error |
|---|---|---|---|---|
Fictive channel depht (Hr) |
[m] |
21.571 |
21.571 |
0.00 % |
Fictive slope (cotan αr) |
[-] |
10.500 |
10.500 |
0.00 % |
Probability of liquefaction |
[-] |
2.93 × 10-3 |
2.93 × 10-3 |
0.00 % |
Representative probability of failure |
[-] |
3.52 × 10-3 |
3.52 × 10-3 |
0.00 % |
β |
[-] |
3.749 |
3.749 |
0.00 % |
P(L > Lallowable) |
[-] |
8.87 × 10^-5^ |
8.86 × 10^-5^ |
0.08 % |
Probability of failure |
[-] |
3.12 × 10^-7^ |
3.12 × 10^-7^ |
0.00 % |
Allowable probability of failure |
[-] |
2.50 × 10-6 |
2.50 × 10-6 |
0.00 % |
Result of Detailed Check |
|
Succeeded |
Succeeded |
|
