5.1 Comparison with SLIQ2D-Windows - Fully saturated slope with 1 layer

Description

The benchmarks in this paragraph are intended to verify the advanced method by comparing D-FLOW SLIDE results with those from the older program SLIQ2D Windows.
 In this benchmark, a fully saturated layer is inputted. The geometry and the material properties for each cases are given in the table below.

SLIQ 2D-Windows results

In SLIQ2D-Windows only the value of the tangent angle is available in the output. The other parameters (such as Ko, the normal stress p and the deviatoric stress q) are not saved and can only be red on the screen, making the comparison difficult. The figures below show the position of the unstable points  and the points considered as instable (i.e. stable points surrounded with instable points) as option Fill Holes is active.

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1a:

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1b: 

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1c:

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1d:

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1e:

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1f:

Results of SLIQ2D-Windows - Overview of the unstable points for bm5-1g:

D-FLOW SLIDE results

Results between SLIQ2D-Windows and D-FLOW SLIDE are exactly the same for the position of the imaginary surface and for the number of instable points, as show in the tables below.

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1a:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1b:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1c:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1d:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1e:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1f:

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-1g:

5.2 Comparison with SLIQ2D-Windows - Partially saturated slope with 2 layers

Description

This benchmark is intended to verify the advanced method by comparing D-FLOW SLIDE results with those from the older program SLIQ2D-Windows, for a 21 m height channel composed of 2 layers where the top layer is partially saturated. The slope of the channel is fixed to 1:3.333 (i.e. Tan α = 0.3).

Benchmark results

Results of SLIQ2D-Windows for bm5-2 - Overview of the unstable points:

D-FLOW SLIDE results

Results between SLIQ2D-Windows and D-FLOW SLIDE are exactly the same for the position of the imaginary surface and for the number of instable points, as show in the tables below.

Comparison between SLIQ2D-Windows and D-FLOW SLIDE for benchmark 5-2:

5.3 Comparison with HMBreach - One sand layer, variable slope with channel depth

Description

This benchmark is intended to verify the advanced method for breaching by comparing D-FLOW SLIDE results with those from the program HMBreach.

Only one material is used with the following properties:

• Friction angle φ = 32°
• Diameter D₅₀ = 200 μm
• Ration D₅₀/D₁₅ = 1.75 which leads to D₁₅ = 115 μm
• Porosity n = 40%
• Density of sand grains ρ_sand = 2650 kg/m³ which leads to γ_sand = ρ_sand × g / 1000 = 26 kN/m³ (with g = 9.81236)
• Density of water ρ_water = 1000 kg/m^₃ which leads to γ_water = ρ_water × g / 1000 = 9.81 kN/m³ (with g = 9.81236)
• Temperature 15°

The soil profile along the channel is composed of 10 layers:

HMBreach results

In HMBreach, the initialization height is varied manually from 0.10 m until 1.00 m with an interval of 0.10 m. Note:  a more accurate computation is obtained with interval 0.01 m.

The value of the sand transport at the top (SZ₀) and the toe (SZ_toe) of the channel are given in the table below and compared with the values calculated by D-Flow Slide.

The critical initialization height (corresponding to the initialization height  for which the ratio SZ_toe / SZ₀ is higher than10) calculated by HMBreach is expected to be equal to h_crit = 0.60 m (see table below).

D-FLOW SLIDE results

Results of HMBreach and D-FLOW SLIDE are very close when the initialization height (h₀) is less than 0.8 m,  as shown in the table below. Above 0.8 m, the sand transport at channel toe differs. However, the critical initialization height corresponding to the initialization height  for which the ratio SZ_toe / SZ₀ is higher than 10, is correct.

Two cases are considered with D-FLOW SLIDE :

• Case A: the allowable critical height (h_allowable) is 0.70 m. As the critical initialization height is higher than the allowable critical height, the slope is safe. So the Advanced check for breaching passes.

• Case B: the allowable critical height (h_allowable) is 0.80 m. As the critical initialization height is equal to the allowable critical height, it means that the probability that a breach flow slide will occur is high. So the Advanced check for breaching fails. 

Benchmark 5-3: Sand transports results for HMBreach and D-FLOW SLIDE:

Benchmark 5-3: Criterium results for HMBreach and D-FLOW SLIDE:

With HMbreach can be computed that the critical initiation height in this case is 0.56 m. The graph below shows the slope geometry (red line) and the sand transport along the sand slope (blue line).

The increasing  sand transport rate is an indication that the erosion is sufficient to maintain a self-accelerating turbidity current. The initial breach can retrogress and grow in height and finally erode the foreshore completely (Breach flow slide).

In D Flow slide the critical height is 0.6 m