Internal Erosion Suite

Blanket Theory Case 4

Case 4 has an impervious top stratum on only the landside of the levee. The pervious substratum is divided into three zones to apply the method of fragments as shown in Figure.

Method of Analysis

The method of analysis is the same as in Case 1.

Levee Geometry

Step 2 characterizes the levee geometry. The input includes the levee crest elevation, landside toe elevation, base width of levee (L₂), and length of the foundation and top stratum beyond the landside levee toe (L₃), as illustrated in Figure.

Figure: Step 2 of BT Case 4 worksheet: Levee geometry.

Pervious Substratum Characterization

The pervious stratum characterization is the same as in Case 1.

Landside Blanket (Top Stratum) Characterization

The landside blanket (top stratum) characterization is the same as in Case 2.

Blanket Theory Assumptions

Step 5 checks the BT (method of fragments) assumptions against the input parameters to ensure essentially vertical equipotential lines. For deterministic analysis, the assumptions are checked for the most likely values of the random variables. For probabilistic analysis, the assumptions are checked for the mean values of the random variables. Values outside of the model assumptions have an orange background. Figure illustrates the check of BT assumptions.

Figure: Step 5 of BT Case 4 worksheet: BT assumptions.

Seepage Characterization

Step 6 calculates the net hydraulic head on the levee (H) the same as in Case 1. The flow or seepage per unit length of the levee (Q_s) is calculated using Equation.

$$Q_{S} = k_{h,f}H\frac{d}{0.43d + L_{2} + L_{3}}$$

where:

k_h,f = horizontal permeability of pervious substratum
H = net hydraulic head on the levee
L₂ = base width of the levee
L₃ = length of the foundation and top stratum beyond the landside levee toe
d = thickness of the pervious substratum

The format for the tabular output is the same as in Case 1.

Likelihood of Heave/Blowout at Landside Toe

Step 7 calculates the excess hydraulic head at the landside levee toe (h_o) using Equation.

$$h_{o} = H \frac{L_3}{0.43d + L_{2} + L_{3}}$$

where:

H = net hydraulic head on the levee
L₂ = base width of the levee
L₃ = length of the foundation and top stratum beyond the landside levee toe
d = thickness of the pervious substratum

The vertical seepage exit gradient at the landside levee toe (i_v) and factor of safety against heave/blowout (based on vertical seepage gradients) at the landside levee toe (FS_vg) are calculated the same as in Case 2. The format for the tabular and graphical output is the same as in Case 2.

Likelihood of Heave/Blowout at Given Distance from Landside Toe

Step 8 calculates the excess hydraulic head at a distance x from the landside levee toe (h_x) using Equation.

$$h_{x} = h_{o}\frac{L_{3}-x}{L_3}$$

where:

h_o = excess hydraulic head at the landside levee toe
L₃ = length of the foundation and top stratum beyond the landside levee toe
x = distance from the landside levee toe

The vertical seepage exit gradient at a distance x from the landside levee toe (i_v,x) and factor of safety against heave/blowout (based on vertical seepage gradients) at a distance x from the landside levee toe (FS_vg,x) are calculated the same as in Case 2. The format for the tabular and graphical output is the same as in Case 2.