**5. Interpretation and analysis of results**

The fluid is assumed to be axisymmetric, extending over a length of 0.117 m in the axial direction z and 0.03 mm in the radial direction r. The model is designed so that inlet pressure is on the left and outlet pressure is on the right (**Figure 2**).

**Figures 3**–**6** shows shear stress that develops at the soil sample interface with flowing flow for pressure P = 3726 (Pa).

**Figure 7** shows that for two clay concentrations, the calculated erosion rate value is 10�<sup>6</sup> kg/s. This erosion rate value is obtained by integrating the erosion law over the entire length of the sample hole and multiplying the result by the initial hole circumference. The erosion constants used are: *cer* <sup>¼</sup> <sup>5</sup>*:*<sup>6</sup> � <sup>10</sup>�<sup>4</sup>*s=<sup>m</sup>* and *<sup>τ</sup>cr* <sup>¼</sup> 7, 1*Pa*. These correspond to a specific soil sample containing 50% kaolinit clay and 50% sand that was tested as reported in Pham [12].

*Prediction of Internal Soil Erosion in Hydraulic Works DOI: http://dx.doi.org/10.5772/intechopen.113104*

**Figure 3.** *X-Wall shear stress in pascal.*

#### **Figure 4.**

*X-wall shear stress mapping in the solid/fluid interface.*

**Figure 8** gives the y + value for the applied pressure pinlet = 3726 Pa and the four concentrations as function of the axial coordinate.

**Figure 9** gives, for the three applied hydraulic gradients and the four concentrations, curves of the axial velocity at the axis of symmetry as function of the axial coordinate.

**Figure 5.** *Wall-shear stress obtained for P = 3726 Pa as function of clay concentration.*

#### **Figure 6.**

*Shear stress at the interface for the case of pinlet* ¼ 3726 *Pa as a function of clay concentration.*

**Figure 7.** *Erosion rate as function of the clay concentration.*

**Figure 10** shows the erosion rate as a function of clay concentration for the three pressure gradients. (10�<sup>6</sup> kg/s).

The results obtained, as shown in **Figure 10**, indicate that the erosion rate increases with clay concentration and with axial coordinate. This contrasts with the onedimensional EHF model, for which the erosion rate does not depend on the axial coordinate.

*Prediction of Internal Soil Erosion in Hydraulic Works DOI: http://dx.doi.org/10.5772/intechopen.113104*

#### **Figure 8.**

*Contours of wall Yplus on wall.*

#### **Figure 9.**

*Contours of velocity magnitude on x = 0.*

**Figure 10.** *Erosion rate as a function of clay concentration for the three pressure gradients (*10�<sup>6</sup>*kg=s).*
