In the proposed example is reported the piping verification of a channel section through the use of GeoStru software GFAS (Finite Element Analysis in Geotechnics).

The geotechnical parameters used in the analyses and the geometries of the investigated sections refer to the Geological Report derived from in situ investigations.

### Cross section geometry

The geometry of the cross section has a trapezoidal shape (Figure 1):

Fig. 1 – Geometry of the cross section subject to piping verification

### Geotechnical parametres

For the section under consideration were used the geotechnical parameters shown in Table 1 of the geologic report below:

Lithology | Color | Unit volume weight [kN/m^{3}] | Cohesion c’ [kN/m^{2}] | Angle of shearing resistance φ [°] | Poisson’s ratio ν [-] | Modulus of elasticity E [kPa] |

New embankment | 20 | 15 | 36 | 0.3 | 5400 | |

Silty clays | 19.2 | 15 | 36 | 0.3 | 4400 |

Tab. 1 – Geotechnical parameters

For the silty clay layer, a permeability coefficient value was assumed to be: k =2.06 x 10^{-6} m/s, while a permeability coefficient value of k =1 x 10^{-6} m/s was assumed for the embankment.

### Gradient method

The **Gradient method** was used for Piping verification.

The viscous action of water causes a transfer of energy between the water and the ground: between two points with Δ_{s} distance apart along a stream line, in fact, there is a hydraulic head Δ_{h}. The corresponding force is called seepage force: when it increases above a certain value, it can cause the phenomenon of Piping which consists in the removal of soil granules and the consequent faster and faster seepage flow until the formation of real flow channels.

The limit velocity of the seepage flow above which removal of soil particles begins to occur corresponds to a so-called critical gradient i_{cr} given by

i_{cr} = (γ_{s} – γ_{w}) / γ_{w} = γ’/ γ_{w}

where:

γ_{s} = saturated unit weight of soil

γ_{w} = unit weight of water

γ’ = effective unit weight

The hydraulic gradient that would result in seepage flow along the flow line is a function of its length L and the pressure drop Δh, i.e., the difference in elevation between predicted maximum flood level and the embankment foot according to the relationship:

i = Δ_{h}/L

The safety factor against Piping is therefore:

Fs= i_{cr} / i = i_{cr} · L /Δ_{h}

The piping verification is performed by checking that the hydraulic gradient i is not higher than the critical hydraulic gradient icr. Wanting to maintain a margin of safety, the critical gradient i_{cr} can be reduced by a partial coefficient γ_{R} = 3.

Permeability data used in the computation:

Soil | Color | Permeability [m/s] |

New embankment | 1E^{-06} | |

Silty clays | 2.06E^{-06} |

Tab.2 – Permeability values used in the computation

The analysis of seepage flow was conducted using GFAS software for Finite Element Analysis in Geotechnics; the results are shown below.

### Study cross section output

Seepage flow

Fig. 2 – Velocity variation of the seepage flow

Fig. 3 – Velocity variation of the seepage flow

**Maximum velocity** V_{max} = 4.94*10^{-7} m/s

Fig. 4 – Piezometric levels

Fig. 5 – Pore pressures

### Piping verification

From the velocity field of the seepage flow, obtained from the analyses with GFAS software, it is observed that the soil affected by seepage forces directed from the bottom to the top is the base soil of the embankment, thus the silty clays, so the critical hydraulic gradient will be calculated considering the saturated unit weight.

From the calculation results, it is observed (see Figure 6) that Δ_{h} is 1.9 m, while the length of the flow path L is about 9.07 m:

Figure 6 – Flow path diagram

therefore, the value of the average gradient is equal to:

As established earlier, wanting to apply a reduction (γ_{R} = 3), it must result:

Therefore:

**The verification is satisfied**

The software automatically determines the line that locates the groundwater line (Figure 7):

Fig. 7 – Free surface

Geotechnical and F.E.M. analysis System – GFAS is a software for nonlinear finite element analysis in geotechnics. A complete solution that integrates all the necessary functionalities for the analysis of multiple geotechnical and geological problems in static and dynamic conditions, such as:

Tunnels, Slope stability, Reinforced soils, Stabilization works, Excavations, Settlements, Soil-Structure interaction, Seepage analysis, Modal dynamic analysis with Eurocodes spectra.

The traditional methods of analysis based on the concept of LIMIT EQUILIBRIUM (LEM) do not allow the determination of stresses and deformations in the analyzed volumes. These limitations have led to the need to integrate the conventional analysis with analysis based on numerical models. These methods use the numerical evaluation of the problem and do not require simplifications to the calculation.

**GFAS** imports geometries from **AUTOCAD** and the from other GEOSTRU software.