{"id":6094,"date":"2021-10-21T10:28:25","date_gmt":"2021-10-21T10:28:25","guid":{"rendered":"https:\/\/blog.geostru.eu\/verifica-a-sifonamento-tramite-lanalisi-ad-elementi-finiti\/"},"modified":"2021-10-27T17:03:17","modified_gmt":"2021-10-27T17:03:17","slug":"piping-verification-using-finite-element-analysis","status":"publish","type":"post","link":"https:\/\/blog.geostru.eu\/en\/piping-verification-using-finite-element-analysis\/","title":{"rendered":"Piping verification using finite element analysis"},"content":{"rendered":"

[vc_row][vc_column][vc_column_text]<\/p>\n

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

The geotechnical parameters used in the analyses and the geometries of the investigated sections refer to the Geological Report derived from in situ investigations.<\/p>\n

[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n

Cross section geometry<\/h3>\n

The geometry of the cross section has a trapezoidal shape (Figure 1):<\/p>\n

[\/vc_column_text][vc_single_image image=”5735″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 1 – Geometry of the cross section subject to piping verification<\/span><\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n

Geotechnical parametres<\/h3>\n

For the section under consideration were used the geotechnical parameters shown in Table 1 of the geologic report below:<\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n\n\n\n\n\n
Lithology<\/strong><\/td>\nColor<\/strong><\/td>\nUnit volume weight [kN\/m3<\/sup>]<\/strong><\/td>\nCohesion c’ [kN\/m2<\/sup>]<\/strong><\/td>\nAngle of shearing resistance \u03c6 [\u00b0]<\/strong><\/td>\nPoisson’s ratio \u03bd [-]<\/strong><\/td>\nModulus of elasticity E [kPa]<\/strong><\/td>\n<\/tr>\n
New embankment<\/td>\n<\/td>\n20<\/td>\n15<\/td>\n36<\/td>\n0.3<\/td>\n5400<\/td>\n<\/tr>\n
Silty clays<\/td>\n<\/td>\n19.2<\/td>\n15<\/td>\n36<\/td>\n0.3<\/td>\n4400<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

[\/vc_column_text][vc_column_text]<\/p>\n

Tab. 1 – Geotechnical parameters<\/span><\/p>\n

For the silty clay layer, a permeability coefficient value was assumed to be: k =2.06 x 10-6<\/sup> m\/s, while a permeability coefficient value of k =1 x 10-6<\/sup> m\/s was assumed for the embankment.<\/p>\n

Gradient method<\/h3>\n

The Gradient method<\/strong> was used for Piping verification.<\/p>\n

The viscous action of water causes a transfer of energy between the water and the ground: between two points with \u0394s<\/sub> distance apart along a stream line, in fact, there is a hydraulic head \u0394h<\/sub>. 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.
\nThe limit velocity of the seepage flow above which removal of soil particles begins to occur corresponds to a so-called critical gradient icr<\/sub> given by<\/p>\n

icr<\/sub> = (\u03b3s<\/sub> – \u03b3w<\/sub>) \/ \u03b3w<\/sub> = \u03b3\u2019\/ \u03b3w<\/sub><\/p>\n

where:<\/p>\n

\u03b3s<\/sub> = saturated unit weight of soil<\/p>\n

\u03b3w<\/sub> = unit weight of water<\/p>\n

\u03b3’ = effective unit weight<\/p>\n

The hydraulic gradient that would result in seepage flow along the flow line is a function of its length L and the pressure drop \u0394h, i.e., the difference in elevation between predicted maximum flood level and the embankment foot according to the relationship:<\/p>\n

i = \u0394h<\/sub>\/L<\/p>\n

The safety factor against Piping is therefore:<\/p>\n

Fs= icr<\/sub> \/ i = icr<\/sub> \u00b7 L \/\u0394h<\/sub><\/p>\n

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 icr<\/sub> can be reduced by a partial coefficient \u03b3R<\/sub> = 3.<\/p>\n

Permeability data used in the computation:<\/p>\n

[\/vc_column_text][vc_row_inner][vc_column_inner width=”1\/3″][\/vc_column_inner][vc_column_inner width=”1\/3″][vc_column_text]<\/p>\n\n\n\n\n\n
Soil<\/strong><\/td>\nColor<\/strong><\/td>\nPermeability [m\/s]<\/strong><\/td>\n<\/tr>\n
New embankment<\/td>\n<\/td>\n1E-06<\/sup><\/td>\n<\/tr>\n
Silty clays<\/td>\n<\/td>\n2.06E-06<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

[\/vc_column_text][\/vc_column_inner][vc_column_inner width=”1\/3″][\/vc_column_inner][\/vc_row_inner][vc_column_text]<\/p>\n

Tab.2 – Permeability values used in the computation<\/span><\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n

The analysis of seepage flow was conducted using GFAS software for Finite Element Analysis in Geotechnics<\/a>; the results are shown below.<\/p>\n

Study cross section output<\/h3>\n

Seepage flow<\/p>\n

[\/vc_column_text][vc_single_image image=”5740″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 2 – Velocity variation of the seepage flow<\/p>\n

[\/vc_column_text][vc_single_image image=”5745″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 3 – Velocity variation of the seepage flow<\/span><\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n

Maximum velocity<\/strong> Vmax<\/sub> = \u00a04.94*10-7<\/sup>\u00a0m\/s<\/p>\n

[\/vc_column_text][vc_single_image image=”6213″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 4 – Piezometric levels<\/span><\/p>\n

[\/vc_column_text][vc_single_image image=”6218″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 5 \u2013 Pore pressures<\/span><\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n

Piping verification<\/h3>\n

From the velocity field of the seepage flow, obtained from the analyses with GFAS software<\/a>, 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.<\/p>\n

[\/vc_column_text][vc_single_image image=”5834″ img_size=”full” add_caption=”yes” alignment=”center”][vc_column_text]<\/p>\n

From the calculation results, it is observed (see Figure 6) that \u0394h<\/sub> is 1.9 m, while the length of the flow path L is about 9.07 m:<\/p>\n

[\/vc_column_text][vc_single_image image=”5870″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Figure 6 \u2013 Flow path diagram<\/span><\/p>\n

[\/vc_column_text][vc_column_text]therefore, the value of the average gradient is equal to:[\/vc_column_text][vc_single_image image=”5838″ img_size=”full” add_caption=”yes” alignment=”center”][vc_column_text]<\/p>\n

As established earlier, wanting to apply a reduction (\u03b3R<\/sub> = 3), it must result:<\/p>\n

[\/vc_column_text][vc_single_image image=”5767″ img_size=”full” add_caption=”yes” alignment=”center”][vc_column_text]<\/p>\n

Therefore:<\/p>\n

[\/vc_column_text][vc_single_image image=”5842″ img_size=”full” add_caption=”yes” alignment=”center”][vc_column_text]<\/p>\n

The verification is satisfied<\/strong><\/span><\/p>\n

[\/vc_column_text][vc_column_text]<\/p>\n

The software automatically determines the line that locates the groundwater line (Figure 7):<\/p>\n

[\/vc_column_text][vc_single_image image=”6222″ img_size=”full” alignment=”center”][vc_column_text]<\/p>\n

Fig. 7 – Free surface<\/span><\/p>\n

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