A new formulation of Signorini's type for seepage problems with free surfaces

Abstract

SUMMARYA new variational inequality formulation for seepage problems with free surfaces is presented, in which a boundary condition of Signorini's type is prescribed over the potential seepage surfaces. This makes the singularity of seepage points eliminated and the location of seepage points determined easily. Compared to other variational formulations, the proposed formulation can effectively overcome the mesh dependency and significantly improve the numerical stability. A very challenging engineering example with complicated geometry and strong inhomogeneity is investigated in detail.

A solution to transient seepage in unsaturated porous media

“…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 w ℓ is illustrated with black arrows indicating the change on liquid velocity. The solution in [9] is highlighted in green while the solution by this paper is highlighted in light blue. We can observe that the final phreatic line matches fairly well the reference one, even though the liquid retention model is not as discrete as in the reference work.…”

“…24 where it can be observed that the pressure-saturation distribution at the end is similar to the distribution obtained in Example 1. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 The reference line is shown in green with square markers [9]. Arrows...…”

“…Arrows indicate the partial relative velocity (×500000). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 The reference line is shown in green with square markers [9]. Arrows indicate the partial relative velocity (×500000).…”

“…To circumvent this problem, a number of strategies has been proposed in the literature and some include iterative techniques while others use mesh adaptivity [4][5][6][7]. The topic is still active with some recent papers published [8][9][10][11][12].…”

Tehnike racunarske inteligencije u modeliranju i identifikaciji indikatora ponasanja brane

“…Они се формирају уз помоћ стварне геометрије објекта и стварних карактеристика материјала и калибришу се према реалним мерењима [3]. Главне врсте таквих модела које се користе у анализи стања брана су филтрациони [4][5][6] и напонско-деформациони модели [7]. Дивац и сар.…”