2. Modeling A#

2.1. Characteristics of modeling#

Modeling A is*bidimensional* and*static nonlinear*. The calculation is carried out using pure mechanics, without hydromechanical coupling (equivalent to a perfectly drained soil).

We can first verify the coherence of the initial state (in particular the boundary conditions with the pre-consolidation state of the soil): mechanical balance must be established when only gravity acts, so the state of the system must not change.

The elastoplastic behavior law used is that of Cam-Clay, cf. [R7.01.14].

The vertical displacement is imposed on the GROUP_MA = “APPUI” representing the interface between the foundation and the ground, and varies between \(0.\) and \(–0.05m\) in 20 time steps between \(t\mathrm{=}0.s\) and \(t=1.0\phantom{\rule{2em}{0ex}}{10}^{+7}s\)

Figure 2: mesh of the shooting foundation for modeling A.

2.2. Tested sizes and results#

The solutions are calculated at points \(O\) and \(F\) and compared to FLAC references. They are first given in terms of equivalent stress \(Q\) as a function of the effective consolidation pressure \(P’\), and summarized in the following tables:

\(P\text{'}=\frac{1}{3}\mathrm{.}\mathit{trace}(\mathrm{\sigma }\text{'})\); \(Q=\sqrt{\frac{3}{2}\mathrm{s}\mathrm{:}\mathrm{s}}\) (where \(\mathrm{s}=\mathrm{\sigma }\text{'}-P\text{'}\mathrm{.}\mathrm{Id}\))

At point \(O\), under the foundation in the center:

\(P’\) [\(\mathit{Pa}\)]	\(Q\) Code_Aster [\(\mathit{Pa}\)]	\(Q\) FLAC [\(\mathit{Pa}\)]	relative error
102000	434	450	-0.035%
110000	19662	20000	-1.689%
120000	25837	26060	-0.855%
130000	29290	29490	-0.679%
146000	34006	34040	-0.100%

At point \(F\):

\(P’\) [\(\mathit{Pa}\)]	\(Q\) Code_Aster [\(\mathit{Pa}\)]	\(Q\) FLAC [\(\mathit{Pa}\)]	relative error
101900	227	76	+199%
100000	4945	4950	-0.110%
98000	9941	10420	-4.593%
96000	15283	16830	-9.190%
94000	20036	21870	-8.385%

The resultant of the forces exerted on the foundation as a function of its sinking is then calculated. This is also compared to the solution given by FLAC:

\(\mathit{UY}\) [\(m\)]	Code_Aster [\(N/m\)]	FLAC [\(N/m\)]	relative error
-0.005	-110105	-108500	+1.479%
-0.02	-129224	-125800	+2.722%
-0.04	-149470	-144600	+3.368%
-0.06	-167066	-160900	+3.832%
-0.0875	-188825	-181100	+4.266%