6. Illustrations and validations
Typical soil mechanics problems are analyzed next to illustrate and validate the program.
6.4. Consolidation
6.4.1 Linear consolidation
The case of linear uniaxial consolidation is considered in the following
table and compared to the analytical solution of Terzaghi [Bow, 1978].
Data are : Young’s modulus = 102, Poisson’s ratio
= 0, void ratio e0 = 0.6, compression index
= 0.2, fluid bulk modulus
F = 1015, Darcy’s coefficient kx =
ky = 10-1.
Fig. 6.11
6.4.2 Consolidation settlement of a superficial footing
The settlement of an infinitely long footing is analyzed as a plane strain
problem. The footing is placed on a soil subject to consolidation. An analytical
solution to this plane strain linear consolidation problem is given in [SCH,
1969]. Material data required for this analysis are : Young's modulus E
= 102, Poisson's ratio
= 0, fluid bulk modulus
F = 102, Darcy's coefficients kx= ky
= 10-1, void ratio e0 = 0.6, compression index
= 0.2, specific weight
w = 10. The geometry and the results are illustrated in the
following figures. The computed results for the vertical pressure distribution
are compared to Schiffmann's solution.
Fig 6.12.a. - Geometry
Fig. 6.12.b -Vertical distribution of tw/p at axis
Fig. 6.12.c - Horizontal distribution of tw/p at depth Z/B = 0
6.4.3 Nonlinear consolidation
Consider the geometry defined infigure 6.13, and the initial state of
stress indicated. The following material data are assumed : friction angle
= 30°, Young modulus E = 28.20, oedometric modulus Eoed
= E(1-
)/(1+
) (1-2
) = 6043, Drucker-Prager yield parameter
= sin
/3 = 0.167, Poisson's ratio
= 0.4, compression index M = 3
= 0.866, void ratio e0 = 1,
yield = 40KPa (from oedometer).
Fig. 6.13
The following results are obtained:
Table 6.7
6.4.4 Secondary consolidation
This analysis is concerned with the long term behavior of concrete pavements on subgrades with differential settlements. The geometrical characteristics of the site and the material data are given in figure6.14 and table 6.8. The site consists in a longitudinal section of 150 m, with a depth of 15 m (the horizontal scale is shown deformed in the figure). A soil column is added at both ends of the site for the adjustment to adjacent road sections.
The analysis starts with an initial state analysis obtained by imposing gravity progressively. The second step consists in a creep analysis for which only the concrete, silt and peat are considered to be subject to creep. The value of the creep parameters is adjusted here so that long term creep (15 years) matches the in situ measurements in the middle of the analyzed section (point A, in Fig. 6.15). The spatial distribution of creep can then be predicted with a good accuracy, as illustrated in figure 6.16.
Fig. 6.14 - Flums-Heiligkreuz road section
Table 6.8 - Material data
Fig. 6.15 - Observed versus computed long term deflection