flexible tank foundation on elastic … tank foundation on elastic saturated soil figure 4 generated...

FLEXIBLE TANK FOUNDATION ON ELASTIC SATURATED SOIL


In this document, the settlement of a flexible tank founded on elastic saturated soil isstudied. It is verified that the settlement at the center of the tank, under homogeneous,isotropic soil conditions, is calculated correctly in PLAXIS.

Used version:

• PLAXIS 2D - Version 2015.02

• PLAXIS 3D - Anniversary edition (AE.01)

Geometry: A circular tank with radius R equal to 23.35 m is founded on elasticsaturated soil. The tank imposes vertical stress ∆q = 263.3 kN/m2 at the soil surface. InPLAXIS 2D an axisymmetric model is used and the vertical stress is represented with aLine load AA. The right and bottom boundaries are set at a distance 5R from the axis ofsymmetry (left boundary) and top surface respectively. Geometry lines are used togenerate a soil cluster for mesh refinement up to 4 m below the tank. Figure 1 illustratesthe model geometry in PLAXIS 2D.

In PLAXIS 3D the whole geometry is modeled and a Surface load is used to representthe vertical stress imposed by the tank. The same distance as in PLAXIS 2D (5R) isselected for the location of the boundaries. The model geometry in PLAXIS 3D ispresented in Figure 2.

4 m

23.35 m

116.75 m

116.75 m

Figure 1 Model geometry (PLAXIS 2D)

Materials: The soil is modeled as Linear elastic and nearly incompressible (ν ' = 0.499),under fully saturated conditions. The adopted material parameters are:

Soil: Linear elastic Drained E ' = 95.8 ×103 kN/m2 ν ' = 0.499

Meshing: The Medium option is selected for the Element distribution. The soil clusterbeneath the tank is locally refined with a Coarseness factor of 0.5. Figure 3 and Figure 4

PLAXIS 2015 | Validation & Verification 1

VALIDATION & VERIFICATION

116.75 m

116.75 m

116.75 m

116.75 m

116.75 m

φ 46.70 m

Figure 2 Model geometry (PLAXIS 3D)

illustrate the generated mesh in PLAXIS 2D and PLAXIS 3D respectively.

Figure 3 Generated mesh (PLAXIS 2D)

Calculations: In the Initial phase, zero initial stresses are generated by using the K0procedure with

∑Mweight equal to zero. The load is activated in a separate phase (Phase

1). A Plastic analysis is performed and the Tolerated error is selected equal to 0.001.

Output: The vertical settlement of the surface (uy ), at the center of the tank, is74.21 mm and 75.12 mm for PLAXIS 2D and PLAXIS 3D respectively. The verticaldisplacement shadings are presented in Figures 5 and 6.

Verification: The settlement at the center of the tank is given by Lancellota (2008):

2 Validation & Verification | PLAXIS 2015


Figure 4 Generated mesh (PLAXIS 3D)

Figure 5 Vertical displacements (PLAXIS 2D)

uy =∆qRIp

E

where Ip is the influence coefficient, which can be determined based on Figure 7.

The settlement at the center of the tank is:

uy =263.3 · 23.35 · 1.15

95.8 · 1000= 0.07380 m = 73.80 mm

The analytically obtained settlement and the computed values in PLAXIS 2D and PLAXIS3D are compared in Table 1. It is concluded that the numerical results are in good



Figure 6 Vertical displacements (PLAXIS 3D)

Figure 7 Influence coefficient Ip, for settlement under uniform load, over circular area (Terzaghi(1948))

agreement with the analytical solution.

Table 1 Comparison between analytical solution and PLAXIS results regarding the settlement atthe center of the tank

Settlement at the center of the tank (mm) Error

Lancellota PLAXIS 2D PLAXIS 3D PLAXIS 2D PLAXIS 3D

73.80 74.21 75.12 + 0.5 % + 1.8 %



REFERENCES

[1] Lancellota, R. (2008). Geotechnical engineering. Balkema.

[2] Terzaghi, K. (1948). Theoretical soil mechanics.


flexible tank foundation on elastic … tank foundation on elastic saturated soil figure 4 generated...

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