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Undrained Load Capacity of Torpedo Anchors in ... - laceo - UFRJ

Undrained Load Capacity of Torpedo Anchors in ... - laceo - UFRJ

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varies from 0 to 0.90m. The self-weight <strong>of</strong> the anchor was kept<br />

constant and equals to 850kN.<br />

Although the undra<strong>in</strong>ed shear strengths were different, all<br />

the scenarios have the same anchor penetration. A study based<br />

on the theoretical model presented by True [11] was conducted<br />

only for soil B and the four flukes anchor. The penetration<br />

achieved by the top <strong>of</strong> the anchor was equal to 16m and this<br />

value was used <strong>in</strong> all analyses.<br />

Moreover, <strong>in</strong> the performed analyses, the extension cone<br />

approximation, Eq.(14), is employed.<br />

Several FE meshes were developed. In average, they have<br />

53770 nodes, 93830 elements lead<strong>in</strong>g to a problem with<br />

161310 degrees <strong>of</strong> freedom.<br />

Results<br />

Figure 10 – Dimensions, <strong>in</strong> m, <strong>of</strong> the analyzed torpedo<br />

anchor.<br />

Effect <strong>of</strong> different undra<strong>in</strong>ed shear strengths<br />

Figures 12 to 14 present the variation <strong>of</strong> the displacement<br />

at the top <strong>of</strong> the anchor with the applied load. These curves<br />

were obta<strong>in</strong>ed <strong>in</strong> the analyses <strong>of</strong> the torpedo anchor with 4<br />

flukes embedded <strong>in</strong> soils A, B and C, respectively. In these<br />

figures, loads are at an angle <strong>of</strong> 45° with the plane <strong>of</strong> the flukes<br />

(plane 1, Fig. 11a) and several different load <strong>in</strong>cl<strong>in</strong>ations with<br />

respect to the horizontal plane are accounted.<br />

These figures po<strong>in</strong>t that the ratio between the displacement<br />

change and the applied load varies with the load <strong>in</strong>cl<strong>in</strong>ation<br />

and, consequently, there is a significant difference between the<br />

vertical and lateral soil stiffness.<br />

7000<br />

6000<br />

Figure 11 – <strong>Torpedo</strong> anchor cross-sections: (a) four, (b)<br />

three and (c) no flukes.<br />

In all analyses, seven load <strong>in</strong>cl<strong>in</strong>ations with respect to the<br />

horizontal plane were considered: 0° (horizontal load), 15°,<br />

30°, 45°, 60°, 75° and 90° (vertical load). All loads, F a , were<br />

applied at the top <strong>of</strong> the anchor, as po<strong>in</strong>ted out <strong>in</strong> Fig. 10.<br />

The soil is considered to be purely cohesive and isotropic<br />

with Young modulus vary<strong>in</strong>g with depth and given by the<br />

expression:<br />

() z<br />

E( z)<br />

= 550⋅ S<br />

(25)<br />

u<br />

Three different undra<strong>in</strong>ed shear strength pr<strong>of</strong>iles were<br />

considered <strong>in</strong> this numerical-based study:<br />

kPa<br />

Soil A: S u ( z)<br />

= 1.5⋅<br />

⋅ z<br />

m<br />

kPa<br />

Soil B: S u ( z)<br />

= 3.0 ⋅ ⋅ z<br />

m<br />

kPa<br />

Soil C: S u ( z)<br />

= 6.0 ⋅ ⋅ z<br />

m<br />

where z is the depth bellow mudl<strong>in</strong>e <strong>in</strong> m.<br />

(26)<br />

<strong>Load</strong> (kN)<br />

5000<br />

4000<br />

3000<br />

0°<br />

15°<br />

2000<br />

30°<br />

45°<br />

60°<br />

1000<br />

75°<br />

90°<br />

0<br />

0.00 0.05 0.10 0.15 0.20 0.25<br />

Displacement at anchor top (m)<br />

Figure 12 – <strong>Load</strong> vs displacement curves <strong>of</strong> a torpedo<br />

anchor with 4 flukes consider<strong>in</strong>g different load <strong>in</strong>cl<strong>in</strong>ations<br />

with the horizontal plane: soil A, 45° with the flukes.<br />

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