CIRCULAR PIPE LOADED LATERALLY IN COHESIVE SOIL

CIRCULAR PIPE LOADED LATERALLY IN COHESIVE SOIL

This document describes an example that has been used to verify the correctimplementation of 3D isoparametric interface elements in PLAXIS 3D. For that purpose,the response of a pipe subjected to horizontal loading under undrained soil conditions isstudied.

Used version:

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

Geometry: Figure 1 illustrates the model considered for a circular pipe embedded insoil. The soil layer thickness has been set to 1 m (unit length is selected for matter ofcomparison with analytical solutions). Due to symmetry, only half of the geometry ismodeled in PLAXIS 3D. The circular pipe diameter D equals 5 m and it is embedded in auniform soil layer, 45 m wide (x-direction) and 35 m long (y-direction). The circular pipe ismodeled using the Surface feature. No material is assigned to the surface representingthe pipe. The interaction between the pipe and the surrounding soil (outside the pipe) ismodeled with an interface. A rectangular region of mesh refinement is designed aroundthe pipe. A line load of Fx = 250 kN/m is applied on half model (which is equivalent to Feq= 500 kN/m for the entire geometry) along the right vertical line shared by the pipe andthe front model boundary. The top and bottom surfaces of the model are fixed inz-direction using Surface displacements. In addition, the bottom surface has Linedisplacements at all four sides (front, rear, left and right) which are given in Table 1.

1.0 m

15 m15 m15 m

8.5 m

9.0 m

Figure 1 Model geometry

Table 1 Bottom surface boundary conditions (line displacements)

Side x-direction y-direction z-direction

Front (y=0.0 m) Free Fixed Fixed

Rear (y=17.5 m) Free Fixed Fixed

Left (x=0.0 m) Fixed Free Fixed

Right (x=45.0 m) Fixed Free Fixed

Materials: The selected material parameters of the plug (material inside the pile) andthe surrounded soil are:

Soil: Mohr-Coulomb Undrained (C) E ' = 30000 kN/m2 ν ' = 0.495 Su = 5 kN/m2

Plug: Linear elastic Drained E ' = 30 ·106 ν ' = 0.495

Meshing: The Expert settings, as shown in Figure 2, are used to generate the mesh.

The soil cluster surrounding the pipe is refined by a Coarseness factor of 0.075. Theoutermost soil cluster is coarsened by a Coarseness factor of 3.0. The resulting mesh isshown in Figure 3.

Calculations: The project is calculated for different values of the interface strength

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Figure 2 Expert settings used to generate the mesh

Figure 3 The finite element mesh

Rinter . The considered values are presented in Table 2. The lineload is activated for allthe calculation phases. For advanced calculation settings, a Tolerated error of 0.001 isselected and the Max steps option for the last phase of Rinter = 0.2 is set to 300. TheSolver type for all phases is set to Pardiso (multicore direct) for faster calculation.

Output: Total displacements at failure for Rinter = 1.0 are shown in Figure 4.

Figure 4 Total displacements at failure, Rinter = 1.0

Verification: The analytical solution for the ultimate capacity of the cylinder is derived byRandolph & Houlsby (1984) as follows:

PsuD

= π + 2∆ + 2cos∆ + 4[cos

∆

2+ sin

∆

2

]

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CIRCULAR PIPE LOADED LATERALLY IN COHESIVE SOIL

where:

sin ∆ = Rinter

Comparison between analytical and PLAXIS 3D results for the ultimate capacity values ispresented in Table 2. In order to obtain the PLAXIS 3D results a point (soil plug node)located at the right side of the cylinder is used, i.e. with coordinates (2.5, 0.0, -0.5),assuming axes origin at the cylinder center line.

Table 2 Comparison between analytical and PLAXIS 3D results for the ultimate capacity values

Rinter Analytical PLAXIS 3D Error

1.0 298.5 kN/m 302.9 kN/m + 1.5 %

0.8 289.1 kN/m 292.6 kN/m + 1.2 %

0.6 277.2 kN/m 280.3 kN/m + 1.1 %

0.4 263.3 kN/m 266.4 kN/m + 1.2 %

0.2 247.1 kN/m 251.2 kN/m + 1.6 %

The initial slope of the load-displacement curve, where the soil behavior is assumed to beelastic, can be expressed according to Baguelin F. & Said (1977) as:

Kxx =8πE '(1 − ν ')

(1 + ν ')[(3 − 4ν ') ln

(Rr0

)2 − 2

3 − 4ν '

]Assuming R = 22.5m and r0 = 2.5 m, based on the horizontal elastic stiffness is Kxx =85940 kN/m.

Figure 5 presents the load-displacement curves obtained in PLAXIS 3D for different Rintervalues. The analytically calculated Kxx value is plot as well.

Figure 5 Load-displacement curves obtained in PLAXIS 3D for different Rinter values

Based on Figure 5, the ultimate horizontal capacity is reached for horizontaldisplacement equal to 1 % of the pile diameter D. The corresponding ultimate capacity

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values are used in Table 2 to calculate the relative error. It can be concluded that PLAXIS3D results are in close agreement with the analytical solution for both ultimate capacityand initial elastic stiffness of a laterally loaded cylinder under undrained soil conditions.

REFERENCES

[1] Baguelin F., Frank, R., Said, Y. (1977). Theoretical study of lateral reactionmechanism of piles. Geotechnique, 27, No. 3, 405–434.

[2] Randolph, M., Houlsby, G. (1984). The limiting pressure on a circular pile loadedlaterally in cohesive soil. Geotechnique, 34, No. 4, 613–623.

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