Rak-50 3149 Deep Excavation

Tutorial 6 – Simulation of a deep excavation

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T06. Simulation of a deep excavation (small-strain stiffness)


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INTRODUCTION

A building pit was constructed in the south of the Netherlands. The pit is 15 m deep and 30 m wide.

A diaphragm wall is constructed using 100 cm diameter bored piles; the wall is anchored by two

rows of pre-stressed ground anchors (Figure 1). In this exercise the deep excavation is simulated

with both the Hardening Soil and the HS-Small model.

The upper 65 m of the subsoil consists of a more or less homogeneous layer of medium dense fine

sand with a unit weight of 18 kN/m3. Underneath the sand layer is a very stiff layer of gravel,

which is not to be included in the model. The groundwater table is very deep and is not to be

considered in the analysis.

The aims of the tutorial are to observe the effects of small-strain stiffness in a deep excavation

problem and to get familiar with the HS-Small model and its most important state variables.

Figure 1. Excavation in Limburg.


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SCHEME OF OPERATIONS

In order to better appreciate the role played by small strain stiffness, the analysis first must be

carried out with the traditional version of the Hardening Soil model. Secondly, repeat the analysis

with the HS-Small model and observe the effects of small-strain stiffness.

In order to minimize the time required for input, it is proposed to adopt the following procedure:

• Create the problem geometry and use the Hardening Soil material parameters.

• Create all calculation phases and start the Hardening Soil analysis.

• Open the Hardening Soil analysis in the Input program and save it as a different project.

• Change the material model from Hardening Soil to HS-Small and enter the additional

parameters.

• Run the HS-Small analysis and compare its results to that of the Hardening Soil analysis.

Important note: After re-opening the project in Plaxis Input in order to either save the project under

a different name or to change material parameters initial stresses MUST be regenerated.

INPUT

Geometry model

Figure 2. Geometry of the model.


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♦ Using the data shown on figure 1 define adequate clusters of soil materials and position of

structural elements.

♦ Anchors are defined by combination of node to node anchor option representing anchor rod

and geogrid element representing grout body.

♦ Diaphragm wall is defined using the plate option while wall/soil contact is set using the

option interface available from the toolbar. Notice that interface needs to be extended 2 m

under the diaphragm wall

Material properties

Soil and interfaces

Hardening Soil (HS) material parameters for the sandy subsoil are given in Table 1. Interface

strength is assumed to Rinter=0.6 along the diaphragm wall. Rinter=1.0 is assigned to the 2 m

extended interface elements below the wall. Therefore, two almost equivalent material sets are

defined. For the HS-Small analysis, simply copy the material sets defined for the HS analysis. Then

change the material model to HS-Small and add the two small-strain parameters given in Table 2.

Table 1: Hardening Soil parameters.

Parameter Symbol Sand_R=0.6 Sand_R=1.0 Unit

Material model Model Hardening-Soil Hardening-Soil -

Type of behaviour Type Drained Drained -

Dry weight γunsat 18.0 18.0 kN/m3

Wet weight γsat 18.0 18.0 kN/m3

Permeability x-dir. Kx 0.0 0.0 m/d

Permeability y-dir. Ky 0.0 0.0 m/d

Young’s modulus E50ref

2.0·104 2.0·10

4 kN/m

2

Oedometer modulus Eoedref

2.0·104 2.0·10

4 kN/m

2

Unloading modulus Eurref

8.0·104 8.0·10

4 kN/m

2

Power m 0.5 0.5 -

Poisson’s ratio ν 0.2 0.2 -

Reference stress Pref 100.0 100.0 kN/m2

Cohesion c 1.0 1.0 kN/m2

Friction angle ϕ 35.0 35.0 °

Dilatancy angle ψ 5.0 5.0 ° Interface strength Rinter 0.6 1.0 -


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Table 2: Small-strain stiffness parameters.

Parameter Symbol Sand_R=0.6 Sand_R=1.0 Unit

Initial shear modulus G0 1.0·105 1.0·10

5 kN/m

2

Threshold shear strain γ0.7 1.5·10-4

1.5·10-4

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Structural element properties

The material parameters for the sheet pile wall as well as the anchors and geogrids representing the

ground anchors are given in Table 3 to 5.

Table 3: Properties of the diaphragm wall (plate)

Parameter Symbol Diaphragm wall Unit

Material Model Model Elastic -

Normal stiffness EA 2.0·107 kN/m

Flexural rigidity EI 1.67·106 kNm

2/m

Weight w 15.0 kN/m/m

Poisson's ratio ν 0.15 -

Table 4: Properties of the anchor rod (node-to-node anchors).

Parameter Symbol Anchor rod Unit

Material Model Model Elastic -

Normal stiffness EA 2.0·105 kN/m

Spacing Ls 1.0 m

Table 5: Property of the grout body (geogrid).

Parameter Symbol Grout body Unit

Normal stiffness EA 2.0 · 105 kN/m

Mesh generation

♦ Select Global coarseness... from the Mesh menu and chose Fine element distribution. Generate

mesh. The generated finite element mesh should resemble the one shown in Figure 3.

♦ Select the all 8 clusters that fall within the rectangle area (0, 0) - (45, 0) - (45,-40) - (0,-40) and

choose the Refine cluster option from the Mesh menu. This will result in a refinement in the

selected area as shown in Figure 4.


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Figure 3. Geometry of the model.

Figure 4. Refined element mesh.

Area that needs further

refinement


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CALCULATION

Initial conditions

In order to define Initial phase properly it is necessary to switch off all structural elements within

the Staged construction mode as they are not present before construction (initial situation).

For generation of initial stresses accept the K0-values proposed by PLAXIS. The K0-values are

calculated from the relation proposed by Jaky: 0K 1 sin ′= − ϕ

As the phreatic line is located below the geometry the generation of pore pressures can be skipped.

Construction phases

The entire construction process consists of six phases. Define the phases, as shown graphically

below. For each phase use the options: Plastic calculation, Staged construction. In the first

calculation phase, the diaphragm wall is activated (Figure 5). In the second phase, the first

excavation takes place (Figure 6).

Figure 5. Phase1, activation of the wall.


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Figure 6. Phase2, excavation of the top part.

Figure 7. Phase 3, activation of the anchor and geotextile (grouting).

Pre-stressing of the anchor to a value of 300 kN/m.


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In the third phase, the first pre-stressed anchor is introduced (Figure 7) as follows:

♦ First the grout-body (the geogrid) is switched on by clicking on the 'geogrid' element.

♦ Now that the grout-body is active, the anchor element needs to be pre-stressed. By double

clicking on a node-to-node anchor a box will appear as indicated below (Figure 8). In the

node-to-node anchor box one can enter the pre-stress force. The letter P indicates that a pre-

stress force will be active in the anchor.

Create the remaining phases, as indicated Figure 9, 10 and 11

Figure 8. Node-to-node anchor properties.

Figure 9. Phase 4, excavation of the second part.


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Figure 10. Phase 5, activation of the second anchor and geotextile (grouting).

Pre-stressing of the anchor to a value of 300 kN/m.

Figure 11. Phase 6, excavation of the third part.


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♦ Select some nodes for the load displacement curves (e.g. top of wall) and start the calculation.

♦ Compare the following output of the Hardening Soil analysis to that of the HS-Small analysis:

• Vertical surface settlements (see for example Figure 12 and 13)

• Excavation heave (14 and 15)

• Wall deflection

• Lateral earth pressure on the wall

• Wall bending moments

Figure 12. HS surface settlement trough Phase 6. Extreme Uy ≈ -17mm.

Figure 13. HS-Small surface settlement trough Phase 6. Extreme Uy ≈ -16mm.

Hint: When processing an anchor in a certain calculation phase the anchor force will exactly

match the prestress force at the end of that phase. In following calculation phases without

prestressing, the anchor force will be influenced by the excavation process.


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Figure 14. HS Deformed mesh at the end of construction Phase 6. Extreme |U| ≈ 73mm.

Figure 15. HSS, Deformed mesh at the end of construction Phase 6. Extreme |U| ≈ 53mm.

Rak-50 3149 Deep Excavation

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