Comparison of different models for analysing foundations on jet grout columns

F. Tschuchnigg, H. F. Schweiger Computational Geotechnics Group, Institute for Soil Mechanics and Foundation Engineering, Graz University of Technology, Graz, Austria

Keywords: embedded beam, finite element, 3D model, ground improvement, jet grout column

ABSTRACT: If ground conditions are such that the load from structures such as high rise buildings cannot be supported by shallow foundations several options exist. An economical alternative to a classical pile or piled raft foundation could be the use of jet grouted columns. In general a large number of jet grouted columns has to be constructed resulting in a problem which is difficult to analyse and numerical methods are increasingly utilised to calculate the performance of such foundations. As a two-dimensional representation of pile groups is usually not sufficient 3D modelling is required, leading to very large models if all piles are discretized with volume elements. An attractive method to reduce the complexity of such models is the use of a so-called embedded pile concept where piles are not explicitly modelled with continuum finite elements but replaced by a special “formulation” which can take into account the behaviour of a pile penetrating a finite element in any orientation. The paper compares the results obtained for a raft supported by jet grouted columns with three different models: a 2D plane strain model, a full 3D model with volume discretisation of the columns and one model with the embedded pile formulation. Finally application of the embedded pile concept to a practical problem is presented.

1 Introduction In general one has several possibilities to model a foundation supported by jet grout columns. The easiest and fastest way is to define a 2D plane strain model in which, depending on the geometry, either the diameter or the stiffness of the jet grouted columns has to be adapted to plane strain conditions. Such a model is convenient for principle studies as variations of inclinations or lengths of the jet grout columns, but due to the geometrical restrictions calculated settlements are not very reliable. Hence in most cases a 3D model is necessary to assess the settlement behaviour of such structures. In a 3D model, when using Plaxis 3D Foundation (Brinkgreve and Swolfs, 2007), one has two alternatives to model jet grout columns. The first option to model such foundations is the standard finite element approach, which means the piles are modelled with volume elements and the interaction of the pile and the surrounding soil is described with interface elements. The roughness of the interaction (soil-structure) is defined with a strength reduction factor Rinter and this factor determines the interface strength with respect to the soil strength. The problem with this approach is that for a large number of jet grouted columns this leads to computationally demanding models which may be beyond the capabilities of the code or simply take to long to analyse from a practical point of view. The alternative way to define piles or columns in a 3D model is the embedded pile approach. An embedded pile consists of a beam element which can be placed in arbitrary direction in the subsoil, embedded interface elements to model the interaction of the structure and the surrounding soil and embedded non-linear spring elements at the pile base to describe the base resistance. When assigning the embedded pile additional nodes are automatically generated inside the existing finite elements and the pile-soil interaction behaviour is linked to the relative displacements between the pile nodes and the existing soil nodes (Sadek and Shahrour, 2004). The connection between the soil and pile nodes is achieved with embedded interface elements. A diameter d, the unit weight γ and the stiffness E is assigned to the embedded beam element, although geometrically it remains a line element. The diameter d in the material data set determines an elastic zone in the soil around the beam, i.e. plastic soil behaviour is excluded (Engin, 2006) with the argument, that in reality the column has a finite thickness d. Maximum skin friction and base resistance is assigned to the special interface elements and therefore the bearing capacity of the pile or column is an input to the analysis and not a result.

2 Comparison of different models This chapter presents the comparison of different models for analysing foundations on jet grout columns. Figure 1 shows the geometry of the example. The soil profile consists of six layers and is modelled with the Hardening Soil model, a double hardening model available in the Plaxis model library. The parameters are given in Table 1. A pre-overburden pressure (POP) of 600kN/m2 is applied to all soil layers except the gravel layer to generate the pre-consolidation pressure. The K0 value in all pre-consolidated layers is set to K0=0.7. The foundation slab is defined as a linear elastic material and the properties are shown in Table 2. The properties of the jet grout piles are discussed in the next sections. Drained conditions are assumed for all analyses.

Figure 1. Geometry of the example

Table 1. Soil model properties

Soil layer γunsat γsat E50,ref Eoed,ref Eur,ref Cref ϕ ψ [kN/m3] [kN/m3] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [ ° ] [ ° ]

Gravel 21.0 21.5 40000 40000 120000 0.1 35.0 5.0

Sandy silt 1 20.0 20.0 15000 15000 45000 20.0 27.5 0.0

Fine to medium dense sand 1 20.0 21.0 20000 20000 60000 5.0 32.5 2.5

Sandy silt 2 20.0 20.0 15000 15000 45000 30.0 27.5 0.0

Fine to medium dense sand 2 20.0 21.0 20000 20000 60000 5.0 32.5 2.5

Stiff base layer 20.0 20.0 30000 30000 90000 30.0 27.5 0.0

Soil layer Type νur pref m K0nc Rf Rinter POP

[ - ] [kN/m2] [ - ] [ - ] [ - ] [ - ] [kN/m2]

Gravel Drained 0.2 100 0.00 0.426 0.9 1.0 0

Sandy silt 1 Drained 0.2 100 0.60 0.538 0.9 1.0 600

Fine to medium dense sand 1 Drained 0.2 100 0.50 0.462 0.9 1.0 600

Sandy silt 2 Drained 0.2 100 0.60 0.538 0.9 1.0 600

Fine to medium dense sand 2 Drained 0.2 100 0.50 0.462 0.9 1.0 600

Stiff base layer Drained 0.2 100 0.60 0.538 0.9 1.0 600

Table 2. Properties for foundation slab

Type γunsat γsat ν Eref Rinter

[kN/m3] [kN/m3] [ - ] [kN/m2] [ - ]

Concrete Drained 25.0 25.0 0.15 28000000 1.0

2.1 2D model This section shows the results of a 2D plane strain model for the example in Figure 1. Two different configurations are studied. In the first one (Figure 2(a)) all jet grout columns are vertical and in the second one the outer piles are inclined (Figure 2(b)). The diameter d has been taken as the true diameter and the stiffnesses of the piles are converted into equivalent stiffnesses according to their spacings (Table 3). The Mohr-Coulomb model is used to describe the behaviour of the jet grouted columns. The interaction between jet grouted columns and the subsoil can be assumed as very rough hence no interface elements are defined between columns and soil. The contour plots of maximum vertical displacements for these two models are presented in Figure 3(a) and 3(b). The value of maximum settlements (uy,max) for the model with vertical piles is 71.5mm and for the model where the outer piles are inclined uy,max is 68mm.

Figure 2. 2D models

Table 3. Properties of the jet grout piles for the 2D model

jet grout pile Diameter Spacing Type γunsat γsat ν Eref cref ϕ [m] [m] [kN/m3] [kN/m3] [ - ] [kN/m2] [kN/m2] [ ° ]

JGP 1 0.8 2.0 Drained 21.5 21.5 0.15 5000000 1350 32.5

JGP 2 0.8 1.0 Drained 21.5 21.5 0.15 2500000 675 32.5

all piles vertical outer piles inclined

(a) (b)

Figure 3. Contour plot of vertical displacements for 2D models

2.2 3D model with standard finite element approach For this calculation the 2D model (Figure 2) is extended to a 3D strip model as shown in Figure 4(a). The jet grout columns are discretized (Figure 4(b)) and described with Mohr-Coulomb material behaviour (Table 4). Again no interfaces are defined between the structure and the column. The soil profile and parameters are the same as for the 2D model. With this approach just one calculation with vertical piles is presented, due to the fact that it is not possible to define inclined volume piles in Plaxis 3D Foundation. The maximum value of settlements uy,max is 70mm, a contour plot of vertical displacements is presented in Figure 5.

Figure 4. 3D model with discretized piles

Table 4. Properties of the discretized jet grout piles for the 3D model

Jet grout pile Diameter Type γunsat γsat ν Eref cref ϕ [m] [kN/m3] [kN/m3] [ - ] [kN/m2] [kN/m2] [ ° ]

JGP 0.8 Drained 21.5 21.5 0.15 10000000 2700 32.5

(a) (b)

0 mm

36 mm

72 mm

all piles vertical outer piles inclined

(a) (b)

Figure 5. Contour plot of vertical displacements with discretized piles

2.3 3D model with embedded piles With this concept it is possible to model piles in arbitrary direction in the soil hence the two models as considered for the plane strain case are presented (Figure 6). The outer piles have an inclination of 1 to 5. The diameter of the embedded piles shown in Figure 6(a) and (b) are not the “real” diameters of the jet grout columns as defined in the input. What is printed here is just the beam element in the middle of the embedded pile but the elastic region around the embedded pile, which is equal to the “real” diameter, is not shown. As mentioned previously the bearing capacity of the embedded piles is an input and in this example defined by a linear skin friction distribution and a base resistance. The input parameters for the embedded piles are given in Table 5. The maximum settlement when all piles are vertical is 73.5mm (Figure 7(a)) and for inclined outer piles uy,max decreases to 69.5mm (Figure 7(b)). The purpose of this example was to compare different modelling approaches for working load conditions and therefore limiting values for skin friction and base resistance have been chosen such that they are well beyond mobilized values for the loads considered.

Figure 6. Foundation with piles for the embedded pile models

(a) (b)

Table 5. Embedded pile properties

γ Eref d Τtop,max Τbot,max Fmax

[kN/m3] [kN/m2] [m] [kN/m] [kN/m] [kN]

Jet grout column γsoil+1.0 10000000 0,8 0.0 502.0 600

Figure 7. Vertical displacements for the embedded pile models

2.4 Conclusion Results, both from plane strain and embedded pile analysis show that the inclination of the outer piles leads to a reduction of vertical displacements of roughly 4mm which corresponds to about 5%. This is due to the fact, that the inclined piles and the vertical piles next to these can mobilize more skin friction. Both 2D models are in good agreement with the embedded pile calculations. The difference of maximum vertical displacements is less then 3%. The difference between the model with the embedded pile concept and the model with volume piles is roughly 5%. The reason therefore is probably an overestimation of the tip resistance in the standard finite element approach (Engin et al., 2007).

3 Application of the embedded pile concept In this section the application of the embedded pile concept for a practical foundation problem is presented. The design calculation based on the bearing capacity of individual piles required about 3000 jet grouted piles and therefore even with the embedded pile option a simplification of the FE-model was necessary. In the model two areas are distinguished, namely ones which are not sensible for the superstructure and in which the load is not very high and ones where the loads are very high and the superstructure is very sensitive to (differential) settlements. The former are modelled as homogenized blocks, meaning that the zones of the sub-soil in which the jet grout columns are installed are defined with smeared properties. For the latter the embedded pile concept is applied. The final model for the application of the embedded pile approach is shown in Figure 8(a). The dimensions of the model are 500/50/400m and it consists of roughly 48000, 15noded wedge elements. In Figure 8(b) a top view of the structural elements without the subsoil is presented. The sensitive section consists of 615 embedded piles with different lengths, inclinations and spacings. The soil profile is the same as in the example before, but the soil properties have been slightly modified. The pre-consolidation pressure in this case is increased to 800kN/m2. The foundation slabs are discretized and defined as linear elastic material. Because of the dimensions of the model and computational limitations it is not possible to model the slabs with all details and therefore some geometric simplifications have been required. The properties of the embedded piles are shown in Table 6. The capacity is defined by a constant skin friction distribution and a base resistance. The constant distribution of the skin friction is probably not realistic, but in working load conditions the skin friction is not fully mobilized hence the distribution plays a minor role. One of the most important information of this calculation is the global settlement behaviour of the construction because the complete structure is modelled, including all areas with significant different load intensities. In Figure

0 mm

37 mm

74 mm (b) (a)

9(a) the vertical displacements of the structural elements are presented. The maximum settlements are in the region where the jet grout columns are modelled in detail with the embedded pile option and a value of 63mm for uy,max is obtained. The subway tunnel, in the left part of the model experiences settlements in the range of 10mm. The difference in load bearing behaviour of the jet grouted columns can also be evaluated. As an example Figure 9(b) shows the distribution of the axial force for an inclined pile in the outer row where the maximum settlements are obtained. The continuous decrease of the axial force confirms that the inclined piles mobilize significant skin friction. On the contrary piles within a group, with small spacings, are not able to mobilize the same degree of skin friction and therefore they are transferring the load via the base resistance into the soil.

Figure 8. Model with embedded piles in sensitive areas

Table 6. Embedded pile properties

γ Eref d Τtop,max Τbot,max Fmax

[kN/m3] [kN/m2] [m] [kN/m] [kN/m] [kN]

Jet grout column γsoil+1.0 10000000 0,8 251.0 251.0 1000

Figure 9. Contour plot of vertical displacements (a) and axial force in an inclined jet grouted column (b)

(a) (b)

(a) (b)

4 Discussion and conclusions A comparison of different models for analysing a foundation supported by jet grout columns and the application of the embedded pile option to a practical problem has been presented. The results from the comparison of different models show that all models give the same order of magnitude for deformations. Altogether the maximum difference in vertical settlements for all different modelling assumptions is less than 5% and as a consequence of minor importance. The application of the embedded piles concept emphasized the benefit of this approach. With this concept it is possible to model a high number of piles or columns because no discretisation of the piles is necessary and very large computational models can be avoided. In the application example of this paper even the embedded pile concept reached its limitations and therefore two types of modelling have been combined. The areas which are not sensitive for the superstructure have been modelled with smeared properties and in sensible zones every single pile is modelled as an embedded pile. The outcome is the global settlement behaviour of the entire structure. However detailed information in the section with embedded piles, for example relative displacements and mobilization of the skin friction is obtained. Another benefit is that the influence of different spacings, pile lengths and diameters can be evaluated with reasonable effort in these sensitive areas. Concerning the distribution of the skin friction along an embedded pile, it is obvious that the mobilization of the skin friction is influenced by the distribution in the failure state, which is an input. In working load conditions this predefined distribution of the skin friction does not change the results significantly but for ultimate limit state analysis assumptions for the distribution of the limiting skin friction, base resistance, elastic region around the pile and mesh coarseness may have a significant influence on the result.

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Engin H.K. 2006. A report on embedded piles. Plaxis internal report.

Sadek M., Shahrour I. 2004. A three dimensional embedded beam element for reinforced geomaterials. Int. J.f.Numerical and Analytical Methods in Geomechanics, 931-946.