3D Modeling of Soil-Foundation-Structure Interaction: Case History at Fly Ash Silo, Maasvlakte Rotterdam

Note: This Case History was first presented in Plaxis Bulletin, Autumn issue 2013, by L.F.J. Bekken, and W.A. Nohl, Fugro GeoServices B.V., Rotterdam, The Netherlands. The initial publication can be found here.

Problem Description

As part of a new power plant at the E.ON site at Maasvlakte, Rotterdam, a fly ash silo was built. The reinforced concrete structure had a total height of 55 m and a diameter of 24 m. The silo was constructed on a 2.5 m thick concrete base slab with a diameter of 32 m, while the foundation was comprised of 59 large diameter bored piles (Ø1.5 m). To inform the foundation design, Cone Penetration Tests (CPT) with depths varying from 40 to 70 m were performed. In addition, a borehole was carried out and undisturbed samples were taken for geotechnical engineering laboratory testing. Based on the CPT data and borehole logs the soil profile was determined, as shown in Table 1.

Table 1: Soil profile (reproduced after Bekken and Nohl, 2013)

Analytical Solution

Based on the pile and soil properties and characteristics, the pile tip level was set within the second sand layer (Sand II, Elevation -29m), while the calculated design pile bearing capacity was estimated to 11.5 MN. The majority of the settlement of the pile group was expected to be due to compression of the second clay layer below pile tip level (Clay II, Elevation -40m). This layer varies in presence and thickness, i.e., at some locations the thickness is 1.5m, while the layer is not encountered at some other locations (Figure 1).

The aforementioned heterogeneity of the subsoil could result in substantial differential settlements, which in turn could lead to higher stresses in the super-structure. Thus, the differential settlements were restricted as per the Client’s specifications. For the evaluation of the performance of the proposed foundation system, the (differential) settlements were estimated both analytically and by using a 3D finite element model.

The analytical method, which was based on Dutch Code guidelines, resulted in uniform settlement of the base slab of approximately 15 cm, when a uniform 1.5 m thick Clay II layer was considered, and 4 cm when the Clay II layer was not considered, as presented in Figure 2. Therefore, the estimated differential settlement could be as high as 11 cm. Based on the analytical results, it could not be concluded that the (differential) settlements meet the Clients requirements.

A limitation of the analytical method is that the structure stiffness is not considered. It is only possible to assume a certain stress distribution. However, this stress distribution, again, depends on the structure stiffness. Moreover, the soil stiffness, in its turn, affects the load distribution on the foundation-structure system. Such an effect is also not included in the analytical computations. 

Advantages of 3D Finite Element Modeling

As indicated above, the actual stress distribution in the soil-foundation-structure system can only be determined by the interaction of the individual elements. Consequently, a realistic soil-foundation-structure interaction analysis, in which both the heterogeneity of the subsoil and the stiffness of the foundation and the structure are incorporated, can be performed through 3D Finite Element Analysis.

The main advantages of the Finite Element Analysis method are:

• Modeling of the stress redistribution within the soil as a result of the foundation/structure stiffness.
• Modeling of the stress redistribution within the foundation/structure as a result of the soil stiffness.
• Modeling of the interaction between the pile and the surrounding soil.
• More advanced soil constitutive models can be implemented, and strain-dependent soil stiffness can be modeled.

The main advantages of a 3D modeling scheme are:

• The 3D geometry of the foundation/structure system can be modeled (circular plate with piles).
• The 3D variability in the thickness and depth of occurrence of the Clay II layer can be modeled.
• The 3D stress distribution in the subsoil can be investigated.

The 3D Finite Element Analyses for this important project were performed using Bentley's widely popular commercial software PLAXIS 3D.

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3D Finite Element Model

The 3D finite element model for the fly ash silo at Maasvlakte, Rotterdam is shown in Figure 3a. The structure was modeled by the dimensions and properties of the foundation slab and the silo wall. The base slab was modeled as a volume element with a linear elastic material behavior. The silo was modeled using plate elements with linear elastic material behavior. Moreover, the connection of the silo wall and the foundation slab was also included in the finite element model.

The sand layers were modeled using the Hardening Soil model with small strain stiffness (HSsmall). The soil stiffness parameters of the HSsmall model were based on the CPT data. The clay layers were modeled with the Soft Soil Creep (SSC) model. The soil parameters were based on CPT and laboratory results. The SSC model is suitable when considering creep, i.e. secondary compression. The creep was taken into account for a period of 30 years. The representative soil parameters of the Sand II layer and the Clay II layer are given in Table 2.

Table 2: Soil parameters for Sand II and Clay II (reproduced after Bekken and Nohl, 2013)

The foundation piles were modeled using the “embedded piles” feature. The piles distribute the structural load to the Sand II layer underlying the 1st clay layer (Clay I). The pile-soil interaction was modeled by a representative skin resistance of 0 kN/m up to the 1st clay layer and 500 kN/m thereafter, as well as with a representative base resistance of 13 MN according to the pile bearing design. The pile-soil interaction was verified for a single foundation pile in the 3D finite element model. In a calibration model, one large diameter bored pile (Ø 1.5 m) with a length of 34 m was modeled in the subsoil.

Based on the finite element calculations it was concluded that the foundation pile would have a vertical displacement of 95 mm due to a representative vertical load of 9 MN. The corresponding axial pile spring stiffness was 95 MN/m. The axial spring stiffness of the pile was in accordance to the calculated spring stiffness for a single pile based on the Dutch codes. Therefore, the pile-soil behavior of a single pile in the 3D finite element model was verified.

Model Results

The vertical (differential) settlements of the concrete base slab are shown in Figure 3b. Based on the numerical model results, an average settlement of 0.12 m for the concrete base slab was computed. Figure 3b indicates a difference in settlements of about 20 mm between the center and the outer section of the base slab. The foundation tilts towards the positive x-axis. The settlement of the concrete base slab is 0.130 m at the section overlying the 1.5 m thick Clay II layer and 0.113 at the diametrically opposite section. Thus, the maximum differential settlement of the base slab is 17 mm at a distance of 32 m, which results in a rotation of approximately 1:2,000.

Due to stress redistributions accounted for by the finite element program the rotation is smaller compared to the analytical model. Based on these results, it could be concluded that the differential settlements meet the Clients requirements.

Moreover, based on the PLAXIS 3D Finite Element Analysis, the pile head forces were also computed, as shown in Figure 4. It was concluded that about 80% of the structural loads were transferred to the piles. The remaining 20% of the structure loads were directly transferred from the foundation slab to the subsoil. If the load was evenly distributed over the 59 piles, the corresponding pile head load would be 5,450 kN/pile. However due to stress redistribution the piles in the area without the Clay II layer carry more load than the piles in areas with the presence of the 1.5 m thick Clay II layer. Therefore, it was observed that the stress redistribution in the 3D finite element analyses resulted in a reduction of differential settlements. Finally, Figure 3 also shows that the pile head forces at the outer ring are larger than the pile head forces at the inner rings.

Conclusions

Based on this Case History, the following conclusions can be drawn:

• Differential settlements obtained using analytical methods can be unrealistic because stress redistributions due to soil-structure interaction are ignored.
• Finite element analyses can incorporate the heterogeneity of the subsoil and the stiffness of the structure in a realistic interaction calculation model. 3D finite element modeling is warranted when the geometry is 3D (circular base plate with foundation piles) and the heterogeneity of the subsoil varies in three directions.
• The calculated differential settlements of the base slab using the 3D finite element model can be considerably smaller than the differential settlements estimated by the analytical methods.
• The finite element analysis also provides important additional information, like bending moments in the superstructure and pile forces.

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