DFG Forschergruppe 1136 GeoTech

Figure 3: ALE simulation of the penetration of a rough rigid strip foundation into dense dry sand (Dr = 0.78). Initial mesh with boundary and contact conditions (left) and deformed computational domain showing the smoothed mesh and distribution of the equivalent shear strain rate (right).

Stavros A. Savidis - Frank Rackwitz - Daniel Aubram

The experimental small-scale tests started in phase I will be refined and continued in phase II of the subproject. They are undertaken to provide more insight into the phenomenology of vibro-injection pile installation. The model tests should particu-larly reveal details concerning the size and shape of the displacement and mixing zones, the transition regions, the velocity and strain distribution, and front propaga-tion. Moreover, the experimental investigations will be employed to check whether the assumptions underlying the numerical model are admissible.

One of the key aspects that should be investigated in further experiments is the continuous injection of the generated annulus between the driven model pile and the water-saturated soil using either grout or surrogates (e.g. bentonite slurry). In these experiments, the injection pressure has to be adapted to the vibration frequency in such a way that the saturated soil is forced to loose shear stiffness or to liquefy locally so that it can be displaced by the supplied grout. This is also the basic principle of vibro-injection pile installation in practice.

Validation and Application of the MMALE Model

The experimental tests carried out here and in the central project are back-calculated by using the developed multi-material arbitrary Lagrangian-Eulerian (MMALE) computational model (see also Figs. 8 to 10) with the objective to eva-luate the ability of the MMALE method compared to conventional finite element simulations.

Within the scope of the research unit, the results of the subproject can help to better understand and quantify the impact of vibro-injection pile installation on the surroun-ding soil and neighboring buildings, and to generally point out the significance of the installation processes for predictive numerical simulations. Based on the adequate numerical modeling of the considered initial boundary value problem by an MMALE method in conjunction with advanced constitutive equations for sand, promising and realistic results can be expected.

Figure 10: Comparison of measured and calculated load-displacement curves of a rigid strip foundation on initially dense sand.

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Figure 9: Distribution of the equivalent shear strain rate in initially dense sand (Dr = 0.78) below a rigid strip foundation at a relative penetration depth of d/Dfund = 0.54. Left: Results of a model test by digital image correlation. Right: back-calculation of the model test using the ALE method (detail).

Figure 8: Quasi-static penetration of a smooth rigid pile into loose dry sand (initial void ratio: e0 = 0.678). Comparison of relative load-displacement curves obtained through model test and ALE simulation.

Figure 7: Detail of a digital image recorded during downward motion of the model pile toe along with the vibro-driving and injection of the shaft annulus with bento-nite slurry (left), and the associated soil velocity field indirectly measured through digital image correlation (right).

Figure 1: Investigation of the applicability of mesh regularization algorithms. Com-parison of a heuristic method (left) and the developed optimization-based algo-rithm (right) by using the example of metal forming.

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Experimental Investigations

In conjunction with the theoretical investigations and supplemental to the central project of the research unit, a model test facility has been designed and constructed (Fig. 4) in order to validate the MMALE method and the computational models for vibro-injection pile installation. The model test facility consists of a watertight contai-ner with glass panel and a special small-scale model pile with vibrator. All compon-ents are in-house development. When the pile is vibro-driven along the glass panel into the water-saturated sand, the pile shaft can be injected with grout as with the RI-piles in practice. The driving and injection process is digitally filmed and subse-quently analyzed by digital image correlation (DIC) software (Fig 5).

A series of preliminary model tests have been carried out and analyzed in phase I of the subproject. In all these tests, a relatively dense sand filling of the container was realized through dry pluviation. The sand filling was dry in one model test, and water-saturated in four other tests. Vibration frequency was 20 Hz in all cases, and the dynamic force ranges between 1,9 kN and 2,4 kN.

During vibro-driving of the model pile in one of the tests (test V5), the pile shaft was injected with bentonite slurry. A preliminary analysis of test V5 is illustrated in Figs. 6 and 7. Fig. 6(a) shows the time response of the vertical displacements of the pile toe, including markers at those configurations where images have been recorded.

Figure 4: Experimental investigations of vibro-injection pile installation. (a) Filled test container with glass panel and model pile. (b) Detail showing glass panel, lower pile guide, and model pile. (c) Tapered pile toe with welded collar and bolt closing the injection tube. (d) Vibrator with controller (frequency converter).

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Figure 5: Workflow of digital image correlation software. Two digital photographs from consecutive deformation states of the granular body are subdivided into search patches and test patches (a), and then the color intensities of each pair of patches are cross-correlated (b). From the field of local incremental displacement vectors obtained (c), the equivalent shear strain rate (d) can be determined.

Figure 6: Results of a model test concerning vibro-injection pile installation in water-saturated sand using bentonite slurry-injection. (a) Time response of vertical pile toe displacements. Soil displacement increments (b) at upward motion of the pile (image 1 to image 2) and (c) at downward motion of the pile (image 5 to image 6).

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Development of the Computational Model

Most algorithms described in part 1 have been implemented and then tested sepa-rately and in conjunction with other algorithms of the MMALE method in order to verify each of them (Fig. 1). The ALE computational models shown here account for only one material per element and time step because the implementation of the multi-material capabilities has not been completed yet. Therefore, the computational models used for the example calculations actually are simplified ALE models, and not MMALE models in the strict sense.

For the examples shown here, only the ALE method achieved a convergent solution. In contrast, calculations applying conventional Lagrangian finite elements terminated at an early stage in all cases due to severe element distortion.

The MMALE finite element method is employed to develop a computational model for vibro-injection pile installation in saturated sand step by step. The modeling pro-cess is more complicated than with Lagrangian elements because of the functiona-lity gained and the increased number of boundary conditions (e.g. flow inlet and outlet). In a first step, the process of grouting is ignored and the vibro-driving of the steel pile is modelled as quasi-static/cyclic penetration. Similar models have been successfully applied in previous investigations (Figs. 2 and 3).

Fully-dynamic vibro-driving and grouting will be modelled in subsequent steps and will complete the MMALE computational model. Concerning the grouting process, two extreme situations may occur: (i) the displacement of the saturated soil by the grout as a whole resulting in an expansion of the pile shaft annulus (analogy: oil on water) and (ii) the mixing of the soil and the grout in which the constitutents retain their original properties though (analogy: oil-water emulsion). The developed multi-material resp. multiphase continuum description based on homogenization theory (see part 1 for more details) can handle both phenomena. In any case, injection of grout into the pore space of the soil is not included in the model due to the assump-tion of impermeable interfaces.

Figure 2: ALE simulation of quasi-static penetration of a smooth rigid pile into loose to medium dense dry sand (initial void ratio: e0 = 0.678). Boundary of the un-deformed FE model and void ratio distribution at a relative penetration depth of d/Dpile = 5.0.

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