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It is very common in practice that geotechnical engineers design earth retaining structures conservatively to meet serviceability and construction requirements, which undoubtedly increases a project’s budget. It is the responsibility of engineers to optimize the design without compromising on safety. Although engineers and researchers try to conduct laboratory experiments as close as possible to reality by simulating the field situations/conditions, limitations and assumptions always exist due to the difficulty involved in truly replicating them. The same is true with analytical approaches, and hence most methods were analyzed in two dimensions (2D) due to the difficulty and analytical complications involved in three-dimensional (3D) analysis.

With the development of technology, numerical analysis using finite element software helps in easing the process of 3D calculations. However, it is always advised to analytically verify the results obtained from numerical analysis. In the present case study, an effort was made by considering a real-time project in Dubai, United Arab Emirates, to perform analytical and numerical studies in determining pullout capacities of anchor blocks in 2D and 3D modes behind a sheet pile wall and observe how consideration of 3D effects using PLAXIS helped in optimizing the design without being too conservative.

Learn more about PLAXIS 2D WorkSuite

Learn more about PLAXIS 3D WorkSuite

The project is located in the emirate of Dubai, U.A.E., wherein it was required to raise the existing ground level at +5.5 m DMD (Dubai Municipality Datum) to +11.75 m DMD, i.e., to a height of 6.25 m above the ground level (see **Figure 1**) within the site limit. In addition, an excavation is expected in the future (toward the right side of the sheet pile wall in Figure 1) down to a level of +2.5 m DMD, i.e., 3.0 m below the existing ground level. A light traffic load (10 kPa) was also expected on the top of fill.

The pullout capacity of anchor blocks in the 2D approach was analytically calculated using methodology based on Rankine, Coulomb, and Log Spiral theories, which is commonly used by U.A.E. geotechnical engineers. After performing the necessary calculations, the allowable pullout capacity of anchor block was found to be 123 kN after considering a safety factor of 1.5, which is too conservative according to our previous experience on similar works. This resulted in either the requirement of large-size anchor blocks, or they would need to be placed very closely to meet the pullout capacity requirement.

Hence, an attempt was made to calculate the pullout resistance of anchor blocks considering 3D effects which are closer to reality. In most cases, analytical solutions are limited to 2D with a sufficient factor of safety. This is primarily due to complications involved in formulating analytical equations considering 3D effect.

However, analytical calculations considering 3D effects were made. Upon performing calculations, the revised allowable pullout resistance of anchor block considering 3D effects increased from 123 kN (in 2D) to 285 kN after considering a safety factor of 1.5. This increased the pullout resistance by 2.3 times when 3D effect was considered and resulted in increased spacing of anchor blocks.

Yet assumptions inevitably exist in formulating any mathematical expressions for engineering problems, specifically while considering 3D effects. Hence, to verify and confirm those results obtained by analytical methods, simultaneous numerical analyses were carried out using PLAXIS, and details pertaining to it can be seen in the following sections.

Pullout capacities of anchors were calculated using numerical 2D and 3D approaches considering plane-strain problems and volumetric modeling using the geotechnical finite element analysis (FEA) software PLAXIS.

In this approach, compacted fill and concrete anchor block were modelled as plane-strain elements (see **Figure 3**). Compacted fill was defined using the Mohr-Coulomb material model. For concrete, a linear elastic material model was adopted in the analysis. An interface element was defined between block and compacted fill with R_{inter}= 0.67. Analysis was conducted in three phases:

- Phase 1: In-situ stage where K
_{o}procedure was used to initialize stress in the model. - Phase 2: Blocks, along with interface elements, were activated in the model.
- Phase 3: Pressure load was activated.

3D finite element analysis (see **Figure 4**) was carried out with compacted fill and concrete anchor blocks were modeled as volumetric elements with interface elements (R_{inter}=0.67) defined between the block and compacted fill. A phase construction sequence followed in the 3D model was the same as the 2D model, with center-to-center spacing between blocks as 2.25 m.

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