**A. INTRODUCTION**

Deep excavations play a vital role in the engineering industry.

From construction of high-rise buildings, underground structures, or transportation systems, the design of deep excavations requires careful consideration to ensure safety, stability, and structural integrity.

In several cases, a deep excavation design needs to comply with internationally recognized standards and guidelines.

In this example, we will create, analyze, and optimize a soldier pile wall deep excavation with two levels of ground anchors, for all available Eurocode 7 load combinations. Eurocode 7, a set of specifications developed by the European Committee for Standardization (CEN), emphasizes the importance of a rigorous and systematic approach to deep excavation modeling, aiming to mitigate risks, enhance stability, and minimize potential hazards.

The following sections present how such a model can be created in minutes with our complete deep excavation design software DeepEX.

We will illustrate important analysis settings software options to quickly and automatic optimize the shoring system, so that it complies with all EC7 requirements. Table 1 presents the soil properties and stratigraphy.

Tables 2 and 3 present the initial wall and support section properties respectively.

**Table 1: Soil properties and stratigraphy**

Soil | Top El. | Description | Unit Weight | Friction Angle | C’ | Eload | exp | qSkin |

(-) | (m) | (-) | (KN/m3) | (deg) | (kPa) | (kPa) | (-) | (kPa) |

F | 0 | Fill - Sand | 19.6 | 30 | 0.6 | 15000 | 0.5 | 50 |

S1 | -2 | Medium Dense Sand | 21 | 34 | 1 | 35000 | 0.4 | 150 |

GT | -7 | Glacial Till | 22 | 36 | 10 | 50000 | 0.4 | 200 |

**Table 2: Initial wall section properties**

Wall Type: | Soldier Piles (Steel Beams with Timber Lagging) |

Pile Section: | HE 300A |

Lagging Thickness: | 5 cm |

Steel Material: | A50 Steel |

Wall depth: | 14 m |

**Table 3: Initial support properties**

Anchor: | Tieback 1 | Tieback 2 |

Elevation on Wall: | - 3m | - 6m |

Structural Section: | 5 x 1.4 cm Strands 270 ksi | 5 x 1.4 cm Strands 270 ksi |

Free Length: | 6.5 m | 5.16 m |

Fixed Length | 8 m | 8 m |

Installation Angle: | 20 deg | 20 deg |

**B. MODEL GENERATION – DEEPEX MODEL WIZARD**

The model wizard is a powerful tool in DeepEX, that allows users to generate any deep excavation model in seconds, including all construction stages. The wizard utilizes a series of tabs, where we can define all project parameters, from analysis settings, project type, to soil properties, support elevations, design standards and more. Figures 1 to 5 present some of the DeepEX wizard options.

**Figure 1: DeepEX Model Wizard – Analysis settings**

**Figure 2: DeepEX Model Wizard – Project type, dimensions & support data**

**Figure 3: DeepEX Model Wizard – Soil properties and boring**

**Figure 4: DeepEX Model Wizard – Wall Section Properties**

**Figure 5: DeepEX Model Wizard – Stages creation, Support Elevations**

The software can automatically create any deep excavation model with all construction stages, as well as linked model copies with each selected standard load combination.

Figure 6 presents the generated construction stages.

Figure 7 shows the load combinations from the selected Eurocode 7 standard.

**Figure 6: Generated model in DeepEX (all stages)**

**Figure 7: Linked design sections with each EC7 load combination**

**C. MODEL ANALYSIS & OPTIMIZATION**

**- Initial Model Analysis**

Initially, we will perform a Limit Equilibrium analysis for all design sections (base model – service, and the sections with the Eurocode 7 load combination).

Figure 8 presents the DeepEX analysis and checking summary table that becomes visible at the end of all computations.

We come to the following conclusions:

1. The displacements and settlements are significant, but we need to verify that with the Non-Linear analysis engine and the Finite Element method that consider the project staging and soil stiffness.

2. The wall shear check ratios are ok for all Eurocode 7 load combinations, but the check is not satisfied for the combinations DA-2 and DA-3.

3. The support structural sections are fine, but we see that at least one of the supports fails geotechnically (pullout) both in service conditions and with all Eurocode 7 load combinations.

4. The wall embedment FS is above 2 for the service conditions & above 1 for all EC7 load combinations (the wall embedment is sufficient – perhaps we can consider reducing the pile installation depth).

**Figure 8: DeepEX – Analysis and checking summary table (initial model)**

**Figure 9: EC7 – DA-2 Combination Results (Stage 5), top support pullout capacity is not sufficient**

**- Top tieback fixed length optimization**

In the optimize tab of DeepEX we can select to optimize the fixed length of a ground anchor, and then click on our top tieback support.

The software will locate the suitable tieback length so that the geotechnical check will be satisfied for all linked design sections.

In this case, the software returns an optimum fixed length of 12m (compared to the 8m we initially assumed).

Figure 10 shows the fixed length optimization procedure in DeepEX.

Figure 11 presents the analysis and checking summary table after the optimization, where we notice that the geotechnical check issue is resolved.

**Figure 10: Tieback fixed length optimization procedure in DeepEX**

**Figure 11: DeepEX – Analysis and checking summary table (after anchor fixed length optimization)**

**- Wall Structural Section Optimization**

In the optimization tab of DeepEX we can select to optimize the wall structural section.

We select the corresponding tool, and we click on the wall we wish to optimize.

The software will run through the database of steel beams that is implemented and show us the 10 structural sections for the H beams (in this case), and the check ratio they would produce if assigned. We can pick any section according to our preference.

In this case we select an IPE 450 section.

Figure 12 shows the wall structural section optimization procedure in DeepEX.

Figure 13 presents the analysis and checking summary table after the optimization, where we notice that the moment check ratio for the EC7 combination DA-2 is above 1.

**Figure 12: Wall structural section optimization procedure in DeepEX**

**Figure 13: DeepEX – Analysis and checking summary table (after wall section optimization)**

**- Support Locations Optimization**

Reviewing the result graphs in all construction stages allows us to notice that the moment capacity in stage 1 (cantilever excavation stage) for the model with EC7 – DA-2 combination is not enough to cover the developed moment in this particular stage (Figure 14 below).

We could consider using a larger pile section for the wall (a fact that increases the moment capacity further), or to excavate less in that particular stage, a fact that would result in smaller developed moments.

We will try reducing the excavation depth by 0.5m, by changing the surface level in stages 1 and 2 (support installation stage) and moving the top support up, to El: -2.5m.

Figure 15 presents the analysis and checking summary table after we did the changes mentioned in this section.

**Figure 14: EC7 – Combination DA-2 – Stage 1: Wall moment exceeds moment capacity.**

**Figure 15: DeepEX – Analysis and checking summary table (after all optimizations)**

**- Check Base Model with Non-Linear and Finite Element Analysis Methods**

While the conventional limit equilibrium approach can be utilized to show critical condition results for all code load combinations as presented above, it is always wise to check our deep excavation models with more rigorous – yet more demanding methods like the beam on elastoplastic foundations method (non-linear analysis) or the finite element analysis approach.

Both methods are more demanding in terms of soil parameters input (soil model, modulus of elasticity) and compliance with some of the Eurocode 7 load combinations.

Nevertheless, with realistic soil properties input they can produce quite realistic wall displacements and settlements.

In DeepEX all 3 main deep excavation methods are available: Conventional, Non-linear spring analysis, Finite Element Method, in order of greater sophistication requiring more careful input, understanding, and interpretation. In this case, we will create copies of the base model (service conditions), and we will analyze it with both methods, assuming a wall friction of 66% of the available soil friction.

Figure 16 presents the analysis result graphs in the final excavation stage (stage 5) for each approach.

**Figure 16: Result graphs & shadings for a) Non-Linear Analysis and b) Finite Element methods**

**D. CONCLUSION**

In this article, the significance of model optimization techniques in deep excavation design was highlighted.

The focus was on ensuring compliance with Eurocode 7 load combination requirements, as well as the use of advanced methods such as Non-Linear analysis and Finite Elements approach to enhance the accuracy and reliability of the models.

While traditionally, designers tend to prioritize increasing the structural and geotechnical capacities of their elements, the article revealed an alternative approach.

By optimizing the support locations, designers can achieve remarkable results in deep excavation models.

With DeepEX this task can become much easier as support elevation optimization algorithms come with the software.

This innovative perspective opens up new possibilities for more efficient and effective designs.

With DeepEX, design engineers can seamlessly align their models with multiple international codes and standards, saving considerable time and effort.

No more tedious manual checks or complex calculations; DeepEX streamlines the process, providing accurate and compliant solutions.

DeepEX empowers engineers to explore the true potential of their designs by subjecting them to non-linear analysis and the cutting-edge Finite Elements approach.

It's a software solution that transcends boundaries, enabling designers to push the limits of creativity and innovation.

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