Temporary excavation for installation of two conduits
- deepexcavation
- Jun 23
- 6 min read
Modelling with DeepEX
Introduction
With the objective of installing two parallel conduits, each 1.2 m in diameter and 2.3 m in length, the present case aims to design a support structure. As a solution, a temporary, flexible Berlin-type retaining wall with two level of bracing is adopted, to ensure safety during the installation process, as illustrated in Figure 1. The excavation has a depth of 7 m, and the conduits will rest on a 0.5 m thick layer of gravel. Since this is a temporary structure, the facing will consist of timber planks, and the supports will be metallic struts.
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Figure 1 – Scheme of the excavation with the details of the installation |
The soil profile comprises three distinct layers. The uppermost layer consists of 3 metres of cemented sand, characterised by a total unit weight of 18 kN/m³, a friction angle of 32°, and an apparent cohesion of 10 kPa attributed to cementation. This is underlain by a stiff clay layer, the top of which coincides with the groundwater table. The clay has a total unit weight of 20 kN/m³ and an undrained shear strength of 50 kPa. Beneath the clay, at a depth of 7 m, lies weathered granite with a unit weight of 23 kN/m³ and a Standard Penetration Test (SPT) N-value exceeding 60.
Model description
The model geometry follows the schematic shown in Figure 2, representing a soldier pile and lagging wall system. Timber lagging (wooden boards) is horizontally installed between vertical steel piles (HP14x89), which are spaced at regular intervals S. The H-piles are embedded into the ground to a depth D, ensuring structural stability and resistance to lateral loads, while the retained excavation height is denoted by H = 7.0 m. The diagram illustrates the typical configuration used for staged excavation support systems, capturing both the structural layout and interaction with the surrounding soil mass (part of the DeepEX software capabilities).
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Figure 2 – Detail of the soldier pile wall - DeepEX software |
The excavation is modelled as shown in Figure 3, with all construction stages explicitly represented. The analysis is carried out in DeepEX software using both the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM). The LEM analysis incorporates active earth pressures and the method of apparent earth pressures proposed by Terzaghi and Peck (1967/1969), as illustrated in Figure 4. The soil is modelled using either the Mohr–Coulomb (granular soil – sand) or Tresca (cohesive soil – clay) constitutive models, as appropriate. The assumed modulus of deformation are; cemented sand, E = 50 MPa; stiff clay, E = 100 MPa; and weathered granite, E = 15 GPa.
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Figure 3 – Model for LEM and FEM analysis - DeepEX software |
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Figure 4 – Apparent pressure diagrams for computing strut loads in braced cuts (Terzaghi and Peck, 1967) |
Figure 5 illustrates the distribution of apparent lateral pressures (in kPa) acting along the wall, determined by the ground stratigraphy and distinct soil properties. The diagram reveals a combined pressure profile, merging the characteristic pressure behaviours of sand and clay layers. In the sandy stratum, the apparent pressure reaches a magnitude of 12.3 kPa, reflecting the granular soil's lower cohesion and frictional resistance. In contrast, the clayey layer exhibits a higher maximum pressure of 35.1 kPa, consistent with its cohesive nature and tendency to exert greater lateral stresses under loading. This contrast shows the influence of soil type on pressure distribution, which is critical for evaluating wall stability and designing appropriate retention systems.
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Figure 5 – Detail of the apparent pressure diagram for the stratigraphy of the soil used in LEM analysis (DeepEX) |
Limit Equilibrium Method (LEM) Analysis
Figure 6 illustrates the apparent earth pressures are plotted on the retained side of the wall and the moments resulting from the analysis.
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Figure 6 – Diagrams of moments and apparent earth pressures resulting from the LEM analysis (DeepEX) |
Key Observations:
The upper zone (12.3 kPa) shows lower pressures, attributed to the cemented sand layer with moderate stiffness.
Apparent Earth Pressures are trapezoidal in the case of the clay layer, with a significant concentration near the struts, reflecting the simplified envelope typically used to design braced cuts.
The maximum pressure (35.1 kPa) reduces gradually until reaching the base of the excavation, where the due pressures develop in order to establish equilibrium.
Discussion:
LEM provides a straightforward way to estimate strut loads and envelope pressures but ignores wall-soil interaction.
The method assumes full mobilization of apparent/passive earth pressures, which may not occur, especially in stiff soils.
Apparent pressure diagrams are idealised and may lead to conservative support loads, particularly in the presence of high-stiffness materials like cemented sand or stiff clay.
Finite Element Method (FEM) Analysis
Figure 7 illustrates the FEM output, showing wall bending moments, effective horizontal pressures, and the stratigraphy with material properties. The FEM results provide a comprehensive representation of the vertical (Figure 8) and horizontal (Figure 9) displacements of the soil.
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Figure 7 - Diagrams of moments and active earth pressures resulting from the FEM analysis (DeepEX) |
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Figure 8 – Vertical displacements - FEM analysis in DeepEX |
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Figure 9 – Horizontal displacements - FEM analysis in DeepEX |
Key Observations:
Soil Pressures: FEM provides a more refined stress distribution along the wall, clearly showing the variation in effective stress with depth and layering. The peak effective horizontal pressure occurs near the base of the wall, reflecting the stiff response of the clayey soil layer.
Wall Bending Moments: The diagram shows maximum moments of about ±33.4 kNm/m near the supports, with opposite signs at different depths. This indicates a classic multi-propped wall bending pattern.
Strut Forces: the presence of struts and the observed changes in pressure and moment indicate their effectiveness in redistributing loads and reducing bending demands.
Discussion:
The use of Mohr-Coulomb or Tresca models with appropriate stiffness parameters (E-values) helps simulate both drained and undrained responses.
The model suggests lower peak wall moments compared to what might be conservatively assumed in LEM, potentially offering design economy.
FEM identifies zones of tension and compression in the wall, useful for reinforcement detailing.
Table 1 presents the results of the stability analysis for the retaining wall and support system, comparing the performance of the Limit Equilibrium Method (LEM) and Finite Element Method (FEM). The table summarizes key design factors including maximum wall moments, shear forces, displacements, support reactions, and safety factors for embedment and basal stability.
The LEM results indicate a more conservative design, with higher wall shear (69.33 kN/m vs. FEM's 57.24 kN/m) and support reactions (116.8 kN/m vs. 105.97 kN/m), but significantly smaller predicted displacements (0.05 cm vs. 0.26 cm). Both methods show satisfactory safety factors for the critical support check (0.615 for LEM vs. 0.559 for FEM), though only LEM provides verification of embedment (FS = 2.005) and basal stability (FS = 2.127).
Table 1 - Summary of the verification of wall and support design
Analysis method | Wall Moment (kN-m/m) | Wall Shear (kN/m) | Wall Displacement (cm) | Max Support Reaction (kN/m) | Critical Support Check | Wall Embed. FS | FS Basal stability |
LEM | 30.68 | 69.33 | 0.05 | 116.8 | 0.615 | 2.005 | 2.127 |
FEM | 33.41 | 57.24 | 0.26 | 105.97 | 0.559 | N/A | N/A |
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Comparison & Interpretation
Table 2 summarizes the key differences between the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM) in analysing retaining structures. LEM adopts idealized earth pressure distributions and neglects wall deformation, leading to simplified strut load estimates and inherently conservative designs. In contrast, FEM computes continuous earth pressure based on soil constitutive models, explicitly accounts for wall deformation, and fully captures soil-structure interaction, resulting in more realistic but potentially less conservative outcomes. While LEM offers computational efficiency for preliminary design, FEM provides detailed insights into system behaviour, emphasizing the value of combining both methods for reliable safety assessments.
Table 2 – Summary of the feature of each analysis method.
Aspect | LEM | FEM |
Earth Pressure | Idealised (apparent pressure) | Continuous distribution based on soil model |
Wall Deformation | Not considered | Explicitly computed |
Strut Loads | Derived from pressure diagrams | Computed based on equilibrium and deformation |
Soil-Structure Interaction | Ignored | Fully captured |
Conservatism | Tends to be conservative | More realistic, possibly less conservative |
Conclusion:
The LEM provided a useful preliminary design approach, allowing for the design of the wall considering the wall embedment check providing a model that verified safety for all subsequent critical performance verification. However, the FEM captured a more realistic behaviour, especially in this case with a stratified profile containing high-stiffness contrasts with the cemented sand over stiff clay and weathered granite. The FEM output confirms that the support system performs effectively, with manageable bending moments and realistic pressure distributions, making it a valuable tool for both verification and design optimisation. The design optimisation led to a solution composed of HP14x89 steel piles, timber lagging, and W10x22 steel profiles for the struts. DeepEX presents the advantage of running both analyses in an integrated framework providing efficiency and robustness to the design and safety verifications.
References
Terzaghi, K., & Peck, R. B. (1967). Soil mechanics in engineering practice (2nd ed.). Wiley.
Peck, R. B. (1969). Deep excavations and tunnelling in soft ground. Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, State-of-the-Art Volume, Mexico City, 225–290.
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