Example 3: Cantilever TERS in Cohesive Soil

1. INTRODUCTION

The objective of this case study is to model and design a support system for a 10 ft deep excavation in cohesive soil, using the geotechnical parameters provided in Figure 1. The analysis considers a surcharge load of 360 psf and assumes the groundwater table is located at the excavation depth. The excavation is evaluated using DeepEX software, applying three methods: the Limit Equilibrium Method (LEM), Non-Linear Analysis (NL), and the Finite Element Method (FEM). The methodology is outlined in the following sections, detailing the assumptions adopted for each method as defined in the software settings, along with the corresponding results.

Figure 1 - Excavation model and support system (Fig: MDOT TERS Software Evaluation Procedure).

2. ABOUT DEEPEX

DeepEX is a superior software solution for the design, analysis, and optimization of deep excavation projects and tunnels. Its superior interactive interface allows users to generate, analyze, review, and evaluate any model quickly and efficiently.

Implemented analysis methods: Limit Equilibrium, Non-Linear analysis (soil springs), and 2D & 3D Finite Element analysis.

Implemented soil pressure methods (LEM): Active/Passive, At-rest, FHWA Apparent, German EAB, Custom Trapezoidal, 2-step Rectangular, WMATA, NYC and more.

Implemented water pressure methods: Hydrostatic, Simplified flow, Full 2D flownet, Balanced pressures, unconfined flow.

Beam analysis methods (LEM): Blum’s method (continuous beam), FHWA simple span, CALTRANS, WMATA, and more.

3. SOIL PROPERTIES

The ground is composed of a firm clay characterized by an undrained shear strength of 1500 psf, a saturated unit weight of 118.4 pcf. Figure 2 presents the soil properties in the input window.

a) b)

Figure 2 – Input window for soil properties definition; a) general definitions, b) Exponential behavior (for B NL FEM analysis)

The problem proposes a minimum fluid pressure of 31.8 pcf (0.0318 ksf), modelled as a minimum driving pressure that increases with depth.

Figure 3 – Minimum driving pressure.

4. WALL SECTION PROPERTIES

The retaining wall is composed of AZ 18 section sheet piles (Figure 4), and the geometry and material properties are described in Figure 5.

Figure 4 – Geometry of the sheet piles section.

Figure 5 – Sheet piles configurations and material properties.

5. CONSTRUCTION STAGES

The construction process is performed in two stages. The first stage corresponds to the wall installation (Figure 6.a). In the subsequent step, the excavation is performed, and the retaining wall is subjected to the actions (see Figure 6.b).

a)

Figure 6 – Model geometry and loading conditions. Initial phase (a), excavation (b).

6. ANALYSIS ASSUMPTIONS

In this example, the following assumptions were made:

• Groundwater conditions: The analysis implements simplified flow to represent groundwater behavior effectively.

• LEM:

  • Wall friction (δ) is set to 0.

  • Shear forces, moments and support reaction was performed with Blum's method.

  • Soil pressures: FHWA.

  • Optimization of wall embedment for FS = 1.5.

    
    

• N-L and FEM: Wall friction (δ) is set to 33% of the soil’s friction angle (ϕ').

• FEM: medium refinement of finite element mesh.

7. DEEPEX ANALYSIS RESULTS

As result from the optimization of wall embedment for a FS = 1.6, D = 5 ft, the necessary to fulfil all the verifications for the retaining wall performance.

A. Limit Equilibrium Analysis -(show moments and horizontal pressures (Figure 7), shear stress (Figure 8).

Figure 7 – LEM, moments and horizontal pressures.

Figure 8 – LEM, shear stresses and wall embedment FS.

B. Non-Linear Analysis - (soil springs) (show moments and horizontal pressures (Figure 9), shear stress and displacements (Figure 10))

Figure 9 – Non-linear, moments and horizontal pressures.

Figure 10 – Non-linear, shear stresses and displacements.

C. Finite Element Analysis - (same as NL analysis (Figure 11, 12) + FEM Mesh, horizontal (Figure 13) & vertical displacement shadings (Figure 14)).

Figure 11 – FEM, moments and horizontal pressures.

Figure 12 – FEM, shear stresses and displacements.

Figure 13 – FEM, mesh and horizontal displacement shadings.

Figure 14 – FEM, mesh and vertical displacement shadings.

8. ANALYSIS SUMMARY & CONCLUSION

The problem in analysis presents an excavation in a firm clay supported by a cantilever wall as a temporary solution. It suggests the existence of a minimum fluid pressure and a surcharge pressure. The software DeepEX presented the solutions to model and analyze the problem, along with its suggestions and assumptions for obtaining the results. The analysis employs three different methods available in the software: Limit Equilibrium Method (LEM), Nonlinear (NL), and Finite Element Method (FEM). The findings illustrate the software's versatility in providing reliable design solutions. Table 1 summarizes the outcomes from all analysis methods.

Table 1: Critical wall results for each method.

Table notes:

STR Moment: Moment stress check, assuming constant axial load on wall (demand/capacity).

STR Shear: Shear stress check (shear force demand/wall shear capacity).

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