Example 2: Cantilever TERS in Cohesionless Soil with Sloped Backfill

1. INTRODUCTION

This case presents a 10 ft depth excavation on a soil characterized by the parameters given in Figure 1, where it is possible to observe a 20º sloped backfill and the groundwater level at the depth of the excavation. The problem is simulated and analyzed using DeepEX software, applying all the available analysis methods – Limit Equilibrium Method (LEM), Non-Linear Analysis (NL) and Finite Element Method (FEM). The following sections illustrate the assumptions for modeling the problem’s geometry and running the analysis, which are defined in the software settings, as well as the results.

Figure 1: Cantilever excavation model (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 soil is characterized by a friction angle of 32º, moist unit weight of 120 pcf, and saturated unit weight of 133.5 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).

4. WALL SECTION PROPERTIES The retaining wall is composed of AZ 19 section sheet piles, with the configurations displayed in Figure 3, which presents the geometry, and material properties are described in Figure 4.

Figure 3 – Geometry of the sheet piles section.

Figure 4 – Sheet piles configurations and material properties.

5. CONSTRUCTION STAGES

The construction process is performed in stages, enabling a gradual transfer of the load to the retaining structure. This approach ensures the safety of both the site and its surroundings. In the initial phase, the software establishes the at-rest conditions (refer to Figure 6.a). In the subsequent step, the retaining wall is subjected to the soil pressures and surface surcharge (see Figure 6.b).

a)

b)

Figure 6 – Model geometry and loading conditions. Initial phase (a), excavation (b). Initial D = 20 ft.

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: Active and passive pressure methods.

  • 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 FSmin = 1.5, the embedment increased to D = 22 ft.

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 9 – Non-linear, moments and horizontal pressures.

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 document presents an analysis of an excavation in cohesionless soil with a sloped backfill supported by a cantilever wall as a temporary solution. The results showcase the capabilities of DeepEX software in modeling and analyzing excavations with retaining structures. 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, detailing the maximum displacements, maximum moments, maximum shear forces, the check ratios for moments and maximum shear stresses, and wall embedment FS.

Table 1: Extended summary for all design sections.

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).