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Example 7: Braced Cofferdam TERS in Cohesionless Soil

  • May 19
  • 4 min read

1. INTRODUCTION


This case study involves a 30 ft deep excavation through a medium dense sand stratum. The soil properties and groundwater level are shown in Figure 1. A uniform surcharge pressure of 360 psf is applied on both sides of the ground surface. A braced cofferdam is proposed as the support system, incorporating three levels of struts positioned at depths of 3 ft, 13 ft, and 22 ft from the top of the excavation. The stability of the excavation is assessed using three analytical approaches: the Limit Equilibrium Method (LEM), Non-Linear Analysis (NL), and the Finite Element Method (FEM). All analyses are performed using the DeepEX software. The subsequent sections outline the analytical framework and present the corresponding results.


Braced cofferdam, model geometry and ground properties (Fig: MDOT TERS Software Evaluation Procedure).
Figure 1: Braced cofferdam, model geometry and ground properties (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 profile is composed by a medium dense sand characterized by: ϕ′ = 32°, γ = 120 pcf, γsat = 133.5, and γ’ = 71.1 pcf. Figure 2 presents the soil properties as displayed in the input window.


Figure 2 – Input window for soil properties definition; general definitions, representation of the soil stratigraphy, and Exponential behavior (for B NL FEM analysis)


4. WALL SECTION PROPERTIES


The retaining wall is composed of AZ 18 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.


Sheet piles configurations and material properties
Figure 4 – Sheet piles configurations and material properties.

5. SUPPORT


The proposed support is composed of 3 levels bracing system at -3 ft, -13, and -22 ft, respectively. Figure 5 presents the geometric and material properties of the strut.


Figure 5 – Support configurations and properties.
Figure 5 – Support configurations and properties.

5. CONSTRUCTION STAGES


The excavation process is modelled in the following stages (Figure 6):


1. Initial installation: The sheet piles are driven through the soil layer down to the depth H + D.

2. Excavation: Excavation proceeds to a depth of -5 ft.

3. Activation of first strut level: The first strut is activated at a depth of -3 ft.

4. Partial excavation: Excavation continues to -15 ft, and the second level of bracing is installed.

5. Activation of second strut level: The second strut is activated at a depth of -13 ft.

6. Excavation: Excavation proceeds to -24 ft.

7. Activation of third strut level: The third strut is activated at a depth of -22 ft.

8. Final excavation: Excavation proceeds to the final depth.


a)
a)

b)
b)

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


7. ANALYSIS ASSUMPTIONS


In this example, the following assumptions were made:


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

  • Surcharge pressure: applied as a field load.

  • LEM:

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

    • Driving pressures: FHWA apparent.

    • Optimization of wall embedment (D) for FS = 1.5.

  • N-L and FEM: The friction between wall and soil equivalent to 33% of the friction angle.

  • FEM: medium refinement of finite element mesh.


7. DEEPEX ANALYSIS RESULTS


This section presents the results of the analysis, including plots of horizontal earth pressures, bending moment diagrams, horizontal displacements, and shear strength distributions for each method, as detailed below. As result of the optimization of the wall embedment for a minimum FS of 1.5, D = 17.5 ft.


A. Limit Equilibrium Analysis -(show moments and horizontal pressures (Figure 7), shear stress (Figure 8), for apparent FHWA pressure as driving pressure (the more unfavorable for the support solicitation).


LEM, moments and horizontal pressures.
Figure 7 – LEM, moments and horizontal pressures.

LEM, shear stresses and wall embedment FS
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))


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

Non-linear, shear stresses and displacements.
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)).


FEM, moments and horizontal pressures.
Figure 11 – FEM, moments and horizontal pressures.

FEM, shear stresses and displacements.
Figure 12 – FEM, shear stresses and displacements.

FEM, mesh and horizontal displacement shadings.
Figure 13 – FEM, mesh and horizontal displacement shadings.

FEM, mesh and vertical displacement shadings.
Figure 14 – FEM, mesh and vertical displacement shadings.

8. ANALYSIS SUMMARY & CONCLUSION


This document presents an analysis of a 30-foot-deep braced excavation through a medium dense sand stratum, subjected to a uniform surcharge load of 360 psf on both sides of the ground surface. The support system consists of a braced cofferdam with three levels of struts installed at depths of 3 ft, 13 ft, and 22 ft from the top of the excavation. The stability of the excavation is assessed using three design approaches: the Limit Equilibrium Method (LEM), Non-Linear Analysis (NL), and the Finite Element Method (FEM). All analyses are carried out using the DeepEX software, which facilitates a detailed evaluation of wall and support system performance under the given soil and loading conditions. Table 1 summarizes the results from all three approaches, including maximum horizontal wall displacements, bending moments, shear forces, and associated safety and design check ratios. Table 2 presents the verification of the support system, detailing strut reaction and critical check. These findings underline the practical relevance and robustness of the analytical approaches for deep excavation design in sandy soils.


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).


Table: Critical support results for each method.

Critical support results for each method.

Table notes:

STR Support ratio: Critical structural stress check for support (force demand/structural capacity).

Critical support check: Critical demand/design capacity ratio (structural or geotechnical).


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