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# Exploring Wedge Analysis Methods for Deep Excavations

## Culmann's Approach vs. Automatic Search Method

### Introduction

In geotechnical engineering, the calculation of lateral earth pressures on excavation walls supporting slope surfaces is crucial for ensuring the stability of structures. While conventional methods like Coulomb's approach serve well for simple scenarios with level surfaces or single slope angles, they may fall short when faced with complex stratigraphies and irregular surfaces. In such cases, employing a wedge analysis approach becomes `imperative. This article delves into two prominent methods used for this purpose: Culmann's approach and the Automatic Search method. We will explore the principles behind each method and illustrate their implementation using DeepEX - a comprehensive shoring design software.

Figure: Examined wedges and calculated soil pressures in DeepEX software

### 1. Culmann's Approach vs. Automatic Search Method

Culmann's Method:

Culmann's method, named after the Swiss engineer Carl Culmann, is a classical approach used for analyzing the stability of slopes and determining the pressure distribution on retaining walls. It assumes that the active earth pressure acts as a series of triangular pressure distributions, with the height of each triangle equal to the height of the retained soil at each level. This method simplifies the calculation process but may not capture the actual pressure distribution accurately, especially for complex geometries.

Automatic Search Method:

The Automatic Search method, also known as the "limit equilibrium method" or "slice method," is a more advanced technique for analyzing the stability of slopes and determining the pressure distribution on retaining walls. Instead of assuming a specific pressure distribution, this method iteratively searches for the critical slip surface within the slope by evaluating the equilibrium of forces and moments. By considering different potential failure surfaces, it provides a more comprehensive analysis of stability conditions. This method is computationally intensive but offers greater accuracy, especially for irregular geometries and complex soil conditions, and it commonly requires more computational effort and specialized software tools like DeepEX for implementation.

In comparison:

Culmann's method is relatively simple and straightforward to apply but may not provide accurate results for all scenarios, particularly for non-homogeneous soils or irregular geometries.

The Automatic Search method is more rigorous and can handle complex situations more effectively by considering various potential failure surfaces. However, it requires more computational effort and may be more challenging to implement without appropriate software tools.

In summary, while Culmann's method offers simplicity and ease of use, the Automatic Search method provides greater accuracy and flexibility, particularly for complex situations. The choice between the two depends on the specific requirements of the analysis and the available computational resources.

### 2. Case Study: Illustrating Wedge Analysis Methods in DeepEX Software

Let's consider a real-world scenario where a deep excavation is required for a construction project. Using DeepEX software, we can input the site's soil properties, excavation geometry, and support system parameters. We can then compare the results obtained using Culmann's approach and the Automatic Search method. DeepEX provides comprehensive visualization tools and analysis capabilities, allowing engineers to make informed decisions regarding excavation wall support design.

- Case Study: Model Description

In the forthcoming paragraphs, we will examine and compare the two analyzed methodologies as they are applied to a deep excavation model featuring secant piles braced by a single row of pipe struts, supporting a 20-feet deep excavation, in proximity to a bench surface. The following tables present the soil properties and stratigraphy, as well as the structural section properties for the walls and supports.

Table: Soil Properties and Stratigraphy

 Soil Top El. Description Total Unit Weight Bulk Unit Weight Friction Angle C’ (-) (ft) (-) (pcf) (pcf) (deg) (psf) F 10 Fill - Sand 125 120 32 0 S1 -5 Medium Dense Sand 130 125 34 0 GT -30 Glacial Till 135 130 36 150

Table: Wall Section Properties

 Wall Type Pile Diameter Wall Spacing Steel Section Concrete Material Steel Material Secant Piles 2.2 ft 3.5 ft W21X73 3 ksi Concrete A50 Steel

Table: Support Properties

 Elevation Pile Type Pile Section Horizontal Spacing Steel Material -6 ft Steel Pipes PP20x0.5 20 ft A50 Steel

- Model Simulation in DeepEX

DeepEX software facilitates the simulation, analysis, and optimization of any deep excavation model within minutes. With its intuitive graphical interface, users can swiftly modify structural sections for walls and supports, and visually construct the model in the interactive workspace for each construction stage. Additionally, DeepEX provides Model Wizards and implements voice and type commands, enabling the rapid generation of deep excavation models in mere seconds. The subsequent figures depict the dialogs for wall and support section properties within DeepEX, alongside options for inputting boring and soil properties, as well as the functionality to quickly generate the soil bench surface. Lastly, we showcase the generated construction stages pertinent to the presented case study.

Figure: Soil properties and stratigraphy in DeepEX

Figure: Automatic bench surface creation options in DeepEX

Figure: Wall properties in DeepEX – Wall depth, position and structural section

Figure: Support properties in DeepEX – Strut elevation, spacing and structural section

Figure: Excavation near a bench surface - Construction stages in DeepEX

- Culmann’s Method: Settings and analysis results in DeepEX

The following figures illustrate the Culmann’s method options in DeepEX software, as well as the calculated soil pressure diagrams and the corresponding wall moment and shear diagrams and the support reaction for the examined scenario.

Figure: Culmann’s method options in DeepEX software

Figure: Culmann’s method - Calculated soil pressures and wall moments in DeepEX (Stage 3)

Figure: Culmann’s method - Calculated wall shear and support reactions in DeepEX (Stage 3)

- Automatic Search Method: Settings and analysis results in DeepEX

The following figures illustrate the Automatic search method options in DeepEX software, as well as the calculated soil pressure diagrams and the corresponding wall moment and shear diagrams and the support reaction for the examined scenario.

Figure: Automatic search method settings in DeepEX

Figure: Automatic search method - Calculated soil pressures and wall moments in DeepEX (Stage 3)

Figure: Automatic search method - Calculated wall shear and support reaction in DeepEX (Stage 3)

Conclusion:

The ability to swiftly assess different wedge analysis methods like Culmann's approach and the Automatic Search method is invaluable for geotechnical design engineers. Having access to specialized software like DeepEX streamlines the process, offering a range of alternatives and facilitating efficient decision-making. By leveraging such tools, engineers can ensure the stability and safety of excavation projects, even in the face of complex geological challenges.

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