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Apparent Earth Pressures in Deep Excavations


Deep excavation projects pose significant engineering challenges, requiring careful consideration of soil-structure interaction to ensure safety and stability. In the pursuit of better understanding the effect of lateral earth pressures that are typically applied on deep excavation, this article examines two major apparent earth pressure diagram approaches:

- FHWA apparent earth pressures

- Peck 1969 apparent earth pressures

The article presents these apparent pressure methods for deep excavations and compares results for different models.

The results are also contrasted against nonlinear and finite elements methods.


Active and passive lateral earth pressure diagrams are typically used in the design of cantilever deep excavations with the classical limit equilibrium approach. Using apparent earth pressures instead of active soil pressures in deep excavations with supports is often recommended due to the following reasons:

1. Conservative Design:

Apparent earth pressures generally provide a conservative approach to deep excavation design. Deep excavations however involve complex soil-structure interaction, and predicting soil behavior accurately can be challenging. Active soil pressures assume that the soil behind the retaining structure is fully mobilized, exerting the maximum pressure on the structure. However, in reality, soil behavior can be variable and may not reach the fully active state. By using apparent earth pressures, designers take a more cautious approach, accounting for potential variations and uncertainties in soil behavior.

2. Safety Margins:

Apparent earth pressures incorporate safety margins by considering both active and passive soil pressures. While active soil pressure acts in the outward direction, passive soil pressure acts inwards against the retaining structure. By considering both, apparent earth pressures provide a more balanced approach, accounting for potential soil movements and reducing the risk of structural failure.

3. Flexibility of Support Systems:

Deep excavations with supports often utilize flexible support systems such as soldier piles, sheet piles, or secant piles. These systems may experience temporary or permanent deformations due to soil movements. Apparent earth pressures consider the potential for these deformations, allowing for a more realistic analysis of the structural response to soil loads. This approach helps engineers design appropriate support systems that can accommodate soil movements without compromising safety.

4. Construction Stages:

Deep excavations are typically constructed in stages, with the installation of supports followed by excavation. During construction, the behavior of the soil may change due to groundwater conditions, soil disturbance, or other factors. Apparent earth pressures account for these changes by considering the actual conditions at each construction stage. This allows engineers to assess the stability of the excavation and the adequacy of the support system throughout the construction process.


To meet the demands of modern construction projects, engineers require advanced software that offers a comprehensive range of apparent earth pressure methods. DeepEX, our cutting-edge shoring design software, rises to this challenge, equipping engineers with a suite of apparent earth pressure methods that facilitate rapid analysis and direct comparisons with more sophisticated approaches like Finite Element Analysis and Soil Springs.

DeepEX software includes a long series of methods for the design of deep excavations (active pressures, active x Load Factor, At-Rest, Peck 1969, FHWA, German EAB Apparent, AASHTO 17 (GSBTW-2), CTA 2017 (Chicago Transit Adj.

Construction Manual), WMATA, New York City DEP and more. The following paragraphs focus on two major approaches that are used globally (FHWA and Peck 1969 apparent earth pressure diagrams).

- FHWA Apparent Earth Pressures

The Federal Highway Administration (FHWA) apparent earth pressure diagrams have become an essential resource for designing vertical flexible retaining walls in transportation projects. These diagrams offer a practical approach to estimate lateral earth pressures, considering soil type and the number of bracing supports.

FHWA diagrams are actually trapezoidal earth pressure diagrams derived from active earth pressures multiplied by a factor of 1.1 to 1.3 (and 0.2 to 0.4 for undrained clays).

FHWA apparent earth pressure diagrams serve as a convenient and efficient tool for preliminary design calculations.

By providing trapezoidal diagrams based on active earth pressures and applicable factors, engineers can quickly assess the lateral forces acting on retaining walls.

The soil-specific recommendations and brace support considerations allow for tailored designs that accommodate the specific project requirements.

Despite their practicality, FHWA apparent earth pressure diagrams have limitations that must be acknowledged.

One critical limitation is the assumption of zero earth pressure at the excavation base. In reality, the soil's lateral forces do not necessarily reduce to zero at that level.

Neglecting the lateral pressures at subgrade can lead to an inadequate wall embedment design, potentially compromising the overall stability of the excavation.

To overcome the limitations of FHWA apparent earth pressure diagrams, engineers should complement their preliminary designs with more advanced and non-linear analysis methods. Techniques such as Finite Element Analysis (FEA) or numerical modeling allow for a more comprehensive understanding of soil-structure interaction, accounting for the complexities and variations in soil behavior.

Non-linear solutions provide a more accurate representation of lateral forces, considering factors like soil arching, wall flexibility, and construction sequence effects.

Figure 1: FHWA Apparent Earth Pressures Diagram for a Multibraced Excavation Model

Figure 2: Soil pressures, Moments & Support Reactions (Active VS FHWA Apparent pressures)

Figure 3: Soil pressures, Moments & Support Reactions (FHWA Apparent pressures VS NonLinear Analysis)

Figure 4: Soil pressures, Moments & Support Reactions (FHWA Apparent pressures VS Finite Element Analysis)

- Peck 1969 Apparent Earth Pressures

The Peck pressure diagrams, introduced by Karl Terzaghi and further refined by Professor Ralph B. Peck in 1969, have revolutionized deep excavation design by offering valuable insights into lateral earth pressures in multilevel braced excavations.

While active and passive earth pressure theories are suitable for simple cases, the complexities of deep excavations demand a more sophisticated approach.

In multilevel braced excavations, where economical designs are crucial, cantilever walls typically reach only shallow depths (around 15ft), necessitating the use of bracing systems to provide stability and support.

Professor Ralph B. Peck's seminal publication in geotechnical engineering presented a series of case studies from Chicago's metro, where measurements of bracing loads in strutted excavations were conducted.

Peck's observations revealed that the measured maximum bracing reactions deviated from predictions based on active or at-rest earth pressure theories.

Through extensive back calculations, Peck noted that upper struts experienced heavier loads than anticipated by active theory, while lower level struts bore less load compared to active pressures.

As a result, Peck proposed the concept of "Apparent" earth pressures, which served as a novel means to determine maximum strut reactions in multilevel braced excavations. By incorporating these apparent earth pressure diagrams into deep excavation design, engineers gain a more comprehensive understanding of lateral forces, enabling the development of stable, cost-effective, and efficient support systems.

Figure 5: Peck Apparent Earth Pressures Diagram for a Multibraced Excavation Model

Figure 6: Soil pressures, Moments & Support Reactions (Active VS Peck Apparent pressures)

Figure 7: Soil pressures, Moments & Support Reactions (Peck Apparent pressures VS NonLinear Analysis)

Figure 8: Soil pressures, Moments & Support Reactions (Peck Apparent pressures VS Finite Element Analysis)


Overall, using apparent earth pressures in deep excavations with multiple supports provides a conservative and realistic design approach, accounting for uncertainties in soil behavior, safety margins, support system flexibility, and construction stages.

It helps ensure the stability and structural integrity of the excavation, reducing the risk of failures or excessive deformations.

DeepEX shoring design software is a game-changer in the field of deep excavation engineering. By offering a series of apparent earth pressure methods, engineers gain a holistic understanding of lateral forces on retaining structures.

The software's speed, efficiency, and direct comparison with advanced methods make it an indispensable tool for optimizing deep excavation designs.

With DeepEX, engineers can confidently tackle the complexities of deep excavation projects, delivering safe, stable, and cost-effective solutions that stand at the forefront of modern construction practices.


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