A Comparative Study Using DeepEX Software
Introduction
When designing retaining walls, tunnels, and shoring systems, engineers must accurately calculate the forces exerted by soil on structures. One key parameter in these calculations is the passive earth pressure coefficient, denoted as Kp. This coefficient describes the lateral soil pressure when a structure pushes against the soil until it reaches a state of failure, such as during wall movement in shoring projects or the active stabilization of tunnel walls.
Accurate Kp calculations are crucial because overestimating or underestimating the earth pressure can result in design failures, either due to structural inadequacy or excessive conservatism leading to inflated project costs. In this article, we will explore several established methods for calculating Kp , comparing them in terms of their underlying assumptions and results. More importantly, we will illustrate how our state-of-the-art software, DeepEX, streamlines these calculations and provides invaluable insights for geotechnical design.
Figure 1: Passive Earth Pressures Coefficient (Kp) Methods in DeepEX
1. Understanding the Passive Earth Pressure Coefficient Kp
The passive earth pressure coefficient represents the ratio of the horizontal earth pressure to the vertical pressure (typically represented by the overburden or the weight of the soil). When a retaining structure moves towards the soil mass, the soil tends to resist this movement, and the resulting resistance is known as passive earth pressure. Kp is a critical factor in geotechnical engineering because it directly influences the design of earth-retaining structures, shoring systems, and underground excavations.
There are several established analytical methods to calculate Kp , each with unique assumptions and approaches. Engineers must carefully choose the right method based on the site’s soil conditions, project requirements, and local design codes.
2. Key Methods for Kp Calculation
The methods for determining Kp vary significantly in their assumptions regarding soil behavior, wall friction, cohesion, and wall inclination. Below, we introduce the key calculation methods integrated into DeepEX.
a. Rankine Method
The Rankine method is one of the simplest and most widely used approaches for calculating passive earth pressure. Developed in the mid-19th century, it assumes that soil is a perfectly rigid-plastic material with no cohesion and that the wall is smooth and vertical. This method is based on the theory of soil wedge failure, where the failure plane is a straight line inclined at an angle dependent on the soil’s internal friction angle ϕ\phiϕ. However, it is a conservative method due to its simplicity, especially when dealing with non-vertical walls or soil with cohesion.
b. Coulomb Method
The Coulomb method extends the Rankine theory by accounting for wall friction, wall inclination, and cohesion in the soil. This method uses a wedge analysis where the passive pressure is calculated based on the equilibrium of forces acting on a wedge of soil assumed to fail against the wall. It provides more flexibility in analyzing cases with sloped walls or backfill.
c. Lancellotta Method
The Lancellotta method provides a more advanced approach to calculate passive earth pressure in cohesive soils. It combines the concepts of limit equilibrium and limit analysis, yielding more accurate estimates for certain soils compared to traditional Rankine or Coulomb theories.
d. Caquot-Kerisel Method
The Caquot-Kerisel method is a refined version of Coulomb's method. It introduces corrections for non-horizontal backfill, wall roughness, and other influencing factors. This method is often regarded as more accurate for complex soil-structure interaction problems and is especially favored in the French engineering practice. It produces higher values of Kp, which makes it more conservative in design.
e. NAVFAC DM 7.2 Method
The NAVFAC DM 7.2 method is derived from the Naval Facilities Engineering Command (NAVFAC) design manual, and it is commonly used in U.S. government and military projects. It provides detailed guidelines for earth pressure calculation, particularly for different soil types and loading conditions. NAVFAC DM 7.2 integrates corrections for wall friction, cohesion, and sloped backfill, and it is often used as a conservative method for infrastructure projects.
f. Eurocode 7 (Analytical and Orr Equation)
The Eurocode 7 is a European standard for geotechnical design. It offers both an analytical approach and an empirical formula, known as the Orr equation, for calculating passive earth pressure. Eurocode 7 emphasizes safety and reliability by incorporating partial factors, making it particularly stringent in the design of retaining structures. This method is becoming increasingly popular worldwide due to the global adoption of Eurocodes.
5 Reasons to Choose DeepEX for Your Next Project |
|
3. Comparison of Methods Using DeepEX
The differences in Kp values produced by these methods can have significant effects on design outcomes, especially for complex projects involving shoring systems or tunnels. To illustrate these differences, we can run simulations using DeepEX, which integrates all the aforementioned methods into its design suite.
DeepEX allows users to quickly switch between methods, offering immediate insights into how each method influences the design. This functionality enables engineers to make informed decisions based on the most appropriate calculation method for the specific project conditions.
Figure 2: Calculation of the Passive Earth Coefficient Kp with different methods in DeepEX
Sample Comparison Simulation Results
Let’s run a comparison for a retaining wall with the following parameters:
Soil Type: Sand with an internal friction angle ϕ=30deg and wall friction 33% of soil friction angle.
Wall Inclination: Vertical
Backfill Slope: Horizontal
Cohesion: 0 kPa (non-cohesive soil)
Method | Kph Value | Relative Conservatism |
Rankine | 3.00 | Low |
Coulomb | 4.08 | High |
Lancellotta | 3.88 | Moderate-High |
Caquot-Kerisel | 3.95 | High |
NAVFAC DM 7.2 | 4.08 | High |
Eurocode 7 (Analytical) | 3.6 | Moderate-High |
Eurocode 7 (Orr) | 3.88 | Moderate-High |
Analysis:As seen from the table above, the Rankine method yields the lowest Kp value due to its simplistic assumptions, making it less conservative. On the other hand, methods like Caquot-Kerisel, NAVFAC, and Eurocode 7 tend to produce higher values, reflecting more conservative designs suited for critical infrastructure projects. DeepEX facilitates quick comparisons like this, allowing engineers to choose the optimal approach based on the project’s risk profile and design specifications.
Figure 3: Active & passive earth pressures in DeepEX – Caquot Kerisel (left) and NAVFAC (right) Kp methods
4. Why DeepEX?
DeepEX simplifies the complex process of calculating passive earth pressure, providing engineers with a user-friendly platform to perform detailed analyses using multiple methods. Here are a few key features that make DeepEX invaluable for geotechnical design:
Comprehensive Method Integration: With methods like Rankine, Coulomb, Caquot-Kerisel, NAVFAC, and Eurocode 7 built-in, engineers can easily explore multiple design scenarios without switching between different tools.
User-Friendly Interface: DeepEX presents complex calculations in an intuitive format, making it accessible to both experienced engineers and those new to geotechnical design.
Real-Time Simulations: Quickly visualize how design changes, such as wall inclination or soil properties, affect the outcome.
Design Validation: DeepEX ensures compliance with global standards like Eurocode 7, which is essential for international projects.
Conclusion
Accurate calculation of the passive earth pressure coefficient Kp is a cornerstone of geotechnical design, particularly in retaining structures and shoring systems. The Rankine, Coulomb, Lancellotta, Caquot-Kerisel, NAVFAC DM 7.2, and Eurocode 7 methods each offer unique approaches to this calculation, and their results can vary significantly depending on the design scenario.
By using DeepEX, engineers can efficiently compare these methods, ensuring that they choose the most appropriate one for their specific project needs. This not only leads to safer, more cost-effective designs but also streamlines the design process, saving time and reducing the potential for errors.
Start exploring the power of DeepEX today and take your geotechnical designs to the next level!
