Shallow Foundation Design and Settlement Analysis Using MATLAB

Hejintao Huang, Cooper Union for the Advancement of Science and Art, Civil Engineering

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Initial Publication Date: October 10, 2024

Summary

This project-based teaching activity guides students in calculating the ultimate and allowable bearing capacities of shallow foundations using Terzaghi's and General Bearing Capacity Equations for various foundation shapes (strip, square, circular) and soil conditions (drained, undrained, layered soils, rigid base, etc). Students will also compute elastic settlement for granular soils and consolidation settlement for cohesive soils, and visualize the results with MATLAB-generated plots showing the impact of foundation width and soil properties on bearing capacity and settlement. The project aims to improve students' computational and analytical skills by integrating geotechnical engineering concepts with MATLAB programming.

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Learning Goals

In this teaching activity, students will develop a comprehensive understanding of shallow foundation design through numerical simulations, focusing on how various soil profiles impact foundation performance.

Students will evaluate foundation stability under different conditions, including layered soils, rigid bases, slopes, and the effects of the water table. They will learn to distinguish between elastic and consolidation settlement by computing settlement for different soil types and addressing multi-layered soil conditions to assess total foundation settlement.

Students will assess the accuracy and reliability of their MATLAB codes by comparing the simulation results with their homework problems, which contain distilled soil profiles for validation.

As part of the learning process, students will enhance their analytical skills by interpreting simulation results. They will analyze factors influencing foundation behavior, synthesize data, and apply computational models to practical design challenges. This experience will also prepare them for senior design projects, which involve more complex boring data and soil conditions.

Context for Use

This teaching activity is designed for fourth-year undergraduate civil engineering students in schools offering Introduction to Foundation Engineering as either a required or elective course, as well as for institutions where it is offered as a graduate-level course. The assignment is a 3-4 week, project-based activity that supplements the instruction of shallow foundation design, providing students with a practical, hands-on experience to enhance their understanding of theoretical concepts. It also serves as a useful complement to traditional homework assignments.

Students are expected to have basic proficiency in MATLAB (working with arrays, functions, and plotting) and a foundational understanding of geotechnical engineering principles such as soil properties, bearing capacity, and settlement analysis. The project fits well into both undergraduate and graduate curricula, offering flexibility for adaptation to different class sizes.

Description and Teaching Materials

The materials for this activity are based on the textbook: Principles of Foundation Engineering by Braja M. Das (10th Edition), which provides the fundamental theory and equations for shallow foundation design and settlement analysis. In class, the key equations and concepts will be introduced and discussed, followed by homework assignments to help students understand their application. Students will then develop their own MATLAB scripts to automate calculations for bearing capacity and settlement. Finally, students will run their scripts using distilled homework soil profiles to validate their answers. All required materials, including slides, homework problems, and guidance for developing MATLAB scripts, will be provided to the students. The project is fully self-contained, and no additional materials are needed beyond those supplied in class, provided the institution has a MATLAB license.

Teaching Notes and Tips

Because this project runs parallel to lecture instruction and homework, it's beneficial for instructors to dedicate a session to reviewing how to code with MATLAB and provide guidance on the script-writing process. This session will help students confidently approach the project by learning how to translate theoretical equations into functional MATLAB code. Given that this is a 3-4 week project, instructors should carefully design the assignment to avoid overwhelming students with excessive work. Breaking the project into manageable parts that align with lecture progress is recommended, allowing students to develop the code in stages as new topics are introduced.


Assessment

Students will be given two main deliverables. These include: 1) weekly submission of their MATLAB script that correctly calculates bearing capacity and settlement for different soil profiles, and 2) a final written report analyzing their results, including a comparison between their MATLAB simulations and homework problems with distilled soil profiles.

Each component will be graded based on accuracy, completeness, and the quality of analysis. The MATLAB scripts will be checked for correct functionality, and the plots will be evaluated for clarity and appropriate interpretation of results. Additionally, students can earn extra credit if they incorporate the Standard Penetration Test into their foundation design calculations to demonstrate the ability to handle real-world data in their simulations.

References and Resources

Textbook: Das, B.M. (2024). Principles of Foundation Engineering, 10th Edition. Cengage Learning, Boston, MA, 874 p.