How to Calculate Coulomb Earth Pressure: Step-by-Step Retaining Wall Example

Learn how to apply Coulomb's Theory to calculate Active and Passive Earth Pressure for a retaining wall. This step-by-step example covers the complex formulas, account for wall friction, soil properties, and backfill slope. 00:00 - Introduction to Coulomb's Earth Pressure Theory 00:08 - Retaining Wall Example Parameters (Soil Properties & Height) 00:33 - Active vs. Passive Pressure Formulas 01:05 - Understanding the Coefficients ($K_a$ and $K_p$) 01:25 - Defining Variables: Friction Angle, Drainage & Effective Stress 01:58 - Defining Wall Geometry: Angle and Wall Friction 03:05 - Part 1: Step-by-Step Active Pressure Calculation 04:28 - Explaining the Sloping Backfill Angle 05:39 - Final Active Pressure Result (101.2 kPa) 06:58 - Part 2: Step-by-Step Passive Pressure Calculation 07:05 - Scenario 2: Calculation with Zero Slope and Vertical Wall 08:27 - Final Passive Pressure Result (1244.3 kPa) 08:52 - Summary and Conclusion In this video, we cover: Defining all variables Calculating the Active Earth Pressure Calculating the Passive Earth Pressure Real-world application with a worked example In this video, I explain how to estimate Coulomb’s active and passive earth pressures acting on a retaining wall using a clear, worked example. This is a core topic in soil mechanics and geotechnical engineering, essential for the design of retaining walls, excavations, and earth‑support systems. We step through the theory, parameters, and formulas, and then apply them numerically so you can clearly see how active and passive pressures are calculated in practice. 🔹 Problem Setup Backfill soil: Sand Unit weight (γ): 20 kN/m³ Friction angle (φ): 30° Wall height (H): 5 m No cohesion (c = 0) Dry backfill (no groundwater pressure) Coulomb earth pressure theory 🔹 What You’ll Learn in This Video ✅ Difference between active and passive earth pressure ✅ Meaning of earth pressure coefficients Ka and Kp ✅ How wall and soil geometry affect earth pressures ✅ Role of: Soil friction angle (φ) Wall friction (δ) Wall inclination (θ) Backfill slope angle (α) ✅ Why active pressure is much smaller than passive pressure ✅ How to apply Coulomb’s formulas correctly ✅ Practical tips for using Excel spreadsheets to avoid calculation errors 🔍 Key Results from the Example 📉 Active Earth Pressure Coefficient Ka ≈ 0.45 Resulting active pressure ≈ 101 kPa 📈 Passive Earth Pressure Coefficient Kp ≈ 4.98 Resulting passive pressure ≈ 1244 kPa ⚠️ Key takeaway: Passive pressure can be an order of magnitude larger than active pressure, but it is not always fully mobilized in practice, which is why careful engineering judgment is required in design. 🎓 Ideal for: Civil & geotechnical engineering students Soil mechanics and retaining wall design courses Exam preparation Engineers revising earth pressure theories 👉 Watch till the end to clearly understand how active and passive pressures are computed and why they differ so much. 📌 Like, subscribe, and share for more clear, practical geotechnical engineering tutorials. #EarthPressure #CoulombTheory #RetainingWalls #SoilMechanics #GeotechnicalEngineering #CivilEngineering Coulomb's earth pressure theory assumes a planar failure surface in cohesionless (sand) backfill. This video explains how to estimate the active and passive pressure acting on a retaining wall. The earth pressure against the retaining wall can then be easily analyzed and approximated. The theory considers the friction angle of soil, the retaining wall geometry, and the friction between the retaining wall and the backfill. The Coulomb's earth pressure method is commonly used in soil mechanics and geotechnical engineering to estimate the stability of earth structures in civil engineering projects. #engineering #civilengineering #geotechnicalengineering #soilmechanics Rankine passive and active pressures are explained in these videos    • Rankine Active and Passive Pressures actin...      • Rankine Active and Passive Pressures on Re...