--- title: "Development of classical bearing capacity theories" subject: "Foundation Engineering" chapter: 6 key: "semester_5/foundation_engineering:classical-bearing-theories-development" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/classical-bearing-theories-development site: BCT Engineering --- # Development of classical bearing capacity theories Foundation Engineering · Chapter 6: Bearing Capacity and Settlement of Shallow Foundations - Asked in: 2080 Bhadra, 6 marks - Video: [The History of Geotechnical Engineering.](https://www.youtube.com/watch?v=Qs2pOGPOorY) — GeoTechs With Clemency - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/classical-bearing-theories-development - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6 ## Question Explain the development of different classical bearing capacity theories. ## Short answer Rankine (1857) used earth pressure, ignoring width and base friction. Prandtl (1921) added a cohesion term for weightless soil. Reissner (1924) included surcharge. Terzaghi (1943) added soil weight, a rough base, and shape factors, giving qu = cNc + qNq + 0.5γBNγ. Meyerhof, Hansen, and Vesic later introduced depth, shape, inclination, and other correction factors, refining Nγ values. ## Answer Classical bearing capacity theories were developed step by step. Each author added a term that the previous theory neglected. 1. **Rankine (1857) and Bell.** Based on Rankine earth pressure. The soil below the footing is in active state and the soil beside it in passive state. For cohesionless soil $q_u = \gamma D_f\left(\dfrac{1+\sin\phi}{1-\sin\phi}\right)^2$. Bell (1915) extended it to $c$–$\phi$ soil: $q_u = \gamma D_f N_\phi^2 + 2c\sqrt{N_\phi}(N_\phi + 1)$ with $N_\phi = \tan^2(45^\circ + \phi/2)$. Pauker's method is a similar approach for cohesionless soil. These ignore footing width and base friction. 2. **Prandtl (1921).** Studied punching of a rigid die into a weightless $c$–$\phi$ medium. Found a failure surface with a wedge, a log-spiral fan and a passive zone, giving $q_u = cN_c$ with $N_c = (N_q - 1)\cot\phi$ and $N_q = e^{\pi\tan\phi}\tan^2(45^\circ + \phi/2)$. The footing is on the surface and soil is weightless. 3. **Reissner (1924).** Extended Prandtl to include the **surcharge** $q = \gamma D_f$, adding the $N_q$ term. 4. **Terzaghi (1943).** Added the **weight of soil** ($N_\gamma$ term), a rough base and the effect of shape (square, circular), and gave $q_u = cN_c + qN_q + 0.5\gamma BN_\gamma$. 5. **Meyerhof (1951, 1963).** Included the shear strength of soil above the base, and gave shape, depth and inclination factors. 6. **Hansen (1970) and Vesic (1973).** Further refined the factors for shape, depth, inclination of load, base and ground tilt, with improved values of $N_\gamma$. So the progression is: Rankine (weight and surcharge, approximate) → Prandtl (cohesion) → Reissner (surcharge) → Terzaghi (soil weight, practical form) → Meyerhof, Hansen, Vesic (general equation with correction factors). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What did Prandtl's theory assume about the soil? A. Soil with weight and a surcharge B. Weightless c-phi soil with the footing on the surface C. Purely cohesionless soil with a rough base D. Compressible soil Answer: B. Prandtl gave qu = cNc for a weightless medium with no surcharge. (Key point: Prandtl) 2. What did Reissner add to Prandtl's theory? A. The surcharge term q = gamma*Df (Nq) B. The soil weight term (Ngamma) C. Shape factors D. Inclination factors Answer: A. Reissner added surcharge; Terzaghi later added soil weight. (Key point: Reissner's contribution) 3. What did Terzaghi add in 1943? A. Depth and inclination factors B. Rankine active and passive states C. Soil weight (Ngamma), a rough base and shape effects D. Only the cohesion term Answer: C. Terzaghi gave the practical three-term equation. (Key point: Terzaghi's contribution) 4. What do Rankine's and Bell's theories ignore? A. Soil friction angle B. Surcharge C. Cohesion in Bell's case D. Footing width and base friction Answer: D. They are based on earth pressure states and ignore width and base friction. (Key point: Rankine limitation) ## Close variants set in other exams - [Limitations of classical bearing theories](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aclassical-theory-limitations) — Foundation Engineering, chapter 6, asked 2× ## Related in Foundation Engineering - [Factors affecting bearing capacity; water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abearing-capacity-factors-water-table) — Foundation Engineering, chapter 6, asked 5× - [Mat bearing capacity: cohesive vs cohesionless](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-bc-cohesive-vs-cohesionless) — Foundation Engineering, chapter 7, asked 2× - [Terzaghi's bearing capacity theory](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aterzaghi-theory-assumptions) — Foundation Engineering, chapter 6 - [Skempton's findings on clay bearing capacity](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Askempton-net-safe-bc) — Foundation Engineering, chapter 6 - [Bearing capacity from plate load curve](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abc-from-load-settlement-sand) — Foundation Engineering, chapter 6 ## Related in other subjects - [Methods of improving bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Aimproving-bc) — Building Technology, chapter 2, asked 2× - [Methods of determining bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Abc-determination-methods) — Building Technology, chapter 2, asked 2× - [Soil exploration and improving bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asoil-exploration-improving-bc-nepal) — Building Technology, chapter 2 - [Safe and ultimate bearing capacity, improvement](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Abc-define-improve-066j) — Building Technology, chapter 2