--- title: "Circular footing 1 m dia, 1000 kN" subject: "Foundation Engineering" chapter: 6 key: "semester_5/foundation_engineering:circular-footing-1m-1000kn" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-1m-1000kn site: BCT Engineering --- # Circular footing 1 m dia, 1000 kN Foundation Engineering · Chapter 6: Bearing Capacity and Settlement of Shallow Foundations - Asked in: 2073 Shrawan, 4+8 marks - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-1m-1000kn - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6 ## Question How do you differentiate whether there will be general or local shear failure at your site? An engineer wants to construct a circular footing of 1 m diameter to transfer the load of 1000 kN with the safety factor of 2.5 to a soil strata with an angle of shearing resistance $30^\circ$, cohesion $10\ \text{kN/m}^2$ and unit weight of $18\ \text{kN/m}^3$. Suggest the engineer what should be the depth of the footing. Take Terzaghi's bearing capacity factors $N_c$, $N_q$ and $N_\gamma$ as 37.2, 22.5 and 19.7 respectively. ## Short answer Differentiate by soil density/stiffness: general shear for dense sand (SPT N>30) or stiff clay with sharp peak; local shear for loose/soft soil, use reduced parameters. For the footing: area 0.785 m2, applied stress 1273 kN/m2, ultimate 3183 kN/m2, solving Terzaghi gives Df ≈ 6.4 m. ## Answer #### Part 1: General or local shear failure at a site The mode depends on the stiffness and compressibility of the soil. - **Sand:** relative density $D_r > 70\%$ (SPT $N > 30$) gives general shear. $D_r < 20\%$ (loose, $N < 10$) gives punching. In between, local shear. - **Clay:** stress–strain curve from an unconfined or triaxial test. A sharp peak at a small strain (below about 5%) means general shear (stiff clay). A strain at failure of about 20% or more with no peak means local or punching shear (soft clay). - **Plate load test:** a clear breaking point in the load–settlement curve indicates general shear. - For local shear, Terzaghi reduces strength: $c' = \tfrac{2}{3}c$ and $\tan\phi' = \tfrac{2}{3}\tan\phi$, and uses $N_c', N_q', N_\gamma'$. #### Part 2: Depth of footing **Given:** circular footing $B = 1$ m, $Q = 1000$ kN, FS = 2.5, $\phi = 30^\circ$, $c = 10$ kN/m², $\gamma = 18$ kN/m³, $N_c = 37.2$, $N_q = 22.5$, $N_\gamma = 19.7$ (general shear assumed). $$ \begin{aligned} A &= \frac{\pi}{4}(1)^2 = 0.7854\ \text{m}^2 \\ q_{applied} &= \frac{1000}{0.7854} = 1273.2\ \text{kN/m}^2 \\ q_u &= 2.5 \times 1273.2 = 3183.1\ \text{kN/m}^2 \end{aligned} $$ Terzaghi (circular): $q_u = 1.3cN_c + \gamma D_fN_q + 0.3\gamma BN_\gamma$ $$ \begin{aligned} 1.3 \times 10 \times 37.2 &= 483.6 \\ 0.3 \times 18 \times 1 \times 19.7 &= 106.4 \\ 3183.1 &= 483.6 + 106.4 + 18 \times 22.5\,D_f \\ D_f &= \frac{2593.1}{405} = 6.40\ \text{m} \end{aligned} $$ **Answer: depth of footing $\approx 6.4$ m.** Since $D_f/B = 6.4 \gg 1$, the footing is really deep and the shallow-footing equation is only an approximation; a larger diameter (for example 2 m) would give a much shallower foundation, which is the practical alternative. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. General shear in sand occurs when: A. Dr < 20% B. N < 10 C. Dr > 70% (SPT N > 30) D. Dr = 30% Answer: C. Dense sand gives general shear. (Key point: Sand classification) 2. Terzaghi's reduction for local shear: A. c' = c/2 B. phi' = phi/2 C. no change D. c' = 2c/3, tan phi' = 2 tan phi/3 Answer: D. Reduced strengths give lower N factors. (Key point: Local shear) 3. Why is the answer unreasonable? A. Df/B = 6.4 is a deep footing, so a larger diameter is practical B. Df is negative C. B too large D. FS too low Answer: A. Shallow equation only approximate. (Key point: Result) ## Related in Foundation Engineering - [General, local and punching shear failure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amodes-shear-failure) — Foundation Engineering, chapter 6, asked 4× - [Circular footing depth, 2000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-depth-2000kn) — Foundation Engineering, chapter 6 - [Circular footing on stiff clay, water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-stiff-clay) — Foundation Engineering, chapter 6 - [Square footing under eccentric load, min depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-eccentric-2000kn) — Foundation Engineering, chapter 6 - [Square footing size in clay, 750 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-clay-750kn) — Foundation Engineering, chapter 6 - [Trench bottom heave safety factor](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atrench-heave-rock) — Foundation Engineering, chapter 4 ## Related in other subjects - [Footing with load transfer check, 1000 kN](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-with-load-transfer-check-1000) — Design of RCC Structure, chapter 11 - [RC wall footing, 1000 kN total load](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arc-wall-footing-1000-kn-total) — Design of RCC Structure, chapter 11 - [Footing for 1600 kN with shear check](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Afooting-for-1600-kn-with-shear) — Design of RCC Structure, chapter 11 - [Normal, shear, bearing stress and factor of safety](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Astress-types-factor-of-safety) — Strength of Materials, chapter 1