--- title: "12 piles, spacing and diameter, 100% efficiency" subject: "Foundation Engineering" chapter: 8 key: "semester_5/foundation_engineering:pile-group-12-circular-spacing-diameter" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-group-12-circular-spacing-diameter site: BCT Engineering --- # 12 piles, spacing and diameter, 100% efficiency Foundation Engineering · Chapter 8: Pile Foundations - Asked in: 2079 Bhadra, 8 marks - Video: [Numerical on Group Capacity of Pile in Clay](https://www.youtube.com/watch?v=UHjqId4wkvc) — Curious Civil Engineer - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-group-12-circular-spacing-diameter - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-8 ## Question 12 circular piles are arranged in a rectangular pattern with spacing to diameter ratio equal to 3.0 in a purely cohesive soil having unconfined compressive strength $q_u = 80\ \text{kN/m}^2$. The length of the pile is 15 m and taking adhesion factor as 0.85, determine the spacing and diameter of the pile considering the 100% efficiency of pile group. ## Short answer For s/d =3, block capacity exceeds sum of individual piles for any practical diameter, ensuring100% group efficiency. Spacing =3d (e.g.,1.2 m for0.40 m diameter); diameter is chosen based on load. ## Answer **Given:** 12 circular piles in a rectangular (4 × 3) pattern, $s/d = 3.0$, $q_u = 80$ kN/m² so $c_u = 40$ kN/m², $L = 15$ m, $\alpha = 0.85$. Efficiency $= 100\%$ means block capacity $\ge$ sum of individual pile capacities. #### Individual pile (diameter $d$) $$ Q_u = \alpha c_u\pi dL + 9c_u\frac{\pi d^2}{4} = 40\left(40.06\,d + 7.07\,d^2\right) $$ Sum for 12 piles $= 40(480.7\,d + 84.8\,d^2)$. #### Block (4 piles by 3 piles, $s = 3d$) $$ \begin{aligned} B_g &= 2s + d = 7d,\quad L_g = 3s + d = 10d \\ Q_{block} &= 2(B_g + L_g)Lc_u + 9c_uB_gL_g = 40\left(510\,d + 630\,d^2\right) \end{aligned} $$ The block capacity ($510d + 630d^2$) is larger than the sum of individual piles ($480.7d + 84.8d^2$) for every diameter, so the group fails as individual piles and **the efficiency is 100% for any $d$ when $s = 3d$**. The ratio $s/d$ governs, not the diameter. #### Minimum spacing For a general ratio $r = s/d$, $B_g = (2r+1)d$ and $L_g = (3r+1)d$. Setting block $=$ sum gives $$ (150r + 60) + 9d\,(6r^2 + 5r + 1) = 480.7 + 84.8\,d $$ The smallest ratio for 100% efficiency therefore depends on $d$: | $d$ (m) | 0.3 | 0.4 | 0.5 | 1.0 | |---|---|---|---|---| | Minimum $s/d$ | 2.22 | 2.11 | 2.02 | 1.72 | So $s/d = 3$ is satisfactory for all practical diameters. The diameter is then fixed by the load to be carried or practical size. For example, with $d = 0.40$ m: $$ s = 3 \times 0.40 = 1.2\ \text{m},\quad Q_u(\text{one pile}) = 686.2\ \text{kN},\quad Q_{u,group} = 8234\ \text{kN} $$ **Answer: spacing $= 3d$ (for example $s = 1.2$ m with a pile diameter of 0.40 m, centre to centre), which gives an efficiency of 100%.** The smallest spacing that still gives 100% efficiency is about $2.1d$ for $d = 0.40$ m (it falls as the diameter increases). The data given do not fix the diameter, so a practical value of 0.3 to 0.5 m is adopted. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. 100% efficiency means: A. Block capacity is half the sum B. Spacing equals diameter C. Block capacity >= sum of individual pile capacities D. Only end bearing acts Answer: C. The group then fails as individual piles, not as a block. (Key point: Meaning of 100% efficiency) 2. For q_u = 80 kN/m2, the cohesion used is: A. 80 kPa B. 160 kPa C. 40 kPa D. 20 kPa Answer: C. c_u = q_u / 2 = 40 kPa. (Key point: Cohesion from q_u) 3. With s = 3d the block capacity compared with the sum of piles is: A. Smaller for small d B. Larger for every d, so efficiency is 100% C. Equal only at d = 0.4 m D. Cannot be compared Answer: B. 510d + 630d^2 exceeds 480.7d + 84.8d^2 for any d. (Key point: Result for s/d = 3) 4. The data do not fix d because: A. Efficiency depends on L only B. Alpha is unknown C. Spacing ratio, not diameter, governs efficiency D. Diameter must be 1.2 m Answer: C. Efficiency is controlled by s/d; d is chosen from load or practical size (0.3 to 0.5 m). (Key point: What fixes the diameter) ## Related in Foundation Engineering - [Pile spacing for 100% efficiency, 16 piles](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-spacing-100-efficiency-square-30cm) — Foundation Engineering, chapter 8, asked 2× - [Spacing of nine piles for efficiency 1](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-nine-spacing) — Foundation Engineering, chapter 8 - [Pile group 16 piles of 50 cm, efficiency](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-16-piles-50cm) — Foundation Engineering, chapter 8 - [Spacing for 4×5 pile group, block failure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-20-piles-block-failure) — Foundation Engineering, chapter 8 - [Friction pile length, 350 mm, 1200 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afriction-pile-350mm-1200kn) — Foundation Engineering, chapter 8 - [Negative skin friction on 16-pile group](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aneg-skin-friction-group-16-piles) — Foundation Engineering, chapter 8 ## Related in other subjects - [10 m cut in cohesive soil, bedrock 15 m](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acut-10m-cohesive-phi-zero-bedrock) — Soil Mechanics, chapter 11 - [Circular arch 100 m: rolling UDL 25 m, 15 m section](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aarch-circular-100m-rolling-50knm-25m) — Theory of Structures I, chapter 6, asked 2× - [Ideal gas turbine 100 kW: pressure ratio, work, efficiency](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aideal-gas-turbine-100kw-pressure-ratio) — Fundamental of Thermodynamics & Heat Transfer, chapter 6