---
title: "Mat bearing capacity: cohesive vs cohesionless"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:mat-bc-cohesive-vs-cohesionless"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-bc-cohesive-vs-cohesionless
site: BCT Engineering
---

# Mat bearing capacity: cohesive vs cohesionless

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2074 Asoj, 4 marks; 2080 Bhadra, 2 marks (asked 2 times)
- Video: [Shallow Foundation: Numerical on Calculation of Safe Bearing Capacity and Permissible Load](https://www.youtube.com/watch?v=rbDpOzdeCOM) — Curious Civil Engineer
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-bc-cohesive-vs-cohesionless
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

Describe the procedure of determining the bearing capacity of cohesive and cohesionless soil in case of mat foundation. What is the basic difference between them?

## Short answer

Cohesive soil (φ=0): Use Skempton: q_nu = c_u N_c, N_c for square = 6(1+0.2D_f/B) ≤ 9, rectangle adjusted; safe q_ns = q_nu/F. Cohesionless: Use Terzaghi with φ; q_u = q N_q + 0.5γ B N_γ, but settlement governs, use SPT-based Meyerhof formula. Key difference: cohesive q_u independent of width, shear controls; cohesionless q_u increases with width, settlement controls.

## Answer

#### Cohesive soil (clay, $\phi = 0$)
1. Find undrained cohesion $c_u$ (from $q_u/2$ of an unconfined test or a vane shear test).
2. Use **Skempton's** bearing capacity factor: for a square mat $N_c = 6\left(1+0.2\dfrac{D_f}{B}\right)\le 9$, and for a rectangle $N_c = \left(0.84+0.16\dfrac{B}{L}\right)N_{c(sq)}$.
3. Net ultimate capacity $q_{nu} = c_uN_c$; net safe capacity $q_{ns} = q_{nu}/F$ ($F \ge 3$).
4. Check that the net pressure $\left(\dfrac{Q}{A} - \gamma D_f\right) \le q_{ns}$ and then check consolidation settlement.

#### Cohesionless soil (sand, gravel)
1. Find $\phi$ from SPT $N$ (corrected for overburden) or direct tests.
2. Use Terzaghi's equation with shape factors, $q_u = qN_q + 0.5\gamma BN_\gamma$ (use $\gamma'$ and correction factors if the water table is near).
3. Obtain the safe pressure: $q_s = q_u/F$ with $F = 3$.
4. As $q_u$ is very large for a wide mat, the **allowable settlement governs**. Use the SPT-based formula $q_{na} = 19.16\,N\,F_d\,\dfrac{S_a}{25.4}$ (Meyerhof, for mats) with $F_d = 1 + 0.33D_f/B \le 1.33$.

#### Basic difference
| Point | Cohesive soil | Cohesionless soil |
|---|---|---|
| Strength parameter | $c_u$ ($\phi=0$) | $\phi$ (from $N$) |
| Effect of width $B$ | None on $q_u$ | $q_u$ increases with $B$ |
| Controlling criterion | Shear or consolidation settlement | Settlement (usually) |
| Method | Skempton | Terzaghi/Meyerhof, SPT |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which method and strength parameter are used for the bearing capacity of a mat on cohesive soil (phi = 0)?
   A. Skempton's Nc with undrained cohesion cu
   B. Terzaghi's Nq with friction angle phi
   C. Meyerhof's SPT formula with N value
   D. Rankine's Kp with unit weight
   Answer: A. For clay the strength is cu (phi = 0) and Skempton's factor Nc gives q_nu = cu Nc. (Key point: Skempton for clay)

2. For a wide mat on sand, which criterion usually governs the design?
   A. Shear failure, since qu is small
   B. Allowable settlement, since qu is very large
   C. Frost depth
   D. Water content of the sand
   Answer: B. qu in sand increases with width B and becomes very large for a mat, so settlement governs. (Key point: Controlling criterion in sand)

3. How does the width B of the foundation affect ultimate bearing capacity in the two soils?
   A. Increases it in clay, none in sand
   B. Increases it in both
   C. No effect in clay, increases it in sand
   D. No effect in either
   Answer: C. In clay (phi = 0) the 0.5 gamma B N_gamma term vanishes so B has no effect, while in sand qu rises with B. (Key point: Effect of width)

4. For a square mat, Skempton's factor is Nc = 6(1 + 0.2 Df/B). What upper limit applies?
   A. 5
   B. 9
   C. 14
   D. No limit
   Answer: B. Nc is limited to 9 (reached at Df/B = 2.5). (Key point: Skempton Nc limits)

## Related in Foundation Engineering

- [Active pressure on wall, cohesive soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acohesive-wall-pressure-diagram) — Foundation Engineering, chapter 3
- [Soil pressure under rigid mat with column loads](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-rigid-soil-pressure-columns) — Foundation Engineering, chapter 7
- [Mat 8 m × 10 m, Skempton net safe pressure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-8x10-skempton) — Foundation Engineering, chapter 7
- [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×
- [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 determining bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Abc-determination-methods) — Building Technology, chapter 2, asked 2×
- [Factors affecting foundation design, improving bearing capacity](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Afactors-design-improve-bc) — Building Technology, chapter 2
- [Mat foundation design procedure](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Amat-foundation-design-procedure) — Design of RCC Structure, chapter 11, asked 3×
- [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