---
title: "Conventional design of mat foundation"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:mat-conventional-design"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-conventional-design
site: BCT Engineering
---

# Conventional design of mat foundation

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2081 Bhadra, 6 marks; 2079 Bhadra, 6 marks; 2072 Chaitra, 4 marks (asked 3 times)
- Video: [Analysis and Design of Mat/Raft Foundation | Conventional Method | Foundation Engineering](https://www.youtube.com/watch?v=3PWamMNS5EE) — Sudip Dhakal
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-conventional-design
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

Explain the conventional (rigid) method of design/analysis of mat foundation with a neat sketch.

## Short answer

Conventional method assumes mat is perfectly rigid and soil pressure is linear (planar). Compute total load and eccentricities; pressure distribution q = Q/A ± My x/Iy ± Mx y/Ix. Divide mat into strips; adjust column loads and soil reactions to achieve strip equilibrium; then design for shear and moment as a continuous beam.

## Answer

The **conventional (rigid) method** treats the mat as an infinitely rigid body, so the soil pressure follows a straight line (planar) distribution.

#### Assumptions
- The mat is rigid, so its deflection is small compared with the soil's.
- The soil pressure is linearly distributed, with its centroid on the line of action of the resultant of the column loads.

#### Steps
1. **Total load:** $Q = Q_1 + Q_2 + \dots + Q_n$ (column loads, plus mat weight if not included).
2. **Eccentricities:** the resultant lies at $(\bar x, \bar y)$ from the centre; $e_x = \dfrac{\sum Q_ix_i}{Q}$ and $e_y = \dfrac{\sum Q_iy_i}{Q}$. So $M_x = Qe_y$ and $M_y = Qe_x$.
3. **Soil pressure** at any point $(x, y)$:

$$
q = \frac{Q}{A} \pm \frac{M_y\,x}{I_y} \pm \frac{M_x\,y}{I_x}
$$

   with $A = BL$, $I_x = \dfrac{BL^3}{12}$ and $I_y = \dfrac{LB^3}{12}$. Check that $q_{max} \le q_{all}$ and $q_{min} > 0$ (no tension).
4. **Divide into strips:** separate the mat into strips of width $B_1$ in each direction, each strip bounded by the centre lines between columns.
5. **Strip loads:** for a strip of length $L_1$, find the average soil pressure $q_{av}$ (from the pressures at its two ends) and the total soil reaction $q_{av}B_1L_1$. The sum of the column loads on the strip, $\Sigma Q$, is generally not equal to this reaction.
6. **Modify the loads** so the strip is in equilibrium. Take the average load $Q_{av} = \dfrac{\Sigma Q + q_{av}B_1L_1}{2}$. Multiply the column loads by $F_c = \dfrac{Q_{av}}{\Sigma Q}$ and the soil pressure by $F_s = \dfrac{Q_{av}}{q_{av}B_1L_1}$.
7. **Shear force and bending moment diagrams** of the strip loaded with the modified column loads and the soil pressure, treated as a continuous beam.
8. **Design:** reinforcement for the moments, and check for punching (two-way) shear at columns and beam shear, as in IS 456.

```text
 Column loads Q1  Q2  Q3
              v   v   v
        ______________________
        ^^^^^^^^^^^^^^^^^^^^^^   <- q (soil pressure)
```

## Check yourself

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

1. Conventional method assumes:
   A. Mat is rigid, soil pressure planar
   B. Mat is flexible
   C. Soil is springs
   D. Pressure is uniform always
   Answer: A. Centroid of pressure on resultant line. (Key point: Rigid assumption)

2. Soil pressure at (x,y):
   A. Q/A only
   B. Q/A ± My x/Iy ± Mx y/Ix
   C. Q*A
   D. M/Q
   Answer: B. Check qmax <= qall and qmin > 0. (Key point: Pressure formula)

3. Why modify strip loads?
   A. To increase loads
   B. Thickness
   C. Sum of column loads is not equal to soil reaction, so equilibrium is enforced
   D. Punching
   Answer: C. Averaging gives equilibrium. (Key point: Strip modification)

## Related in Foundation Engineering

- [Assumptions of conventional mat analysis](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-assumptions-conventional) — Foundation Engineering, chapter 7
- [Why design a mat foundation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awhy-design-mat) — Foundation Engineering, chapter 7
- [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
- [Compensated foundation and types of mat](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acompensated-foundation-mat-types) — Foundation Engineering, chapter 7, asked 7×
- [Major criteria in foundation design](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afoundation-design-criteria) — Foundation Engineering, chapter 1, asked 4×
- [Define foundation; design criteria](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Adefine-foundation-criteria) — Foundation Engineering, chapter 1, asked 2×

## Related in other subjects

- [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×
- [Steps of grounding mat design](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agrounding-mat-design-steps) — Power Plant Design, chapter 4, asked 5×
- [Step and touch potential in mat design](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Astep-touch-potential) — Power Plant Design, chapter 4
- [OO design cycle vs conventional cycle](https://www.bctengineer.com/question.md?key=semester_6%2Fobject_oriented_analysis_and_design%3Aoo-design-cycle-vs-conventional) — Object Oriented Analysis and Design, chapter 1