Mat foundation design procedure

A mat (raft) foundation is a large, continuous slab that supports the whole building (or several columns) and spreads the load over the full plan area. It is used when soil is weak, when isolated footings would cover more than about half the plan area, or to reduce differential settlement.

Design steps

1. Collect the data: column loads and positions (dead + live, and moments), safe bearing capacity of the soil, grades of concrete and steel, depth of foundation.
2. Find the resultant of all column loads, $\sum P$, and its position $(\bar x, \bar y)$. Choose the plan size of the mat (with edge projections) so that its centroid coincides, or nearly coincides, with the resultant. Eccentricity $e =$ resultant - centroid should be small.
3. Area: $A = \dfrac{\sum P (1 + 0.1)}{q_{a}}$ (10% allowance for self-weight), and check that net upward pressure $$q = \frac{\sum P}{A} \pm \frac{\sum P\, e_x}{Z_y} \pm \frac{\sum P\, e_y}{Z_x} \le q_a, \quad q_{min} \ge 0.$$
4. Choose the method of analysis:
   • Rigid (conventional) method: if the column spacing is less than $1.75/\lambda$ (where $\lambda = \sqrt[4]{k_sB/4E_cI}$), the mat is taken as rigid. Contact pressure is linear. The mat is divided into strips between the column lines, each strip is analysed as a continuous beam under the pressure and the column loads, and the shear and bending moment diagrams are drawn.
   • Flexible method (beam on elastic foundation, or finite element/ plate on springs), when the mat is not rigid.
5. Thickness: determine the depth from punching shear around the heaviest columns (at $d/2$) and one-way shear at $d$ from the face of the column or wall (shear reinforcement is avoided when possible). Check also the bending requirement.
6. Bending moments and reinforcement: calculate positive and negative moments in each strip in both directions; design steel at top and bottom in each direction. Because the soil pressure acts upward and the columns act as supports, the bending is the reverse of a floor slab: bottom steel is needed under the columns and top steel at mid-span between columns. Provide minimum steel of 0.12% each way.
7. Check the development length, the bearing at the column base and the settlement.
8. Detailing: top and bottom mesh in both directions, extra bars at columns, cover 50 mm (75 mm if cast against the soil without blinding), dowels for the column bars, construction joints and waterproofing if below ground water.

A mat can be a plain slab, a slab with beams (ribbed), or a cellular/ box type.