Footing size from plate load test curve

Given: plate $B_p = 0.3$ m on sand. Net load $Q = 3200$ kN, allowable footing settlement $S_f = 25$ mm, square footing $B \times B$.

The figure could not be read exactly, so the plate readings below are assumed (typical for sand): pressure (kN/m²) 0, 100, 200, 300, 400, 500, 600, 700, 800 against settlement (mm) 0, 1.5, 4, 7.5, 12, 17.5, 24, 33, 45. If your curve differs, repeat the same steps with your own readings.

Method (Terzaghi–Peck, sand)

The settlement of a footing and a plate under the same pressure are related by

$$\frac{S_f}{S_p} = \left[\frac{B(B_p + 0.3)}{B_p(B + 0.3)}\right]^2 = \left[\frac{2B}{B + 0.3}\right]^2 \quad (B_p = 0.3\ \text{m})$$

So for each trial size $B$: the pressure is $q = 3200/B^2$; the plate settlement equivalent to 25 mm is $S_p = 25\left(\dfrac{B+0.3}{2B}\right)^2$; read the plate settlement from the curve at pressure $q$ and compare.

The plate settlement read from the curve equals the required value at $B \approx 3.27$ m (pressure $\approx 299$ kN/m²). At $B = 3.3$ m the curve gives 7.28 mm, which is below the required 7.44 mm, so the footing settles less than 25 mm.

Safety check

The pressure is $\approx 300$ kN/m², which is well below the failure region of the curve (the curve keeps rising smoothly up to 800 kN/m²), so shear failure is not critical. The ultimate capacity of the footing is $q_{up} \times B/B_p$ (about 11 times the plate value), which gives a large factor of safety.

Answer: provide a square footing of about 3.3 m × 3.3 m (pressure $\approx 294$ kN/m², settlement below 25 mm), on the assumed curve.