Differential Settlement of a School Block Founded on an Old Pond Fill
A three-storey school building with isolated footings 2.0 m x 2.0 m founded at 1.5 m depth has developed diagonal cracks at the corners of the ground-floor walls, and a differential settlement of 45 mm has been measured between the two ends over 18 m, four years after construction. The borelog shows 0–1.5 m loose fill (N = 4); 1.5–5.5 m soft to medium clay (Cc = 0.35, e0 = 1.10, Cv = 1.2 m²/year, effective overburden at mid-depth = 65 kPa); below 5.5 m dense sand. An old map shows a demolished pond covering the northern third of the site. The footing load is 600 kN service, and the designer used an allowable bearing pressure of 120 kPa 'from the SPT N-value' without a settlement check.
1. Compute the consolidation settlement of the clay layer under a typical footing and test the adequacy of the 120 kPa allowable bearing pressure.
Read the worked answer
Step 1 - Applied and net pressure. Gross contact pressure = 600/(2 x 2) = 150 kPa. Overburden removed at 1.5 m (fill, γ ≈ 18 kN/m³) = 27 kPa. Net pressure increase qn = 150 − 27 = 123 kPa.
Step 2 - Stress increment at the clay mid-depth. Mid-depth is 3.5 m below ground, i.e. z = 2.0 m below the footing base. Using 2:1 spread: Δσ = qn x B²/(B + z)² = 123 x 4/(4 x 4) = 30.8 kPa.
Step 3 - Consolidation settlement. S = [Cc H/(1 + e0)] log10[(σ′0 + Δσ)/σ′0] = [0.35 x 4000/2.10] x log10(95.8/65) = 667 x 0.168 = 112 mm.
Step 4 - Test the SBC. 112 mm is far beyond the 75 mm normally permitted for isolated footings on clay, and the measured 45 mm at four years is entirely consistent with this once partial consolidation is allowed for (see next task).
Judgement. The 120 kPa 'from the N-value' is a bearing-capacity figure and is irrelevant here: bearing capacity is not the problem - the clay is nowhere near shear failure. In a soft clay the design is governed by settlement, and an SPT N-value in clay correlates poorly with compressibility and not at all with Cc or Cv. The allowable pressure should have been back-calculated from a permissible settlement, which would have given a much lower value or demanded a raft/piles. The 120 kPa is unconservative by a factor of roughly 1.5 on settlement alone, and the design should be treated as deficient rather than marginal.
2. Explain the pattern of damage using the site history, and estimate how much settlement is still to come.
Read the worked answer
Why differential. The northern third of the site is a demolished pond. Pond fills are heterogeneous, often organic, with a much higher e0 and Cc than the natural clay and with secondary compression continuing for years. The northern footings therefore sit on a thicker, more compressible sequence than the southern ones, and they also have a deeper zone of fill below the founding level. Over 18 m the resulting tilt is fully capable of producing the 45 mm differential, and the diagonal cracking at wall corners is the classic signature of a stiff wall on a tilting foundation: cracks open on the tensile diagonal and are widest at the corners of openings.
How much is left. Taking single drainage (dense sand below, relatively impermeable fill above), H = 4 m: T = Cv t/H² = 1.2 x 4/16 = 0.30, which corresponds to U ≈ 0.61. Settlement expected by year 4 = 0.61 x 112 = 68 mm, against 45 mm measured - the same order, and the shortfall is readily explained by the footing being stiff and the pressure bulb spreading, so the 2:1 assumption overestimates the increment somewhat. Residual = 112 − 45 = ≈ 65 mm still to occur, of which a good part is secondary compression in the pond fill and will never be fully arrested.
Judgement. The building is still settling. Cosmetic repairs now will simply re-crack, and the crack widths will keep growing; that is the crucial point for the client, who will otherwise ask only for plastering.
3. Recommend a remedial strategy and list the additional investigation you would order before any work starts.
Read the worked answer
Investigation first - the diagnosis must be confirmed physically, not inferred from one borelog.
- Two or three additional boreholes located on the pond-filled northern third and on the southern third, with undisturbed sampling of the clay and consolidation tests (Cc, Cv, σ′p) and organic content on the fill; the single borelog is not enough to explain a 45 mm differential.
- Level survey of all columns and a floor-level contour plan, repeated at three-month intervals, to establish whether settlement is still active or has arrested. A levelling history is the single most useful piece of evidence.
- Crack monitors (tell-tales) across the main cracks, plus a check for foundation movement by exposing one footing and measuring its depth and dimensions against the drawing.
- Chemical tests (sulphate, pH) on the fill to rule out sulphate attack on the footing concrete as a contributor.
Remedial strategy.
- If settlement is still active and the differential is structural, underpin the northern footings with mini-piles or root piles taken to the dense sand below 5.5 m, with a reinforced capping beam tying the underpinned and original footings together to control further differential movement.
- Where the building is lightly loaded and the clay is thin, cement or lime grouting / jet grouting of the fill and upper clay may be sufficient, but only after a trial.
- Excavate and replace pond fill only if it lies within the depth of new work; do not attempt to dig out under an existing footing.
- Structural repair: stitch the masonry cracks with dowels and mesh, and re-point only after movement has been arrested, never before.
- Long-term: institute biannual levelling for at least two years and record it in the building's maintenance file.