Liquefaction beneath a Proposed Mat Foundation: Numbers vs the Neighbour Argument
A three-story office building is proposed on 6 m of loose hydraulic fill over 4 m of normally consolidated bay mud (su = 25 kPa) over dense sand. Fill: N60 = 6–9, fines content 8–14%, CPT Ic ≈ 2.3, total unit weight 18 kN/m³. Groundwater is at 1.5 m. The design earthquake is Mw 6.8 with a peak ground acceleration of 0.35g at the surface; the site is 12 km from the fault. Preliminary (N1)60 in the fill at 4 m depth is about 8. The client wants a shallow mat to save money and points out that a nearby 1970s warehouse on spread footings performed "fine" in 1989.
1. Compute the cyclic stress ratio at 4 m depth, compare it with the cyclic resistance ratio, and state what the resulting factor of safety means physically.
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Seismic demand (CSR):
CSR = 0.65 · (a_max/g) · (σv/σ′v) · r_d
- σv = 4 m × 18 kN/m³ = 72 kPa
- u = (4 − 1.5) × 9.81 = 24.5 kPa → σ′v = 47.5 kPa
- r_d at 4 m ≈ 0.97
- CSR = 0.65 × 0.35 × (72/47.5) × 0.97 ≈ 0.33
Note the amplification from the shallow water table: the effective-stress ratio is 1.52, so a modest 0.35g becomes a demanding 0.33 CSR.
Capacity (CRR): for (N1)60 ≈ 8 and clean-sand reference, CRR₇.₅ ≈ 0.08; with 12% fines, allow a modest increase to about 0.10.
Adjust for magnitude: MSF = 10^2.24 / M^2.56 = 173.8 / 6.8^2.56 ≈ 1.29, so CRR ≈ 0.13.
Factor of safety = 0.13 / 0.33 ≈ 0.39.
Physically: the fill is roughly two-and-a-half times weaker than the shaking demands. This is not a marginal case requiring judgment about whether to apply a correction - it means pore-pressure build-up during the design event should be expected to reach initial effective stress, i.e. full liquefaction of the fill.
2. Estimate the consequences for the mat foundation and recommend a foundation strategy, considering both the fill and the bay mud.
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Liquefaction settlement of the fill: at (N1)60 ≈ 8 and CSR ≈ 0.33, Ishihara-type strain correlations give roughly 2.5–3.5% volumetric strain → 6 m × 0.03 ≈ 0.18 m (range 0.15–0.21 m) of post-liquefaction settlement. That settlement will not be uniform: where N60 is 6 instead of 9 and the fill is thicker, differentials of half the total or more are plausible.
Bay mud: su = 25 kPa gives a bearing capacity of roughly Nc·su ≈ 130 kPa - comfortably above the ~30–50 kPa the building imposes, so bearing is not the governing issue. Consolidation is. Four metres of normally consolidated clay under a stress increment of 40–50 kPa will yield on the order of 0.15–0.30 m of primary settlement, on a time scale of years to decades.
Combined: the building would see something in the range of 0.3–0.5 m with severe differential components, plus loss of lateral support (the liquefied fill can spread and drag the mat). A shallow mat is not viable.
Options, in order of preference:
- Deep foundations - driven piles or drilled shafts carried through the fill and mud into the dense sand, with the pile design accounting for downdrag and lateral spreading loads on the upper section.
- Ground improvement of the fill plus pre-consolidation or wick drains in the mud, if the schedule permits a surcharge period.
- Partial or full removal and replacement of the fill, combined with a piled or improved foundation for the mud.
Increase the CPT program to establish layer continuity, run a dissipation test in the mud for ch, and obtain undisturbed samples for compression index - the numbers above are correlations, and the mud is the long-term settlement driver.
3. Evaluate the client's "the warehouse did fine" argument and specify what evidence would actually settle the question.
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Why the argument is weak:
- Different demand. If the warehouse is even a few kilometres away, the 1989 shaking and site response there differed; a single accelerogram history is not a design basis. Older low-rise warehouses are also short-period structures with different dynamic response.
- Survivorship and reporting bias. "Performed fine" usually means "did not collapse." Settlement of 100 mm, cracked slabs, or sand boils are commonly ignored or unrecorded. Unless someone looked, absence of observed damage is not absence of liquefaction.
- Different ground. Fill thickness and mud thickness vary over a tidal-fill site; a warehouse several hundred metres away may sit on thinner fill or on older, denser material.
- Wrong failure mode. A flexible, lightly loaded warehouse can tolerate differential settlement that would crack a mat and rack a three-story frame. Building performance is not a ground performance test.
Evidence that would settle it:
- Pre- and post-1989 floor-slab and exterior surveys, or any record of sand boils, lateral spreading, or foundation repairs at the warehouse.
- A CPT/SPT pair at the warehouse site so its (N1)60 and fill thickness can be compared directly with the new site.
- A ground-motion estimate for 1989 at each site, to see whether the warehouse was ever subjected to anything close to 0.35g.
The defensible approach is to treat the warehouse as a source of hypotheses to test, not as a design precedent.