Ground improvement
Aggregate columns (vibro stone columns or rammed aggregate piers) under an embankment or a wide load, by FHWA GEC 13 (FHWA-NHI-16-027, 2017) Chapter 5: the unit cell and area replacement ratio, the stresses on the columns and the soil with the engineer's stress concentration ratio, the column bearing resistance, the settlement of the treated ground by Priebe's improvement factor, by stress reduction or by the two-layer method for rammed aggregate piers, and the composite strength for a stability analysis.
Inputs of the ground improvement #
- Columns: the system, the grid (triangular, square, or an entered ratio A/Ac), spacing s and diameter d (GEC 13: 3.0 to 3.6 ft columns at 5 to 12 ft are common), the stress concentration ratio n (2 to 5 for stone columns, 2.5 for preliminary design; 5 to 10 for rammed aggregate piers under embankments, about 10 under rigid footings), the column friction angle φc (40 to 45° stone, 45 to 50° rammed piers), the column unit weight and length.
- Soil and load: the applied pressure q (fill unit weight times height for an embankment), the compressible layer's thickness, γsat, water table, su, and its settlement model: normally consolidated clay (Cc, e0) or elastic (Es).
- Design criteria: the settlement method, the pier stiffness modulus kg (75 to 360 pci under rigid footings, less for embankments), the column bearing factor Nc (22 for stiffer inorganic soils, 18 for peat, organic or very soft clay) with a factor of safety of 3, an allowable soil pressure between the columns (0: no check), and the settlement limit.
Auto-design varies the spacing (6-in steps) for the fewest columns. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Column stress ≤ Nc·su / FS | GEC 13 Eqs. 5-5, 5-6 |
| Soil stress ≤ the allowable (optional) | GEC 13 Eq. 5-4 |
| Settlement of the treated ground ≤ the limit | Untreated: Cc·H/(1 + e0)·log((σ'0 + Δq)/σ'0) or Δq·H/Es (Eqs. 5-14, 5-15); Priebe: ÷ n0 = 1 + as[(5 − as)/(4Kac(1 − as)) − 1]; stress reduction: × σsoil/q; rammed piers: qg/kg + the settlement below the piers (Eqs. 5-11 to 5-13) |
| Composite strength (reported) | τ = (1 − as)·cu + as·σv·tanφc, γ = γsc·as + γsoil(1 − as) (Eqs. 5-7, 5-8) |
| Columns shorter than the layer (advisory) | The soil below the columns settles unimproved |
The drawings show a plan of the column grid with the spacing and the replacement ratio, and a section through the treated layer with the column length.
Limitations #
- Priebe's closed form is written from knowledge (Priebe 1995 is not on disk; GEC 13 shows it only as a curve); it is an upper-bound estimate (GEC 13 4.1.2.6). Eq. 5-7 is printed unclearly in GEC 13 and is used as τ = (1 − as)·cu + as·σv·tanφc (to confirm against the code text).
- No time rate of settlement (radial drainage), liquefaction mitigation, bulging of single columns, group or global stability; the field verification program is the engineer's.
Verification examples #
Verification status: 8 values compared in 2 examples (2 published, 0 hand calculations from the cited equations): 8 within tolerance, 0 recorded deviations. Thin: only 2 published examples. Code basis: the provisions it uses were read in the target edition.
FHWA GEC 13 (2017) 4.3 Design Examples (backend/tests/test_verify_ground_improvement.py):
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| 4.3.1 Rammed aggregate piers: 2.75 ft at 5 ft, n = 6, kg = 65 pci, q = 2,500 psf | σ'0, untreated settlement, Ra, qg, suz | 432 psf, 22 in., 0.27, 6,383 psf, 0.68 in. | (test run) |
| 4.3.2 Stone columns: A/Ac = 3.6, q = 1,875 psf, 50 ft clay | σ'0, untreated settlement, settlement ratio | 1,440 psf, 27 in., 2.7 (chart) | (test run) |
The example rounds Ra to 0.27 (exact 0.2744 for the triangular grid), which puts its qg 0.9 % above the exact value. Its settlement ratio is read from the Priebe curve; the closed form gives 2.81 with φc = 40°.