Vibro Stone Column Area Replacement Ratio Calculator

What this calculation does not cover

• The diameter entered is the nominal design diameter, not the column that gets built. Vibro columns bulge in soft layers and neck in stiff ones, and the achieved diameter is normally back-calculated from the stone consumption recorded for each column. Because area goes with the square of the diameter, a 0.8 m column that finishes at 0.9 m raises the ratio from 0.145 to 0.184 at 2.0 m centres.
• The tributary area is hard-coded as (√3/2) x spacing², which is the equilateral triangular grid and nothing else. Feeding a square-grid spacing into this page returns a ratio about 15% higher than the correct figure, because a square grid's tributary area is spacing² — 0.8 m (2.6 ft) columns at 2.0 m (6.5 ft) centres give 0.145 on a triangular grid but 0.126 on a square one.
• The area replacement ratio is a plan geometry fraction, not a settlement or bearing capacity result. Settlement improvement methods such as Priebe's also need the friction angle of the stone, the stiffness or undrained shear strength of the soil and the stress concentration that develops between column and soil, and this page takes no soil parameter at all — it returns the same ratio for a dense sand and for a clay too soft to confine a column. Two sites with an identical ratio can settle by very different amounts.
• The tributary area assumes a large regular grid in which every column is ringed by neighbours. Columns at the perimeter of a small group get less lateral confinement, which is why an extra row of columns beyond the loaded footprint is commonly specified, so for a pad footing carrying only a handful of columns this ratio overstates the improvement actually acting at the edge.
• This is a plan-area quantity that carries no information about depth. It does not distinguish columns founded on a competent stratum from floating columns, and it says nothing about compression of the untreated soil below the column toes, which frequently governs total settlement. It also takes no account of the stone's drainage function in accelerating consolidation, or of the densification of surrounding granular soil that governs liquefaction mitigation designs.