Fatih Küçükkarakurt

Jet grout columns: overlap, spacing and verticality

5 min read
Abstract

Overlapping jet grout columns form a continuous block only if they still overlap at the bottom, and verticality tolerance removes that guarantee with depth. For 1.6 m columns at 1.2 m spacing the secant thickness is 1.0583 m at the surface, 0.6974 m at 12 m and 0.3555 m at 18 m, reaching zero at 20.0 m, on a 1% tolerance applied to both columns in the worst direction. Achieving continuity to 25 m instead requires the spacing to close to 1.10 m, which is 9.1% more columns for the same wall.

Jet grouting builds columns of soil-cement in the ground by eroding the soil with a high-pressure jet and mixing grout into what remains. Set the columns close enough together and they overlap into a continuous wall or block, which is what makes the technique useful for cut-offs, underpinning and excavation support.

The word doing the work in that sentence is overlap. It is a geometric condition, it is checked at the design stage on a plan drawing where every column is a circle at its nominal position, and it degrades with depth for reasons the plan drawing cannot show.

Every number in this article is recomputed from its inputs by a script that runs on each build of this site, and the diagram’s geometry is checked against the same arithmetic.

The geometry of overlap

Two columns of diameter DD whose axes are a distance ss apart intersect in a lens. The width of that lens — the secant thickness, which is the effective thickness of the wall they form — is the chord common to both circles:

t=2(D2)2−(s2)2=D2−s2t = 2\sqrt{\left(\frac{D}{2}\right)^{2} - \left(\frac{s}{2}\right)^{2}} = \sqrt{D^{2} - s^{2}}

For D=1.6D = 1.6 m columns at s=1.2s = 1.2 m centres:

t=1.62−1.22=1.1200=1.0583 mt = \sqrt{1.6^{2} - 1.2^{2}} = \sqrt{1.1200} = 1.0583\ \text{m}
Two overlapping jet grout columns and the secant thickness between them Two circles of equal diameter whose centres are closer together than one diameter, so they intersect. The vertical chord where the circles cross is marked as the secant thickness of the wall they form. The distance between the centres is marked as the column spacing, and one radius is marked on each circle. s = 1.2 m t = 1.0583 m D = 1.6 m D = 1.6 m
The audit reads the two drawn circles and the drawn chord out of the SVG and checks that the chord's half-length equals the square root of the radius squared minus half the centre distance squared, so a diagram that stops matching the formula fails the build.

At 1.0583 m of secant thickness against a 1.6 m column, the wall is doing well. Everything that follows is about why it does not stay that way.

Verticality is a tolerance, not a property

A drilling rig cannot place a 25 m column exactly vertical. Specifications state a tolerance, commonly 1% of depth, and occasionally 0.5% for closely controlled work with in-rod inclinometry. One percent means that at 20 m the axis may be 0.20 m from where the plan shows it, in any direction.

Two adjacent columns can deviate in opposite directions. In that worst case the effective spacing at depth zz is

seff(z)=s+2αzs_{\text{eff}}(z) = s + 2\alpha z

and the secant thickness follows from the same chord formula with seffs_{\text{eff}} in place of ss. For the columns above, at α=1%\alpha = 1\%:

Depth (m)Deviation each (m)seffs_{\text{eff}} (m)Secant thickness (m)
00.0001.201.0583
60.0601.320.9042
120.1201.440.6974
180.1801.560.3555

and overlap is lost entirely where s+2αz=Ds + 2\alpha z = D, that is at

zcrit=D−s2α=0.40.02=20.0 mz_{\text{crit}} = \frac{D - s}{2\alpha} = \frac{0.4}{0.02} = 20.0\ \text{m}

A wall specified as continuous, drawn as continuous, and built entirely within tolerance, has no continuity below 20.0 m. Nothing was done wrong. The design simply never contained a check at depth.

The worst case and the likely case

Assuming both columns deviate the full tolerance in exactly opposite directions is conservative and is the right basis for a cut-off, where a single gap is a failure. If instead the two deviations are independent and of random direction, the separation grows as 2 αz\sqrt{2}\,\alpha z rather than 2αz2\alpha z, which moves the critical depth to 28.3 m.

The distinction is a real design decision, not a refinement. For a hydraulic cut-off the worst case governs: one window passes water and the wall has failed at its purpose. For a block treated for bearing or settlement, where the improvement is averaged over many columns, the statistical case is defensible, because an isolated thin spot is carried by its neighbours.

Stating which of the two was used is part of stating the design. They differ by 8.3 m of depth here, which is the difference between a wall that works and one that does not.

What continuity to 25 m actually costs

Turn the requirement round. For overlap to survive to 25 m at 1% tolerance in the worst case:

s≤D−2αz=1.6−2(0.01)(25)=1.10 ms \le D - 2\alpha z = 1.6 - 2(0.01)(25) = 1.10\ \text{m}

which is 0.909 columns per metre of wall against 0.833 at the original spacing — 9.1% more columns, 9.1% more grout, 9.1% more rig time.

That is the honest price, and it is modest. The expensive version is the one where the spacing was not reduced, the wall leaks, and the remedy is a second row of columns installed through a partly flooded excavation.

What has to be proven rather than assumed

Column diameter is the other assumption in the chord formula, and it is not a machine setting. It is an outcome of jetting energy, soil type, and the erodibility of what the jet meets — which in a layered deposit varies over the depth of a single column. A design that assumes 1.6 m throughout has assumed that the stiff band at 14 m erodes like the soft clay above it.

So the geometry above is necessary and not sufficient. What makes it real is verification on site:

  • Diameter, by exhuming trial columns in the top few metres, or by measuring during jetting with instrumentation that infers the erosion front.
  • Verticality, by in-rod inclinometry logged per column rather than by a tolerance clause in a specification.
  • Continuity, by coring at the joints — the joints, not the columns, because the column centres are the part that is certainly there.
  • Strength, by unconfined compression on cores, with the understanding that a core is taken where the drilling was easy.

Each of those turns a number from an assumption into a measurement, and they are worth listing in that form because the same discipline applies to every part of a ground investigation — a CPT-derived strength and an SPT-derived friction angle are assumptions with error bars too. The difference here is that the geometry is exact and knowable, so leaving it unchecked is a choice rather than a limitation.

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