SPT: N60, (N1)60, and five routes to a friction angle

The standard penetration test is the most-performed and least-standard test in ground investigation. A sampler of fixed dimensions is driven by a hammer of fixed mass falling a fixed distance, and the blows to drive it 300 mm are counted. Everything in that sentence is specified. What is not specified, in practice, is how much of the hammer’s potential energy arrives at the sampler, and that is the quantity the blow count actually measures.

This article takes one field blow count and carries it to a friction angle, showing every factor. The exercise is worth doing once in full because it makes visible how much of the final number was decided by the drilling rig rather than by the ground.

Every number in this article is recomputed from its inputs by a script that runs on each build of this site.

The testPermalink to “The test”#

$N$ = 18 blows at 6.0 m in a medium sand. Above the water table at 2 m the unit weight is 19.0 kN/m³; below it, 20.5 kN/m³. So

Energy: the correction that dominatesPermalink to “Energy: the correction that dominates”#

Theoretical hammer energy is 475 J. Delivered energy depends on the release mechanism, the anvil, and how the operator handles the rope. Measured energy ratios in service run from about 45% for a donut hammer released by rope and cathead to about 80% for a modern automatic trip hammer. The convention is to normalise everything to 60%:

with $C_B$ for borehole diameter, $C_S$ for sampler liner, and $C_R$ for rod length. For a standard 100 mm hole and a standard sampler both are 1.0; at 6 m of rods, $C_R = 0.85$.

The same 18 blows, in the same hole, in the same sand. The automatic rig’s $N_{60}$ is 1.78 times the donut rig’s, and no report that quotes only $N$ allows the reader to undo it. If a data sheet does not state the measured energy ratio, the single largest correction in the chain has been guessed.

Overburden: the correction that is a choicePermalink to “Overburden: the correction that is a choice”#

Blow count also rises with depth because the sand is confined more strongly. For anything that depends on relative density rather than on strength at the test depth, the value is normalised to a reference stress of 100 kPa:

giving $(N_1)_{60}$ of 12.8, 17.0 and 22.7 for the three rigs. The cap at 1.7 matters near the surface, where the formula would otherwise multiply a shallow blow count by an arbitrary amount; here it is not reached.

Note that this correction requires $\sigma'_v$, which requires the unit weights and the water table — the same circularity the CPT chain has, and for the same reason.

Five correlations, one blow countPermalink to “Five correlations, one blow count”#

Take the safety hammer column, $N_{60} = 15.3$ and $(N_1)_{60} = 17.0$, and apply five published relationships:

The Kulhawy & Mayne form is the only one that takes the stress level as a separate argument rather than folding it into $(N_1)_{60}$:

The five span 8.0 degrees. In terms of the quantity that actually enters a bearing capacity or earth pressure calculation, $\tan\varphi'$, the ratio between the extremes is 1.35 — so the choice of correlation moves a computed passive resistance by more than a third.

What the spread is, and is notPermalink to “What the spread is, and is not”#

It is not scatter in the test. Every one of the five numbers came from the identical blow count. It is the disagreement between correlations that were fitted to different databases: different sands, different fines contents, different ages of deposit, different reference stress ranges. Two of them cluster near 31–32° and two near 38–39°, which is not a continuum of opinion but two families — the older correlations were largely fitted against direct shear on reconstituted samples, the later ones against triaxial tests on frozen undisturbed samples of natural sands that had structure the reconstituted specimens did not.

That history is the reason a design value is not the average. Averaging five estimates whose disagreement is systematic produces a number that no author would defend, and it disguises the choice rather than making it. The defensible procedure is to select the correlation whose fitting database most resembles the deposit in hand, state which one was used, and record the alternative it was chosen over.

The correction nobody appliesPermalink to “The correction nobody applies”#

There is also a fines correction, a correction for the age of the deposit, and — for gravelly soils — the fact that a single gravel particle jammed in the shoe can double the blow count and cannot be detected in the record. The SPT is not a precision instrument, and it is not defended here as one.

What it is, is nearly universal, cheap, performed in the same hole as sampling, and backed by seventy years of case histories. Those are real advantages, and the way to keep them is to carry the corrections explicitly rather than to treat a raw $N$ as if it meant something. The moment the energy ratio, the rod length factor and the chosen correlation appear as named inputs in a calculation rather than as assumptions in someone’s head, the result becomes something another engineer can disagree with productively — which is the same argument for putting a derivation in a tool rather than a spreadsheet, and it applies from classification all the way down.