> For the complete documentation index, see [llms.txt](https://docs.openbrim.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.openbrim.org/technical-background/soil-structure-interaction/axial-soil-models/axial-tz-soil-models/drilled-shaft-igm-cohesive-tz-oneill-et-al-1996.md).

# Drilled Shaft IGM Cohesive TZ (O'Neill) \[O'Neill et al., 1996]

\[O'Neill et al., 1996] developed design models for drilled shafts in intermediate geomaterials (IGM), materials at the boundary between soil and rock. Categories 1 (argillaceous: heavily overconsolidated clay, clay-shale, saprolite, mudstone) and 2 (calcareous rock: limestone, limerock) are cohesive IGMs with $$q\_u$$ between 0.5 and 5 MPa; their side load transfer is Model 1 of the report (Chapter 4, formula sheet Table 17), derived from finite element analyses of smooth and rough sockets and verified against full-scale tests.

### Ultimate Side Resistance

Rough sockets fail through the rock (McVay et al., 1992):

$$
\tag{1}
f\_{su} = 0.5\sqrt{q\_u}\sqrt{q\_t}
$$

Smooth sockets fail at the interface:

$$
\tag{2}
f\_{su} = \alpha q\_u
$$

where $$q\_u$$ is the unconfined compressive strength, $$q\_t$$ the split tensile strength and $$α$$ the factor of Figure 34 of the report (a function of $$σ\_n/p\_a$$ and $$q\_u/p\_a$$), entered on the soil layer for smooth sockets. If the mass modulus is lower than the intact modulus, $$f\_{su}$$ is reduced:

| $$E\_m/E\_i$$    | 1 | 0.5 | 0.3 | 0.1  | 0.05 |
| ---------------- | - | --- | --- | ---- | ---- |
| reduction factor | 1 | 0.8 | 0.7 | 0.55 | 0.45 |

### Load Transfer

The normal stress from the fluid concrete on the borehole wall and the characteristic parameter $$n$$ (rough sockets):

$$
\tag{3}
\sigma\_n = M\gamma\_cz\_c, \qquad n = \frac{\sigma\_n}{q\_u}
$$

with a water table at depth $$z\_w$$ below the top of the concrete:

$$
\tag{4}
\sigma\_n = M\[\gamma'\_c(z\_c-z\_w)+\gamma\_cz\_w]
$$

where $$γ\_c$$ is the unit weight of the concrete ($$γ'\_c$$ buoyant), $$z\_c$$ the distance from the top of the concrete column to the point, and $$M$$ the factor for the fluidity of the concrete:

| $$z\_c$$ (m) | slump 125 mm | 175 mm | 225 mm |
| ------------ | ------------ | ------ | ------ |
| 0            | 1.00         | 1.00   | 1.00   |
| 4            | 0.50         | 0.95   | 1.00   |
| 8            | 0.45         | 0.75   | 1.00   |
| 12           | 0.35         | 0.65   | 0.90   |

For smooth sockets $$n$$ is read from Figure 36 of the report and entered on the layer. With the socket length $$L$$, the socket diameter $$D$$, the concrete modulus $$E\_c$$ and the mass modulus $$E\_m$$:

$$
\tag{5}
\Omega = 1.14\Bigl(\frac{L}{D}\Bigr)^{0.5}-0.05\Bigl\[\Bigl(\frac{L}{D}\Bigr)^{0.5}-1\Bigr]\log\_{10}\Bigl(\frac{E\_c}{E\_m}\Bigr)-0.44
$$

$$
\tag{6}
\Gamma = 0.37\Bigl(\frac{L}{D}\Bigr)^{0.5}-0.15\Bigl\[\Bigl(\frac{L}{D}\Bigr)^{0.5}-1\Bigr]\log\_{10}\Bigl(\frac{E\_c}{E\_m}\Bigr)+0.13
$$

$$
\tag{7}
\Theta\_f(w) = \frac{E\_m\Omega}{\pi L\Gamma f\_{su}}w, \qquad K\_f = n+\frac{(\Theta\_f-n)(1-n)}{\Theta\_f-2n+1} \leq 1
$$

$$
\tag{8}
t = \Theta\_ff\_{su} \ (\Theta\_f < n), \qquad t = K\_ff\_{su} \ (\Theta\_f \geq n)
$$

where $$w$$ is the vertical displacement of the shaft. The socket length and the concrete modulus are taken from the pile (the length of the pile inside the layer and the section material).

***

\[O'Neill et al., 1996] O'Neill, M. W., Townsend, F. C., Hassan, K. M., Buller, A., and Chan, P. S. (1996). *Load Transfer for Drilled Shafts in Intermediate Geomaterials.* Report FHWA-RD-95-172, Federal Highway Administration, McLean, VA.


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