> 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-non-cohesive-tz-mayne-and-harris-1993.md).

# Drilled Shaft IGM Non-Cohesive TZ (Mayne and Harris) \[Mayne and Harris, 1993]

Category 3 intermediate geomaterials are very dense granular materials (residual and completely decomposed rock, granular glacial till) with $$N\_{60}$$ between 50 and 100. \[Mayne and Harris, 1993] correlated their properties with SPT results in Piedmont residuum and computed the socket load-settlement curve with the elastic solution of Randolph and Wroth; \[O'Neill et al., 1996] adopted the method as Model 2 (Chapter 2, Eqs. 41–54, and Chapter 4) with one change for sockets drilled under slurry.

### Ultimate Side Resistance

$$
\tag{1}
\sigma'*p = 0.2N*{60}p\_a, \qquad OCR = \frac{\sigma'*p}{\sigma'*{v0}}
$$

$$
\tag{2}
\phi' = \arctan\Bigl\[\Bigl(\frac{N\_{60}}{12.2+20.3\sigma'\_{v0}/p\_a}\Bigr)^{0.34}\Bigr]
$$

$$
\tag{3}
K\_0 = (1-\sin\phi')OCR^{\sin\phi'}, \qquad f\_{max} = K\_0\sigma'\_{v0}\tan\phi'
$$

where $$σ'*{v0}$$ is the effective vertical stress, $$p\_a$$ the atmospheric pressure and $$N*{60}$$ in blows per 0.3 m. Where the borehole is drilled under slurry with good construction control, $$f\_{max} = K\_0\sigma'\_{v0}\tan(0.75\phi')$$.

### Socket Load-Settlement and t-z Curve

The side resistance is fully mobilized at the socket settlement $$w\_{t1}$$ at the end of the elastic segment of the load-settlement curve:

$$
\tag{4}
E\_s = 22p\_aN\_{60}^{0.82}, \qquad \lambda = 2(1+\nu)\frac{E\_p}{E\_{sL}}, \qquad \zeta = \ln\Bigl{\frac{2L}{D}\[0.25+(2.5\rho(1-\nu)-0.25)\xi]\Bigr}, \qquad \mu L = 2\Bigl(\frac{2}{\zeta\lambda}\Bigr)^{0.5}\frac{L}{D}
$$

$$
\tag{5}
I = 4(1+\nu)\frac{1+\frac{8\eta\tanh(\mu L)L}{\pi\lambda(1-\nu)\xi\mu LD}}{\frac{4\eta}{(1-\nu)\xi}+\frac{4\pi\rho\tanh(\mu L)L}{\zeta\mu LD}}
$$

$$
\tag{6}
Q\_{s,max} = f\_{max}\pi DL, \qquad Q\_{t1} = \frac{Q\_{s,max}}{1-\frac{I}{\xi\cosh(\mu L)(1-\nu)(1+\nu)}}, \qquad w\_{t1} = \frac{Q\_{t1}I}{E\_{sL}D}
$$

where,

$$L$$, $$D$$ = socket length and diameter\
$$E\_p$$ = modulus of the shaft\
$$E\_{sL}$$ = modulus of the geomaterial at the base level of the socket, $$E\_{sm}$$ at mid-socket ($$ρ = E\_{sm}/E\_{sL}$$ = 1 for a uniform layer)\
$$ξ = E\_{sL}/E\_b$$ = ratio of the side to the base modulus (2.5 for Piedmont residuum)\
$$η$$ = 1 for straight shafts\
$$ν$$ = Poisson's ratio (about 0.3)

The *t-z* curve is bilinear: linear from the origin to ($$w\_{t1}$$, $$f\_{max}$$) and constant beyond. $$f\_{max}$$ at the node uses the effective stress at the node; the socket quantities use the side resistance at mid-socket. The socket length and the shaft modulus are taken from the pile.

{% hint style="info" %}
The Georgia Tech report of Mayne and Harris is not on file; the method is implemented from the FHWA report of O'Neill et al. (1996), which reproduces and revises it.
{% endhint %}

***

\[Mayne and Harris, 1993] Mayne, P. W. and Harris, D. E. (1993). *Axial Load-Displacement Behavior of Drilled Shaft Foundations in Piedmont Residuum.* FHWA Reference No. 41-30-2175, Georgia Tech Research Corporation, Atlanta. (Report not on file.)

\[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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