> 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-gravelly-sand-and-gravel-tz-rollins-rollins-et-al-2005.md).

# Drilled Shaft Gravelly Sand and Gravel TZ (Rollins) \[Rollins et al., 2005]

\[Rollins et al., 2005] performed 28 axial uplift load tests on drilled shafts in soil profiles ranging from uniform medium sand to well-graded sandy gravel and combined them with load tests from the literature. Measured side friction in gravelly soils was two to four times the values predicted by the sand equations, and modified $$β$$ equations and normalized load-transfer curves were proposed. Two models are provided: *Gravelly Sand* for 25–50 % gravel-size particles and *Gravel* for more than 50 %, both for $$N\_{SPT}$$ above 25 (for lower blow counts the [Drilled Shaft Sand](/technical-background/soil-structure-interaction/axial-soil-models/axial-tz-soil-models/drilled-shaft-sand-tz-reese-and-oneill-oneil-et-al.-1999.md) curve should be considered).

### Ultimate Side Resistance

$$
\tag{1}
t\_u = \beta\sigma'\_z
$$

Gravelly sand ($$z$$ in m):

$$
\tag{2}
\beta = 2.0-0.15z^{0.75}, \qquad 0.25 \leq \beta \leq 1.8
$$

Gravel ($$z$$ in m):

$$
\tag{3}
\beta = 3.4e^{-0.085z}, \qquad 0.25 \leq \beta \leq 3.0
$$

where,

$$t\_u$$ = ultimate unit side resistance\
$$σ'\_z$$ = effective vertical stress at the depth in question\
$$β$$ = shaft friction factor (computed from depth when the input is left at 0, otherwise the input value is used)\
$$z$$ = depth

### t-z Curves

Lower-bound, average and upper-bound trend lines were fitted to the data, in terms of the normalized displacement $$R = z/D × 100$$ (displacement in percent of the shaft diameter).

Gravelly sand, lower bound:

$$
\tag{4}
\frac{t}{t\_u} = 0.019R^4-0.0638R^3-0.0944R^2+0.7141R \ (R \leq 2.4), \qquad 0.9193 \ (R > 2.4)
$$

Gravelly sand, average:

$$
\tag{5}
\frac{t}{t\_u} = -0.0762R^4+0.4477R^3-1.093R^2+1.473R \ (R \leq 2.0), \qquad 0.9364 \ (R > 2.0)
$$

Gravel, lower bound:

$$
\tag{6}
\frac{t}{t\_u} = -0.0563R^6+0.5044R^5-1.8135R^4+3.3012R^3-3.2091R^2+1.92R \ (R \leq 2.4), \qquad 1.0 \ (R > 2.4)
$$

Gravel, average:

$$
\tag{7}
\frac{t}{t\_u} = -0.2849R^6+2.0834R^5-5.9633R^4+8.4884R^3-6.4289R^2+2.8837R \ (R \leq 2.18), \qquad 0.9906 \ (R > 2.18)
$$

Gravel, upper bound:

$$
\tag{8}
\frac{t}{t\_u} = -0.49R^6+3.1232R^5-7.8847R^4+10.201R^3-7.5169R^2+3.491R \ (R \leq 1.88), \qquad 1.0 \ (R > 1.88)
$$

The trend line is selected on the soil layer (Lower = 0, Average = 1, Upper = 2). The tip resistance of shafts in these soils uses the [Drilled Shaft Sand](/technical-background/soil-structure-interaction/axial-soil-models/axial-qz-soil-models/drilled-shaft-sand-qz-reese-and-oneill-oneil-et-al.-1999.md) *q-z* curve, since no dedicated tip tests exist.

{% hint style="info" %}
The JGGE article is not yet on file. The $$β$$ equations are taken from the companion conference paper \[Rollins et al., 1997], which is on file: Eq. (2) above is its Eq. (4), in which $$z$$ is in metres (the equivalent coefficient for $$z$$ in feet is 0.15 × 0.3048^0.75 = 0.0615). The trend-line polynomials are implemented as they are reported in the secondary literature, where the upper-bound polynomial for gravelly sand is printed incompletely; the upper bound of the gravelly-sand model therefore uses the average fit until \[Rollins et al., 2005] is obtained and the coefficients can be taken from the article itself.
{% endhint %}

***

\[Rollins et al., 2005] Rollins, K. M., Clayton, R. J., Mikesell, R. C., and Blaise, B. C. (2005). Drilled shaft side friction in gravelly soils. *Journal of Geotechnical and Geoenvironmental Engineering*, 131(8):987–1003. (Article not on file.)

\[Rollins et al., 1997] Rollins, K. M., Clayton, R. J., and Mikesell, R. C. (1997). Ultimate side friction of drilled shafts in gravels. In *Proc. 14th ICSMFE*, Hamburg.


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation by asking a question.

Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters:

```
GET https://docs.openbrim.org/technical-background/soil-structure-interaction/axial-soil-models/axial-tz-soil-models/drilled-shaft-gravelly-sand-and-gravel-tz-rollins-rollins-et-al-2005.md?ask=<question>&goal=<user_goal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.