> 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/lateral-soil-models/loess-johnson-et-al-2006.md).

# Loess (Johnson) \[Johnson et al., 2006]

\[Johnson et al., 2006] developed a hyperbolic secant-modulus *p-y* model for loess from full-scale lateral load tests on 30 in and 42 in drilled shafts in Kansas. The ultimate resistance is correlated to the CPT cone tip resistance, and cyclic degradation is built into the ultimate resistance. Only the CPT tip resistance is required as a soil input (Chapter 6 and Appendix D.5 of the report).

### Ultimate Resistance

$$
\tag{1}
P\_{uo} = N\_{po}q\_c = 0.409q\_c
$$

$$
\tag{2}
P\_u = \frac{P\_{uo}b}{1+0.24\log\_{10}(N)}
$$

where,

$$q\_c$$ = CPT cone tip resistance\
$$P\_{uo}$$ = ultimate soil resistance per unit area\
$$b$$ = pile diameter\
$$N$$ = number of load cycles (1 for static loading; 10 is used for the cyclic curve)\
$$P\_u$$ = ultimate soil resistance per unit length of pile

### p-y Curve

The reference displacement $$Y\_i$$ is the displacement at which the initial tangent intersects the ultimate resistance asymptote; the best fit to the load tests was

$$
\tag{3}
Y\_i = 0.117 \ in
$$

$$
\tag{4}
E\_i = \frac{P\_u}{Y\_i}
$$

$$
\tag{5}
Y'\_h = \frac{Y}{Y\_i}+a\Bigl(1-e^{-Y/Y\_i}\Bigr), \qquad a = 0.10
$$

$$
\tag{6}
E\_s = \frac{E\_i}{1+Y'\_h}
$$

$$
\tag{7}
P = E\_sY
$$

where,

$$E\_i$$ = initial modulus per unit length of pile\
$$E\_s$$ = secant modulus at displacement $$Y$$\
$$Y'\_h$$ = hyperbolic displacement term\
$$a$$ = dimensionless correlation constant

The report notes that $$Y\_i$$ was fitted to one loess formation and may be sensitive to soil type; the ultimate resistance correlation is expected to transfer between sites.

{% hint style="info" %}
OpenBrIM follows the report as published. Some implementations of this model additionally scale $$q\_c$$ from 0.5 at the ground surface to 1.0 at a depth of 2\*\*$$b$$\*\*, and use the mapping $$y\_h = (Y/Y\_i)\[1+0.1e^{-Y/Y\_i}]$$; neither adjustment is applied here.
{% endhint %}

***

\[Johnson et al., 2006] Johnson, R. M., Parsons, R. L., Dapp, S. D., and Brown, D. A. (2006). *Soil Characterization and p-y Curve Development for Loess.* Report No. K-TRAN: KU-05-3, Kansas Department of Transportation, Topeka.


---

# 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/lateral-soil-models/loess-johnson-et-al-2006.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.