> 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/c-phi-soil-reese-and-van-impe-2011.md).

# c-phi Soil (Reese and Van Impe) \[Reese and Van Impe, 2011]

Soils that mobilize both cohesion and internal friction (cemented sands, unsaturated cohesive soils, silts) are covered by the procedure of \[Reese and Van Impe, 2011], Section 3.10, which follows the [Sand (Reese)](/technical-background/soil-structure-interaction/lateral-soil-models/sand-reese-reese-et-al-1974.md) curve construction and adds the cohesive component of resistance after the concept of Evans and Duncan (1982) and the observations of \[Ismael, 1990]. The model documented here is the implementation of that procedure in FB-MultiPier's *C-Phi* model (Help Manual, Sec. 13.7.7).

### Ultimate Resistance

The ultimate resistance is the factored frictional component (Eqn 13.7.BO of the FB-MultiPier Help Manual):

$$
\tag{1}
p\_{ult} = Ap\_{ult\phi}
$$

The frictional component is the lesser of the wedge and flow values of \[Reese et al., 1974] (Eqs. 3.60 and 3.61):

$$
\tag{2}
\begin{aligned}
p\_{ult\phi} = \gamma' z\Bigl\[\frac{K\_0\tan(\phi)\sin(\beta)}{\tan(\beta-\phi)\cos(\alpha)}+\frac{\tan(\beta)}{\tan(\beta-\phi)}(b+z\tan(\beta)\tan(\alpha)) \\
+K\_0z\tan(\beta)(\tan(\phi)\sin(\beta)-\tan(\alpha))-K\_ab\Bigl]
\end{aligned}
$$

$$
\tag{3}
p\_{ult\phi} = K\_ab\gamma' z (\tan^8(\beta)-1)+K\_0b\gamma' z \tan(\phi)\tan^4(\beta)
$$

and the cohesive component, which enters the peak resistance $$p\_m$$ below, is the lesser of (Eqs. 3.62 and 3.63, Eqn 13.7.BQ):

$$
\tag{4}
p\_{ultc} = \Bigl\[3+\frac{\gamma'}{c}z+\frac{J}{b}z\Bigl]cb, \qquad p\_{ultc} = 9cb
$$

where,

$$ϕ$$ = internal friction angle, $$α$$ = $$ϕ$$/2, $$β$$ = π/4 + $$ϕ$$/2\
$$c$$ = cohesion\
$$γ'$$ = effective unit weight\
$$z$$ = depth, $$b$$ = pile diameter\
$$K\_0$$ = 0.4, $$K\_a$$ = tan²(π/4 − $$ϕ$$/2)\
$$J$$ = 0.5\
$$A$$ = $$\bar{A\_s}$$ (static) or $$\bar{A\_c}$$ (cyclic) from Fig. 3.24 of the reference, the same coefficients as for [Sand (Reese)](/technical-background/soil-structure-interaction/lateral-soil-models/sand-reese-reese-et-al-1974.md)

### p-y Curve

The curve has the four portions of the Reese sand curve (Fig. 3.29 of the reference):

$$
\tag{5}
y\_u = 3b/80, \qquad y\_m = b/60
$$

$$
\tag{6}
p\_m = 1.5p\_{ult\phi}+p\_{ultc} \qquad (Eq. \ 3.65, \ Eqn \ 13.7.BR)
$$

$$
\tag{7}
p = (k\_{py}z)y \quad (initial \ straight \ line)
$$

$$
\tag{8}
p = \bar{C}y^{1/n}, \qquad m = \frac{p\_{ult}-p\_m}{y\_u-y\_m}, \qquad n = \frac{p\_m}{|m|y\_m}, \qquad \bar{C} = \frac{p\_m}{y\_m^{1/n}}, \qquad y\_k = \Bigl(\frac{\bar{C}}{k\_{py}z}\Bigr)^{n/(n-1)}
$$

followed by the straight line from ($$y\_m$$, $$p\_m$$) to ($$y\_u$$, $$p\_{ult}$$) and a constant $$p\_{ult}$$ beyond $$y\_u$$. Because the cohesive component is in $$p\_m$$ and not in $$p\_{ult}$$, the curve peaks at $$y\_m$$ and softens to $$p\_{ult}$$ at $$y\_u$$ whenever the cohesion is not zero; the slope magnitude $$|m|$$ is used in the exponent (Eqn 13.7.BT) so that the parabola is real on that softening branch. The initial stiffness $$k\_{py}$$ is entered as the Subgrade Modulus of the layer; per Eq. 3.67 it is $$k\_c + k\_ϕ$$ for cemented sand and $$k\_ϕ$$ for non-cemented silt (Figs. 3.30 and 3.31 of the reference).

{% hint style="info" %}
Eq. 3.64 of \[Reese and Van Impe, 2011] adds the cohesive component to $$p\_{ult}$$ as well as to $$p\_m$$. OpenBrIM follows the FB-MultiPier implementation, which keeps it only in $$p\_m$$, so that the curves generated by OpenBrIM reproduce FB-MultiPier's *C-Phi* output; the book's form gives a higher ultimate resistance in cemented soils.
{% endhint %}

***

\[Reese and Van Impe, 2011] Reese, L. C. and Van Impe, W. F. (2011). *Single piles and pile groups under lateral loading*, 2nd ed., Section 3.10. CRC Press/Balkema.

\[Ismael, 1990] Ismael, N. F. (1990). Behavior of laterally loaded bored piles in cemented sands. *Journal of Geotechnical Engineering*, 116(11):1678–1699. (Article not on file.)

\[Reese et al., 1974] Reese, L. C., Cox, W. R., and Koop, F. D. (1974). Analysis of laterally loaded piles in sand. In *Offshore Technology Conference*, OTC 2080.


---

# 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/c-phi-soil-reese-and-van-impe-2011.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.