> 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-qz-soil-models/driven-pile-sand-qz-mosher-vijayvergiya-1977.md).

# Driven Pile Sand QZ (Mosher) \[Vijayvergiya, 1977]

The tip load-displacement relationship used with the Mosher side-resistance criteria is the power curve of \[Vijayvergiya, 1977]:

$$
\tag{1}
q = q\_u\Bigl(\frac{z}{z\_c}\Bigr)^n
$$

where,

$$q$$ = unit end bearing resistance\
$$q\_u$$ = nominal unit end bearing resistance, the value of the curve at $$z = z\_c$$\
$$z$$ = vertical displacement of the pile tip\
$$z\_c$$ = critical tip displacement at which $$q\_u$$ is reached; \[Mosher, 1984] assumed 0.25 in, \[Vijayvergiya, 1977] relates it to the pile width\
$$n$$ = exponent, 1/3 by default (\[Vijayvergiya, 1977]); \[Mosher, 1984] (Table 6, Eqs. 49a–c) lists 1/2 for loose ($$ϕ$$ 28–31°), 1/3 for medium dense (32–34°) and 1/4 for dense sand (35–38°)

Where $$q\_u$$ is not known, Figure 72 of \[Mosher, 1984] (after Castello, 1980) relates it to relative depth and friction angle.

{% hint style="warning" %}
The power curve is not capped at $$q\_u$$: as in FB-MultiPier (Help Manual 6.0, Eqn 13.8.B), the resistance keeps growing past $$z\_c$$, so $$q\_u$$ is the resistance at the critical displacement rather than an upper limit. With $$z\_c$$ = 0.25 in and $$n$$ = 1/3 the curve reaches 2.4 $$q\_u$$ at 3.6 in of tip movement.
{% endhint %}

{% hint style="info" %}
Neither the Ports '77 paper nor the WES report is yet on file, so the model is implemented as it is reported in the secondary literature. It will be checked against \[Vijayvergiya, 1977] and \[Mosher, 1984] once the originals are obtained.
{% endhint %}

***

\[Vijayvergiya, 1977] Vijayvergiya, V. N. (1977). Load-movement characteristics of piles. In *Proc. Ports '77*, ASCE, Vol. II, 269–286. (Paper not on file.)

\[Mosher, 1984] Mosher, R. L. (1984). *Load Transfer Criteria for Numerical Analysis of Axially Loaded Piles in Sand.* Technical Report K-84-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg. (Report not on file.)


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