> 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/limestone-mcvay-mcvay-and-niraula-2004.md).

# Limestone (McVay) \[McVay and Niraula, 2004]

\[McVay and Niraula, 2004] back-computed *p-y* curves for Florida limestone from twelve centrifuge lateral load tests on 6 ft and 9 ft diameter drilled shafts in synthetic limestone with unconfined compressive strengths of 10 tsf and 20 tsf. Two families of curves were derived: one that neglects the shaft side shear (so its lateral resistance implicitly contains the contribution of the axial side shear) and one corrected for it. Both were normalized so that a single trend line covers all diameters and rock strengths.

This model uses the trend line **without the side-shear correction** (Fig. 6.2 of the report), where $$P/(D^{0.9}q\_u^{0.25})$$ is plotted against $$y/D$$. It is intended for use with the axial springs of the shaft, i.e. when the side shear is mobilized separately; the version corrected for side shear is [Limestone Uncoupled (McVay)](/technical-background/soil-structure-interaction/lateral-soil-models/limestone-uncoupled-mcvay-mcvay-and-niraula-2004.md).

The curve is piecewise linear with an initial slope, a secondary slope and an ultimate resistance:

$$
\tag{1}
p = 10750b^{0.9}q\_u^{0.25}\Bigl(\frac{y}{b}\Bigr) \quad for \quad 0 < \frac{y}{b} < 0.004
$$

$$
\tag{2}
p = b^{0.9}q\_u^{0.25}\Bigl\[823\Bigl(\frac{y}{b}\Bigr)+40\Bigr] \quad for \quad 0.004 \leq \frac{y}{b} < 0.1
$$

$$
\tag{3}
p = p\_u = 122.3b^{0.9}q\_u^{0.25} \quad for \quad \frac{y}{b} \geq 0.1
$$

where,

$$p$$ = horizontal rock resistance per unit length (kips/ft)\
$$q\_u$$ = unconfined compressive strength of the rock (ksf)\
$$b$$ = shaft diameter (ft)\
$$y$$ = horizontal displacement (ft)

The relationship is unit dependent (kips, feet, ksf). The report recommends field verification: the curves are based on two rock strengths and twelve tests, and joints, cracks and secondary structure may change the response.

{% hint style="info" %}
The exponent of the first branch is sometimes printed as $$b^{0.09}$$ in the secondary literature. That is a misprint for $$b^{0.9}$$: the three branches are one normalized trend line in $$P/(D^{0.9}q\_u^{0.25})$$, and only $$b^{0.9}$$ makes the initial slope meet Eq. (2) at the stated $$y/b = 0.004$$ break.
{% endhint %}

***

\[McVay and Niraula, 2004] McVay, M. C. and Niraula, L. (2004). *Development of P-Y Curves for Large Diameter Piles/Drilled Shafts in Limestone for FBPIER.* Report BC354-59, Florida Department of Transportation, University of Florida, Gainesville.


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