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).

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.

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.

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[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.