Table 4 Empirical equations and their limitations for permeability estimates

Hazen

\(k = 6 \times 10^{ - 4} \times \frac{g}{v} \times [1 + 10(n - 0.26)] \times (d_{10} )^{2}\)

C_u < 5

0.1 < d₁₀ < 3.0

Kozeny-Carman

\(k = 8.3 \times 10^{ - 3} \times \frac{g}{v} \times \left[ {\frac{{n^{3} }}{{(1 - n)^{2} }}} \right] \times (d_{10} )^{2}\)

0.5 < d₁₀ < 4.0

Terzaghi

\(k = 0.0084 \times \frac{g}{v} \times \left[ {\frac{n - 0.13}{{\sqrt[3]{1 - n}}}} \right]^{2} \times (d_{10} )^{2}\)

–

Chapuis

\(k = 1.5 \times (d_{10} )^{2} \times \frac{{e^{3} }}{1 + e} \times \frac{{1 + e_{{\rm max} } }}{{(e_{{\rm max} } )^{3} }}\)

–

Slitcher

\(k = 1 \times 10^{ - 2} \times \frac{g}{v} \times n^{3.287} \times (d_{10} )^{2}\)

0.01 < d₁₀ < 5.0

USBR

\(k = 4.8 \times 10^{ - 3} \times \frac{g}{v} \times (d_{20} )^{0.3} \times (d_{20} )^{2}\)

C_u < 5

NAVFAC

\(k = 10^{1.291e - 0.6435} \times (d_{10} )10^{{(0.5504 - 0.2937{\text{e}})}}\)

2 < C_u < 12

0.1 < d₁₀ < 2.0

0.3 < e < 0.7

\(1.4 < \frac{{d_{10} }}{{d_{5} }}\)

Alyamani and Sen

\(k = 1300 \times [I_{0} + 0.025(d_{50} - d_{10} )]^{2}\)

–

Breyer

\(k = 6 \times 10^{ - 4} \times \frac{g}{v} \times \log \left[ {\frac{500}{{C_{\text{u}} }}} \right] \times (d_{10} )^{2}\)

0.06 < d₁₀ < 0.6

1 < C_u < 20