Geotechnical Engineering

275/33310–15FE Reference Handbook 10.4 · Geotechnical · Density of granular soils

Handbook formula

Relative Density of Sand

D_{r} = \frac{e _{m a x} - e}{e _{m a x} - e _{m i n}}

Dr (or ID) places the in-place void ratio between laboratory loosest (emax) and densest (emin) states. Dr = 0 is very loose; Dr = 1 (100%) is very dense. Equivalent form using dry unit weights: Dr = [(γ_d − γ_dmin)/(γ_dmax − γ_dmin)] × (γ_dmax / γ_d). Used for sands and nonplastic silts, not clays.

$D_{r}$: Relative density
$e$: In-place void ratio
$e_{m a x}$: Maximum void ratio (loosest)
$e_{m i n}$: Minimum void ratio (densest)

Step-by-step solved example

emax = 0.85, emin = 0.35, in-place e = 0.50. Find Dr.

e between emax and emin on the phase diagram.

1. Numerator and span
emax − e = 0.35. emax − emin = 0.50.
$e_{m a x} - e = 0.35$
2. Relative density
Dr = 0.35/0.50 = 0.70 = 70%.
$D_{r} = 0.70$

Answer: 0.70 (70%)

10 practice questions

0/10 correct

1.e = emax means the sand is

2.e = emin corresponds to

3.emax = 0.90, emin = 0.40, e = 0.65. Dr =

4.Relative density is NOT used for

5.A dense sand typically has Dr about

6.As Dr increases, expected φ of a sand

7.γ_dmax corresponds to

8.emax = 0.80, emin = 0.40, Dr = 0.25. In-place e =

9.The unit-weight form of Dr includes an extra factor γ_dmax/γ_d because

10.SPT N-values in sand generally increase as Dr