Question

A soil has a dry density of 17.5kN/m^3. It has densities corresponding to most compact and loosest state as 18.5 kN/m^3 and 13 kN/m^3 respectively. The relative density of the soil is ______

(a) 0.871

(b) 0.865

(c) 0.869

(d) 0.860

I have been asked this question in my homework.

This key question is from Density Index and Relative Compaction in section Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

The correct choice is (b) 0.865

To explain I would say: Given,

Dry density γd=17.5 kN/m^3

Maximum dry density γd,max=18.5kN/m^3

Minimum dry density γd,mim=13kN/m^3

Relative density ID= \(\frac{(γ_d-γ_{d,min})γ_{d,max}}{((γ_{d,max}-γ_{d,min}) γ_d )}\)

ID = \(\frac{((17.5-13)*18.5)}{((18.5-13)*17.5)}\)

ID=0.865.