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VashaNatasha [74]
3 years ago
11

The wet density of a gravel was found to be 2.32 Mg/m^3 and the field water content was 16%. In the laboratory, the density of t

he solids was found to be 2.70 Mg/m^3, and the maximum and minimum void ratios were 0.59 and 0.28, respectively. Calculate the relative density (Dr) of the gravel in the field.
Physics
1 answer:
Sholpan [36]3 years ago
3 0

Answer:

the relative density of the gravel in the field is 0.7365 or 73.65%

Explanation:

Given that;

wet density of gravel r_{b} = 2.3 Mg/m³

field water content w = 16%

density of solids in lab r_{s} = 2.70 Mg/m³

Maximum void ratio e_{max} = 0.59

Minimum void ratio e_{mini} = 0.28

first we determine the dry density of gravel  r_{d} =  r_{b} / 1+ w

 r_{d} = 2.3 Mg/m³ / 1 + 0.16 = 2.3/1.16 = 1.9827 Mg/m³

we know that;  r_{w} = 1000 kg/m³ = 1 g/cm³

Specific Gravity of soil G = r_{s}  / r_{w}  = 2.70 Mg/m³ / 1 = 2.70 Mg/m³  

eo = ((G×r_{w})/r_{d}) - 1

eo = (( 2.70 × 1) / 1.9827 ) - 1

eo = 1.3617 - 1

Co = 0.3617

so Relative density I_{D} will be;

I_{D} = e_{max}  - eo  / e_{max} - e_{mini}

we substitute

I_{D} = 0.59  - 0.3617 / 0.59 - 0.28

I_{D} = 0.2283 / 0.31

I_{D} = 0.7365 or 73.65%

Therefore;  the relative density of the gravel in the field is 0.7365 or 73.65%

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