q define water content void ratio and dry density

Question

Q. Define water content, void ratio and dry density of a soil. If wet density of a soil is 1.9 gm per cm at a moisture content of 24%, what will be its dry density?

 Ans.- Water Content - The water content w also called the moisture content is defined as the ratio of weight of water w_w to the weight of solids w_d in a given mass of soil.

              w = w_w  / w_d  x 100

            The water content is generally expressed as a percentage.

Void ratio - Void ratio e of a given soil sample is the ratio of the volume of voids to the volume of soil solids in the given soil mass.

            Thus   e = v_v / v_{s  ,}    v_v  = Volume of voids.  v_s = Volume of soil solids.

Dry Density - The dry density γ_d  or the dry unit weight is the weight of solids per unit of total volume ( Prior to drying ) of the soil mass.

                 g_d  = W_d / V.   or γ_d   = g / (1 + w)

Solution :  Given -  Wet density of a soil γ  = 1.9 gm /cm²  

                Moisture content w = 24% = 0.24

                 Dry density γ_d   = g / (1 + w) =  1.9 / 1 + 0.24 = 1.9 / 1.24 = 1.53 gm / cm²   Ans.