Some important relations in between properties of soil

1.    Relation between W_s , W_w and w

                                                    from phase diagram,

total weight W = W_s + W_w + W_a

                                             = W_s + W_w + 0     (∵ W_a = 0)

                                = W_s{1+ (W_w/ W_s)}

                                                 W = W_s(1 + w)        (∵ w = W_w/ W_s ) 

           W_s = W / (1+w)

where, W_s = weight of solids

W_w = weight of water

W_a = weight of air

w = water content

1.    Relation between e and n 

we know that,

Porosity, n = V_v / V

 

n = V_v / (V_s + V_v)

 

n = (V_v/ V_s) / { 1+(V_v/ V_s)}

 

           n = e / (1+e)               (∴e = V_v/ V_s)

  Relation  between  e, S, w and G 

we know that,

Void ratio, e = V_v/ V_s

 

e = (V_v/ V_s) * (V_w/ V_w)

 

e = (V_v/ V_w) * (V_w/ V_s)

 

e =  (V_v/ V_w)*{(W_w /  γ_w ) / (W_s /  γ_s )}     (∴ γ_w = W_w/V_w)

 (∴γ_s = W_s/V_w)

e = (V_v/ V_w)* (W_w/ W_s)*(G_s. γ_w/ γ_w)    (∴ G_s = γ_s/ γ_w)

 

e = w G_s / S

 

Se = wG