Capillarity Permeability Test – To Determine the Coefficient of Permeability(K) of Soil

Capillarity Permeability Test

In the previous articles, We have discussed Falling Head Permeameter and Constant Head Permeameter for the determination of the coefficient of permeability of the soil. In this article, we are going to discuss the capillarity permeability test or the horizontal capillarity test, which is another method used for determining the coefficient of permeability as well as the value of the capillarity height of the soil sample.

Capillarity Permeability Test
Capillarity Permeability Test

In this test, a sample of dry soil, at the desired density is placed in a transparent glass or lucite tube, about 4cm in diameter and 35 cm long. Water is allowed to flow through the soil sample from one end, under a constant head  h_0 and the other end is kept open to the atmosphere through an air vent tube.

At any time interval ‘t’ after the beginning of the test, let the capillary water travels through a distance x from point A to B. At the point A, there is a pressure head  h_0 , while at the point B, there is a pressure deficiency  h_c ( i.e., a negative pressure head ).

Head lost in causing flow from A to B (x distance apart)

  = h_{0} - (-h_{c}) = h_{0} + h_{c} 

 Hydraulic gradient
 i = \frac{h_{0} + h_{c}}{x}  

 From Darcy's law  

  v = K.i    [Where      v_{s} = \frac{v}{n}  ]

 Or,  n.v _{s}  = K.i 
     Where  v  = Discharge velocity,
       v_{s}    = Seepage velocity
      and   n   = Porosity

But seepage velocity =  \frac{dx}{dt} 

If the coefficient of permeability is designated as  K_u at a partial saturation  S , then the above expression may be rewritten as:

 S.n.v_{s} = K_{u}.i  

 S.n. \frac{dx}{dt}  = K_{u}. \frac{h_{0} + h_{c}}{x}   

Or,  x.dx = \frac{K_{u}}{S.n} (h_{0} +h_{c}) . dt   

Integrating between the limit  x_1 and  x_2 for  x , and corresponding values of time  t_1 and  t_2 , we get

 \int_{x_{1}}^{x_{2}} x.dx = \frac{K_{u}}{S.n}(h_{0}+h_{c})\int_{t_{1}}^{t_{2}} dt  

  \left |\frac{x^2}{2}  \right |_{x_1}^{x_2} = \frac{K_{u}}{S.n} (h_{0}+h_{c})\left |t  \right |_{t_1}^{t_2}  

  \frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} =   \frac{2K_{u}}{S.n} (h_{0}+h_{c})   

If  S = 100% ( that means S= 1). Now, the above expression becomes

   \frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} =   \frac{2K_{u}}{n} (h_{0}+h_{c})   

In the above equation, there are two unknowns:  k and  h_c . In order to overcome this difficulty, the test is performed in two stages, with two different heads of water  h_0 . The first set of observations is taken under a head  h_{(0)1} up to capillary saturation penetrating about half the length of the test tube.

As the capillarity saturation proceeds, the value of  x is recorded at various time intervals. A graph between  x^2 and  t will give a straight line, and its slope is given as:

   \frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} =   m_1   

In the second stage, for the next half of the tube, is performed with head  h_{(0)2} , and the recorded values of x and t are again used to plot a graph between  x^2 and  t . The slope of this line, say  m_2 , is now determined.

    \frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} =   m_2   

Knowing the two slopes, the values of  h_0 and  k can be computed by the following two-equation.

 \frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} =   m_1 =  \frac{2K_{u}}{S.n} (h_{0(1)}+h_{c})

\frac{(x_{2}^{2} - x_{1}^{2})}{(t_{2} - t_{1})} = m_2 = \frac{2K_{u}}{S.n} (h_{0(2)}+h_{c})

The degree of saturation S can also be found by measuring the wet mass of the soil sample at the end of the experiment. The porosity is computed from the known dry mass, volume and specific gravity.

Read More:

Factors Affecting The Permeability

Permeability of Soil – Darcy’s law