# Effect of Bentonite Addition on the Properties of Fly Ash as a Material for Landfill Sealing Layers
## 2 Materials and Methods
### Methods
In laboratory conditions, saturation of the soil takes place by the back pressure saturation method. The higher the plasticity of cohesive soil, the higher the value of back pressure that is needed to reach the value of \(B=1\)[39]. In the case of some soil types, it might be unjustified to consider full saturation when \(B\) reaches value equal to or near 1. Therefore, from the relation of \(B\) parameter to degree of saturation \(S_{\rm r}\), minimum value of \(B\) can be determined [39]. The cohesive soils might be saturated to a degree that the water voids are continuous and some of the air voids are occluded. Under such conditions, it can be assumed that the soil is in a quasi-saturated state [40]. For the compacted fly ash, the minimum value of \(B=0.8\) was established for describing sufficient saturation-quasi-saturation [14]. In Figure 5, the relation between \(B\) parameter and degree of saturation of the tested materials is presented. It can be observed in Figure 5 that when the \(B\) parameter achieved the value around 0.8 and higher, the degree of saturation \(S_{\rm r}\) changed slightly. Therefore, \(B=0.8\) can be considered as a minimum value of sufficient saturation (quasi-saturation) of fly ash and fly ash-bentonite mixture. The consolidation cell was modified to measure the hydraulic conductivity at the end of each load increment. The hydraulic  
Figure 5: The relation between \(B\) parameter and degree of saturation \(S_{\rm r}\) for tested fly ash and fly ash-bentonite mixture. conductivity tests were carried out with vertical drainage condition from base to top of the tested specimens. The schematic for the test in the consolidometer is shown in Figure 6.  
The flow of water through a fully saturated soil has been described by [PERSON]'s law according to empirical Equation (3):  
\[q=Aki \tag{3}\]  
or  
\[v=\frac{q}{A}=ki \tag{4}\]  
where \(q\) is the volume of water flowing per unit time, \(k\) is the coefficient of permeability, \(A\) is the cross-sectional area, \(v\) is the discharge velocity and \(i\) is the hydraulic gradient \(i=\Delta H/l\), where \(\Delta H\) is the difference in elevation of water levels in the piezometers and \(l\) is the length of the flow path. In Reference [41], \(k\) is described as hydraulic conductivity, which depends on features and properties of the material and the fluid flowing through the material. These parameters include density and viscosity of the fluid, grain-size distribution and porosity of the soil. There is a deviation from [PERSON]'s law at low hydraulic gradients [42]. Seepage through the cohesive soils is initiated when the hydraulic gradient exceeds a certain value called the initial gradient \(i_{0}\). The fluid flow can be described by nonlinear (non-Darcian) relationship determined by [PERSON] [43; 44]:  
\[v=\kappa i^{n},\text{ when }i<i_{1} \tag{5}\]  
\[v=k(i-i_{0}),\text{ when }i\geq i_{1}, \tag{6}\]  
where \(v\) is flow velocity, \(k\) is the coefficient of permeability of the linear flow at high gradient; \(k\) is the permeability coefficient described by an exponential relationship; \(i_{1}\) is the hydraulic gradient needed to overcome the maximum binding energy of mobile pore water \(i_{1}=\frac{i_{0}n}{(n-1)}\), \(n\)--constant dependent on soil type, void ratio and temperature. According to classical geotechnical approaches [45], factors that affect hydraulic conductivity of fine-grained soils are: soil composition, characteristic of the fluid flows through the soil, structure, and degree of saturation during the permeation. Tests of hydraulic conductivity were conducted on quasi-saturated samples, where the \(B\) parameter had values from 0.79 to 0.84. Afterwards the \(B\) parameter reached the required value, the consolidation tests (lasting 24 h) were carried out. The loading steps for fly ash specimens were as follows: 25, 50,  
Figure 6: The Rowe-Barden consolidation cell set up for hydraulic conductivity test with vertical drainage to the top face.