The soil-water characteristic curve relates suction to saturation (S), volumetric water content (θ) and hydraulic conductivity (k) and the corresponding functional forms are θ(Ψ), k(Ψ) and S(Ψ) respectively. In PLAXIS, the van Genuchten functional forms S(Ψ) and k(Ψ) can be entered in every soil/rock material data set in two ways. One way to generate these functional forms is to directly input the van Genuchten parameters and the second way is to use a Spline function to fit smooth curves to tabulated data. The van Genuchten parameters or the Spline function for any soil is input in the Groundwater tab of the Material properties and selecting User-defined for the data set.
To get parameters which are suitable for input in PLAXIS a step-wise procedure is provided to input the van Genuchten functional forms for direct input or as a spline function. The procedure converts the functional form θ(Ψ) and k(Ψ) to the functional form S(Ψ) and krel(Ψ) or vice versa.
Often within the realm of geotechnical analysis, it is required to convert measured data concerning the degree of saturation to volumetric water content (or vice versa) for its use in either Finite Element or Limit Equilibrium Analysis in PLAXIS or SEEP/W or PLAXIS LE. To interconvert between the functional forms we need to understand porosity and its relationship with the degree of saturation. The relationship between the degree of saturation and volumetric water content is defined by the following equation:
θ = S ƞ
where S is the degree of saturation, ƞ is the soil porosity and θ is the volumetric water content.
If we know S at any suction value and we know ƞ, we can then calculate θ. If ƞ remains constant throughout a transient analysis, we can convert saturation to volumetric water content at any suction value. This is because in a flow-only transient analysis the porosity does not change as described below.
The following phase diagram shows the different phases in a soil. Fig 1a shows an unsaturated soil comprising three phases which are soil solids, water and air. The volume of soil solids, water and air are denoted by Vs, Vw and Va, respectively. The total volume Vt = Va + Vw + Vs. Volume of voids Vv = Va + Vw.
On the other hand, Fig 1b shows the phase diagram for a fully saturated soil in which there are only two phases of water and soil solids because the volume of air gets filled by water.
Porosity is defined as (Va+Vw )/Vtotal
In a flow-only transient analysis, the volume of voids remains the same at any point in time and hence the porosity remains the same whether the soil is unsaturated or saturated as seen in both Fig 1a and Fig 1b.
The closed-form relationship for the van Genuchten functional form θ(Ψ) is given by the following equation:
where θres is the residual volumetric water content, θsat is the saturated volumetric water content. α', n and m are curve-fitting parameters.α' is the reciprocal of the air-entry value with units of 1/kPa n controls the shape of the θ(Ψ) plot after the air-entry value. m = 1-1/n
Similarly, the closed-form relationship for the functional form k(Ψ) is given by the following equation:
where ksat is the saturated hydraulic conductivity.
The input fitting parameters for the functional form S(Ψ) and krel(Ψ) are ga, gn, gc, gl and krel and ksat which are explained below.
The closed-form relationships for the functional forms S(Ψ) and krel(Ψ) are given below:
where Sres is the residual degree of saturation, Ssat is the saturated degree of saturation and krel is the relative hydraulic conductivity.ga is reciprocal of air-entry value similar to α' with units of 1/m so its value is determined by dividing α' by the unit weight of water.gn controls the shape of the S(Ψ) plot after the air-entry value so gn = n.gc = 1- 1/gn gl is a fitting parameter controlling the shape of the krel(Ψ) plot and affects the effective degree of saturation Seff and can be taken as 0 for some soils.
Based on the relationships provided above, the van Genuchten’s parameters can be interconverted from the functional form k(Ψ) and θ(Ψ) to the functional form S(Ψ) and krel(Ψ) and vice versa.
The Spline function requires direct input of the capillary height Ψ, relative hydraulic conductivity krel, and the degree of saturation which are all positive values. Data for the Spline function can be entered in the PLAXIS Groundwater tab of the Material properties and selecting User-defined for the data set and then selecting Spline for the Model.
This gives the data for spline fit in the functional forms S(Ψ) and krel(Ψ)
Note: If the suction head data points for the k(Ψ) and θ(Ψ) plots do not coincide then manually read the S values at the suction values corresponding to the k(Ψ) data points.
This gives the data for spline fit in the functional forms θ(Ψ) and k(Ψ)
Note: If the suction head data points for the krel(Ψ) and S(Ψ) plots do not coincide then manually read the θ values at the suction values corresponding to the krel(Ψ) data points.