The Two-Point Method for the Soil-Water Characteristic Curve

by Murray D. Fredlund, Delwyn G. Fredlund and Hung Q. Vu

The soil-water characteristic curve (SWCC) generally has two primary defining points; namely: 1.) the water content and suction at the air entry value for the soil, and 2.) the water content and soil suction at residual conditions. There are also two additional points that define the extreme limits on the SWCC; namely, completely saturated conditions under zero suction (i.e., saturated water content and porosity), and completely dry conditions (i.e., zero water content and a soil suction of 1,000,000 kPa).

Is it possible to generate data points along the entire range of the SWCC if I have an estimate of the air entry value and residual conditions for a soil?

Here, we will provide a simple means of generating a SWCC dataset.

Application of the Soil-Water Characteristic Curve

Computer modeling of a physical process in an unsaturated soil (e.g., seepage) requires that one or more unsaturated soil property functions for each soil strata. There are numerous procedures to arrive at the unsaturated soil properties. Virtually in every situation requires an initial assessment of a representative soil-water characteristic curve, SWCC, for each soil strata.

Implementation Procedure to Obtain a Representative SWCC

The SWCC can either be measured or estimated using one of several available techniques. For example, a number of laboratory or field tests may have been performed on a particular soil. However, it will be necessary to select one desorption SWCC (i.e., drying curve) and one adsorption curve (i.e., wetting curve) to represent each soil strata. In the end, each soil strata will have a single air entry value and residual conditions. The following points describe procedures that can be used arrive at a representative SWCC for a particular soil type.

1. A number of grain size curves may have been measured on soil samples taken in the field. It is possible to utilize one of several proposed pedo-transfer function procedures to estimate the SWCC (Fredlund et al, 2002). An analysis of all the data allows the engineer to arrive at an estimate for the air entry value, the residual conditions, as well as the saturated initial porosity for the soil.
2. It is possible to use measured grain size distributions to undertake "database" mining to find SWCCs measured on similar soils in the past. An analysis of all the SWCC data allows the engineer to arrive at an estimate for the air entry value, the residual conditions, as well as the saturated initial porosity for the soil.
3. It is possible to measure the SWCC in the laboratory on a number of samples. An analysis of all the laboratory data allows the engineer to arrive at an estimate for the air entry value, the residual conditions, as well as the saturated initial porosity for the soil.

In each of the above cases, the objective is to arrive at an estimate for the air entry value, the residual conditions, as well as the saturated initial porosity that can best represent a particular soil. The air entry value, the residual conditions, as well as the saturated initial porosity will represent the desorption (or drying) SWCC curve for the soil strata. Usually the adsorption (or wetting) SWCC curve is estimated from the drying curve by translating the inflection point a certain percentage of a log cycle.

The following section illustrates how "two points" (plus the initial porosity), can be used as input to SVFlux for the generation of an equally spaced dataset. The artificially generated dataset can be used to estimate unsaturated soil property functions. The unsaturated soil property functions can be computed using SVFlux.

Figure 1: Two-Point SWCC Generation parameters, as seen in SVFlux

Definition of Variables

Figure 2 shows the definition of variables used in the calculation of the SWCC. The degree of saturation versus soil suction graph provides the most definitive way to identify the air entry value, ψ_ae and the residual conditions, ψ_r for a soil. However, if the soil undergoes negligible volume change as soil suction is increased, then the air entry value and residual suction are the same as for the gravimetric and volumetric plots versus soil suction.

Figure 2: Definition of variables used to calculate the SWCC (after Pham 2005)

The SWCC consists of three straight lines with slopes of S₁, S₂, and S₃ on a logarithmic scale (Pham 2005). The slope S₁ refers to the slope between the saturated conditions at a low suction (e.g., 0.1 kPa) and the air entry value, computed on the gravimetric water content scale. The slope S₂ refers to the slope of a line between the air entry value and residual conditions computed on the gravimetric water content scale. The slope S₃ refers to the slope of a line between residual conditions and completely dry conditions at a soil suction of 1,000,000 kPa computed on the gravimetric water content scale. The equation of the three straight lines of the SWCC can be written:

where w_sat is gravimetric saturated water content (decimal); ψ_sat is a low suction corresponding to saturated conditions (kPa); w_ae is gravimetric water content at air entry value; ψ_ae is air entry value; w_r is gravimetric residual water content; ψ_r is residual suction; and,

The following equations show relationships amongst void ratio, e; dry density, ρ_d; gravimetric water content, w; volumetric water content, θ_w; and degree of saturation, S:

where G_s is specific gravity (2.65 in this example).

Gravimetric water contents must be represented in terms of volumetric water contents in SVFlux. To generate this two-point SWCC, enter the parameters into SVFlux as shown above in Figure 1. The input data are as follows: saturated volumetric water content, θ_sat is 0.3; saturated suction, ψ_sat is given a value of 0.1 kPa; saturation at the air entry value is 98%; air entry value for the soil, ψ_ae is 0.5 kPa; saturation at residual conditions is 18%; and residual suction, ψ_r is 3000 kPa. Equations 5 to 8 are calculated from the basic volume-mass information.

Generating the graph shows volumetric water content versus soil suction, as shown here:

Figure 4: Volumetric water content versus soil suction for a soil with an air entry value of 5 kPa and a residual suction of 3000 kPa

Using SVFlux to Generate an SWCC

SVFlux is part of our SVOffice suite, and is available from our downloads page. The user can change any of the soil parameters within SVFlux and regenerate the associated graphical plots immediately. The user can also generate the SWCC dataset, which can be copied to a computer clipboard and then used with other software packages if desired. It is also possible to best-fit the dataset with any of the commonly used mathematical equations for the SWCC (e.g., van Genuchten, Fredlund & Xing, and Others), or to compute any of the unsaturated soil property functions using the generated suction versus water content dataset along with the saturated soil properties.

References

Fredlund, D. G. (2002). "Use of the soil-water characteristic curve in the implementation of unsaturated soil mechanics". Proceedings of the Third International Conference on Unsaturated Soils, UNSAT 2002, Keynote Address, March 10-13, Vol. 3, Recife, Brazil.

Fredlund, D. G. (2006). "The 2005 Terzaghi Lecture: Unsaturated soil mechanics in engineering practice". Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 132(3), 286-321.

Fredlund, M. D., Wilson, G. W., and Fredlund, D. G. (2002). "Use of grain-size distribution for the estimation of the soil-water characteristic curve". Canadian Geotechnical Journal, 39(5), 1103-1117.

Fredlund, D. G., Rahardjo, H., Leong, E. C., and Ng, C. W. W. (2001). "Suggestions and recommendations for the interpretation of soil-water characteristic curves". Proceedings of the 14th Southeast Asian Geotechnical Conference, December 10-14, Vol. 1, pp. 503-508, Hong Kong.

Gitirana, de F. N. G. Jr., and Fredlund, D. G. (2005). "Unsaturated soil mechanics as a series of partial differential equations". Keynote Address Proceedings of the International Conference on Problematic Soils, pp. 3-30, May 25-27, Farmagusta, N. Cyprus.

Pham, Q. H. (2005). "A volume-mass constitutive model for unsaturated soils". Ph.D. Thesis, Department of Civil and Geological Engineering, University of Saskatchewan, SK, Canada.