Prediction of the Soil-Water Characteristic Curve from Grain-Size Distribution and Volume-Mass Properties

This paper presents a method of estimating the soil-water characteristic curve from the grain-size distribution curve and volume-mass properties. The grain-size distribution is divided into small groups of uniformly-sized particles. A packing porosity and soil-water characteristic curve is assumed for each group of particles. The incremental soil-water characteristic curves are then summed to produce a final soil-water characteristic curve. Prediction of the soil-water characteristic curve from grain-size distribution allows for a inexpensive description of the behavior of unsaturated soils. The soil-water characteristic curve forms the basis for computer modelling of processes in unsaturated soils. INTRODUCTION This paper presents a model for the prediction of the soil-water characteristic curve, (SWCC), based on the particle-size distribution, dry density, void ratio, and specific gravity of a soil. The model first fits a modification of the Fredlund & Xing (1994) equation to the grain-size distribution curve (Figure 1). The grain-size distribution curve is then analyzed as an incremental series of particle sizes from the smallest to the largest in order to build an overall soil-water characteristic curve. Small increments of uniform-sized particles are transposed to obtain a SWCC representing the average particle size. Once the entire grain-size distribution curve is incrementally analyzed, the individual soilwater characteristic curves are superimposed to give the SWCC for the entire soil. In order to build the general SWCC, it must be assumed that the SWCC for each uniform particle size is relatively unique. Typical soilwater characteristic curves and grain-size distribution curves for a mixture of sand, silt, and clay were obtained from SoilVision (Fredlund, 1996), which contains over 6000 soils. The soil-water characteristic curves were then fitted with the Fredlund & Xing (1994) equation. This provided an approximation for the curve fitting parameters in the Fredlund & Xing (1994) equation classified according to dominant particle size. Parameters used in the Fredlund & Xing (1994) equation for soils composed entirely of sand or entirely of clay are easy to obtain. Uniform soils containing only mid-range particle sizes are more difficult to obtain and as a result some estimation is required. During development of the algorithm to predict the SWCC, it was decided that provision must be made for the storage of grain-size information. If grain-size information was to be stored, a method of mathematically representing each grain-size curve should be found. The benefits of a mathematical fit would be two-fold. A grain-size curve fit with a 3 Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997 2 mathematical equation would then allow further computations to be performed on the curve. It was reasoned that a prediction of the soil-water characteristic curve would be possible if the grain-size distribution could be fit with an equation. This idea was then implemented in the form of a least-squares curve-fitting algorithm which allowed for fitting of the grain-size distribution data. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0.0001 0.001 0.01 0.1 1 10 100 Particle Size (mm) P er ce nt P as si ng Fit curve Experimental Figure 1 Fit of grain-size curve using a modified Fredlund & Xing (1994) equation (# 10741) The second benefit of mathematically representing each grain-size curve was that it would provide coefficients of indices by which grain-size curves could be classified. This would allow the ability to search the database for soils with grain-size curves within a specified band. This technique has proven invaluable in performing sensitivity analyses on soil parameters. THEORY FOR MATHEMATICALLY REPRESENTING THE GRAIN-SIZE DISTRIBUTION CURVE Previous research work to fit the grain-size curves was reviewed (Wagner, 1994). The research by Wagner presented several lognormal distributions capable of fitting the grain-size curve. Providing a meaningful representation of the grain-size data in the extremes proved difficult for a lognormal distribution. Due to similarity between the shape of the grain-size distribution and the shape of the soilwater characteristic curve, a different approach was taken. The Fredlund & Xing (1994) equation, which had previously been used to fit SWCC data, provided a flexible and continuous equation that could be fit by the nonlinear regression using three parameters. The equation was modified to permit the fitting of grain-size curves. The modified equation, [0.1], 3 Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997 3 allowed for a continuous fit and proper definition of the extremes of the curve.