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Prediction of the Soil-Water Characteristic Curve from Grain-Size

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

                                          Murray D. Fredlund
                                           D.G. Fredlund
                                            G.W. Wilson
                                    Department of Civil Engineering
                                       University of Saskatchewan
                                           Saskatoon, Sask.
                                                S7N 5A9
                          Fax: (306) 966-5427 Email: mdf128@engr.usask.ca


ABSTRACT
   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.

                                                      water characteristic curves and grain-size
INTRODUCTION                                          distribution curves for a mixture of sand, silt,
   This paper presents a model for the                and clay were obtained from SoilVision
prediction of the soil-water characteristic           (Fredlund, 1996), which contains over 6000
curve, (SWCC), based on the particle-size             soils. The soil-water characteristic curves were
distribution, dry density, void ratio, and specific   then fitted with the Fredlund & Xing (1994)
gravity of a soil. The model first fits a             equation. This provided an approximation for
modification of the Fredlund & Xing (1994)            the curve fitting parameters in the Fredlund &
equation to the grain-size distribution curve         Xing (1994) equation classified according to
(Figure 1). The grain-size distribution curve is      dominant particle size. Parameters used in the
then analyzed as an incremental series of             Fredlund & Xing (1994) equation for soils
particle sizes from the smallest to the largest in    composed entirely of sand or entirely of clay
order to build an overall soil-water                  are easy to obtain. Uniform soils containing
characteristic curve. Small increments of             only mid-range particle sizes are more difficult
uniform-sized particles are transposed to obtain      to obtain and as a result some estimation is
a SWCC representing the average particle size.        required.
Once the entire grain-size distribution curve is
incrementally analyzed, the individual soil-             During development of the algorithm to
water characteristic curves are superimposed to       predict the SWCC, it was decided that
give the SWCC for the entire soil.                    provision must be made for the storage of
                                                      grain-size information. If grain-size information
   In order to build the general SWCC, it must        was to be stored, a method of mathematically
be assumed that the SWCC for each uniform             representing each grain-size curve should be
particle size is relatively unique. Typical soil-     found. The benefits of a mathematical fit
                                                      would be two-fold. A grain-size curve fit with a
                                  3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997
mathematical equation would then allow                                          fit with an equation. This idea was then
further computations to be performed on the                                     implemented in the form of a least-squares
curve. It was reasoned that a prediction of the                                 curve-fitting algorithm which allowed for fitting
soil-water characteristic curve would be                                        of the grain-size distribution data.
possible if the grain-size distribution could be



                       100%
                       90%                     Fit curve
                       80%                     Experimental
     Percent Passing




                       70%
                       60%
                       50%
                       40%
                       30%
                       20%
                       10%
                         0%
                          0.0001            0.001               0.01                0.1                  1                  10   100
                                                                Particle Size (mm)

                       Figure 1 Fit of grain-size curve using a modified Fredlund & Xing (1994) equation (# 10741)



   The second benefit of mathematically                                         research by Wagner presented several
representing each grain-size curve was that it                                  lognormal distributions capable of fitting the
would provide coefficients of indices by which                                  grain-size curve. Providing a meaningful
grain-size curves could be classified. This                                     representation of the grain-size data in the
would allow the ability to search the database                                  extremes proved difficult for a lognormal
for soils with grain-size curves within a                                       distribution.
specified band. This technique has proven
invaluable in performing sensitivity analyses on                                   Due to similarity between the shape of the
soil parameters.                                                                grain-size distribution and the shape of the soil-
                                                                                water characteristic curve, a different approach
                                                                                was taken. The Fredlund & Xing (1994)
THEORY FOR MATHEMATICALLY                                                       equation, which had previously been used to fit
REPRESENTING THE GRAIN-SIZE                                                     SWCC data, provided a flexible and continuous
DISTRIBUTION CURVE                                                              equation that could be fit by the nonlinear
                                                                                regression using three parameters. The
   Previous research work to fit the grain-size
                                                                                equation was modified to permit the fitting of
curves was reviewed (Wagner, 1994). The
                                                                                grain-size curves. The modified equation, [0.1],
                                                                                                                                       2
                      3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997
allowed for a continuous fit and proper                             definition of the extremes of the curve.

                                                                             7
                                                                                 
                                                                    dr   
                                                              ln 1 +                                       [0.1]
                                        1                            d  
               Pp (d ) =                                    1 −             
                                                              ln 1 + d r   
                                                       gm
                                        ga  
                                              gn

                           ln exp(1) +                                  
                                         d                  dm   
                                                                              
                              
                                                          

   where:
       Pp(d)    =          percent passing a particular grain-size, d
       ga       =          fitting parameter corresponding to the initial break in the grain-size curve,
       gn       =          fitting parameter corresponding to the maximum slope of grain-size curve,
       gm       =          fitting parameter corresponding to the curvature of the grain-size curve,
       d        =          particle diameter (mm),
       dr       =          residual particle diameter (mm),
       dm       =          minimum particle diameter (mm)

                                                                    Aberg, 1996) It appeared that a theoretical
THEORY OF PREDICTING THE                                            approach to the problem would hopefully
SOIL-WATER CHARACTERISTIC                                           provide superior predictions.
CURVE FROM THE GRAIN-SIZE
                                                                        The second approach was theoretical and
DISTRIBUTION
                                                                    involved converting the grain-size distribution
   The mathematical fit of the grain-size                           to a pore-size distribution which was then
distribution led to the development of an                           developed into a SWCC (Arya, 1981). This
algorithm capable of predicting the soil-water                      research was duplicated and compared to
characteristic curve. A review of current                           experimental data. Difficulty was encountered
research showed that one of two approaches                          in generating a reasonable SWCC along the
have typically been taken in the prediction of                      entire range. Predicted soil-water characteristic
the soil-water characteristic curve from grain-                     curves typically showed abnormal “humps” and
size. The first approach entails a statistical                      fell to zero volumetric water content long
estimation of properties describing the SWCC                        before the experimental data was completely
from grain-size and volume-mass properties                          desaturated (Figure 2).
(Gupta, 1979; Ahuja, 1985; Ghosh; 1980;




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                                          3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997


                                   0.35
                                                                                                        Actual

        Volumetric Water Content
                                    0.3

                                   0.25                                                                 Estimation from
                                                                                                        pore-size
                                    0.2

                                   0.15

                                    0.1

                                   0.05

                                     0
                                      0.01                    1                 100                      10000                 1000000
                                                                           Suction (kPa)

     Figure 2 Illustration of abnormalities associated with prediction of SWCC from pore-size distribution


   A new approach is proposed for predicting
the soil-water characteristic curve from the                                                This resulted in the production of two plots,
grain-size distribution curve. It was assumed                                           one for the ‘n’ parameter, and one for the ‘m’
that a soil composed entirely of a uniform,                                             parameter. These plots described the variation
homogeneous particle size would have a unique                                           in the ‘n’ and ‘m’ parameters with grain-size.
soil-water characteristic curve. The shape of                                           This allowed n and m parameters to be
the SWCC for pure sands, pure silts and pure                                            estimated for any soil composed of uniform
clays was known. Using a best-fit analysis with                                         diameter particles.
the Fredlund & Xing (1994) equation, three
parameters were computed for each soil type.                                               The grain-size distribution curve can be
It was then assumed that these parameters                                               divided up into small divisions of uniform soil
could be associated with a dominant particle                                            particles. Starting at the smallest diameter size,
size on the grain-size plot. The uniqueness of                                          a packing porosity was estimated (Harr, 1977)
the soil parameters was confirmed by querying                                           for each division and a soil-water characteristic
the SoilVision database for plots of the ‘n’ and                                        curve estimated as shown in Figure 3. The
‘m’ parameters versus the percent sand, silt,                                           divisional soil-water characteristic curves can
and clay of a soil. It was hypothesized that as a                                       then be summed starting with the smallest
soil tended towards uniformity, the ‘n’ and ‘m’                                         particle size and continuing until the volume of
parameters would show a trend towards a                                                 pore space is equal to that of the entire
particular value. The particle sizes falling                                            heterogeneous soil. The result is a theoretically
between pure clays, pure silts and pure sands                                           predicted soil-water characteristic curve.
were then approximated.




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                               3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                        100%
                        90%             Fit curve
                        80%             Experimental
      Percent Passing

                        70%
                        60%
                        50%
                        40%
                        30%
                        20%
                        10%
                         0%
                          0.0001                      0.01                            1                         100

                                                         Particle Size (mm)
                               Figure 3 Small divisions of particle size used to build complete SWCC


                                                                             fit the experimental data as well as
IMPLEMENTATION OF THE SWCC                                                   experimental data points and generated data
PREDICTION INTO SOILVISION                                                   points on the best fit curve. Figure 5 shows the
   Information relevant to describing the grain-                             second page of the grain-size distribution form.
size distribution is organized in a single form in
the SoilVision knowledge-based system. Figure                                   The header on the form allows for a number
4 shows the grain-size form for the knowledge-                               of helpful functions and algorithms. If soil data
based system. Two pages are required to                                      consists of % Coarse, % Sand, % Silt, %Clay
present the information. The first page contains                             or D10, D20, D30, D50, or D60 data on page
parameters controlling the fit of grain-size, the                            two of the main soil form, pressing a button
smallest particle diameter, the error between                                will convert this data into experimental points
the fit data and experimental data, the error                                along the grain-size distribution graph. Once
between predicted SWCC and experimental                                      experimental data is obtained, pressing Fit
data predicted and experimental data, and                                    Curve! will initiate the linear regression
                                                                             algorithm that will best-fit the equation to
counters which Access® uses to identify
                                                                             experimental data. The results of the fit can be
individual records. Page one also contains the
                                                                             viewed by pressing the Graph! button and a
packing porosity field which controls the
                                                                             soil-water characteristic curve can be predicted
prediction of the soil-water characteristic
                                                                             by pressing the Predict SWCC... button.
curve. Page two displays the equation used to




                                                                                                                             5
                    3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                              Figure 4 Page one of the grain-size distribution form




                              Figure 5 Page two of the grain-size distribution form



                                                                  error. A good curve fit of the grain-size curve
CONCLUSIONS                                                       is essential for the prediction of a reasonable
   The readapted Fredlund & Xing (1994)                           soil-water characteristic curve. The minimum
equation produces a satisfactory fit of the                       particle size was also found to have an
grain-size distribution. Figure 3 shows that the                  influence on the prediction of the soil-water
experimental data can be fit with a minimal                       characteristic curve prediction. If the minimum
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                     3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997
particle size variable was too low, the                            the accuracy of the prediction algorithm
overabundance of clay size particles woul                          appears to be reasonable. Results tended to be
dominate the prediction. If the minimum                            sensitive to the packing porosity and more
particle size was too high, an absence of                          research is required in this regard. Soils with
smaller particles would result in the soil drying                  experimental data for both the grain-size curve
out prematurely.                                                   and the soil-water characteristic curve were
                                                                   extracted from the database. The results of
   The prediction of soil-water characteristic                     comparisons between experimental and
curve from the grain-size distribution was                         predicted data can be seen in Figure 6, Figure
found to be particularly accurate for sands, and                   7, Figure 8, Figure 9, Figure 10, Figure 11,
reasonably accurate for silts. Clays, tills and                    Figure 12, and Figure 13.
loams were more difficult to predict although




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                                        3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                           100%
                             90%                     Fit curve
                             80%                     Experimental
       Percent Passing


                             70%
                             60%
                             50%
                             40%
                             30%
                             20%
                             10%
                              0%
                               0.0001             0.001              0.01               0.1                1               10         100
                                                                   Particle Size (m m )
                                                Figure 6 Grain-size distribution fit for a Sand (# 10720)


                           0.40

                           0.35
Volumetric Water Content




                                                                                                Predicted from Grain-size
                           0.30
                                                                                                Experimental
                           0.25

                           0.20

                           0.15

                           0.10

                           0.05

                           0.00
                                  0.1            1               10              100             1000            10000            100000 1000000
                                                                         Soil Suction (kPa)
                              Figure 7 Comparison between experimental and predicted curves for Sand (# 10720)



                                                                                                                                             8
                                        3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                              100%
                              90%                  Fit Curve
                              80%                  Experimental
            Percent Passing

                              70%
                              60%
                              50%
                              40%
                              30%
                              20%
                              10%
                               0%
                                0.0001             0.001             0.01               0.1                1               10        100
                                                                   Particle Size (mm)
                                           Figure 8 Grain-size distribution fit for a Loamy Sand (# 10741)



                           0.40
Volumetric Water Content




                           0.35
                                                                                                Predicted from Grain-size
                           0.30
                                                                                                Experimental
                           0.25

                           0.20

                           0.15

                           0.10

                           0.05

                           0.00
                                  0.1            1               10               100             1000            10000           100000 1000000
                                                                          Soil Suction (kPa)
                           Figure 9 Comparison between experimental and predicted curves for a Loamy Sand (# 10702)



                                                                                                                                            9
                                        3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                            100%
                             90%                     Fit curve
                             80%                     Experimental
          Percent Passing

                             70%
                             60%
                             50%
                             40%
                             30%
                             20%
                             10%
                              0%
                               0.0001              0.001             0.01               0.1                1               10         100
                                                                   Particle Size (mm)
                                                   Figure 10 Grain-size distribution for a Sand (# 350)


                           0.40
Volumetric Water Content




                           0.35
                                                                                                Predicted from Grain-size
                           0.30
                                                                                                Experimental
                           0.25
                           0.20
                           0.15
                           0.10
                           0.05
                           0.00
                                  0.1            1               10              100             1000            10000            100000 1000000

                                                                         Soil Suction (kPa)
                              Figure 11 Comparison between experimental and predicted data for a Sand (# 350)




                                                                                                                                            10
                                        3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997




                           100%
                             90%                     Fit Curve
                             80%                     Experimental
        Percent Passing

                             70%
                             60%
                             50%
                             40%
                             30%
                             20%
                             10%
                              0%
                               0.0001             0.001              0.01               0.1                1               10         100
                                                                   Particle Size (mm)
                                              Figure 12 Grain-size distribution for a Silt Loam (# 10861)


                           0.40
                                                                                                        Predicted from Grain-size
Volumetric Water Content




                           0.35
                                                                                                        Experimental
                           0.30

                           0.25

                           0.20

                           0.15

                           0.10

                           0.05

                           0.00
                                  0.1            1               10              100             1000            10000            100000 1000000
                                                                         Soil Suction (kPa)
                            Figure 13 Comparison between experimental and predicted data for a Silt Loam (# 10861)




                                                                                                                                            11
                    3rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, 1997
                                                                  Fredlund, M.D., Sillers, W.S., Fredlund, D.G.,
ACKNOWLEDGEMENTS                                                     Wilson, G.W., 1996, Design of a
   I wish to acknowledge the help of G.W.                            knowledge-based system for unsaturated
Wilson in forming some of the ideas for this                         soil properties, Third Canadian Conference
prediction. Also of note was the help I recieved                     on Computing in Civil and Building
from Sai Vanapalli locating previous research                        Engineering, pp. 659-677
done in this field.
                                                                  Ghosh, R.K., 1980, Estimation of soil-
                                                                    moisture characteristics from mechanical
REFERENCES                                                          properties of soils, Soil Science Journal,
                                                                    Vol. 130, No. 2, pp. 60-63
Aberg, B., 1996, Void sizes in granular soils,
  Journal of Geotechnical Engineering, Vol.
                                                                  Gupta, S.C., and Larson, W.E., 1979,
  122, No. 3, pp. 236-239
                                                                    Estimating soil-water retention
                                                                    characteristics from particle size distribution,
Ahuja, L.R., Naney, J.W., and Williams, R.D.,
                                                                    organic matter percent, and bulk density,
  1985, Estimating soil-water characteristics
                                                                    Water Resources Research Journal, Vol. 15,
  from simpler properties or limited data, Soil
                                                                    No. 6, pp. 1633-1635
  Sci. Soc. Am. Journal., Vol. 49, pp. 1100-
  1105.
                                                                  Harr, M.E., 1977, Mechanics of particulate
                                                                    media, McGraw - Hill International Book
Arya, L.M., and Paris J.F., 1981, A
                                                                    Company, New York, 27-33
  physicoempirical model to predict the soil
  moisture characteristic from particle-size
                                                                  Wagner, L.E., and Ding, D., 1994,
  distribution and bulk density data, Soil
                                                                    Representing aggregate size distributions as
  Science Society of America Journal, Vol.
                                                                    modified lognormal distributions, American
  45, pp. 1023-1030.
                                                                    Society of Agricultural Engineers, Vol. 37,
                                                                    No. 3, pp. 815-821




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