Nomenclature
Chapter 4 Water Retention Characteristic Curve of Fly Ash
4.3 Effect of measurement methodologies on WRCC of FA
55
applications for establishing the WRCC of cohesionless materials like FA. It may be useful only for determining the residual portion of the WRCC of FA.
56
10-1 100 101 102 103 104 105 106 0.0
0.1 0.2 0.3 0.4 0.5 0.6
10-1 100 101 102 103 104 105 106 0.0
0.1 0.2 0.3 0.4 0.5 0.6
10-1 100 101 102 103 104 105 106 0.0
0.1 0.2 0.3 0.4 0.5 0.6
10-1 100 101 102 103 104 105 106 0.0
0.1 0.2 0.3 0.4 0.5 0.6
FFA BFA
TM; MPS; EQT; W P4
(kPa)
NFA PA
Figure 4.4 Comparison of measured WRCC obtained using different methodologies
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The WRCC of FA was mathematically quantified by fitting Fredlund and Xing (FX) (Fredlund and Xing 1994) and van Genuchten (vG) (van Genuchten 1980) WRCC model to the experimental data. Equations 4.1 and 4.2 represent FX and vG models, respectively.
f f
n m
f r
r s
h a h
1 exp ln
1 1 10
ln 1 ln 1 )
( 6
(4.1)
vg nvg
mvgr s r
a
1
(4.2)
Where, mvg= 1-(1/nvg), θ(ψ) is the volumetric water content at suction ψ; θr is the residual volumetric water content; θs is the volumetric water content at saturation; avg and af are fitting parameters primarily dependent on the air entry value (AEV); nvg and nf are fitting parameters that are dependent on the rate of extraction of water from the soil; mf is the fitting parameter that depends on θr; and hr is the suction (in kPa) corresponding to residual state.
The FX and vG WRCC equation parameters were obtained by using SoilVision 4.21 and RETC code (SoilVision 4.21 2009; van Genuchten et al. 1991). SoilVision is a well- established database software for determining parameters of WRCC equations by following non-linear regression algorithm based on the quasi-Newton method (SoilVision 4.21 2009).
To understand the importance of the residual suction data (> 103 kPa) measured with the WP4, the results of FFA were combined with the individual TM, MPS, and EQT measurements for WRCC parameter quantification. The WRCC equations fitted to the individual and combined results of FFA are depicted in Figures 4.5 and 4.6. The plots for other FAs were similar and thus not presented here for the sake of brevity. The fitting parameters obtained are listed in Tables 4.2 to 4.5 for individual measurements and combinations. It can be noted from Figure 4.5 that TM data might not be adequate for quantifying the FA as compared to MPS and EQT data, which approaches the residual state.
The EQT has the advantage of having a few additional suction data towards the residual portion relative to the MPS. Figure 4.6 shows the utility of using residual suction data from TH-1392_10610413
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the WP4 in combination with TM results for better quantification of WRCC equations.
However, the influence of combined residual data on MPS and EQT measurements was not significant. The residual portion of the WRCC represented by vG is different from that represented by FX in Figures 4.5 and 4.6. The appended WP4 data with EQT in Figure 4.6 clearly indicate that vG equation defines the residual state better than FX. For better understanding, the WRCC parameters obtained for individual and combination measurements were compared as below.
10-1100 101 102 103 104 105 106 0.00
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
10-1 100 101 102 103 104 105 10610-1100 101 102 103 104 105 106 TM
MPS
(kPa)
Measured data; FX fit; vG fit
EQT
Figure 4.5 WRCC equations fitted to individual measurements of FFA
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Figure 4.6 WRCC equations fitted to combined measurements of FFA
Tables 4.2 and 4.3 present a comparison of FX and vG WRCC equation parameters, respectively, for all FAs corresponding to individual measurements. For all the cases, parameters obtained based on WP4 results are high. Specifically, the AEV obtained based on WP4 results was one order of magnitude greater than those obtained by other measurement techniques. This is not expected for cohesionless materials such as FA. Similarly, af, nf, and AEV values obtained based on TM measurements were marginally different from MPS and EQT results. Such an observation indicates that the inadequate range of the TM and inaccurate range of measurement by WP4 for suction less than 1000 kPa can lead to improper WRCC equation parameterization. However, it is quite interesting to note that for a particular measurement methodology, all FAs considered in this study exhibited comparable AEV and θr. A similar observation was made for vG WRCC, as shown in Table 4.3. All vG parameters based on WP4 measurements exhibited differences in comparison with TM, MPS
10-1100 101 102 103 104 105 106 0.00
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
10-1100 101 102 103 104 105 10610-1 100 101 102 103 104 105 106
TM+WP4
MPS+WP4
(kPa)
Measured data; FX fit; vG fit
EQT+WP4
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Tables 4.4 and 4.5 were presented to study the influence of combined data on WRCC parameterization of FAs. It was noted that af, mf, θr, and AEV values of individual and combined results are comparable for all methodologies used in this study. The parameter nf
of TM and TM+WP4 measurements varied marginally, whereas nf based on MPS and MPS+WP4 was different from EQT results. Again, avg and nvg parameters based on TM+WP4 measurements varied marginally from TM values and were close to MPS measurements, EQT measurements, and the combination results. The comparison indicates that the values of the parameters were influenced more by the low suction range. This was explicit from the parameters obtained for TM+WP4 measurements, which were close to those obtained for TM results. The WRCC parameters of different FAs varied and cannot be considered unique. However, the implication of marginal parametric variations of FAs corresponding to a particular measurement methodology needs to be further investigated.
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Table 4.2 Comparison of FX WRCC parameters of FA for different methodologies FX Parameter Materials
Measurement method TM MPS EQT WP4
af(kPa)
FFA 44.86 29.02 50.27 696