Matric Potential (kPa)
4. A REVIEW OF SOIL COMPACTION MODELLING
4.2 Pseudo-Analytical Models
4.2.3 An overview of some of the pseudo-analytical soil compaction models that have been developed
Values for ai, a2 and a? were derived by O'Sullivan et al. (1994). The VCL tends to pivot about a point in the v -In P space as the water content changes. X was estimated from N and the coordinates of the pivot point, vp and pp (Equation 4.6).
N-vn
X = '- (4.6)
lnPP
The coordinates of the pivot point varied according to soil type (O'Sullivan et a/., 1994).
Defossez and Richard (2002) noted that the effect of the water content modelled by O'Sullivan et al. (1999) is higher than the effect of saturation described by Equation 4.3 in the model developed by Larson et al. (1980).
Now that the theory of most pseudo-analytical models has been described, the next section provides an overview of some of the pseudo-analytical models that have been developed and gives a specific evaluation of two pseudo-analytical models developed by Gupta et al. (1985) and O'Sullivan et al. (1999).
4.2.3 An overview of some of the pseudo-analytical soil compaction models that
Table 4.2 Summary of pseudo-analytical soil compaction models
Model Author Gupta et al. (1985) Binger and Wells (1992) Blackwell and Soane (1981)
Smith (1985)
O'Sullivan ef a/. (1999)
Stress - Strain behavioural component
Uses equation developed by Larson et al. (1980)
Uses equation developed by Larson et al. (1980)
Uses critical state theory to describe volume change Uses critical state theory to describe volume change Uses critical state theory to describe volume change
Context
Compaction in agricultural soils due to traffic
Effect of surface mining systems onSC
Simplified model to predict SC in agriculture
Able to compare SC caused by various wheel configurations and arrangements
Simplified Excel based model, that is easy for students to use
Gupta et al. (1985) verified their model on three different sites with two types of soil structure (see Table 4.3). They performed the wheeling tests under different water conditions for each site.
Table 4.3 Summary of the tests conducted by Gupta et al. (1985) and O'Sullivan et al.
(1999) (after Defossez and Richard, 2002)
Author
Gupta et al.
(1985)
O'Sullivan et al. (1999)
Site
Plot 1 Plot 2 Plot 3 Plot 1 Plot 2
Texture
Silty loam Loam Loam Silty loam Loam
Structural state
Homogeneous 1 m layer Homogeneous
1 m layer Ploughed 0.5 m
layer Homogeneous
0.5m layer Dense underlying subsoil at 0.35
m
Soil moisture
(g-g~1) 0.27 0.25 0.2 0.17 0.13 0.24
0.21
Way of loading
1 pass 1 pass
1 pass 1 pass
1 pass
Mean vertical
stress (kPa)
150 130 211 260 320 40 80 100
The maximum increase in dry density was found to be 0.3 Mg.m" . Each wheeling test was modelled by the calculation of dry density along the load axis and outside the load axis. These calculations take into account the mean soil water content above the plough pan. Gupta et al. (1985) calibrated their model using the concentration factor £to obtain better agreements between observed and simulated observations. They presented a model sensitivity analysis as a function of £ The change in predicted bulk density was shown to be within the error of the field measurements. Figure 4.5 illustrates a
comparison between the simulation and the measured data for the first site for dry density on the central load axis.
0.8
0.1
0.2
| 0.3
0.4
0.5
0.6 >—»
_|—n ^_
Pd (Mg.m^)
1.2 1.4 1.6 1.8
- • — i — ' —r —' — | — • ~ ~1— • — ! — ' — ' — • "
--&-• before wheeling -K— after wheeling
simulation
Figure 4.5 Comparison of simulated and measured observations for the model developed by Gupta et al. (1985). These results are from Plot 1 (see Table 4.3)
Figure 4.5 shows that the simulated and measured observations follow the same trends.
Gupta et al. (1985) found that the model did not perform well in the third plot. This was attributed to clods in the soil. Table 4.4 shows the maximum difference between the measured and simulated bulk densities as a function of depth in the three plots.
Compaction intensity is defined as the maximum difference observed when comparing the initial and final bulk density profiles as a function of depth. The simulation error (Apt,) is defined as the maximum difference when comparing the simulated and measured profiles of bulk density against depth (Defossez and Richard, 2002). Table 4.4 shows that the simulation error was between 0.12 and 0.33 Mg.m"3 for the trials run by Gupta et al. (1985). The error was found to be higher on the ploughed layer and lower on the artificially homogenous layers.
O'Sullivan et al. (1999) tested their model on two soil types and two types of soil structure (see Table 4.3). Their simulations of the dry density profile beneath the centre line of the tyres included the variation of water content through the soil, where as Gupta
et al. (1985) only took into account the mean water content above the plough pan.
O'SuUivan et al. (1999) tested two tractors in order to range the mean vertical pressure from 40 to 80 kPa. They found that the model accurately predicted the compaction events (see Figure 4.6).
Table 4.4 Evaluation of the models developed by Gupta et al. (1985) and O'SuUivan et al. (1999) (after Defossez and Richard, 2002)
Author
Gupta et al.
(1985) O'SuUivan et al.
(1999)
Site Plot 1 Plot 2 Plot 3 Plot 1 Plot 2
Tested model outputs 2D profile of dry
density pb(x,z) 1D profile of dry
density pb(z)
Compaction intensity
0.3 Mg m~3
0.2 Mg m"a
- 0.24 Mg m"3 0.22 Mg m"3
0.22 Mg m"3
Simulation error 4ob = 0.12Mgm"3
zlpb = 0.13Mgm"3
Apb = 0.33 Mg m"3 Apb = + 0.08 Mg m"3 Apb = 0.03 Mg m"3
Apb = 0.2 Mg rrf3
0.8
p^Mg.nrr3)
1 1.2 1.4 1,6 i a
0.1
? 0.2 a o
•n 0.3
0.4
0.5
1"" 1 1 1 -
1 '
1 !
-i-
• i i
i 1— [ l r — i - J - I —l— t -
i * i
! \ I x
i * ' / /1 ' «X/
\ VK
\N
W\
\j *\
H v \
: * v \
' v v\
v 1 L... 1 1 • .1 l _ 1 1— 1 1 —
1-"—1 1
<
•
. . .
Plot 1
- - G - - before wheeling -X— after wheeling
——— simulation
Figure 4.6 Comparison of simulated and measured observations for the model developed by O'SuUivan et al. (1999). These results are from Plot 1 (see Table 4.3)
Table 4.4 shows that the SC events caused an increase in dry bulk density of between 0.22 - 0.24 Mg.m"3. The differences between the measured and simulated observations were 0.08 and 0.03 Mg.m"3 for both experiments. The simulation with the plough pan at a 0.35 m depth yielded larger simulation errors. Table 4.4 confirms that both of these
models performed relatively well. The model developed by O'Sullivan et al. (1999) appeared to perform better than the model developed by Gupta et al. (1985). One of the pseudo-analytical models not described in this section is the SC model SOCOMO developed by (van den Akker (2004). This model will be described in detail in Section 4.4. The next section in this document gives a brief description of the finite element method (FEM) of modelling SC. It also provides the reader with a few model examples.