Directory UMM :Data Elmu:jurnal:S:Soil & Tillage Research:Vol54.Issue1-2.Mar2000:

Soil & Tillage Research 54 (2000) 41±53

A compartmental model to simulate temporal changes
in soil structure under two cropping systems with
annual mouldboard ploughing in a silt loam
J. Roger-Estradea,*, G. Richardb, H. Manichonc
a
INRA, Laboratoire d'Agronomie INRA INA-PG, BP 01, 78850 Thiverval-Grignon, France
INRA, Unite d'Agronomie de Laon-PeÂronne, Rue Fernad Christ, 02007 Laon Cedex, France
c
CIRAD-CA, Agropolis, BP 5035, 34032 Montpellier Cedex, France

b

Received 7 October 1998; received in revised form 21 May 1999; accepted 1 December 1999

Abstract
A practical model of the soil structure dynamics in ploughed ®elds can be a powerful aid to farmers attempting to optimise
their management practices. This paper describes a compartmental model that simulates the changes over several years in an
indicator of the effects of cropping systems on soil structure. This indicator, the proportion of severely compacted clods in the
ploughed layer, was measured in two plots at the INRA Experimental Centre at Grignon (Yvelines, France), where two

cropping systems produced very different compaction conditions in a silt loam. The ploughed layer was considered to be a set
of elementary compartments delimited by the wheel tracks and actions of tillage tools. The percentage of severely compacted
clods in each elementary volume changed with time due to transfer between compartments during mouldboard ploughing,
compaction and fragmentation. The proportion of severely compacted clods changed exponentially until it reached a plateau,
after about 8 years. The equilibrium values of the indicator were very similar to those measured in the experimental plots. The
model was very sensitive to the rate at which severely compacted clods were lost, probably because the vertical distribution of
these clods in the soil pro®le was not taken into account in this compartmental model. The model in its present state can be
used to compare the effects on soil structure of various technical changes. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Cropping system; Soil structure; Soil compaction; Soil fragmentation; Mouldboard ploughing; Compartmental model

1. Introduction
The structure of the soil in the ploughed layer of a
cultivated ®eld is in¯uenced by external factors, both
man-made (e.g., wheeling, tillage tools) or natural
*

Corresponding author. Tel.: ‡33-1-30-81-54-12; fax: ‡33-130-81-54-25.
E-mail address: jroger@jouy.inra.fr (J. Roger-Estrade).

(e.g., climate, fauna, roots). These factors can cause

compaction, fragmentation or even displacement of
the soil (Boizard et al., 1994). The combined effects of
these factors alter the characteristics of the soil which
de®ne its structure (Dexter, 1988; Stengel, 1990),
particularly the spatial arrangement, size and shape
of the soil particles, and consequently the pore space
volume. A cropping system is characterised by the
scheduling and nature of the cultivation operations

0167-1987/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 1 9 8 7 ( 9 9 ) 0 0 1 1 1 - 7

42

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

used for successive crops. Each of these operations is
de®ned (Manichon, 1988) by (1) the nature of the
mechanical stress it applies to the soil, and by (2) the
size and the spatial location of the soil volumes

affected by this stress. Thus, the soil structure generally varies greatly, at a metric or decimetric scale,
from one part of a cultivated ®eld to another. The
scheduling of successive operations also determines
the conditions under which the stress occurs and thus
the reaction of the soil. It also determines the intensity,
and sometimes the nature, of the action of natural
factors. It is dif®cult to forecast the overall effect of a
cropping system on the evolution of the structure of
the ploughed layer, for at least three reasons. First,
most studies on the intrinsic properties of the material
have been done in the laboratory, and their results are
not readily transposable to the ®eld (Kay et al., 1988).
Second, many studies on changes in soil structure have
examined only one of the processes involved. They are
generally devoted to compaction (Ragahvan et al.,
1990), and few have examined fragmentation and
displacement. Third, available models describing
the processes in¯uencing soil structure use input
and output variables that are in general not compatible. It is thus impossible to predict the effect of
successive operations when they involve different

mechanical processes.
Soil structure (in interaction with climate) in¯uences crop yield, (Hadas et al., 1978; Tardieu and
Manichon, 1987), soil biological activity (Sims,
1990), the transport of water and solutes (Jarvis
et al., 1991; Gerke and Van Genuchten, 1993; Pikul
and Zuzel, 1994; Curmi et al., 1996), emissions of
nitrous oxide from the soil (Ball et al., 1997), and the
risk of water erosion (Bresson and Boif®n, 1990). A
model that could predict changes in soil structure at

the ®eld scale under the in¯uence of management
practices would thus be very useful for evaluating
improvements in sustainable cropping systems.
This paper describes a compartmental model which
concerns cropping systems including annual ploughing. It was established in a ®eld trial designed in such a
manner that the tool width and location of wheel
tracks allowed a precise analysis of the effects of
compaction, fragmentation and soil displacement on
soil structure dynamics. We studied two plots where
the cropping systems produced very different degrees

of compaction conditions. Soil structure was ®rst
described using a morphological description of the
ploughed layer. This method (Manichon, 1982, 1987)
allows the zones and clods showing different compaction degrees in a soil pro®le to be identi®ed visually
and classi®ed from macroscopic features. Then we
evaluated an indicator of soil structure, the proportion
(in mass) of severely compacted clods within the
ploughed layer. The objectives of this study were
(1) to describe the assumptions of the model, (2) to
describe the model itself, and (3) to discuss its ability
to simulate the changes in the indicator of soil structure over time.

2. Material and methods
2.1. De®nition of the indicator of soil structure
Manichon (1982, 1987) proposed a method for
describing the soil structure in cultivated layers that
is based on the morphology of the soil elements
created by tillage: ®ne soil and clods (diameter
>2 cm). The method identi®es three types of clods
(Table 1) on the basis of their morphology, mainly the

Table 1
De®nition of internal clod structure (from Manichon, 1982)
Type of internal
clod structure

Morphology

Apparent structural porosity

Bulk density of air
dried clodsa (g cmÿ3)

D
F
G

Smooth-breaking faces
Near D, but with nascent cracks
Aggregates whose morphology varies.

Structural porosity is visible. Very rough
breaking faces

Very low to zero
Variable, crack type
Variable (quantity and morphology)
of various types (cracks, voids between
the aggregates, tubular)

1.74±1.85
1.67±1.80
1.35±1.70

a
Min±max values of the bulk density measured on three populations of clods (D, G and F) sampled in the tilled layer of the experimental
plots at the INRA Experimental Center in Grignon (Manichon, 1982; Coulomb et al., 1990).

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

Fig. 1. The relationships between the clod types and ®ne soil.

Numbers beside arrows refer to the assumptions about the
processes responsible for these relationships: 1: creation of a
continuous structure (effects of severe compaction under wheel
tracks; possibly creation under special climatic conditions for
swelling clay soils (Ney, 1987)); 2: fragmentation by tillage tools;
3: agglomeration of aggregates (effects of moderate compaction,
climate or fauna); 4: fragmentation by climate (swelling and
shrinkage); 5: ¯uctuations without any change in the internal
structure of the clods. See Table 1 for de®nition of clod structure.

importance and characteristics of the apparent structural porosity. These three clod types and ®ne soil coexist within the ploughed layer in proportions that
depend on the cropping system (Manichon and RogerEstrade, 1990; Coulomb et al., 1990). The composition of a given soil volume in the ploughed layer
changes in response to the mechanical stresses
applied, which may cause transformation from one
state to another by fragmentation or compaction. The
type and degree of change, in a given texture, depend
on the initial state (structure and moisture content) of
the soil volume and on the energy of the stress applied
(Koolen, 1994). These processes are shown in Fig. 1.
The spatial variations in the structure of the whole

ploughed layer are mainly due to the fact that the
different soil volumes in this horizon are subjected to
different mechanical stresses, depending on their location (depth and position relative to the wheel tracks).
Thus climate (arrow 4 in Fig. 1) has its greatest effect
near the soil surface. The fragmentation caused by
tillage during seed bed preparation (arrow 2 in Fig. 1)
is also greater in the upper part of the soil pro®le. On
the other hand, climate has very little direct action on
soil structure below the seed bed, in a temperate

43

climate for a loamy soil. In the same way, the soil
volumes which are severely compacted during wheeling are those located beneath the wheel tracks
(Richard et al., 1999). When compaction is not severe
(low axle load, low moisture content, zones located
near the wheel tracks beside the rut), it creates G clods
(arrow 3 in Fig. 1). Severe compaction (high moisture
content, high load intensity, repeated passages over the
same place) creates soil volumes having a D internal

structure, whatever the initial structure of the material
(arrow 1 in Fig. 1). These compacted volumes are
generally decimetre-sized. They are reduced by fragmentation during tillage (arrow 2 in Fig. 1), without
altering their internal structure (Coulomb, 1992; Coulomb et al., 1993). Finally, the turnover and lateral
displacement of the furrow slices cut by the plough
also increases the spatial variation in the ploughed
structure, mixing materials from different soil
volumes (Kouwenhoven and Terpsta, 1972; RogerEstrade, 1991), and bringing soil volumes which were
at the bottom of the pro®le protected from the action of
climate, to the surface (Hadas, 1997).
Thus, soil structure within the ploughed layer is, at a
given moment, the result of a balance between compaction (creating D clods), fragmentation (reducing
them to ®ne soil or decreasing their size) and displacement during ploughing (mixing D clods from
different volumes). The proportion of D clods within
the ploughed layer is therefore an indicator of this
balance. We have used it as an indicator of the effects
of the cropping system on soil structure. The model
describes the changes in this indicator, from one year
to another.
2.2. Tillage and site characteristics

The INRA Experimental Centre at Grignon (Yvelines) is in the west part of the French Paris Basin. The
soil is an Orthic Luvisol, according to the FAO
classi®cation, developed from a loess of the recent
WuÈrm, about 2 m below which is a calcareous rock.
The ploughed layer (0±25 cm) of the two experimental
plots contained an average of 235 g clay kgÿ1, 665 g
silt kgÿ1, 93 g sand kgÿ1, 14 g organic matter kgÿ1,
and 5 g CaCO3 kgÿ1. We selected two cropping systems. The ®rst (CS1) had a cropping sequence in
which sowing occurred only in autumn and harvesting
only in summer: winter wheat (Triticium aestivum L.)

44

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

and winter rape (Brassica napus L.). The risk of
compaction was low in this case. The second crop
sequence (CS2) was maize (Zea mays L.)/winter
wheat, so that one harvest took place in autumn every
second year, when the soil in this region is often very
wet, causing a greater risk of compaction than in the
CS1 plot.
The experimental ®elds were divided into plots of
30 m17.5 m. These dimensions were adapted to the
experimental equipment used for crop management.
The tractor used for all cultivation operations had a
distance between the centres of the two rear wheels of
1.75 m, and the rear tyres were 35 cm wide. The tools
for seed bed preparation and seed drilling were also
1.75 m wide. Thus, the preparation and sowing tracks
could be located so that each experimental plot was
divided into 10 bands of one seed drill width. Each
band was bordered by two wheel tracks (Fig. 2). In
these experimental ®elds, each track was wheeled
twice for each operation: the tractor rolled in the
rut made at the preceding passage. Each wheel track
was common to two adjacent bands. Therefore, a
periodic pattern could be de®ned by one wheel track
(the corresponding position in the soil pro®le was
labelled L1) associated to the part of the band located
between two wheel tracks (labelled L3). All passages
were along these tracks once the plot was ploughed
and until harvested. A positioning system also allowed
the plots to be located at the same place every year,
which caused the wheel tracks to be in the same place

from one year to the next, with a precision of about
0.35 m. Wheel passages during harvesting (combine
harvester, maize picker, trailers) were not restricted to
the L1 position.
2.3. Soil structure observations
The soil structure in the ploughed layers of plots
CS1 and CS2 was examined using two methods: (1)
macroscopic observation of soil pro®les, and (2)
determination of the proportion of D clods. The soil
pro®les (whose width corresponded to that of one seed
drill and depth was 0.6 m) were located perpendicular
to the tillage direction and were examined while the
plots bore winter wheat. The macroscopic structural
features of the ploughed layer were mapped, using the
method of Manichon (1982, 1987).
The proportion of compacted clods in the L3 compartment was measured on four pro®les of each type.
All the soil was removed from the L3 compartment,
and separated into six samples, carefully positioned
from left to right of this compartment. Air-dried soil
was weighed and sieved to separate the ®ne soil from
the clods larger than 2 cm. The D and F clods were
separated from the G clods by their greater bulk
density. Preliminary observations of clods from the
tilled layer of plots at the Grignon Experimental
Centre (Manichon, 1982; Coulomb et al., 1993) had
shown that air-dried D and F clods were best separated
from the G clods by the bulk density threshold of

Fig. 2. Partition of the ploughed layer in the experimental plots in the INRA experimental centre at Grignon. L1 position is the part of the soil
pro®le located under the seed bed, below the wheel tracks and L3 position is the part of the soil pro®le located under the seed bed, outside the
wheel tracks.

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

1.67 g cmÿ3 (Table 1). Clods were sealed with paraf®n
and placed in a ZnCl2 solution whose density was this
threshold value. As there was very few F clods, the
fraction with a bulk density greater than
1.67 g cmÿ3was de®ned as the D fraction. The D
fraction was weighed. We computed the ratio of the
mass of the D fraction to the total mass of soil for each
sample. The mean of these six values gave the mean
proportion of D clods in the L3 position. The soil from
position L1 was also sampled to evaluate the proportion of D in this part of the pro®le.
2.4. Model structure
The ploughed layer is considered to be a set of
elementary volumes (compartments) delimited by the
action of the plough. The proportion of D clods in each
elementary volume is similar to a concentration which
changes time under the in¯uence of the processes
mentioned above. Each compartment is described
by its D content at a speci®c date each year, chosen
by convention just before harvesting. Three types of
¯ow are responsible for the changes in the D content in
a compartment: (1) the creation of D clods by compaction, (2) their transfer between compartments during ploughing due to lateral displacement of the
furrow slice (as the direction of displacement is
reversed from one year to the next, the reversibility
of the transfer between compartments is not simultaneous: the direction of the lateral displacement during
ploughing is reversed from one year to the next), and
(3) the loss of D clods due to seed bed preparation and
climate action.
2.4.1. De®nition of the compartments
One position L1 and one position L3 were assumed
to describe the basic pattern characteristic of these
experimental plots (Fig. 2). The L1 position contained
one compartment and L3 contained four compartments. These ®ve compartments all had the same
width (35 cm), corresponding to the wheel track width
in L1 and the width of the furrow slices cut by the
plough in L3. As we could only consider a ®nite
number of compartments, we added a loop to the
model. We assumed that the compartments on one
side of the pattern received soil from the compartments at the other side of the adjacent identical pattern
during ploughing. Every year ploughing caused redis-

45

tribution of the soil between compartments by lateral
displacement. We assumed that the coincidence
between the limits of the compartments and those
of the furrow slices was perfect. Thus, position L1 (the
®rst compartment) corresponded to a single furrow
slice cut every year.
2.4.2. Creation of D clods
In the CS1 plot, creation only occurred in the ®rst
compartment, as this was the only one which was
wheeled enough after ploughing to be compacted (soil
structure was not degraded during harvest as it
occurred in dry condition in summer). We assumed
that this compartment was entirely compacted every
year (D contentˆ100%), whatever the soil moisture
content during cultivation, because of the repeated
passages during the crop cycle. In the CS2 plot,
compaction also occurred in compartments of the
L3 position, during the maize harvest in autumn. This
operation was performed with a one row maize picker,
attached to the same tractor that was used for the other
®eld operations. There was thus one wheel track on
each maize inter-row and each track was wheeled
twice (once by the left-side wheels, once by the
right-side ones at the next passage, except for the ®rst
and the last passages in the plot). As the inter-row
spacing was 80 cm, there were two maize rows in each
band. The tractor rolled over the L1 position to harvest
one row, and over the L3 position to harvest the next
row. The trailer passages used the ruts of the tractor
carrying the maize picker. The repeated passages, the
generally high soil water content during maize harvest
and the weight of the maize picker (ca. 1 Mg), led to a
severe compaction under the wheel tracks at the L3
position. This was taken into account in the model by
compacting one compartment of the L3 position every
second year; its D content was set at 100%. As the
locations of the passages were not recorded, the
number of the compacted compartment in L3 was
randomly chosen from among the four of them.
2.4.3. Transfer coef®cients
We assumed that the transfer coef®cients remained
unchanged from one year to another (no change in the
plough characteristics). Assuming that the D clods
were uniformly distributed within the furrow slices,
we considered the proportion of D clods leaving a
given compartment during ploughing to be equal to

46

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

the proportion of soil leaving this same compartment.
There is only one model in the literature describing the
turnover and lateral displacement of furrows during
ploughing (Bous®eld, 1880). This has been used by
several authors (Nichols and Reed, 1934; SoÈhne,
1959; Feuerlin, 1966; HeÂnin et al., 1969). The above
model assumes that the furrow slice is turned upside
down and remains rigid during this movement. When
this movement is projected on a plane perpendicular to
the direction of motion of the plough, it consists of a
double revolution around two centres (D and C0 in
Fig. 3). The inclination of the furrow is given by the
sine of the angle a between the furrow border and the
plough pan, equal to the ratio P/L, where P is the
ploughing depth and L is the ploughing width. The soil
from compartment i cannot be projected further than
compartment i‡2 (Fig. 3). So, all the soil from one
compartment is redistributed within the two adjacent
compartments. The transfer coef®cients are then equal
to the proportion of soil belonging to compartment i
projected to compartment i‡2 (noted c) and i‡1
(noted 1ÿc). The value of c was estimated by a
geometrical analysis of the furrow section (A0 B0 C0 D0 )
in Fig. 3. Proportion of soil transferred from compartment i to compartment i‡2 was assimilated to the
proportion of the surface of the furrow section corre-

sponding to the area (EA0 B0 F) in Fig. 3. The remaining
part of the furrow section, 1ÿc, was assimilated to the
proportion of the surface of the furrow section corresponding to the area (EFC0 D0 ). The ploughing width
and depth at the Grignon Experimental Centre were 35
and 25 cm, respectively. The corresponding value of c
is 24.4%.
2.4.4. Loss of D clods
The D clods were only lost from the surface layer of
the ploughed horizon during seed bed preparation and
under the in¯uence of climate (fragmentation due to
swelling and shrinkage). The D clods in this layer were
fragmented and gradually transformed to ®ne soil. So
the D content was zero in the seed bed just before
harvest. With Coulomb et al. (1993), we assumed that
there was no loss of D clods during ploughing. We also
assumed that the loss of D clods from one compartment was proportional to the total D content of the
compartment at that time. As D clods were assumed to
be uniformly distributed throughout the compartments, the rate of loss was assumed to be equal to
the proportion of soil in the seed bed layer. This
coef®cient (noted r) was the same for all the compartments in L3, and was estimated to be the ratio between
the seed bed depth and the total depth of the ploughed

Fig. 3. Model of the furrow movement during ploughing. The ®gure shows a section of the furrow in a plane perpendicular to the direction of
motion of the plough. Vertical bars are the limits of the compartments i, i‡1, i‡2. A0 , B0 , C0 and D0 are the positions of the points A, B, C and
D, respectively, after ploughing. The transfer coef®cient (c) was assimilated to the proportion of the furrow projected from compartment i to
compartment i‡2 (i.e., the ratio of the surface of area (EA0 B0 F, dark grey) to the total surface of the furrow section (A0 B0 C0 D0 )).

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

Fig. 4. The compartmental model adapted to the CS1 plot. A is the
proportion of compacted clods (D content) to which the ®rst
compartment (corresponding to the L1 position) is forced every
year. r is the annual rate of D clod loss and c (resp. 1ÿc) is the
proportion of D clods transferred from compartment i to
compartment i‡2 (resp. compartment i‡1) every year. The
parameter values for the CS1 plot are Aˆ100%, rˆ20% and
cˆ24.4%. As the direction of the displacement is reversed from
one year to the next, the direction of the lateral displacement during
ploughing is similarly reversed from one year (above) to the next
(below).

layer. The average seed bed depth in Grignon was
5 cm and the ploughing depth was 25 cm. So, r was
calculated as follows:
r ˆ 5=25 ˆ 0:20:

(1)

Fig. 4 shows the model adapted to the CS1 plot in a
diagram form. The associated mathematical model is
given in Appendix A.

3. Results
3.1. Proportion of D clods
Fig. 5 shows the maps of the CS1 and CS2 plots,
summarising the data over several years. Both systems
had massive structures under the wheel tracks, and the
corresponding compartment of the soil pro®le (L1)

47

had a very low structural porosity. There was no
difference between the two seed beds, which were
entirely composed of ®ne soil. However, soil structure
in the part of the pro®le below the seed bed and outside
the wheel tracks (L3) appeared to be different in CS1
and CS2. The CS1 plot showed wide variations in the
spatial distribution of the compacted clods, which
were more frequent near the L1 compartment of the
left part of the map, and rarer in the centre of the
pro®le. The CS2 plot had a greater proportion of
compacted clods over the whole pro®le, and these
clods were more regularly distributed within the L3
compartment, although they were slightly more frequent in the part of the L3 compartment near the left
wheel track. The size distributions were also different:
the clods were, on average, bigger in CS2.
Table 2 shows the measured D contents in the L1
and L3 positions of the four pro®les investigated in
each plot. The D content was near 100% in L1 of both
CS1 and CS2 plots. This is coherent with the observations of the pro®les, which showed that soil structure
was massive under the wheeled part of the plots. In L3,
D content appeared to be about twice as great in CS2
as in CS1. The proportion was signi®cantly higher in
the sub-sample taken near the L1 compartment (No. 1)
than in the other compartments of the L3 position.
Thus, the two cropping systems resulted in different
soil structures in the ploughed layer, which were
perceptible not only from a morphological description
of the structure of the ploughed layer (Fig. 5), but also
by measuring the proportion of D clods in the L3
position of the pro®le. This result validates the choice
of the indicator of soil structure.
3.2. Simulations
3.2.1. CS1 plot
The initial conditions in CS1 and CS2 were ®xed
with a D content of zero in the four compartments of
the position L3. The results of the simulation are
shown in Fig. 6. The change with time in the D content
in position L3 (mean of the four compartments) was an
8-year initial phase, in which change was exponential,
followed by a plateau, when the system was in steady
state (Fig. 6a). The simulated content at equilibrium
was 36%. This value is very close to the measured
value of 33% (Table 2). Thus, the D clods represented,
at equilibrium, about one third of the total mass of soil

48

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

Fig. 5. Typical structural map of a soil pro®le in the CS1 plot (above) or a CS2 plot (below).

in the L3 position. The increase in the D content
occurred while there was no compaction in the L3
position and was thus only due to lateral transfer
during ploughing. The alternating direction of lateral

displacement from one year to the next during ploughing and the fact that the parameters were constant
throughout the simulation, rapidly brought the system
to a steady state. Other simulations, not presented

Table 2
Proportion of compacted clods (D internal structure) in the wheeled (L1, 1 sample) and the no-wheeled (L3, 6 samples) positions measured in
the four pro®les of the CS1 plot (above) and the CS2 plot (below)
Profile

L1 position

L3 position
1

2

3

4

5

6

Mean of the six samples
in the L3 position

CS1 plot
I
II
III
IV
Mean

97a
93
95
98
96a

40
62
56
59
54b

11
19
40
30
25c

34
16
39
19
27c

32
27
36
47
35c

29
30
27
34
30c

33
29
26
28
29c

30ab
30a
37a
36a
33

CS2 plot
I
II
III
IV
Mean

94
98
93
99
96a

62
69
53
59
67b

64
62
71
65
65b

79
77
69
70
74b

56
68
73
63
65b

77
76
78
79
78b

73
66
73
55
67b

68a
70a
70a
65a
68

Values are in percentages (g gÿ1).
The same letter in a same column or a same line indicates that the mean, in this line or column, are not different at the 10% level (analysis
of variance performed after log-transformation of the variables).
a

b

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

49

can be attributed to the lateral displacement of the
furrow slice during ploughing. When the system was
in a steady state, the alternating directions of displacement produced great symmetry between the compartments of L3 from one year to the next, with the highest
content in the second compartment when displacement was to the right and in the ®fth when the furrow
slice was displaced to the left.
3.2.2. CS2 plots
The changes in the D content in the four compartments of L3 are shown in Fig. 7a, for three random
examples. The general shape of the curve was similar
to that for the CS1 plots, but the mean value at

Fig. 6. Results of the simulation of the CS1 plot: (a) change with
time in the proportion of compacted clods (D content, %) in the L3
position (mean of the D content of the four compartments
belonging to the part of the pro®le located outside the wheel
tracks); (b) simulated D contents at equilibrium of each of the four
compartments (labelled 2±5) of position L3 (22nd year after lateral
displacement of the furrow towards the right).

here, have shown that the equilibrium content did not
depend on the initial D content. If a perturbation was
introduced in the simulation (by adding compaction to
a compartment of L3) while the system was in steady
state, the simulated value of the indicator deviated
from the initial trajectory, then returned to the equilibrium value after some years of simulation under the
initial conditions. The steady state is stable (Jacquez,
1985; PaveÂ, 1994). The model allowed us to simulate
the differences between compartments within the L3
position (Fig. 6b). The equilibrium values for the
compartments were rather different. Those near the
L1 position had higher values than those at the other
end of the pattern. This is consistent with the observations of soil pro®les shown in Fig. 5. This difference

Fig. 7. Results of the simulation of the CS2 plot: (a) change with
time in the proportion of compacted clods (D content, %) in the L3
position (mean of the D content of the four compartments
belonging to the part of the pro®le located outside the wheel
tracks); (b) simulated D contents (at equilibrium) of each of the
four compartments (labelled 2±5) of the L3 position (22nd year
after lateral displacement of the furrows toward the right).

50

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

equilibrium was higher, and the D content oscillated
around this average value after a period of 8 years. The
mean content was around 61%. As the value in Table 2
for the CS2 plots was measured when the crop was
wheat (i.e., after a maize harvest), they should be
compared to the mean values of the odd years in the
simulation, when the system is in a steady state. This
value is 66.5%.
The steady state of the system appeared to be
dynamically stable (PaveÂ, 1994), oscillating more or
less regularly around an equilibrium value that was
signi®cantly higher than that for the CS1 plots. The D
content obtained in the 22nd year of simulation in each
of the four compartments of L3 is shown in Fig. 7b.
The differences between compartments were less
marked than those in the simulation of the CS1 plots,
which is consistent with the observations of soil
pro®les shown in Fig. 5.

4. Discussion
The formalisation of the mathematical model led us
to make some simplifying assumptions concerning the
dynamics of soil structure in the ploughed layer. A ®rst
group of assumptions was related to the input and
output of D clods, a second group to the transfers
between compartments of the ploughed layer. The ®rst
group of assumptions were (1) the creation of 100% D
in the ®rst compartment every year and in one of the
four compartments of L3 once in every 2 years in the
CS2 plots, (2) no creation of D clods when harvesting
takes place in summer, and (3) the loss of all the D
clods in the seed bed.
Concerning the creation of D clods, the extension of
this model to farm conditions must better take into
account the compaction process. The repetition of the
passages at the same place in Grignon insured maximum compaction in L1 and L3. Noteworthy is the
fact that these traf®c rules are speci®c to the Experimental Centre at Grignon. They were adopted because
the small size of the experimental plots and to prevent
an uncontrolled extension of the compacted zones. We
need a more precise modelling of compaction in
cultivated ®elds before we can extend the model to
situations where the wheel passages are not so strictly
located. The present model allows integration of this
new information. It will also be necessary to have

accurate data on the water content in the plot and its
spatial variation (particularly as a function of depth)
before we can extend the model to farm situations.
This factor is most important for ®eld compaction with
a speci®c machinery (GueÂrif, 1990). We also considered D clods to be only created in soil volumes located
just beneath the tyres. This is consistent with the data
of Richard et al. (1999) for a similar soil type, showing
that zones of maximal compaction (with a D internal
structure) are located under the ruts.
Concerning the loss of D clods, we performed a
sensitivity analysis of the rate of loss of D clods
(parameter r). The value of this parameter was changed from 16 to 24% (corresponding, for a ploughing
depth of 25 cm, to a depth of 4±16 cm during seedbed
preparation). The equilibrium D content of the L3
position is shown in Fig. 8, as a function of the r value.
The equilibrium value dropped as the loss rate
increased: the D content was divided by three when
the secondary tillage depth was increased from 4 to
16 cm. This high sensitivity is probably due to the fact
that destruction of the D clods was overestimated
when the rate of loss was uniformly applied to all
the D of the compartments. Actually, D clods located
under the seed bed are protected from fragmentation.
The model would probably be less sensitive to the loss
rate if the vertical position of the D clods were taken
into account.

Fig. 8. Sensitivity of the model to the loss rate: proportion of
compacted clods in the L3 position at equilibrium as a function of
the annual rate of loss of the compacted clods (parameter r of the
model). The conditions for the simulations are those of the CS1
plot.

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

The second group of assumptions concerns: (1) the
way the turnover of the furrow slice was modelled
(particularly the fact that we assume that the furrow
remains rigid during this movement), (2) the coincidence between the limits of the compartments and
the passage of the plough, and (3) the uniform distribution of the D clods in the compartments (leading
to the assumption of transfer from one compartment to
another proportional to the existing stock of D clods).
A more realistic model of the plough action (randomising the location of the plough passage, or introducing changes in the furrow shape) would change the
values of the transfer coef®cients and the form of the
transfer matrix. Simulations, not presented here, made
with different transfer matrixes have shown that the
equilibrium values for the D content in the position L3
were not very sensitive to the form of this matrix. But
the distribution of the D clods between compartments
was greatly effected. We also tested the sensitivity of
the model to the value of the transfer coef®cient
(parameter c). This parameter depends on the ploughing width and depth. The c values obtained when the
ploughing width was increased from 30 to 50 cm and
the ploughing depth from 25 to 50 cm, ranged from 7
to 29% (Fig. 9). Equilibrium values of the D content of
the L3 position obtained when c was increased in this
way, increased slightly from 27 to 37%.

51

5. Conclusions
The similarities between the experimental values
and the simulations con®rm that the indicator selected
is suitable for assessing the cumulative effects of
cropping systems on soil structure in the ploughed
layer. This similarity also reinforces the validity of the
main assumption, that the interaction between the soil
conditions and the cultivation operations (location of
passages, depth of tool action, etc) determines the
changes in soil structure in the ploughed layer. It is
thus necessary to take into account all the cultivation
operations (and not only soil tillage) for modelling
changes in soil structure of the ploughed layer. Our
results for instance outlined the importance of the
effects of late harvesting on soil structure.
These results indicate that this method of modelling
the changes in soil structure at the soil pro®le level and
taking into account the successive cultivation operations of a cropping system is valid. The model in its
present state can be used to compare the effects on soil
structure of technical changes, such as working width.
But some aspects of the model must be improved.
The great sensitivity to the depth of secondary tillage
must be reduced. The main cause of this sensitivity is
that we have not taken into account the spatial distribution of the D clods within the ploughed layer,
where D clods are lost only from the upper part of this
horizon. The sensitivity would be reduced if we could
eliminate the D clods only in the upper part of
ploughed. This calls for a different method of simulation, on which we are presently working.
Secondly, the indicator is only based on evaluation
of the overall proportion of D clods in the ploughed
layer. This is not suf®cient to assess the effects of soil
structure on the rooting system. We also need to know
the size distribution of the compacted clods in the
ploughed layer (Tardieu and Manichon, 1987). This
requires simulating the changes in the clods size by
assessing fragmentation more accurately.

Appendix A.
Fig. 9. Sensitivity of the model to the value of the transfer
coef®cient: proportion of compacted clods in the position L3 at
equilibrium as a function of the annual proportion of these clods
transferred from one compartment to the next (parameter c of the
model). The conditions for simulation are those of the CS1 plot.

The following equations correspond to the diagram
shown in Fig. 4, for the compartment 3. Let us
consider xt3 to be the D content in this compartment
in year t, just before harvest. xt3 is the percentage of the

52

J. Roger-Estrade et al. / Soil & Tillage Research 54 (2000) 41±53

total soil in this compartment whose internal structure
is D. If ploughing has displaced the soil to the right in
year t, we have:
(all the soil in the third compartment
xt3 ˆ 0
xtÿ1
3
(proportion of the
has left this compartment) ‡cxtÿ1
1
volume of the ®rst compartment projected into the
(proportion of the volume of
third one) ‡…1 ÿ c†xtÿ1
2
the second compartment projected into the third one).
Some of the D clods disappear during seed bed
preparation and under the in¯uence of climate during
the crop cycle:
tÿ1
tÿ1
xt3 ˆ ‰0
xtÿ1
3 ‡ cx1 ‡ …1 ÿ c†x2 Š…1 ÿ r†

…r being the rate of loss†:

also zero because transfers towards the ®rst compartment have been neglected, and the D content in this
compartment is set at 1. The reasoning is the same
when ploughing throws the soil to the left; we have in
this case:
Xt ˆ …1 ÿ r† M0 Xtÿ1 ‡ Ut ;
with
2
3
xt1
0
6 xt2 7
6 0
6 t7
6
6 x3 7 ˆ …1ÿr† 6 0
6 t7
6
4x 5
4 c
4
t
x5
1ÿc
Xt
2

32 tÿ1 3 2 3
0
0
0
0
1
x1
6 tÿ1 7 6 7
0 1ÿc
c
0 7
76 x2tÿ1 7 6 0 7
6
7 6 7
0
0
1ÿc
c 7
76 x 3 7 ‡ 6 0 7
5 405
0
0
0
1ÿc 54 xtÿ1
4
c
0
0
0
0
xtÿ1
5
M0
Xtÿ1
Ut

Thus, at the end of the crop cycle:
tÿ1
xt3 ˆ ‰cxtÿ1
1 ‡ …1 ÿ c†x2 Š…1 ÿ r†:

References

We proceed in the same way for compartments 2, 4
and 5. The ®rst compartment is special: this compartment has a given D content (from compartments 4 and
5) after ploughing; the successive wheel passages
increase this content to 100% during cultivation after
ploughing. This simpli®es the equation for this compartment. Its D content is assumed to be constant at 1.
For the ®ve compartments we have:
xt1 ˆ ÿ1;


tÿ1
…1 ÿ r†;
xt2 ˆ …1 ÿ c†xtÿ1
1 ‡ cx5
ÿ tÿ1


t
tÿ1
x3 ˆ cx1 ‡ …1 ÿ c†x2 …1 ÿ r†;
ÿ


…1 ÿ r†;
xt4 ˆ cxtÿ1
‡ …1 ÿ c†xtÿ1
2
3
ÿ tÿ1


t
tÿ1
x5 ˆ cx3 ‡ …1 ÿ c†x4 …1 ÿ r†;
Using matrix notations, these equations become
Xt ˆ …1 ÿ r† M Xtÿ1 ‡ Ut ;
with
xt1
6 xt2 7
6 t7
6 x3 7 ˆ
6 t7
4x 5
4
xt5
t
3

2

X

2

0
0
0
0
6 1ÿc
0
0
0
6
1ÿc
0
0
…1ÿ r† 6
6 c
4 0
c
1ÿc
0
0
0
c
1ÿc
M

32 tÿ1 3 2 3
1
0
x1
6 tÿ1 7 6 7
c7
76 x2tÿ1 7 6 0 7
7 6 7
6
07
76 x3 7 ‡ 6 0 7
5 405
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xtÿ1
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Xtÿ1
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The matrix M is the transfer matrix: each element of
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column) is the transfer rate from compartment j to
compartment i. The coef®cients on the diagonal are
zero, because no soil from one compartment remains
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