1

Fig. 1. The experimental design at Kuru. On the right 20 m sample plot divided to four subplots with penetration resistance and rut depth measurement points (●) and soil sample plots (○).

Table 1. Soil characteristics at the study plots. VWC = Volumetric water content (%) at 0–10 cm, 10–20 cm depth in mineral soil, PR = Penetration resistance (Mpa) at 20 cm, 10–40 cm depth, BD = Soil bulk density (g cm–3) at 0–10 cm, 10–20 cm depth in mineral soil, ARP = Average steel rod penetration (cm), Org. layer = Depth of organic layer (cm), Soil type (EN ISO 2002, 2004): Sandy Silt (1); Silty sand (2).
Plot VWC 0–10
Mean
(std.dev.)
%
VWC 10–20
Mean
(std.dev.)
%
PR 20
Mean

(std.dev.)

MPa
PR 10–40
Mean
(std.dev.)
MPa
BD 0–10
Mean
(std.dev.)
g
cm–3
BD 10–20
Mean
(std.dev.)
g
cm–3
ARP
Mean
(std.dev)
cm
Org. layer
Mean
(std.dev.)
cm
Soil type
11 39.62
(3.84)
26.58
(7.18)
1.63
(1.43)
1.80
(0.83)
1.35
(0.10)
1,32
(0.20)
64.47
(24.01)
10.45
(1.84)
2
12 31.31
(2.34)
33.93
(3.50)
1.46
(0.97)
1.55
(0.54)
1.12
(0.14)
1.24
(0.06)
55.80
(14.83)
9.60
(1.27)
2
13 32.77
(2.32)
37.93
(3.65)
1.37
(0.88)
1.38
(0.49)
1.17
(0.08)
1.26
(0.04)
66.32
(6.57)
10.82
(0.95)
2/1
14 64.35
(-)
46.12
(-)
1.02
(1.04)
1.35
(0.43)
0.73
(-)
1.27
(-)
54.00
(-)
12.00
(-)
2
All 35.41
(7.14)
33.93
(6.96)
1.45
(1.11)
1.56
(0.64)
1.19
(0.17)
1.27
(0.12)
61.82
(17.05)
10.33
(1.50)
 
21 39.18
(4.26)
34.38
(3.54)
1.38
(1.19)
1.56
(0.84)
1.29
(0.18)
1.43
(0.14)
49.59
(4.88)
13.06
(1.51)
2
22 25.26
(3.55)
28.62
(2.40)
1.85
(1.13)
1.75
(0.76)
1.17
(0.11)
1.36
(0.06)
55.30
(2.46)
9.90
(0.74)
2/1
23 29.28
(1.66)
32.38
(3.51)
1.41
(0.66)
1.38
(0.44)
1.00
(0.12)
1.22
(0.10)
51.61
(1.54)
7.42
(0.79)
2
24 41.88
(-)
36,48
(-)
0.88
(1.00)
1.51
(0.85)
0.95
(-)
1.58
(-)
24.00
(-)
10.00
(-)
2
All 31.34
(6.92)
31.59
(4.07)
1.50
(1.04)
1.56
(0.72)
1.14
(0.18)
1.34
(0.14)
51.10
(6.98)
10.06
(2.43)
 
All 33.47
(7.28)
32.65
(5.93)
1.48
(1.07)
1.56
(0.68)
1.17
(0.18)
1.31
(0.14)
56.57
(14.17)
10.20
(2.01)
2

Fig. 2. Particle size distributions of study plots.

3

Fig. 3. Penetration resistance profiles of study plots before harvesting.

4

Fig. 4. Relationships between volumetric water content (VWC, %) at 0–10 cm depth in mineral soil, penetration resistance before harvesting (PR, MPa), average at the depth of 20 cm and bulk density (BD, g cm-3) at 0–10 cm depth in mineral soil.

5

Fig. 5. The average rut depths of the study plots.

Table 2. Pearson correlation coefficients between rut depths (after one harvester pass and three forwarder passes) and soil properties calculated as averages for the test tracks. VWC = volumetric water content (%) 0–10/10–20 cm depth, BD = soil bulk density (g cm-3) 0–10/10–20 cm depth, PR = penetration resistance (MPa) 0–20/5–40 cm depth, Org. layer = depth of organic layer (cm), Stonin. = average rod penetration (cm), Volume = Stand volume before harvesting (m3 ha-1), Harv. rut = rut depth after harvester pass (cm), Rut = rut depth after three forwarder passes (cm).
VWC
0–10
VWC
10–20
BD
0–10
BD
10–20
PR
0–20
PR
5–40
Org. layer Stonin. Volume Harv.
rut
Rut
VWC
0–10
Pearson Correlation 1 .003 .297** .219* –.294** –.081 .416** .082 .287** .269** .445**
Sig. (2-tailed) .974 .001 .020 .002 .395 .000 .389 .002 .004 .000
VWC
10–20
Pearson Correlation 1 –.115 –.091 –.132 –.198* .216* –.018 .094 –.070 –.049
Sig. (2-tailed) .227 .335 .165 .036 .022 .848 .320 .463 .610
BD
0–10
Pearson Correlation 1 .246** .009 .202* .542** .130 .259** –.009 .058
Sig. (2-tailed) .009 .923 .032 .000 .171 .006 .921 .542
BD
10–20
Pearson Correlation 1 –.049 .070 .641** –.493** .206* .096 .195*
Sig. (2-tailed) .609 .462 .000 .000 .029 .310 .038
PR
0–20
Pearson Correlation 1 .785** –.110 –.087 –.075 –.240* –.296**
Sig. (2-tailed) .000 .248 .359 .427 .010 .001
PR
5–40
Pearson Correlation 1 .050 –.048 .026 –.310** –.307**
Sig. (2-tailed) .598 .614 .785 .001 .001
Org.
layer
Pearson Correlation 1 .007 .493** .165 .276**
Sig. (2-tailed) .941 .000 .081 .003
Stonin. Pearson Correlation 1 .019 .186* .146
Sig. (2-tailed) .843 .049 .122
Volume Pearson Correlation 1 .100 .207*
Sig. (2-tailed) .293 .027
Harv.
rut
Pearson Correlation 1 .787**
Sig. (2-tailed) .000
Rut Pearson Correlation 1
Sig. (2-tailed)
** = Correlation is significant at the 0.01 level (2-tailed).
* = Correlation is significant at the 0.05 level (2-tailed).
Table 3. Mixed-linear models predicting the logarithm of the average rut depth (cm) in a measurement point. CM = Cumulative mass driven over measurement point (kg), VWC = Volumetric water content (%) at 0–10 cm depth in mineral soil, PR = Penetration resistance (MPa) at 5–40 cm depth, OL = organic layer depth (cm), Hr = harvester rut depth (cm), σ2plot = variance for the plot, σ2meas = variance for successive measurements, ρplot and ρmeas correlation coefficients for measurement points within plot and for successive measurements. AIC = Akaike´s Information Criterion.
Model Parameter 1
Estimate
(SE)
Sig. 2
Estimate
(SE)
Sig. 3
Estimate
(SE)
Sig. 4
Estimate
(SE)
Sig. 5
Estimate
(SE)
Sig.
Fixed            
  Intercept 1.1785
(0.200)
0.000 0.028
(0.337)
0.935 –0.168
(0.148)
0.704 0.312
(0.483)
0.522 0.313
(0.097)
0.002
  CM 0.0000084
(0.0000004)
0.000 0.0000084
(0.000)
0.000 0.0000084
(0.0000004)
0.000 0.0000084
(0.0000004)
0.000 0.0000065
(0.000)
0.000
  PR –0.375
(0.121)
0.002 –0.375
(0.120)
0.002
  VWC 0.018
(0.009)
0.067
  OL, cm 0.079
(0.042)
0.066 0.084
(0.043)
0.059
  Hr     0.190
(0.017)
0.000
Random    
  σ2plot 0.631
(0.105)
0.000 0.647
(0.106)
0.000 0.652
(0.105)
0.000 0.610
(0.103)
0.000 0.349
(0.054)
0.000
  ρplot 0.173
(0.126)
0.170 0.035
(0.122)
0.776 0.060
(0.121)
0.619 0.157
(0.127)
0.216 0.138
(0.114)
0.223
  σ2meas 0.319
(0.043)
0.000 0.320
(0.043)
0.000 0.317
(0.042)
0.000 0.319
(0.043)
0.000 0.177
(0.017)
0.000
  ρmeas 0.531
(0.067)
0.000 0.531
(0.067)
0.000 0.526
(0.121)
0.000 0.529
(0.067)
0.000 0.213
(0.083)
0.010
AIC 1255.8   1266.1 1263.0 1256.5 911.8
6

Fig. 6. The influence of volumetric water content (%) at 0–10 cm depth in mineral soil on rut formation estimated with model 2 in Table 3.

7

Fig. 7. The allowed total overpassed mass keeping final rut depth under 10 cm as a function of harvester rut depth (model 5 of Table 3).

8

Fig. 8. Penetration resistance (PR, MPa) at the depth of 10–40 cm, after consecutive machine passes. Measurements are adjusted for rut depths.

9

Fig. 9. Average penetration resistance (PR, MPa) of 6 subplots after consecutive machine passes at soil depths of 20, 30 and 40 cm. Measurements are adjusted for rut depths.

10

Fig. 10. Penetration resistance profiles before and after harvesting. Measurements after harvesting are adjusted for average rut depth.

11

Fig. 11. Relationships between volumetric water content VWC (%) at 0–10 cm depth in mineral soil before harvesting, rut depth and penetration resistance PR (MPa) at the depth of 30 cm (adjusted for rut depth) after 6 machine passes.

Table 4. Mixed-linear models predicting the logarithm of the average PR (MPa) at the depth of 10–40 cm in a measurement point. CM = Cumulative mass driven over measurement point (kg), VWC = Volumetric water content (%) at 10–20 cm depth in mineral soil, BD = soil bulk density (g cm–3) at 10–20 cm depth in mineral soil, Rdepth = rut depth (cm), σ2p = variance for the plot, σ2pm = variance for the measurement point, σ2meas and ρmeas variance and correlation coefficients for successive measurements. AIC = Akaike´s Information Criterion.
Model Parameter 1
Estimate
(SE)
Sig. 2
Estimate
(SE)
Sig. 3
Estimate
(SE)
Sig. 4
Estimate
(SE)
Sig.
Fixed        
  Intercept 3.601
(0.879)
0.022 3.539
(0.482)
0.000 3.094
(0.629)
0.012 2.997
(0.392)
0.000
  CM 0.00000131
(0.0000004)
0.002 0.00000130
(0.0000004)
0.002 0.00000291
(0.0000006)
0.000 0.00000312
(0.0000006)
0.0000
  VWC –0.042
(0.016)
0.075 –0.042
(0.009)
0.000 –0.036
(0.012)
0.047 –0.035
(0.007)
0.000
  BD –1.324
(0.436)
0.050 –1.288
(0.242)
0.000 –1,064
(0.313)
0.034 –1.012
(0.197)
0.000
  Rdepth –0.033
(0.008)
0.000 –0.038
(0.008)
0.000
Random
  σ2p 0.025
(0.024)
0.302 0.011
(0.012)
0.369
  σ2pm 0.006
(0.008)
0.490 0.021
(0.012)
0.087 0.000
(0.007)
0.958 0.006
(0.008)
0.482
  σ2meas 0.118
(0.014)
0.000 0.119
(0.014)
0.000 0.115
(0.013)
0.000 0.116
(0.013)
0.000
  ρmeas 0.096
(0.0099)
0.333 0.109
(0.101)
0.278 0.080
(0.096)
0.406 0.086
(0.097)
0.371
AIC 205.6 210.8 199.2 200.6