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Appendix According to Bekker (1960) the sinkage zx at any point below a track supported by small diameter wheels can be determined in the following way: z x � W � 0. 41* s * 2* l * k * s l 0 l 1, 23* x �1 � s 2 * Ph.D. Thesis Dirk Ansorge (2007) l 0 l �1 Eq. 7 Whereby the sinkage depends on the load W, the length of the track in contact with the soil l [m], the parameter k (n is assumed to be one in this case), half the distance between the rollers s [m], the track slag l/l0, and the position x [m] for which the sinkage should be calculated along the track line. For the sinkage below the last roller x equals s and the equation reduces to: z x � W � 0. 82* s * 2* l * k * s l 0 � l 1 Eq. 8 Both equations assume an n-factor = 1 which is a very soft soil. The implications of this and possible changes will be discussed later. The following drawing will explain the dimensions further: Figure 45: Track dimensions 11.1.7.3 Bekker-Theory applied s l 0 l The necessary diagrams to gain n and k were drawn from plate sinkage data of a 142 mm diameter plate from the soil bin for a DBD of 1.2 g/cm 3 , 1.4 g/cm 3 , 1.6 g/cm 3 , respectively. Measurements were replicated three times. For a first approximation, no correction for plate geometry was introduced and no statistical analysis was carried out. The spread of the data for each soil condition looked reasonable. The corresponding n and k values for the given soil conditions are summarized in Table 8. z 237
Appendix Table 8: n and k depending on initial DBD Soil Density n k Soft 1.2 g/cm 3 Medium 1.4 g/cm 3 Dense 1.6 g/cm 3 11.1.7.3.1 Sinkage of Tyres 0.89 700 0.62 2150 0.42 2400 The values from Table 8 were used in Eq. 6 to calculate the sinkage of the rear tyres only on medium soil condition; however the front tyres were calculated on all three soil conditions. The sinkage data for the soft and dense soil condition is from Antille (2006) and the medium condition from Ansorge (2005). The tracks have not been included at this stage. As breadth of the tyre once the width of the tyre was used and in a second step (as suggested by Bekker, 1960) half the length of the foot print as this was always shorter than the width of the tyre. The estimated rut depth is plotted against the measured rut depth in Figure 46. Predicted Depth (mm) 500 450 400 350 300 250 200 150 100 50 0 0 100 200 300 400 500 Measured Depth (mm) Real Contact Width 1:1 Line Half Contact Length Triaxial Fast Real Width Triaxia Fast, Half Length Linear (1:1 Line) Figure 46: Predicted vs. Measured depth of the tyres from plate sinkage data The predicted and measured rut depths for the dense and medium soil condition show tolerable deviation, whereby using the tyre width for the shortest contact length results in a slightly underpredicted sinkage compared to using half the contact length which results in a slightly overpredicted rut depth. However, on soft soil conditions, the deviation is about 100 %. This might be due to the fact that the Bekker model assumes an infinite soil depth below, whereas in the soil bin, the maximum depth is 750 mm. On medium soil conditions, the results could be replicated using the plate sinkage data gained from tests in the triaxial test as described in Section 2.8. This shows that plate sinkage tests can be used for both the Ph.D. Thesis Dirk Ansorge (2007) 238
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Cranfield University School of Appl
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Abstract Ancillary experiments show
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Table of Contents TABLE OF CONTENTS
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Table of Contents 4.1.3 Analysis of
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Table of Contents 11.1.1.1 Comparis
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List of Figures and Tables Figure 3
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List of Figures and Tables Figure 1
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Nomenclature NOMENCLATURE Abbreviat
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Introduction 1 INTRODUCTION 1.1 Bac
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Introduction � Ansorge, D. and Go
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Introduction 1.2 Aim To elucidate t
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Introduction a) the soil compaction
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Experimental Methods 2.1.1.1 Test F
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Experimental Methods had been mount
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Experimental Methods track; the loa
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Experimental Methods 800/10.5/2.5 t
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Experimental Methods term. In the m
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Experimental Methods Soil Surface F
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Experimental Methods Depth (cm) 0 1
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Experimental Methods ence surface c
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Experimental Methods chine derives
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Experimental Methods depth. The dat
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Experimental Methods with water and
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Experimental Methods 2.4 Statistica
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Laboratory Studies Into Undercarria
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Field Study With Full Size Combine
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Alleviation of Soil Compaction Howe
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Alleviation of Soil Compaction not
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Alleviation of Soil Compaction in a
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Alleviation of Soil Compaction diff
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Soil Compaction Models sibilities t
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Soil Compaction Models depends on t
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Soil Compaction Models Wroth (1968)
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Soil Compaction Models however, the
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Soil Compaction Models level. Criti
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Soil Compaction Models Utilizing Ke
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Soil Compaction Models average of m
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Soil Compaction Models Depth (mm) -
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Soil Compaction Models ture content
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Soil Compaction Models with four ot
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Soil Compaction Models Predicted In
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Soil Compaction Models Depth (mm) -
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Soil Compaction Models and 13.7 % b
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Soil Compaction Models Rel. Density
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Soil Compaction Models VCL paramete
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Soil Compaction Models The approach
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Soil Compaction Models surface stay
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Soil Compaction Models This result
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Soil Compaction Models 6.6.1.3 Wate
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Soil Compaction Models σσ 1 (kPA)
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Soil Compaction Models pressure to
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Soil Compaction Models The response
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Soil Compaction Models On medium so
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Soil Compaction Models SOILFLEX tak
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Ancillary Experiments 7 ANCILLARY E
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Ancillary Experiments Average conta
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Ancillary Experiments In order to c
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Ancillary Experiments contrary, the
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Ancillary Experiments Figure 102: S
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Ancillary Experiments track and the
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Ancillary Experiments even when hav
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Ancillary Experiments 7.3.2 Influen
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Ancillary Experiments The results f
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Ancillary Experiments Figure 117: S
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Ancillary Experiments Contact Press
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Ancillary Experiments Figure 123: F
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Ancillary Experiments Sinkage (mm)
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Ancillary Experiments model which o
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Ancillary Experiments 7.3.5 The Inf
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Ancillary Experiments 7.3.7 Discuss
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Ancillary Experiments Terzaghi (194
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Ancillary Experiments contact area.
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Ancillary Experiments soil forward
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Conclusions � The longitudinal so
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Bibliography 10 BIBLIOGRAPHY Aboaba
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Bibliography Defossez, P., Richard,
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Bibliography Gregory, A.S.; Whalley
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Bibliography Lamande, M., Schjonnin
Page 203 and 204: Bibliography Seig, D., 1985. Soil C
Page 205 and 206: Appendix 11 APPENDIX Ph.D. Thesis D
Page 207 and 208: Appendix Figure 32: VCL sample at t
Page 209 and 210: Appendix comparison at the deepest
Page 211 and 212: Appendix Estimated Pressure (kPa) 2
Page 213 and 214: Appendix 11.1.1.2.1 SOCOMO One of t
Page 215 and 216: Appendix by Seig (1985) who showed
Page 217 and 218: Appendix Soil water content 15 % an
Page 219 and 220: Appendix Adapting critical state so
Page 221 and 222: Appendix density is obtained by add
Page 223 and 224: Appendix Table 5: Values of constan
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Page 227 and 228: Appendix 11.1.3.1 Dense/Hard and Lo
Page 229 and 230: Appendix 11.1.3.2 Stratified Soil C
Page 231 and 232: Appendix To summarize the ability t
Page 233 and 234: Appendix In the following the predi
Page 235 and 236: Appendix concentration factor of 4,
Page 237 and 238: Appendix 11.1.5.1 Confining Pressur
Page 239 and 240: Appendix Figure 24. The VCL created
Page 241 and 242: Appendix Rel. Density 2 1,9 1,8 1,7
Page 243 and 244: Appendix relation of � 1 to � 2
Page 245 and 246: Appendix Rel. Density 2 1,9 1,8 1,7
Page 247 and 248: Appendix Rel. Density 1,7 1,68 1,66
Page 249 and 250: Appendix Depth (mm) 0,0 100,0 200,0
Page 251 and 252: Appendix Figure 42: Plate in cookin
Page 253: Appendix � z � � �� k c p
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Page 259 and 260: Appendix with a slight deviation fr
Page 261: Appendix Table 12: DBD values for a
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