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Appendix 11.1.2.2 Practical Derivation of VCL Parameters As shown in Section 6.2.1 the semi-empirically estimated contact pressure from O’Sullivan et al. (1998), which is equal to � 1 in their model, is in good agreement with the contact pressure determined from measured contact area and tyre load from Ansorge (2005) and this study. The confining pressures � 2 and � 3 can be derived from the following equation gained by O’Sullivan et al. (1998) from empirical regression lines: � 1 ln c1 � z � c2 � A � c � n � 3 �� Eq. 1 where z is the depth (m), A is the contact area (m 2 ) and � is the concentration factor. c1, c2, and c3 are constants whose values are given in Table 5 and depend on the calculated stress ratio. To calculate � 2 and � 3 Eq. 1 would have to be solved for all tyres at each depth within the soil according to O’Sullivan et al. (1998). To simplify the approach a depth z of 0.4 m representing the average depth in the soil profile and a contact area A of 0.8 m 2 were assumed and � was varied from three to five representing possible soil conditions (dense to soft) as proposed by Fröhlich (1934). The resulting dependencies of � 2 and � 3 on � 1 are listed in Table 7 including the sum of � 2 and � 3 as this eases the calculation of mean normal pressure. In a first approximation � = 5 was chosen to calculate p from the contact pressures given in Table 7 of the treatments by Ansorge (2005) and this study. Knowing the initial density of 1.38 g/cm 3 and the average increase, final density can be calculated. Relative density (RD) is gained by dividing final dry bulk density (Final DBD) into 2.66. The average increase (AvI), the final DBD and RD are also given in Table 7. Figure 7 shows relative density vs. pressure. A logarithmic regression line was fitted to the data points representing a VCL for the sandy loam soil at a moisture content of approximately 9 % at which the experiments were conducted. The VCL for the sandy loam soil given by O’Sullivan et al. (1998) is also included for reference. Ph.D. Thesis Dirk Ansorge (2007) 205
Appendix Table 5: Values of constants c1, c2, and c3 to estimate stress ratio depending on depth, Constant contact area and � (O’Sullivan et al., 1998) � c1 5.30 4.66 c2 2.08 2.06 c3 0.21 0.32 Table 6: � 2 and � 3 depending on � 1 � 2 � � 2 � 3 Sum of � 2 and � 3 3 4 5 � 1 / 2.96 � 1 / 3.24 0.65 � 1 � 1 / 3.65 � 1 / 4.46 0.50 � 1 � 1 / 4.51 � 1 / 6.147 0.38 � 1 Table 7: Treatments and corresponding increase in DBD, final DBD, relative DBD and � 2 and � 3 , contact pressure and mean normal pressure for � = 5 Treatment (Section width[mm]/Load [t]/Inflation Pressure [bar]) AvI Final Ph.D. Thesis Dirk Ansorge (2007) DBD RD � 1 � 3 � 2 + � 3 Contact Pressure ( � 1 ) 900/5/0.5 5.66 1.458 1.817 29 76 35 500-70/4.5/2.3 14.27 1.577 1.681 54 142 65 500-85/4.5/1.4 11.06 1.533 1.729 42 110 51 600/4.5/1.4 11.00 1.532 1.730 43 114 52 700/4.5/1.0 10.59 1.526 1.736 36 96 44 900/10.5/1.9 17.30 1.619 1.637 43 112 52 800/10.5/2.5 17.36 1.620 1.636 64 169 78 800/10.5/1.25 11.59 1.540 1.721 41 107 49 680/10.5/2.2 17.73 1.625 1.631 58 152 70 Roller 1.380 1.928 22 58 26 The intercept and slope of the VCL were used in COMPSOIL. In order to see how the prediction performs with these modified parameters, the measured data is compared to the predicted data in Figure 8 for six individual tyres and close general agreement was achieved. Soil displacement is successfully predicted using COMPSOIL and the parameters of the VCL from the soil bin with a heuristically chosen concentration factor of � =5. 206 P
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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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Page 175 and 176: Ancillary Experiments Contact Press
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Page 179 and 180: Ancillary Experiments Sinkage (mm)
Page 181 and 182: Ancillary Experiments model which o
Page 183 and 184: Ancillary Experiments 7.3.5 The Inf
Page 185 and 186: Ancillary Experiments 7.3.7 Discuss
Page 187 and 188: Ancillary Experiments Terzaghi (194
Page 189 and 190: Ancillary Experiments contact area.
Page 191 and 192: Ancillary Experiments soil forward
Page 193 and 194: Conclusions � The longitudinal so
Page 195 and 196: Bibliography 10 BIBLIOGRAPHY Aboaba
Page 197 and 198: Bibliography Defossez, P., Richard,
Page 199 and 200: Bibliography Gregory, A.S.; Whalley
Page 201 and 202: 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: Appendix density is obtained by add
Page 225 and 226: Appendix choice of a concentration
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 and 254: Appendix � z � � �� k c p
Page 255 and 256: Appendix Table 8: n and k depending
Page 257 and 258: Appendix to the plate sinkage equat
Page 259 and 260: Appendix with a slight deviation fr
Page 261: Appendix Table 12: DBD values for a
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