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Soil mechanics for off-road vehicle engineering
Journal o f Terramechanics, 1979, Vol. 16, No. 4, pp. 191 to 194 Pergamon Press Ltd. Printed in Great Britain International Society for Terrain Vehicle Systems
0022-4898/79/1201--0191 802.00/11
BOOK REVIEW* SOIL MECHANICS
FOR OFF-ROAD
VEHICLE ENGINEERING
L. L. KAgAHAT~I and E. A. NOWATZKI: Soil Mechanics for Off-Ro=d Vehicle Engineering, 515 pp. Trans Tech Publications, Clausthal, Germany (1978). $54.00 or S Fr 135.00. ALTHOUGH transportation over natural terrain has been in existence for centuries, until recently the development of off-road vehicles has been based, by and large, on past experiences and the "cut and try" methodology. The publication of Dr. M. G. Bekker's books, Theory of Land Locomotion in 1956 and Off-the-Road Locomotion and Introduction to Terrain-Vehicle Systems in subsequent years, has stimulated a great deal of interest in the systemic development of the basic princip!es of the mechanics of land locomotion. The objective is to formulate guiding principles for the more rational development, design, and evaluation of cross-country vehicles. It has long been recognized that to provide a sound basis for the development of land locomotion mechanics, a proper understanding of the physical nature of vehicleterrain interaction is essential. Over the years, a number of researchers, too numerous to name, have made significant contributions to the knowledge of the physical processes of vehicle-terrain interaction. In the mid-1960s, the writer of this review and Dr. A. R. Reece of the University of Newcastle upon Tyne conducted an extensive investigation into the physical processes of wheel-soil interaction using photographic techniques. From this study it was clearly established that failure zones developed in dense soils under the action of a moving wheel and that there was a close correlation between the failure behavior of soil and the performance of the vehicle running gear. The shapes of the failure zones and the trajectories of soil particles beneath a moving wheel under various operating conditions were also clearly identified. This development has stimulated considerable interest in the application of the theory of plastic equilibrium of soil mechanics to the prediction of the performance of vehicle running gear over unprepared terrain. It is satisfying to see that the authors of this book have expended serious effort in applying the theory of plasticity to the elucidation of the mechanics of land locomotion. This book is an interesting addition to the literature of terramechanics. This book consists of three parts. The first part deals witb the fundamentals of soil mechanics for problems in off-road locomotion, including the characterization of soils, characteristics of soil behavior, *Reprinted from the Canadian Geotechnical Journal, Vol. 16, No. 3, 1979, with permission of the Editor-in-Chief. 191
192
BOOK REVIEW
and the theories for the determination of stress states in soil under applied load. In the discussion of the application of the theory of elasticity, it would have been m o r e complete if some of the well-known methods, such as that proposed by Fr6hlich, for predicting the stress distribution in granular masses had been included. These methods have found applications in the study of soil compaction caused by vehicular loads. The second part of the book presents the plasticity theory for soils, including the discussion of the differential equations of plastic equilibrium, numerical solutions of the differential equations, limit theorems of plasticity, and the applications of plasticity theory to general soil-structure interaction problems. This part is well-organized and clearly presented. The third part discusses the applications of soil mechanics theories to problems of vehicle mobility. This is the part that describes the unique contributions made by the authors in applying the theory of plasticity to the mechanics of land locomotion. The methodology for predicting the performance of vehicle running gear based on the theory of plasticity involves the solutions of differential equations for the limiting equilibrium of the soil masses in the failure zones using the Mohr-Coulomb yield (failure) criterion. To initiate the solution processes and to obtain unique solutions to particular problems, certain information on the vehicle-terrain interface, such as the interface friction angle 8 or more generally the direction of the major principal stresses on the interface, must be specified or assumed at the outset. This is one of the most important issues and yet one of the most uncertain parts of the whole methodology in applyihg the theory of plasticity to the prediction of cross-country vehicle performance, which will be elaborated later. The third part of the book has indeed demonstrated that the application of the theory of plasticity could provide a better insight into the physical nature of vehicleterrain interaction, such as the elucidation of the phenomenon of slip-sinkage, and could establish a theoretical reference with which the actual performance of crosscountry vehicles may be compared under certain circumstances. It should be recognized, however, that there are severe limitations to the application of the methodology based on the plasticity theory to the prediction and evaluation of vehicle mobility in practice. Firstly, the theory of plasticity as presented in the book is based on the assumption that the terrain behaves like a rigid, perfectly plastic material. This means that the terrain does not deform significantly until the stresses within certain boundaries reach a certain level at which failure occurs. Beyond this point, the strain increases rapidly, while the stress remains constant. Although dense sand and the like may exhibit behavior close to that of a rigid, perfectly plastic material, a wide range of terrains, including muskeg and snow, encountered in cross-country operations have a high degree of compressibility, and their behavior does not conform to that of a rigid, perfectly plastic material. Consequently, failure zones in these terrains under vehicular loads do not develop in a manner similar to that assumed in the theory, and the sinkage of the vehicle running gear is primarily due to the compression of the terrain and not due to the plastic flow of the terrain material. From a vehicle mobility viewpoint, terrains with a high degree of compressibility are of greater concern to vehicle designers and users than dense sand and the like. Thus, the usefulness of the
BOOK REVIEW
193
methodology based on the plasticity theory in vehicle mobility study is limited in practice. Secondly, as mentioned previously, to initiatethe numerical procedures to predict the performance of vehicle running gear based on the plasticitytheory, certain information on the vehicle running gear-terrain interface, such as the interface friction an#c, must be specified at the outset. The approaches to specifying the required boundary conditions presented in the book arc primarily empirical in nature. In o(hcr words, the elaborate numerical procedures stillheavily rely on empirical data as inputs. For instance, in the prediction of the performance of driven rigid wheels and pneumatic tires,it is suggested in the book that the empirical shear stress-slip relationship proposed by Janosi and Hanamoto be used to estimate the interface frictionangle. In the analysis of the rigid track-soil interaction,it is suggested that an empirical prcssure-sinkage equation proposed by Pcrloffand Rahim bc used as inputs to the solution processes. It is noted that these empirical relationships suggestcd as inputs to the elaborate numcrical procedures arc similar to those used in various semiempirical methods currently available for predicting off-road vehicle performance. Furthermore, some of the assumptions made regarding the boundary conditions on vehicle-terrain interface required for initiating the solution processes appear to bc without justifiabletheoretical basis. For instance, in the procedures for predicting the performance of towed rigid wheels, it is suggested that the interface frictionangle be assumed to decrease linearlyfrom the entry and the exitpoints towards the center and become zero at-the angle of separation, and that the value of 5 bc assumed to be in the range of I/2-I/3 of the angle of internal shearing resistanceof the soil~0at the entry point. In the analysis of the mcchanics of towed tires,on the other hand, it is suggested that the angle 5 bc assumed to be I/4 of ¢p at entry and exit points. Selection of some of the input paramctcrs, such as the rear angle for towed rigidwheels ~,, the angic for defining the startof tiredcflection~' and that for defining the location where the tire returns to undcflcctcd shape ~' ', appears to be arbitrary. [n addition, some of the basic parameters required for the solution processes, such as slip parameters j0 and K, have not bccn clearly defined, and the way in which these paramcters may bc measured has not been explained. For instance, only empirical relationships between the values of j0 and K and the cone index or cone index gradient arc given in the book. All of these point to the fact that even though an elaborate numerical procedure based on the plasticity theory has been formulated for evaluation of vehicle mobility, the solutions to any particular problems stillheavily rely on either empirical inputs or assumed boundary conditions on the vchicle-terrain interface, some of which do not necessarily have any justifiabletheoretical basis. Thirdly, the solution procedures described in the book are for two-dimensional vehicle-terrain interaction problems. While this may be adequate in some cases, a variety of problems require that thrcc-dimensional effectsbe taken into consideration. To develop three-dimensional failurc patterns beneath a vehicle running gear and to formulate corresponding numerical procedures will greatly increase the complexity of the solution processes. In closing, it can bc said that dcspitc thc problems mcntioned above, the authors of the book have made contributions to the advancement of the mechanics of land locomotion. M u c h more effort,however, will be required to develop thc methodology
194
BOOK REVIEW
presented in the book to the point where it can be considered reliable and practically useful to all those involved in the development of off-road vehicle technology. This book is recommended to researchers specialized in the mechanics of vehicleterrain interaction.
Department qf Mechanical and Aeronautical Engineering Carleton University Ottawa, Ontario KIS 5B6 Canada
Jo YUNG WONG
0022-4898/79/1201--0191 802.00/11
BOOK REVIEW* SOIL MECHANICS
FOR OFF-ROAD
VEHICLE ENGINEERING
L. L. KAgAHAT~I and E. A. NOWATZKI: Soil Mechanics for Off-Ro=d Vehicle Engineering, 515 pp. Trans Tech Publications, Clausthal, Germany (1978). $54.00 or S Fr 135.00. ALTHOUGH transportation over natural terrain has been in existence for centuries, until recently the development of off-road vehicles has been based, by and large, on past experiences and the "cut and try" methodology. The publication of Dr. M. G. Bekker's books, Theory of Land Locomotion in 1956 and Off-the-Road Locomotion and Introduction to Terrain-Vehicle Systems in subsequent years, has stimulated a great deal of interest in the systemic development of the basic princip!es of the mechanics of land locomotion. The objective is to formulate guiding principles for the more rational development, design, and evaluation of cross-country vehicles. It has long been recognized that to provide a sound basis for the development of land locomotion mechanics, a proper understanding of the physical nature of vehicleterrain interaction is essential. Over the years, a number of researchers, too numerous to name, have made significant contributions to the knowledge of the physical processes of vehicle-terrain interaction. In the mid-1960s, the writer of this review and Dr. A. R. Reece of the University of Newcastle upon Tyne conducted an extensive investigation into the physical processes of wheel-soil interaction using photographic techniques. From this study it was clearly established that failure zones developed in dense soils under the action of a moving wheel and that there was a close correlation between the failure behavior of soil and the performance of the vehicle running gear. The shapes of the failure zones and the trajectories of soil particles beneath a moving wheel under various operating conditions were also clearly identified. This development has stimulated considerable interest in the application of the theory of plastic equilibrium of soil mechanics to the prediction of the performance of vehicle running gear over unprepared terrain. It is satisfying to see that the authors of this book have expended serious effort in applying the theory of plasticity to the elucidation of the mechanics of land locomotion. This book is an interesting addition to the literature of terramechanics. This book consists of three parts. The first part deals witb the fundamentals of soil mechanics for problems in off-road locomotion, including the characterization of soils, characteristics of soil behavior, *Reprinted from the Canadian Geotechnical Journal, Vol. 16, No. 3, 1979, with permission of the Editor-in-Chief. 191
192
BOOK REVIEW
and the theories for the determination of stress states in soil under applied load. In the discussion of the application of the theory of elasticity, it would have been m o r e complete if some of the well-known methods, such as that proposed by Fr6hlich, for predicting the stress distribution in granular masses had been included. These methods have found applications in the study of soil compaction caused by vehicular loads. The second part of the book presents the plasticity theory for soils, including the discussion of the differential equations of plastic equilibrium, numerical solutions of the differential equations, limit theorems of plasticity, and the applications of plasticity theory to general soil-structure interaction problems. This part is well-organized and clearly presented. The third part discusses the applications of soil mechanics theories to problems of vehicle mobility. This is the part that describes the unique contributions made by the authors in applying the theory of plasticity to the mechanics of land locomotion. The methodology for predicting the performance of vehicle running gear based on the theory of plasticity involves the solutions of differential equations for the limiting equilibrium of the soil masses in the failure zones using the Mohr-Coulomb yield (failure) criterion. To initiate the solution processes and to obtain unique solutions to particular problems, certain information on the vehicle-terrain interface, such as the interface friction angle 8 or more generally the direction of the major principal stresses on the interface, must be specified or assumed at the outset. This is one of the most important issues and yet one of the most uncertain parts of the whole methodology in applyihg the theory of plasticity to the prediction of cross-country vehicle performance, which will be elaborated later. The third part of the book has indeed demonstrated that the application of the theory of plasticity could provide a better insight into the physical nature of vehicleterrain interaction, such as the elucidation of the phenomenon of slip-sinkage, and could establish a theoretical reference with which the actual performance of crosscountry vehicles may be compared under certain circumstances. It should be recognized, however, that there are severe limitations to the application of the methodology based on the plasticity theory to the prediction and evaluation of vehicle mobility in practice. Firstly, the theory of plasticity as presented in the book is based on the assumption that the terrain behaves like a rigid, perfectly plastic material. This means that the terrain does not deform significantly until the stresses within certain boundaries reach a certain level at which failure occurs. Beyond this point, the strain increases rapidly, while the stress remains constant. Although dense sand and the like may exhibit behavior close to that of a rigid, perfectly plastic material, a wide range of terrains, including muskeg and snow, encountered in cross-country operations have a high degree of compressibility, and their behavior does not conform to that of a rigid, perfectly plastic material. Consequently, failure zones in these terrains under vehicular loads do not develop in a manner similar to that assumed in the theory, and the sinkage of the vehicle running gear is primarily due to the compression of the terrain and not due to the plastic flow of the terrain material. From a vehicle mobility viewpoint, terrains with a high degree of compressibility are of greater concern to vehicle designers and users than dense sand and the like. Thus, the usefulness of the
BOOK REVIEW
193
methodology based on the plasticity theory in vehicle mobility study is limited in practice. Secondly, as mentioned previously, to initiatethe numerical procedures to predict the performance of vehicle running gear based on the plasticitytheory, certain information on the vehicle running gear-terrain interface, such as the interface friction an#c, must be specified at the outset. The approaches to specifying the required boundary conditions presented in the book arc primarily empirical in nature. In o(hcr words, the elaborate numerical procedures stillheavily rely on empirical data as inputs. For instance, in the prediction of the performance of driven rigid wheels and pneumatic tires,it is suggested in the book that the empirical shear stress-slip relationship proposed by Janosi and Hanamoto be used to estimate the interface frictionangle. In the analysis of the rigid track-soil interaction,it is suggested that an empirical prcssure-sinkage equation proposed by Pcrloffand Rahim bc used as inputs to the solution processes. It is noted that these empirical relationships suggestcd as inputs to the elaborate numcrical procedures arc similar to those used in various semiempirical methods currently available for predicting off-road vehicle performance. Furthermore, some of the assumptions made regarding the boundary conditions on vehicle-terrain interface required for initiating the solution processes appear to bc without justifiabletheoretical basis. For instance, in the procedures for predicting the performance of towed rigid wheels, it is suggested that the interface frictionangle be assumed to decrease linearlyfrom the entry and the exitpoints towards the center and become zero at-the angle of separation, and that the value of 5 bc assumed to be in the range of I/2-I/3 of the angle of internal shearing resistanceof the soil~0at the entry point. In the analysis of the mcchanics of towed tires,on the other hand, it is suggested that the angle 5 bc assumed to be I/4 of ¢p at entry and exit points. Selection of some of the input paramctcrs, such as the rear angle for towed rigidwheels ~,, the angic for defining the startof tiredcflection~' and that for defining the location where the tire returns to undcflcctcd shape ~' ', appears to be arbitrary. [n addition, some of the basic parameters required for the solution processes, such as slip parameters j0 and K, have not bccn clearly defined, and the way in which these paramcters may bc measured has not been explained. For instance, only empirical relationships between the values of j0 and K and the cone index or cone index gradient arc given in the book. All of these point to the fact that even though an elaborate numerical procedure based on the plasticity theory has been formulated for evaluation of vehicle mobility, the solutions to any particular problems stillheavily rely on either empirical inputs or assumed boundary conditions on the vchicle-terrain interface, some of which do not necessarily have any justifiabletheoretical basis. Thirdly, the solution procedures described in the book are for two-dimensional vehicle-terrain interaction problems. While this may be adequate in some cases, a variety of problems require that thrcc-dimensional effectsbe taken into consideration. To develop three-dimensional failurc patterns beneath a vehicle running gear and to formulate corresponding numerical procedures will greatly increase the complexity of the solution processes. In closing, it can bc said that dcspitc thc problems mcntioned above, the authors of the book have made contributions to the advancement of the mechanics of land locomotion. M u c h more effort,however, will be required to develop thc methodology
194
BOOK REVIEW
presented in the book to the point where it can be considered reliable and practically useful to all those involved in the development of off-road vehicle technology. This book is recommended to researchers specialized in the mechanics of vehicleterrain interaction.
Department qf Mechanical and Aeronautical Engineering Carleton University Ottawa, Ontario KIS 5B6 Canada
Jo YUNG WONG