Critical State Soil Mechanics Phần 1 docx

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In no event will this web page or webmaster be held liable, nor does this web page or its webmaster provide insurance against liability, for any damages including lost profits, lost savings or any other incidental or consequential damages arising from the use or inability to use the information contained within. This site is not an official site of Prentice-Hall, the University of Tennessee at Chattanooga, Vulcan Foundation Equipment or Vulcan Iron Works Inc. (Tennessee Corporation). All references to sources of equipment, parts, service or repairs do not constitute an endorsement. Critical State Soil Mechanics Andrew Schofield and Peter Wroth Lecturers in Engineering at Cambridge University Preface This book is about the mechanical properties of saturated remoulded soil. It is written at the level of understanding of a final-year undergraduate student of civil engineering; it should also be of direct interest to post-graduate students and to practising civil engineers who are concerned with testing soil specimens or designing works that involve soil. Our purpose is to focus attention on the critical state concept and demonstrate what we believe to be its importance in a proper understanding of the mechanical behaviour of soils. We have tried to achieve this by means of various simple mechanical models that represent (with varying degrees of accuracy) the laboratory behaviour of remoulded soils. We have not written a standard text on soil mechanics, and, as a consequence, we have purposely not considered partly saturated, structured, anisotropic, sensitive, or stabilized soil. We have not discussed dynamic, seismic, or damping properties of soils; we have deliberately omitted such topics as the prediction of settlement based on Boussinesq’s functions for elastic stress distributions as they are not directly relevant to our purpose. The material presented in this book is largely drawn from the courses of lectures and associated laboratory classes that we offered to our final year civil engineering undergraduates and advanced students in 1965/6 and 1966/7. Their courses also included material covered by standard textbooks such as Soil Mechanics in Engineering Practice by K. Terzaghi and R. B. Peck (Wiley 1948), Fundamentals of Soil Mechanics by D. W. Taylor (Wiley 1948) or Principles of Soil Mechanics by R. F. Scott (Addison-Wesley 1963). In order to create a proper background for the critical state concept we have felt it necessary to emphasize certain aspects of continuum mechanics related to stress and strain in chapter 2 and to develop the well-established theories of seepage and one-dimensional consolidation in chapters 3 and 4. We have discussed the theoretical treatment of these two topics only in relation to the routine experiments conducted in the laboratory by our students, where they obtained close experimental confirmation of the relevance of these theories to saturated remoulded soil samples. Modifications of these theories, application to field problems, three-dimensional consolidation, and consideration of secondary effects, etc., are beyond the scope of this book. In chapters 5 and 6, we develop two models for the yielding of soil as isotropic plastic materials. These models were given the names Granta-gravel and Cam-clay from that river that runs past our laboratory, which is called the Granta in its upper reaches and the Cam in its lower reaches. These names have the advantage that each relates to one specific artificial material with a certain distinct stress – strain character. Granta-gravel is an ideal rigid/plastic material leading directly to Cam-clay which is an ideal elastic/plastic material. It was not intended that Granta-gravel should be a model for the yielding of dense sand at some early stage of stressing before failure: at that stage, where Rowe’s concept of stress dilatancy offers a better interpretation of actual test data, the simple Granta-gravel model remains quite rigid. However, at peak stress, when Granta-gravel does yield, the model fits our purpose and it serves to introduce Taylor’s dilatancy calculation towards the end of chapter 5. Chapter 6 ends with a radical interpretation of the index tests that are widely used for soil classification, and chapter 7 includes a suggested computation of ‘triaxial’ test data that allows students to interpret much significant data which are neglected in normal methods of analysis. The remainder of chapter 7 and chapter 8 are devoted to testing the relevance of the two models, and to suggesting criteria based on the critical state concept for choice of strength parameters in design problems. Chapter 9 begins by drawing attention to the actual work of Coulomb – which is often inaccurately reported – and its development at Gothenberg; and then introduces Sokolovski’s calculations of two-dimensional fields of limiting stress into which we consider it appropriate to introduce critical state strength parameters. We conclude in chapter 10 by demonstrating the place that the critical state concept has in our understanding of the mechanical behaviour of soils. We wish to acknowledge the continual encouragement and very necessary support given by Professor Sir John Baker, O.B.E., Sc.D., F.R.S., of all the work in the soil mechanics group within his Department. We are very conscious that this book represents only part of the output of the research group that our teacher, colleague, and friend, Ken Roscoe, has built up over the past twenty years, and we owe him our unbounded gratitude. We are indebted to E. C. Hambly who kindly read the manuscript and made many valuable comments and criticisms, and we thank Mrs Holt-Smith for typing the manuscript and helping us in the final effort of completing this text. A. N. Schofield and C. P. Wroth To K. H. Roscoe [...]... saturated soil v = 1 + Gs w (1. 6) Typical values are as follows: sand with Gs = 2.65 when in a loose state with v = 1. 8 will have γ = 1. 92γw; in a dense state with v = 1. 5 will have γ = 2 .10 γw; clay with Gs = 2.75 when at the liquid limit might have w = 0.7 and then with v = 1+ 2.75×0.7 = 2.92 it will have γ = 1. 60γw; at the plastic limit it might have w = 0.3 and then with v = 1+ 2.75×0.3 = 1. 83 it will... function Ordinate of critical state line Caquot’s angle Parameter relating swelling with compression Critical state frictional constant Major principal stress Common point of idealized critical state lines 5 .14 (VVS) 9.5 3.7 5.9 (VVS) 9.5 6.6 5.7 (VVS) 9.5 6.9 1 Basic concepts 1. 1 Introduction This book is about conceptual models that represent the mechanical behaviour of saturated remoulded soil Each model... pore-water In this book we will only consider fully saturated soil, with the space (v − 1) full of pore-water 8 Fig 1. 4 Specific Volume of Saturated Soil The total weight when saturated is {Gs + (v − 1) }γ w and dry is Gsγw These weights within a total volume v lead to the definition of G + v 1 G +e γw = s γw saturated bulk density, γ = s v 1+ e (1. 5) Gs and dry bulk density, γ d = γ w v It is useful to... clay soils Fig 1. 3 Liquid Limit Test Groove (After Lambe20) Skempton13 found that there is a correlation between the plasticity index of a soil and the proportion of particles of clay size in the soil If a given specimen of clay soil is mixed with various proportions of silt soil then there is a constant ratio of plasticity index Activity= percentage finer than two microns The activity of clay soil. .. objects in that imaginary scene The diversity of sizes of soil particles means that a complete survey of their geometry in a soil specimen is not feasible If we select a volume of 1 m3 of soil, large enough to contain one of the largest particles (a boulder) then this volume could also contain of the order of 10 8 sand grains and of the order of 10 16 clay particles A further problem in attempting such... Rosenqvist .15 In effect, when we reaffirm the standard soil engineering practice of regarding the mechanical grading and index properties as the basis of soil classification, we are asserting that the influence of mineralogy, chemistry and origin of a soil on its mechanical is behaviour is adequately measured by these simple index tests 1. 5 Water Content and Density of Saturated Soil Specimens If a soil. .. with effective diameter D, and if we calculate a time 18 µ z tD = (1. 4) (Gs − 1) γ w D 2 then before time tD the concentration of sediment at the sampling depth ( z = 10 0 mm) would remain at its initial value WV/500: at time tD the particles initially at the surface of the tube would sink past the depth z = 10 0 mm, and thereafter, as is shown in Fig 1. 1, there would be clear liquid at the depth z It is... = 3πµνd (1. 1) The force must be in equilibrium with the buoyant weight of the sphere, so that 3πµνd = π (Gs 1) γ w d 3 (1. 2) 6 where Gsγw is the weight of unit volume of the solid material of the sphere and γw is the weight of unit volume of water Hence, if a single sphere is observed steadily falling through a distance z in a time t, it can be calculated to have a diameter 1 ⎧ 18 µ z⎫ 2 (1. 3) d =⎨... the mathematical consequences of older models 1. 8 The Critical State Concept The kernel of our ideas is the concept that soil and other granular materials, if continuously distorted until they flow as a frictional fluid, will come into a well-defined critical state determined by two equations q = Mp Γ = v + λ ln p The constants M, Γ, and λ represent basic soil- material properties, and the parameters... volume of solids Existing soil mechanics texts use an alternative symbol e called ‘voids ratio’ which is the ratio between the volume of ‘voids’ or pore space and the volume of solids: v = 1 + e A further alternative symbol n called porosity is defined by n = (v − 1) / v = e / v Figure 1. 4(a) illustrates diagrammatically the unit volume of solids occupying a space v, and Fig 1. 4(b) shows separately the . Fundamentals of Soil Mechanics by D. W. Taylor (Wiley 19 48) or Principles of Soil Mechanics by R. F. Scott (Addison-Wesley 19 63). In order to create a proper background for the critical state concept. introduce critical state strength parameters. We conclude in chapter 10 by demonstrating the place that the critical state concept has in our understanding of the mechanical behaviour of soils students in 19 65/6 and 19 66/7. Their courses also included material covered by standard textbooks such as Soil Mechanics in Engineering Practice by K. Terzaghi and R. B. Peck (Wiley 19 48), Fundamentals