0 Conlusion 0. Sope We have introdued the new ritial state onept among older onepts of lassial soil mehanis, but it would be wrong to leave any impression at the end of this book that the new onept merely rejuvenates the lassial alulations. In this brief onlusion we onentrate only on the new onept of ritial states and try to illustrate in a ompat manner the new insight into the mehanial behaviour of soil under three headings: 0. We aquire a new basis for engineering judgement of the state of ground and the onsequenes of proposed works. 0. We an review existing tests and devise new ones. 0.4 We an initiate new researh into soil deformation and flow. 0. Granta-gravel Reviewed Let us review the Granta-gravel model in Fig. 0.(a), where we plot six urved λ- lines at equal spaings lettered VV, AA, BB, CC, DD, and EE on the (v, p) plane. The double line CC represents the ritial states and the line VV represents virgin isotropi ompression of Granta-gravel. Between VV and CC we have wet states of soil in whih it onsolidates in Terzaghi s manner, and AA and BB are typial urves of anisotropi ompression. Under applied loading the wet soil flows and develops positive porepressures or drains and hardens; the whole soil body tends to deform plastially, and hene, the typial drainage paths are long and the undrained problem ours resulting in immediate limiting equilibrium problems whih involve alulations with k = u and ρ = 0. Fig. 0. Review of Granta-gravel In ontrast, the urves DD and EE are in the dry states of soil in whih it ruptures and slips in Coulomb s manner as a rubble of bloks. Eah thin slip zone has a short drainage path and the drained problem ours resulting in long-term limiting equilibrium
0 problems whih involve alulations with k = 0 and ρ at a value onsistent with the ritial states. Aross the Fig. 0.(a) we draw two bold lines that orrespond to two interesting engineering problems. The first line is at onstant effetive spherial pressure p and it intersets the λ-lines at speifi volumes v v, v, v,andv. The seond line is at onstant a, b d e speifi volume v and it intersets the λ-lines at pa, pb, p, pd,and pe. In Fig. 0.(b) we plot the stable state boundary urve that orresponds to the first line; what does the figure imply? We an think of va, vb, v, vd, and ve as being the alternative speifi volumes to whih a layer of saturated remoulded Granta-gravel an be ompated by alternative inreasingly ostly ompation operations. Suppose that the layer will eventually form part of an embankment in whih it will be under some partiular value of effetive spherial pressure p. We onsider what benefit is to be gained from inreased ompation, and Fig. 0.(b) shows that from v a to v b to v there is a steady inrease in strength q, but from v to vd to ve further ompation is wasted. For, while individual bloks might have inreasing strengths (near the dotted line in Fig. 0.(b)), the engineering design of the embankment would have to proeed on the assumption that the bloks would be ruptured in the long-term problem and that the relevant strength parameter was Mp. There is no gain in guaranteed strength with inreased ompation beyond the ritial state. Fig. 0. The Crust of a Sedimentary Deposit
0 The seond line in Fig. 0.(a) at onstant speifi volume leads in Fig. 0. to three diagrams. Figure 0.() is idential to part of Fig. 0.(a) rotated through 90, and 0.(b) shows the stable state boundary urve that orresponds to the seond line; what do these figures imply? Figure 0.(a) shows a sedimentary deposit of saturated remoulded (isotropi and homogeneous) Granta-gravel with partiles falling on to the surfae and forming a deposit of onstant speifi volume v. As the deposit builds up so the effetive spherial pressure on any layer of material steadily inreases; we plot the axis of p inreasing downwards with depth in the deposit. In Fig. 0.() the deposit of Granta-gravel remains rigid at speifi volume of v to a depth at whih anisotropi ompression (under K0 onditions) ours under effetive spherial pressure p a. The sediment above that depth forms a sort of rust: we an ask what would be the response of material at various depths to any disturbane. During any deformation the Granta-gravel will require a suffiient supply of power to satisfy the basi equation, (5.9), pv& + q & ε = Mp & ε. v At a depth where the effetive spherial pressure is p a, there is enough power available from plasti ollapse of volume to satisfy eq. (5.9) without any need for a large additional deviatori stress to ause the disturbane. At a smaller depth, where the effetive spherial pressure is only p b, there is less power available from plasti ollapse of volume and more deviatori stress would be needed to ause the disturbane: that is to say, the material gains strength higher in the rust. At a ritial depth where the effetive spherial pressure is p, there is no plasti ollapse of volume, and the rust has its greatest strength. Above the ritial depth we expet the material to deform as a rubble of slipping bloks in Coulomb s manner. A small digression is appropriate about the possible tension zones in Fig. 0.(b). Introduing > = = 0 into the generalized stress parameters briefly suggested in 8. + + p * =, q* = ( σ ' ) + ( σ ' ) + ( σ ' ) we find p* =, q* =,and q * p * =, whih gives one radial line shown in Fig. 0.(b). Another radial line with q * p * =. 5 orresponds with σ = > 0 where we find * = ( σ ' ).5 < ( q * p *) < ' = p and q * =. These two lines indiate the range of values in whih one or more of the prinipal effetive stress omponents (,, ) beomes zero. In that zone we an have stressed soil bodies with one stressfree fae, whih implies that slight tension raks or loal pitting of the surfae of the sedimentary deposit ould our. Finally, moving down through the deposit in Fig. 0.(a) we have first a shallow zone of possible tension raks above a zone of slipping rubble; below a ritial depth (whih is a funtion of v ) the material would behave as a stiff mud, readily expelling water under small deviatori stress, and finally all material below the depth assoiated with p a is in some state of anisotropi ompression at a speifi volume less than v. A Granta-gravel sediment would not experiene this anisotropi ompression until it was overlain by a thikness of rust formed by subsequent sediment.
04 In Fig. 0.(b) we have onsidered the value of ompation to alternative speifi volumes, and in Fig. 0. the state of a sedimentary deposit. Clearly with the ritial state onept we have aquired a new basis for engineering judgement of the state of ground and the onsequenes of proposed works. 0. Test Equipment We have seen (6.9) that the plastiity index orresponds to a ritial state property that ould be measured with more preision by other tests, suh as indentation by a falling one. Our disussion of the refined axial-test apparatus of 7. shows that an apparatus whih attains this high standard an give data of altogether greater value than the onventional slow strain-ontrolled axial-test apparatus in urrent use. The new ritial state onept gives an edge to our deisions on the value of various piees of existing test equipment. All that we have written in this book has been onerned with saturated remoulded soil. Of ourse engineers need to test unsaturated soil, to test natural anisotropi or sensitive soil, and to test soil in situ. The new ritial state onept enables us to separate effets that an be assoiated with isotropi behaviour from these speial effets that are not predited by the ritial state models. The ritial state onept gives a rational basis for design of new tests that explore aspets of behaviour about whih little is known at present. 0.4 Soil Deformation and Flow The limiting equilibrium alulations that we have introdued in hapters 8 and 9 orrespond to problems of the strength of a soil body experiening imposed total stress hanges indiated by the arrows from B and D in Fig. 0.(a). The arrow from B orresponds to a problem of immediate limiting equilibrium (suh as that disussed in 8.7), and the arrow from D orresponds to a problem of long-term limiting equilibrium (suh as that disussed in 8.8). Fig. 0. Engineering Design Properties However, we have not onsidered in this book a wide lass of ivil engineering design problems onerned with the stiffness of a soil body. For example, in Fig. 0.(b) the arrow of effetive stress hange from D might orrespond to the distortion of firm ground beneath the base of a deep-bored ylinder foundation, and the arrow of effetive stress hange from B might orrespond to the distortion of soft ground around a sheet-piled exavation. This type of design problem must beome inreasingly important in ivil engineering pratie, and it is lear that a better understanding of the stiffness of soil and its strain harateristis is required.
05 The ritial state models that we have disussed in this book provide the basis for alulation of deformation in the rather speial ase of yielding of wet soil. These models as they stand will not allow predition of distortion for the loading of Fig. 0. beause they are rigid for suh loading, but researh experiments and theoretial modifiations to the models (for example, to allow reoverable distortion) do suggest the existene of ontours of equal distortion inrements suh as those shown in Fig. 0.(b). In addition to researh experiments on axial-test speimens, a wide variety of other experiments on models and on other shapes of speimen is being onduted by us and our olleagues and by researh workers in our own and in other laboratories. In reading reports of suh researh it is helpful to reall the differenes between Figs. 0.(a) and (b). Engineering design alulations at present onentrate on strength: as inreasing skill is shown by designers so stiffness beomes a problem of inreasing importane. Present researh whih explores the stiffness of apparently rigid soil bodies should prove to be of inreasing importane to engineering designers as their skill in design inreases. Fig. 0.4 Material Handling Properties Throughout this book we have taken the ivil engineer s viewpoint that it is, in general, undesirable for soil-material to move. We ould equally well have taken the viewpoint of a material-handling engineer who wants powders and rubble to move freely. In Fig. 0.4 we repeat the (q, p) and (v, p) diagrams and indiate in a very rude manner the differene between states (p, v, q) in whih the material (a) oozes as wet mud, (b) slips as a rubble of bloks (that stik to eah other with an adhesion that depends on the pressure between the bloks), and () flows in the ritial states. Clearly there are others as well as the ivil engineer who may profit from the onept of.8 that granular materials, if ontinuously distorted until they flow as a fritional fluid, will ome into a well-defined ritial state.