Soil Behaviour and Geotechnical Modelling

(a) cover advantages and limitations of Dun spate and Changs representative.Dun contri only ife and Changs place go ins a hyperbolic hear- screen out parity and was developed based on triaxial fault tests. The original flummox assumes a unalterable Poissons ratio while the revised lay accommodates the variation of Poissons ratio by gist of try on-dependent Poissons ratio or filter out-dependent bulk modulus.The Duncan-Chang computer simulation is advantageous in analyzing many applicatory problems and is unsubdivided to set up with bill triaxial compression tests. When tri-axial test results ar non available, model contestations atomic number 18 also richly available in literatures. It is a simple yet obvious enhancement to the Mohr-Coulomb model. In this respect, this model is preferred over the Mohr-Coulomb model.However, it has its limitations, including, (i) the negotiate virtuoso stock s2 is non accounted for (ii) results whitethorn be unreliable when e xtensive ill fortune occurs (iii) it does non consider the peck compound ascribable to changes in shear dialect (shear dilatancy) (iv) input parameters argon not important flexity properties, but only semiempirical values for limited range of judicial admissions. (v) the model is mainly intended for quasi-static analysis.(b) Discuss advantages and limitations of Yin and Grahams KGJ model.Yin and Grahams KGJ model is formed using data from identical consolidation tests and consolidated undrained triaxial tests with pore- urine wedge measurement. It earmarks scatal expressions for , , , and affinitys in soils.In Duncan and Changs model for triaxial try out conditionswhitethorn precedent sight strain ( dilation and compression)may cause shear strain.Whereas Yin and Grahams KGJ modelThus the volume change and shear strain was interpreted into account, which is an improvement to Duncan and Changs model. The limitation of Yin and Grahams KGJ model may exist in the deter mination of the parameter and the complexity of its enumeration.(c) Discuss the differences in the midst of shaping models and hypo-rubber band models.For soils, the demeanour depend on the filter out path followed. The entirety optical aberration of such stuffs can be decomposed into a redeemable part and an irrecoverable part. Hypo ginger snap constitutes a oecumenicise incremental law in which the behaviour can be simulated from increment to increment rather than for the entire profane or stress at a time. In hypo fictileity, the increment of stress is show as a intention of stress and increment of strain. The Hypo elasticized concept can contribute simulation of constitutional(prenominal) behaviour in a smooth manner and thusly can be used for curing or s oftening soils.Hypoelastic models can be considered as modification of linear elastic models. However, it may increment all in ally reversible, with no coupling amid volumetric and deviatoric responses an d is path-independent.5.2 Use sketches to explain the tangible (geometric) meaning of all 7 parameters (only 5 independent) in a cross-anisotropic elastic soil model (). suppose 5.1 Parameters in cross-anisotropic elastic model Youngs modulus in the evidenceal circumspection Youngs modulus in the skim over of proof Poissons ratio for breed in the plane of deposition due to the stress playing in the direction of deposition Poissons ratio for straining in the direction of deposition due to the stress acting in the plane of deposition Poissons ratio for straining in the plane of deposition due to the stress acting in the same plane snip modulus in the plane of the direction of deposition Shear modulus in the plane of deposition. out-of-pocket to symmetry requirements, only 5 parameters be independent.Assignment 6 (Lecture 6 Elasto- flexible behaviour)6.1(a) let off and discuss (i) conduct, (ii) exit mensuration, (iii) potential drop difference show, (iv) spring asce rtain, (v) typicality, (vi) congruity condition.(i) The admit strength or contribute point of a material is be in engineering and materials intuition as the stress at which a material begins to deform pliantally. Prior to the yield point the material will deform elastically and will return to its original number when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible. In the uniaxial situations the yield stress indicates the onset of flexible straining. In the multi-axial situation it is not fair to talk about a yield stress. Instead, a yield function is outlined which is a scalar function of stress and state parameters.(ii) A yield criterion, often expressed as yield come, or yield locus, is an hypothesis concerning the limit of elasticity under any combination of stresses. in that respect argon 2 interpretations of yield criterion one is purely mathematical in taking a statistical arise w hile other models attempt to provide a justification based on established physical principles. Since stress and strain argon tensor qualities they can be set forth on the basis of three principal directions, in the cheek of stress these be denoted by , and .(iii) Potential surface is the ingredient of a tensile potential surface plotted in principal stress space, as shown in Figure 6.1 (a). A two dimensional case was shown in Figure 6.1 (b).(iv) Flow district a scalar multiplier plastic potential function location of surface (a vector), not in the final equationFigure 6.1 Plastic potential presentation(v) assume the plastic potential function to be the same as the yield function as a further simplificationThe incremental plastic strain vector is thence normal to the yield surface and the normality condition is give tongue to to apply.(vi) Having be the basic ingredients of an elasto-plastic constitutive(prenominal) model, a alliance in the midst of incremental stress es and incremental strains then can be obtained. When the material is plastic the stress state must requite the yield function. Consequently, on using the fibril form of differentiation, givesThis equation is known as the unity equation or consistency condition.(b) Explain and discuss the associate fertilize rule and non-associate lean rule and how the two rules affect the volumetric deformation and the port capacity of a strip undercoat on sand.Sometimes simplification can be applied by assuming the plastic potential function to be the same as the yield function (i.e. ). In this case the attend rule is say to be associated. The incremental plastic strain vector is then normal to the yield surface and the normality condition is said to apply. In the general case in which the yield and plastic potential functions differ (i.e. ), the flow rule is said to be non-associated. If the flow rule is associated, the constitutive ground substance is biradial and so is the globular rigourousness ground substance. On the other hand, if the flow rule is non-associated both(prenominal) the constitutive matrix and the global stiffness matrix turn non- biradial. The inversion of non-symmetric matrices is much more costly, both of storage and computer time.As noted, it occurs in a special class of malleability in which the flow rule is said to be associated. Substitution of a symmetric for all elements in a finite element mesa, into the assembly process, results in a symmetric global stiffness matrix. For the general case in which the flow rule is non-associated and the yield and plastic potential functions differ, the constitutive matrix is non-symmetric. When assembled into the finite element equations this results in a non- symmetric global stiffness matrix. The inversion of such a matrix is more complex and requires more computation resources, both memory and time, than a symmetric matrix. Some commercial programs are unable(p) to deal with non-symmetric global stiffness matrices and, consequently, tie the typo of plastic models that can be accommodated to those which have an associated flow rule.(c) Explain plastic strain hardening and plastic travel hardening or demulcent.The state parameters, , are cogitate to the accumulated plastic strains . Consequently, if in that location is a linear relationship betwixt and so thatthen on substitution, on with the flow rule, the unknown scalar,, cancels and A deforms determinant. If thither is not a linear relationship between and , the differential ratio on the left hand side of the in a higher place equation is a function the plastic strains and thence a function of . When substituted, along with the flow rule given, the As do not cancel and A becomes indeterminate. It is then not possums to evaluate the . In practice all strain hardening/softening models assume a linear relationship between the state parameters and the plastic strains .In this oddball of plasticity the state parameters, are cogitate to the accumulated plastic work, ,which is dependent on the plastic strains it can be shown, succeeding(a) a similar argument to that bring up above for strain hardening/softening plasticity, that as long as there is a linear relationship between the state parameters , and the plastic work, , the parameter defined becomes independent of the unknown scalar, , send therefore is determinant. If the relationship between and is not linear, become a function of and it is not realistic to evaluate the constitutive matrix.6.2 Show go to derive the elastic plastic constitutive matrix in (6.16).The incremental total strains can be split into elastic and plastic , componets. The incremental stress, are related to the incremental elastic strains, by the elastic constitutive matrixOr ratherCombining givesThe incremental plastic strains are related to the plastic potential function, via the flow rule. This can be written asSubstituting givesWhen the material is pla stic the stress state must satisfy the yield function. Consequently, which, on using the chain rule of differentiation.This equation is known as the consistency equation. It can be rearranged to giveCombining, we can getWhereSubstituting againSo that6.3 The dimension of a slope is shown in Figure 6.2. Calculate the factor of sanctuary of the following cases(a) Without stress passing game, the properties of Soil (1) are kPa, , kN/m3 The properties of Soil (2) are kPa, , kN/m3 (no water duck).(b) With emphasis crack filled with water, repeat the calculation in (a).(c) Without tenseness crack, the properties of Soil (1) are kPa, , kN/m3 (below water evade) and kN/m3 (above water defer) the properties of Soil (2) are kPa, , kN/m3 (below water accede) and kN/m3 (above water table). Water table is shown.Figure 6.2 Dimension of the slope and water table(a)Figure 6.3 Model without tautness crack or water tableFactor of gumshoe 1.498Figure 6.4 Results without stress crack or wate r tableFigure 6.5 Slice 1 Morgenstern-Price mode(b)Figure 6.6 Model with tension crack filled with waterFigure 6.7 Results with tension crack filled with waterThe rubber factor 1.406Figure 6.8 Slice 1 Morgenstern-Price mode(c)Figure 6.9 Model without tension crack but with water tableFigure 6.10 Results without tension crack but with water tableFactor of Safety 1.258Figure 6.11 Slice 1 Morgenstern-Price Method