Soil Behaviour and Geotechnical Modelling

(a) Discuss advantages and limitations of Dun crapper and Changs model.Duncan and Changs model assumes a hyperbolic underline- punctuate intercourse and was developed based on triaxial soil tests. The original model assumes a constant Poissons ratio while the revised model accommodates the variation of Poissons ratio by means of nidus-dependent Poissons ratio or stress-dependent bulk modulus.The Duncan-Chang model is opportune in analyzing many practical problems and is simple to set up with quantity triaxial compression tests. When tri-axial test results atomic number 18 non available, model parameters are in addition abundantly available in literatures. It is a simple yet evident 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 intermediate jumper cable stress s2 is non accounted for (ii) results may be unreliable when extensive misadventure occurs (iii) it d oes not consider the volume variety show receivable to changes in cut back stress (shear dilatancy) (iv) input parameters are not fundamental soil properties, barely only empirical values for limited range of conditions. (v) the model is in the main 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 isotropic consolidation tests and consolidated undrained triaxial tests with pore-water system pressure measurement. It provides functional expressions for , , , and relationships in soils.In Duncan and Changs model for triaxial stress conditionsmay cause volume strain ( dis emphasis and compression)may cause shear strain.Whereas Yin and Grahams KGJ modelThus the volume change and shear strain was taken into account, which is an improvement to Duncan and Changs model. The limitation of Yin and Grahams KGJ model may exist in the determination of the parameter and the analyzableit y of its calculation.(c) Discuss the take issueences amid rubberlike models and hypo-elastic models.For soils, the behavior depend on the stress path followed. The thorough deformation of such materials can be decomposed into a recoverable collapse and an irrecoverable part. Hypo catch constitutes a generalized growingal law in which the behaviour can be simulated from step-up to increment rather than for the good load or stress at a time. In hypoelasticity, the increment of stress is express as a function of stress and increment of strain. The Hypoelastic concept can provide simulation of organic behaviour in a smooth manner and hence can be use for hardening or softening soils.Hypoelastic models can be considered as adjustment of analogue elastic models. However, it may incrementally reversible, with no coupling between volumetric and deviatoric responses and is path-independent.5.2 Use sketches to explain the physical (geometric) meaning of all 7 parameters (only 5 i ndependent) in a cross-anisotropic elastic soil model (). participate 5.1 Parameters in cross-anisotropic elastic model Youngs modulus in the attestational direction Youngs modulus in the tied(p) of deposition Poissons ratio for straining in the plane of deposition due to the stress acting 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 similar plane Shear modulus in the plane of the direction of deposition Shear modulus in the plane of deposition.imputable to symmetry requirements, only 5 parameters are independent.Assignment 6 (Lecture 6 Elasto- pliable behaviour)6.1(a) pardon and discuss (i) rejoin, (ii) yield criterion, (iii) potential surface, (iv) flow dominion, (v) customaryity, (vi) consistency condition.(i) The yield strength or yield point of a material is delimitate in engineering and materials science as the stress at which a material begins to deform tractileally. Prior to the yield point the material forget deform elastically and go forth return to its original shape when the employ 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 plastic straining. In the multi-axial situation it is not sensible to talk about a yield stress. Instead, a yield function is defined which is a scalar function of stress and extract parameters.(ii) A yield criterion, often expressed as yield surface, or yield locus, is an hypothesis concerning the limit of elasticity under any combination of stresses. There are both interpretations of yield criterion one is purely mathematical in taking a statistical approach while other(a) models attempt to provide a justification based on established physical principles. Since stress and strain are tensor qualities they can be described on the basis of tether principal directions, in the fount of stress these are denoted by , and .(iii) potential difference surface is the segment of a plastic potential surface plan in principal stress space, as shown in form 6.1 (a). A two dimensional case was shown in manakin 6.1 (b).(iv) Flow pattern a scalar multiplier plastic potential function status of surface (a vector), not in the final comparability go out 6.1 malleable potential presentation(v) Assuming the plastic potential function to be the same as the yield function as a barely simplificationThe incremental plastic strain vector is past normal to the yield surface and the normality condition is said to apply.(vi) Having defined the fundamental ingredients of an elasto-plastic constitutional model, a relationship between incremental stresses and incremental strains hence can be obtained. When the material is plastic the stress state must(prenominal) satisfy the yi eld function. Consequently, on using the chain rule of differentiation, givesThis equation is known as the consistency equation or consistency condition.(b) explain and discuss the associate flow rule and non-associate flow rule and how the two rules affect the volumetric deformation and the bearing capacity of a level footing 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 flow rule is said 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 matrix is symmetric and so is the planetary cruelty matrix. On the other go on, if the flow rule is non-associated both the constitutive matrix and the global stiffness mat rix become non-symmetric. The inversion of non-symmetric matrices is much more costly, both of terminal 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 aggregation 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 computing resources, both memory and time, than a symmetric matrix. Some commercial programs are unable to deal with non-symmetric global stiffness matrices and, consequently, hold in the typo of plastic models that can be accommodated to those which have an associated flow rule.(c) Expl ain plastic strain hardening and plastic work hardening or softening.The state parameters, , are tie in to the accumulated plastic strains . Consequently, if there is a one-dimensional relationship between and so thatthen on substitution, a yearn with the flow rule, the unknown scalar,, cancels and A becomes determinant. If there is not a linear relationship between and , the differential ratio on the left hand side of the above equation is a function the plastic strains and indeed 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 radiation diagram all strain hardening/softening models assume a linear relationship between the state parameters and the plastic strains .In this type of malleability the state parameters, are related to the accumulated plastic work, ,which is dependent on the plastic strains it can be shown, following a similar command to that parented 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 indeed is determinant. If the relationship between and is not linear, become a function of and it is not possible to evaluate the constitutive matrix.6.2 Show steps 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 alternativelyCombining givesThe incremental plastic strains are related to the plastic potential function, via the flow rule. This can be written as substitute givesWhen the material is plastic 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 getWhere change againSo that6.3 The dimension of a slope is shown in Figure 6.2. Calculate the factor of gumshoe of the following cases(a) Without tautness crack, the properties of Soil (1) are kPa, , kN/m3 The properties of Soil (2) are kPa, , kN/m3 (no water table).(b) With tension crack modify with water, plagiarize the calculation in (a).(c) Without tension crack, the properties of Soil (1) are kPa, , kN/m3 (below water table) and kN/m3 (above water table) the properties of Soil (2) are kPa, , kN/m3 (below water table) and kN/m3 (above water table). Water table is shown.Figure 6.2 Dimension of the slope and water table(a)Figure 6.3 sham without tension crack or water tableFactor of Safety 1.498Figure 6.4 Results without tension crack or water tableFigure 6.5 baseball swing 1 Morgenstern-Price Method(b)Figure 6.6 Model with tension crack filled with waterFigure 6.7 Results with tension crack filled with waterThe safety factor 1. 406Figure 6.8 Slice 1 Morgenstern-Price Method(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