1 Basic mechanics of soilsLoads from foundations and walls apply stresses in the ground. Settlements are caused by strains in the ground. To analyze the conditions within a material under loading, we must consider the stress-strain behavior. The relationship between a strain and stress is termed stiffness. The maximum value of stress that may be sustained is termed strength.1.1 Analysis of stress and strain1）Special stress and strain states2）Mohr circle construction3）Parameters for stress and strainStresses and strains occur in all directions and to do settlement and stability analyses it is often necessary to relate the stresses in a particular direction to those in other directions.normal stress σ = F n / Ashear stressτ = F s/ A normal strain ε = δz / z oshear strainγ = δh / z oNote that compressive stresses and strains are positive, counter-clockwise shear stress and strain are positive, and that these are total stresses (see effective stress).1.1.1 Special stress and strain statesIn general, the stresses and strains in the three dimensions will all be different.There are three special cases which are important in ground engineering:General case princpal stressesAxially symmetric or triaxial statesStresses and strains in two dorections are equal.σ'x = σ'y and εx = εyRelevant to conditions near relatively small foundations,piles, anchors and other concentrated load s.P lane strain:Strain in one direction = 0εy = 0Relevant to conditions near long foundations,embankments, retaining walls and other long structures.One-dimensional compression:Strain in two directions = 0εx = εy = 0Relevant to conditions below wide foundations orrelatively thin compressible soil layers.Uniaxial compressionσ'x = σ'y = 0This is an artifical case which is only possible for soil isthere are negative pore water pressures.1.1.2 Mohr circle constructionrelate to a particular plane within an element of soil. Ingeneral, the stresses on another plane will be different.To visualise the stresses on all the possible planes,a graph called the Mohr circle is drawn by plotting a(normal stress, shear stress) point for a plane at everypossible angle.There are special planes on which the shearstress is zero (i.e. the circle crosses the normal stressaxis), and the state of stress (i.e. the circle) can be described by the normal stresses acting on these planes; these are called the principal stresses '1 and '3 .1.1.3 Parameters for stress and strainIn common soil tests, cylindrical samples are used in which the axial and radial stresses and strains are principal stresses and strains. For analysis of test data, and to develop soil mechanics theories, it is usual to combine these into mean (or normal) components which influence volume changes, and deviator (or shearing) components which influence shape changes.In the Mohr circle construction t' is the radius of the circle and s' defines its centre. Note: Total and effective stresses are related to pore pressure u:p' = p - u s' = s - u q' = q t' = t1.2 StrengthThe shear strength of a material is most simply described as the maximum shear stress it can sustain: When the shear stress is incre ased, the shear strain increases; there will be a limiting condition at which the shear strain becomes very large and the material fails; the shear stress f is then the shear strength of the material. The simple type of failure shown here is associatedwith ductile or plastic materials. If the material is brittle (like a piece of chalk), the failure may be sudden and catastrophic with loss of strength after failure.1.2.1 Types of failureMaterials can fail under different loading conditions. In each case, however, failure is associated with the limiting radius of the Mohr circle, i.e. the maximum shear stress. The following common examples are shown in terms of total stresses:ShearingShear strength = τfσnf = normal stress at failureUniaxial extensionTensile strength σtf = 2τfUniaxial compressionCompressive strength σcf = 2τfNote:Water has no strength f = 0.Hence vertical and horizontal stresses are equal and the Mohr circle becomes a point.1.2.2 Strength criteriaA strength criterion is a formula which relates the strength of a material to some other parameters: these are material parameters and may include other stresses.For soils there are three important strength criteria: the correct criterion depends on the nature of the soil and on whether the loading is drained or undrained.In General, course grained soils will "drain" very quickly (in engineering terms) following loading. Thefore development of excess pore pressure will not occur; volume change associated with increments of effective stress will control the behaviour and the Mohr-Coulomb criteria will be valid.Fine grained saturated soils will respond to loading initially by generating e xcess pore water pressures and remaining at constant volume. At this stage the Tresca criteria, which uses total stress to represent undrained behaviour, should be used. This is the short term or immediate loading response. Once the pore pressure has dissapated, after a certain time, the effective stresses have incresed and the Mohr-Coulomb criterion will describe the strength mobilised. This is the long term loading response.1.2.2.1 Tresca criterionThe strength is independent of the normal stress since the response to loading simple increases the pore water pressure and not theeffective stress.The shear strength f is a materialparameter which is known as the undrained shearstrength su.τf = (σa - σr) = constant1.2.2.2 Mohr-Coulomb (c'=0) criterionThe strength increases linearly with increasingnormal stress and is zero when the normal stress is zero.'f = 'n tan '' is the angle of frictionIn the Mohr-Coulomb criterion the materialparameter is the angle of friction and materials which meet this criterion are known as frictional. In soils, the Mohr-Coulomb criterion applies when the normal stress is an effective normal stress.1.2.2.3 Mohr-Coulomb (c'>0) criterionThe strength increases linearly with increasingnormal stress and is positive when the normal stress iszero.'f = c' + 'n tan '' is the angle of frictionc' is the 'cohesion' interceptIn soils, the Mohr-Coulomb criterion applies when the normal stress is an effective normal stress. In soils, the cohesion in the effective stress Mohr-Coulomb criterion is not the same as the cohesion (or undrained strength su) in the Tresca criterion.1.2.3Typical values of shear strengthOften the value of c' deduced from laboratory test results (in the shear testing apperatus) may appear to indicate some shar strength at ' = 0. i.e. the particles 'cohereing' together or are 'cemented' in some way. Often this is due to fitting a c', ' l ine to the experimental data and an 'apparent' cohesion may be deduced due to suction or dilatancy.1 土的基本性质来自地基和墙壁的荷载会在土地上产生应力。