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1、1 Basic mechanicsof 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 and is termed stiffness. The max
2、imum value of stress that may be sustained is termed strength.Analysis of stress and strain1) 2) 3)Stresses 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 stres
3、sshear stresst = Fs / Anormal strain area AEZI = 8z / zoshear strainzo6hGeneral caseprincpal stressesNote that compressive stresses and strains are positive, counter-clockwise shear stress and strain are positive, and that these are total stresses (see ).1.1.1 Special stress and strain statesIn gene
4、ral, the stresses and strains in the three dimensions will all be different.There are three special cases which are important in ground engineering:Axially symmetric or triaxial statesStresses and strains in two dorections are equal.bx = by and 8x =弓Relevant to conditions near relatively small found
5、ations, piles, anchors and other concentrated loads.Plane strain:Strain in one direction = 08y = 0Relevant to conditions near long foundations, embankments, retaining walls and other long structures.One-dimensional compression:Strain in two directions = 0Relevant to conditions below wide foundations
6、 or relatively thin compressible soil layers.Uniaxial compressionbx = by = 0This is an artifical case which is only possible for soil is there are negative pore water pressures.112 Mohr circle constructionValues of normal stress and shear stress must relate to a particular plane within an element of
7、 soil. In general, 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 every possible angle.There are special planes on which the shear stress is
8、 zero . the circle crosses the normal stress axis), and the state of stress . the circle) can be described by the normal stresses acting on theseplanes; 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
9、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 c
10、hanges.stressstrainmeanp=(b+2q) / 3s=b+b) / 2e = AV/V = (s + 2)8 =(S + S )deviatorq =(ba - b r)t =(ba - br)/ 2e = 2 (s - 8) / 38y = (8a - 8r)axial radialIn 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 press
11、ure u:p = p - u s = s - u q= q t = tStrengthThe shear strength of a material is most simply described as the maximum shear stress it can sustain: When the shear stress is increased, the shear strain increases; there will be a limiting condition at which the shear strain becomes very large and the ma
12、terial 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.121 Ty
13、pes of failureMaterials can fail under different loading conditions. In each case, however, failure is associated with the limiting radius of the Mohr circle, . the maximum shear stress. The following common examples are shown in terms of total stresses:ShearingShear strength = 气% = normal stress at
14、 failureUniaxial extensionTensile strength b = 2t tffUniaxial compressionCompressive strength b = 2t cffNote: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 str
15、ength 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 soil
16、s 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 respon
17、d to loading initially by generating excess 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 immediateloading response. Once the pore pressure has dissapated,
18、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 criterionStrength envelopeThe strength is independent of the normal stress since the response to loading simple increa
19、ses the pore water pressure and not the effective stress.The shear strength f is a material parameter which is known as the undrained shear strength su.气=(b - b) = constantSirength envelope1222 Mohr-Coulomb (c=0) criterionThe strength increases linearly with increasing normal stress and is zero when
20、 the normal stress is zero.f = n tan is the angle of frictionIn the Mohr-Coulomb criterion the material parameter 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 stres
21、s.Strength envelope122.3 Mohr-Coulomb (c0) criterionThe strength increases linearly with increasing normal stress and is positive when the normal stress is zero.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
22、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.1.2.3 Typical values of shear strengthUndrained shear strengthsu (kPa)Hard soilsu 150 kPaStiff soilsu = 75 150 kPaFirm soi
23、lsu = 40 75 kPaSoft soilsu = 20 40kPaVery soft soilsu (kPa)?/B (deg)Compact sands035?- 45?Loose sands030?- 35?Unweathered overconsolidated claycritical state018?25?peak state10 25 kPa20?28?residual0 5 kPa8?15?/TDOften the value of c deduced from laboratory test results (in the shear testing apperatu
24、s) may appear to indicate some shar strength at = 0. . the particles cohereing together or are cemented in some way. Often this is due to fitting a c, line to the experimental data and anapparent cohesion may be deduced due to or1 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。土地的应变产生沉降。分析一种材料在 荷载下的变形，我们必须考虑其应力应变关系。应变和应
25、力之间的关系称为刚度。可持续 承受的最大应力值称为强度。应力与应变分析1）应力应变状态2）建立摩尔圆3）应力和应变的参数应力和应变发生在所有方向，而做沉降与稳定性分析时需要涉及的应力方向往往只要 求一个特定的方向上，而不是其他方向。正应力b = Fn / A剪切应力t = Fs / Aarea A正应变 = &/ zo 切应变二注意到压应力和应变是正值，按逆时针转向的剪应力和应变都是正值，并且这些是所有的应力（注 意应力效果）1.1.1应力与应变分析一般情况下，应力和应变在三个 方向都是不同的。有三种特殊情形对地面工程非常 重要：% sz.主应力一般情况W &%电平面应变：在一个方向上应变等于
26、0乌=0相关条件适用于长地基，路堤，土挡墙和其他长结构。A：轴向R：径向V：竖直H：水平轴向对称或三轴状态应力和应变在两个方向上是相等的.b； = b；和 x =乌相关条件适用于相对较小的基础，桩， 锚和其他集中荷载。一维压缩：在两个方向上应变等于0相关条件适用于地下宽基础或较薄的6位%的V：竖直H：水平可压缩土壤层。单轴压缩bx = by = 0这是一个人工案例并且只可用于有负 孔隙水压力的土壤。1.12建立摩尔圆一个土壤颗粒的正应力和剪应力的值必须与要相对 于一个特定平面。一般来说，在另一个平面的应力是不同的。想象下应力在所有可能的平面上，为绘制出一个平面上 每一个可能角度的正应力或剪应力
27、点，就画出了一个莫尔 圆。用于这些平面上；这些力被称为的主应力1和3在特殊的平面上剪应力为零（即圆过正应力轴），并且应力状态（即圆）可以被描述为正应力作CT- 113参数的应力和应变在平常的土壤试验中，圆柱样品用于在轴径向应力 和应变是主应力和应变的情况下。分析测试数据，并制 定土力学的理论，把理论用于那些影响量的变化的平均（或正常）组件上，和影响形状改变的偏压（或剪切）组件上。应力应变1c.、=axial=radial1平均p=(b+2q )/ 3s= b+b )/ 2e = AV/V = (s + 2sr)8 =(S + S )1偏压q =(ba - b r)t =(ba - br)/ 2
28、e = 2 (s - 8) / 38y = (8a - 8r)在建立摩尔圆中t是圆的半径，s是定义圆的中心。注：总有效应力与孔隙压力u有关：p = p - u s = s - u q = q强度t = t一种材料的剪切强度常被简单地描述为能承受的最大剪应力：当剪应力增加， 剪应变也增加；剪应变会有个极限情况，即当剪应变非常大时，材料被破坏；剪应力u uf就是材料的剪切强度。这种情形下的简单试件破坏可以代表铸铁或塑性材料。如果 材料是脆性（比如一根粉笔），试件的破坏在强度的损失后可能会是突然并且是灾难 y性的。121 Types of failure试件破坏类型材料可以在不同加载条件下被破坏。但
29、是在每一种情况下，材料破坏都受限于莫尔圆的半径，即最 大剪应力。以下显示的常见例子是按总应力来划分的: 剪切剪切强度二Tf正应力破坏值二b nf单轴延伸单轴压缩抗压强度b, = 2tcff注：水没有力f = 0.因此，垂直和水平应力相等并且莫尔圆成为一个点。122强度准则强度准则是一个涉及一种材料强度的其他一些参数的公式：这些材料参数可能包括其他应力。例如土壤有三个重要的强度标准：正确的标准取决于土壤的性质及是否是排水和不排水加载。一般来说，流体状土壤颗粒在加载中将“流失”很快（在工程方面）。因此超孔隙水压力将不会发生;体积变化与有效应力增量将控制其形状，而且莫尔-库仑准则仍是是有效的。.细粒
30、状饱和土壤将响应加载最初产生超孔隙水压力并且体积保持常数值。在这个阶段，采用特 雷斯卡标准，即用总应力代表不排水行为。这是短期或即刻反应。一旦孔隙压力消失，经过一定的时间， 有效应力将增长而且莫尔-库仑准则将描述力的变化。这是长期荷载响应。1221特雷斯卡准则伴随着荷载的简单增加孔隙水压力和非有效应 力，正应力将是一个独立的强度被称为不排水抗剪强度su的剪切强度f是一个材料参数。Tf =（榛-气）=常数1.2.2.2莫尔-库仑（c= 0）标准强度伴随着正应力的增加呈线性增加，并且当正应力 为0时强度也为0.f = n tan f是摩擦角在莫尔-库仑准则中材料参数就是摩擦角并且符合这个准则的材料
31、称为具有摩擦性的。在土壤中， 莫尔一库仑准则适用于正应力是一个有效正应力。1.2.2.3莫尔-库仑（c 0）标准强度伴随着正应力的增加呈线性增加，并且当正应力为0时强度为正值.f = c + n tanf是摩擦角Strength envelope6I(TC是凝聚力截距在土壤中，莫尔一库仑准则适用于正应力是一个有效正应力。在土壤中，莫尔-库仑准则中凝聚力 的有效应力与在特雷斯卡准则中的凝聚力（或不排水强度su）是不一样的。1.2.4剪切强度的典型值不排水抗剪强度Su (kPa)硬土su 150 kPa粘性土su = 75 150 kPa坚硬的土su = 40 75 kPa通常c值在推实验室测试结果（在剪切测试仪）导出，可能会在c = 0.出现一些莎尔强度即颗粒粘 在一起或以其他方式胶结在一起。往往这是为了 c值，强度包络线的实验数据和一种明显凝聚 力可以由于吸入或扩容推断。
