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1、<p> 1 Basic mechanics of soils</p><p> Loads from foundations and walls apply stresses in the ground. Settlements are caused by strains in the ground. To analyze the conditions within a material u
2、nder 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.</p><p> 1.1
3、 Analysis of stress and strain</p><p> 1)Special stress and strain states </p><p> 2)Mohr circle construction </p><p> 3)Parameters for stress and strain </p><p>
4、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. </p><p> Note th
5、at compressive stresses and strains are positive, counter-clockwise shear stress and strain are positive, and that these are total stresses (see effective stress).</p><p> 1.1.1 Special stress and strain s
6、tates</p><p> 1.1.2 Mohr circle construction</p><p> Values of normal stress and shear stress must relate to a particular plane within an element of soil. In general, the stresses on another
7、plane will be different. </p><p> 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 possibl
8、e angle.</p><p> There are special planes on which the shear stress is zero (i.e. the circle crosses the normal stress axis), and the state of stress (i.e. the circle) can be described by the normal stresse
9、s acting on these planes; these are called the principal stresses ?'1 and ?'3 .</p><p> 1.1.3 Parameters for stress and strain</p><p> In common soil tests, cylindrical samples are u
10、sed 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
11、which influence volume changes, and deviator (or shearing) components which influence shape changes. </p><p> In the Mohr circle construction t' is the radius of the circle and s' defines its centre
12、. </p><p> Note: Total and effective stresses are related to pore pressure u: </p><p> p' = p - u </p><p> s' = s - u </p><p><b> q' = q </b>
13、;</p><p><b> t' = t </b></p><p> 1.2 Strength</p><p> The shear strength of a material is most simply described as the maximum shear stress it can sustain: When
14、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 material fails; the shear stress ?f is then the shear strength of the
15、 material. The simple type of failure shown here is associated with ductile or plastic materials. If the material is brittle (like a piece of chalk), the failure may be sudd</p><p> 1.2.1 Types of failure&
16、lt;/p><p> Materials 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 e
17、xamples are shown in terms of total stresses:</p><p><b> Shearing</b></p><p> Shear strength = ?f </p><p> ?nf = normal stress at failure</p><p> Uniaxi
18、al extension </p><p> Tensile strength ?tf = 2?f </p><p> Uniaxial compression </p><p> Compressive strength ?cf = 2?f</p><p> Note: Water has no strength ?f = 0.
19、Hence vertical and horizontal stresses are equal and the Mohr circle becomes a point. </p><p> 1.2.2 Strength criteria</p><p> A strength criterion is a formula which relates the strength o
20、f a material to some other parameters: these are material parameters and may include other stresses.</p><p> For soils there are three important strength criteria: the correct criterion depends on the natur
21、e of the soil and on whether the loading is drained or undrained.</p><p> In General, course grained soils will "drain" very quickly (in engineering terms) following loading. Thefore development o
22、f 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.</p><p> Fine grained saturated soi
23、ls will respond 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
24、. 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 mobilise
25、d. This is the long term loading r</p><p> 1.2.2.1 Tresca criterion</p><p> The strength is independent of the normal stress since the response to loading simple increases the pore wate
26、r pressure and not the effective stress.</p><p> The shear strength ?f is a material parameter which is known as the undrained shear strength su.</p><p> ?f = (?a - ?r) = constant </p>
27、<p> 1.2.2.2 Mohr-Coulomb (c'=0) criterion</p><p> The strength increases linearly with increasing normal stress and is zero when the normal stress is zero.?'f = ?'n tan?'?' is
28、the angle of friction</p><p> In 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 crit
29、erion applies when the normal stress is an effective normal stress.</p><p> 1.2.2.3 Mohr-Coulomb (c'>0) criterion</p><p> The strength increases linearly with increasing normal stress
30、and is positive when the normal stress is zero.?'f = c' + ?'n tan?'?' is the angle of frictionc' is the 'cohesion' intercept</p><p> In soils, the Mohr-Coulomb criterion a
31、pplies 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.</p
32、><p> Typical values of shear strength</p><p> Often the value of c' deduced from laboratory test results (in the shear testing apperatus) may appear to indicate some shar strength at ?'
33、= 0. i.e. the particles 'cohereing' together or are 'cemented' in some way. Often this is due to fitting a c', ?' line to the experimental data and an 'apparent' cohesion may be deduced du
34、e to suction or dilatancy.</p><p><b> 1 土的基本性質</b></p><p> 來自地基和墻壁的荷載會在土地上產(chǎn)生應力。土地的應變產(chǎn)生沉降。分析一種材料在荷載下的變形,我們必須考慮其應力應變關系。應變和應力之間的關系稱為剛度。可持續(xù)承受的最大應力值稱為強度。</p><p> 1.1 應力與應
35、變分析</p><p><b> 1)應力應變狀態(tài)</b></p><p><b> 2)建立摩爾圓</b></p><p> 3)應力和應變的參數(shù)</p><p> 應力和應變發(fā)生在所有方向,而做沉降與穩(wěn)定性分析時需要涉及的應力方向往往只要求一個特定的方向上,而不是其他方向。</p&
36、gt;<p> 注意到壓應力和應變是正值,按逆時針轉向的剪應力和應變都是正值,并且這些是所有的應力(注意應力效果)</p><p> 1.1.1 應力與應變分析</p><p> 1.1.2 建立摩爾圓</p><p> 一個土壤顆粒的正應力和剪應力的值必須與要相對于一個特定平面。一般來說,在另一個平面的應力是不同的。 </p>
37、<p> 想象下應力在所有可能的平面上,為繪制出一個平面上每一個可能角度的正應力或剪應力點,就畫出了一個莫爾圓。</p><p> 在特殊的平面上剪應力為零(即圓過正應力軸),并且應力狀態(tài)(即圓)可以被描述為正應力作用于這些平面上;這些力被稱為的主應力’1和’3</p><p> 1.1.3 參數(shù)的應力和應變</p><p> 在平常的土壤試
38、驗中,圓柱樣品用于在軸徑向應力和應變是主應力和應變的情況下。分析測試數(shù)據(jù),并制定土力學的理論,把理論用于那些影響量的變化的平均(或正常)組件上,和影響形狀改變的偏壓(或剪切)組件上。</p><p> 在建立摩爾圓中t是圓的半徑,s是定義圓的中心。</p><p> 注:總有效應力與孔隙壓力u有關:</p><p> p' = p - u </p
39、><p> s' = s - u </p><p><b> q' = q </b></p><p><b> t' = t </b></p><p><b> 1.2 強度</b></p><p> 一種材料的剪切強度常
40、被簡單地描述為能承受的最大剪應力:當剪應力增加,剪應變也增加;剪應變會有個極限情況,即當剪應變非常大時,材料被破壞;剪應力f就是材料的剪切強度。這種情形下的簡單試件破壞可以代表鑄鐵或塑性材料。如果材料是脆性(比如一根粉筆),試件的破壞在強度的損失后可能會是突然并且是災難性的。</p><p> 1.2.1 Types of failure試件破壞類型</p><p> 材料可以在不同
41、加載條件下被破壞。但是在每一種情況下,材料破壞都受限于莫爾圓的半徑,即最大剪應力。以下顯示的常見例子是按總應力來劃分的:</p><p><b> 剪切</b></p><p><b> 剪切強度= ?f</b></p><p> 正應力破壞值= ?nf </p><p><b>
42、 單軸延伸</b></p><p> 抗拉強度 ?tf = 2?f</p><p><b> 單軸壓縮</b></p><p> 抗壓強度 ?cf = 2?f</p><p> 注: 水沒有力?f = 0. 因此,垂直和水平應力相等并且莫爾圓成為一個點。</p><p>
43、 1.2.2 強度準則</p><p> 強度準則是一個涉及一種材料強度的其他一些參數(shù)的公式:這些材料參數(shù)可能包括其他應力。</p><p> 例如土壤有三個重要的強度標準:正確的標準取決于土壤的性質及是否是排水和不排水加載。</p><p> 一般來說,流體狀土壤顆粒在加載中將“流失”很快(在工程方面)。因此超孔隙水壓力將不會發(fā)生;體積變化與有效應力增量將
44、控制其形狀,而且莫爾-庫侖準則仍是是有效的。</p><p> . 細粒狀飽和土壤將響應加載最初產(chǎn)生超孔隙水壓力并且體積保持常數(shù)值。在這個階段,采用特雷斯卡標準,即用總應力代表不排水行為。這是短期或即刻反應。一旦孔隙壓力消失,經(jīng)過一定的時間,有效應力將增長而且莫爾-庫侖準則將描述力的變化。這是長期荷載響應。</p><p> 1.2.2.1特雷斯卡準則</p><p
45、> 伴隨著荷載的簡單增加孔隙水壓力和非有效應力,正應力將是一個獨立的強度</p><p> 被稱為不排水抗剪強度su的剪切強度f是一個材料參數(shù)。</p><p> ?f = (?a - ?r) =常數(shù)</p><p> 1.2.2.2 莫爾-庫侖(c’= 0)標準</p><p> 強度伴隨著正應力的增加呈線性增加,并且當正
46、應力為0時強度也為0.?'f = ?'n tan?'?' f是摩擦角在莫爾-庫侖準則中材料參數(shù)就是摩擦角并且符合這個準則的材料稱為具有摩擦性的。在土壤中,莫爾-庫侖準則適用于正應力是一個有效正應力。</p><p> 1.2.2.3 莫爾-庫侖(c’> 0)標準</p><p> 強度伴隨著正應力的增加呈線性增加,并且當正應力為0時強度為正
47、值.</p><p> ?'f = c' + ?'n tan?'?'f是摩擦角c'是‘凝聚力’截距</p><p> 在土壤中,莫爾-庫侖準則適用于正應力是一個有效正應力。在土壤中,莫爾-庫侖準則中凝聚力的有效應力與在特雷斯卡準則中的凝聚力(或不排水強度su)是不一樣的。</p><p><b>
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