變形巖石應(yīng)變分析

1、第四章第四章 變形巖石應(yīng)變分析基礎(chǔ)變形巖石應(yīng)變分析基礎(chǔ)1本章主要內(nèi)容本章主要內(nèi)容v 變形、位移和應(yīng)變的概念變形、位移和應(yīng)變的概念v 旋轉(zhuǎn)應(yīng)變與非旋轉(zhuǎn)應(yīng)變旋轉(zhuǎn)應(yīng)變與非旋轉(zhuǎn)應(yīng)變v 遞進(jìn)變形、全量應(yīng)變與增量應(yīng)變遞進(jìn)變形、全量應(yīng)變與增量應(yīng)變v 巖石的變形階段巖石的變形階段2變形和位移變形和位移 當(dāng)?shù)貧ぶ袔r石體受到應(yīng)力作用后，其當(dāng)?shù)貧ぶ袔r石體受到應(yīng)力作用后，其內(nèi)部各質(zhì)點(diǎn)經(jīng)受了一系列的位移，從而使內(nèi)部各質(zhì)點(diǎn)經(jīng)受了一系列的位移，從而使巖石體的初始形狀、方位或位置發(fā)生了改巖石體的初始形狀、方位或位置發(fā)生了改變，這種改變就稱為變，這種改變就稱為變形變形。q 變形變形3q 位移位移物體內(nèi)部各質(zhì)點(diǎn)的位移是通過(guò)其初始

2、位置和終物體內(nèi)部各質(zhì)點(diǎn)的位移是通過(guò)其初始位置和終止位置的變化來(lái)表示，質(zhì)點(diǎn)的初始位置和終止止位置的變化來(lái)表示，質(zhì)點(diǎn)的初始位置和終止位置的連線叫位移矢量。位置的連線叫位移矢量。4平移旋轉(zhuǎn)(虛線為可能的路徑）形變體變P0P1P0P0P0P1P1P1巖石發(fā)生變形的四種形式巖石發(fā)生變形的四種形式567Deformation and Strain8describes the collective displacements of points in a body; in other words, it describes the complete transformation from the initi

3、al to the final geometry of a body. This change can include a (movement from one place to the other), a (spin around an axis), and a (change in shape). describes the changes of points in a body relative to each other; so, it describes the distortion of a body. 9Deformation and StrainSo, strain is a

4、component of deformation and therefore not a synonym. In essence, we have defined deformation and strain relative to a frame of reference. Deformation describes the complete displacement field of points in a body relative to an external reference frame, such as the edges of the paper on which Figure

5、 4.2 is drawn. Strain, on the other hand, describes the displacement field of points relative to each other. This requires a reference frame within the body, an internal reference frame, like the edges of the square.When the rotation and distortion components are zero, we only have a translation. Th

6、is translation is formally called , because the body undergoes no shape change while it moves.When the translation and distortion components are zero, we have only rotation of the body. By analogy to translation, we call this component , or simply ;When translation and spin are both zero, the body u

7、ndergoes ; this component is described by .Summary 10Deformation is described by:1. Rigid-body translation (or translation)2. Rigid-body rotation (or spin)3. Strain4. Volume change (or dilation)11伸長(zhǎng)度伸長(zhǎng)度(Extension)：?jiǎn)挝婚L(zhǎng)度的改變量：?jiǎn)挝婚L(zhǎng)度的改變量 e = (l - l0) / l0 長(zhǎng)度比長(zhǎng)度比(Stretch)：變形后的長(zhǎng)度與原長(zhǎng)之比：變形后的長(zhǎng)度與原長(zhǎng)之比 S = l / l0

8、 = 1 + e平方長(zhǎng)度比平方長(zhǎng)度比 = （1 + e）2倒數(shù)平方長(zhǎng)度比倒數(shù)平方長(zhǎng)度比 = 1/000llllle一般把伸長(zhǎng)時(shí)一般把伸長(zhǎng)時(shí)的線應(yīng)變?nèi)≌木€應(yīng)變?nèi)≌?，縮短時(shí)的值，縮短時(shí)的線應(yīng)變?nèi)∝?fù)值。線應(yīng)變?nèi)∝?fù)值。q 線應(yīng)變線應(yīng)變1213Angular Shear: Measure of Change in Angles between Lines14To determine the angular shear along a given line, L, in a strained body, it is essential to identify a line that was origi

9、nally perpendicular to L. Angular shear describes the departure of this line from its perpendicular relation with L (left figure). The full description requires a sign (positive equals counterclockwise; negative equals clockwise) and a magnitude expressed in degrees.Sign conventions for angular shea

10、r. (A) Determination of the angular shear of line A requires identifying a line, in this case B, which was originally perpendicular to A. The original orientation of line B relative to line A is shown by the dash line. Angular shear of line A is the shift in angle of B original versus B final. Becau

11、se the shift is clockwise, the angular shear is negative (-). (B) In this example the angular shear of line A is 150. A counterclockwise shift is denoted by a positive (+) sign.15(A)Block containing reference circles and lines, before deformation. (B)Shape of the block after deformation. Original re

12、ference circles now are ellipses. The originally mutually perpendicular reference lines have all changed length, and most have changed orientation as well.(C) Angular shear along any line can be determined by first identifying a line originally perpendicular to it, and then measuring the angular shi

13、ft. Remember, counterclockwise shifts are positive (+); clockwise shifts are negative (-).For ellipse cd (see Figure B), the angular shear along c is +30 and the angular shear along d is -30 (see Figure C).For ellipse ed,(see Figure B), the angular shear along e is +38, and the angular shear along f

14、 is -38 (see Figure C). Finally, for ellipse gh (see Figure B) the angular shear along g is +20, and the angular shear along h is -20.Shear Strain16Let us consider how points on a line move as a response to angular shear. Points 1 to 4 on line A0 in Figure 2.52A are translated by various distances a

15、s a result of the rotation of the line on which they reside. Line A0 is the locus of points 1 to 4. Line Af is the locus of the same points in their deformed locations (Figure 2.52B). Since angular shear was systematic and deformation was homogeneous, line Af remains straight. Points 1 to 4 move a d

16、istance that is directly related to the angular shear and to the distance of each point above the point of intersection with the complementary line. If the distance of each point above the intersection is denoted as y (Figure 2.52B), the horizontal distance of translation can be found as follows (Ra

17、msay, 1967):Thus tan is another way of describing relative shifts in orientations of lines that were originally perpendicular. It is called shear strain, symbolized by the Greek letter gamma (),17Shear strain along a line (i.e., along a given direction) may be positive ornegative, depending on the s

18、ense of rotation (deflection) of the line originallyperpendicular to it. The range of shear strain is zero to infinity. For the exampleshown in Figure 2.52B, the shear strain of line Bf is -tan 30, or -0.58. The shear strain of line Af is +tan 30, or 10.58.1819Strain describes the distortion of a bo

19、dy in response to an applied force. Strain is homogeneous when any two portions of the body that were similar in form and orientation before are similar in form and orientation after strain.We define homogeneous strain by its geometric consequences:1. Originally straight lines remain straight.2. Ori

20、ginally parallel lines remain parallel.3. Circles become ellipses; in three dimensions, spheres become ellipsoids.When one or more of these three restrictions does not apply, we call the strain heterogeneous (Figure 4.3c). Because conditions (1) and (2) are maintained duringthe deformation component

21、s of translation and rotation, deformation is homogeneous by definition if the strain is homogeneous.strain ellipse and strain ellipsoid 20In a homogeneously strained, two-dimensional body there will be at least two that do not rotate relative to each other, meaning that their angleremains the same

22、before and after strain. What is a material line? A material line connects features, such as an array of grains, that are recognizable throughout abodys strain history. The behavior of four material lines is illustrated in Figure 4.4 for the two-dimensional case, in which a circle changes into an el

23、lipse. In homogeneousstrain, two orientations of material lines remain perpendicular before and after strain. These two material lines form the axes of an ellipse that is called .Analogously, in three dimensions we have three material lines that remain perpendicular after strain and they define the

24、axes of an ellipsoid, . The lines that are perpendicular before and after strain are called the .應(yīng)變橢圓：二維變形中初始單位圓經(jīng)變形形成的橢圓應(yīng)變橢圓：二維變形中初始單位圓經(jīng)變形形成的橢圓應(yīng)變主軸：應(yīng)變橢圓的長(zhǎng)、短軸方向，該方向上只有線應(yīng)應(yīng)變主軸：應(yīng)變橢圓的長(zhǎng)、短軸方向，該方向上只有線應(yīng) 變而無(wú)剪切應(yīng)變。變而無(wú)剪切應(yīng)變。最大應(yīng)變與最小應(yīng)變：應(yīng)變主軸方向上的線應(yīng)變，即應(yīng)變最大應(yīng)變與最小應(yīng)變：應(yīng)變主軸方向上的線應(yīng)變，即應(yīng)變 橢圓長(zhǎng)、短軸半徑的長(zhǎng)度，其值分別為橢圓長(zhǎng)、短軸半徑的長(zhǎng)度，其值分別為11/2和

25、和21/2應(yīng)變橢圓軸比：應(yīng)變橢圓的長(zhǎng)、短軸比應(yīng)變橢圓軸比：應(yīng)變橢圓的長(zhǎng)、短軸比Rs 11/2/21/2211 1 (X)(X)2 2 (Y)(Y)3 3 (Z)222324應(yīng)變橢球體形態(tài)類型及其幾何表示法應(yīng)變橢球體形態(tài)類型及其幾何表示法a=X/Y, b=Y/Z, 各種應(yīng)變橢球體的形態(tài)可以用不同的圖解各種應(yīng)變橢球體的形態(tài)可以用不同的圖解來(lái)表示，常用的是弗林（來(lái)表示，常用的是弗林（Flinn）圖解，這是）圖解，這是一種用主應(yīng)變比一種用主應(yīng)變比a及及b作為坐標(biāo)軸的二維圖解。作為坐標(biāo)軸的二維圖解。abK=0K=任意一種形態(tài)的橢球體都可在圖任意一種形態(tài)的橢球體都可在圖中表示為一點(diǎn)，如圖中的中表示為一點(diǎn)，

26、如圖中的P點(diǎn)，該點(diǎn)，該點(diǎn)的位置就反映了應(yīng)變橢球體的點(diǎn)的位置就反映了應(yīng)變橢球體的形態(tài)和應(yīng)變強(qiáng)度。橢球體的形態(tài)形態(tài)和應(yīng)變強(qiáng)度。橢球體的形態(tài)用參數(shù)用參數(shù)k表示，表示，k=tg=(a-1)/(b-1)K值的物理意義：相當(dāng)于值的物理意義：相當(dāng)于P點(diǎn)到原點(diǎn)到原點(diǎn)連線的斜率。點(diǎn)連線的斜率。25k=0k=0：軸對(duì)稱壓縮，鐵餅型；：軸對(duì)稱壓縮，鐵餅型；1k01k0：壓扁型；：壓扁型；k=1k=1： 平面應(yīng)變平面應(yīng)變k1k1：拉伸應(yīng)變；：拉伸應(yīng)變；k=k=：?jiǎn)屋S拉伸，雪茄型：?jiǎn)屋S拉伸，雪茄型 在形變時(shí)體積不變的條件在形變時(shí)體積不變的條件下，依據(jù)下，依據(jù)k值可分為五種形值可分為五種形態(tài)類型的應(yīng)變橢球體態(tài)類型的應(yīng)變橢

27、球體26 Pancake shaped ellipsoid leads to S tectonites (strong schistosity, no lineation), cigar shaped ellipsoid leads to L tectonites (strong lineation, no schistosity). L=S tectonites are produced by plane strain. When strain is homogeneous it transforms an imaginary sphere into an ellipsoid (3 perp

28、endicular axes 123) called the Finite Strain Ellipsoid from which it is easy to characterize the style of strain and its intensity. When strain is heterogeneous we are stuffed as the characterization of a potatoid is extremely difficult. Fortunately it is always possible to define a scale at which s

29、train is, in first approximation, homogeneous. The strain, as geometrically characterized by an ellipsoid, is so easy to assess that only two parameters K and D completely define the style of strain (shape of ellipsoid) and the amount of strain (ellipsoidicity, ie how far it is from a perfect sphere

30、) respectively. As shown on the right these two parameters are both function of the ratio 1/2 and 2/3. K and D do not request knowledge of the radius of the initial sphere only knowledge of the principal axes of the finite strain ellipsoid.27：物體變形最終狀態(tài)與初始狀態(tài)對(duì)比發(fā)生的變化；物體變形最終狀態(tài)與初始狀態(tài)對(duì)比發(fā)生的變化；：物體從初始狀態(tài)變化到最終狀態(tài)

31、的過(guò)程是一個(gè)由許多：物體從初始狀態(tài)變化到最終狀態(tài)的過(guò)程是一個(gè)由許多次微量應(yīng)變的逐次疊加過(guò)程，該過(guò)程即為遞進(jìn)變形；次微量應(yīng)變的逐次疊加過(guò)程，該過(guò)程即為遞進(jìn)變形；：遞進(jìn)變形中某一瞬間正在發(fā)生的小應(yīng)變叫增量應(yīng)變；：遞進(jìn)變形中某一瞬間正在發(fā)生的小應(yīng)變叫增量應(yīng)變；：如果所取的變形瞬間非常微小，其間發(fā)生的微量應(yīng)：如果所取的變形瞬間非常微小，其間發(fā)生的微量應(yīng)變?yōu)闊o(wú)限小應(yīng)變。變?yōu)闊o(wú)限小應(yīng)變。遞進(jìn)變形遞進(jìn)變形28COAXIAL AND NON-COAXIALSTRAIN ACCUMULATION29In the general case for strain, the principal incremental

32、 strain axes are not necessarily the same throughout the strain history.The principal incremental strain axes rotate relative to the finite strain axes, a scenario that is called The case in which the same material lines remain the principal strain axes at each increment is called coaxial strain acc

33、umulation. So, with coaxial strain accumulation there is no rotation of the incremental strain axes with respect to the finite strain axes.The case in which the same material lines remain the principal strain axes at each incrementis called .Simple shear，pure shear and general shear30The component d

34、escribing the rotation of material lines with respect to the principal strain axes is called the , which is a measure of the degree of non-coaxiality.If there is zero internal vorticity, the strain history is coaxial (as in Figure 4.6b), which is sometimes called .The non-coaxial strain history in F

35、igure 4.6a describes the case in which thedistance perpendicular to the shear plane (or the thickness of our stack of cards) remains constant; this is also known as . In reality, a combination of simple shear and pure shear occurs, which we call (or general non-coaxial strain accumulation; Figure 4.

36、7). kinematic vorticity number31Internal vorticity is quantified by the kinematic vorticity number, Wk, which relates the angular velocity and the stretching rate of material lines.For pure shear Wk = 0 (Figure 4.8a), for general shear 0 Wk 1 (Figure 4.8b), and for simple shear Wk = 1 (Figure 4.8c).

37、 Rigid-body rotation or spin can also be described by the kinematic vorticity number (in this case, Wk = ; Figure 4.8d), but remember that this rotational component of deformation is distinct from the internal vorticity of strain. 32Using Figure 4.6 as an example, the deformation history shown in Fi

38、gure 4.6a represents non-coaxial, nonrotational deformation. The orientation of the shear plane does not rotate between each step, but the incremental strain axes do rotate. The strain history in Figure 4.6b represents coaxial, nonrotational deformation, because the incremental axes remain parallel.

39、Types of strain3334ACDBOdabccAbOO56 2033 4040剛 體 旋 轉(zhuǎn) 22 40簡(jiǎn)單剪切（單剪）純剪無(wú)旋變形無(wú)旋變形， 1 1和和 3 3質(zhì)點(diǎn)線方向在變形前后保持不變。質(zhì)點(diǎn)線方向在變形前后保持不變。如果體積不變而且如果體積不變而且 2 2=0=0，則稱為純剪切。，則稱為純剪切。35共軸與非共軸遞進(jìn)變形中應(yīng)變主軸物質(zhì)（質(zhì)點(diǎn)）線的變化共軸與非共軸遞進(jìn)變形中應(yīng)變主軸物質(zhì)（質(zhì)點(diǎn)）線的變化共軸變形中，組成應(yīng)變主軸的物質(zhì)（質(zhì)點(diǎn)）線不變共軸變形中，組成應(yīng)變主軸的物質(zhì)（質(zhì)點(diǎn)）線不變非共軸變形中，組成應(yīng)變主軸的質(zhì)點(diǎn)線是不斷變化的非共軸變形中，組成應(yīng)變主軸的質(zhì)點(diǎn)線是不斷變化的3

40、6純剪切：一種均勻共軸變形，應(yīng)變橢球體中主軸質(zhì)點(diǎn)線純剪切：一種均勻共軸變形，應(yīng)變橢球體中主軸質(zhì)點(diǎn)線 在變形前后保持不變且具有同一方位。在變形前后保持不變且具有同一方位。簡(jiǎn)單剪切：一種無(wú)體應(yīng)變的均勻非共軸變形，由物體質(zhì)簡(jiǎn)單剪切：一種無(wú)體應(yīng)變的均勻非共軸變形，由物體質(zhì) 點(diǎn)沿彼此平行的方向相對(duì)滑動(dòng)形成。點(diǎn)沿彼此平行的方向相對(duì)滑動(dòng)形成。37在簡(jiǎn)單剪切中，與剪切方向平行的方向上無(wú)線應(yīng)變，三在簡(jiǎn)單剪切中，與剪切方向平行的方向上無(wú)線應(yīng)變，三維上剪切面上無(wú)應(yīng)變，所以維上剪切面上無(wú)應(yīng)變，所以Y軸為無(wú)應(yīng)變軸，故此簡(jiǎn)單軸為無(wú)應(yīng)變軸，故此簡(jiǎn)單剪切屬于平面應(yīng)變。另外剪切帶的厚度也保持不變。剪切屬于平面應(yīng)變。另外剪切帶的

41、厚度也保持不變。剪切面剪切面剪切方向剪切方向剪切帶厚度剪切帶厚度38STRAIN PATH39The measure of strain that compares the initial and final configuration is called, identified by subscript f, which is independent of the details of the steps toward the final configuration. When these intermediate strain steps are determined they are c

42、alled , identified by subscript i.(1) 持續(xù)拉伸區(qū)持續(xù)拉伸區(qū)(2) 先壓縮后拉伸，變形先壓縮后拉伸，變形 后長(zhǎng)度超過(guò)原長(zhǎng)后長(zhǎng)度超過(guò)原長(zhǎng)(3) 先壓縮后拉伸，變形先壓縮后拉伸，變形 后長(zhǎng)度未達(dá)到原長(zhǎng)后長(zhǎng)度未達(dá)到原長(zhǎng)(4) 持續(xù)壓縮區(qū)持續(xù)壓縮區(qū)40有限應(yīng)變：巖石變形程度的量度有限應(yīng)變：巖石變形程度的量度有限應(yīng)變（狀態(tài)）的表示：應(yīng)變橢球的主軸長(zhǎng)度有限應(yīng)變（狀態(tài)）的表示：應(yīng)變橢球的主軸長(zhǎng)度 比（比（RsRs）和主軸方向）和主軸方向應(yīng)變標(biāo)志體：變形巖石中可用于測(cè)量和計(jì)算應(yīng)變應(yīng)變標(biāo)志體：變形巖石中可用于測(cè)量和計(jì)算應(yīng)變 狀態(tài)的標(biāo)志性物體狀態(tài)的標(biāo)志性物體41礫石、砂粒、氣孔

43、、鮞粒、礫石、砂粒、氣孔、鮞粒、放射蟲(chóng)、還原斑等放射蟲(chóng)、還原斑等原始形狀規(guī)則的標(biāo)志物：原始形狀規(guī)則的標(biāo)志物：變形化石和變形晶體等變形化石和變形晶體等與變形有關(guān)的小型構(gòu)造標(biāo)志物：與變形有關(guān)的小型構(gòu)造標(biāo)志物：壓力影、生長(zhǎng)礦物纖維、石香腸壓力影、生長(zhǎng)礦物纖維、石香腸構(gòu)造、線理、面理、節(jié)理等構(gòu)造、線理、面理、節(jié)理等已知原始形狀的已知原始形狀的其它標(biāo)志物其它標(biāo)志物原始為圓球或原始為圓球或橢球的標(biāo)志體橢球的標(biāo)志體應(yīng)變標(biāo)志體應(yīng)變標(biāo)志體42431.尋找三軸及主平面方向；尋找三軸及主平面方向；2.在在XZ、XY和和YZ面上測(cè)量標(biāo)志體的長(zhǎng)、短軸；面上測(cè)量標(biāo)志體的長(zhǎng)、短軸；3.投圖；投圖；4.求斜率得求斜率得X/Z

44、、X/Y和和Y/Z。5.還可用線性回歸及最小二乘法進(jìn)行計(jì)算機(jī)處理還可用線性回歸及最小二乘法進(jìn)行計(jì)算機(jī)處理44原理：應(yīng)變標(biāo)志體變形前并非球體，而是隨機(jī)分布的具有原始原理：應(yīng)變標(biāo)志體變形前并非球體，而是隨機(jī)分布的具有原始軸比（軸比（ Ri ）的橢球體，變形后形態(tài)和長(zhǎng)軸方位均發(fā)生變化。其）的橢球體，變形后形態(tài)和長(zhǎng)軸方位均發(fā)生變化。其最終的形態(tài)（軸比，最終的形態(tài)（軸比， Rf ）和方位（長(zhǎng)軸方向，）和方位（長(zhǎng)軸方向，）取決于測(cè)量取決于測(cè)量標(biāo)志初始軸比（標(biāo)志初始軸比（Ri）、初始長(zhǎng)軸方向（）、初始長(zhǎng)軸方向（）、及應(yīng)變橢圓軸比）、及應(yīng)變橢圓軸比（Rs），關(guān)系如下：），關(guān)系如下：RiRsRf) 1)(1()

45、 1(2) 1)(1(2cos22222sfifsisfiRRRRRRRRR測(cè)量標(biāo)志體：測(cè)量標(biāo)志體：礫石、鮞粒、還原斑礦物顆粒等礫石、鮞粒、還原斑礦物顆粒等4550資料線：變形前長(zhǎng)軸與應(yīng)變主軸成資料線：變形前長(zhǎng)軸與應(yīng)變主軸成45的的不同軸比的橢球變形后所在的方向與軸比。不同軸比的橢球變形后所在的方向與軸比。RfRf46472）在透明紙上畫(huà)上左上圖的）在透明紙上畫(huà)上左上圖的Rf和和軸并標(biāo)上刻度，同時(shí)標(biāo)上參考方向軸并標(biāo)上刻度，同時(shí)標(biāo)上參考方向3 3）測(cè)量標(biāo)志體的長(zhǎng)短軸比（）測(cè)量標(biāo)志體的長(zhǎng)短軸比（RfRf）及其與參考方向的夾角（）及其與參考方向的夾角（ ）4 4）將測(cè)量數(shù)據(jù)投到透明紙上）將測(cè)量數(shù)據(jù)投

46、到透明紙上5 5）將帶有測(cè)量數(shù)據(jù)的透明紙蒙在如左上圖那樣的曲線圖上，使透明紙和曲線）將帶有測(cè)量數(shù)據(jù)的透明紙蒙在如左上圖那樣的曲線圖上，使透明紙和曲線圖中的圖中的軸重合，對(duì)不同軸重合，對(duì)不同RsRs的曲線圖逐個(gè)套用，直到找到一個(gè)曲線圖，其上的的曲線圖逐個(gè)套用，直到找到一個(gè)曲線圖，其上的5050資料線和主軸將所有數(shù)據(jù)點(diǎn)四等分。此時(shí)該曲線圖的資料線和主軸將所有數(shù)據(jù)點(diǎn)四等分。此時(shí)該曲線圖的RsRs即為測(cè)量值即為測(cè)量值6 6）透明紙上的參考軸與曲線圖主軸的夾角即為參考軸與實(shí)際應(yīng)變主軸的夾角）透明紙上的參考軸與曲線圖主軸的夾角即為參考軸與實(shí)際應(yīng)變主軸的夾角測(cè)量方法：測(cè)量方法：1）根據(jù)應(yīng)變標(biāo)志體長(zhǎng)軸的統(tǒng)計(jì)方

47、位，）根據(jù)應(yīng)變標(biāo)志體長(zhǎng)軸的統(tǒng)計(jì)方位，在測(cè)量面上標(biāo)一參考的應(yīng)變主軸方向。在測(cè)量面上標(biāo)一參考的應(yīng)變主軸方向。4849要求：應(yīng)變標(biāo)志體變形后可辨認(rèn)變形前相互垂直的標(biāo)志線。要求：應(yīng)變標(biāo)志體變形后可辨認(rèn)變形前相互垂直的標(biāo)志線。3. 摩爾圓法摩爾圓法50122/1122121251521.Means, W.D.,1976,Stress and Strain, Spring Verlag New York, Inc中文譯本：中文譯本：應(yīng)力與應(yīng)變應(yīng)力與應(yīng)變，美美 W.D.米恩斯，淮南米恩斯，淮南煤炭學(xué)院譯，煤炭工業(yè)出版社出版，煤炭學(xué)院譯，煤炭工業(yè)出版社出版，1980.102.The techniques of

48、 modern structural geology. v.1,strain analysis / John G. R. 中文譯本：中文譯本：現(xiàn)代構(gòu)造地質(zhì)學(xué)方法現(xiàn)代構(gòu)造地質(zhì)學(xué)方法.第一卷應(yīng)變分析第一卷應(yīng)變分析徐樹(shù)桐主譯徐樹(shù)桐主譯 1991年，年，參考書(shū)籍參考書(shū)籍53ADDITIONAL READING 154Elliott, D., 1972. Deformation paths in structural geology. Geological Society of America Bulletin, 83, 26212638.Erslev, E. A., 1988. Normalized center-to-center strain analysis of packed aggregates. Journal of Structural Geology, 10, 201209.Fry, N., 1979. Random point distributions and strain measurement in rocks. Tectonophysics, 60, 89104.Groshong, R. H., Jr., 1972. Strain calculated from twining in calcite. Geological S