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1、<p><b> 外文翻譯</b></p><p><b> Problems</b></p><p> 1 From the data given in figure 4.18,calculate the tangent modulus and Poisson’s ratio for the initial elastic be
2、havior of limestone withσ3= 2.0MPa.</p><p> 2 A porous sandstone has a uniaxial compressive strength of σc=75MPa. the results of a series of triaxial compression tests plotted on shear stress-normal stress
3、axes give a linear Coulomb peak strength envelope having a slope of 45o</p><p> Determine the axial stress at peak strength of a jacketed specimen subjected to a confining pressure of σ3= 10MPa. If the jack
4、et had been punctured during the test and the pore pressure had built up to a equal to the confining pressure ,what would the peak axial stress have been?</p><p> 3(a) Establish an approximate peak strength
5、 envelope for the marble for which the date shown in Figure 4.19 were obtained.</p><p> 3(b) In what ways might the observed stress-strain behavior of the specimens have differed had the tests been carried
6、out in a conventional testing machine having a longitudinal stiffness of 2.0 GNm-1? Assume that all specimens were 50mm in diameter 100mm long.</p><p> ROCK STRENGTH AND DEFORMABILITY</p><p>
7、4 A series of laboratory tests on intact specimens of quartzite gave the following mean peak strengths. The units of stress are MPa, and compression is taken as positive.</p><p> Develop a peak strength cri
8、terion for the quartzite for use in underground excavation design. Experience has shown that in situ uniaxial compressive strength of the quartzite is one-half the laboratory value.</p><p> 5 A series of tr
9、iaxial compression tests on specimens of a slate gave the following results:</p><p> In each test ,failure occurred by shear along the cleavage. Determine the shear strength criterion for cleavage plans.<
10、;/p><p> 6 In a further series of tests on the slate for which the data of Problem 5 were obtained, it was found that, when failure occurred in directions other than along the cleavage, the peak strength of ro
11、ck material was given by </p><p> σ1=150+2.8σ3</p><p> where σ1 and σ3 are in MPa.</p><p> Construct a graph showing the expected variation of peak axial stress at a confining pr
12、essure of 10 MPa, as the angle between the cleavage and the specimen axis varies from 0oto90o.</p><p> 7 The following results were obtained in a series of direct shear tests carried out on 100 mm square sp
13、ecimens of granite containing clean, rough, dry joints.</p><p> Determine the basic friction angle and the initial roughness angle for the joint surfaces.</p><p> Establish a peak shear streng
14、th criterion for the joints, suitable for use in the range of normal stresses, 0-4MPa.</p><p> Assuming linear shear stress-shear displacement relations to peak shear strength, investigate the influence of
15、normal stress on the shear stiffness of the joints.</p><p> 8 A triaxial compression test is to be carried out on a specimen of granite referred to in Problem 7 with the joint plane inclined at 35o to the s
16、pecimen axis. A confining pressure of σ3=1.5MPa and an axial stress of σ1=3.3MPa are to be applied. Then a joint water pressure will be introduced and gradually increased with σ1 and σ3 held constant. At what joint water
17、 pressure is slip on the joint expected to occur? Repeat the calculation for a similar test in which σ1=4.7MPa and σ3=1.5MPa.</p><p> 9 In the plane of cross section of an excavation, a rock mass contains f
18、our sets of discontinuities mutually inclined at 45o. The shear strengths of all discontinuities are given by a linear Coulomb criterion with c’=100kPa and φ’=30o.</p><p> Develop an isotropic strength crit
19、erion for the rock mass that approximate the strength obtained by applying Jaeger’s single plane of weakness theory in several parts.</p><p> 10 A certain slate can be treated as a transversely isotropic e
20、lastic material. Block samples of the slate are available from which cores may be prepared with the cleavage at chosen angles to the specimen axes.</p><p> Nominate a set of tests that could be used to dete
21、rmine the five independent elastic constants in equation 2.42 required to characterize the stress-strain behavior of the slate in uniaxial compression. What measurements should be taken in each of these tests? </p>
22、<p> 5 Pre-mining state of stress</p><p> 5.1 Specification of the pre-mining state of stress</p><p> The design of an underground structure in rock differs from other types of struct
23、ural design in the nature of the loads operating in the system. In conventional surface structures, the geometry of the structure and its operating duty define the loads imposed on the system. For an underground rock str
24、ucture, the rock medium is subject to initial stress prior to excavation. The final, post-excavation state of stress in the structure is the resultant of the initial state of stress and stresses indu</p><p>
25、 The method of specifying the in situ state of stress at a point in a rock mass, relative to a set of reference axes, is demonstrated in Figure 5.1. A convenient set of Cartesian global reference axes is established by
26、orienting the x axis towards mine north, y towards mine east, and z vertically downwards. The ambient stress components expressed relative to these axes are denoted pxx , pyy, p zz, p xy, pyz, p zx. Using the methods est
27、ablished in Chapter 2, it is possible to determine, from these</p><p> The assumption made in this discussion is that it is possible to determine the in situ state of stress in a way which yields representa
28、tive magnitudes of the components of the field stress tensor throughout a problem domain. The state of stress in the rock mass is inferred to be spatially quite variable, due to the presence of structural features such a
29、s faults or local variation in rock material properties. Spatial variation in the field stress tensor may be sometimes observed as an apparent vi</p><p> Pzz=γz (5.1)
30、 </p><p> Where γ is the rock unit weight, and z is the depth below ground surface.</p><p> Failure to satisfy this equilibrium condition (equation5.1)in any field de
31、termination of the pre-mining state of stress may be a valid indication of heterogeneity of the stress field. For example, the vertical normal stress component might be expected to be less than the value calculated from
32、equation 5.1, for observations made in the axial plane of an anticlinal fold.</p><p> A common but unjustified assumption in the estimation of the in situ state of stress is a condition of uniaxial strain (
33、‘complete lateral restraint’)during development of gravitational loading of a formation by superincumbent rock. For elastic rock mass behavior, horizontal normal stress components are then given by</p><p>&l
34、t;b> (5.2)</b></p><p> Where ν is Poisson’s ratio for the rock mass.</p><p> If it is also assumed that the shear stress components p xy, pyz, p zx are zero, the normal stresses defi
35、ned by equations 5.1and 5.2 are principal stresses. </p><p> Reports and summaries of field observations (Hooker et al.,1972;Brown and Hoek,1978) indicate that for depths of stress determinations of mining
36、engineering interest, equation 5.2 is rarely satisfied, and the vertical direction is rarely a principal stress direction. These conditions arise from the complex load path and geological history to which an element of r
37、ock is typically subjected in reaching its current equilibrium state during and following orebody formation. </p><p> 譯文 問題 1在σ3 = 2.0MPa的條件下,石灰石的初始彈性行為包括計算切線模量和泊松比可由圖4.18所給出的數(shù)據(jù)顯示出來。 2多孔砂巖的單軸抗壓強度σc=75MP
38、a 。由一系列的三軸壓縮試驗結果繪制出的剪應力正常應力軸顯示的庫侖強度峰值線性強度包絡圖有一個45o的傾斜。 確定套嵌標本遭受的圍壓σ3=10MPa軸向強度應力峰值。如果套嵌在試驗過程中被刺破,孔隙水壓力已建立起一個平衡的圍壓值,那么軸向應力峰值又會怎樣? 3 ( a )建立一個大理巖近似峰值強度包絡圖如圖4.19所示。 3 ( b )通過采取何種方式可以觀測到試樣的應力應變行為由不同的試驗進行了常規(guī)試驗機上得出的線性剛度
39、為2.0GNm-1 ?假定所有標本,直徑為50mm長100毫米。 巖石強度和應變4一系列完整的石英巖試樣的實驗室試驗給出了以下平均強度峰值。應力的單位是兆帕,并且壓縮性為剛性。 </p><p> 制定一個石英巖的峰值強度標準用于地下洞室的開挖設計。經(jīng)驗表明,石英巖的原位單軸抗壓強度值是實驗室所測值的一半。 </p><p> 5一系列板巖試樣的三軸壓縮試驗結果如下: </
40、p><p> 在每一個試樣中,試樣沿著解理面發(fā)生剪切破壞。進而確定解理平面圖的抗剪強度標準。6在問題5所得數(shù)據(jù)的基礎上,對板巖做了一系列進一步的實驗,人們發(fā)現(xiàn),當破壞方向不是沿著解理時,巖石材料的峰值強度由公式 σ1=150+2.8σ3 計算得到。其中σ1和σ3的單位為MPa。</p><p> 構建一個圖表顯示了軸向應力峰值在圍壓為10兆帕時的預期變化,因為解理和試樣軸向之間的夾角
41、從0o到90o 變化。</p><p> 7以下結果是在一系列100毫米見方的含有新鮮,粗糙,隱形裂隙交織的花崗巖試樣上進行直接剪切試驗得到的。</p><p> (a)確定交接面處的基本摩擦角和初始粗糙度。 (b)建立一個節(jié)理峰值抗剪強度標準,適用于正應力變化范圍為0-4MPa。 (c)假設線性剪切應力——剪切位移和峰值抗剪強度有關,研究正應力對節(jié)理剪切剛度的影響。 8三軸壓縮
42、試驗是在問題7所提到的花崗巖試樣上進行的,這個試樣的節(jié)理面向軸線以35o傾斜。施加σ3=1.5MPa的圍壓和σ1=3.3MPa軸向應力。這時節(jié)理水壓力將會隨著σ1和σ3的保持不變而逐漸增大。當節(jié)理水壓力為多大時節(jié)理將發(fā)生預期滑動平移?重復計算在σ1 = 4.7MPa和σ3 =1.5MPa時的類似試驗。 </p><p> 9在交叉的開挖橫斷面,巖體包含四處相互傾斜45o的不連續(xù)面。所有不連續(xù)面的抗剪強度均由C&
43、#39;= 100kPa,φ'=30o時的線性庫倫準則得出。 制定一套巖體各向同性強度準則,這與耶格爾的單一薄弱面理論的很多方面都相似。10某板巖可以視為橫斷的各向同性彈性材料。塊狀板巖試樣可取自節(jié)理與軸向成選定角度的試樣上。</p><p> 提出一系列試驗,可用于確定公式2.42中五個獨立的彈性常數(shù),此公式可以描述板巖在單軸壓縮試驗中的應力應變特性。</p><p&g
44、t; 5前采礦應力狀態(tài) 5.1前采礦應力狀態(tài)規(guī)范 巖石中的地下結構設計,不同于在自然荷載系統(tǒng)作用下的其他類型的結構設計。</p><p> 在傳統(tǒng)的表面構造中,建筑物的幾何構造和和它的運作效率限制了加在其上的荷載。對于一個巖石地下結構,巖石介質(zhì)在開挖之前經(jīng)受初始應力。最后,結構中的后期開挖應力狀態(tài)是初始應力狀態(tài)和開挖引起的應力的結果。既然開挖引起的應力和初始應力狀態(tài)有關,所以很明顯,前采礦應力狀態(tài)的規(guī)范
45、和測定是所有設計分析的必要先決條件。 該方法是說明巖體中一點原位應力狀態(tài),它和一系列參照軸有關,如圖5.1所示。建立一個合適的笛卡兒全球參照軸,X軸方向指向煤礦北部方向,Y軸指向煤礦東部,Z軸為向下的垂直方向。環(huán)境應力分量表示和這些軸有關,這些應力分量表示為pxx , pyy, p zz, p xy, pyz, p zx。使用方法建立在第2章,從這些應力分量就可以判斷場地主要應力pi(i=1,2,3)的重要性。還有三個軸各自的方
46、向余弦向量(λxi, λyi, λzi)。相應每個主軸方向的角度產(chǎn)生傾角 αi和方向角,或傾方位角βi 。規(guī)定以p1:p2:p3=1.0:q:r形式確定的主應力的比例,完善了預開采應力狀態(tài)規(guī)范,q和r不僅僅是單一的。</p><p> 這方面討論中的假定有可能確定在原地應力狀態(tài),對于通過一個課題領域產(chǎn)生的地應力張量的分量方式產(chǎn)生重要的代表性。巖體應力狀態(tài)趨于相對空間變量,主要是由于諸如斷層和巖石材料的局部變質(zhì)等
47、結構特征的出現(xiàn)??臻g地應力張量時常以潛在的垂直方向的破壞方程觀測到。由于地面總是免于牽引,簡單的靜力學要求垂直正應力分量在次表層點,可通過公式5.1給出 Pzz = γz ( 5.1 ) γ—巖石單位重量</p><p><b> Z—地表以下深度</b></p><p> 不能
48、滿足這一平衡條件(方程5.1 )在任何領域確定前采礦應力狀態(tài)可能是一個非均質(zhì)性應力場的有效跡象。例如,垂直正應力分量可能會預計將低于方程5.1計算的數(shù)值,由于背斜軸面的觀測數(shù)據(jù)。</p><p> 一個共同的,但不合理的假設,在上覆巖層的重力荷載的加載過程中,估計原位地應力狀態(tài)是一個單軸應變條件(完全側限)。彈性巖體特征,橫向正應力分量,可通過公式5.2給出 (5.2)</p>
49、<p><b> 巖體的泊松比</b></p><p> 如果還假定抗剪強度分量p xy, pyz, p zx為零,按公式5.1和5.2定義的正應力是主應力。 實地觀測(胡克等人,1972年;布朗和胡克,1978年)的報告和摘要表明,公式5.2不能滿足采礦工程所需的應力測試深度,垂直方向不是主要的應力方向。這些條件源于復雜的負載路徑和地質(zhì)歷史即巖石元素
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