外文翻译-块度大小对煤的抗压强度的影响

翻译部分Effect of size on the compressive strength of coalH. MoomivandFaculty of Engineering, University of Urmia, IranABSTRACT: The compressive strength of coal depends on the distribution, type and condition of discontinuities. In the smaller specimen, the probability of finding larger discontinuities is smaller and the compressive strength is thus higher. All groups of laboratory and in situ test results were analyzed by a DataFit computer program separately. It was shown that the effect of size on the compressive strength of 10 different groups of coal is not the same. Compressive strength of different groups of coal specimens had a high scatter for the same size and strength-size relationship bad high deviation when all groups of results were mixed. Compressive strength of specimens was divided by the compressive strength of a specimen having a size equal to d (in this analysis 50.8 mm) in any group of test results. Consequently the dimension of strength in all series of tests was omitted and the relationship between the ratio of compressive strengths and size for all groups of results was determined. From extrapolating laboratory and in situ test results, the relationship between compressive strength and size of all cubic coal specimens was derived.1 INTRODUCTIONThe discontinuities of various sizes are present in rock mass. The compressive strength, as a function of discontinuities, increases with a decrease in size of rock specimens, A new definition for size effect on the compressive strength has been given as it can represent the phenomenon. Most of the experimental results available are for coal and are concerned especially with the compressive strength of cubes of various edge dimensions. The effect of size on the compressive strength of coal has been investigated by conducting tests both in the laboratory and in situ. The effect of size on the compressive strength of all laboratory and in situ test results of cubic coal specimens has been analysed using DataFit computer program (1992). From extrapolating laboratory and in situ test results, the relationship between compressive strength and size of all cubic coal specimens has been derived.2 EFFECT OF SIZE ON THE COMPRESSIVE STRENGTH OF COAL SPECIMENS2.1 Laboratory testsCoal contains various discontinuities such as cracks, pores, etc. The compressive strength of rock (coal) depends on the distribution, type and condition of discontinuities. In the smaller specimen, the probability of finding larger discontinuities is smaller and the compressive strength is thus higher. The effect of size on the compressive strength of different types of rock specimens is not the same (Moomivand, 1993).The compressive strength increases with a decrease in size of coal specimens (Daniels and K = a coefficient depending upon the chemical and physical properties of the coal.2.2 In situ testsIn the. cutting and curing of a rock specimen for laboratory testing, not only are cracks, joints and weaknesses reduced from a large size (rock mass) to a small laboratory size but also with the transporting of specimens from mines to the laboratory and with the cutting of samples to a small size, the environment changes which can affect strength. When the specimens are dried at a constant temperature over a period of a few weeks, a smaller specimen may be drier than a larger one. Therefore, the moisture content of different size specimens cannot be constant. Also, the moisture content of a larger specimen will be less homogeneous from its centre to its surface in comparison to a smaller specimen.Bieniawski (1968) conducted in situ compression tests of sixty cubical coal specimens having edge dimension from 0.019m to 2.012m underground. He classified the tests into three groups, a small size (up to 0.076 m), a medium size (up to 0.457 m) and a large size (up to 2.012 m). He showed -that compressive strength decreases with increasing specimen size and becomes constant when it reaches the critical specimen size (about 1.524 m), and suggested three different equations for different sizes of specimen as follows:a) Initial constant strength relationship (0(;=constant). For this case a specific value was not given for the edge dimension and other , investigators have found significant variations in strength with sizes in this region (Evans 1970). Different methods were employed to prepare these 3 groups which probably have affected the results obtained (Bieniawski 1977).b) The subsequent strength reduction relationship: For W/Hl and Wl.524m,(2)5.01672.4HWcwhere c= compressive strength of pillar having width equal to W and height equal to H.c) The final constant strength relationship:For W/H1 and W1.524m,(3)HW1.572.8cPratt et al. (1972) performed in situ tests on quartz diorite and granodiorite specimens ranging from 0.305m to 2.743m in length and laboratory tests ranging from 0.081 m to 0.305 m. They concluded that compressive strength decreases with an increase in the size and asymptotically approaching a constant value for specimens having edge dimension greater than 0.914 m. This critical size for diorite is less than the critical size for coal that was obtained by Bieniawski (1968).Peng (1993) suggested that there is no difference between the density of cleats in a coal pillar and the density of cleats in a laboratory size specimen, provided the specimen size is larger than the cleat spacing and large fractures or joints are not commonly found in all underground coal pillars. Therefore strength of laboratory size coal specimens is equal to the strength of underground coal pillars. But various experimental results suggest that the size has an effect on the compressive strength of coal specimens. As a matter of fact, the discontinuities of various sizes are present in rock mass. Probably the density of larger discontinuities decreases with a decrease of specimen size. Statistically the number of larger discontinuities present in smaller specimens is smaller and the compressive strength is thus higher. Therefore, the strength, as a function of distribution of discontinuities of different sizes, increases with a decrease of specimen size. In critical size and onward the distribution of discontinuities of different sizes is the same with an increase in the specimen size and the compressive strength approaches a constant value.3 EXTRAPOLATION OF THE LABORATORY AND IN SITU TEST RESULTS OF COALLaboratory and in situ investigations have been carried out by various authors to study the strength-size relationship on different materials, and most of the experiments have been conducted on coal. An analysis of 10 groups of results derived by various authors on coal cubes has been carried out. The best fit function to relate the compressive strength with size has been found to be: c1=KD (4)where c1= compressive strength in MPa; D = edge dimensions in cm; and K and are constants.Values of K and in Equation (4) for different groups of test results are given in Table 1 and relationships are according to Figure 1. K varies from 22.52 to 101.78 and a varies from 0.139 to -1.311. Compressive strength of different groups of coal specimens has a high scatter for the same size (compressive strength is from 22.52 MPa to 101.78 MPa for 1 cm cube in different groups of Table 1 Values of K and in Equation (4) with correlation coeffcient (r) and standard for ten groups of test results of cubical coal specimens.K Correlation(r) Standard deviation Group name35.63 -0.139 0.775 1.01 Pocahonts No.4 (Gaddy 1956)22.52 -0.176 0.696 4.51 Deep Durffryn (Evans et al. 1961)27.26 -0.179 0.434 3.29 Clintwood (Gaddy 1956）33.95 -0.285 0.481 9.46 West Virginia (Lawall so Equation (4) with constant values of K and to fit the 10 groups of test results together cannot represent the strength-size relationship. The following equation is used to represent strength-size relationship for rocks:ndcD1(5)where c1= compressive strength of a cubic rock specimen with edge dimension D; d= compressive strength of a cubic rock specimen with edge dimension d; and n = a constant for a given type of rock (n0; for n=0, size has no effect on the strength).For extrapolation of the relationship between compressive strength and size of different types of coal, compressive strength of specimens is divided by the compressive strength of a specimen having a size equal to d (in this analysis 50,8 mm) in any group of test results. Consequently the dimension of strength in all series of tests is omitted and the relationship between the ratio of compressive strengths and size for all laboratory and in situ test results has been determined using DataFit computer program. The value of n in Equation (5) has been determined to be 0.296 with correlation coefficient (r) of 0.817 and standard deviation of 0.244.The number of small scale tests is higher than the number of in situ large scale tests and the best fit is more close to the small scale results. Considering only the results of small specimens with size from 0.32 cm to 25.4 cm, the value of n has been determined to be 0.259 with correlation coefficient 58.91 -1.311 0.257 19.93 Barnsley Hards (Evans et al. 1961)Figure 1 Relationship between unconfined compressive strength and size of all groups of coal specimensof 0.743 and standard deviation of 0.248. If results of some small and large specimens with size from 1.91 cm to 162.56 cm are considered, n becomes 0.433 with correlation coefficient of 0.885 and standard deviation of 0.189. The ratio of strengths versus size of specimens is given in Figure 2.Figure 2 Relationship between ratio of compressive strengths ( c1/ c2) and size of all cubic coal specimens.4 CONCLUSIONSCoal contains discontinuities of various sizes. In the smaller specimen, the probability of finding larger discontinuities is smaller and the compressive strength is thus higher. The relationship between ratio of strengths and size of all groups including laboratory and in situ test results was determined. The relationship between compressive strength and size of all available cubic coal specimens is expressed in the form of Equation (5); and 0.259n0.433. Thecompressive strength decreases with an increase in size and asymptotically approaching a constant value at size equal to 1 m and onward. Size effect is more pronounced in small scale specimens Equation (5) and Figure 2 and difference in the strength due to increase in the edge dimensions of specimens is negligible at critical size and onward.5 REFERENCESBieniawski, Z.T. 1968. The effect of specimen size on compressive strength of coal. International Journal of Rock Mechanics and Mining Sciences: Vol.5,pp.25-335.Bieniawski, Z.T.1977. Discussions A review of pillar strength fomulas by W.A. Hustrulid. Rock Mechanics: Vol.10,pp.107-110.Daniels, J. 123-127.Gaddy, F.L. 1956. A study of the ultimate strength of coal as related to the absolute size of the cubical specimens tested. Engineering Experiment Station: Bulletion 112,Virginia Polytechnic Institute.Greenwald, H.P., H.C. Howarth & I. Hartmann 1939. Experiments on strength of small piallars of coal in the Pittsburgh bed. U.S. Bureau of Mines: Technical Paper 605.Lawall, C.E. & C.T. Holland 1937. Some physical characteristic of West Virginia coals. Engineering Experiment Station: Research Bulltion 17, West Virginia University.Moomivand, H. 1993. Effect of geometry on the unconfined compressive strength of pillars, M.E. Thesis, University of New South Wales.Peng, S.S. 1993. Strength of laboratory size coal specimens vs. underground coal pillars. Mining Engineering: Vol. 45, pp.157-158.Pratt, H.R., A.D. Black, W.S. Brown & W.F. Brace 1972. The effect of specimen size on the mechanical properties of unjoined diorite. International Journal of Rock Mechanics and Mining Sciences: Vol.9,pp. 513-529.Rice, G. 1992. Test of the strength of roof supports used in anthracite mines of pennsylvania. U.S. Bureau of Mines: Bulletin 303, 44 p.Steart, F.A. 1954. Strength and stability of pillars in coal mines. Journal of Chenical, Metallurgical and Mining Society of South Africa: Vol. 54,pp. 309-325.块度大小对煤的抗压强度的影响H.默米万德(H.Moomivand)伊朗尤迈加(Urmia)大学工程学院摘要：煤的抗压强度决定于煤体中不连续结构的分布、类型和状态。在较小的煤样中，发现大的不连续结构的可能性也较小，因此其抗压强度较高。用计算机数据处理程序分别对各组实验室或现场的测试结果进行分析，得出了在 10 组不同的煤中，块度对其抗压强度的影响是不同的。当将各组结果综合在一起时，得出对同一块度的不同组煤样，抗压强度有一个很大的离散度，强度和块度的关系有很大的偏离。用煤样的抗压强度除以任意一组测试结果中边长为 d(这里 d 取 50.8mm)的煤样的抗压强度，因而省去了测量所有系列的强度值，并且确定了在所有各组测试结果中的抗压强度比值和块度的关系。从实验室和现场的测试结果进行推导，得出了所有立方体煤样抗压强度和块度的比例关系。1引言岩体中存在多种不连续结构，由于这些不连续结构的作用，抗压强度随岩样块度的减小而增加。已经有了新的关于块度对抗压强度影响的解说。大部分应用于煤的实验主要集中于不同边长的立方体煤样的抗压强度。在实验室和现场都对块度对煤的抗压强度的影响进行了研究。已经用计算机数据处理程序对从实验室或现场得到的立方体煤样的测试结果进行了分析。从实验室或现场测试结果中，推出了立方体煤样抗压强度和块度间的关系。2煤样块度对其抗压强度的影响2.1 实验室测试煤体中包含多种多样的不连续结构，如裂隙、孔隙等。岩石（煤）的抗压强度取决于不连续结构的类型、分布和状态。在较小的样本中，找到大的不连续结构的可能性也较小，因此其抗压强度也较高。对不同类型的岩石样本，块度对其抗压强度的影响也不相同（H.默米万德(H.Moomivand)） 。抗压强度随煤样块度的减小而增加（丹尼耳斯（Daniels）和莫瑞 (Moore)1907 ，瑞斯 (Rice)1929 ，拉奥 (Lawall) 和郝兰德 (Holland)1937 ，斯提而特 (Steart)1954 ，卡德 (Gaddy)1956 ，伊万斯伊特奥 (Evans et al.)1961 ） 。卡德(Gaddy)测试了匹兹堡（Pittsburgh）,可林特伍德（Clintwood） ，包加恒特斯四号（Pocahonts No.4）,哈兰（Harlan ）和马克尔（Marker）这 5种不同的煤层边长在 0.0511.626m 之间的煤样，从而提出了以下的抗压强度和煤样块度之间的关系： cl =KD-0.5 （1） 式中 cl为边长为 D 的立方体煤样的抗压强度，K 是由煤的化学和物理性质决定的系数。2.2 现场实测在挖掘和处理用以实验室测试的岩样是，不仅裂隙、节理和一些软弱结构要从大的规模（岩体）减小到实验室中较小的规模，并且在把样本从矿井运到实验室再切成小块的过程中，环境的变化要影响岩块的强度。当样本在常温下干燥几周后，小块样本可能比大块变得更干燥，因此，不同大小样本的含湿量也将不同。并且，大块样本与小块相比，从中心到表面的含湿量要更不均匀。比涅威斯基（Bieniawski） （1968）对地下现场的边长在 0.0192.017m 之间的 60 个立方体煤样进行了压缩测试。他把测试结果分作三组：小块（不大于0.076m） ，中等块度（不大于 0.457m）和大块（不大于 2.012m） 。他得出了抗压强度随样本的块度的增加而减小，当达到临界尺寸后，抗压强度变为一常量。并且他建议对不同尺寸的样本采用以下三个不同的公式：a） 初始定常强度（ c=constant）：对这种情况还没有得出一个具体的边长，其他研究者得出的在此块度范围内的强度有很大不同（伊万斯 1970）(Evans)。用不同的方法将样本同样分成三组，可能影响得出的结果比涅威斯基（Bieniawski 1977） 。b）随之的强度降低关系：如果 W/H1，并且 W1.524m则 c=4.772W0.16/H0.55 （2） 式中 c为宽为 W,高为 H 的煤的抗压强度c)最终的定常强度关系：如果 W/H1，并且 W1.524m则 c=2.758+1.517W/H （3） 普瑞特伊特奥（Pratt et al.） （1972）分别对现场的边长为 0.3052.743m 和实验室的边长为 0.0810.305m 之间的石英闪长岩和花岗闪长岩进行了测试。他们得出结论：对于边长大于 0.914m 的岩样，抗压强度随岩样块度增加而减小，并逐渐达到一个常量。这个对于闪长岩的临界尺寸要小于本涅威斯基（Bieniawski）得出的煤的临界尺寸。表 1 10 组立方体煤样的测试结果中公式（4）的 K、 值及相应的相互关系系数(r)和标准偏差K 相互关系系数(r)标准偏差组名35.63 -0.139 0.775 1.01包加恒特斯四号煤（卡德 1956）（Pocahonts No.4 (Gaddy)）22.52 -0.176 0.696 4.51帝谱达夫瑞恩（伊万斯伊特奥 1961）(Deep Durffryn (Evans et al.)27.26 -0.179 0.434 3.29可林特伍德(卡德 1956)（Clintwood (Gaddy)）33.95 -0.285 0.481 9.46西弗吉尼亚(拉奥和郝兰德 1937)(West Virginia (Lawall & Holland)49.99 -0.425 0.908 5.42南非（比涅威斯基 1968）(South Africa（Bieniawski）)81.36 -0.436 0.614 7.97哈兰（卡德 1956）（Harlan (Gaddy)）101.78 -0.445 0.994 0.91马克尔（卡德 1956）（Marker (Gaddy)）43.04 -0.463 0.385 5.01丹尼耳斯和莫瑞 1907（Daniels & Moore)59.14 -0.467 0.942 2.46匹兹堡(瑞斯 1929,格林伍德伊特奥 1939，卡德 1956)（Pittsburgh (Rice，Greenwald et al.，Gaddy)）58.91 -1.311 0.257 19.93巴恩斯莱哈得斯（伊万斯伊特奥 1961）（Barnsley Hards (Evans et al.)）彭（Peng） （1973）提出如果样本块度大于劈理间隙，并且大的裂隙或节理并不是在所有的煤体中都经常看到，则煤柱和实验室煤样之间的裂隙密度将不存在差异，从而实验室煤样的强度将等于井下煤柱的强度。但是大量的实验结果表明煤柱的尺寸对抗压强度有影响。事实上，岩体中存在各种规模的不连续结构，大的不连续结构的密度可能随煤柱尺寸的减小而减小。统计表明，在较小的煤样中的大的不连续结构要更少，从而抗压强度就较高。因此，由于不同规模的不连续结构的分布的作用，强度随样本块度的减小而增加，在小于临界尺寸时，随着煤样块度的增加，不同规模的不连续结构的分布是相同的，从而抗压强度接近一个常量。3 由煤的实验室和现场实验结果得出的结论已有很多学者在实验室和现场对不同材料的强度块度关系进行了研究，并且大多数实验是针对煤岩进行的。通过对这许多学者对立方体煤样研究得出的 10 组结果进行的分析，找到了在抗压强度和煤样块度间的最佳函数关系： cl =KD （4）式中 cl=抗压强度，MPaD=边长，cmK， 为常数。公式（4）中的 K， 在不同组中的测试结果由表 1 给出。其间关系由图 1确定。K 的取值范围为 22.52101.78， 的取值范围为-0.1391.311。对同一块度的不同煤其抗压强度有很高的离散度，因此由 10 组测试结果得出的带有常数 K、 的公式（4）不能代表强度块度关系。以下公式用来描述岩石的强度块度关系： cl/ d=（d/D） n （5） 式中 cl=边长为 D 的立方体岩样的抗压强度 d=边长为 d 的立方体岩样的抗压强度n=对给定岩石类型的常数为了推导出不同类型的煤的抗压强度块度关系，用煤样的抗压强度除以任意一组测试结果中边长为 d(这里 d 取 50.8mm)的煤样的抗压强度，因而省去了测量所有系列的强度值，并且通过计算机数据处理程序确定了在所有实验室和现场测试结果中的抗压强度比值和块度的关系。已确定了在相互关系系数为 0.187，标准差为 0.244 时公式（5）中的 n 值为 0.296。小型测试的次数小于现场实测的次数，因而这个最适合的关系更接近于小型测试结果，就块度在 0.3225.4m 之间的小块煤样而言，n 值被定为 0.259，此时相互关系系数为 0.743，标准差为 0.248。如果考虑到一些块度在1.91162.56cm 之间的小块或大块煤样，n 值变为 0.433，此时相互关系系数为 0.885，标准差为 0.189。图 2 给出了强度的比值和块度的关系。图 1 在各组煤样中单向抗压强度和块度间的关系4结论煤中包含多种规模的不连续结构，在较小的煤样中，发现大的不连续结构的可能性也较小，因此其抗压强度高。已经确定了实验室和现场所有实验结果中强度比值和块度的关系。抗压单向抗压强度，MPa块度，cm图 2 在所有立方体煤样中抗压强度的比值（ cl/ d）和块度的关系强度和立方体煤样块度之间的关系用公式（5）的形式表达，其中0.259n0.433。抗压强度随块度的增加而减小，并在块度大于1m时逐渐达到一个常量。小块煤样中块度影响更加显著（公式（5）和图2） ，当块度达到临界值后，由边长的增加而引起的强度的变化就可以忽略不记了。强度比值块度，cm