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翻譯部分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)5.01672.4HWc??where σc= compressive strength of pillar having width equal to W and height equal to H.c) The final constant strength relationship:For W/H≥1 and W≥1.524m,(3)HW1.572.8c???Pratt 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:σ c1=KDα (4)where σ c1= compressive strength in MPa; D = edge dimensions in cm; and K and α are constants.Values of K and α 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 α in Equation (4) with correlation coeffcient (r) and standard for ten groups of test results of cubical coal specimens.K α 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 α 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:ndcD????????1(5)whereσ c1= compressive strength of a cubic rock specimen with edge dimension D; σ d= compressive strength of a cubic rock specimen with edge dimension d; and n = a constant for a given type of rock (n≥0; 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 (σ c1/σ 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 0.259n≤0.433. 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.塊度大小對煤的抗壓強度的影響H.默米萬德(H.Moomivand)伊朗尤邁加(Urmia)大學(xué)工程學(xué)院摘要：煤的抗壓強度決定于煤體中不連續(xù)結(jié)構(gòu)的分布、類型和狀態(tài)。在較小的煤樣中，發(fā)現(xiàn)大的不連續(xù)結(jié)構(gòu)的可能性也較小，因此其抗壓強度較高。用計算機數(shù)據(jù)處理程序分別對各組實驗室或現(xiàn)場的測試結(jié)果進(jìn)行分析，得出了在 10 組不同的煤中，塊度對其抗壓強度的影響是不同的。當(dāng)將各組結(jié)果綜合在一起時，得出對同一塊度的不同組煤樣，抗壓強度有一個很大的離散度，強度和塊度的關(guān)系有很大的偏離。用煤樣的抗壓強度除以任意一組測試結(jié)果中邊長為 d(這里 d 取 50.8mm)的煤樣的抗壓強度，因而省去了測量所有系列的強度值，并且確定了在所有各組測試結(jié)果中的抗壓強度比值和塊度的關(guān)系。從實驗室和現(xiàn)場的測試結(jié)果進(jìn)行推導(dǎo)，得出了所有立方體煤樣抗壓強度和塊度的比例關(guān)系。1．引言巖體中存在多種不連續(xù)結(jié)構(gòu)，由于這些不連續(xù)結(jié)構(gòu)的作用，抗壓強度隨巖樣塊度的減小而增加。已經(jīng)有了新的關(guān)于塊度對抗壓強度影響的解說。大部分應(yīng)用于煤的實驗主要集中于不同邊長的立方體煤樣的抗壓強度。在實驗室和現(xiàn)場都對塊度對煤的抗壓強度的影響進(jìn)行了研究。已經(jīng)用計算機數(shù)據(jù)處理程序?qū)膶嶒炇一颥F(xiàn)場得到的立方體煤樣的測試結(jié)果進(jìn)行了分析。從實驗室或現(xiàn)場測試結(jié)果中，推出了立方體煤樣抗壓強度和塊度間的關(guān)系。2．煤樣塊度對其抗壓強度的影響2.1 實驗室測試煤體中包含多種多樣的不連續(xù)結(jié)構(gòu)，如裂隙、孔隙等。巖石（煤）的抗壓強度取決于不連續(xù)結(jié)構(gòu)的類型、分布和狀態(tài)。在較小的樣本中，找到大的不連續(xù)結(jié)構(gòu)的可能性也較小，因此其抗壓強度也較高。對不同類型的巖石樣本，塊度對其抗壓強度的影響也不相同（H.默米萬德(H.Moomivand)） 。抗壓強度隨煤樣塊度的減小而增加（丹尼耳斯（Daniels）和莫瑞 (Moore)1907 ，瑞斯 (Rice)1929 ，拉奧 (Lawall) 和郝蘭德 (Holland)1937 ，斯提而特 (Steart)1954 ，卡德 (Gaddy)1956 ，伊萬斯·伊特·奧 (Evans et al.)1961 ） ?？ǖ?Gaddy)測試了匹茲堡（Pittsburgh）,可林特伍德（Clintwood） ，包加恒特斯四號（Pocahonts No.4）,哈蘭（Harlan ）和馬克爾（Marker）這 5種不同的煤層邊長在 0.051～1.626m 之間的煤樣，從而提出了以下的抗壓強度和煤樣塊度之間的關(guān)系：σ cl =KD-0.5 （1） 式中 σ cl為邊長為 D 的立方體煤樣的抗壓強度，K 是由煤的化學(xué)和物理性質(zhì)決定的系數(shù)。2.2 現(xiàn)場實測在挖掘和處理用以實驗室測試的巖樣是，不僅裂隙、節(jié)理和一些軟弱結(jié)構(gòu)要從大的規(guī)模（巖體）減小到實驗室中較小的規(guī)模，并且在把樣本從礦井運到實驗室再切成小塊的過程中，環(huán)境的變化要影響巖塊的強度。當(dāng)樣本在常溫下干燥幾周后，小塊樣本可能比大塊變得更干燥，因此，不同大小樣本的含濕量也將不同。并且，大塊樣本與小塊相比，從中心到表面的含濕量要更不均勻。比涅威斯基（Bieniawski） （1968）對地下現(xiàn)場的邊長在 0.019～2.017m 之間的 60 個立方體煤樣進(jìn)行了壓縮測試。他把測試結(jié)果分作三組：小塊（不大于0.076m） ，中等塊度（不大于 0.457m）和大塊（不大于 2.012m） 。他得出了抗壓強度隨樣本的塊度的增加而減小，當(dāng)達(dá)到臨界尺寸后，抗壓強度變?yōu)橐怀Ａ?。并且他建議對不同尺寸的樣本采用以下三個不同的公式：a） 初始定常強度（σ c=constant）：對這種情況還沒有得出一個具體的邊長，其他研究者得出的在此塊度范圍內(nèi)的強度有很大不同（伊萬斯 1970）(Evans)。用不同的方法將樣本同樣分成三組，可能影響得出的結(jié)果比涅威斯基（Bieniawski 1977） 。b）隨之的強度降低關(guān)系：如果 W/H1，并且 W1.524m則 σ c=4.772W0.16/H0.55 （2） 式中 σ c為寬為 W,高為 H 的煤的抗壓強度c)最終的定常強度關(guān)系：如果 W/H≥1，并且 W≥1.524m則 σ c=2.758+1.517W/H （3） 普瑞特·伊特·奧（Pratt et al.） （1972）分別對現(xiàn)場的邊長為 0.305～2.743m 和實驗室的邊長為 0.081～0.305m 之間的石英閃長巖和花崗閃長巖進(jìn)行了測試。他們得出結(jié)論：對于邊長大于 0.914m 的巖樣，抗壓強度隨巖樣塊度增加而減小，并逐漸達(dá)到一個常量。這個對于閃長巖的臨界尺寸要小于本涅威斯基（Bieniawski）得出的煤的臨界尺寸。表 1 10 組立方體煤樣的測試結(jié)果中公式（4）的 K、α 值及相應(yīng)的相互關(guān)系系數(shù)(r)和標(biāo)準(zhǔn)偏差K α相互關(guān)系系數(shù)(r)標(biāo)準(zhǔn)偏差組名35.63 -0.139 0.775 1.01包加恒特斯四號煤（卡德 1956）（Pocahonts No.4 (Gaddy)）22.52 -0.176 0.696 4.51帝譜·達(dá)夫瑞恩（伊萬斯·伊特·奧 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西弗吉尼亞(拉奧和郝蘭德 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哈蘭（卡德 1956）（Harlan (Gaddy)）101.78 -0.445 0.994 0.91馬克爾（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匹茲堡(瑞斯 1929,格林伍德·伊特·奧 1939，卡德 1956)（Pittsburgh (Rice，Greenwald et al.，Gaddy)）58.91 -1.311 0.257 19.93巴恩斯萊·哈得斯（伊萬斯·伊特·奧 1961）（Barnsley Hards (Evans et al.)）彭（Peng） （1973）提出如果樣本塊度大于劈理間隙，并且大的裂隙或節(jié)理并不是在所有的煤體中都經(jīng)?？吹剑瑒t煤柱和實驗室煤樣之間的裂隙密度將不存在差異，從而實驗室煤樣的強度將等于井下煤柱的強度。但是大量的實驗結(jié)果表明煤柱的尺寸對抗壓強度有影響。事實上，巖體中存在各種規(guī)模的不連續(xù)結(jié)構(gòu)，大的不連續(xù)結(jié)構(gòu)的密度可能隨煤柱尺寸的減小而減小。統(tǒng)計表明，在較小的煤樣中的大的不連續(xù)結(jié)構(gòu)要更少，從而抗壓強度就較高。因此，由于不同規(guī)模的不連續(xù)結(jié)構(gòu)的分布的作用，強度隨樣本塊度的減小而增加，在小于臨界尺寸時，隨著煤樣塊度的增加，不同規(guī)模的不連續(xù)結(jié)構(gòu)的分布是相同的，從而抗壓強度接近一個常量。3． 由煤的實驗室和現(xiàn)場實驗結(jié)果得出的結(jié)論已有很多學(xué)者在實驗室和現(xiàn)場對不同材料的強度——塊度關(guān)系進(jìn)行了研究，并且大多數(shù)實驗是針對煤巖進(jìn)行的。通過對這許多學(xué)者對立方體煤樣研究得出的 10 組結(jié)果進(jìn)行的分析，找到了在抗壓強度和煤樣塊度間的最佳函數(shù)關(guān)系：σ cl =KDα （4）式中 σ cl=抗壓強度，MPaD=邊長，cmK，α 為常數(shù)。公式（4）中的 K，α 在不同組中的測試結(jié)果由表 1 給出。其間關(guān)系由圖 1確定。K 的取值范圍為 22.52～101.78，α 的取值范圍為-0.139～1.311。對同一塊度的不同煤其抗壓強度有很高的離散度，因此由 10 組測試結(jié)果得出的帶有常數(shù) K、α 的公式（4）不能代表強度——塊度關(guān)系。以下公式用來描述巖石的強度——塊度關(guān)系：σ cl/σ d=（d/D） n （5） 式中 σ cl=邊長為 D 的立方體巖樣的抗壓強度σ d=邊長為 d 的立方體巖樣的抗壓強度n=對給定巖石類型的常數(shù)為了推導(dǎo)出不同類型的煤的抗壓強度——塊度關(guān)系，用煤樣的抗壓強度除以任意一組測試結(jié)果中邊長為 d(這里 d 取 50.8mm)的煤樣的抗壓強度，因而省去了測量所有系列的強度值，并且通過計算機數(shù)據(jù)處理程序確定了在所有實驗室和現(xiàn)場測試結(jié)果中的抗壓強度比值和塊度的關(guān)系。已確定了在相互關(guān)系系數(shù)為 0.187，標(biāo)準(zhǔn)差為 0.244 時公式（5）中的 n 值為 0.296。小型測試的次數(shù)小于現(xiàn)場實測的次數(shù)，因而這個最適合的關(guān)系更接近于小型測試結(jié)果，就塊度在 0.32～25.4m 之間的小塊煤樣而言，n 值被定為 0.259，此時相互關(guān)系系數(shù)為 0.743，標(biāo)準(zhǔn)差為 0.248。如果考慮到一些塊度在1.91～162.56cm 之間的小塊或大塊煤樣，n 值變?yōu)?0.433，此時相互關(guān)系系數(shù)為 0.885，標(biāo)準(zhǔn)差為 0.189。圖 2 給出了強度的比值和塊度的關(guān)系。圖 1 在各組煤樣中單向抗壓強度和塊度間的關(guān)系4．結(jié)論煤中包含多種規(guī)模的不連續(xù)結(jié)構(gòu)，在較小的煤樣中，發(fā)現(xiàn)大的不連續(xù)結(jié)構(gòu)的可能性也較小，因此其抗壓強度高。已經(jīng)確定了實驗室和現(xiàn)場所有實驗結(jié)果中強度比值和塊度的關(guān)系?？箟簡蜗蚩箟簭姸?，MPa塊度，cm圖 2 在所有立方體煤樣中抗壓強度的比值（σ cl/σ d）和塊度的關(guān)系強度和立方體煤樣塊度之間的關(guān)系用公式（5）的形式表達(dá)，其中0.259＜n≤0.433?？箟簭姸入S塊度的增加而減小，并在塊度大于1m時逐漸達(dá)到一個常量。小塊煤樣中塊度影響更加顯著（公式（5）和圖2） ，當(dāng)塊度達(dá)到臨界值后，由邊長的增加而引起的強度的變化就可以忽略不記了。強度比值塊度，cm