岩石试验抗压、抗拉区间强度及代表值可信度研究
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摘要
研究岩石区间非定值强度问题以期适应实验室试验有限性、随机性的特点,以此反映岩石强度参数取值的区间性特征及可能性分布。首先,提出了岩石的抗压区间强度、抗拉区间强度的概念;其次,基于区间分析、未确知数学理论,结合实验室实际,给出了区间强度的求解方法,并提出了区间内不同强度代表值的可信度确定方法,有利于工程计算时强度参数的选取。最后,通过小样本和大样本的分析比较,对本文方法的合理性进行了验证。小样本研究表明,取可信度为95%时,岩石抗压、抗拉强度代表值小于常规均值计算得到的值,且常规均值计算求取的岩石抗压、抗拉强度代表值可信度在65%左右,可见通过常规均值计算的结果是偏危险的;将某矿山砂岩的320个试样(大样本)随机分成64组,每组5个试样(小样本),研究发现,320个岩样强度呈正态分布,把平均值238.17 MPa作为该区域砂岩的名义值,64个传统均值有32个的取值的大于名义值,证明小样本下(5个样本),用传统均值代表岩石强度其保证率为50%;64个区间强度有55个包含名义值,准确率为86%,且另外6个区间强度上限值均小于名义值,可见用区间强度代表岩石强度的保证率为95%。区间强度较传统均值更充分地表达了岩石强度的信息,完善了岩石强度参数确定方法,为实际工程设计施工、强度校核及可靠性研究中岩石强度参数的取值提供一条新途径。
The interval parameters of rock tensile and compression strength to meet the strength of the limited laboratory tests and the characteristics of randomness and to reflect the range of features and the possibility of distribution are studied.Firstly,the concepts of the interval compression strength and the tensile strength are proposed.Secondly,based on the interval analysis,the blind data theory and laboratory practice,the solution method for the interval strength is proposed.Representative values of rock tensile and compression strength tests and their corresponding faith degrees are obtained using the theory of unascertained mathematics in favor of the project selection.Finally,the availability of the proposed methods is demonstrated by analying small and big samples.The small-sample results show that representative values of the rock strength and tensile strength by the proposed methods are smaller than those of the recommended methods by the conventional average values when the faith degree is 95%,and the faith degree of the conventional average values of rock strength is about 65%.It can be seen the representative conventional average values are dangerous.320 rock specimens(big-sample) in a mine are divided into 64 groups,and each group has 5 rock specimens.The results show that 320 rock specimens follow the normal distributions.The average value of 238.17 MPa is regarded as the true value,and half of 64 conventional average values of strength are larger than the true value.It means that the warrant rate is 50%.55 of 64 interval values of strength contain the true value,and the accuracy rate is 86%.The upper values from another 6 interval strengths are larger than the true value,which means that the warrant rate is 95% when the interval values of strength are representative values.It shows that the method is reasonable.The interval parameters of rock tensile and compression strength improve the rock strength parameters.It provides a new method to select rock strength parameters for conducting the reliability analysis,design and safety verification in actual engineering.
The interval parameters of rock tensile and compression strength to meet the strength of the limited laboratory tests and the characteristics of randomness and to reflect the range of features and the possibility of distribution are studied.Firstly,the concepts of the interval compression strength and the tensile strength are proposed.Secondly,based on the interval analysis,the blind data theory and laboratory practice,the solution method for the interval strength is proposed.Representative values of rock tensile and compression strength tests and their corresponding faith degrees are obtained using the theory of unascertained mathematics in favor of the project selection.Finally,the availability of the proposed methods is demonstrated by analying small and big samples.The small-sample results show that representative values of the rock strength and tensile strength by the proposed methods are smaller than those of the recommended methods by the conventional average values when the faith degree is 95%,and the faith degree of the conventional average values of rock strength is about 65%.It can be seen the representative conventional average values are dangerous.320 rock specimens(big-sample) in a mine are divided into 64 groups,and each group has 5 rock specimens.The results show that 320 rock specimens follow the normal distributions.The average value of 238.17 MPa is regarded as the true value,and half of 64 conventional average values of strength are larger than the true value.It means that the warrant rate is 50%.55 of 64 interval values of strength contain the true value,and the accuracy rate is 86%.The upper values from another 6 interval strengths are larger than the true value,which means that the warrant rate is 95% when the interval values of strength are representative values.It shows that the method is reasonable.The interval parameters of rock tensile and compression strength improve the rock strength parameters.It provides a new method to select rock strength parameters for conducting the reliability analysis,design and safety verification in actual engineering.
引文
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[10]董陇军,赵国彦,宫凤强.尾矿坝稳定性分析的区间非定值模型及应用[J].中南大学学报(自然科学版),(录用待刊)2011.(DONG Long-jun,ZHAO Guo-yan,GONGFeng-qiang.Interval non-real number model and itsapplication for analysis stability of Tailing dam[J].Journal ofCenter South University(Science and Natural Edition),(Accept)2011.(in Chinese))
[11]董陇军,赵国彦.未确知均值分级方法及在回采巷道围岩分类中的应用[J].解放军理工大学学报(自然科学版),2009,10(6):575–579.(DONG Long-jun,ZHAO Guo-yan.Unascertained average classification method for classifyingsurrounding rocks of mining roadways[J],Journal of PLAUniversity of Science and Technology(Natural ScienceEdition),2009,10(6):575–579.(in Chinese))
[12]CHRISTIAN J T.Geotechnical engineering reliability:howwell do we know what we are doing?[J].Journal ofGeotechnical and Geoenvironmental Engineering,2004,130(10):985–1003.
[13]YAKOV B H.A non-probabilistic concept of reliability[J].Structural Safety,1994,36(14):227–245.
[14]YAKOV B H.A non-probabilistic measure of reliability oflinear systems based on expansion of convex models[J].Structural Safety,1995,37(17):91–109.
[15]尤明庆.岩石力学的性质[M].北京:地质出版社,2007.(YOU Ming-qing.Mechanical properties of rocks[M].Beijing:Geological Publishing House,2007.(in Chinese))
[16]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56–60.(GUOShu-xiang,LüZhen-zhou,FENG Yuan-sheng.Anon-probabilistic model of structural reliability based oninterval analysis[J].Journal of Computational Mechanics,2001,18(1):56–60.(in Chinese))
[17]MOORE R E.Interval Analysis[M].Englewood Cliffs:Prentice-Hall,1966.
[18]ALEFELD GOTZ,MAYER GUNTER.Interval analysis:theory and applications[J].Journal of Computational andApplied Mathenatics,121(1–2):421–464.
[19]刘开第,吴和琴,庞彦军,等.不确定性信息数学处理及应用[M].北京:科学出版社,1999.(LIU Kai-di,WUHe-qin,PANG Yan-jun,et al.Mathematics treatment andapplication of uncertainty information[M].Beijing:SciencePress,1999.(in Chinese))
[2]ISRM.Suggested methods for determining the uniaxialcompressive strength and deformability of rock materials[J].International Journal Rock Mechanics and Mining Scienceand Geomech Abstr,1979,16:135–140.
[3]原地质矿产部.岩石物理力学试验规程(DY-94)[M].北京:地质出版社,1994.(Ministry Geology and Mining of China.Standards of physical and mechanical test of mining and rocktypes(DY-94)[M].Beijing:Geological Publishing House,1994.81.(in Chinese))
[4].KOSTAK B.BIELENSTEIN H U Strength distribution inhard rock[J].International Journal of Rock Mechanics andMining Science,1971,4(4):501–521.
[5]山口梅太郎.花こぅ岩の强度试验にぉける试验片の数につぃて[J].材料,1966,16:520–528.(YAMAGUCHI U.The number of specimens required for testing the strength ofgranite[J].Journal of the Society of Materials Science,1966,16(160):520–528(in Japanese))
[6]董陇军,李夕兵,宫凤强.膨胀土胀缩等级分类的未确知均值聚类方法及应用[J].中南大学学报(自然科学版),2008,39(5):1075–1080.(DONG Long-jun,LI Xi-bing,GONG Feng-qiang.Unascertained average clustering methodfor classification of grade of shrink and expansion forexpansive soils and its application[J].Journal of CentralSouth University(Science and Technology),2008,39(5):1075–1080.(in Chinese))
[7]董陇军,李夕兵,宫凤强.开采地面沉陷预测的未确知聚类预测模型[J].中国地质灾害与防治学报,2008,19(2):95–99.(DONG Long-jun,LI Xi-bing,GONG Feng-qiang.Predicting surface subsidence induced by mining based onunascertained clustering method[J].Chinese Journal ofGeological Hazard and Control,2008,19(2):95–99.(inChinese))
[8]董陇军,王飞跃.基于未确知测度的边坡地震稳定性综合评价[J].中国地质灾害与防治学报,2007,18(4):74–78.(DONG Longjun,WANG Feiyue.Comprehensive evaluationon seismic stability of slopes based on unascertainedmeasurement[J].Chinese Journal of Geological Hazard andControl,2007,18(4):74–78.(in Chinese))
[9]DONG Long-jun,PENG Gang-jian,FU Yu-hua,et al.Unascertained measurement classifying model of goafcollapse prediction[J].Journal of Coal Science&Engineering,2008,14(2):221–224.
[10]董陇军,赵国彦,宫凤强.尾矿坝稳定性分析的区间非定值模型及应用[J].中南大学学报(自然科学版),(录用待刊)2011.(DONG Long-jun,ZHAO Guo-yan,GONGFeng-qiang.Interval non-real number model and itsapplication for analysis stability of Tailing dam[J].Journal ofCenter South University(Science and Natural Edition),(Accept)2011.(in Chinese))
[11]董陇军,赵国彦.未确知均值分级方法及在回采巷道围岩分类中的应用[J].解放军理工大学学报(自然科学版),2009,10(6):575–579.(DONG Long-jun,ZHAO Guo-yan.Unascertained average classification method for classifyingsurrounding rocks of mining roadways[J],Journal of PLAUniversity of Science and Technology(Natural ScienceEdition),2009,10(6):575–579.(in Chinese))
[12]CHRISTIAN J T.Geotechnical engineering reliability:howwell do we know what we are doing?[J].Journal ofGeotechnical and Geoenvironmental Engineering,2004,130(10):985–1003.
[13]YAKOV B H.A non-probabilistic concept of reliability[J].Structural Safety,1994,36(14):227–245.
[14]YAKOV B H.A non-probabilistic measure of reliability oflinear systems based on expansion of convex models[J].Structural Safety,1995,37(17):91–109.
[15]尤明庆.岩石力学的性质[M].北京:地质出版社,2007.(YOU Ming-qing.Mechanical properties of rocks[M].Beijing:Geological Publishing House,2007.(in Chinese))
[16]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56–60.(GUOShu-xiang,LüZhen-zhou,FENG Yuan-sheng.Anon-probabilistic model of structural reliability based oninterval analysis[J].Journal of Computational Mechanics,2001,18(1):56–60.(in Chinese))
[17]MOORE R E.Interval Analysis[M].Englewood Cliffs:Prentice-Hall,1966.
[18]ALEFELD GOTZ,MAYER GUNTER.Interval analysis:theory and applications[J].Journal of Computational andApplied Mathenatics,121(1–2):421–464.
[19]刘开第,吴和琴,庞彦军,等.不确定性信息数学处理及应用[M].北京:科学出版社,1999.(LIU Kai-di,WUHe-qin,PANG Yan-jun,et al.Mathematics treatment andapplication of uncertainty information[M].Beijing:SciencePress,1999.(in Chinese))
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