基于多元回归分析的地质力学模型试验中相似材料的快速配比研究
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摘要
在地质力学模型试验中,为获得相似材料的快速配比,通过正交设计试验配制了相似材料,对相似材料进行称重和单轴压缩变形试验,分别得到密度、弹性模量和抗压强度.对试验所得数据进行为了极差分析和方差分析,得到各因素的敏感性和显著性.为了快速获得各因素的配比方案,通过运用Matlab软件对试验所得数据进行多元线性回归分析构建数学模型,设因素A、B、C为X1、X2、X3,密度、弹性模量和抗压强度为Y1、Y2、Y3,得到3个关于X和Y的经验方程,能够根据给定密度、弹性模量和抗压强度算出所需各种原材料的含量.通对试验数据对所得经验方程进行了精度检验,所得结果误差较小,说明所得数学模型符合要求.
In geomechanical model tests,barite powder,limestone powder,gypsum powder,glycerin and water are used as raw materials.The weight ratio of limestone powder to gypsum plus limestone powder,the weight ratio of barite powder to gypsum plus limestone powder,the weight ratio of glycerol to glycerol plus water were selected as A,B and C.The similar material was prepared by the orthogonal design test,density,elastic modulus and compressive strength of the similar materials were obtained by weighing and uniaxial compression tests.The sensitivity and significance of each factor were obtained for range analysis and variance analysis.In order to quickly obtain a matching scheme,this paper will use multiple linear regression analysis in the geomechanical model test.The results show that the sensitivity and significance are consistent in range analysis and variance analysis,with the increase of the factor A and the increase of the modulus of elasticity and the compressive strength,the density of the barite powder has a positive correlation with the density of the similar materials.In the multivariate regression analysis,factors A,B and C were selected as X1,X2 and X3,density,elastic modulus,and compressive strength were selected as Y1,Y2 and Y3.Through multiple regression analysis of the data obtained from the test,three empirical formulas for X and Y were obtained,and the required amounts of various raw materials can be calculated based on arbitrary density,elastic modulus,and compressive strength.The accuracy test of the empirical formula obtained by using five sets of test data shows that the error of the obtained result is small,indicating that the obtained mathematical model meets the requirements.
In geomechanical model tests,barite powder,limestone powder,gypsum powder,glycerin and water are used as raw materials.The weight ratio of limestone powder to gypsum plus limestone powder,the weight ratio of barite powder to gypsum plus limestone powder,the weight ratio of glycerol to glycerol plus water were selected as A,B and C.The similar material was prepared by the orthogonal design test,density,elastic modulus and compressive strength of the similar materials were obtained by weighing and uniaxial compression tests.The sensitivity and significance of each factor were obtained for range analysis and variance analysis.In order to quickly obtain a matching scheme,this paper will use multiple linear regression analysis in the geomechanical model test.The results show that the sensitivity and significance are consistent in range analysis and variance analysis,with the increase of the factor A and the increase of the modulus of elasticity and the compressive strength,the density of the barite powder has a positive correlation with the density of the similar materials.In the multivariate regression analysis,factors A,B and C were selected as X1,X2 and X3,density,elastic modulus,and compressive strength were selected as Y1,Y2 and Y3.Through multiple regression analysis of the data obtained from the test,three empirical formulas for X and Y were obtained,and the required amounts of various raw materials can be calculated based on arbitrary density,elastic modulus,and compressive strength.The accuracy test of the empirical formula obtained by using five sets of test data shows that the error of the obtained result is small,indicating that the obtained mathematical model meets the requirements.
引文
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[3]董金玉,杨继红,杨国香,等.基于正交设计的模型试验相似材料的配比试验研究[J].煤炭学报,2012,37(1):44-49.
[4]黄国军,周澄,赵海涛.牛头山双曲拱坝整体稳定三维地质力学模型试验研究[J].西北水电,2004(2):49-52.
[5]韩伯鲤,陈霞龄,宋一乐,等.岩体相似材料的研究[J].武汉水利电力大学学报(工学版),1997,30(2):6-9.
[6]张强勇,陈旭光,张宁,等.交变气压风险条件下层状盐岩地下储气库注采气大型三维地质力学试验研究[J].岩石力学与工程学报,2010,29(12):2410-2419.
[7]CHEN S J,WANG H L,ZHANG J W,et al.Experimental study on low-strength similar-material proportioning and properties for coal mining[J].Advances in Materials Science and Engineering,2015(3):1-6.
[8]李文杰,葛毅鹏,张芳芳.基于相似理论的相似材料配比试验研究[J].洛阳理工学院学报(自然科学版),2013,23(1):7-12.
[9]CHENG W M,SUN L L,WANG G,et al.Experimental research on coal seam similar material proportion and its application[J].International Journal of Mining Science and Technology,2016,26(5):913-918.
[10]袁宗盼,陈新民,袁媛,等.地质力学模型相似材料配比的正交试验研究[J].防灾减灾工程学报,2014,34(2):197-202.
[11]肖杰.相似材料模型试验原料选择及配比试验研究[D].北京:北京交通大学,2013.
[12]黄星星.锦屏一级水电站岩体相似材料的配比试验及回归分析[D].成都:成都理工大学,2012.
[13]张群,张彦会,张炯,等.基于Matlab模型异步电机控制代码的开发[J].广西工学院学报,2013,24(1):24-28.
[14]胡伟平.基于回归分析的人脸老化模型构建[J].广西科技大学学报,2016,27(3):39-44.
[15]史小萌,刘保国,亓轶.水泥石膏胶结相似材料在固-流耦合试验中的适用性[J].岩土力学,2015,36(9):2624-2630.
[16]中华人民共和国建设部.JGJ 70-1990:建筑砂浆基本性能试验方法[M].北京:中国建筑工业出版社,1991.
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