基于对数螺旋线离散算法的露天煤矿边坡稳定性研究
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摘要
对数螺旋线破坏机构可充分满足土体速度分离要求,因此对数螺旋线在边坡稳定性上限分析中广泛应用。但由于在平面直角坐标系下对数螺旋线无法显化处理,现阶段上限分析法对均质边坡稳定性分析给出了较好的解答,对于非均质边坡稳定性研究相对较少。为探究上限分析方法在非均质边坡稳定性分析中的应用,基于离散算法提出一种对数螺旋线拟合新方法,并将该方法应用于露天煤矿边坡稳定性上限分析工程实践中,同时基于能量平衡条件编制最危险滑面搜索及稳定系数计算循环程序,并应用剩余推力法从稳定系数与最危险滑面2个角度评价上限分析方法计算结果的准确性。研究结果表明:基于对数螺旋线离散算法计算结果与原曲线具有高度一致性,可保证相关系数大于0.999 5,同时该方法稳定性分析结果具有高度准确性,从稳定系数角度分析该方法计算结果为严格意义上限解,计算误差便于估算,从最危险滑面角度分析,该方法求得的最危险滑面可充分满足速度分离要求,具有更强的工程实践意义。
The logarithmic spiral damage mechanism can fully meet requirements of soil velocity separation,so the logarithmic spiral is widely used in the upper limit analysis of slope stability.However,since the logarithmic spiral can't be manifested in Cartesian Coordinate System,the current upper bound analysis method gives a perfect solution to the homogeneous slopes stability analysis although the research of heterogeneous slope stability is relatively rare.In order to disscus the application of upper limit analysis method in heterogeneous slope stability,the authors proposed a new method of logarithmic spiral fitting based on discrete algorithm,and applied this method to the engineering practice of upper limit analysis of slope stability in open-pit mine.At the same time,the most dangerous slip surface and the slope stability coefficient calculation cycle program was compiled based on energy balance condition,and the residual thrust method was used to evaluate accuracy of calculation result of upper limit analysis method from two angles of stability coefficient and the most dangerous slip surface.The results show that the logarithmic spiral discrete algorithm is highly consistent with the original curve,which can guarantee the requirement R2≥0.999 5.At the same time,the stability analysis results are highly accurate.The calculation result is analyzed from perspective of stability coefficient.From the perspective of stability factors,the calculation result is strictly the upper bound solution,and the calculation error is easy to estimate.From the perspective of the most dangerous slip surface,the most dangerous slip surface obtained by this method can fully satisfy the requirements of speed separation and has a stronger engineering practice significance.
The logarithmic spiral damage mechanism can fully meet requirements of soil velocity separation,so the logarithmic spiral is widely used in the upper limit analysis of slope stability.However,since the logarithmic spiral can't be manifested in Cartesian Coordinate System,the current upper bound analysis method gives a perfect solution to the homogeneous slopes stability analysis although the research of heterogeneous slope stability is relatively rare.In order to disscus the application of upper limit analysis method in heterogeneous slope stability,the authors proposed a new method of logarithmic spiral fitting based on discrete algorithm,and applied this method to the engineering practice of upper limit analysis of slope stability in open-pit mine.At the same time,the most dangerous slip surface and the slope stability coefficient calculation cycle program was compiled based on energy balance condition,and the residual thrust method was used to evaluate accuracy of calculation result of upper limit analysis method from two angles of stability coefficient and the most dangerous slip surface.The results show that the logarithmic spiral discrete algorithm is highly consistent with the original curve,which can guarantee the requirement R2≥0.999 5.At the same time,the stability analysis results are highly accurate.The calculation result is analyzed from perspective of stability coefficient.From the perspective of stability factors,the calculation result is strictly the upper bound solution,and the calculation error is easy to estimate.From the perspective of the most dangerous slip surface,the most dangerous slip surface obtained by this method can fully satisfy the requirements of speed separation and has a stronger engineering practice significance.
引文
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[16]王东,王珍,曹兰柱,等.近水平煤层露天矿边坡三维稳定性研究[J].煤炭科学技术,2016,44(8):86-90.WANG Dong,WANG Zhen,CAO Lanzhu,et al.Study on 3D stability of slope in surface mine with sub-horizontal seams[J].Coal Science and Technology,2016,44(8):86-90.
[17]张宜虎,尹红梅,简文星.剩余推力法及其在斜坡稳定性评价中的应用[J].岩土力学,2004,25(4):628-631.ZHANG Yihu,YIN Hongmei,JIAN Wenxing.The remained slip force method considering the effect of rainfall and its application to assessment of slope stability[J].Rock and Soil Mechanics,2004,25(4):628-631.
[18]曹兰柱,王珍,王东,等.露天煤矿端帮逆倾软岩边坡稳定性研究[J].煤炭科学技术,2017,45(3):1-6.CAO Lanzhu,WANG Zhen,WANG Dong,et al.Study on stability of reversed inclined soft rock slope at end slope of surface mine[J].Coal Science and Technology,2017,45(3):1-6.
[19]徐青,陈士军,陈胜宏.滑坡稳定分析剩余推力法的改进研究[J].岩土力学,2005,37(3):465-470.XU Qing,CHEN Shijun,CHEN Shenghong.Study on the improved residual threst method for landslide stability analysis[J].Rock and Soil Mechanics,2005,37(3):465-470.
[20]张小艳,张立翔,李泽.基于塑性极限分析上限法理论的土质边坡可靠度分析[J].岩土力学,2018,39(5):1840-1850.ZHANG Xiaoyan,ZHANG Lixiang,LI Ze.Reliability analysis of soil slope based on upper bound method of limit analysis[J].Rock and Soil Mechanics,2018,39(5):1840-1850.
[2]郑颖人,孔亮.广义塑性力学及其运用[J].中国工程科学,2005,7(11):25-40.ZHENG Yingren,KONG Liang.Generalized plastic mechanics and its application[J].Engineering Science,2005,7(11):25-40.
[3]郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用[J].岩石力学与工程学报,2004,23(19):3381-3388.ZHENG Yingren,ZHAO Shangyi.Application of strength reduction FEM in soil and rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3381-3388.
[4]DRUCKER D C,GREENBERG H J,PRAGER W.The safety factor of an elastic-plastic body in plane strain[J].Journal of Applied Mechanics Transactions of the ASME,1951,18(4):371-378.
[5]DRUCKER D C,PRAGER W,GREENBERG H J.Extended limit design theorems for continuous media[J].Quarterly of Applied Mathematics,1952,9(4):381-389.
[6]CHEN W F.Limit analysis and soil plasticity[M].New York:Elsevier Scientific Publishing Co,1975.
[7]聂卫平,徐卫亚,王伟,等.大型地下洞室极限位移预测与稳定性分析[J].岩石力学与工程学报,2012,31(9):1901-1907.NIE Weiping,XU Weiya,WANG Wei,et al.Limit displacement prediction and stability analysis of large underground caverns[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(9):1901-1907.
[8]YANG X L,YIN J H.Slope stability analysis with nonlinear failure criterion[J].Journal of Engineering Mechanics,2004,130(3):267-273.
[9]胡卫东,曹文贵.基于非对称破坏模式的临坡地基承载力上限极限分析方法[J].中国公路学报,2014,27(6):1-9.HU Weidong,CAO Wengui.Upper limit limit analysis method for ultimate bearing capacity of ground foundation adjacent to slope based on asymmetry failure mode[J].China Journal of Highways and Transport,2014,27(6):1-9.
[10]YANG X L.Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion[J].Theoretical and Applied Fracture Mechanics,2007,47(1):46-56.
[11]王根龙,伍法权,张军慧.非均质土坡稳定性分析评价的刚体单元上限法[J].岩石力学与工程学报,2008,27(S2):3425-3430.WANG Genlong,WU Faquan,ZHANG Junhui.Upper bound approach of rigid elements for inhomogeneous soil slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(S2):3425-3430.
[12]孙志彬,潘秋景,杨小礼,等.非均质边坡上限分析的离散机构及应用[J].岩石力学与工程学报,2017,36(7):1680-1688.SUN Zhibin,PAN Qiujing,YANG Xiaoli,et al.Discrete mechanism for upper bound analysis of non-homogeneous slopes[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1680-1688.
[13]陈祖煜.土力学经典问题的塑性力学上、下限解[J].岩土工程学报,2002,24(1):1-11.CHEN Zuyu.Limit analysis for the classic problems of soil mechanics[J].Chinese Journal of Geotechnical Engineering,2002,24(1):1-11.
[14]王珍,曹兰柱,王东.非均质边坡稳定性上限分析评价研究[J].岩土力学,2019,40(2):737-742.WANG Zhen,CAO Lanzhu,WANG Dong.Evaluation on upper limit of heterogeneous slope stability[J].Rock and Soil Mechanics,2019,40(2):737-742.
[15]曹兰柱,李广贺,王东,等.露天矿顺倾软弱基底内排土场边坡空间形态优化[J].煤炭科学技术,2018,46(2):163-167.CAO Lanzhu,LI Guanghe,WANG Dong,et al.Optimization on spatial morphology slope of in pit dumping site at inclined weakbasement of surface mine[J].Coal Science and Technology,2018,46(2):163-167.
[16]王东,王珍,曹兰柱,等.近水平煤层露天矿边坡三维稳定性研究[J].煤炭科学技术,2016,44(8):86-90.WANG Dong,WANG Zhen,CAO Lanzhu,et al.Study on 3D stability of slope in surface mine with sub-horizontal seams[J].Coal Science and Technology,2016,44(8):86-90.
[17]张宜虎,尹红梅,简文星.剩余推力法及其在斜坡稳定性评价中的应用[J].岩土力学,2004,25(4):628-631.ZHANG Yihu,YIN Hongmei,JIAN Wenxing.The remained slip force method considering the effect of rainfall and its application to assessment of slope stability[J].Rock and Soil Mechanics,2004,25(4):628-631.
[18]曹兰柱,王珍,王东,等.露天煤矿端帮逆倾软岩边坡稳定性研究[J].煤炭科学技术,2017,45(3):1-6.CAO Lanzhu,WANG Zhen,WANG Dong,et al.Study on stability of reversed inclined soft rock slope at end slope of surface mine[J].Coal Science and Technology,2017,45(3):1-6.
[19]徐青,陈士军,陈胜宏.滑坡稳定分析剩余推力法的改进研究[J].岩土力学,2005,37(3):465-470.XU Qing,CHEN Shijun,CHEN Shenghong.Study on the improved residual threst method for landslide stability analysis[J].Rock and Soil Mechanics,2005,37(3):465-470.
[20]张小艳,张立翔,李泽.基于塑性极限分析上限法理论的土质边坡可靠度分析[J].岩土力学,2018,39(5):1840-1850.ZHANG Xiaoyan,ZHANG Lixiang,LI Ze.Reliability analysis of soil slope based on upper bound method of limit analysis[J].Rock and Soil Mechanics,2018,39(5):1840-1850.