基于极限分析下限法的溶洞顶板承载力研究
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摘要
在已有的极限分析下限法求解格式的基础上,直接以超载系数作为目标函数,将应力边界分为超载边界和不超载边界,建立求极限承载力下限法的非线性规划模型,并使用内点法求解最优解。通过模拟土体的三轴试验验证了本方法和程序的正确性,并将程序应用于溶洞顶板承载力的研究中,在已有极限分析下限法对溶洞顶板承载力研究的基础上,进一步考虑了水平向地应力对溶洞顶板承载力的影响。研究结果表明,在溶洞顶板厚度相同的前提下,溶洞跨高比l的值对溶洞顶板承载力影响非常显著;在溶洞尺寸相同的前提下,溶洞顶板厚度只在一定范围内对溶洞极限承载力有影响,超过这个范围后,其影响可不考虑;考虑水平向地应力在顶板厚度较大、跨高比较小时对承载力影响较大,在使用下限法计算溶洞顶板极限承载力时不能忽略水平向地应力的影响。
Based on the existing solution format of lower bound analysis method, stress boundary is directly divided into overload boundary and non-overload boundary by taking the overload coefficient as the objective function. A nonlinear programming model is established to solve the lower bound solution of bearing capacity of karst roof ultimate, and the internal point method is used to solve the optimal solution. The accuracy of the method and program is verified by simulating triaxial tests, and then the program is used to study the bearing capacity of karst roof. The influences of horizontal ground stress on the bearing capacity of karst roof are further considered based on the studies on the bearing capacity of karst roof using the lower bound method. The results show that the karst span has a significant effect on the bearing capacity of karst roof, regardless of whether the karst horizontal and the stress boundary conditions are the same. When the karst size is the same, the thickness of the karst roof has a great influence on the ultimate bearing capacity in a certain range, and the effect is not significant after exceeding this range. Considering the horizontal ground stress has a great influence on the bearing capacity when the thickness of the roof is large and the height of the span is relatively small, the influences of horizontal ground stress can not be neglected when the ultimate bearing capacity of the karst roof is calculated using the lower bound method.
Based on the existing solution format of lower bound analysis method, stress boundary is directly divided into overload boundary and non-overload boundary by taking the overload coefficient as the objective function. A nonlinear programming model is established to solve the lower bound solution of bearing capacity of karst roof ultimate, and the internal point method is used to solve the optimal solution. The accuracy of the method and program is verified by simulating triaxial tests, and then the program is used to study the bearing capacity of karst roof. The influences of horizontal ground stress on the bearing capacity of karst roof are further considered based on the studies on the bearing capacity of karst roof using the lower bound method. The results show that the karst span has a significant effect on the bearing capacity of karst roof, regardless of whether the karst horizontal and the stress boundary conditions are the same. When the karst size is the same, the thickness of the karst roof has a great influence on the ultimate bearing capacity in a certain range, and the effect is not significant after exceeding this range. Considering the horizontal ground stress has a great influence on the bearing capacity when the thickness of the roof is large and the height of the span is relatively small, the influences of horizontal ground stress can not be neglected when the ultimate bearing capacity of the karst roof is calculated using the lower bound method.
引文
[1]DRUCKER D C,PRAGER W.Soil mechanics and plastic analysis of limit design[J].Quarterly of Applied Mathematics,1952,10(2):157-165.
[2]SLOAN S W.Lower bound limit analysis using finite elements and linear programming[J].International Journal for Numerical&Analytical Methods in Geomechanics,2010,12(1):61-77.
[3]ZOUAIN N,HERSKOVITS J,BORGES LA,et al.Aniterative algorithm for limit analysis with nonlinear yield functions[J].International Journal of Solids and Structures,1993,30(10):1397-1417.
[4]BAUS R L,WANG M C.Bearing capacity of strip footing above void[J].Journal of Geotechnical Engineering,ASCE,1983,117(5):753-765.
[5]张细仁.溶洞地铁隧道地基承载力下限法研究[D].长沙:中南大学,2014.(ZHANG Xi-ren.Study on the lower bound analysis method to obtain bearing capacity of subway tunnel in karst areas[D].Changsha:Central South University,2014.(in Chinese))
[6]李泽,刘毅,周宇,等.基于混合离散的砌石挡土墙边坡极限承载力下限分析[J].岩土力学,2018,39(3):1100-1108.(LI Ze,LIU Yi,ZHOU Yu,et al.Lower bound analysis of ultimate bearing capacity of stone masonry retaining wall slope using mixed numerical discretisation[J].Rock and Soil Mechanics,2018,39(3):1100-1108.(in Chinese))
[7]杨昕光,迟世春.土石坝坡极限抗震能力的下限有限元法[J].岩土工程学报,2013,35(7):1202-1209.(YANGXin-guang,CHI Shi-chun.Lower bound FEM for limit aseismic capacity of earth-rockfill dams[J].Chinese Journal of Geotechnical Engineering,2013,35(7):1202-1209.(in Chinese))
[8]李仁江,盛谦,张勇慧.溶洞顶板极限承载力研究[J].岩土力学,2007,28(8):1621-1625.(LI Ren-jiang,SHENGQian,ZHANG Yong-hui.Study on ultimate bearing capacity of upper rock plate of karst cave[J].Rock and Soil Mechanics,2007,28(8):1621-1625.(in Chinese))
[9]GB 50218-94工程岩体分级标准[S].1995.(GB 50218-94Engineering rock mass classification standard[S].1995.(in Chinese))
[2]SLOAN S W.Lower bound limit analysis using finite elements and linear programming[J].International Journal for Numerical&Analytical Methods in Geomechanics,2010,12(1):61-77.
[3]ZOUAIN N,HERSKOVITS J,BORGES LA,et al.Aniterative algorithm for limit analysis with nonlinear yield functions[J].International Journal of Solids and Structures,1993,30(10):1397-1417.
[4]BAUS R L,WANG M C.Bearing capacity of strip footing above void[J].Journal of Geotechnical Engineering,ASCE,1983,117(5):753-765.
[5]张细仁.溶洞地铁隧道地基承载力下限法研究[D].长沙:中南大学,2014.(ZHANG Xi-ren.Study on the lower bound analysis method to obtain bearing capacity of subway tunnel in karst areas[D].Changsha:Central South University,2014.(in Chinese))
[6]李泽,刘毅,周宇,等.基于混合离散的砌石挡土墙边坡极限承载力下限分析[J].岩土力学,2018,39(3):1100-1108.(LI Ze,LIU Yi,ZHOU Yu,et al.Lower bound analysis of ultimate bearing capacity of stone masonry retaining wall slope using mixed numerical discretisation[J].Rock and Soil Mechanics,2018,39(3):1100-1108.(in Chinese))
[7]杨昕光,迟世春.土石坝坡极限抗震能力的下限有限元法[J].岩土工程学报,2013,35(7):1202-1209.(YANGXin-guang,CHI Shi-chun.Lower bound FEM for limit aseismic capacity of earth-rockfill dams[J].Chinese Journal of Geotechnical Engineering,2013,35(7):1202-1209.(in Chinese))
[8]李仁江,盛谦,张勇慧.溶洞顶板极限承载力研究[J].岩土力学,2007,28(8):1621-1625.(LI Ren-jiang,SHENGQian,ZHANG Yong-hui.Study on ultimate bearing capacity of upper rock plate of karst cave[J].Rock and Soil Mechanics,2007,28(8):1621-1625.(in Chinese))
[9]GB 50218-94工程岩体分级标准[S].1995.(GB 50218-94Engineering rock mass classification standard[S].1995.(in Chinese))