《厦门大学学报（自然科学版）》

针对专业文献和教科书中对岩石地基极限承载力计算公式和承载力系数图中普遍存在的不一致性问题,根据Bell解的原理和假设,以岩石地基极限平衡原理详细推导了岩石地基的极限承载力的计算公式,并给出了相对应的极限承载力系数Nc、Nγ和Nq的正确表达式.在此基础上进一步利用MATLAB软件进行编程,分析并绘制了承载力系数的函数图,在分析中扩大了内摩擦角的上下限取值范围,纠正了目前各文献中存在的错误和不一致性问题,也更清晰地表达了各承载力系数在更大的范围内随内摩擦角变化的趋势,有利于正确认识和掌握Bell解的方法.

In view of the inconsistency in the calculation formulas of ultimate bearing capacity and coefficient graph of rock foundation in some literature and textbooks,according to the principle and assumption about Bell solution determining ultimate bearing capacity of rock foundation,and based on the limit equilibrium principle of rock foundation,this paper derives the calculation formulas and provides the correct expression of bearing capacity factors Nc,Nγ and Nq without the depth of burial.Meanwhile,by means of MATLAB software to image mapping function of bearing capacity factors correctly,we expand the upper-lower limit of internal friction angle,and correct the error and inconsistency in some literature and textbooks.Furthermore the trend of the variation of the bearing capacity factors in the larger internal friction angle are also more clearly expressed,it is easier to understand and master the Bell solution.

引言
1 计算模型的建立
2 Bell解承载力系数推导[1]
3 承载力系数的图像表达
4 结论

图3 Rankine主动破坏区B块[3]<br/>Fig.3 Rankine Active Failure Block B[3]

图3 Rankine主动破坏区B块[3]
Fig.3 Rankine Active Failure Block B[3]

图1 岩基示意图[3]<br/>Fig.1 Schematic diagram of rock foundation[3]

图1 岩基示意图[3]
Fig.1 Schematic diagram of rock foundation[3]

图2 Rankine被动破坏区A块[3]<br/>Fig.2 Rankine passive failure block A[3]

图2 Rankine被动破坏区A块[3]
Fig.2 Rankine passive failure block A[3]

图4 承载力系数与内摩擦角的关系(φ∈[15°,45°])<br/>Fig.4 The factors of bearing capacity(φ∈[15°,45°])

图4 承载力系数与内摩擦角的关系(φ∈[15°,45°])
Fig.4 The factors of bearing capacity(φ∈[15°,45°])

图5 承载力系数(φ∈[0°,90°])<br/>Fig.5 The factors of bearing capacity(φ∈[0°,90°])

图5 承载力系数(φ∈[0°,90°])
Fig.5 The factors of bearing capacity(φ∈[0°,90°])

图6 文献[7]中的承载力系数<br/>Fig.6 The factors of bearing capacity in reference [7]

图6 文献[7]中的承载力系数
Fig.6 The factors of bearing capacity in reference [7]

图7 文献[2]中的承载力系数<br/>Fig.7 The factors of bearing capacity in reference [2]

图7 文献[2]中的承载力系数
Fig.7 The factors of bearing capacity in reference [2]

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[2] WYLLIE D C.Foundations on rock[M].London:Chapman and Hall,1992:140-149.
[3] 宋建波.剪切破坏模式下岩石地基极限承载力确定方法[D].昆明:昆明理工大学,1999:34-36.
[4] HOEK E,BROWN E.Underground excavation in rock[M].London:Inst of Mining & Metallurgy,1980:165-183.
[5] 宋建波,于远忠.剪切破坏模式下均质岩基极限承载力的Bell解[J].岩石力学与工程学报,2002,21(3):410-412.
[6] 严春风,徐健.岩体Hoek-Brown经验强度准则参数随机特征分析[J].岩石力学与工程学报,1999:18(5):497-502.
[7] 张永兴.岩石力学[M].2版.北京:中国建筑工业出版社,2008:185-186.
[8] SOWERS G F.Introductory soil mechanics and foundations [M].New York:Macmillan,1979:395-396.
[9] SERRANO A,OLALLA C.Ultimate bearing capacity of rock masses[J].Int J Rock Mech Mining Sciences & Geomech Abstr,1994,31(2):93-106.
[10] PRANDTL L.Über die eindringungsfestigkeit(Härte)plastischer baustoffe and die festigkeit von schneiden[J].Z Angew Math Mech,1921(1):15-20.
[11] 郑大同.地基极限承载力的计算[M].北京:中国建筑工业出版社出版社,1979:3-10.

备注

引言

1 计算模型的建立

2 Bell解承载力系数推导[1]

3 承载力系数的图像表达

4 结论

学报简介

备注

引言

1 计算模型的建立

2 Bell解承载力系数推导[1]

3 承载力系数的图像表达

4 结 论

学报简介

4 结论