岩石结构的蠕变稳定性理论研究
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摘要
岩石的结构是极其复杂的非连续和非均质体,其力学属性具有非线性、
各向异性及随时间变化的流变特性。岩石工程结构失稳前特征即应力状态保
持不变,且是突然破坏释放能量,即蠕变失稳。所以开展岩石蠕变破坏机理
的研究对岩石工程的长期稳定性具有重要的理论意义和实际价值。
本文主要从岩石全程应力应变特征和蠕变曲线出发进行研究,建立蠕变
失稳模型,把模型中的两个参数看作是随岩石的变形而变化,得出失稳判据
和改进的蠕变方程,进而解释了岩石蠕变的第三阶段失稳现象;同时从不同
角度推导出模型的各种解析解,这些方程表明岩石的本构关系、变形模量与
加载条件和历史有关,验证了该模型是能描述岩石的衰减蠕变、稳定蠕变与
加速蠕变三种情况的比较完善的流变模型。
结合蠕变模型和流变力学的一般解法,推导出了采空区悬顶板梁临界载
荷及应力的粘弹塑性解析解,并对其稳定性进行了分析;推导出圆形洞室周
围岩石任意点的位移随时间增长而变化的方程,并得出了粘塑性区半径;建
立了含软弱夹层的层状边坡板梁失稳模型,改进了欧拉公式具有时间效应,
提出了一种边坡失稳的分析方法。
The structure of rock is extremely complicated discontinuous and heterogeneous body, its mechanics property has non-linear, anisotropism and rheology characteristic, which changed over time. The characteristic stress state of rock structure is keeping constant before its losing steady, and suddenly destroyed with releasing energy, namely creep is losing steady. So it is important theory meaning and reality value to long-term stability of rock engineering to launch research of rock creeping destroying mechanism.
The text proceeds from the whole stress-strain characteristic and creep curve of rock, set up creep losing steady model, regard two parameters of model as changing with deformation of rock, draw losing steady criterion and modified creep equation, and then has explained losing steady phenomenon at the third stage of rock creep; At the same time we derived out analytical solution of the creep model from different angles, and indicate constitutive of rock and deformation of modulus which relate to the condition and history of loading, and prove that it is a perfect rheology model which can describe decay creep, stability creep and accelerate creep of rock.
The text combines creep model and general solution of rheology mechanics, deriving out visco-elasto-plastic analytic solution of critical load and stress of operation goaf hanging beam, and analyzed its stability; Deriving out displacement of wall rock which increases with time changes, and has drawn radius of plasticity district; Set up losing steady beam model of slope containing weak intermediate layer, modified Euler formula has a time effect, putting forward losing steady analytical method of the slope.
各向异性及随时间变化的流变特性。岩石工程结构失稳前特征即应力状态保
持不变,且是突然破坏释放能量,即蠕变失稳。所以开展岩石蠕变破坏机理
的研究对岩石工程的长期稳定性具有重要的理论意义和实际价值。
本文主要从岩石全程应力应变特征和蠕变曲线出发进行研究,建立蠕变
失稳模型,把模型中的两个参数看作是随岩石的变形而变化,得出失稳判据
和改进的蠕变方程,进而解释了岩石蠕变的第三阶段失稳现象;同时从不同
角度推导出模型的各种解析解,这些方程表明岩石的本构关系、变形模量与
加载条件和历史有关,验证了该模型是能描述岩石的衰减蠕变、稳定蠕变与
加速蠕变三种情况的比较完善的流变模型。
结合蠕变模型和流变力学的一般解法,推导出了采空区悬顶板梁临界载
荷及应力的粘弹塑性解析解,并对其稳定性进行了分析;推导出圆形洞室周
围岩石任意点的位移随时间增长而变化的方程,并得出了粘塑性区半径;建
立了含软弱夹层的层状边坡板梁失稳模型,改进了欧拉公式具有时间效应,
提出了一种边坡失稳的分析方法。
The structure of rock is extremely complicated discontinuous and heterogeneous body, its mechanics property has non-linear, anisotropism and rheology characteristic, which changed over time. The characteristic stress state of rock structure is keeping constant before its losing steady, and suddenly destroyed with releasing energy, namely creep is losing steady. So it is important theory meaning and reality value to long-term stability of rock engineering to launch research of rock creeping destroying mechanism.
The text proceeds from the whole stress-strain characteristic and creep curve of rock, set up creep losing steady model, regard two parameters of model as changing with deformation of rock, draw losing steady criterion and modified creep equation, and then has explained losing steady phenomenon at the third stage of rock creep; At the same time we derived out analytical solution of the creep model from different angles, and indicate constitutive of rock and deformation of modulus which relate to the condition and history of loading, and prove that it is a perfect rheology model which can describe decay creep, stability creep and accelerate creep of rock.
The text combines creep model and general solution of rheology mechanics, deriving out visco-elasto-plastic analytic solution of critical load and stress of operation goaf hanging beam, and analyzed its stability; Deriving out displacement of wall rock which increases with time changes, and has drawn radius of plasticity district; Set up losing steady beam model of slope containing weak intermediate layer, modified Euler formula has a time effect, putting forward losing steady analytical method of the slope.
引文
[1] 范广勤.岩土工程流变力学[M].北京:煤炭工业出版社,1993.
[2] 刘雄.岩石流变学概论[M].北京:地质出版社,1994.
[3] 周维垣.高等岩石力学[M].北京:水利电力出版社,1990.
[4] 孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[5] 郑哲敏.21世纪初的力学发展趋势[J].力学进展.1995,25(4)
[6] 徐平,夏熙伦.三峡工程花岗岩蠕变特性试验研究[J].岩土工程学报.1996,18(4):63~67
[7] 章根德,何鲜,朱维耀.岩石介质流变学[M].北京:科学出版社.1999
[8] 夏熙伦,徐平,丁秀丽.岩石流变特性及高边坡稳定性流变分析[J].岩石力学与工程学报,1996,15(4):312～322.
[9] 张有天,周维垣.岩石高边坡的变形与稳定[M].北京:中国水利水电出版社,1999
[10] 徐平,甘军,丁秀丽.三峡工程船闸高边坡岩体长期变形及稳定性有限元分析[J].长江科学院院报。1999,16(2):31~34
[11] 朱维申,邱祥波,李术才等.损伤流变模型在三峡船闸高边坡稳定分析的初步应用[J].岩石力学与工程学报.1997,16(5):431～436
[12] 徐日庆,龚晓南.粘弹性本构模型的识别与变形预报[J].水利学报,1998,(4):75～80
[13] 朱浮声,薛琳.粘弹性围岩力学参数反分析的一种数值法[J].岩石力学与工程学报,1997,16(5):478～482
[14] 章梦涛.冲击地压失稳理论与数值模拟计算.岩石力学与工程学报.1987.6(3)
[15] 章梦涛,潘一山,梁冰,王来贵编著.煤岩流体力学[M].科学出版社,1995
[16] 王启宏.材料流变学[M].北京:中国建筑工业出版社.1983
[17] 王来贵等.岩石试件的流变失稳理论及判据[J].1994.13(3):93~97
[18] 王来贵,黄润秋等,岩石力学系统运动稳定性及其应用[M],北京:地质出版社,1998,57-58.
[19] 王来贵,黄润秋,张倬元,王士天.滑坡灾害发生的动力学模型[J],自然科学进展,1998,8(2).
[20] 徐平,杨挺青.岩石流变试验与本构模型辨识[J].2001.20
[21] 郭增玉,张朝鹏,夏旺民.高湿度Q2 黄土的非线性流变本构模型及参数[J].岩石力学与工程学报,2000,19(6):780-784.
[22] 袁 静,龚晓南,益德清.岩土流变模型的比较研究[J].岩石力学与工程学报,2001,20(6):772-779
[23] 孙 钧,黄 伟.岩石力学参数弹塑性反演问题的优化方法[J].岩石力学与工程学报, 1992, 11(3):221-229
[24] 刘晶辉,王山长,杨洪海,软弱夹层流变试验长期强度确定方法[J],勘察科学技术,1996,5,3-7
[25] 陈宗基.根据流变学与地球动力学观点研究新奥法岩石.岩石力学与工程学报[J],1988,7(2)
[26] 张忠亭,王宏,陶振宇. 岩石蠕变特性研究进展概况.长江科学院院报[J],1996,13
[26] 王子潮.土地馒橄榄岩流变性研究进展及其动力学意义[J].地球物理学进展,1995, 10(2) :1-15
[27] Nicolas A,Poirier JP(林传勇,尘兰斌译)变质岩的晶质塑性和固态流变[M]
北京:科学出版,1985.154— 160
[28] 袁龙蔚,流变力学[M],科学出版社,1986.
[29] 杨绪灿等,黏塑性力学概论[M],中国铁路出版社,1985
[30] 杨挺青,黏弹性力学[M],华中理工大学出版社,1990
[31] 袁龙蔚,缺陷体流变学[M],国防工业出版社,1986.
[32] 周筑宝等,一种可用于分析流变断裂过程的损伤力学计算模型[J],湘潭大学学报,1989
[33] Pan Y W, Dong J J. Time-dependent tunnel convergence: Formulation of the model [J]. Int J Rock Mech Min Sci & Geomech Abstr, 1991
[34] Biot.MA. Theory of stress-strain relations in an isotropic visco elasticity and relation phenomena[J]. JAppPhy, 1954,25(11):1385-I391
[35] 宋德彰.岩质材料非线性流变属性及其力学模型[J].同济大学学报,1991,19
(4):395-401
[36] 陈宗基,康文法.岩石的封闭应力、蠕变和扩容及本构方程.岩石力学与工程学报,1991, 10(4): 299-312
[37] 杨绪灿,杨桂通,徐秉业.粘塑性力学概论.北京:中国铁道出版社,1985
[38] Cristescu N, Fota D, Medves E. Tunnel support analysis incorporating rock creep. Int J Rock Mech Min Sci&Geomech Abstr, 1987, 24(6): 321^-330
[39] 朱素平.岩石的流变性与地下工程结构的稳定性研究:[学位论文].徐州;中国矿业大学采矿系,1989
[40] 朱素平等.地下圆形隧道围岩稳定性的粘弹性力学分析[J].同济大学学报, 1994, 22(3)
[41] Perzyna. Fundamental problem in visco-plasticity [J].V Adv in Appl Mech, 1966, (9) : 243-377.
[42] Zinkie wicz O C,Cormeau I C. Visco-plasticity and creep in elastic solids a unified numerical solution approach[J]. Int J Num Nbth in Engrg ,1974,(8) :821-845.
[43] Cormeau I. Numerical stability in quasi7static elasto-viscoplasticity[J]. Int J Num Meth in Engrg ,1975,(9) :109-127.
[44] 邵国建等.地下洞室群的弹粘塑性有限元分析[J].河海大学学报,2001,29(6).
[45] 康红普.软岩巷道底臌的机理及防治[M].煤炭工业出版社,1993
[46] 张良辉等.隧道围岩的弹塑性解析解[J]。岩土工程学报,1997,19(4)
[47] 芮勇勤等.露天煤矿边坡中软弱夹层的蠕动变形特性分析[J].东北大学学报.1999.20(6)
[48] 杨天鸿等.顺层蠕动边坡变形破坏机理及稳定性动态分析[J].工程地质学报.2003.11(2)
[49] 何学秋著.含瓦斯煤岩流变动力学.中国矿业大学出版社[M].1995
[50] 曹树刚,边金,李鹏。岩石蠕变本构关系及改进的西原正夫模型[J],岩石力学与工程学报,2002,21(5)。
[2] 刘雄.岩石流变学概论[M].北京:地质出版社,1994.
[3] 周维垣.高等岩石力学[M].北京:水利电力出版社,1990.
[4] 孙钧.岩土材料流变及其工程应用[M].北京:中国建筑工业出版社,1999.
[5] 郑哲敏.21世纪初的力学发展趋势[J].力学进展.1995,25(4)
[6] 徐平,夏熙伦.三峡工程花岗岩蠕变特性试验研究[J].岩土工程学报.1996,18(4):63~67
[7] 章根德,何鲜,朱维耀.岩石介质流变学[M].北京:科学出版社.1999
[8] 夏熙伦,徐平,丁秀丽.岩石流变特性及高边坡稳定性流变分析[J].岩石力学与工程学报,1996,15(4):312～322.
[9] 张有天,周维垣.岩石高边坡的变形与稳定[M].北京:中国水利水电出版社,1999
[10] 徐平,甘军,丁秀丽.三峡工程船闸高边坡岩体长期变形及稳定性有限元分析[J].长江科学院院报。1999,16(2):31~34
[11] 朱维申,邱祥波,李术才等.损伤流变模型在三峡船闸高边坡稳定分析的初步应用[J].岩石力学与工程学报.1997,16(5):431～436
[12] 徐日庆,龚晓南.粘弹性本构模型的识别与变形预报[J].水利学报,1998,(4):75～80
[13] 朱浮声,薛琳.粘弹性围岩力学参数反分析的一种数值法[J].岩石力学与工程学报,1997,16(5):478～482
[14] 章梦涛.冲击地压失稳理论与数值模拟计算.岩石力学与工程学报.1987.6(3)
[15] 章梦涛,潘一山,梁冰,王来贵编著.煤岩流体力学[M].科学出版社,1995
[16] 王启宏.材料流变学[M].北京:中国建筑工业出版社.1983
[17] 王来贵等.岩石试件的流变失稳理论及判据[J].1994.13(3):93~97
[18] 王来贵,黄润秋等,岩石力学系统运动稳定性及其应用[M],北京:地质出版社,1998,57-58.
[19] 王来贵,黄润秋,张倬元,王士天.滑坡灾害发生的动力学模型[J],自然科学进展,1998,8(2).
[20] 徐平,杨挺青.岩石流变试验与本构模型辨识[J].2001.20
[21] 郭增玉,张朝鹏,夏旺民.高湿度Q2 黄土的非线性流变本构模型及参数[J].岩石力学与工程学报,2000,19(6):780-784.
[22] 袁 静,龚晓南,益德清.岩土流变模型的比较研究[J].岩石力学与工程学报,2001,20(6):772-779
[23] 孙 钧,黄 伟.岩石力学参数弹塑性反演问题的优化方法[J].岩石力学与工程学报, 1992, 11(3):221-229
[24] 刘晶辉,王山长,杨洪海,软弱夹层流变试验长期强度确定方法[J],勘察科学技术,1996,5,3-7
[25] 陈宗基.根据流变学与地球动力学观点研究新奥法岩石.岩石力学与工程学报[J],1988,7(2)
[26] 张忠亭,王宏,陶振宇. 岩石蠕变特性研究进展概况.长江科学院院报[J],1996,13
[26] 王子潮.土地馒橄榄岩流变性研究进展及其动力学意义[J].地球物理学进展,1995, 10(2) :1-15
[27] Nicolas A,Poirier JP(林传勇,尘兰斌译)变质岩的晶质塑性和固态流变[M]
北京:科学出版,1985.154— 160
[28] 袁龙蔚,流变力学[M],科学出版社,1986.
[29] 杨绪灿等,黏塑性力学概论[M],中国铁路出版社,1985
[30] 杨挺青,黏弹性力学[M],华中理工大学出版社,1990
[31] 袁龙蔚,缺陷体流变学[M],国防工业出版社,1986.
[32] 周筑宝等,一种可用于分析流变断裂过程的损伤力学计算模型[J],湘潭大学学报,1989
[33] Pan Y W, Dong J J. Time-dependent tunnel convergence: Formulation of the model [J]. Int J Rock Mech Min Sci & Geomech Abstr, 1991
[34] Biot.MA. Theory of stress-strain relations in an isotropic visco elasticity and relation phenomena[J]. JAppPhy, 1954,25(11):1385-I391
[35] 宋德彰.岩质材料非线性流变属性及其力学模型[J].同济大学学报,1991,19
(4):395-401
[36] 陈宗基,康文法.岩石的封闭应力、蠕变和扩容及本构方程.岩石力学与工程学报,1991, 10(4): 299-312
[37] 杨绪灿,杨桂通,徐秉业.粘塑性力学概论.北京:中国铁道出版社,1985
[38] Cristescu N, Fota D, Medves E. Tunnel support analysis incorporating rock creep. Int J Rock Mech Min Sci&Geomech Abstr, 1987, 24(6): 321^-330
[39] 朱素平.岩石的流变性与地下工程结构的稳定性研究:[学位论文].徐州;中国矿业大学采矿系,1989
[40] 朱素平等.地下圆形隧道围岩稳定性的粘弹性力学分析[J].同济大学学报, 1994, 22(3)
[41] Perzyna. Fundamental problem in visco-plasticity [J].V Adv in Appl Mech, 1966, (9) : 243-377.
[42] Zinkie wicz O C,Cormeau I C. Visco-plasticity and creep in elastic solids a unified numerical solution approach[J]. Int J Num Nbth in Engrg ,1974,(8) :821-845.
[43] Cormeau I. Numerical stability in quasi7static elasto-viscoplasticity[J]. Int J Num Meth in Engrg ,1975,(9) :109-127.
[44] 邵国建等.地下洞室群的弹粘塑性有限元分析[J].河海大学学报,2001,29(6).
[45] 康红普.软岩巷道底臌的机理及防治[M].煤炭工业出版社,1993
[46] 张良辉等.隧道围岩的弹塑性解析解[J]。岩土工程学报,1997,19(4)
[47] 芮勇勤等.露天煤矿边坡中软弱夹层的蠕动变形特性分析[J].东北大学学报.1999.20(6)
[48] 杨天鸿等.顺层蠕动边坡变形破坏机理及稳定性动态分析[J].工程地质学报.2003.11(2)
[49] 何学秋著.含瓦斯煤岩流变动力学.中国矿业大学出版社[M].1995
[50] 曹树刚,边金,李鹏。岩石蠕变本构关系及改进的西原正夫模型[J],岩石力学与工程学报,2002,21(5)。