动荷载下岩石变形特性是岩土工程界的常见问题之一。为研究岩石低动应力下变形特性,基于分数阶微积分构建分数阶黏壶,将分数阶黏壶替换Burgers模型中Maxwell常值黏壶,建立了可反映低动应力荷载作用下岩石变形规律的分数阶Burgers模型(Fractional-order Burgers Model,FBM)。将动荷载分解为一个静力荷载和一个平均应力值为0的循环荷载,基于流变力学理论给出了静力作用下基于分数阶Burgers模型的岩石流变本构方程,再根据黏弹性力学理论,考虑岩石损伤、裂隙及塑性变形对动荷载下岩石储能柔量和耗能柔量造成的影响,引入储能和耗能柔量变化量,构建了循环荷载下基于分数阶Burgers模型的岩石动态响应本构方程式,最后将已获得的岩石流变本构方程式与动态响应本构方程式叠加,即得到一种新的岩石本构方程。与已有的试验结果相比,改进Burgers模型可较好地描述低动应力状态下岩石减速、等速2个阶段的变形特征,且模型参数可运用数值方法简便得到。
Abstract
The deformation characteristics of rock under dynamic loading is a common problem in geotechnical engineering. In this article, a Fractional order Burgers Model (FBM) which reflects the deformation characteristics of rock under low dynamic stress is established by replacing constant Maxwell dashpot of Burgers model with fractional order dashpot based on fractional calculus. The dynamic loading is decomposed into a static loading and a cyclic loading with an zero average stress by stress decomposition method. According to rheological mechanics theory, the rheology constitutive equation for rock based on FBM is given under the static loading; and meanwhile according to viscoelastic mechanics theory, the dynamic response constitutive equation of rock based on FBM is deduced under the cyclic loading in consideration of the influence of rock damage, fracture and plastic deformation on energy storage and energy dissipation compliance. Furthermore, a new constitutive equation for rock is obtained by superimposing the constitutive equations under the two stress conditions. Compared with existing test results of rock under dynamic loading, the FBM could better describe the deformation characteristics of rock under low dynamic stress in deceleration stage and constant velocity stage; moreover the FBM parameters can be obtained conveniently by numerical methods.
关键词
岩石动力学 /
低动应力 /
分数阶黏壶 /
分数阶Burgers模型 /
流变力学
Key words
rock dynamic mechanics /
low dynamic stress /
fractional order dashpot /
Fractional order Burgers Model (FBM) /
rheological mechanics
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参考文献
[1] 葛修润, 卢应发.循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报, 1992,14(3):56-60.
[2] 葛修润.周期荷载下岩石大型三轴试件的变形和强度特性研究[J].岩土力学, 1987, 8(2): 11-18.
[3] 林卓英, 吴玉山.岩石在循环荷载作用下的强度及变形特征[J].岩土力学, 1987, 8(3): 31-37.
[4] 徐建光，张平,李宁.循环荷载下断续裂隙岩体的变形特性[J].岩土工程学报, 2008,30(6): 802-806.
[5] 左宇军,李夕兵,唐春安, 等. 受静载荷的岩石在周期载荷作下破坏的试验研究[J].岩土力学,2007,28(5):927-932.
[6] 陈运平，王思敬，王恩志.循环荷载下层理岩石的弹性和衰减各向异性[J].岩石力学与工程学报, 2006,25(11):2233-2239.
[7] 肖建清，冯夏庭，丁德馨，等. 常幅循环荷载作用下岩石的滞后及阻尼效应研究[J].岩石力学与工程学报, 2010, 29(8):1678-1783.
[8] 冯春林，毕忠伟，吴永丰，等. 循环荷载下岩石临界强度的定[J].金属矿山, 2011, (2): 13-16.
[9] 朱明礼，朱珍德，李刚，等.循环荷载作用下花岗岩动力特性试验研究[J].岩石力学与工程学报,2009,28(1):2749-2754.
[10] 李树春，许江，陶云奇，等.岩石低周疲劳损伤模型与损伤变量表达方法[J].岩土力学,2006, 30(6):1611-1619.
[11] 许宏发，王武，方秦，等.循环荷载下岩石塑性应变演化模型[J].解放军理工大学学报（自然科学版）, 2012, 13(3): 282-286.
[12] 郭建强，黄质宏.循环荷载作用下岩石疲劳本构模型初探[J].岩土工程学报, 2015, 37(9): 1698-1703.
[13] 王军保，刘新荣，黄明，等.低频循环荷载下盐岩轴向蠕变的Burgers模型分析[J].岩土力学, 2014,35(4):934-941.
[14] 王者超，赵建刚，李术才，等.循环荷载作用下花岗岩疲劳力学性质及其本构模型[J].岩石力学与工程学报, 2012,31(9):1187-1900.
[15] 靳丹丹，马芳芳，么焕民.Riemann Liouville 分数阶微积分的定义及其性质[J].哈尔滨师范大学自然科学学报,2011,27(3):21-23.
[16] 杨挺青.黏弹性力学[M].武汉:华中理工大学出版社，1990.
[17] R M克里斯坦森.黏弹性力学引论[M].郝松林,老亮译.北京:科学出版社,1990.
[18] 丁祖德．高速铁路隧道基底软岩动力特性及结构安全性研究[D].长沙：中南大学，2012.
基金
国家自然科学基金项目(51608141);贵州大学引进人才科研项目(贵大人基合字(2015)16)
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