岩石非线性弹性的实验研究及其P-M模型的理论解释
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摘要
岩石介质由于自身的不均匀性如微孔隙和微裂纹的普遍存在,可以认为是非线性弹性介质,它的重要特征之一就是应力-应变曲线的滞回现象。对不同的岩石样品在MTS伺服压力机上进行了一系列的循环加、卸载实验,得到了不同岩石的应力-应变的滞回曲线。Preisach-Mayergoyz模型(简称P-M模型)是一种从微观概率分布入手研究滞回现象的理论。在简要阐述了该模型的基本原理后,研究了微观模型参数变化对宏观力学性质(如应力-应变曲线和动静态弹性模量等)的影响,结合一组实验数据推算出岩石样品的模型参数,利用这些参数得出其他组的理论曲线,发现理论曲线与实验得到的应力-应变曲线、弹性模量曲线基本吻合。这证明P-M模型在模拟岩石中的微孔隙和微裂纹在低应力状态下对岩石力学性质的影响时是一种有效的方法。最后,对模型的适用范围和改进办法进行了讨论。
Rock can be considered as nonlinear elastic medium because of heterogeneity with the ubiquitousmicro-holes and micro-cracks. An important character of rock is the hysteretic phenomenon in the stress-strain curve. From experiments of a series of load-unload cycles for rock samples by MTS pressure machine,the hysteretic stress-strain curves of different rock samples are acquired. Preisach-Mayergoyz (P-M) model is a theorystarting with microscopic probability distribution to discuss hysteretic phenomenon. After briefly describing the fundamental of the P-M model,the influence of P-M model parameters on macroscopic mechanical characters,such as the stress-strain curve,dynamic and static moduli,etc,is investigated. Then,the parameters of a set of rock samples are figured out to establish P space,and to calculate the theory curves of the other sets of samples. The calculation results fit the experiment data very well. It is proved that P-M model is an effective method to simulate the influence of micro-holes and micro-cracks on the mechanical characters of rock in low stress state. Theapplicable range of the model and some improved ways to the model are also discussed.
Rock can be considered as nonlinear elastic medium because of heterogeneity with the ubiquitousmicro-holes and micro-cracks. An important character of rock is the hysteretic phenomenon in the stress-strain curve. From experiments of a series of load-unload cycles for rock samples by MTS pressure machine,the hysteretic stress-strain curves of different rock samples are acquired. Preisach-Mayergoyz (P-M) model is a theorystarting with microscopic probability distribution to discuss hysteretic phenomenon. After briefly describing the fundamental of the P-M model,the influence of P-M model parameters on macroscopic mechanical characters,such as the stress-strain curve,dynamic and static moduli,etc,is investigated. Then,the parameters of a set of rock samples are figured out to establish P space,and to calculate the theory curves of the other sets of samples. The calculation results fit the experiment data very well. It is proved that P-M model is an effective method to simulate the influence of micro-holes and micro-cracks on the mechanical characters of rock in low stress state. Theapplicable range of the model and some improved ways to the model are also discussed.
引文
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2 Boitnott G N. The role of rock joints in non-linear attenuation inmoderate strain amplitude regimes ， semiannual report[R].Alcuquerque NM：Phillips Lab，Kirtland Air Force Base， 1992
3 Gist G A，Fluid effects on velocity and attenuation in sandstones[J]. J.Acoust. Soc. Am.，1994，96：1 158～1 173
4 McCall K R，Guyer R A. Equation of state and wave propagation in hysteretic nonlinear elastic materials[J]. Jounal of GeophysicalResearch，1994，99：23 887～23 897
5 Guyer R A，McCall K R，Boitnott G N. Hysteresis，discrete memory，and nonlinear wave propagation in rock：a new paradigm[J]. Phys. Rev.Lett.，1995，74(17)：3 491～3 494
6 Mayeroyz D. Hysteresis models from the mathematical and controltheory points of view[J]. J. Appl. Phys.，1985，57(1)：3803～3805
7 McCall K R，Guyer R A. A new theoretical paradigm to describehysteresis，discrete memory and nonlinear elastic wave propagationinrock[J]. Nonlinear Processes in Geophysics，1996，(3)：89～101
8 Guyer R A，McCall K R，Boitnott G N，et al. Quantitativeimplementation of Preisach-Mayergoyz space to find static anddynamic elastic moduli in rock[J]. Jounal of Geophysical Research，1997，102：5 281～5 293
9 Guyer R A，Johnson P A. Nonlinear mesoscopic elasticity：evidece fora new class of materials[J]. Physics Today，1999，30：30～36
10 Van Den Abeele K E A，Carmeliet J，Johnson P A，et al. Influence ofwater saturation on the nonlinear elastic mesoscopic response in earthmaterials and the implications to the mechanism of nonlinearity[J].Jounal of Geophysical Research，2002，107(B6)：4～11
11 Carmeliet J ， Van Den Abeele K E A. Application of thePreisach-Mayergoyz space model to analyze moisture effects on thenonlinear elastic response of rock[J]. Geophys. Rev. lett.，2002，29(7)：1～4
12 陈 颙. 地壳岩石的力学性能-- 理论基础与实验方法[M]. 北京：地震出版社，1988
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