Spherocylindrical microplane constitutive model for shale and other anisotropic rocks
Spherocylindrical microplane constitutive model for shale and other anisotropic rocks
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页岩和其他各向异性岩石的球柱微平面本构模型
DOI：
10.1016/j.jmps.2017.03.006
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发表时间：
2017-06
影响因子：
5.3
通讯作者：
Caner
中科院分区：
文献类型：
--
作者：
Li Cunbao;Caner
各向异性材料非弹性行为的本构方程是一个具有挑战性的问题。提出了一种新的球柱面微平面本构模型，该模型满足正交各向异性材料的非弹性断裂行为的挑战，特别是页岩，其是横观各向同性的，并且对于水力压裂（aka fracking）以及许多岩土结构是重要的。其基本思想是将一个圆柱形微平面系统耦合到经典的球形微平面系统。每个系统都受到相同的应变张量，而它们的应力张量叠加。球形相是类似于以前的混凝土和各向同性岩石的微平面模型。所有空间取向的球形微平面上的应力的积分依赖于先前开发的球形表面上的最佳高斯积分。圆柱形相是产生横向各向同性的物质，它只涉及垂直于各向同性平面的微平面，或垫层，并增强该平面的刚度和强度。与除谱模型外的所有微平面模型不同，本模型能再现横观各向同性页岩的所有五个独立弹性常数。反之亦然，从这些常数，可以很容易地计算出所有的微平面弹性模量，如果平面内与平面外的弹性模量比不是太大（通常小于3.75，适用于所有页岩），则这些弹性模量都是正的。定向微裂纹开口，摩擦微滑移和层面行为可以更直观地模拟比谱的方法。数据拟合表明，微平面抗力随与层理夹角的变化呈非单调变化，在60°处抗压抗力最小。提出了一种显式分步结构分析的鲁棒算法。像所有的微平面模型一样，有许多材料参数，但它们可以按顺序识别。最后，与大量的页岩测试数据的比较验证了模型。
Constitutive equations for inelastic behavior of anisotropic materials have been a challenge for decades. Presented is a new spherocylindrical microplane constitutive model that meets this challenge for the inelastic fracturing behavior of orthotropic materials, and particularly the shale, which is transversely isotropic and is important for hydraulic fracturing (aka fracking) as well as many geotechnical structures. The basic idea is to couple a cylindrical microplane system to the classical spherical microplane system. Each system is subjected to the same strain tensor while their stress tensors are superposed. The spherical phase is similar to the previous microplane models for concrete and isotropic rock. The integration of stresses over spherical microplanes of all spatial orientations relies on the previously developed optimal Gaussian integration over a spherical surface. The cylindrical phase, which is what creates the transverse isotropy, involves only microplanes that are normal to plane of isotropy, or the bedding layers, and enhance the stiffness and strength in that plane. Unlike all the microplane models except the spectral one, the present one can reproduce all the five independent elastic constants of transversely isotropic shales. Vice versa, from these constants, one can easily calculate all the microplane elastic moduli, which are all positive if the elastic in-to-out-of plane moduli ratio is not too big (usually less than 3.75, which applies to all shales). Oriented micro-crack openings, frictional micro-slips and bedding plane behavior can be modeled more intuitively than with the spectral approach. Data fitting shows that the microplane resistance depends on the angle with the bedding layers non-monotonically, and compressive resistance reaches a minimum at 60°. A robust algorithm for explicit step-by-step structural analysis is formulated. Like all microplane models, there are many material parameters, but they can be identified sequentially. Finally, comparisons with extensive test data for shale validate the model.
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DOI：
10.1061/(asce)0733-9399(1991)117:10(2429
发表时间：
1991-10
期刊：
Journal of Engineering Mechanics-asce
影响因子：
--
作者：
I. Carol;Z. Bažant;P. Prat
通讯作者：
I. Carol;Z. Bažant;P. Prat
影响因子：
2.6
作者：
C. Sayers
通讯作者：
C. Sayers
DOI：
10.1061/(asce)0733-9410(1986)112:4(458
发表时间：
1986-04
期刊：
Journal of Geotechnical Engineering
影响因子：
--
作者：
Z. Bažant;Jin Keun Kim
通讯作者：
Z. Bažant;Jin Keun Kim
影响因子：
--
作者：
Chandong Chang;M. Zoback
通讯作者：
Chandong Chang;M. Zoback
影响因子：
5.3
作者：
Liang Chen;J. Shao;H. Huang
通讯作者：
Liang Chen;J. Shao;H. Huang