Conditions for compaction and shear bands in a transversely isotropic material
Conditions for compaction and shear bands in a transversely isotropic material
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横观各向同性材料中的压实带和剪切带的条件
DOI：
10.1016/s0020-7683(02)00173-7
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发表时间：
2002
影响因子：
3.6
通讯作者：
J. Rudnicki
中科院分区：
文献类型：
--
作者：
J. Rudnicki
本文推导了用于模拟轴对称压缩试验中地质材料响应的横向各向同性本构关系的局部化变形条件。分析考虑了带胀缩或压实的剪切带和纯压实带的可能性。后者是垂直于最大主压应力方向的局部纯压缩变形（无剪切）平面区。在野外和实验室中，已在多孔岩石中观察到压实带。预计当单轴变形的增量切线模量消失时，它们就会发生。恒定侧向应力下切线模量E的临界值为- 9Kνr/2，其中ν为（恒定侧向应力下）侧向与轴向变形增量之比的负值，r为导致轴向零变形的轴向与侧向应力增量之比，K为与侧向应力和变形增量相关的模量。剪切带形成的临界切线模量的表达式更为复杂，除了r、ν和K外，还取决于剪切模量Gland Gt，它分别控制平行和垂直于对称轴的平面上的剪切增量。材料参数的不确定性阻止了与观测结果的详细比较，但结果与压缩体积应变（ν<1/2）的低角度剪切带（法线距对称轴小于45°）的观测结果一致。此外，如果Gland gare相对于K较小，r在1附近，则这些带的临界切线模量可能为正。
This paper derives conditions for localized deformation for a transversely isotropic constitutive relation intended to model the response of geological materials in the axisymmetric compression test. The analysis considers the possibility of shear bands, with dilation or compaction, and pure compaction bands. The latter are planar zones of localized pure compressive deformation (without shear) that form perpendicular to the direction of the maximum principal compressive stress. Compaction bands have been observed in porous rock in the field and in the laboratory. They are predicted to occur when the incremental tangent modulus for uniaxial deformation vanishes. The critical value of the tangent modulus E for constant lateral stress is −9Kνr/2, where ν is the negative of the ratio of increments of lateral to axial deformation (at constant lateral stress), r is the ratio of axial to lateral stress increments causing zero axial deformation, and K is the modulus relating increments of lateral stress and deformation. The expression for the critical tangent modulus for shear band formation is more complex and depends, in addition to r, ν, and K, on the shear moduli Gland Gt, governing increments of shear in planes parallel and perpendicular to the axis of symmetry, respectively. Uncertainty about material parameters prevents a detailed comparison with observations but the results are consistent with observations of low angle shear bands (with normals less than 45° from the symmetry axis) for compressive volumetric strain (ν<1/2). In addition, the critical tangent modulus for such bands may be positive if Gland Gtare small relative to K and r is around unity.