Micromechanics of brittle creep in rocks
Micromechanics of brittle creep in rocks
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DOI：
10.1029/2012jb009299
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发表时间：
2012-08-25
影响因子：
3.9
通讯作者：
Meredith, P. G.
中科院分区：
文献类型：
--
作者：
Brantut, N.;Baud, P.;Meredith, P. G.
在上地壳中，孔隙水的化学影响通过亚临界裂纹扩展促进了与时间相关的脆性变形。亚临界裂纹扩展使得岩石在远低于其短期破坏强度的应力下甚至在恒定的施加应力下变形和破坏（“脆性蠕变”）。在这里，我们提供了一个描述三轴应力条件下水饱和岩石随时间变化的脆性蠕变的微观力学模型。宏观脆性蠕变是根据亚临界裂纹扩展导致的压应力下的微裂纹扩展来建模的。由于压缩裂纹扩展而产生的增量应变源自 Ashby 和 Sammis (1990) 的滑翼裂纹模型，裂纹长度演化则根据 Charles 定律计算。该模型计算出的宏观应变和应变率是非线性的，与花岗岩、低孔隙率砂岩和玄武岩样品上获得的实验结果非常吻合。初次蠕变（减速应变）对应于减速裂纹扩展，因为应力强度因子随着压缩裂纹长度的增加而初始减小。第三次蠕变（接近失效时加速应变）对应于由于裂纹相互作用而导致的裂纹扩展速率的增加。具有明显恒定应变率的二次蠕变作为这两个端元相之间的拐点而出现。拐点处的最小应变率可以作为模型参数、有效围压和温度的函数进行分析估计，这为该过程提供了近似的蠕变定律。蠕变定律用于推断由于施加应力的作用而作为上地壳深度的函数的长期应变率：这样，亚临界裂纹以相当于内聚力降低的方式降低了失效应力。我们还研究了多孔岩石中与压力溶解的竞争，并表明随着深度的增加和应变率的降低，从亚临界裂纹到压力溶解主导的蠕变的转变发生。
In the upper crust, the chemical influence of pore water promotes time dependent brittle deformation through sub-critical crack growth. Sub-critical crack growth allows rocks to deform and fail at stresses well below their short-term failure strength, and even at constant applied stress ("brittle creep"). Here we provide a micromechanical model describing time dependent brittle creep of water-saturated rocks under triaxial stress conditions. Macroscopic brittle creep is modeled on the basis of microcrack extension under compressive stresses due to sub-critical crack growth. The incremental strains due to the growth of cracks in compression are derived from the sliding wing crack model of Ashby and Sammis (1990), and the crack length evolution is computed from Charles' law. The macroscopic strains and strain rates computed from the model are non linear, and compare well with experimental results obtained on granite, low porosity sandstone and basalt rock samples. Primary creep (decelerating strain) corresponds to decelerating crack growth, due to an initial decrease in stress intensity factor with increasing crack length in compression. Tertiary creep (accelerating strain as failure is approached) corresponds to an increase in crack growth rate due to crack interactions. Secondary creep with apparently constant strain rate arises as an inflexion between those two end-member phases. The minimum strain rate at the inflexion point can be estimated analytically as a function of model parameters, effective confining pressure and temperature, which provides an approximate creep law for the process. The creep law is used to infer the long term strain rate as a function of depth in the upper crust due to the action of the applied stresses: in this way, sub-critical cracking reduces the failure stress in a manner equivalent to a decrease in cohesion. We also investigate the competition with pressure solution in porous rocks, and show that the transition from sub-critical cracking to pressure solution dominated creep occurs with increasing depth and decreasing strain rates.