On the Applicability of Nadai and Mogi Failure Criteria to Porous Sandstones
On the Applicability of Nadai and Mogi Failure Criteria to Porous Sandstones
复制标题
论Nadai和Mogi破坏准则对多孔砂岩的适用性
DOI：
10.1007/s00603-018-1508-z
复制
发表时间：
2018
影响因子：
6.2
通讯作者：
M. Ingraham
中科院分区：
文献类型：
--
作者：
Xiaodong Ma;M. Ingraham
多孔砂岩广泛分布于地壳中。它们的多孔结构是流体流动和储存的理想选择。因此，它促进了许多油气藏的形成，并用于废水和二氧化碳的处理。与油气开采和废物储存有关的活动引起局部应力变化，并可能因此导致砂岩破坏。因此，了解导致失效的应力条件至关重要。大量的实验研究有助于理解导致多孔砂岩破坏的应力条件。轴对称试验（σ2 = σ3或σ2 = σ1）确定多孔砂岩的破坏对约束（σ3）敏感（例如，Wong和Baud 2012）。根据主应力对轴对称测试数据进行分析促进了二维破坏标准的应用，例如库仑和莫尔（Jæger等人，2007年）。或者，根据主应力不变量（八面体剪应力τoct、三维平均应力σoct和二维平均应力σm，2）分析失效数据，得出三维失效准则，如Nadai（1950）[即，τoct = f（σoct）]和Mogi（1971）[即，τoct = f（σm，2）]。Nadai和Mogi准则也适用于常规和真三轴破坏数据。真三轴试验（σ1 ≥ σ2 ≥ σ3）虽然比轴对称试验少得多，但已明确证明了σ2和/或偏应力状态对破坏的影响（Mogi 1971，2007; Haimson 2006，以及其中的参考文献）。原位岩石通常处于真三轴应力状态（σ1 ≥ σ2 ≥ σ3）;因此，真三轴破坏数据和标准更能代表实际多孔砂岩特性。除了先前的努力（例如，Mogi 2007; Takahashi和Koide 1989; Wawersik等人1997），最近对多孔砂岩进行了一些广泛的真三轴实验。这些真三轴试验为制定破坏准则提供了重要数据，因为它们涵盖了广泛的应力条件[从轴对称压缩（σ2 = σ3）到轴对称拉伸（σ2 = σ1）]。Oku等人（2007年）测试了从TCDP（台湾车笼埔断层钻探项目）获得的孔隙度约为7%的砂岩，证实了在结晶岩石中观察到的脆性破坏对σ2的依赖性（Haimson 2006年）。英格拉哈姆等人（2013年）对Castlegate砂岩（26%孔隙度）进行了测试，并揭示了失效对平均应力和偏应力状态的依赖性，这是高孔隙度砂岩的特征。Ma和Haimson（2016年）以及Ma等人（2017年a）测试了两种多孔砂岩（Coconino和Bentheim，孔隙度分别为17.5%和24%）的σ3，范围在0之间。
Porous sandstones are widespread in the Earth’s crust. Their porous structure is ideal for fluid flow and storage. As such, it facilitates the formation of many oil and gas reservoirs, and is used for the disposal of waste water and CO2. Activities related to hydrocarbon extraction and waste storage induce local stress changes, and may consequently cause the sandstones to fail. Therefore, the knowledge of stress conditions leading to failure is of critical importance. A number of experimental studies have contributed to the understanding of the stress conditions leading to failure in porous sandstones. Axisymmetric tests (σ2 = σ3 or σ2 = σ1) established that failure of porous sandstones is sensitive to confinement (σ3) (e.g., Wong and Baud 2012). Analysis of axisymmetric test data in terms of principal stresses fostered the application of two-dimensional failure criteria such as Coulomb and Mohr (Jæger et al. 2007). Alternatively, analyzing failure data in terms of principal stress invariants (octahedral shear stress τoct, three-dimensional mean stress σoct, and two-dimensional mean stress σm,2) has led to threedimensional failure criteria such as Nadai (1950) [i.e., τoct = f (σoct)] and Mogi (1971) [i.e., τoct = f (σm,2)]. The Nadai and Mogi criteria are also applicable to both conventional and true triaxial failure data. True triaxial tests (σ1 ≥ σ2 ≥ σ3), though much fewer than axisymmetric tests, have unequivocally demonstrated the effect of σ2 and/or the deviatoric stress state on failure (Mogi 1971, 2007; Haimson 2006, and references therein). Rock in situ is generally subject to a true triaxial stress regime (σ1 ≥ σ2 ≥ σ3); hence, true triaxial failure data and criteria are more representative of the actual porous sandstone behavior. In addition to previous endeavors (e.g., Mogi 2007; Takahashi and Koide 1989; Wawersik et al. 1997), a few extensive true triaxial experiments were recently conducted on porous sandstones. These true triaxial tests provide important data for developing failure criteria, because they covered a wide spectrum of stress conditions [from axisymmetric compression (σ2 = σ3) to axisymmetric extension (σ2 = σ1)]. Oku et al. (2007) tested a sandstone of ~ 7% porosity obtained from TCDP (Taiwan Chelungpu-fault Drilling Project), confirming the dependence of brittle failure on σ2 as observed in crystalline rocks (Haimson 2006). Ingraham et al. (2013) performed tests on Castlegate sandstone (26% porosity) and revealed the failure dependency on mean stress and deviatoric stress state, characteristic of high-porosity sandstones. Ma and Haimson (2016) and Ma et al. (2017a) tested two porous sandstones (Coconino and Bentheim, 17.5 and 24% porosity, respectively) for σ3 ranging between 0 Xiaodong Ma is formerly in Geological Engineering Program, University of Wisconsin-Madison.