最大有效力矩准则的理论拓展

童亨茂; 王明阳; 郝化武; 赵丹

最大有效力矩准则的理论拓展

中国石油大学(北京)油气资源与探测国家重点实验室, 北京102249

基金项目:

国家自然科学基金项目 40772086

CNPC油气勘探超前共性科技项目 07-01C-01-04

详细信息

作者简介:
童亨茂(1967-), 男, 博士, 中国石油大学(北京)副教授, 主要从事盆地构造分析、构造物理模拟和构造裂缝预测等方面的研究和教学工作。E-mail:tong-hm@163.com

中图分类号: P551
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出版历程
- 收稿日期: 2011-05-13
- 刊出日期: 2011-12-01

THEORETICAL DEVELOPMENT OF MAXIMUM EFFECTIVE MOMENT CRITERION

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China

摘要

摘要: 在分析"导致变形带内先存面理或层理发生转动的最大有效力矩与先存面理或层理方向有关"的基础上, 对最大有效力矩准则(M_eff=0.5(σ₁-σ₃) Lsin2αsinα)进行理论上的拓展, 提出了可以判定任意方向先存面理最大有效力矩的准则——泛最大有效力矩准则(M_G-eff=0.5(σ₁-σ₃)Lsin2αsin(α-θ)), 其中当先存面理与最大主压应力(σ₁)平行时, 则成为最大有效力矩准则。该准则的理论分析表明:①当先存面理与σ₁平行时, 在σ₁左右两侧±54.7°方向出现2个有效力矩的最大值, 形成共轭的变形带, 钝角(109.4°)对着σ₁方向; ②当先存面理与σ₁斜交时, 在σ₁的另一侧出现1个有效力矩的最大值, 从而只出现一个方向的变形带, 并随着先存面理偏离σ₁方向, 变形带与σ₁的夹角逐渐减小(从θ=0°时的54.7°, 减小到θ=90°时的35.3°), 而与先存面理之间的夹角逐渐增大(从θ=0°时的54.7°, 增加到θ=90°时的125.3°); ③当先存面理与σ₁垂直时, 在σ₁左右两侧± 35.3°方向出现2个有效力矩的最大值, 也形成共轭的变形带, 但锐角(70.6°)对着σ₁方向。在主应变平面上变形带与先存面理方向及变形带剪切方向(左旋或右旋)已知的情况下, 可以确定最大主压应力方向。泛最大有效力矩准则克服了最大有效力矩准则与滑移线理论不相容的问题, 可以解释大多膝褶带非共轭发育等多种现象, 预期在韧性变形域中具有广阔的应用前景。
- 最大有效力矩 /
- 韧性变形 /
- 先存面理 /
- 变形带 /
- 共轭
Abstract: Theoretical analysis shows that the Maximum Effective Moment, which cause preexisting cleavage or bedding to rotate, is related to the direction of pre-existing cleavage or bedding, and the Maximum Effective Moment Criterion (M_eff=0.5(σ₁-σ₃) Lsin2αsinα, simplified as MEMC) proposed by Zheng et al is theoretically expanded to General Criterion of Maximum Effective Moment (M_G-eff=0.5(σ₁-σ₃) Lsin2αsin (α-θ), simplified as GCMEM), which can be used to determine the Maximum Effective Moment with any direction of cleavage in this paper.MEMC is a special case of GCMEM when cleavage is parallel to maximum principal compressive stress (σ₁).Theoretical analysis of GCMEM shows that:① when cleavage is parallel to σ₁, there occur two values of Maximum Effective Moment symmetrically on either side of σ₁ in the direction of ± 54.7°, and two conjugate deformation zone are predicted to appear with obtuse angle (109.4°) facing σ₁ direction.② When cleavage is oblique to σ₁, one Maximum Effective Moment, along which one deformation zone will appear, is predicted to occur on other side of σ₁, and the angle between deformation zone and σ₁ will decrease (from 54.7 ° when θ=0° reduced to 35.3° when θ=90°), while the angle between pre-existing cleavage and deformation zone will increase (from 54.7° when θ=0° increased to 125.3° when θ=90°) with pre-existing cleavage deviating from the σ₁ direction.③ when cleavage is perpendicular to σ₁, there also occur two values of Maximum Effective Moment symmetrically on either side of σ₁ in the direction of ± 35.3°, but two conjugate deformation zone with acute angle (70.6°) facing σ₁ direction.When the directions of pre-existing cleavage and deformation zone on principal strain surface and shear direction (sinistral or dextral) are known, the direction of maximum principal stress can be determined.GCMEM overcomes the incompatibility of MEMC with Slip Line Theory, and can be used to explain most of the kink zone development and other non-conjugate phenomena.It is expected to have wide application prospects in ductile deformation field.
- Maximum Effective Moment /
- ductile deformation /
- pre-existing cleavage /
- deformation zone /
- conjugate

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图 1 最大有效力矩准则力学分析示意图^[1]

α-σ₁与面理的夹角; θ-σ₁与面理法线的夹角; H-有效力臂长度; L-σ₁方向的单位长度

Figure 1. A sketch map of mechanical analysis of the Maximum Effective Moment Criterion

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图 2 不同方位先存面理有效力矩计算参数示意图

AC的延伸方向为先存面理方向, 先存面理与σ₁的夹角为θ(从σ₁到先存面理, 逆时针为正), 变形带(BC方向)与σ₁的夹角为α(从σ₁到先存面理, 逆时针为正), AC为先存面理的单位长度L。单位长度先存面理沿变形带剪切弯曲的力臂为AB (H), 有效力矩为AB (H=Lsin (α-θ))与沿变形带剪应力(0.5(σ₁-σ₃) sin2α)的乘积(0.5(σ₁-σ₃) Lsin2αsin (α-θ))

Figure 2. Calculating parameters of effective moment of pre-exiting cleavages with different directions

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图 3 不同方位先存面理沿不同方向的有效力矩分量sin2αsin (α-θ)的等值线图

a, b, c为不同方位先存面理sin2αsin (α-θ)值的极值分布线, 每一方位的先存面理都有3个极值点, 其中a中的A点(θ=90°)、b中的B点(θ=0°)以及c上的所有点(sin2αsin (α-θ))的绝对值都是最大值, 这样, 当θ=90°或θ=0°时, 有2个最大值, 其他的都只有1个最大值。图中数值的符号代表力矩的方向, 顺时针转动为正, 逆时针转动为负

Figure 3. Contour map of the effective moment component of pre-exiting cleavages with different directions

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图 4 7个特征方位的先存面理的有效力矩分量sin2αsin(α-θ)与α变化关系及最大值分布图

Figure 4. Relationship between sin2αsin(α-θ) and α and the distributions of their maximum values

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图 5 5个特征方位先存面理所对应的变形带及剪切方向关系图(虚线为先存面理方向)

Figure 5. Relationship between deformation zone and shear direction of different pre-exiting cleavages

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图 6 利用先存面理与变形带间夹角ϕ及变形带剪切方向确定主压应力方位示意图

a-变形带左旋剪切, 从变形带起逆时针方向测量ϕ(为ϕ_a), 并计算确定α(α_a), 从而确定σ₁方向; b-变形带右旋剪切, 从变形带起顺时针方向测量ϕ(为ϕ_b), 并计算确定α(α_b), 从而确定σ₁方向; a和b中先存面理与变形带的方向一致, 但变形带的剪切方向不一致, 结果导致σ₁方向相差90°(ϕ_b-ϕ_a=90°); 虚线为先存面理方向

Figure 6. Principle compressive stress direction determined by the angle ϕ and the shear direction of deformation zone

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表 1 不同方位先存面理出现最大有效力矩的方位及其组合

Table 1. Directions and potential deformation zones of the maximum effective moment of the different cleavages

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