Abstract A polymodal faulting phenomenon is further explored here that comprises penecontemporaneous fractures showing finite dispersion of strikes and dips with poles confined in one annular or two arc regions in stereographic projection. The fracture pattern represents three-dimensional strain of rocks with characteristics distinct from previously known bi-, four- or poly-modal faulting, and thus is unable to be interpreted in terms of the corresponding theories such as conjugate faulting, slip on preexisting weak planes and tensile crack interaction, respectively. Here, a super-critical stress model is advanced to decode stress significance of the specific fracture pattern with a particular emphasis on model prediction for orientations of failure surfaces. The model is an extension of the slip model of Reches (1983) that prescribes formation of four sets of faults in orthorhombic symmetry conforming to the Coulomb-Mohr criterion of τ=C+μσ (equivalent to C=F=τ-μσ where C is cohesion of rocks and F is function of shear stress τ, normal stress σ and friction coefficient μ). The mechanic boundary condition means a super-critical stress state (Fmax>C) because stress resolution allows only two sets of planes to coevally have maximum value of F and thus shear fail equally according to Andersonian (1905, 1951) conjugate faulting derivation that corresponds to a critical stress state, i.e., Fmax is just equal to C. This super-critical stress state further means that there are some planes on which F>C certainly on verge of faulting at least possessing a not even lower tendency than those planes on which C=F, and thus polymodal faulting results. The planes with F≥C tend to be areal distribution with arc or annular geometry in stereographic projection of poles. Given the Coulomb-Mohr friction and failure criteria are not fundamentally different, the super-critical model may also apply to initial failure of intact rocks. The new model represents a major reorganization in thinking about shear failure of rocks and fracturing patterns. Several natural examples are provided with fracture patterns fit to the super-critical model proposed here.

中文翻译：

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岩石多峰断层的超临界应力模型

摘要 这里进一步探讨了一种多峰断层现象，它包括准同期断裂，显示出走向和倾角的有限分散，极点限制在立体投影中的一个环形或两个弧形区域。断裂模式代表岩石的三维应变，其特征不同于先前已知的双模态、四模态或多模态断层，因此无法用共轭断层、先前存在的弱平面上的滑动等相应理论来解释和拉伸裂纹相互作用。在这里，超临界应力模型被提出来解码特定断裂模式的应力重要性，特别强调对失效表面方向的模型预测。该模型是 Reches (1983) 滑动模型的扩展，该模型规定四组正交对称断层的形成符合库仑莫尔准则 τ=C+μσ（相当于 C=F=τ-μσ，其中 C是岩石的内聚力，F 是剪应力 τ、正应力 σ 和摩擦系数 μ 的函数）。机械边界条件意味着超临界应力状态 (Fmax>C)，因为应力分辨率只允许两组平面同时具有 F 的最大值，因此根据 Andersonian (1905, 1951) 共轭断层推导，剪切失效相等到临界应力状态，即 Fmax 刚好等于 C。这种超临界应力状态进一步意味着有一些平面上 F> C 肯定处于断层的边缘，至少比那些 C=F 的平面具有甚至更低的趋势，因此导致多峰断层。F≥C的平面在极点的立体投影中倾向于呈弧形或环形几何的面分布。鉴于库仑-莫尔摩擦和破坏准则没有根本不同，超临界模型也可能适用于完整岩石的初始破坏。新模型代表了对岩石剪切破坏和压裂模式的思考的重大重组。提供了几个自然示例，其中包含适合此处提出的超临界模型的断裂模式。鉴于库仑-莫尔摩擦和破坏准则没有根本不同，超临界模型也可能适用于完整岩石的初始破坏。新模型代表了对岩石剪切破坏和压裂模式的思考的重大重组。提供了几个自然示例，其中包含适合此处提出的超临界模型的断裂模式。鉴于库仑-莫尔摩擦和破坏准则没有根本不同，超临界模型也可能适用于完整岩石的初始破坏。新模型代表了对岩石剪切破坏和压裂模式的思考的重大重组。提供了几个自然示例，其中包含适合此处提出的超临界模型的断裂模式。