The processes of deformation and failure in rocks are unavoidably accompanied by the absorption, storage, dissipation, and release of energy. To explore energy allocation during rock shear fracturing, two series of single loading and unloading preset angle shear tests at inclined angles of 60° and 50° were performed on red sandstone and granite by varying the experimental unloading level. The area integral approach was employed to interpret the load–displacement responses of the rock specimens via calculation of the energy parameters (referring to the external input energy, internal elastic energy and internal dissipation energy). The interpretations of the results revealed that the increase in the experimental unloading level nonlinearly increases the internal elastic energy, internal dissipation energy and external input energy; these relationships can be described by quadratic functions. It was also realized that under different experimental unloading levels, not only the internal elastic energy but also the internal dissipation energy is closely proportional to the external input energy. The proportional energy relationship can be used to quantify the internal elastic energy and internal dissipation energy at any expected experimental unloading levels, and a real-time calculation model for the internal elastic energy and internal dissipation energy in the pre-peak duration (including the peak point) was introduced. Meanwhile, an invariable feature for the ultimate internal elastic index W ed (the ratio of ultimate internal elastic energy to peak internal dissipation energy) was captured via quantitative analysis. Additionally, the energy allocation manner and transfer mechanisms of rocks bearing varied loading forms (including uniaxial compression, Brazilian splitting, point load, semicircular bending, and preset angle shear) were also comprehensively compared considering three basic rock fracture modes: the tensile, shear, and hybrid failure (mixed tensile-shear) modes. Thus, the proportional distribution patterns of internal elastic energy and internal dissipation energy or the linear correlations among the three energy parameters can be universally observed during the failure of homogeneous rocks, despite distinct loading forms under one-dimensional stress conditions.

中文翻译：

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预置角剪切条件下岩石的线性储能与耗散规律

岩石的变形破坏过程不可避免地伴随着能量的吸收、储存、耗散和释放。为探索岩石剪切压裂过程中的能量分配，通过改变实验卸载水平，对红砂岩和花岗岩进行了60°和50°倾斜角的两组单次加载和卸载预设角剪切试验。采用面积积分方法通过计算能量参数（指外部输入能量、内部弹性能量和内部耗散能量）来解释岩石试样的载荷-位移响应。结果的解释表明，实验卸载水平的增加非线性地增加了内部弹性能、内部耗散能和外部输入能量；这些关系可以用二次函数来描述。还认识到，在不同的实验卸载水平下，不仅内部弹性能量而且内部耗散能量都与外部输入能量密切相关。比例能量关系可用于量化任何预期的实验卸载水平下的内弹性能和内耗散能，以及前峰值持续时间（包括峰值）内弹性能和内耗散能的实时计算模型点）介绍。同时，通过定量分析捕获了极限内弹性指数 W ed （极限内弹性能与峰值内耗散能之比）的不变特征。此外，综合比较了承受不同载荷形式（包括单轴压缩、巴西劈裂、点载荷、半圆弯曲和预置角剪切）的岩石的能量分配方式和传递机制，考虑了三种基本的岩石断裂模式：拉伸、剪切和混合破坏（混合拉伸剪切）模式。因此，尽管在一维应力条件下加载形式不同，但在均质岩石破坏过程中，内弹性能和内耗能的比例分布模式或三个能量参数之间的线性相关性可以普遍观察到。和预设角剪切）也考虑三种基本岩石断裂模式进行了综合比较：拉伸、剪切和混合破坏（拉伸-剪切混合）模式。因此，尽管在一维应力条件下加载形式不同，但在均质岩石破坏过程中，内弹性能和内耗能的比例分布模式或三个能量参数之间的线性相关性可以普遍观察到。和预设角剪切）也考虑三种基本岩石断裂模式进行了综合比较：拉伸、剪切和混合破坏（拉伸-剪切混合）模式。因此，尽管在一维应力条件下加载形式不同，但在均质岩石破坏过程中，内弹性能和内耗能的比例分布模式或三个能量参数之间的线性相关性可以普遍观察到。