With the increase of underground mining depth in coal mines, the distribution of stress fields in deep mining becomes more complex, and the stress localization characteristics are obvious. In order to obtain the local mechanical properties and energy evolution of sandstone, this article is based on the three-point bending experiment and combined with the localized failure theory to explore the evolution law of stress field, deformation field, and energy field of sandstone specimen under tensile stress during the three-point bending experiment. The results show that during the three-point bending test of sandstone, with the increase of the span of the three-point bending test, the peak stress at the characteristic point shows an increasing trend, and the peak stress has obvious regional characteristics. In the vertical direction, the peak stress at the characteristic points in the upper part of the neutral layer is larger, and the peak stress at the characteristic points in the lower part of the neutral layer is smaller. In the horizontal direction, the peak stress at the characteristic points in the near field is higher, and the peak stress at the characteristic points in the middle field and the far field is smaller. The stress field and the deformation field have a good corresponding relationship. The upper far-field peak strain tends to decrease with the increase of the span, and the upper near-field peak strain first decreases and then increases with the increase of the span. The lower near-field peak strain tends to decrease and then increase with increasing span, and the lower far-field peak strain fluctuates with increasing span. The energy field is dependent on the stress field and the deformation field, showing obvious regional characteristics. The energy storage and release capacity of the upper area are higher than those of the lower area. The overall performance of the loading energy storage, rebound energy release, and crack propagation energy release in different areas can be described as far field < mid-field << near field. The near-field energy at different spans presents the characteristics of two stages. When the span is between 140 mm and 150 mm, the near-field energy shows a rapid decreasing trend, and when the span is between 150 mm and 180 mm, the near-field energy presents an obvious increasing trend.

中文翻译：

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砂岩三点弯曲试验力学特性及能量演化

随着煤矿井下开采深度的增加，深部开采应力场分布更加复杂，应力局域化特征明显。为了获得砂岩的局部力学性质和能量演化，本文基于三点弯曲实验，结合局部破坏理论，探索了砂岩试件应力场、变形场、能量场的演化规律。在三点弯曲实验中处于拉伸应力下。结果表明，在砂岩三点弯曲试验过程中，随着三点弯曲试验跨度的增大，特征点处的峰值应力呈增大趋势，峰值应力具有明显的区域特征。在垂直方向上，中性层上部特征点处的峰值应力较大，中性层下部特征点处的峰值应力较小。在水平方向上，近场特征点处的峰值应力较高，中场和远场特征点处的峰值应力较小。应力场和变形场有很好的对应关系。上远场峰值应变随着跨度的增加而趋于减小，上近场峰值应变随着跨度的增加先减小后增大。下近场峰值应变随跨度的增加呈先减小后增大的趋势，下远场峰值应变随跨度的增大而波动。能量场依赖于应力场和变形场，表现出明显的区域特征。上部区域的储能和释放能力高于下部区域。不同区域加载储能、回弹能量释放和裂纹扩展能量释放的综合性能可描述为远场<中场<近场。不同跨距的近场能量呈现两级特征。当跨距在140~150 mm之间时，近场能量呈现快速下降趋势，当跨距在150~180 mm之间时，近场能量呈现明显的上升趋势。上部区域的储能和释放能力高于下部区域。不同区域加载储能、回弹能量释放和裂纹扩展能量释放的综合性能可描述为远场<中场<近场。不同跨距的近场能量呈现两级特征。当跨距在140~150 mm之间时，近场能量呈现快速下降趋势，当跨距在150~180 mm之间时，近场能量呈现明显的上升趋势。上部区域的储能和释放能力高于下部区域。不同区域加载储能、回弹能量释放和裂纹扩展能量释放的综合性能可描述为远场<中场<近场。不同跨距的近场能量呈现两级特征。当跨距在140~150 mm之间时，近场能量呈现快速下降趋势，当跨距在150~180 mm之间时，近场能量呈现明显的上升趋势。不同跨距的近场能量呈现两级特征。当跨距在140~150 mm之间时，近场能量呈现快速下降趋势，当跨距在150~180 mm之间时，近场能量呈现明显的上升趋势。不同跨距的近场能量呈现两级特征。当跨距在140~150 mm之间时，近场能量呈现快速下降趋势，当跨距在150~180 mm之间时，近场能量呈现明显的上升趋势。