Beam theory is a proxy for the behavior of intact, deforming roof strata above underground openings. Strong, stiff, intact strata have the ability to store significant strain energy when underground openings have large spans, as is typical of longwall operations. When strata fail, they may release some or all of this strain energy. Released energy is partitioned between fracture, thermal, and seismic energy. The tensile failure surface in simply supported beams is predicted to be free of shear stress. This prediction and the kinematic inability of crack slip during fracture make significant dissipation of energy by friction unlikely. In this study, the failure energy partitioning of Nugget Sandstone specimens is examined. Tensile fractures in specimens were induced using three-point loading tests. Elastic waves emanating from fracture events were recorded using an array of accelerometers. Accelerometers were placed within two crack lengths of the fracture surface, and the acceleration records are similar to strong motion seismic records. Spectral analysis was performed and used to develop synthetic, well-behaved, acceleration signals. Synthetic velocity signals were used to estimate radiated seismic energy generated by fracture. These estimates of radiated seismic energy demonstrate a potential means to constrain the minimum seismic partition. Fracture testing was performed on additional samples to estimate the fracture toughness of the sandstone. Synthesis of this data demonstrate a potential means to constrain a maximum seismic partition. Bounding the seismic partition for this type of fracture event could aid the detection and evaluation of seismicity emanating from longwall operations. Having better information about the location and magnitude of mining-induced seismicity within longwall overburdens could lead to better understanding of extraction sequencing and rock behavior in general. These energy estimates also support the hypothesis that dissipation of thermal energy by friction is small in bending tensile failure.

中文翻译：

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块状砂岩试样三点加载试验中拉伸破坏后的能量分配

梁理论代表了地下开口上方完整、变形的屋顶地层的行为。当地下洞口具有大跨度时，坚固、坚硬、完整的地层能够储存显着的应变能，这是长壁作业的典型特征。当地层发生故障时，它们可能会释放部分或全部这种应变能。释放的能量在断裂能、热能和地震能之间分配。预计简支梁的拉伸破坏面没有剪应力。这种预测和断裂过程中裂纹滑移的运动学无能使得摩擦不太可能显着耗散能量。在这项研究中，检查了块状砂岩标本的破坏能量分配。使用三点加载试验诱导试样中的拉伸断裂。使用一系列加速度计记录从断裂事件发出的弹性波。加速度计被放置在断裂面的两个裂纹长度内，加速度记录类似于强运动地震记录。进行了频谱分析并用于开发合成的、表现良好的加速度信号。合成速度信号用于估计裂缝产生的辐射地震能量。这些辐射地震能量的估计证明了一种限制最小地震分区的潜在手段。对额外的样品进行断裂测试以估计砂岩的断裂韧度。该数据的综合证明了一种限制最大地震分区的潜在手段。为这种类型的裂缝事件确定地震分区的边界可以帮助检测和评估长壁作业产生的地震活动。更好地了解长壁覆盖层内采矿引起的地震活动的位置和震级，可以更好地了解一般的开采顺序和岩石行为。这些能量估计也支持这样的假设，即在弯曲拉伸破坏中摩擦热能的耗散很小。