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Understanding bone strength is important when assessing bone diseases and their treatment. Bending experiments are often used to determine strength. Then, flexural stresses are calculated from elastic bending theory. With a brittle failure criterion, the maximum flexural tensile stress is equated to (nominal) strength. However, bone is not a perfectly brittle material. A quasi-brittle failure criterion is more appropriate. Such an approach allows for material failure to occur before full fracture. The extent of the subcritical damage domain then introduces a length scale. The intrinsic strength of the bone is calculated from the critical load at fracture and the failure process zone dimensions relative to the specimen size. We apply this approach to human cortical bone specimens extracted from a femur. We determine strength measures in the untreated reference state and after treatment with the selective estrogen receptor modulator raloxifene. We find that the common nominal strength measure does not distinguish between treatments. However, the dimensions of the failure process zone differ between treatments. Intrinsic strength measures then are demonstrated as descriptors of bone strength sensitive to treatment. An extrapolation of laboratory data to whole bone is demonstrated. 

Abstract Fluids with different densities often coexist in subsurface fractures and lead to variable‐density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable‐density fluids in vertical fractures by combining three‐dimensional (3D) pore‐scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce the unstable runlet using 3D numerical simulations and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh‐Taylor instability (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough‐walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications. 

contain conspicuous acknowledgement of where and by whom the paper was presented. ABSTRACT: Shear strength along discontinuities plays a crucial role in the stability of rock structures. The development of geophysical methods to remotely monitor and assess changes in shear strength is essential to the identification of rock hazards that can lead to the loss of life and failure of civilian infrastructure. In this study, compressional and shear ultrasonic waves were used to monitor slip along discontinuities (with different surface profiles) during shearing. A series of laboratory direct shear experiments were performed on two gypsum blocks separated by a frictional discontinuity. The gypsum blocks had perfectly matched contact surfaces with a half-cycle sine wave profile that spanned the central third of the discontinuity, surrounded by planar surfaces. The amplitude of the half-cycle sine wave was varied and ranged between 2 to 10 times the height of the asperities. Compressional, P, and shear, S, ultrasonic waves were continuously transmitted and recorded throughout the shearing process, while Digital Image Correlation (DIC) was used to capture surface displacements. At low normal stresses, distinct maxima in the normalized P and S wave transmitted amplitudes occurred before shear failure in regions where dilation was observed. Where dilation was not detected, an increase in transmitted wave amplitude was observed, even after the peak shear stress was achieved. At high normal stresses, dilation was suppressed, which was associated with an increase in wave amplitude with shear stress until the peak, and then a decrease in amplitude. Monitoring changes in transmitted wave amplitude is a potential method for the detection of dilation along rock discontinuities.