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Published in C. R. Kitchin, Astrophysical Techniques, 2020
The final stage of self-calibration is required for optical systems and for radio systems when the baselines become more than a few kilometres in length because the atmospheric effects then differ from one telescope to another. Under such circumstances with three or more elements, we may use the closure phase that is independent of the atmospheric phase delays. The closure phase is defined as the sum of the observed phases for the three baselines made by three elements of the interferometer. It is independent of the atmospheric phase delays as we may see by defining the phases for the three baselines, it in the absence of an atmosphere to be ϕ12, ϕ23 and ϕ31 and the atmospheric phase delays at each element as a1, a2 and a3. The observed phases are then ϕ12+a1−a2ϕ23+a2−a3ϕ31+a3−a1
Experimental and analytical investigations on strength and deformation behaviour of red sandstone under conventional triaxial compression
Published in European Journal of Environmental and Civil Engineering, 2023
Hai-Ling Shi, Lun-Yang Zhao, Qi-Zhi Zhu
In Figure 4, the peak strength of the tested specimens is observed to increase substantially with the increase in confining pressure. The axial stress–strain curves initially show a non-linear (concave) deformation, which usually results from the closure of pre-existing micro-cracks and pores. Furthermore, this stage of micro-cracks and pores closure also depends on the confining pressure. With the increase in confining pressure, this stage gradually weakened. This is the consequence of the confining pressure acting to close the pre-existing micro-cracks and pores prior to the start of deformation. After the micro-cracks and pores closure phase, the stage of elastic deformation dominates the linear portions of the stress–strain curves. With the continuous increase in axial deformation, the stress–strain curves begin to deviate from the linear behaviour, marking the yielding of the specimens. This is the so-called strain hardening phase. It is noted that when the deviatoric stress reaches a critical value (peak strength), plastic dilation failure occurs and the damage increases rapidly, leading to the failure of rock specimens. Due to the limitations of the testing equipment, we failed to obtain the residual strength after the strain softening stage. However, it is still possible to tentatively conclude from the curves around peak strengths that the confining pressure influences the failure modes of the specimens. More details on this point will be addressed in Subsection 3.3.