PSI - Issue 45
Ali et al. / Structural Integrity Procedia 00 (2023) 000 – 000
Zulfiqar Ali et al. / Procedia Structural Integrity 45 (2023) 60 – 65
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It was observed that the gradient change in the first cycle governs the separation point in the TMM, and it is not related to the curve of the second cycle. Thus, an effective approach to applying and interpreting the TMM is by analyzing the gradient change in the stress-tangent modulus curve in the first cycle after preloading the specimen. This can simply be accomplished with a change of gradient function, which estimates partial derivatives by calculating the gradient of a given vector based on known values of the function at specific points. Moreover, since the tangent modulus in most of the rocks shows an increasing trend until the load exceeds the previously applied maximum stress, the change is the gradient can simply be inferred as the peak value attained, hence a function which returns a vector with local maxima (peak) of the input data can also be used. Alternatively, we can identify all the change points at which the statistical property (mean and slope) of the tangent modulus curves changes abruptly. The “changepts” function is the best tool for the job, detail formulation of which can be found in (Killick et al. 2012). In Fig. 4(a) “findpeak” was used in combination of “changepoi nt ” functions to approximate the gradient change in the stress-tangent modulus curve. The gradient change was observed to occur at the approximate applied prestress levels, yielding a FR value of 0.94, which is a very good indication of the rock stress memory.
TMM
Modified TMM
Modified TMM
TMM
Fig. 4. TMM and Modified TMM curves of Sandstone specimen showing measured and applied stresses.
We applied this technique to all the rock specimens subjected to the time delay and found that the modified method was consistent and able to detect gradient change in the tangent modulus curves of all rock types regardless of the time delay. The effect of the time delay is significantly reduced, and the resulting FR values fall within the acceptable range of 0.9 to 1.1. The results for all rock types tested under various time delays are shown in Fig. 5 which is consistent with DRA results reported in Ali et al. 2022.
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