Alomari Esraa, Ng Kam, Khatri Lokendra
Civil and Architectural Engineering and Construction Management, University of Wyoming, Laramie, WY 82071, USA.
Materials (Basel). 2024 Dec 6;17(23):5973. doi: 10.3390/ma17235973.
A new model is developed to predict the mechanical behavior of brittle sandstone under triaxial compression. The proposed model aims to determine the normalized critical crack length (), through which the failure strength () of sandstone can be estimated based on fracture mechanics applied to secondary cracks emanating from pre-existing flaws, while considering the interaction of neighboring cracks. In this study, the wing crack model developed by Ashby and Hallam (1986) was adopted to account for the total stress intensity at the crack tip () as the summation of the stress intensity due to crack initiation and crack interaction. The proposed model is developed by first deriving the and then setting the crack length equal to the . Next, the total stress intensity is set equal to the rock fracture toughness in the original equation of , resulting in an estimate of the . Finally, to evaluate the performance of the proposed model on predicting , theoretical results are compared with laboratory data obtained on sandstone formations collected from Wyoming and the published literature. Moreover, the predicted by our proposed model is compared with those predicted from other failure criteria from the literature. The comparison shows that the proposed model better predicts the rock failure strength under triaxial compression, based on the lowest RMSE and MAD values of 36.95 and 30.93, respectively.
开发了一种新模型来预测脆性砂岩在三轴压缩下的力学行为。该模型旨在确定归一化临界裂纹长度（），基于应用于从既有缺陷产生的次生裂纹的断裂力学，同时考虑相邻裂纹的相互作用，通过该长度可以估算砂岩的破坏强度（）。在本研究中，采用了阿什比和哈勒姆（1986年）开发的翼裂纹模型，将裂纹尖端的总应力强度（）视为裂纹萌生和裂纹相互作用引起的应力强度之和。所提出的模型首先通过推导 然后将裂纹长度设置为 来开发。接下来，在 的原始方程中将总应力强度设置为岩石断裂韧性，从而得到 的估计值。最后，为了评估所提出模型在预测 方面的性能，将理论结果与从怀俄明州采集的砂岩地层获得的实验室数据以及已发表的文献进行了比较。此外，将我们提出的模型预测的 与文献中其他破坏准则预测的结果进行了比较。比较表明，基于分别为36.95和30.93的最低均方根误差（RMSE）和平均绝对偏差（MAD）值，所提出的模型能更好地预测三轴压缩下的岩石破坏强度。
