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Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

100%

Zhou S. , Zhang J. , You L. , Zhang Q.

tom Vol. 23, no. 2

231--241

Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.

Study of anisotropic strength properties of shale

100%

Zheng D. , Miska S. , Ziaja M. , Zhang J.

tom Vol. 36, no. 1

93--112

Shale has been known to be the source of wellbore instability during the drilling process. Organic rich shales are anisotropic due to their laminated structure and chemical properties. The goal of this study is to evaluate anisotropic mechanical properties of shale by triaxial tests, and predict shale anisotropic properties by well logging data interpretation. Shale samples were prepared with bedding plane inclination angles equal to 0 degrees, 45 degrees, and 90 degrees. Young's modulus, shear modulus, and Poisson’s ratio in different directions were measured for a sample with 0 degrees bedding plane inclination angle. Parameters of the stiffness tensor were calculated by mechanical properties. Compressive strength was measured under different confining pressures of 0 psi, 500 psi, 1000 psi, and 1500 psi. The strength properties of shale samples were evaluated by both compressive strength and tensile strength. Simple Plane of Weakness and Modified Cam Clay failure criteria were applied to describe shear failure mechanisms. A scanning electron microscope method was used for the comparison of micro structures between the intact shale sample and failed sample with different bedding plane inclination angles. Well logging data was used to connect experimental lab data and field data. Compressional wave velocity was predicted with different inclination angles by stiffness parameters. The predicted compressional wave velocity for a 45-degree inclination angle showed a perfect fit with the field logging data. Steps of inverse sonic log data to stiffness parameters were shown by a flow chart. The UCS strength for 0 degrees and 45 degrees was predicted by several empirical relations using sonic logging data. The safe mud window for this special shale formation is predicted by experimental data. As shown in experimental results, our shale sample has a weak direction for both failure criteria. Well logging data and experimental data can be connected, especially by sonic log data. However, to predict shale anisotropic strength through well logging still requires more effort. The novelty of the process which connects experimental results and well logging data will be helpful for solving instability problems occurring in shale formation.