**5. Conclusions**

1. Two critical parameters were introduced to modify the T–K criterion, i.e., the lamina angle (θ) based on the stress equilibrium equation along the lamina surface, and the lamina friction coefficient (μ*lamina*) related to the different laminated rock type.

2. Stress is prone to concentrate on the lamina when the lamina angle is in the effective low and medium range. The low-angle lamina always induces fractures in the expansively open state with the bigger failure aperture, and the medium-angle lamina always induces fractures in the shear sliding trend. On the contrary, stress is prone to concentrate on the surrounding rock body, when the lamina angle is outside of the effective range, and contributes less to the compressed fractures in the laminated rock.

3. The bedding fractures of the Yanchang Formation in the Himalayan stress field were simulated based on the new rock failure criteria proposed in this work. It is concluded that these bedding fractures tend to propagate under the conditions of lower maximum principal stress, higher minimum principal stress, and larger stratigraphic dip.

**Author Contributions:** Conceptualization, Y.L.; Data curation, Q.W., Z.J. and D.L.; Formal analysis, D.L.; Funding acquisition, W.Y., Z.J. and Y.S.; Investigation, Q.W. and Y.L.; Methodology, Q.W. and Y.L.; Project administration, W.Y., Y.S. and Q.L.; Resources, D.L.; Software, Y.L. and D.L.; Supervision, W.Y., Z.J., Y.S., S.J. and Q.L.; Validation, Y.L.; Visualization, Y.L.; Writing—original draft, Q.W. and Y.L.; Writing—review & editing, Q.W. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was financially supported by the Science Foundation for top-notch innovative talents of China University of Petroleum, Beijing (No. 2462017BJB07), the National Science and Technology Major Project (No. 2016ZX05034-001 and 2017ZX05035-002), and the Key Scientific and Technological Project of Yanchang Oilfield (No. ycsy2015ky-B-01-09).

**Acknowledgments:** We highly appreciate two anonymous reviewers for their valuable and constructive comments, which are significantly helpful for us to improve the quality of our research achievements. Special acknowledgment is also given to the Scientific Research Institute of Petroleum Exploration and Development from the Shaanxi Yanchang Petroleum (Group) Co., Ltd. for providing the samples used in this study.

**Conflicts of Interest:** The authors declare no conflict of interest.
