A Statistical Model of Tensile Strength of Sandstone in Consideration of Size Effect and Loading Mode

YANG Li-yun; WANG Zhi-bin; ZHANG Peng; QIAN Gui-an; ZHANG Dong-bin; LIN Chang-yu

doi:10.11988/ckyyb.202107902022

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Journal of Changjiang River Scientific Research Institute ›› 2022, Vol. 39 ›› Issue (11) : 94-101. DOI: 10.11988/ckyyb.202107902022

ROCKSOIL ENGINEERING

A Statistical Model of Tensile Strength of Sandstone in Consideration of Size Effect and Loading Mode

YANG Li-yun¹, WANG Zhi-bin¹, ZHANG Peng^1,2, QIAN Gui-an³, ZHANG Dong-bin¹, LIN Chang-yu¹

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Abstract

In view of the size effect in the process of rock tensile strength testing, we designed three groups of grey sandstone split tests with different diameters (50 mm, 75 mm and 100 mm) and a group of three-point bending tests. Based on the theory of cumulative failure probability of generalized weakest chain, we investigated into the mutual conversion of the measured tensile strength of grey sandstone splitting tensile strength under geometrically similar and non-geometrically similar conditions. Results show that: 1) When the diameter of disc sample increased from 50 mm to 100 mm, the corresponding average value of split tensile strength gradually decreased in a steep first and then gentle trend. The average tensile strength measured by the three-point bending method is about 1.18-1.4 times of the average split tensile strength. 2) The statistical model of grey sandstone established by the size-effect statistical method can obtain the splitting tensile strength of grey sandstone of different sizes under the premise of a given failure probability. Furthermore, we calculated the equivalent strength coefficient under split loading mode by the approximate integration method, and obtained the calculation formula of equivalent strength coefficient. In association with the calculation method of equivalent strength coefficient under the three-point bending loading mode, the conversion of tensile strength measured by Brazilian splitting and three-point bending loading is realized.

Key words

:grey sandstone / tensile strength / size effect / loading mode / Brazilian splitting / three-point bending / statistical model

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YANG Li-yun, WANG Zhi-bin, ZHANG Peng, QIAN Gui-an, ZHANG Dong-bin, LIN Chang-yu. A Statistical Model of Tensile Strength of Sandstone in Consideration of Size Effect and Loading Mode[J]. Journal of Changjiang River Scientific Research Institute. 2022, 39(11): 94-101 https://doi.org/10.11988/ckyyb.202107902022

References

[1] ISRM. Suggested Methodsfor Determining Tensile Strength of Rock Materials. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1978, 15(3): 99-103.
[2] 杨同, 王宝学, 高谦, 等. 岩石弯曲拉伸试验研究. 勘察科学技术,2004(6):3-5,53.
[3] MASOUMI H,ROSHAN H,HEDAYAT A. Scale-size Dependency of Intact Rock under Point-load and Indirect Tensile Brazilian Testing. Science Letter,2018,15(3):1-15.
[4] 刘宝琛, 张寄生, 杜奇中. 岩石抗压强度的尺寸效应. 岩石力学与工程学报,1998, 17(6): 611-614.
[5] 伍法权,乔磊,管圣功,等.小尺寸岩样单轴压缩试验尺寸效应研究.岩石力学与工程学报,2021,40(5):865-873.
[6] THURO K, PLINNINGER R J, ZAH S, et al. Scale Effects in Rock Strength Properties. Part 1: Unconfined Compressive Test and Brazilian Test∥Rock Mechanics: A Challenge for Society: Proceedings of the ISRM Regional Symposium Eurock 2001, Espoo, Finland, June 4-7, 2001: 169-174.
[7] 邓华锋, 李建林, 朱敏, 等. 圆盘厚径比对岩石劈裂抗拉强度影响的试验研究. 岩石力学与工程学报, 2012, 31(4): 792-798.
[8] 徐快乐, 刘聪颖, 倪鑫, 等. 砂岩巴西劈裂抗拉强度的尺寸效应研究. raybet体育在线院报, 2020, 37(2): 126-129.
[9] 黄正均, 任奋华, 李远, 等. 不同试验方法下岩石抗拉强度及破裂特性.实验技术与管理, 2020, 37(10): 45-49.
[10] LEI W S. A Generalized Weakest-Link Model for Size Effect on Strength of Quasi-brittle Materials. Journal of Materials Science, 2018, 53(2): 1227-1245.
[11] LEI W S.A Framework for Statistical Modeling of Plastic Yielding Initiated Cleavage Fracture of Structural Steels. Philosophical Magazine, 2016, 96(35): 3586-3631.
[12] LEI W S. A Cumulative Failure Probability Model for Cleavage Fracture In Ferritic Steels. Mechanics of Materials, 2016, 93: 184-198.
[13] LEI W S. Fracture Probability of a Randomly Oriented Microcrack under Multi-Axial Loading for the Normal Tensile Stress Criterion. Theoretical and Applied Fracture Mechanics, 2016, 85: 164-172.
[14] LEI W S. Evaluation of the Basic Formulations for the Cumulative Probability of Brittle Fracture with Two Different Spatial Distributions of Microcracks. Fatigue & Fracture of Engineering Materials & Structures, 2016, 39(5): 611-623.
[15] QIAN G, ZHAI J, YU Z,et al. Non-proportional Size Scaling of Strength of Concrete in Uniaxial and Biaxial Loading Conditions. Fatigue & Fracture of Engineering Materials & Structures, 2018, 41: 1733-1745.
[16] WEIBULL W.A Statistical Theory of Strength of Materials. Generalstabens Litografiska Anstalts Frlag, 1939, 151: 1-45.
[17] WEIBULL W. A Statistical Distribution of Function of Wide Applicability. Applied Mechanics, 1951, 18: 293-297.
[18] GRIFFITH A A. The Phenomena of Rupture and Flow in Solids.Philosophical Transactions of the Royal Society:Mathematical Physical and Engineering Sciences, 1920, A221(4):163-198.
[19] CHAU K T. A Three-dimensional Analytic Solution for the Brazilian Test∥Frontiers of Rock Mechanics and Sustainable Development in the 21st Century: Proceedings of the 2001 ISRM International Symposium, the 2nd Asian Rock Mechanics Symposium (ISRM 2001-2nd ARMS). Beijing, China. September 11-14, 2001: 157-160.
[20] 喻勇. 质疑岩石巴西圆盘拉伸强度试验. 岩石力学与工程学报, 2005,24(7): 1150-1157.
[21] 孙训方. 材料力学. 北京: 高等教育出版社, 2009.
[22] 叶剑红,杨洋,常中华,等.巴西劈裂试验应力场解析解应力函数解法.工程地质学报,2009,17(4):528-532.
[23] YE J H, WU F Q, SUN J Z. Estimation of the Tensile Elastic Modulus Using Brazilian Disc by Applying Diametrically Opposed Concentrated Loads. International Journal of Rock Mechanics and Mining Sciences, 2008, 46(3): 568-576.