Strength criterion for Jurassic sandy mudstone based on energy theory
WANG Xiaoyun1，CHENG Hua1，2，3，RONG Chuanxin1，WANG Zongjin4，YAO Zhishu1，ZHANG Liangliang1
(1. School of Civil Engineering and Architecture，Anhui University of Science and Technology，Huainan，Anhui 232001，China；2. School of Resources and Environmental Engineering，Anhui University，Hefei，Anhui 230022，China；3. Building Structure
and Underground Engineering Anhui Provincial Key Laboratory，Anhui Jianzhu University，Hefei，Anhui 230601，China；
4. China Coal Special Drilling Co.，Ltd.，Hefei，Anhui 230001，China)
Abstract：In order to clarify the physical and mechanical properties，energy evolution law and failure mechanical behavior of the weakly cemented Jurassic sandstone mudstone in the western region，triaxial compression tests are carried out on the weakly cemented Jurassic sandstone mudstone under natural and saturated conditions. Based on the experimental outcomes and the principle of energy conservation，the physical and mechanical characteristics，modes of failure，and energy evolution laws of the sandstone mudstone under both conditions have been determined. Furthermore，an energy intensity criterion for the sandstone mudstone has been developed based on its nonlinear relationship between the density of elastic potential energy and confining pressure，complemented by the provision of an appropriate formula for calculating shear stress. Ultimately，the validity of the energy intensity criterion has been confirmed by comparing it with three classical strength criteria against experimental outcomes. The study shows that，(1) both the peak strength and the softening coefficient of the sandstone mudstone under two different states increase with confining pressure，yet the rate at which the softening coefficient increases is inversely related to the confining pressure；under uniaxial conditions，the failure mode is characterized by splitting tensile rupture，and under triaxial conditions，the failure mode is characterized by shear rupture. (2) Both the total strain energy density and the dissipated energy density of the sandstone mudstone under the two conditions are directly proportional to axial strain，while the elastic energy density increases initially and then decreases as axial strain grows；at the peak stress，the total strain energy density，elastic energy density，and dissipated energy density all show a nonlinear increase with rising confining pressure. (3) The energy intensity criterion is represented as an equilateral but non-isosceles hexagon on the deviatoric plane and as an irregular hexagonal pyramid in the principal stress space，characterized by well-defined physical meanings of its parameters and a simple solution approach. (4) In contrast to other strength criteria，the energy intensity criterion，along with its formula for calculating shear stress，provides greater precision in calculations and covers a wider scope of applications. The research outcomes can offer beneficial insights for the investigation of strength criteria for Jurassic sandstone mudstone in the western areas，as well as for analogous weakly cemented geological formations.
[1] 程 桦，郭龙辉，姚直书，等. 钻井法凿井气–液–固耦合排渣流场及刀盘吸渣口优化[J]. 煤炭学报，2024，49(1)：426–441. (CHENG Hua，GUO Longhui，YAO Zhishu，et al. Research on the gas-liquid-solid coupled slag discharge flow field and optimization of cutterhead slag suction port in shaft drilling[J]. Journal of China Coal Society，2024，49(1)：426–441.(in Chinese))
[2] GUO L H，CHENG H，YAO Z S，et al. CFD-DEM method is used to study the multi-phase coupling slag discharge flow field of gas-lift reverse circulation in drilling shaft sinking[J]. Scientific Reports，2024：13853.
[3] 程 桦，郭龙辉，姚直书，等. 钻井法凿井气举反循环多相排渣运移规律及其洗井参数优化试验研究[J]. 中国矿业大学学报，2024，53(2)：224–237.(CHENG Hua，GUO Longhui，YAO Zhishu，et al. Experimental study on transport law of multiphase slag discharge and optimization of well washing parameters in gas lift reverse circulation of drilling shaft sinking[J]. Journal of China University of Mining and Technology，2024，53(2)：224–237.(in Chinese))
[4] ZHANG Z Z，GAO F. Experimental investigation on the energy evolution of dry and water-saturated red sandstones[J]. International Journal of Mining Science and Technology，2015，25：383–388.
[5] WANG C L，HE B B，HOU X L，et al. Stress-energy mechanism for rock failure evolution based on damage mechanics in hard rock[J]. Rock Mechanics and Rock Engineering，2020，53：1 021–1 037.
[6] 李子运，吴 光，黄天柱，等. 三轴循环荷载作用下页岩能量演化规律及强度失效判据研究[J]. 岩石力学与工程学报，2018，37(3)：662–670.(LI Ziyun，WU Guang，HUANG Tianzhu，et al. Variation of energy and criteria for strength failure of shale under traixial cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(3)：662–670.(in Chinese))
[7] MENG Q B，ZHANG M W，HAN L J，et al. Effects of acoustic emission and energy evolution of rock specimens under the uniaxial cyclic loading and unloading compression[J]. Rock Mechanics and Rock Engineering，2016，49：3 873–3 886.
[8] 张 尧，李波波，许 江，等. 基于能量耗散的煤岩三轴受压损伤演化特征研究[J]. 岩石力学与工程学报，2021，40(8)：1 614–1 627. (ZHANG Yao，LI Bobo，XU Jiang，et al. Study on triaxial compression damage evolution characteristics of coal based on energy dissipation[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(8)：1 614–1 627.(in Chinese))
[9] LI D Y，SUN Z，XIE T，et al. Energy evolution characteristics of hard rock during triaxial failure with different loading and unloading paths[J]. Engineering Geology，2017，228：270–281.
[10] 贾 蓬，毛松泽，孙占阳，等. 冻融损伤砂岩的能量演化及分段本构模型[J]. 中南大学学报：自然科学版，2023，54(3)：908–919.(JIA Peng，MAO Songze，SUN Zhanyang，et al. Energy evolution and piecewise constitutive model of freeze-thaw damaged sandstone[J]. Journal of Central South University：Science and Technology，2023，54(3)：908–919.(in Chinese))
[11] MENG Q B，LIU J F，HUANG B X，et al. Effects of confining pressure and temperature on the energy evolution of rocks under triaxial cyclic loading and unloading conditions[J]. Rock Mechanics and Rock Engineering，2022，55(2)：773–798.
[12] 赵延林，谭 涛，张春阳，等. 水–力耦合作用下砂岩力学特性与能量演化及强度准则适用性分析[J]. 煤炭学报，2023，48(9)： 3 323–3 335.(ZHAO Yanlin，TAN Tao，ZHANG Chunyang，et al. Mechanical properties and energy evolution and the applicability of strength criteria of sandstone under hydro-mechanical coupling[J]. Journal of China Coal Society，2023，48(9)：3 323–3 335.(in Chinese))
[13] 刘新喜，李 玉，范子坚，等. 干湿循环作用下单裂隙炭质页岩能量演化与破坏特征研究[J]. 岩土力学，2022，43(7)：1 761–1 771. (LIU Xinxi，LI Yu，FAN Zijian，et al. Energy evolution and failure characteristics of single fissure carbonaceous shale under drying-wetting cycles[J]. Rock and Soil Mechanics，2022，43(7)： 1 761–1 771.(in Chinese))
[14] LABUZ J F，ZANG A. Mohr-Coulomb failure criterion[J]. Rock Mechanics and Rock Engineering，2012，45(6)：975–979.
[15] 李 斌，刘艳章，林坤峰. 非线性Mohr-Coulomb准则适用范围及其改进研究[J]. 岩土力学，2016，37(3)：637–646.(LI Bin，LIU Yanzhang，LIN Kunfeng. Application scope of nonlinear Mohr- Coulomb criterion and its modification[J]. Rock and Soil Mechanics，2016，37(3)：637–646.(in Chinese))
[16] 汪 斌，朱杰兵，邬爱清，等. 高应力下岩石非线性强度特性的试验验证[J]. 岩石力学与工程学报，2010，29(3)：542–548.(WANG Bin，ZHU Jiebing，WU Aiqing，et al. Experimental validation of nonlinear strength property of rock under high geostress[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(3)：542–548. (in Chinese))
[17] HOEK E. Strength of jointed rock masses[J]. Géotechnique，1983，23(3)：187–223.
[18] HOEK E. Estimating Mohr-Coulomb friction andcohesion values from the Hoek-Brown failure criterion[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1990，27(3)：227–229.
[19] ALEJANO L R，BOBET A. Drucker-Prager criterion[J]. Rock Mechanics and Rock Engineering，2012，45(6)：995–999.
[20] 郭建强，蒋建国，刘新荣，等. 基于弹性应变能D–P强度准则修正[J]. 土木工程学报，2021，54(6)：110–116.(GUO Jianqiang，JIANG Jianguo，LIU Xinrong，et al. Modification of Drucker-Prager strength criterion based on the elastic strain energy[J]. China Civil Engineering Journal，2021，54(6)：110–116.(in Chinese))
[21] DA FONTOURA S A B. Lade and modified Lade 3D rock strength criterion[J]. Rock Mechanics and Rock Engineering，2012，45(6)： 1 001–1 006.
[22] 刘德稳，孙微微，邓勇亮，等. 对“基于Lade-Duncan和SMP两种强度准则的岩石残余应力研究”的讨论[J]. 岩石力学与工程学报，2014，33(1)：209–212.(LIU Dewen，SUN Weiwei，DENG Yongliang，et al. Discussion on“Study of residual stress of rock based on Lade-Duncan and SMP strength criterion”[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(1)：209–212.(in Chinese))
[23] LI Z，ZHOU H，HU D W，et al. Yield criterion for rocklike geomaterials based on strain energy and CMP model[J]. International Journal of Geomechanics，2020，20(3)：04020013.
[24] HAO T S，LIANG W G. A new improved failure criterion for salt rock based on energy method[J]. Rock Mechanics and Rock Engineering，2016，49：1 721–1 731.
[25] LIU X S，NING J G，TAN Y L，et al. Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading[J]. International Journal of Rock Mechanics and Mining Sciences，2016，85：7–32.
[26] 张亮亮，程 桦，王晓健. 常规三轴压缩下高强混凝土能量演化与破坏准则[J]. 吉林大学学报：工学版，2025，待刊.(ZHANG Liangliang，CHENG Hua，WANG Xiaojian. Energy evolution law and failure criterion of high strength concrete under conventional triaxial compression[J]. Journal of Jilin University：Engineering and Technology，2025，to be pressed.(in Chinese))
[27] 乔 兰，王 旭，李 远. 深部花岗闪长岩破坏过程声发射及特征应力特性试验研究[J]. 岩石力学与工程学报，2014，33(增1)： 2 773–2 778.(QIAO Lan，WANG Xu，LI Yuan. Study of acoustic emission and characteristic stress in deep granodiorite failure process[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(Supp.1)：2 773–2 778.(in Chinese))
[28] 刘天为，何江达，徐文杰. 大理岩三轴压缩破坏的能量特征分析[J]. 岩土工程学报，2013，35(2)：395–400.(LIU Tianwei，HE Jiangda，XU Wenjie. Energy properties of failure of marble samples under triaxial compression[J]. Chinese Journal of Geotechnical Engineering，2013，35(2)：395–400.(in Chinese))
[29] 周 辉，李 震，杨艳霜，等. 岩石统一能量屈服准则[J]. 岩石力学与工程学报，2013，32(11)：2 170–2 184.(ZHOU Hui，LI Zhen，YANG Yanshuang，et al. nifeied energy yield criterion of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(11)：2 170–2 184.(in Chinese))
[30] 张 佳. 岩石压缩能量演化规律及非线性演化模型研究[J]. 煤炭科学技术，2021，49(8)：73–80.(ZHANG Jia. Study on evolution law of rock compression energy and nonlinear evolution model[J]. Coal Science and Technology，2021，49(8)：73–80.(in Chinese))
[31] YOU M Q. Three independent parameters to describe conventional triaxial compressive strength of intact rocks[J]. Journal of Rock Mechanics and Geotechnical Engineering，2010，2(4)：350–356.
[32] 张 磊，刘保国. 考虑抗拉强度的岩石强度准则对比分析[J]. 工程力学，2016，33(11)：201–207.(ZHANG Lei，LIU Baoguo. A comparison study of rock strength criterion considering tensile strength[J]. Engineering Mechanics，2016，33(11)：201–207.(in Chinese))
2025, Vol. 44 
