龙马溪页岩各向异性特征及其强度准则适用性评价

Anisotropic Characteristics of the Longmaxi Shale and Evaluation of the Applicability of Strength Criteria

摘要: 页岩的层理结构导致其力学参数和强度呈现显著各向异性特征，准确评价该特征并优选适用的强度准则对页岩气安全高效开发至关重要。本文以我国龙马溪组页岩为研究对象，通过系统调研国内外文献，收集整理了不同层理角度(0˚~90˚)下的单轴/三轴压缩及巴西劈裂实验数据，明确了页岩抗压强度、抗拉强度、杨氏模量及泊松比的各向异性变化规律及比值范围。基于整理的实验数据，采用网格搜索法确定了SWP、WPP及ML-G等抗压强度准则和Barron、SPW、N-Z、L-P、L-A等抗拉强度准则的材料参数，并计算了不同角度下的理论强度值。通过均方根误差(RMSE)、决定系数(R²)、相对误差(MRE)及最大误差(MaxError)等多维度评价指标体系，对各强度准则的适用性进行了定量评价。结果表明：龙马溪页岩抗压强度各向异性比值范围为0.81~1.70 (横向/纵向)，抗拉强度为0.81~3.10，杨氏模量为0.79~2.47，泊松比为0.84~1.72；Barron准则在抗拉强度预测中表现最优(RMSE = 0.60218, R² = 0.92770)，ML-G准则在抗压强度预测中精度最高(RMSE = 24.19507, R² = 0.90698)。研究结果对于正确认识页岩各向异性特征和页岩气钻井井壁稳定性分析具有重要意义。

Abstract: The bedding structure of shale results in significant anisotropy in its mechanical properties and strength; accurately assessing this characteristic and selecting appropriate strength criteria are crucial for the safe and efficient development of shale gas. This study focuses on the Longmaxi Formation shale in China. Through a systematic review of domestic and international literature, experimental data from uniaxial/triaxial compression and Brazilian split tests at different bedding angles (0˚~90˚) were collected and organized. The study clarified the anisotropic variation patterns and ratio ranges of the shale’s compressive strength, tensile strength, Young’s modulus, and Poisson’s ratio. Based on the compiled experimental data, the grid search method was employed to determine the material parameters for compressive strength criteria such as SWP, WPP, and ML-G, as well as tensile strength criteria including Barron, SPW, N-Z, L-P, and L-A, and to calculate the theoretical strength values at different angles. A multi-dimensional evaluation system comprising root mean square error (RMSE), coefficient of determination (R²), relative error (MRE), and maximum error (MaxError) was used to quantitatively assess the applicability of each strength criterion. The results indicate that the anisotropy ratios for compressive strength in Longmaxi Shale range from 0.81 to 1.70 (transverse/longitudinal), tensile strength ranges from 0.81 to 3.10, Young’s modulus ranges from 0.79 to 2.47, and Poisson’s ratio ranges from 0.84 to 1.72; The Barron criterion performed best in tensile strength prediction (RMSE = 0.60218, R² = 0.92770), while the ML-G criterion demonstrated the highest accuracy in compressive strength prediction (RMSE = 24.19507, R² = 0.90698). These findings are of great significance for accurately understanding the anisotropic characteristics of shale and for analyzing wellbore stability during shale gas drilling.