1 引言
岩体的强度和变形行为在很大程度上取决于岩石的"完整 "强度和不连续面的强度,不连续面如节理、层面、叶脉等。当岩体中存在大部分这样的弱面时,岩体就会产生各向异性的强度和变形行为,在这种岩体中开挖的边坡其滑动面不仅沿着弱面破坏,也在岩体内的岩桥里发生破坏,因而评估这种类型的边坡稳定性非常困难。
澳大利亚的Pilbara矿就处在这种岩体中,边坡的破坏不仅发生在单个台阶,也发生在多个台阶中,下面左图所示的是一个边坡破坏实例,右图所示的是各项异性岩体模型。
2 文献调查
由于Pilbara矿岩体各向异性导致的复杂性,因此进行了许多岩体强度和边坡稳定性研究。下面列出了GeotechSet数据集内的相关文献:
[1] Pit Slope Design in Pilbara Iron Deposits – Deposit A West Angelas, Western Australia
[2] Limit Equilibrium Analysis of a Planar Sliding Example in the Pilbara Region of Western Australia – Comparison of Modelling Discrete Structure to Three Anisotropic Shear Strength Models
[3] Applying unsaturated soil mechanics principals to assess the stability of large open pit slopes developed in overburden materials in the Pilbara, Australia
[4] Application of ANOVA and Tuckey-Cramer statistical analysis to test the similarity of rock mass strength properties across the banded Iron formations of the Pilbara region in Western Australia
[5] The numerical simulation of anisotropic rock mass shear strength in Hamersley rock formations of the Pilbara using ABAQUS
[6] An investigation into the shear strength of bedding planes in shale materials from the Hamersley group rocks of the Pilbara region in Western Australia
[7] The shear strength of bedding partings in shales of the Pilbara: the similarity of non-dilatational angles, mineralogy relationships, and nominal roughness
[8] Utilising data science to test similarity of rock mass unit strength distributions in the Pilbara
[9] The effect of anisotropy orientation on the sedimentary rock strength estimated by point load testing strength, Pilbara, Australia
[10] The intact rock strength of anisotropic rocks in the Pilbara: the use of field estimations, practical limitations of calibrations and statistical bias
[11] Preliminary review of the geotechnical characteristics and shear strength estimates of small scale anisotropic waveform formations of the Pilbara, Western Australia
[12] Geotechnical optimisation of Southern Ridge Cutback 3 at Tom Price mining operations
[13] Practical Use of the Ubiquitous-Joint Constitutive Model for the Simulation of Anisotropic Rock Masses
[14] Directional shear strength models in 2D and 3D limit equilibrium analyses to assess the stability of anisotropic rock slopes in the Pilbara region of Western Australia
[15] Three-Dimensional Analysis of Pit Slope Stability in Anisotropic Rock Masses
[16] Three-dimensional limit equilibrium slope stability analyses, method, and design acceptance criteria uncertainties
3 2D和3D安全系数比较
Rocscience在最近的一篇论文[On the comparison of 2D and 3D stability analyses of an anisotropic slope]中对Pilbara矿的边坡稳定性进行了参数化研究(parametric study),分析了三种不同模型的安全系数:第一个是真三维模型,第二个是从真三维模型切出来的一个二维模型,第三个是拉伸(extrude)这个二维模型形成的伪三维模型。
然后比较在不同条件下计算的安全系数,这些变化的条件包括: (1) 使用了Cuckoo和Particle Swarm搜索方法; (2) 使用了不同的滑动面数量,也就是搜索方法中的Nests和Particles的数值;(3) 使用了不同的边坡深度限制(不设置和15m); (4) 使用了不同的材料模型,线性(Mohr-Coulomb)和非线性(Generalized Hoek-Brown, Shear-Normal, Barton-Bandis)。参数研究的结果显示:
(1) 对于真3D,非线性材料模型计算的安全系数较低,线性材料模型计算的安全系数较高;滑动面的数量设置的越大,计算的安全系数越小;边坡深度限制产生出较高的安全系数。
(2) 对于2D,计算的安全系数比3D小,大约小25%,线性模型计算的安全系数比非线性模型高,大约高30%左右 ,PS搜索方法比Cuckoo计算的安全系数低。
(3) 在伪3D(Pseudo 3D)计算中, 拉伸的长度影响着安全系数,边坡深度限制产生出较高的安全系数。
4 结束语
在高度各向异性的岩体中,3D分析能够计算出更真实的破坏面,3D分析比2D分析计算出来的安全系数高,这是由于3D计算正确地包含了端部效应(end effects)和不同方向的强度,在二维分析中不可能包含这些因素,非线性材料模型计算出较低的安全系数。因此如果边坡的几何形状、破坏机理或者材料强度的空间变异很大,应该进行真三维稳定性分析。Pilbara矿的边坡是一个非常好的岩体各向异性案例,今后还将继续对此进行研究。
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