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采用量纲分析的方法给出直边坡几何参数和物理力学参数决定边坡稳定系数的通式。首先,边坡高度H和边坡角α被确定为直边坡的几何参数,抗拉强度σt、黏聚力C、内摩擦角和岩土比重γ被确定为直边坡的物理力学参数;其次,采用量纲分析的方法,形式上给出边坡稳定系数F的通式,F=qαpα(C/Hγ)pcφpφ(σt/Hγ)pσ;再次,为了得到待定系数q和待定指数pα、pc、pφ、pσ,通过最小二乘法对数万个计算结果进行回归分析(每个结果都是通过FLAC计算将确定的直边坡参数与它的稳定系数形成对应)。结果表明,在一定的取值范围内,边坡稳定系数的表达式为F=4.63/α(C/Hγ)0.17φ0.83。可见,受MohrCoulomb和拉应力两个强度准则控制的岩土材料形成的直边坡的稳定性受无量纲的黏聚力、边坡角(角度)、内摩擦角(角度)的控制,与抗拉强度关系不大。无量纲黏聚力是黏聚力除以边坡高度和岩土比重。
By using the method of dimension analysis, the general formula for determining the slope stability coefficient is given by the geometric parameters and the physical and mechanical parameters of straight slope. First, the slope height H and the slope angle α are determined as the geometrical parameters of the straight slope, and the tensile strength σt, cohesion C, internal friction angle φ and the geotechnical specific gravity γ are determined as the physical-mechanical parameters of the straight slope ; Secondly, using the method of dimension analysis, the general formula of slope stability factor F is formally given, and F = qαpα (C / Hγ) pcφpφ (σt / Hγ) pσ. Third, in order to obtain the undetermined coefficient q and the undetermined index pα , Pc, pφ, pσ. Regression analysis was performed on the tens of thousands of calculated results by the least-square method (each result corresponds to a straight-slope parameter determined by FLAC calculation to its stable coefficient). The results show that within a certain range of values, the slope stability factor is expressed as F = 4.63 / α (C / Hγ) 0.17φ0.83. It can be seen that the stability of the straight slope formed by the geomaterials controlled by MohrCoulomb and tensile strength is controlled by dimensionless cohesion, slope angle (angle), internal friction angle (angle) Tensile strength has little to do. Dimensionless cohesion is cohesion divided by the slope height and geotechnical gravity.