基于有限元强度折减法的边坡失稳判据统一性研究

Study on Consistence of Slope Stability Criteria Based on the Finite Element Strength Reduction Method

采用有限元强度折减法进行边坡稳定性分析时,常用的计算收敛性、塑性区贯通性和特征点位移突变性等3种失稳判据未能体现出很好的统一性。采用Mohr-Coulomb屈服准则,针对3个典型边坡(坡角α、坡高H),系统分析了不同单元相对尺寸L/H、剪胀角ψ时各种失稳判据的适用性和统一性。结果表明,3种判据下的边坡安全系数均随单元相对尺寸的减小逐渐逼近Spencer解,但依据计算收敛性得到的边坡安全系数偏差普遍较大;单元相对尺寸较大(L/H≥1/30)时,剪胀角取值对计算的收敛性影响显著,而对塑性区贯通和特征点位移突变时机的影响较小。当单元相对尺寸足够小(L/H=1/60)和ψ=0或φ(内摩擦角)时,3种判据具有良好的统一性;边坡破坏过程出现明显的组合破坏特征,受拉破坏区域和塑性区可以构成较为平滑的潜在滑动面,说明采用单一的压剪屈服破坏准则(如M-C屈服准则)将过高估计边坡的安全系数。

When the finite element strength reduction method is applied to analyze slope stability, usu- ally the divergence of numerical calculation, the connectivity of plastic zone and the abruptness of dis- placement of feature parts are taken as the main criteria of slope stability, while the three kinds of in- stability criteria lack consistency. Based on the Mohr-Coulomb yield criterion, three typical slopes （with varying slope angle a and height H） are built. Then the applicability and consistency of the three kinds of stability criterion are analyzed in different conditions, namely varying element size（L/H）, di- lation angle（c） and integral type of element. The characteristics of slope failure in the process of cal- culation are analyzed. The results show that factors of safety with the three stability criteria are grad- ually approaching the Spencer solution when element size is reduced. Meanwhile, when element size is largerthan L/H≥1/30, slope safety factors obtained by divergence of numerical calculation diverge greatly. Moreover,dilation angle has a strong effect on the calculation convergence, but a weak effect on connectivity of plastic zone and abruptness time of displacement of feature parts. When element size is small enough （L/H= 1/60） and ;=0 or φ（ffriction angle）, the three stability criteria have favora- ble consistency. Combined failure characteristics arise during the process of slope failure, and tensile damage region and plastic zone can constitute a smooth potential slip surface, which means that single compression- shear yield failure criterion （such as M-C yield criteria） may lead to larger slope safety factor.