网格自适应有限元极限分析在边坡稳定分析中的应用

发布时间：2019-06-08 07:06

【摘要】：基于有限元极限分析理论,不需要像传统极限分析方法在计算之前对破坏形式进行假设,结构的破坏形式通过计算自动寻找出。为了避免Mohr-Coulomb屈服准则屈服面导数存在奇异点,通用的非线性规划算法无法直接应用的问题,对Mohr-Coulomb屈服准则进行二次圆锥优化,改写为一个等式约束和一个二阶锥约束,并写入到极限分析公式推导中。对材料的理想弹塑性假设,将研究区域划分为两种:塑性滑动区域和弹性区域;强度折减过程中安全系数最终是由滑动带的抵抗力决定的,材料的内摩擦角φ和粘聚力c直接影响了抵抗力的大小,滑动带为边坡失稳的塑性流动区域。基于有限元极限分析数值解的精度在很大程度上依赖网格布局,而安全系数的求解误差主要来源于塑性滑动区,对于塑性区网格进行局部加密优化成为提高有限元计算精度的重要途径。(1)在对初始粗划分网格的模型计算分析的基础上,将离散后单元的应力应变数据导出,依据预先设定的应力/应变阀值,通过优化后的屈服准则对导出的单元衡量其屈服准则残余或等效变形,标记出塑性区域网格单元,对标记网格单元即整个塑性滑动区域进行网格局部优化处理,在一次优化过程中指定区域的单元数量增加一倍,区域重新规划后网格单元在数量和质量均有所提高,再一次对模型计算。以上过程为网格自适应有限元计算系统一次迭代,循环迭代直到达到预设计算精度。网格自适应有限元算法实现了网格划分过程中局部区域有目的自动化加密,结合实际工程二维边坡例证了自适应算法使有限元计算在效率和精度上得到很大提升。(2)基于网格自适应有限元算法,从数值的角度揭示出边坡失稳的动态机理,边坡失稳进程中,塑性变形区域由坡角处不断沿滑动带方向向坡顶发展,当塑性区域发展到一定位置时,剩余尚处于弹性变形的区域应力与塑性区残余应力之和不足以抵抗下滑力时,坡顶区域土体开始受拉,提供拉应力抵抗下滑力,直到拉应力达到土的最大抗拉强度,此时土体完全发生破坏,边坡整体开始滑动。边坡失稳的外部监测点的位移-时间曲线中,结构变形有弹性阶段过渡到弹塑性阶段时会出现一个明显的转折点,此时处在滑块上的监测点和没有处在滑块上的监测点位移-时间曲线会出现分化,线性发生变化,可以作为预测预报信息点。在应力/应变-时间曲线中坡顶出现拉应力时,外部扰动已达到边坡失稳的极限状态,坡顶拉裂缝的出现可以作为判断边坡破坏的最后阶段。(3)边坡稳定对土材料参数敏感性分析,不同的弹性模量和泊松比值下,计算安全系数和应力/应变云图以及塑性区的大小、位置等各方面均无差异,模型计算中弹性模量和泊松比仅作为中间变量引入计算,对结果无实质性影响。重度的变化直接影响着边坡的安全系数,对滑动带的位置和大小无影响,塑性区残余应力大小未发生变化。粘聚力和内摩擦角对塑性区位置的影响是相反的,随着两者值的增大,滑动带以其最下端位置为轴心分别向下和向上转动,粘聚力越大发生深层滑坡的可能性越大,内摩擦角越大发生浅层滑坡的可能性越大,两者相反的特点也正好解释了在有限元极限分析计算中强度折减为什么要使两者同步折减。另外内摩擦角和粘聚力的大小还影响着塑性区残余应力的大小,粘聚力越大塑性区残余应力越小,假如无限大,那么接近脆性,残余应力几乎为0,这和事实相符,而内摩擦角越大,塑性区残余应力越大。
[Abstract]:Based on the finite element limit analysis theory, it is not necessary to assume the damage form before the calculation of the traditional limit analysis method, and the damage form of the structure is automatically searched through calculation. In order to avoid the singular point of the yield surface derivative of the Mohr-Coulomb yield criterion, the general nonlinear programming algorithm can't be applied directly, and the Mohr-Coulomb yield criterion is optimized by the quadratic cone, which is rewritten into an equality constraint and a second order cone constraint, and is written into the limit analysis formula derivation. The study area is divided into two types: plastic sliding area and elastic area. The safety factor in strength reduction is determined by the resistance of the sliding band, and the internal friction angle and the cohesive force c of the material directly influence the resistance. The sliding band is the plastic flow area of the slope instability. The precision of the numerical solution based on the finite element limit is dependent on the grid layout to a large extent, and the solution error of the safety factor is mainly from the plastic sliding area, and the local encryption optimization for the plastic area grid is an important way to improve the calculation accuracy of the finite element. (1) the stress-strain data of the discrete back unit is derived on the basis of the model calculation analysis of the initial rough dividing grid, the yield criterion residual or equivalent deformation of the derived unit is measured by the optimized yield criterion according to the pre-set stress/ strain threshold value, a plastic area grid unit is marked, the whole plastic sliding area of the marked grid unit, i.e. the whole plastic sliding area is subjected to a grid local optimization process, the number of units in the specified area is doubled in the one-time optimization process, and the number and the quality of the grid units are improved after the area re-planning, And then calculating the model again. The above process is a one-time iteration of the grid self-adaptive finite element calculation system, and the loop iteration is repeated until the preset calculation accuracy is reached. In this paper, the mesh self-adaptive finite element algorithm is used to realize the automatic encryption of the local area in the process of grid division, and the two-dimensional slope of the project is used to illustrate the adaptive algorithm to make the calculation of the finite element greatly improved in efficiency and precision. (2) Based on the mesh self-adaptive finite element method, the dynamic mechanism of the slope instability is revealed from the angle of the numerical value, and the plastic deformation area is continuously developed in the direction of the sliding belt in the direction of the sliding belt from the angle of the slope, and when the plastic region is developed to a certain position, when the sum of the residual stress of the residual stress in the elastic deformation and the residual stress of the plastic region is insufficient to resist the sliding force, the soil body in the top region of the slope is in tension, and the tensile stress is provided to resist the sliding force until the tensile stress reaches the maximum tensile strength of the soil, The whole slope of the side slope is started to slide. in the displacement-time curve of the external monitoring point of the slope instability, a significant turning point appears when the structural deformation is in the elastic phase transition to the elastic-plastic phase, the monitoring point on the slide block and the displacement-time curve of the monitoring point which are not on the slide block can be differentiated, The linear change can be used as the prediction information point. In the case of tensile stress in the top of the slope in the stress/ strain-time curve, the external disturbance has reached the limit state of the slope instability, and the occurrence of the slope-top-pull crack can be used as the final stage to judge the slope failure. (3) The stability of the slope has no difference in the sensitivity analysis of soil material parameters, different elastic modulus and Poisson's ratio value, the calculation safety factor and the stress/ strain cloud picture and the size and position of the plastic zone, In the model calculation, the elastic modulus and the Poisson's ratio are calculated only as the intermediate variable, and there is no material effect on the results. The severe change directly affects the safety factor of the slope, and has no effect on the position and size of the sliding belt, and the residual stress in the plastic zone is not changed. the influence of the cohesion and the internal friction angle on the position of the plastic region is the opposite, with the increase of the value of the two, the sliding belt is rotated downwards and upwards at the most lower end position of the sliding belt, the greater the cohesion is, the greater the possibility of the deep landslide, The larger the internal friction angle, the greater the probability of the shallow landslide, and the opposite characteristics of the two also explain the reason why the strength is reduced in the finite element limit analysis calculation. In addition, the size of the residual stress in the plastic region is also affected by the size of the internal friction angle and the cohesive force, and the smaller the residual stress in the plastic region, the smaller the residual stress in the plastic region, if it is infinite, the residual stress is almost zero, which is in line with the fact, and the larger the internal friction angle, the greater the residual stress in the plastic region.
【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU43

【共引文献】