APPLICATION OF THE RANDOM FIELD METHOD BASED ON FELA IN THE ANALYSIS OF SLOPE EXCAVATION STABILITY CONSIDERING RAINFALL INFILTRATION
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摘要: 黑山共和国南北高速公路项目部分路段处于复理石地区，降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性，给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例，采用有限元极限分析方法（FELA），考虑岩土材料强度的空间变异性，利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场，同时考虑开挖岩层的节理分布，分析边坡在分级开挖过程中，各施工步骤的稳定性和破坏模式。与有限元分析结果相比，随机场条件下，部分情况开挖阶段安全系数低于限值，并出现局部破坏和整体破坏两种形式。结合不饱和土理论，模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟，得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形，使得破坏模式趋向于整体破坏，安全系数分布区间变小。锚杆能带动更多土体进入工作状态，同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同，同等支护条件下，雨季边坡安全系数分布区间更大，且均值明显降低。Abstract: Montenegro's Bar-Boljare highway traverses across the flysch area. Rainfall concentration, spatial variability and stratified distribution of geotechnical materials have brought challenges to the slope construction. Common design method such as slice method and finite element method cannot fully consider the uncertainty of geotechnical material, the results given with uniqueness and certainty cannot reflect the uncertainty of slope stability. Taking a slope of the project as an example, the finite element limit analysis method (FELA) is used to obtain the distribution interval of safety factors considering the spatial variability of the strength of geomaterials and the upper and lower bound limit theorem. Based on the investigation data, the mean value, standard deviation and spatial correlation length of materials were obtained and the two-dimensional random field was reconstructed to describe the shear strength index. Meanwhile, the joint distribution of the excavated rock strata was taken into account to analyze the stabilities and failure modes of each construction step of the slope during the graded excavation. Compared with the results of finite element analysis, the safety factor in part of the excavation stage is lower than the limit value in random field, and there are two forms of failure, namely local failure and overall failure. Combined with the unsaturated soil theory, the infiltration depth of rain water under the condition of heavy rain is simulated and the intensity parameters after reduction are used to recalculate in the saturated area. Through Monte Carlo simulation, the probability density distribution function of safety factor, volume of sliding body, bending moment of retaining wall and internal force of anchor is obtained. Due to the constraint of retaining wall structure on soil deformation, the failure mode tends to be overall failure, and the distribution range of safety coefficient becomes smaller. The bolt can drive more soil into the working state, which also restricts the distribution range of safety coefficient. The failure area of slope in dry season is different from that in rainy season. Under the same supporting conditions, the distribution range of safety coefficient of slope in rainy season is larger, and the mean value is obviously reduced.
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图 4 模拟结果的概率密度曲线及统计指标
Figure 4. Probability density curves and statistical indexes of the simulation results
图 7 降雨前后的概率密度曲线及统计指标
Figure 7. Probability density curves and statistical indexes before and after the rain
表 1 旱季(雨季)情况模拟参数
Table 1. Simulated parameters for dry season and rainy season (data in bracket)
材料名称 容重γ/(kN/m3) 刚度参数 节理方向α/(°) 强度参数 模量E/MPa 泊松比/υ 黏聚力c/kPa 内摩擦角φ/(°) Cov/% Clx/m Cly/m 风化表土 20(21) 15 0.3 — 13(4) 30(24) 10 20 1 复理石 22(24) 750 0.32 — 35(25) 42(30) — — — 复理石(薄弱面) 21(22) 100 0.3 45°顺坡 5(4) 30(24) 20 20 1 基岩 23(24) 1600 0.3 — 110 54 — — — 
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表 2 支护结构物模拟参数
Table 2. Simulated parameters for the support structure
材料名称 材料模型 EA/kN 极限力Fy/kN 间距d/m 模量E/MPa 锚固面积A/(cm2/m) 屈服应力σ0/MPa 极限弯矩My/(kN·m) 泊松比v 重度γkN/m3 分布质量w/(kg/m/m) 锚杆锚固段 Geogrid — — — 195000 200 500 — — — — 锚杆自由段 Connector 420000 3000 2.5 — — — — — — — 喷混挡墙 Plate 315000/m 5000/m — — — — 800 — — 0.25 重力式挡墙 LinerElastic — — — 31500 — — — 0.15 24 —
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表 3 Van Genuchten-Mualem模型模拟参数
Table 3. Simulated parameters for the Van Genuchten-Mualem model
参数名 饱和含水率θs 残余含水率θr 形状参数α 形状参数n L 水平饱和渗透系数Kh/(m/s) 竖向饱和渗透系数Kv/(m/s) 取值 0.41 0.065 2 1.41 0.5 0.01 0.001
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