Face Stability of Shield Tunnel in Sandy Cobble Stratum with Continuum-Based Discrete Element Method
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摘要: 为探究砂卵石地层中盾构开挖工作面失稳现象的机理，采用CDEM （continuum-based discrete element method）可变形块体离散元方法，建立准连续介质模型，对砂卵石土三轴压缩试验开展数值模拟，以分析其细观力学特性；基于“颗粒流动”、“土拱效应”、“超挖出土”等特点，通过平面三角块体离散元建立模拟砂卵石地层盾构开挖面超挖出土的二维动态离散元模型，研究土拱效应、空洞区发展等开挖面失稳的渐进演化机制. 研究结果表明：砂卵石土三轴压缩试验宏观应力应变曲线可分为线弹性阶段、弹塑性阶段、理想塑性阶段；卵石作为粗粒相颗粒存在骨架增强作用，砂卵石接触界面对宏观强度具有弱化作用；通过以土拱效应为标定准则的Hopper Flow标定试验可有效得到不同尺度平面三角形离散单元摩擦角的转换关系；土拱效应显著存在于开挖面前方并随着开挖面超挖出土渐进发展，达到极限状态后逐渐破坏消散；空洞区始于螺旋输送机底部，随超挖出土逐步向上方和前方扩展，最终在击穿承载土拱后到达地表，形成“水滴状”空洞区；从不同角度提出了三类超挖量的控制标准.Abstract: The instability mechanism of shield tunnel excavation working face in a sandy cobble stratum was explored, and the CDEM (continuum-based discrete element method) was adopted to establish a quasi-continuous numerical model. Triaxial compression tests of sand-cobble soil were carried out numerically to analyse its macro–mesoscopic mechanical characteristics. Based on the features of " particle flow”, " soil arch effect”, and " over-excavation”, a 2D dynamic discrete element model was established to simulate the tunnel working face over-excavation with plane triangular blocks. The progressive instability mechanisms of the tunnel face (such as soil arch effect and cavity zone) were studied. The results show that the macroscopic stress-strain curve of the sandy cobble soil triaxial compression test can be divided into linear elastic, elastoplastic, and ideal plastic stages. The cobble enhances the soil structure as coarse granular particles. The contact surface of the cobble and sand weakens the macroscopic strength. The Hopper flow calibration test with the soil arching effect as the calibration criterion can effectively obtain the friction angle transformation relationships of discrete plane triangles of different scales. The arching effect is notably ahead of the face, develops gradually with over-excavation, and finally dissipates gradually after reaching the limit state. Void regions start from the bottom of the screw conveyor, develop forward and upward gradually with over-excavation and finally cut through the load-bearing arch, reaching the ground surface and forming water-drop shaped void regions. Three types of control standards for over-excavation are proposed based on different strategies.
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图 3 不同围压下偏应力-轴应变关系曲线
Figure 3. Deviation curves of stress versus strain under different confining pressures
图 4 不同含石率条件下偏应力-轴应变关系
Figure 4. Deviation curves of stress versus strain for different cobble content rates
图 6 不同开挖阶段最小主应力云图
Figure 6. Minimum principal stress contours in different excavation stages
图 7 不同开挖阶段单元接触状态云图
Figure 7. Contact condition contours in different excavation stages
图 8 地表沉降-超挖量时程曲线
Figure 8. Curves of ground settlements versus over-excavation volumes
表 1 单元力学参数
Table 1. Mechanical parameters of elements
位置 单元模型 密度/（kg•m–3） 弹性模量/MPa 泊松比 摩擦角/（°） 法向刚度/GPa 切向刚度/GPa 砂土层 M-C弹塑性 1 950 20 0.35 35 卵石层 线弹性 2 800 40 000 0.20 接触界面 脆断弹簧 11 400 40 
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表 2 不同模型试验结果
Table 2. Results of different models
试样 弹性力/kPa 极限应变/% 初始切线模量/MPa 峰值应力/kPa 最终状态 砂卵石（考
虑界面接触）744 3.0 24.5 1185 理想塑性 砂卵石（无
界面接触）737 2.9 25.4 1419 弹塑性 均质砂土 738 3.8 20.0 1035 理想塑性 注：单元尺寸为0.03 m，围压为300 kPa.
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表 3 模型基本参数
Table 3. Basic parameters of the model
项目 数值 盾构直径/m 5.7 出土口高度/m 1.0 开挖面顶部埋深/m 3.0 模型尺寸（B × H）/m 12 × 12 开挖面距左侧边界距离/m 3.0 划分单元总数（WV = 40%） 33 720 界面接触弹簧总数（WV = 40%） 155 843 最小单元尺寸/m 0.080
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表 4 材料基本参数
Table 4. Basic parameters of the materials
单元 密度/（kg•m–3） 弹性模量/MPa 泊松比 砂土 1 950 20 0.35 卵石 2 800 400 0.20 挡板 7 850 1 000 0.20 衬砌 2 500 320 0.20
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表 5 界面接触单元基本参数
Table 5. Basic parameters of the jointed elements
界面材料 法向与切向接触刚度/MPa 摩擦角/（°） 砂土-砂土 800 11 砂土-卵石 800 6 砂土-挡板 4 000 6 卵石-挡板 4 000 6
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