Three-dimensional uplift simulation of anchor plates in sand using material point method
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摘要: 土体中锚板的上拔过程存在复杂的锚土相互作用，掌握其变形及破坏机制对于确定锚板的极限承载力和优化设计具有重要的意义。采用三维物质点法（MPM）模拟了砂土中圆形锚板的上拔过程，探究了不同埋深条件下土体的位移场分布及锚板的上拔破坏机制，并结合极限平衡法研究了砂土密实度、锚板尺寸和埋深等因素对其极限承载力的影响。结果表明，临界埋深比主要受土体性质影响，受锚板直径的影响较小。当埋深比小于临界埋深比时，土体表现为浅埋破坏，破坏面延伸至地表，其形状在松砂中为圆台状，在密砂中为曲面状；当埋深比大于临界埋深比时，土体中的破坏面呈灯泡状，且不延展至地表。当上拔位移较大时，锚板上方出现土体绕流现象。保持埋深比不变，锚板直径越大，则极限承载力越大，上拔承载力系数越小。砂土密实度对锚板上拔力–位移曲线有较大的影响，密砂中的极限承载力明显大于松砂，且两者的差值随埋深比的增加而增大。Abstract: There are complex anchor-soil interactions in the uplift process of the anchor plate, and it is of great significance to master the deformation mechanism and displacement distribution of the soil to predict the uplift bearing capacity and optimize the design. Based on the three-dimensional material point method (MPM) to simulate the uplift of the anchor plate, the uplift failure mechanism under different embedment depth ratios is explored, and the influences of soil compactness, diameter and embedment depth ratio of the anchor plate on the peak bearing capacity are analyzed using limit equilibrium method. The results show that the limit embedment depth ratio is mainly affected by the nature of the soil, but less affected by the diameter. When the embedment depth ratio is less than the critical one, the soil exhibits shallow embedment failure, and the failure surface extends to the surface. Its shape is truncated cone-shaped in loose sand and curved in dense sand. When the embedment depth ratio is greater than the critical one, the damage surface in the soil is bulb-shaped and does not extend to the surface. When the uplift displacement is large, the soil above the anchor plate appears to flow around. When the embedment depth ratio remains unchanged, the larger the plate diameter, the greater the ultimate bearing capacity, and the smaller the uplift bearing capacity coefficient. Considering the softening effects, the load-displacement response in the uplift process of loose sand and dense sand is different. The ultimate bearing capacity of the dense sand is greater than that of the loose sand, and the difference between them increases with the increase of the embedment depth ratio.
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Keywords:
- material point method /
- anchor plate /
- failure plane /
- ultimate bearing capacity /
- interaction
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图 2 锚板上拔数值模型（xoz平面）
Figure 2. Numerical model for uplift of anchor plate (in xoz plane)
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图 4 锚板上拔承载力系数–埋深比关系曲线
Figure 4. Curves of uplift factor-embedment depth ratio of anchor plates
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图 5 xoz平面不同埋深比条件下等效塑性应变云图(d=100 mm)
Figure 5. Contours of equivalent plastic strain under different embedment depth ratios in xoz plane
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图 7 三维等效塑性应变云图(d=50 mm)
Figure 7. Contours of three-dimensional equivalent plastic strain
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图 9 不同上拔阶段位移矢量场(d=200 mm，h/d=2)
Figure 9. Displacement vector fields at different uplift stages
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图 10 不同上拔阶段位移矢量场(d=200 mm，h/d=6)
Figure 10. Displacement vector fields at different uplift stages
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图 11 密砂中峰值位移时土体位移矢量图(d=50 m，h/d=6)
Figure 11. Vector diagram of soil displacement at peak displacement in dense sand
表 1 砂土的物理力学参数
Table 1 Physical and mechanical parameters of soil
砂土 重度γ/(kN∙m-3) 相对密实度Dr/% 内摩擦角φ/(°) 剪胀角ψ/(°) 变形模量E/(kN∙m-2) 黏聚力c/kPa 泊松比ν 松砂 15.5 28.8 31.8 4 25000 0.5 0.2 密砂 17.5 76.2 — — 30000 0.5 0.3 
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表 2 MC软化模型的计算参数
Table 2 Computational parameters of MC softening model
锚板直径d/mm 埋深比h/d 峰值内摩擦角φp/(°) 峰值剪胀角ψp/(°) 50 2 51.46 24.57 4 49.79 22.49 5 49.36 21.95 6 48.82 21.28 8 48.13 20.41 100 2 49.79 22.49 4 48.13 20.41 5 47.77 19.97 6 47.16 19.20 8 46.47 18.33 200 1 49.79 22.49 2 48.13 20.41 3 47.16 19.20 4 46.47 18.33 5 46.19 17.99 6 45.49 17.12
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表 3 计算参数
Table 3 Computational parameters
锚板直径
d/mm上拔速度v/(mm·s-1) 时间步长
Δt/s总上拔位移u0/mm 50 1 1.0 10 100 2 0.5 30 200 5 0.5 50
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