Seismic Performance Analysis of Slope Reinforced by Pile-Anchor Combination Based on Newmark Model
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摘要:
抗滑桩和锚索组合结构可以充分发挥抗滑桩的刚性约束和锚索的主动张拉来控制边坡变形，表现出良好的抗震性能，已被广泛应用于强震区滑坡防治.然而，目前关于桩锚组合结构加固边坡的地震动力响应研究较少，其协同抗震机制尚不明确.基于Newmark模型，提出了一种考虑地震时程特性的桩锚组合结构加固边坡的动力响应分析方法.并将该方法应用于山东高速公路高边坡，分析了不同加固方式下边坡的永久位移、安全系数以及支护结构的内力.结果表明，桩锚组合结构有效减小了边坡永久位移，确保边坡的稳定性；桩锚组合支护相较于仅锚支护和仅桩支护，锚固端的最大锚固拉力、桩身最大剪力和最大弯矩均有所减小；随着黏聚力和内摩擦角的增大，边坡屈服加速度呈正比例增加，而永久位移则从急剧减小过渡到缓慢下降，其中黏聚力的影响更为显著.桩锚组合结构通过形成主动受力体系，增大了边坡的屈服加速度，实现了桩和锚索的协调受力，防止滑面附近应力过度集中，是一种高效的加固方式.
Abstract:The composite structure of anti-slide pile and anchor cable can give full play to the rigid constraint of anti-slide pile and the active tension of anchor cable to control slope deformation, showing good seismic performance, and has been widely used in landslide prevention in strong earthquake areas. However, at present, there is little research on the seismic dynamic response of slope strengthened by pile-anchor composite structure, and its cooperative seismic mechanism is not clear. Based on Newmark model, this paper presents a dynamic response analysis method of slope strengthened by pile-anchor composite structure considering earthquake time-history characteristics. The method is applied to the high slope of Shandong expressway, and the permanent displacement, safety factor and internal force of supporting structure of the slope with different reinforcement methods are analyzed. The results show that the pile-anchor composite structure effectively reduces the permanent displacement of the slope and ensures the stability of the slope. Compared with only anchor support and only pile support, the maximum anchorage tension at the anchorage end, the maximum shear force and the maximum bending moment of the pile body are reduced. With the increase of cohesion and internal friction angle, the yield acceleration of slope increases in direct proportion, while the permanent displacement transitions from sharp decrease to slow decrease, in which the influence of cohesion is more significant. By forming an active stress system, the pile-anchor composite structure increases the yield acceleration of the slope, realizes the coordinated stress of the pile and the anchor cable, and prevents excessive stress concentration near the sliding surface, which is an efficient reinforcement method.
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图 1 双曲主干曲线(Fkramer, 1995)
Fig. 1. Hyperbolic backbone curve(Fkramer, 1995)
图 2 Newmark位移滑块模型(Jibson and Michael, 2009)
Fig. 2. Newmark displacement slider mode(Jibson and Michael, 2009)
图 3 Newmark位移计算示意图(Wilson and Keefer, 1983)
Fig. 3. Newmark displacement calculation diagram(Wilson and Keefer, 1983)
图 4 基于Newmark模型的桩锚组合加固边坡动力响应分析方法计算流程
Fig. 4. Calculation flow chart of dynamic response analysis method of slope reinforced by pile-anchor combination based on Newmark model
图 5 济南-潍坊高速公路边坡案例现场图和剖面图
a.施工期间边坡坡顶坍塌现场图; b.设计修改后的边坡现场图; c.修改后的边坡剖面图
Fig. 5. On-site and cross-sectional diagrams of the slope case study along the Jinan-Weifang expressway
图 6 不同工况下边坡的支护设计
a.未支护; b.仅锚支护; c.仅桩支护; d.桩锚组合支护
Fig. 6. Support design diagram of slope under different working conditions
图 7 峰值加速度为0.15 g的不同地震波时程记录
a.El Centro波地震时程记录; b.鲁甸波地震时程记录; c.汶川波地震时程记录
Fig. 7. Time history records of different seismic waves with peak acceleration of 0.15 g
图 8 不同工况下边坡竖向位移变化云图
a.未支护; b.仅锚支护; c.仅桩支护; d.桩锚组合支护
Fig. 8. Nephogram of vertical displacement change of slope under different working conditions
图 9 不同地震波作用下边坡永久位移-时间变化曲线
a.El Centro波作用下边坡永久位移-时间变化曲线; b.鲁甸波作用下边坡永久位移-时间变化曲线; c.汶川波作用下边坡永久位移-时间变化曲线
Fig. 9. Permanent displacement-time curves of slope under different seismic waves
图 10 El Centro波作用时不同工况边坡平均加速度、速度、累积变形随时间变化曲线
a.未支护; b.仅锚支护; c, 仅桩支护; d.桩锚组合支护
Fig. 10. Curve of average acceleration, velocity and cumulative deformation of slope under different working conditions under the action of EI Centro wave with time
图 11 不同工况下边坡安全系数随时间变化曲线
Fig. 11. Curves of slope safety factor with time under different working conditions
图 12 不同地震波下锚固段轴力分布
a.El Centro波作用下锚固段轴力分布; b.鲁甸波作用下锚固段轴力分布; c.汶川波作用下锚固段轴力分布
Fig. 12. Axial force distribution of anchorage section under different seismic waves
图 13 不同地震波下桩身最大弯矩分布
a.El Centro波作用下桩身最大弯矩分布; b.鲁甸波作用下桩身最大弯矩分布; c.汶川波作用下桩身最大弯矩分布
Fig. 13. Distribution diagrams of maximum bending moment of pile under different seismic waves
图 14 不同地震波下桩身最大剪力分布
a.El Centro波作用下桩身最大剪力分布图; b.鲁甸波作用下桩身最大剪力分布图; c.汶川波作用下桩身最大剪力分布图
Fig. 14. Distribution diagrams of maximum shear force of pile under different seismic waves
图 15 黏聚力(a)和内摩擦角(b)对边坡屈服加速度和永久变形的敏感性
Fig. 15. Sensitivity of cohesion (a) and internal friction angle (b) to yield acceleration and permanent deformation of slope
图 16 黏聚力、内摩擦角对边坡屈服加速度(a)和永久位移参数敏感度(b)曲线
a.黏聚力、内摩擦角对边坡屈服加速度的参数敏感度曲线; b.黏聚力、内摩擦角对永久位移的参数敏感度曲线
Fig. 16. Sensitivity curves of cohesion and internal friction angle to yield acceleration (a) and permanent displacement parameters (b) of slope
表 1 边坡各层物理力学参数
Table 1. Physical and mechanical parameters of each rock formation
层号 岩石名称 重度γ(kN/m3) 黏聚力c(kPa) 内摩擦角φ(°) 阻尼比D 泊松比ν 1 土层 17.5 13 12 0.1 0.26 2 土岩界面 18 10 12 0.1 0.25 3 岩层 21 2 000 32 0.1 0.31 
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表 2 加固材料参数
Table 2. Parameters of reinforcement materials
加固方式 弹性模量(kPa) 截面积(m2) 截面惯性矩(m4) 轴向预应力(kN) 倾角(°) 长度(m) 桩 2×108 0.025 45 5×10-4 / / 16 锚索锚固段 2×108 0.006 36 2.5×10-4 / 20 12 锚索自由段 2×108 0.006 36 / 500 20 6
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表 3 不同地震波作用时不同工况边坡屈服加速度和永久位移表
Table 3. Yield acceleration and permanent displacement of slope under different working conditions under different seismic waves
支护方式 未支护 仅锚
支护仅桩
支护桩锚组合支护 屈服加速度(m/s2) 0.014 1 0.015 8 0.017 4 0.025 4 El Centro波永久位移(m) 0.078 6 0.047 0 0.042 6 0.008 4 鲁甸波永久位移(m) 0.051 1 0.031 8 0.027 8 0.007 0 汶川波永久位移(m) 0.013 1 0.002 7 0.004 5 0.000 2
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表 4 Newmark位移范围与失效概率之间的关系
Table 4. Relation between Newmark displacement range and failure probability
Newmark位移(cm) 滑坡发生的可能性 0~1 低(0~2%) 1~5 中等(2%~15%) 5~15 高(15%~32%) > 15 很高(> 32%)
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