Dynamic response of slopes in hilly regions of loess and analysis method for their seismic subsidence deformation
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摘要: 黄土丘陵区易发生震陷型边坡失稳。通过动力离心模型试验和有限差分非线性动力分析方法研究地震时黄土边坡的动力响应及变形机制，探究了地震作用下概化黄土边坡的加速度及位移响应，提出了基于动单剪试验条件下黄土震陷系数经验公式及黄土场地震陷量估算方法，并应用于黄土边坡震陷变形计算。结果表明：黄土边坡对地震荷载具有放大效应，加速度放大系数沿高程呈非线性增大，且坡面动力放大效应大于坡体内部；边坡的震陷量与土层厚度关系密切，土层震陷系数随高程呈对数式增加；地震作用下黄土边坡的破坏形式是水平滑移变形与竖向震陷变形双向耦合的结果，震陷变形表现显著，边坡向临空面滑动，坡顶张拉裂隙和坡面错位裂隙大量发育，震陷沉降不均导致坡面形成错位阶梯。Abstract: The hilly region of loess is prone to slope instability of seismic subsidence. Through the dynamic centrifugal model tests and the finite difference nonlinear dynamic analysis methods, the dynamic response and deformation mechanism of loess slopes under earthquakes are studied. The acceleration and displacement responses of the generalized loess slopes under earthquakes are explored. The empirical formula for the seismic subsidence coefficient of loess and the method for estimating the seismic subsidence of loess field are proposed based on the dynamic single shear tests, and they are also used to calculate the seismic subsidence of loess slopes. The results show that the loess slope has a magnification effect on the seismic loads, the acceleration magnification coefficient increases nonlinearly along the elevation, and the dynamic magnification effects of the slope surface are greater than those inside the slope. The seismic subsidence of the slope is closely related to the thickness of the soil layer. The seismic subsidence coefficient increases logarithmically with elevation. The failure form of loess slopes under earthquakes is the result of the two-way coupling of horizontal sliding deformation and vertical seismic subsidence deformation. The tensile fissures at the top of the slope and the dislocation fissures on the slope surface are widely developed, and the uneven settlement of the seismic subsidence leads to the formation of dislocation steps on the slope surface.
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图 1 动力离心试验模型设计及传感器布置
Figure 1. Design and arrangement of sensors for dynamic centrifugal model tests
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图 2 汶川地震紫坪铺站台实测地震波（PGA≈0.2g）
Figure 2. Measured seismic waves at Zipingpu platform of Wenchuan Earthquake (PGA≈0.2g)
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图 4 黄土边坡沿坡面加速度响应规律
Figure 4. Time-history curves of horizontal displacement of slope surface at monitoring points
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图 5 黄土边坡沿坡肩铅垂线加速度响应规律
Figure 5. Acceleration response laws of loess slope along vertical line of slope shoulder
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图 6 坡面监测点水平位移时程曲线
Figure 6. Time-history curves of horizontal displacement of slope surface at monitoring points
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图 8 监测点动剪应变时程曲线（A7）
Figure 8. Time-history curve of dynamic shear strain of monitoring points
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图 9 不同高度震陷系数及震陷累积位移
Figure 9. Seismic subsidence coefficients and cumulative displacements at different elevations
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图 10 黄土边坡震陷变形等值线图
Figure 10. Contours of seismic subsidence deformation of loess slope
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图 11 地震作用下竖向位移时程曲线（0.3g）
Figure 11. Time-history curves of vertical displacement under earthquakes
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图 12 离心机试验黄土边坡破坏特征
Figure 12. Failure characteristics of loess slope in centrifugal model tests
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图 13 震陷型黄土边坡破坏特征
Figure 13. Failure characteristics of loess slope of seismic subsidence
表 1 兰州黄土基本物理性质指标
Table 1 Basic physical properties of Lanzhou loess
天然密度ρ/(g·cm-3) 含水率w/% 干密度ρd/(g·cm-3) 液限wL/% 塑限wP/% 塑性指数IP/% 1.38 8.2 1.27 28.2 17.2 11.0 
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表 2 黄土边坡数值计算参数
Table 2 Numerical parameters of loess slope
体积模量/MPa 剪切模量/MPa 泊松比 密度ρ(g·cm-3) 黏聚力c/kPa 内摩擦角φ/(°) 27.5 12.7 0.3 1.38 30 26
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1. 钱法桥，邓亚虹，刘凡，门欢. 黄土地震滑坡研究综述与展望. 中国地质灾害与防治学报. 2024(05): 5-20 . 
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