Seismic Dynamic Response and Critical Displacement for Instability of Loess Landslides
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摘要: 黄土地震滑坡是我国西北黄土高原地区常见且危害极大的地震地质灾害之一。考虑其地震动力响应建立失稳临界位移判据是同震滑坡识别和地震滑坡预警的关键。本文以典型黄土斜坡为原型，采用振动台模型试验（几何相似比1∶10），输入0.05～0.6 g不同幅值的卧龙波与El Centro波，以PGA、Arias强度的放大系数为强度参数指标，揭示水平地震作用下模型斜坡的地震动响应规律；结合坡体宏观变形以及加速度与陀螺仪倾角的微观监测数据，分析了斜坡地震变形破坏过程，构建黄土斜坡地震震裂山体和失稳滑动的临界位移判据。结果表明：随输入地震波幅值自0.05～0.2 g小幅值、0.2～0.4 g中等幅值、0.4～0.6 g高幅值的增大，坡体地震动PGA和Arias强度放大系数呈现波动增大的非线性变化特征；整体上坡体地震动放大系数随着斜坡高度的增大而增大，Arias强度放大效应强于PGA，坡体上部最大放大系数分别达2.1和1.8；坡体表面放大系数略高于坡体内部，但小于潜在滑移面附近地震放大系数；斜坡地震动响应受输入地震波主导频率与场地卓越频率耦合作用控制，二者接近时放大效应更为显著。地震动作用下黄土滑坡为“震裂—滑动”的破坏模式，模型斜坡在台面输入0.3 g卧龙波时坡体上部出现微裂隙，0.4～0.5 g时斜坡表面裂纹逐步由细小短裂缝扩展为竖向贯穿的深裂缝，对应震裂山体临界位移为0.2～3.5 cm；0.6 g地震波作用下裂缝贯通滑坡并沿黄土和泥岩接触面滑动，对应滑坡失稳临界位移9.85 cm，相应未考虑地震动地形放大效应计算所得黄土斜坡震裂山体临界位移区间为0～1.35 cm，地震滑坡的临界位移为4 cm。研究成果有望提升同震滑坡的识别精度和危险性评估定量化水平。Abstract: The loess seismic landslide is one of the most common and harmful seismic geological disasters in the Loess Plateau of Northwest China. Considering its seismic dynamic response, the establishment of instability critical displacement criterion is the key to co-seismic landslide identification and earthquake landslide early warning. In this paper, the typical loess slope is taken as the prototype, and the shaking table model test (geometric similarity ratio 1 : 10) is adopted. The Wolong ground motion and El Centro wave with different amplitudes of 0.05～0.6 g are input, and the amplification coefficients of PGA and Arias intensity are used as strength parameters to reveal the ground motion response characteristics of the model slope under horizontal earthquake. Combined with the microscopic monitoring data of the macroscopic deformation and acceleration of the slope and the inclination angle of the gyroscope, the seismic deformation and failure process of the slope is analyzed, and the critical displacement criterion of the earthquake shattered mountain and unstable sliding of the loess slope is constructed. The results show that with the increase of input seismic wave amplitude from 0.05～0.2 g, medium amplitude from 0.2～0.4 g, and high amplitude from 0.4～0.6 g, the PGA and Arias intensity amplification coefficients of slope ground motion show nonlinear variation characteristics of increasing fluctuation. The amplification factor of ground motion on the whole slope increases with the increase of slope height, and the amplification effect of Arias intensity is stronger than that of PGA. The maximum amplification factors of the upper part of the slope are 2.1 and 1.8, respectively. The surface amplification factor of the slope is slightly higher than that inside the slope, which is less than the seismic amplification factor near the potential slip surface. The slope ground motion response is controlled by the coupling effect of the dominant frequency of the input seismic wave and the predominant frequency of the site, and the amplification effect is more significant when the two are close. The failure mode of loess landslide under the action of earthquake ground motion is ' shatter-sliding '. When the model slope is input with 0.3 g Wolong wave on the platform, micro-cracks appear on the upper part of the slope, and the surface cracks of 0.4～0.5 g slope gradually expand from small short cracks to vertical penetrating deep cracks, corresponding to the critical displacement of the shattered mountain is 0.2～3.5 cm. Under the action of 0.6 g seismic wave, the crack penetrates the landslide and slides along the contact surface of loess and mudstone, corresponding to the critical displacement of landslide instability of 9.85 cm. The corresponding critical displacement interval of loess slope shattered mountain calculated without considering the topographic amplification effect of ground motion is 0～1.35 cm, and the critical displacement of seismic landslide is 4 cm. The research results are expected to improve the identification accuracy and quantitative level of risk assessment of co-seismic landslides.
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图 5 斜坡竖直方向PGA放大系数变化曲线
Figure 5. Variation curve of the PGA amplification factor in the vertical direction of the slope
图 6 斜坡竖直方向Arias强度放大系数变化曲线
Figure 6. Variation curve of the Arias intensity amplification factor in the vertical direction of the slope
图 7 斜坡C5～B3水平方向PGA放大系数变化曲线
Figure 7. Variation curve of the PGA amplification factor in the horizontal direction along the slope from C5 to B3
图 8 斜坡水平D3～B2方向PGA放大系数变化曲线
Figure 8. Variation curve of the PGA amplification factor in the horizontal direction along the slope from D3 to B2
图 9 斜坡E3～B1水平方向PGA放大系数变化曲线
Figure 9. Variation curve of the PGA amplification factor in the horizontal direction along the slope from E3 to B1
图 10 斜坡F1～C2水平方向PGA放大系数变化曲线
Figure 10. Variation curve of the PGA amplification factor in the horizontal direction along the slope from F1 to C2
图 11 输入不同峰值条件下坡面监测点PGA放大系数变化曲线
Figure 11. Variation curve of the PGA amplification factor at slope-surface monitoring points under different input peak values
图 12 输入不同峰值条件下沿坡面监测点Arias强度放大系数变化曲线
Figure 12. Variation curve of the Arias intensity amplification factor at monitoring points along the slope surface under different input peak values
图 13 不同波形下所有监测点PGA对比
Figure 13. PGA comparison for all monitoring points under different waveforms
图 14 黄土层内B组不同波形下PGA放大系数比较
Figure 14. Comparison of the PGA amplification factor for different waveforms
图 15 0.2 g卧龙波作用下斜坡变形迹象与陀螺仪倾角变换曲线
Figure 15. Slope deformation signs and gyroscope angular transformation curveunder the 0.2 g Wolong ground motion
图 16 0.3 g卧龙波作用下斜坡变形迹象与陀螺仪倾角变换曲线
Figure 16. Slope deformation signs and gyroscope angular transformation curve under 0.3 g Wolong wave action
图 17 0.4 ～0.5 g卧龙波作用下斜坡变形迹象与陀螺仪倾角变换曲线
Figure 17. Slope deformation signs and gyroscope angular transformation curve under 0.4～0.5 g Wolong wave action
图 18 0.6 g卧龙波作用下斜坡变形迹象
Figure 18. Slope deformation indicators under 0.6 g Wolong wave action
图 21 Newmark累积位移计算原理（黄健航等，2025）
Figure 21. Principle of Newmark cumulative displacement calculation（Huang et al，2025）
图 22 斜坡裂缝贯通时临界位移（未考虑地形效应）
Figure 22. Critical displacement at the moment of slope crack coalescence （excluding topographic effects）
图 23 裂缝产生时临界位移（考虑地形效应）
Figure 23. Critical displacement for crack initiation （considering topographic effects）
图 24 裂缝贯通时临界位移（考虑地形效应）
Figure 24. Critical displacement for crack coalescence （considering topographic effects）
图 25 斜坡滑动时临界位移（未考虑地形效应）
Figure 25. Critical displacement for slope sliding （excluding topographic effects）
图 26 斜坡滑动时临界位移（考虑地形效应）
Figure 26. Critical displacement for slope sliding （considering topographic effects）
表 1 原型斜坡物理力学参数
Table 1. Prototype slope physical and mechanical parameters
土层名称 土层密度ρ/(g·cm−3) 弹性模量E/MPa 泊松比μ 内摩擦角φ/° 黏聚力c/kPa 黄土 1.35 23 0.3 23 30 泥岩 2.0 623 0.3 34.2 680 
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表 2 振动台模型试验相似关系
Table 2. Similarity relationships for the shaking table model test
物理量 量纲 相似律 相似比(模型/原型) 备注 坡高H L CH 1/10 控制量 土体密度ρ ML−3 Cρ 1 控制量 重力加速度g LT−2 Cg 1 控制量 土体重度γ ML−2T−2 Cγ=CρCg 1 — 坡度θ — 1 1 — 含水率w — 1 1 — 土体黏聚力c ML−1T−2 Cc=CρCgCH 1/10 — 土体内摩擦角φ — 1 1 — 土体弹性模量E ML−1T−2 CE=CρCgCH 1/10 — 土体泊松比μ — 1 1 — 地震加速度a LT−2 Ca=Cg 1 — 地震荷载主频f T−1 Cf=CH−0.5Cg0.5 100.5 — 持续时间ts T Cts=CH0.5Cg−0.5 (1/10)0.5 —
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表 3 相似材料的物理力学参数
Table 3. Physico-mechanical parameters of similar materials.
土层名称 土层密度ρ/(g·cm−3) 泊松比μ 内摩擦角φ/° 黏聚力c/kPa 黄土 1.35 0.3 23° 3 泥岩 2.0 0.3 34.2 110
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表 4 振动台试验加载工况
Table 4. Loading conditions for the shaking table test
工况 水平向加载波形 振幅/g 备注 1 白噪声 0.05 — 2 卧龙波 0.05 — 3 白噪声 0.05 — 4 卧龙波 0.1 — 5 白噪声 0.05 — 6 El Centro波 0.1 — 7 白噪声 0.05 — 8 卧龙波 0.2 — 9 白噪声 0.05 — 10 卧龙波 0.3 裂缝产生 11 白噪声 0.05 — 12 卧龙波 0.4 裂缝扩展 13 白噪声 0.05 — 14 卧龙波 0.5 裂缝贯通 15 白噪声 0.05 — 16 卧龙波 0.6 斜坡破坏
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表 5 地震波频带比例
Table 5. Proportion of seismic wave frequency bands
地震波类型 频带范围/Hz B1频率占比/% B2频率占比/% B3频率占比/% 白噪声 0～3.125 3.26 3.13 4.73 3.125～6.25 23.34 23.74 31.39 6.25～9.375 21.77 23.00 16.37 9.375～12.5 33.14 32.16 37.64 12.5～15.625 0.02 0.02 0.02 15.625～18.75 0.27 0.26 0.31 18.75～21.875 13.86 15.64 7.30 21.875～25 2.07 2.07 2.23 卧龙波 0～3.125 1.36 1.25 1.14 3.125～6.25 11.09 9.62 9.81 6.25～9.375 61.65 63.43 59.63 9.375～12.5 10.30 9.10 9.04 12.5～15.625 3.08 3.62 6.49 15.625～18.75 2.56 2.58 3.00 18.75～21.875 6.47 7.43 6.66 21.875～25 3.48 2.95 4.22 El Centro波 0～3.125 15.15 13.84 12.93 3.125～6.25 23.10 21.43 20.65 6.25～9.375 19.57 21.95 20.36 9.375～12.5 17.13 16.29 15.72 12.5～15.625 3.38 3.05 5.40 15.625～18.75 4.19 3.81 5.53 18.75～21.875 12.17 15.28 13.45 21.875～25 5.32 4.43 5.97
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