Research on Dynamic Failure of Bedrock-Overburden Layered Accumulation Slope Considering Influence of Soil Layer Dip
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摘要:
为研究土层倾角对边坡动力失稳的影响，基于振动台模型试验，研究不同土层倾角的层状堆积体基覆型边坡在地震作用下的失稳特征和动力响应规律. 通过改变基覆界面倾角，设计表面为直线形、凹形、凸形的3类边坡，在此基础上开展边坡振动台模型试验，得到3种变倾角边坡的失稳模式；并通过考虑边坡破坏的加速度放大效应，结合土体应力状态与摩尔-库仑强度理论，探究边坡动力响应机理及边坡失稳临界条件. 试验结果表明：凹形边坡在破坏时破坏特征集中在上部土层，凸形边坡集中在下部土层，直线形边坡则是出现上部土层拉裂、下部土层剪切滑移的破坏模式；相同震级下，凹形边坡加速度放大系数最小，直线形边坡、凹形边坡与凸形边坡的加速度放大效应分别集中在坡顶、坡肩与坡顶后缘位置；随着变倾角系数的增大，边坡失稳临界加速度相应增大. 研究结果可为层状堆积体基覆型边坡工程的抗震设计、稳定性评价和防灾减灾提供科学依据.
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关键词:
- 层状堆积体基覆型边坡 /
- 土层倾角 /
- 模型试验 /
- 失稳特征 /
- 动力响应
Abstract:To investigate the influence of soil layer dip on the dynamic failure of slopes, the failure characteristics and dynamic response laws of bedrock-overburden layered accumulation slopes with different soil layer dips under seismic action were studied based on shaking table model tests. By varying the bedrock-overburden interface dip, three types of slopes with linear, concave, and convex surfaces were designed. Shaking table model tests were subsequently conducted on these slopes, yielding the failure modes of the three types of slopes with various dips. By taking into account the acceleration amplification effect of slope failure, the soil stress state, and the Mohr-Coulomb strength theory, the dynamic response mechanism of slopes and the critical conditions for slope failure were explored. The test results show that the failure characteristics of the concave slope are concentrated in the upper soil layer during the slope failure process, while those of the convex slope are concentrated in the lower soil layer. By contrast, the linear slope exhibits a failure mode characterized by tensile cracking in the upper soil layer and shear sliding in the lower soil layer. Under the same seismic magnitude, the concave slope exhibits the smallest acceleration amplification coefficient, and the acceleration amplification effects of the linear slope, concave slope, and convex slope are concentrated at the slope crest, slope shoulder, and the rear edge of the slope crest, respectively. With the increase in the various dip coefficients, the critical acceleration for slope failure increases accordingly. The research results can provide a scientific basis for the anti-seismic design, stability evaluation, and disaster prevention and mitigation of engineering projects involving bedrock-overburden layered accumulation slopes.
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图 4 非完全满足相似律的0.6 m边坡数值模拟结果（单位：m）
Figure 4. Numerical simulation results of 0.6 m slope with incomplete satisfaction of similarity law (unit: m)
图 5 原型15 m边坡数值模拟结果（单位：m）
Figure 5. Numerical simulation results of 15 m prototype slope (unit: m)
图 6 完全满足相似律的0.6 m边坡数值模拟结果（单位：m）
Figure 6. Numerical simulation results of 0.6 m slope with complete satisfaction of similarity law (unit: m)
图 7 地震作用下直线形黏土-砂土组边坡破坏过程
Figure 7. Failure process of linear slope in clay-sand group during seismic action
图 8 地震作用下直线形砂土-黏土组边坡破坏过程
Figure 8. Failure process of linear slope in sand-clay group during seismic action
图 9 地震作用下“凹形”黏土-砂土组边坡破坏过程
Figure 9. Failure process of concave slope in clay-sand group under seismic action
图 10 地震作用下“凸形”黏土-砂土组边坡破坏过程
Figure 10. Failure process of convex slope in clay-sand group under seismic action
图 11 直线形不同土层分布下边坡加速度放大系数对比
Figure 11. Comparison of acceleration amplification coefficients of linear slopes with different soil layer distributions
图 12 相同震级下各变倾角边坡加速度放大系数对比
Figure 12. Comparison of acceleration amplification coefficients of slopes with various dips under the same seismic magnitude
图 13 变倾角下边坡失稳临界条件曲线
Figure 13. Critical condition curve of slope failure under different dips
图 15 土体在水平荷载作用下摩尔强度包络线图
Figure 15. Mohr strength envelope of soils under horizontal load action
图 16 反向水平地震力作用下摩尔强度包络线图
Figure 16. Mohr strength envelope under negative horizontal seismic force action
图 17 正向水平地震力作用下摩尔强度包络线图
Figure 17. Mohr strength envelope under positive horizontal seismic force action
表 1 边坡模型试验参数及相似关系
Table 1. Similarity relationship of physical quantities in slope model test
物理量 量纲 相似律 物理量试验取值（实际值） 边坡高度 H L CH=25 0.6 m 黏土土体重度 γ1 ML−2T−2 $ C_{\gamma_{_1}} $=1 13 kN/m3 砂土土体重度 γ2 ML−2T−2 $ C_{\gamma_{_2}} $=1 16 kN/m3 重力加速度 g LT−2 Cg=1 9.8 m/s2 坡顶宽度 L L CL=25 0.3 m 黏土层厚度 d1 L ${C_{{d _1}}} $=25 0.2 m 砂土层厚度 d2 L ${C_{{d _2}}} $=25 0.2 m 上覆土层倾角 β1 1 30°/45° 下覆土层倾角 β2 1 30°/45° 基覆界面倾角 θ1 1 52° 基覆界面倾角 θ2 1 10° 黏土黏聚力 c1 ML−1T−2 Cc=CγCH=25 23.2 kPa 砂土黏聚力 c2 ML−1T−2 Cc=CγCH=25 5.4 kPa 黏土内摩擦角 φ1 1 22° 砂土内摩擦角 φ2 1 38° 黏土压缩模量 Es1 ML−1T−2 $ C_{E_{\mathrm{s1}}} $=CγCH=25 18.6 MPa 砂土压缩模量 Es2 ML−1T−2 $C_{E_{\mathrm{s2}}} $=CγCH=25 38.2 MPa 黏土泊松比 μ1 1 0.4 砂土泊松比 μ2 1 0.3 基覆界面与黏土的摩擦系数 1 0.3 基覆界面与砂土的摩擦系数 1 0.7 黏土与砂土的摩擦系数 1 0.45 黏土含水率 ω1 1 10% 砂土含水率 ω2 1 5% 地震荷载峰值
加速度 aLT−2 Ca=Cg=1 （0.1～0.5） g 地震荷载主频 f T−1 Cf=$C_H^{-0.5} $，
Cg0.5=0.210 Hz 地震持续时间 t T Ct=$C_H^{0.5} $，Cg−0.5=5 20 s 
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表 2 试验工况设计表
Table 2. Design of test working conditions
工况编号 土层分布 黏土层厚度/cm 砂土层厚度/cm 上覆土层倾角/（°） 下覆土层倾角/（°） 地震波类型 地震波频率/Hz 1 黏土-砂土 35 35 45 45 正弦波 10 2 黏土-砂土 35 35 45 30 正弦波 10 3 黏土-砂土 35 35 30 45 正弦波 10 4 砂土-黏土 35 35 45 45 正弦波 10
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表 3 数值模拟材料参数
Table 3. Material parameters in numerical simulation
类型 土体重度/（kN·m−3） 弹性模量/MPa 泊松比 黏聚力/kPa 内摩擦角/（°） 频率/Hz 黏土 砂土 黏土 砂土 黏土 砂土 黏土 砂土 黏土 砂土 非完全满足相似律的 0.6 m 边坡 13 16 8.68 28.38 0.4 0.3 13 16 8.68 28.38 0.4 原型 15 m 边坡 13 16 8.68 28.38 0.4 0.3 13 16 8.68 28.38 0.4 完全满足相似律的 0.6 m 边坡 13 16 0.35 1.14 0.4 0.3 13 16 0.35 1.14 0.4 注：压缩模量Es与弹性模量E换算公式为E$ =E_{\mathrm{s}}\left(1-\dfrac{2 \mu^2}{1-\mu}\right) $，µ为泊松比.
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表 4 地震作用下变倾角边坡失稳模式
Table 4. Slope failure modes with various dips under seismic action
工况 变倾角形式及土层分布 失稳模式示意 失稳加速度 失稳模式 1 直线形
（黏土-砂土）
0.30g 上部黏土拉裂-下部砂土局部滑移破坏 2 凹形
（黏土-砂土）
0.40g 上部黏土溃滑破坏（下部砂土稳定） 3 凸形
（黏土-砂土）
0.25g 下部砂土浅层剪切破坏（上部黏土稳定） 4 直线形
（砂土-黏土）
0.30g 上部砂土局部剪切滑移破坏 注：黑色虚线为原始边坡轮廓线；黑色实线为破坏后边坡轮廓线；红色实线为边坡破坏线.
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