Research of dynamic response patterns of high steep rock slope under earthquake effects
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摘要: 在西南山区高陡单面斜坡研究基础上运用FLAC3D有限差分法对双面斜坡的动力响应规律进行分析，研究了斜坡坡高、坡角及顶宽变化对响应规律的影响，结果发现：对斜坡输入不同中心频率Ricker子波时，坡体卓越频率整体处于1~4 Hz之间，且斜坡不同部位卓越频率不尽相同。从规律上看，坡高决定了斜坡动力响应的表现形式，体现在坡高较低时加速度放大系数等值线平行于坡底而增大后变为平行于坡面展布的闭合区域，反映在放大效果上即为加速度随坡高线性增加（坡高较低时），而后呈现增减反复出现的情况（坡高较高时）；另外，坡角增大未影响斜坡动力响应的表现形式，仅改变了斜坡内部放大系数等值线的走向，使得陡倾斜坡加速度水平及竖向放大效果均大于缓倾斜坡。双面斜坡随坡形变化的动力响应规律与单面坡近乎相同，但由坡形改变所致地震波反射与折射现象使得双面坡对地震波的放大效果更加明显，表现为放大系数等值线密集程度增大，加速度较相同单面斜坡成倍增加。Abstract: Base on the research of single-sided high steep slopes in southwestern China, dynamic responses of double-sided slopes are analysed which include changes of height, angle and width. Results show that predominant frequencies of slopes mainly concentrate in 1~4 Hz when inputting Ricker waves with varying center frequencies and the results alter in different parts of the slope. Dynamic response patterns mainly depend on slope height, contours of amplification coefficients parallel to the bottom of slope at lower heights while distribute as closed regions near surface when height increases. This means numerical value of amplification linearly increase with the height of the slope at a relatively low height but fluctuate at a great height. In addition, slope angle changes the direction of contours and makes amplification factors greater in steep slope, but dynamic patterns of slope are unaffected by those changes. Double-sided slopes show similar dynamic pattern with the single ones, but reflection and refraction of quake waves caused by slope shape make the amplification greater in double-sided slopes, which manifest as intensified contours and multiplied acceleration.
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Key words:
- earthquake /
- high steep rock slopes /
- topography /
- dynamic response /
- amplification effect /
- numerical simulation
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图 1 计算选用的斜坡模型尺寸及边界条件设置
H—坡高；α—坡度
Figure 1. Scales and boundary conditions of the slope model
图 2 计算选用的Ricker子波与正弦地震波
Figure 2. Ricker wavelet and sinusoidal seimic wave for calculation
图 3 斜坡计算模型设置及加速度记录
a—坡肩(A1)加速度时程记录；b—坡脚(A5)加速度时程记录
Figure 3. The calculation model and acceleration records of the slope
图 4 Ricker波作用下斜坡坡面加速度监测曲线
Figure 4. Monitoring curves of the slope surface acceleration under the action of Ricker wave
图 5 不同高度斜坡加速度放大系数等值线图
Max-加速度放大系数最大值
Figure 5. Contours of slope acceleration amplification coefficients with different slope heights
图 6 高陡斜坡不同位置加速度放大系数拟合曲线
Figure 6. Fitting curves of acceleration amplification coefficients in different places of the high steep slope
图 7 不同坡角下高陡斜坡加速度放大系数等值线图
Figure 7. Contours of acceleration amplification coefficients at different angles of the high steep slopes
图 8 双面高陡斜坡计算模型及监测点布置
Figure 8. The model and monitoring points of the double-sided high steep slope
图 9 不同坡高及顶宽双面斜坡加速度放大系数等值线图
Figure 9. Contours of acceleration amplification coefficients of double-sided slopes with different heights and widths
图 10 不同坡角双面斜坡加速度放大系数等值线图
Figure 10. Contours of acceleration amplification factors of double-sided slopes with different angles
图 11 双面及单面斜坡加速度放大系数随坡角变化拟合曲线
Figure 11. Fitting curves of acceleration amplification coefficients with the change of slope angles of double and single-sided slopes
图 12 坡面加速度放大系数随顶宽变化拟合曲线(以坡高200 m为例)
Figure 12. Fitting curves of acceleration amplification coefficients with the change of crest widths of slope surface(Taking 200 m slope as an example)
表 1 岩质斜坡计算选用的物理力学参数(据王文沛等，2019)
Table 1. Physical and mechanical parameters for the rock slope (Wang et al., 2019)
密度ρ/
(kg·m-3)体积模量
G/GPa剪切模量
G/GPa内摩擦角
φ/(°)粘聚力
C/MPa抗拉强度
Rm/MPa2690 23.3 14 40 1.8 5.56 
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