Numerical simulation of seismic dynamic load effect of fault slope
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摘要: 地震荷载作用下，断层两侧边坡稳定性一直是研究重点，本文主要探讨动态加载对不同位置坡体产生的地震动效应。首先，建立一个截面大小为500 km×100 km的有限元二维动态铲形断层模型，在地表断层两侧构建对称边坡来模拟滑坡地形。然后加载脉冲震源，通过对震源（深度为14 km）处节点指定加速度的方法，模拟计算地震发生后100 s内地震波传播对距断层分别为1 km，30 km及100 km的不同边坡震动产生的影响。结果显示：边坡震动强度随着震源距的增加而快速衰减，下盘的衰减比上盘更为强烈；距断层相同位置处，上盘比下盘振动幅度大；相同山体的不同位置上，水平方向振幅随断层距增大而衰减；垂直方向振幅，相同高程处的振幅相近，高程越高振幅相对减小；随着断层距的增加，山体的水平和垂直方向振幅都逐渐变小；震源距较远位置处的振幅比近震源位置小很多，说明近震位置处振动强度大，即在同等地质条件下，近断层的上盘区域更易发生滑坡。Abstract: Slope stability on both sides of seismogenic fault under seismic loading has been the focus of academic study. We mainly discuss the seismic effect of dynamic loading on slopes at different positions in this paper. First, we conduct a two-dimensional dynamic finite-element model of spade shaped fault with the size of 500 km×100 km. The symmetrical slopes on both sides of the fault are considered as the landslide terrain. Then, to simulate the earthquake effect, we set a pulse source at the depth of 14 km. The impact of seismic wave propagation on slopes with distance 1 km, 30 km, and 100 km from the fault is analyzed in the first 100 s after earthquake happens. The results demonstrated that the vibration intensity decays rapidly with distance from the source, and that the decay rate at hanging side is more moderate than that of the footwall. With the same distance from the fault, the vibration amplitude of hanging side is larger than the footwall. In different locations of the same surface bulge, vibration amplitude decays with distance from the fault in horizontally. The vibration amplitude in vertical direction is similar to that of the same elevation position. The location with higher elevation has a relatively smaller amplitude. As the distance from the fault increases, amplitudes of surface bulge in horizontal and vertical direction become smaller gradually. The results show that in a place far away from the source, the amplitude of the point is much smaller than the near one which means at where the vibration intensity is larger. With the same geological setting, the near fault hanging side is easier to have landslide.
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Keywords:
- finite element /
- earthquake /
- listric fault /
- slope stability
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本目录中的地震参数来自“中国地震台站观测报告”(简称“月报”)． 其中， 国内及邻区给出M≥4.7的事件， 全球给出M≥6.0的事件． “月报”由中国地震台网中心按月做出．
本目录中的发震时刻采用协调世界时(UTC)； 为了方便中国读者， 也给出北京时(BTC)． 震中位置除给出经纬度外， 还给出参考地区名， 它仅用作查阅参考， 不包含任何政治意义； 还给出测定震源位置的台数(n)和标准偏差(SD)．
面波震级MS是用中周期宽频带SK地震仪记录， 采用北京台1965年面波震级公式MS=lg(AH/T)+1.66 lg(Δ)+3.5 (1°＜Δ＜130°)求得， AH是两水平分向最大面波位移的矢量合成位移． MS7是对763长周期地震仪记录， 采用国际上推荐的面波震级公式MS7=lg(AV/T)+1.66 lg(Δ)+3.3 (20°＜Δ＜160°)求得， AV是垂直向面波最大地动位移． mb是短周期体波震级， ML是近震震级. 为避免混乱, 震级之间一律不换算．
中国及邻区地震目录(2016年5—6月， M≥4.7)Catalog of earthquakes within and near China (May--June， 2016, M≥4.7)编号 发震时刻 地理坐标 深度/km 震级 标准偏差(SD) 使用台数(n) 地区 UTC BTC日-时 纬度/°N 经度/°E MS MS7 ML mb 月-日 时:分:秒 1 05-04 09:24:0.3 04-17 23.27 103.22 10 4.8 4.4 4.5 4.3 2.3 67 云南省 2 11 01:15:48.1 11-09 32.01 95.08 10 5.7 5.6 5.2 5.0 2.7 101 西藏自治区 3 12 03:17:13.0 12-11 24.68 122.00 15 6.3 6.3 6.3 5.2 2.1 103 台湾岛 4 12 04:29:56.3 12-12 24.83 122.02 15 6.1 6.1 6.1 5.1 1.7 102 台湾岛 5 13 08:24:12.5 13-16 24.86 121.90 6 5.2 5.0 5.1 4.6 2.0 101 台湾岛 6 14 03:32:48.9 14-11 24.20 121.81 6 4.9 4.8 4.5 4.3 2.3 68 台湾岛 7 15 17:02:29.5 16-01 39.76 75.46 10 4.3 4.1 4.7 4.3 3.1 29 新疆自治区南部 8 17 16:48:51.2 18-00 26.13 99.56 20 5.0 4.6 4.9 4.7 2.6 76 云南省 9 17 17:05:11.8 18-01 26.08 99.58 10 4.6 4.2 4.7 4.6 2.5 77 云南省 10 19 11:50:08.6 19-19 27.00 127.00 110 4.7 1.9 74 琉球群岛 11 21 20:51:40.1 22-04 22.95 120.58 6 4.5 4.4 4.7 4.4 2.0 86 台湾岛 12 22 01:48:45.6 22-09 28.27 87.62 10 5.4 5.2 4.9 1.9 75 尼泊尔 13 22 02:05:53.1 22-10 28.42 87.59 10 5.1 4.8 4.8 1.6 69 尼泊尔 14 22 09:08:04.0 22-17 41.62 120.09 6 4.5 4.2 4.8 4.3 2.3 65 中国东北部 15 31 05:23:46.5 31-13 25.45 122.48 245 5.7 1.8 91 台湾岛 16 06-05 02:47:49.4 05-10 28.88 128.38 201 4.9 1.6 89 中国东海 17 19 03:05:10.4 19-11 42.10 81.46 5 4.2 3.8 4.9 4.5 3.0 39 新疆自治区南部 18 19 18:20:54.4 20-02 20.61 120.72 10 5.3 5.3 4.8 5.0 2.3 93 菲律宾群岛地区 19 23 21:05:26.3 24-05 23.52 123.53 10 6.0 5.8 5.4 1.5 96 琉球群岛西南部 20 26 11:17:09.6 26-19 39.43 73.40 10 6.9 6.8 6.8 5.7 1.5 100 塔吉克斯坦 21 27 06:25:37.1 27-14 39.45 73.31 19 4.6 4.3 4.5 4.7 1.3 69 塔吉克斯坦 22 27 10:13:06.0 27-18 31.89 104.41 10 4.5 4.3 4.8 4.6 2.4 77 四川省 23 27 19:28:48.1 28-03 39.52 73.44 13 4.8 4.6 4.8 4.8 1.4 80 吉尔吉斯斯坦 24 28 21:38:01.3 29-05 39.51 73.32 7 5.5 5.4 5.5 5.2 1.4 98 吉尔吉斯斯坦 25 29 08:08:10.5 29-16 39.46 73.18 7 4.5 4.3 4.7 4.8 1.5 69 塔吉克斯坦 26 29 15:23:10.0 29-23 27.40 126.50 190 4.7 1.5 61 琉球群岛 全球地震目录(2016年5—6月， M≥6.0)Catalog of earthquakes all over the world (May--June， 2016， M≥6.0)编号 发震时刻 地理坐标 深度/km 震级 标准偏差(SD) 使用台数(n) 地区 UTC BTC日-时 纬度/°N 经度/°E MS MS7 mb 月-日 时:分:秒 1 05-08 07:34:02.0 08-15 16.50N 97.70W 30 6.0 5.7 1.4 59 墨西哥格雷罗海岸近海 2 12 03:17:13.0 12-11 24.68N 122.00E 15 6.3 6.3 5.2 2.1 103 台湾岛 3 12 04:29:56.3 12-12 24.83N 122.02E 15 6.1 6.1 5.1 1.7 102 台湾岛 4 18 07:57:02.5 18-15 0.49N 79.79W 32 6.8 6.8 2.1 88 厄瓜多尔海岸近海 5 18 16:46:41.3 19-00 0.49N 79.68W 30 6.9 6.9 2.4 89 厄瓜多尔海岸近海 6 28 05:38:47.3 28-13 22.01S 178.15W 400 6.2 1.3 99 斐济以南地区 7 28 09:46:58.3 28-17 56.15S 27.15W 70 7.1 7.0 2.4 74 南桑德韦奇群岛地区 8 06-01 22:55:58.6 02-06 2.10S 100.65E 50 6.6 6.3 6.2 1.4 100 苏门答腊南部 9 07 10:51:37.7 07-18 18.40N 105.15W 10 6.5 6.2 5.4 2.5 57 墨西哥哈利斯科海岸 近海 10 07 10:58:01.0 07-18 18.50N 105.10W 10 6.7 6.3 2.7 13 墨西哥哈利斯科海岸 近海 11 07 19:15:16.0 08-03 1.34N 126.34E 50 6.1 6.0 6.0 1.4 100 马鲁古海峡 12 10 03:25:22.5 10-11 13.00N 86.95W 10 6.5 6.3 2.7 66 尼加拉瓜海岸近海 13 10 04:17:42.0 10-12 8.66S 160.58E 30 6.0 5.8 5.6 0.8 102 所罗门群岛 14 19 09:47:20.0 19-17 20.45S 169.50E 10 6.2 6.0 5.1 1.9 86 瓦努阿图(新赫布里底) 15 21 16:26:33.9 22-00 22.61N 44.97W 10 6.4 6.2 5.6 2.1 66 北大西洋海岭 16 23 21:05:26.3 24-05 23.52N 123.53E 10 6.0 5.8 5.4 1.5 96 琉球群岛西南部 17 26 11:17:09.6 26-19 39.43N 73.40E 10 6.9 6.8 5.7 1.5 100 塔吉克斯坦 -
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图 2 边坡点位分布示意图
R与L分别代表点在断层的右侧与左侧；a为边坡编号；1号和3号点等高
Figure 2. Sketch map of the results analysis
R and L represent points on the right and left sides of the fault，respectively；a is the slope numbers of the fault；points 1 and 3 at the same height
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图 3 水平方向断层左（a）右（b）两侧不同边坡相同位置位移变化比较
L和R表示断层的左右两侧，a，b，c代表边坡，1，2，3为边坡的不同位置，La1即代表断层左侧第一个边坡1号点位振动图，下同
Figure 3. Displacement variation comparison of different slopes in the same location on both sides of the fault in horizontal direction
Different color represent the vibration figure of different location；L，R represent the left and right sides of the fault；a，b，c represent the side slope from the near to the distant；the number represents different location on the side slope；La1 represents the vibration figure of the No.1 point of first side slope on the left of the fault，the same below
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图 5 水平方向断层左（a）右（b）两侧相同边坡不同位置位移变化比较
Figure 5. Displacement variation comparison of the same side slope in different location on left side （a） and right side （b） of the fault in horizontal direction
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图 4 水平方向距断层两侧边坡a，b在1号 （a）和3号 （b）点位移变化比较
Figure 4. Displacement variation comparison of point 1 （a），3 （b） of slope a and b from both sides of the fault in horizontal direction
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图 6 垂直方向断层左（a）右（b）两侧不同边坡相同位置位移变化比较
Figure 6. Displacement variation comparison of different side slope in the same location on left side （a） and right side （b） of the fault in vertical direction
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图 8 垂直方向断层左（a）右（b）两侧相同边坡不同位置位移变化比较
Figure 8. Displacement variation comparison of the same side slope in different location on left side （a） and right side （b） of the fault in vertical direction
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图 7 断层两侧边坡a，b垂直方向上1号（a）和3号（b）点位移变化比较
Figure 7. Displacement variation comparison of point 1 （a），3 （b） of side slopes a，b from both sides of the fault in vertical direction
介质 密度/（kg·m−3） 泊松比 弹性模量/1010 Pa 介质 密度/（kg·m−3） 泊松比 弹性模量/1010 Pa 地壳 2.7 0.25 8.37 断层 2.7 0.25 5.45 低速层 2.7 0.31 3.35 边坡 2.7 0.25 8.37 地幔 3.3 0.30 12.10 
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表 2 x方向不同位置最大振幅及时刻
Table 2 Maximum amplitude and its time in different places of along x direction
边坡位置 边坡a振动方向 边坡b振动方向 边坡c振动方向 正方向 负方向 正方向 负方向 正方向 负方向 时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m上盘1号点 6.25 1.50 4.40 −0.35 5.60 0.50 - - 22.1 0.024 0 - - 上盘2号点 6.70 1.50 5.60 −0.60 6.00 0.60 - - 27.90 0.029 0 - - 上盘3号点 5.60 0.82 3.75 −0.30 6.25 0.65 - - 31.80 0.025 0 - - 下盘1号点 10.00 1.00 10.06 −0.35 13.75 0.22 - - 45.0 0.012 5 - - 下盘2号点 8.00 1.20 6.90 −0.30 13.00 0.20 - - 45.0 0.012 5 - - 下盘3号点 7.50 1.06 9.40 −0.24 10.06 0.18 - - 45.0 0.012 5 - -
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表 3 z方向不同位置最大振幅及时刻
Table 3 Maximum amplitude and its time in different place of z direction
边坡位置 边坡a振动方向 边坡b振动方向 边坡c振动方向 正方向 负方向 正方向 负方向 正方向 负方向 时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m时刻
/s最大振幅
/m上盘1号点 3.50 0.93 7.35 −0.74 8.8 0.14 5.59 −0.36 21.11 0.007 4 17.22 −0.014 上盘2号点 7.78 0.57 6.67 −0.82 9.44 0.29 6.11 −0.46 40.55 0.006 1 17.78 −0.013 上盘3号点 7.77 0.91 5.55 −1.04 14.11 0.14 6.11 −0.29 21.11 0.007 8 21.94 −0.013 下盘1号点 4.70 0.81 6.47 −0.59 9.41 0.15 12.78 −0.09 32.22 0.002 3 - - 下盘2号点 5.55 0.71 10.55 −0.64 17.78 0.14 16.67 0.11 33.33 0.003 4 - - 下盘3号点 6.11 0.59 8.89 −0.38 19.41 0.13 20.00 −0.11 31.67 0.002 1 - -
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