Three-dimensional numerical simulation of rupture process of overlying soil caused by buried normal fault movement
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摘要: 通过建立三维数值模型，对隐伏正断层在均匀错动和倾斜错动方式下土体的破裂过程进行研究。利用应力罗德参数和等效塑性应变分别对断层错动过程中上覆土体的应力状态和破坏形式进行分析，并提出土体破裂的判别方法。通过对数值模拟结果的分析得到以下结论：① 在断层错动过程中，下盘一侧受断层错动影响的上覆土体的应力状态经压剪→纯剪→拉剪逐渐变化，而上盘一侧上覆土体的应力状态变化较为复杂，经压剪→纯剪→拉剪→纯剪→压剪重复变化；② 在断层均匀错动过程中，断层下盘一侧土体的破裂率先出现在地表拉剪区内，随错动量的增大，破裂带向两侧、向深部扩展；同时，下盘一侧土体的底部产生破坏，并斜向上扩展，逐渐与顶部破裂相连；③ 在断层倾斜错动过程中，地表破裂出现的位置和上覆土体的厚度有关。对于厚度较大的土体，正断层倾斜错动能够在地表形成与断层走向有一定夹角、且与断层长度相比长度很短的地表破裂或地裂缝，而数值模拟可对正断层错动导致的地表破裂的模式加以补充，为研究地裂缝的形成机理和分布形式提供依据。Abstract: The rupture process of overlying soil caused by uniform movement and inclined movement of buried normal fault was studied by setting a three-dimensional numerical model. The stress state and failure style of overlying soil are respectively analyzed by using stress Lode parameter and equivalent plastic strain during fault movement, and a discrimination method of soil rupture is recommended. The conclusions are drawn as follows through analyzing the results of numerical simulation: ① As affected by fault movement, the stress state of overlying soil on the footwall side of the fault varies via compression-shear → pure-shear → tension-shear during fault movement, and the soil stress state on the upper wall side of the fault is fairly complex, which repetitively varies via compression-shear → pure-shear → tension-shear → pure-shear → compression-shear. ② For the uniform movement of the fault, the surface soil ruptures firstly occur at the tension-shear area on the footwall side of the fault, and with fault movement increased, the ruptures develop towards both sides as well as downward. Meantime, the bottom soil failures occur on the footwall side of the fault and develop obliquely upward, and finally connected with the rupture of surface soil. ③ For the inclined movement of the fault, the positions of soil rupture are relative with the thickness of overlying soil. When the overlying soil is thick, the surface soil ruptures or ground fissures occur due to the fault movement, which have an angle with the fault strike, and are much shorter than the fault. The numerical simulations can reveal the surface soil rupture patterns and will provide the basis for the studies on the origin and distributed patterns of ground fissures.
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Keywords:
- rupture /
- overlying soil /
- stress state /
- plastic deformation /
- normal fault /
- numerical simulation
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图 3 埋深3.0 m地层沉降变形模拟位错量TD与试验位错量SD的比较
Figure 3. The numerical calculation amount of dislocation SD versus testing amount of dislocation TD at buried depth of 3.0 m
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图 4 不同位置土单元应力罗德参数μσ随断层错动位移量的变化
（a） 地表土体；（b） 土体埋深为37.5 m；（c） 土体埋深为62.5 m；（d） 土体埋深为87.5 m
Figure 4. The change of stress Lode parameter of soil mass at different positions with fault dislocation
（a） Surface soil mass；（b） The soil mass buried at depth of 37.5 m；（c） The soil mass buried at depth of 62.5 m；（d） The soil mass buried at depth of 87.5 m
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图 5 不同倾角的断层错动对上覆土体应力罗德参数μσ变化的影响
（a） 地表土体；（b） 土体埋深为37.5 m；（c） 土体埋深为62.5 m；（d） 土体埋深为87.5 m
Figure 5. The change of stress Lode parameter of overlying soil mass with different dip angles
（a） Surface soil mass；（b） The soil mass buried at depth of 37.5 m；（c） The soil mass buried at depth of 62.5 m；（d） The soil mass buried at depth of 87.5 m
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图 6 不同位置土体的累积等效塑性应变随断层位错量的变化
（a） 地表土体；（b） 土体埋深为37.5 m；（c） 土体埋深为62.5 m；（d） 土体埋深为87.5 m
Figure 6. The change of cumulative equivalent plastic strain of soil mass at different positions with fault dislocation
（a） Surface soil mass；（b） The soil mass buried at depth of 37.5 m；（c） The soil mass buried at depth of 62.5 m；（d） The soil mass buried at depth of 87.5 m
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图 7 断层倾角对累积等效塑性应变的影响
（a） 地表土体；（b） 土体埋深为37.5 m；（c） 土体埋深为62.5 m；（d） 土体埋深为87.5 m
Figure 7. The effect of fault dip angle on cumulative equivalent plastic strain
（a） Surface soil mass；（b） The soil mass buried at depth of 37.5 m；（c） The soil mass buried at depth of 62.5 m；（d） The soil mass buried at depth of 87.5 m
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图 8 断层均匀错动致上覆土体破裂的3个阶段
（a） 断层错动0.82 m；（b） 断层错动1.05 m；（c） 断层错动1.28 m；（d） 断层错动2.1 m
Figure 8. The three stages of overlying soil rupture process caused by uniform fault movement
（a） The fault movement was 0.82 m；（b） The fault movement was 1.05 m；（c） The fault movement was 1.28 m；（d） The fault movement was 2.1 m
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图 9 断层均匀错动致上覆土体破裂过程示意图
Figure 9. The diagram of overlying soil rupture process caused by uniform fault movement
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图 1 正断层错动方式
（a） 均匀错动；（b） 倾斜错动
Figure 1. The movement patterns of normal fault
（a） Uniform movement；（b） Inclined movement
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图 10 断层倾斜错动致上覆土体破裂过程
（a） 初始破裂；（b） 破裂扩展；（c） 破裂贯通
Figure 10. The overlying soil rupture process caused by inclined movement
（a） The initial rupture stage；（b） The rupture extension stage；（c） The rupture connection stage
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图 11 断层倾斜错动过程中上覆土体厚度对地表破裂形式的影响
（a） 土体厚度为 100 m；（b） 土体厚度为 200 m；（c） 土体厚度为 300 m；（d） 土体厚度为 400 m
Figure 11. The effect of overlying soil thickness on the surface rupture pattern during inclined fault movement
（a） The overlying soil is 100 m thick；（b） The overlying soil is 200 m thick；（c） The overlying soil is 300 m thick；（d） The overlying soil is 400 m thick
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图 12 点P1，P2间的距离与上覆土体厚度的关系
Figure 12. The relations between the overlying soil thickness and the distance from point P1 to P2
表 1 模型参数
Table 1 Model parameters
名称 变形模量
/（108Pa）泊松比 密度
/（kg·m−3）内摩擦
角/°黏聚力
/kPa土层 2.4 0.3 1 970 35 38.5 岩石 225 0.2 2 140 断层带 68 0.21 2 040 
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表 2 所选单元的位置及编号
Table 2 The location and number of selected elements
土体埋深/m 距段层带距离/m −200 −160 −120 −80 −40 断层带 40 80 120 160 12.5 B1 C1 D1 E1 F1 G1 H1 I1 J1 K1 37.5 B2 C2 D2 E2 F2 G2 H2 I2 J2 K2 62.5 B3 C3 D3 E3 F3 G3 H3 I3 J3 K3 87.5 B4 C4 D4 E4 F4 G4 H4 I4 J4 K4
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