断裂引起的应变量计算方法

许顺山; Nieto-SamaniegoAF; Alaniz-ÁlvarezSA

断裂引起的应变量计算方法

墨西哥国立自治大学, 地球科学中心, 墨西哥 76001

基金项目:

墨西哥自然科学基金项目 89867

详细信息

作者简介:
许顺山(1963-), 男, 1998年于中国地质大学获博士学位。2000年到2004年在墨西哥国立自治大学和石油研究院做博士后工作。现为墨西哥国立自治大学教授。主要从事构造地质及石油地质工作。E-mail:sxu@dragon.geociencias.unam.mx

中图分类号: P54
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出版历程
- 收稿日期: 2008-09-16
- 刊出日期: 2008-12-01

METHODS TO CALCULATE THE FAULT-RELATED STRAIN

National Autonomous University of Mexico

摘要

摘要: 本文介绍了断裂引起的应变量计算方法。断裂作用可导致连续应变和非连续应变。连续应变与断裂位移断裂长度比值及断裂面上有效应力成正相关关系。影响非连续应变的因素有:断裂几何形态、断裂的旋转性、断裂规模。已经提出三种断裂旋转机制:刚性旋转, 垂直剪切和斜向剪切。对于这三种机制, 我们分别建立了断裂非连续应变的计算公式。这些公式与断裂的旋转角度和位移大小相关。刚性旋转时, 断块内部没有任何塑性变形, 因此地层的长度没有变化。它引起的非连续应变最小。垂直剪切作用使断块内地层变形, 但水平方向的地层长度不变。推算的公式表明, 对于相同的原始数据, 它引起的非连续应变比刚性旋转机制引起的非连续应变大。斜向剪切也使断块内地层变形, 但水平方向的长度也不变。在同等条件下, 它引起的非连续应变比垂直剪切机制引起的非连续应变大。
- 断裂 /
- 断裂应变 /
- 断裂旋转 /
- 垂直剪切 /
- 斜向剪切
Abstract: This paper presents some methods for calculation of fault strain. The faulting can produce continuous and discontinuous strain. The continuous strain has positive relationship with the ratio of fault displacement vs fault length and with the effective stress on the fault plane. When calculating the discontinuous fault strain, we should consider three factors that affect the establishment of equations: fault geometry, fault rotation, and fault size or fault displacement. There have been three mechanisms of fault rotation: rigid-body, vertical shear, and oblique shear. For these models, the calculation equations are established, respectively. These equations are related to the rotation angle and displacement of fault. For the rigid-body model, the fault has no internal deformation, thus the bed remain its length after rotation. The discontinuous strain due to this mechanism is smallest. The vertical shear produces bed deformation, whereas the horizontal length of bed does not change.The established equation indicates that, using the same data, the discontinuous fault strain is larger than that for the rigid-body model. Similarly, the oblique shear also causes bed deformation, but the horizontal length of bed remains constant. The obtained equation implies that the discontinuous fault strain is larger than that for the vertical shear model in the same condition.
- fault /
- fault strain /
- fault rotation /
- vertical shear /
- oblique shear

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图 1 一系列地堑和地垒引起地壳水平拉伸为L_f -L₀。所以水平方向的应变为(L_f -L₀) L₀

Figure 1. The horizontal extension due to grabens and horsts is L_f -L₀. Therefore, the horizontal strain is (L_f -L₀) L₀

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图 2 断裂引起的塑性应变随深度和D/L比率的变化

纵坐标表示深度, 深度单位为千米。横坐标表示应变, 单位为%

Figure 2. Map showing the relationships between plastic strain due to faulting and D/L ratio and depth of deformation

Depth (km)is shown in the axis X and strain (%)is shown in the axis Y

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图 3 断裂刚性旋转示意图

(a)表示断裂还没有位移时的状态; (b)表示断裂发生位移同时发生旋转, 断裂倾角变小。在问号处留下的空隙没有得到很好的解释。断裂旋转的角度等于地层的倾角, 也就是θ =δ₀-δ

Figure 3. Diagram of the rigid -body mechanism

(a)The initial state in which the faults are with no displacement; (b)The fault dips decrease with the rotation of faults.The spaces with interrogation marks are not well explained. The rotated angle of the bed is equal to that of the faults, that is to say, θ =δ₀-δ

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图 4 断裂旋转的简单剪切模型

(a)垂直剪切机制; (b)斜向剪切机制.剪切强度在靠近断裂时逐渐变大

Figure 4. Simple shear models for fault rotation

(a) Vertical shear model; (b) Oblique shear model. For two models, the shear stress increases close to the fault plane

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图 5 断裂和地层都不发生旋转的断块示意图

(a)为断裂运动前的状态; (b)为断裂运动后的状态

Figure 5. Diagram showing no rotation of both faults and bed

(a) The state before the movement of faults; (b) The state after the movement of faults

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图 6 刚性旋转机制断块示意图

断裂旋转以后, 地层长度不发生变化

Figure 6. Diagram showing rigid -body rotation of faults and bed

After rotation, the length of bed did not change

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图 7 垂直剪切机制断块示意图

断裂旋转使地层的长度发生变化

Figure 7. Sketch showing the vertical shear model

The bed has changed its length after vertical shear

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图 8 垂直剪切机制与斜向剪切机制拉伸量的对比

α为剪切方向与垂直方向的夹角(据Westaway和Kusznir, 1993^[10]修改)

Figure 8. Comparison of extension between the vertical shear and oblique shear

The angle α is the intersection angle between shear and vertical direction (M odified from Westaway and Kusznir, 1993^[10])

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图 9 墨西哥中央桌子山San Miguelito地区剖面地质图

标志体为Cantera未熔结凝灰岩(据Xu等2004^[12]修改)

Figure 9. Geological section from the San Miguelito of Mesa Central, Mexico

The marker bed is Cantera unwelded tuff (Modified from Xu et al., 2004^[12])

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表 1 据断裂形态和断裂旋转性的断裂分类(Wernicke, 1982) ^[6]

Table 1. The types of faults based on the geometry and rotation of faults^[6]

表 2 图 9中各断块的断裂应变计算(据Xu等2004^[12])

Table 2. Results of strains of the fault blocks in Fig. 9 (From Xu et al., 2004^[12])

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