The Late Quaternary Activity Characteristics of the Dulan South Fault in the Qaidam Block
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摘要: 青藏高原是新生代期间印度与欧亚板块持续强烈陆陆碰撞作用下形成的陆内活动造山带，发育了复杂的活动断裂系统，并成为东亚显著的陆内强震活动区。已有学者对高原活动断裂的研究多集中于地块边界带上，缺少对块体内部变形的研究。近期在开展青海省海西州都兰县察汗乌苏镇地震小区划工作中，调查发现在柴达木地块东南部的都兰次级断块内部存在明显的晚第四纪活断层−都兰南断裂。通过对都兰南断裂开展详细的野外地质调查、高分辨率遥感影像解译和无人机低空摄影精细测量等，得到该断裂的构造地貌特征、空间几何展布及运动特性，并通过开挖探槽和地质测年等，对其最新活动时代及滑动速率等进行初步约束。研究结果表明，该断裂为全长约43 km、全新世活动的左旋走滑断裂，并在其东段存在长约6 km的地表破裂带。在该断裂东段，地表的晚第四纪累积左旋位移达（14.5±1.8）m，西段的左旋走滑量为（6.7±0.8）m，初步估算其东段的水平走滑速率为1.56～1.9 mm/a，西段的水平走滑速率为0.9～1.16 mm/a。该断裂的发现及全新世活动的厘定表明，青藏高原内部活动构造变形样式复杂，断块内部通常存在不同程度的弥散变形。因此，断块内部的强震危险性不容忽视。该活动断裂的发现为认识都兰次级断块内部变形样式、应变分配等提供了参考，为都兰地区地震危险性的认知提供了支撑，对防御和减轻区域地震灾害风险具有一定指导意义。Abstract: The Qinghai Tibet Plateau is an intracontinental active orogenic belt formed under the continuous strong continental collision between India and Eurasia during the Cenozoic era. It has developed an extremely complex active fault system and has become an extremely significant intracontinental strong earthquake activity area in East Asia. Previous studies on active faults in the plateau have focused more on the boundary zone of the block, but paid less attention to the internal deformation of the block. Recently, during the seismic zoning of Chahanwusu Town, Dulan County, Haixi Prefecture, Qinghai Province, it was found that there was an obvious late Quaternary active fault - Dulan South fault in the Dulan secondary fault block in the southeast of Qaidam block. Through detailed field geological survey, high-resolution remote sensing image interpretation and low altitude photography fine measurement of the Dulan South fault, the structural and geomorphic characteristics, spatial geometric distribution and movement characteristics of the fault are obtained. The latest activity age and sliding rate are preliminarily constrained by excavation of trench and geological dating. The results show that the fault is a 43 km long, Holocene left lateral strike slip fault, and there is a 6 km long surface fracture zone at its east end. In the east section of the fault, the accumulated left lateral displacement of the surface in the late Quaternary is (14.5 ± 1.8) m, and the left lateral strike slip of the west section is (6.7 ± 0.8) m. It is preliminarily estimated that the horizontal strike slip rate in the east section is about 1.56～1.9 mm/a, and that in the west section is about 0.9～1.16 mm/a. The discovery of the fault and the determination of Holocene activity indicate that the active tectonic deformation style in the Qinghai Tibet Plateau is very complex, and there is usually dispersion deformation in the fault block with different degrees. Therefore, the risk of strong earthquakes in the fault block cannot be ignored. The new discovery of this active fault provides an important basis for understanding the internal deformation style and strain distribution of Dulan sub-fault block, provides strong support for the recognition of seismic risk in Dulan area, and has a certain guiding significance for the prevention and mitigation of regional seismic disaster risk.
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Key words:
- Dulan South fault /
- Holocene activities /
- Surface rupture /
- Left lateral strike slip /
- Motion rate
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引言
关于场地地震反应的分析已有大量研究成果，研究表明土壤在地震作用下会表现出材料非线性效应ADDIN EN.CITE.DATA（Joyner等，1975；Huang等，2001；Arslan等，2006；Hosseini等，2012）。等效线性化方法ADDIN EN.CITE.DATA（Schnabel等，1972；Idriss等，1992；Bardet等，2000；王笃国等，2016）是一种频域方法，通过在不同土体应变条件下选择等效阻尼比和剪切模量，将非线性问题转化为线性问题。当采用材料非线性本构模型描述土体非线性时，需采用时间积分算法求解非线性动力有限元方程。时间积分算法可分为隐式方法和显式方法。隐式算法每时刻需求解线性代数方程组，计算效率相对较低，如Wilson-θ法和Newmark法等。显式算法无需求解线性代数方程组，适合于强非线性和自由度数目较大的问题。研究者已提出多种显式时间积分算法ADDIN EN.CITE.DATA（Chung等，1994；王进廷等，2002；Belytschko等，2014）。作者近期提出一种二阶精度的单步显式算法，该算法适合变时步问题，在线弹性范围内稳定性较好。本文将该算法推广至求解非线性动力有限元方程中，并将其应用于地震波垂直入射时非线性地震反应分析。
1. 非线性动力有限元方程的显式时间积分算法
设已知非线性体系第${t_i}$时步的受力状态，求解第${t_{i + 1}}$时步的非线性结构动力学方程：
$${\boldsymbol{M}}{{\boldsymbol{\ddot u}}_{i + 1}}{\boldsymbol{ + C}}{{\boldsymbol{\dot u}}_{i + 1}} + {\boldsymbol{f}}_{i + 1}^S{\boldsymbol{ = }}{{\boldsymbol{f}}_{i + 1}}$$ (1) 式中M、C、${{\boldsymbol{f}}^S}$和${\boldsymbol{f}}$分别表示非线性体系的质量矩阵、阻尼矩阵、内力向量和外荷载向量；u表示位移，点号对时间t求导，i+1表示第${t_{i + 1}}$时刻。第i+1时刻时间步长为：
$${\boldsymbol{\Delta }}{t_i} = {t_{i + 1}} - {t_i}$$ (2) 文献显式方法求解非线性方程（1）的过程如下，第i+1时刻位移${{\boldsymbol{u}}_{i + 1}}$为：
$${{\boldsymbol{u}}_{i + 1}} = {{\boldsymbol{u}}_i} + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}{{\boldsymbol{\dot u}}_i} + \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}^2}}{2}{{\boldsymbol{\ddot u}}_i}$$ (3) 第i+1时刻位移增量$\mathit{\Delta }{{\boldsymbol{u}}_i}$、内力增量$\mathit{\Delta }{\boldsymbol{f}}_i^S$和内力全量${\boldsymbol{f}}_{i + 1}^S$分别为：
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{u}}_i} = {{\boldsymbol{u}}_{i + 1}} - {{\boldsymbol{u}}_i}$$ (4) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{f}}_i^S = {\boldsymbol{f}}(\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{u}}_i})$$ (5) $${\boldsymbol{f}}_{i + 1}^S = {\boldsymbol{f}}_i^S + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{f}}_i^S$$ (6) 第i+1时刻预估速度${{\boldsymbol{\dot {\tilde u}}}_{i + 1}}$、预估加速度${{\boldsymbol{\ddot {\tilde u}}}_{i + 1}}$、速度${{\boldsymbol{\dot u}}_{i + 1}}$和加速度${{\boldsymbol{\ddot u}}_{i + 1}}$分别为
$${{\boldsymbol{\dot {\tilde u}}}_{i + 1}} = {{\boldsymbol{\dot u}}_i} + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}{{\boldsymbol{\ddot u}}_i}$$ (7) $${{\boldsymbol{\ddot {\tilde u}}}_{i + 1}} = {{\boldsymbol{M}}^{ - 1}}({{\boldsymbol{f}}_{i + 1}} - {\boldsymbol{C\dot {\tilde u}}}_{i + 1}^{} - {\boldsymbol{f}}_{i + 1}^S)$$ (8) $${{\boldsymbol{\dot u}}_{i + 1}} = {{\boldsymbol{\dot u}}_i} + \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}}}{2}({{\boldsymbol{\ddot u}}_i} + {{\boldsymbol{\ddot {\tilde u}}}_{i + 1}})$$ (9) $${{\boldsymbol{\ddot u}}_{i + 1}} = {{\boldsymbol{M}}^{ - 1}}({{\boldsymbol{f}}_{i + 1}} - {\boldsymbol{C\dot u}}_{i + 1}^{} - {\boldsymbol{f}}_{i + 1}^S)$$ (10) 式（3）—式（10）为求解式（1）的显式算法。算法中需由位移增量计算内力增量，目前常用的应力计算方法包括向前欧拉法、向后欧拉法和完全隐式计算法等ADDIN EN.CITE.DATA（Sloan等，1992；2001；Ahadi等，2003）。下面给出式（5）由位移增量计算内力增量的过程，即一种带误差控制的修正欧拉算法。
对于每个有限单元，由位移增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{u}}_i^e$计算应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$的表达式为：
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e = {{\boldsymbol{B}}^e}\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{u}}_i^e$$ (11) 式中Be为应变矩阵。将ti时刻单元应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$赋值给子步应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$，ti时刻单元应力${\boldsymbol{ \pmb{\mathit{ σ}} }}_i^e$赋值给${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e$，初始化子步应变增量和应力状态分别为：
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e \leftarrow \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$$ (12) $${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e \leftarrow {\boldsymbol{ \pmb{\mathit{ σ}} }}_i^e$$ (13) 每个子步中应力增量计算思路见图 1，具体计算公式如下：
$${\boldsymbol{D}}_1^e = {\boldsymbol{D}}({\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e)$$ (14) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e = {\boldsymbol{D}}_1^e\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (15) $${\boldsymbol{D}}_2^e = {\boldsymbol{D}}({\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e)$$ (16) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e = {\boldsymbol{D}}_2^e\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (17) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e = \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e}}{2}$$ (18) 式中${{\boldsymbol{D}}^e}$为单元应力-应变关系矩阵。判断每个子步中应力增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{ \pmb{\mathit{ σ}} }}_s}$是否符合精度要求的误差判断式为：
$${e_r} = \frac{{\left\| {\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e - \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e} \right\|}}{{\left\| {{\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e} \right\|}}$$ (19) 判断误差er是否小于预先给定的判断值st，条件不满足时，缩小子步应变增量为：
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e \leftarrow A\sqrt {{{{s_t}} \mathord{\left/ {\vphantom {{{s_t}} {{e_r}}}} \right. } {{e_r}}}} \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (20) 式中A为误差峰值系数。采用缩小的子步应变增量重新进行式（14）—式（19）的计算与判断，循环直至满足精度要求，更新剩余应变增量和应力状态分别为：
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e \leftarrow \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e - \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (21) $${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e \leftarrow {\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e$$ (22) 利用更新剩余应变增量和应力状态循环执行式（14）—式（20），直至剩余应变增量小于等于零结束。
利用求得的第i+1时刻单元应力可得到单元应力增量和内力增量分别为：
$$ \Delta \boldsymbol{\sigma }_i^e = \boldsymbol{\sigma }_{i + 1}^e - \boldsymbol{\sigma }_i^e $$ (23) $$ \Delta {\boldsymbol{f}}_i^S{\rm{ = }}\sum\limits_e {\int {{{\boldsymbol{B}}^{e{\rm{T}}}}\boldsymbol{\Delta }{\boldsymbol{\sigma }}_i^e{\bf{d}}A} } $$ (24) 2. 地震波垂直入射时场地非线性地震反应分析
本节将上述非线性有限元方程的显式时间积分算法应用于地震波垂直入射时场地非线性地震反应分析中。假定基岩为线弹性半空间，考虑基岩上覆土层的材料非线性，不考虑土体阻尼。在土层下部设置黏性边界条件模拟半空间基岩的辐射阻尼，并在该处以等效结点力的方式实现地震动输入。
计算模型见图 2，选取A点作为观测点。土体非线性材料本构模型选取邓肯-张模型，土体线弹性参数见表 1，未给出配套的非线性参数，故算例中的非线性参数参考实际情况选取，后续研究中将使用更真实表现土体非线性行为的本构模型及真实工程场地参数。算例中的大气压参数取100kPa，内摩擦角增量取0°。入射地震动分别选取狄拉克脉冲和实测地震动（Gilroy Array #3，Coyote Lake, 1979）。入射狄拉克脉冲见图 3，观测点结果见图 4，实测地震动见图 5，观测点结果见图 6。图 4、图 6中给出采用中心差分法的计算结果作为参考解，由图 4、图 6可知，本文算法与中心差分法计算结果吻合较好，说明本文算法的有效性。
图 2 大开车站沿线土层纵断面构造Figure 2. Site condition of the Daikai subway station in vertical direction表 1 土层参数Table 1. Parameters of soils土质 深度/
m$\rho $/
（g/cm3）cs /
（m/s）v
-EN
-Rf
-c/
（MPa）θ/（°） D
-F
-人工填土 0—1.0 1.9 140 0.33 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 1.0—5.1 1.9 140 0.32 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 5.1—8.3 1.9 170 0.32 0.36 0.768 0.120 31.0 1.11 0.015 更新世粘土 8.3—11.4 1.9 190 0.40 0.44 0.822 0.188 28.4 1.01 0.012 更新世粘土 11.4—17.2 1.9 240 0.30 0.44 0.822 0.188 28.4 1.01 0.012 更新世砂土 17.2—22.2 2.0 330 0.26 0.51 0.840 0.300 30.0 1.02 0.011 基岩 ＞22.2 2.0 330 0.26 - - - - - - 
图 3 狄拉克脉冲速度和加速度时程图Figure 3. Velocity and acceleration time history of the Dirac pulse
图 4 狄拉克脉冲入射时场地反应分析结果Figure 4. Results of site analysis under the incident of Dirac pulse
图 5 实测地震动速度和加速度时程图Figure 5. Velocity and acceleration time history of the seismic motion
图 6 实测地震动入射时场地反应分析结果Figure 6. Results of site reaction analysis under the incident of the seismic motion表 1中ρ、cs、v、EN、Rf、c、θ为模型参数，分别表示密度、剪切波速、泊松比、无量纲幂次、破坏比、土的内聚力、土的摩擦角。D、F为试验常数。
3. 结论
本文发展一种求解材料非线性结构动力学方程的显式时间积分算法，并应用于地震波竖直入射时非线性地震反应分析中，通过算例验证了该方法的有效性。该显式算法具有无需对角阻尼矩阵、单步、稳定性良好等优点。本文考虑了邓肯-张非线性弹性本构模型，下步研究可考虑将该显式算法扩展到弹塑性本构模型及更能反映土层真实变形的本构模型中。
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图 3 都兰南断裂地表破裂遥感影像（影像据Google map，红色箭头为断裂疑似位置）
Figure 3. Remote sensing image of surface ruptures at the Dulan South fault （According to google map, the red arrow is the suspected location of the break）
图 6 沿地表破裂发育的断层凹槽、反向陡坎和断塞塘
Figure 6. Fault grooves, reverse steep ridges and fault ponds develop along surface ruptures
图 7 G109国道以西1.5 km处断裂沿线地貌特征
Figure 7. Landform features along the fault 1.5 km to the west of G109 national highway
图 8 G109国道以西1.5 km处断裂沿线左旋位移
Figure 8. Photo of left-handed displacement along the fault line 1.5 km west of G109 national highway
图 9 探槽与断裂位置示意
Figure 9. Schematic diagram of the location of exploration trenches and faults
表 1 地表破裂沿线冲沟左旋位错实测位移
Table 1. Measured displacement table of left-handed dislocation of gullies along the surface rupture
实测水平位移点 水平位移/m 平均水平位移/m S1 11.7±1.2 14.5±1.8 S2 14.5±1.5 S3 15.8±1.5 S4 16.0±1.6 
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表 2 断层陡坎垂直高度实测位移
Table 2. Measured displacement of vertical height of fault scarp
实测垂直位移点 垂直位移/m 平均垂直位移/m P1 1.0 0.85 P2 0.6 P3 0.8 P4 1.0
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表 3 断裂沿线冲沟左旋位错实测位移
Table 3. Measured displacement table of gully left-handed dislocation along the fault
实测水平位移点 水平位移/m 平均水平位移/m S5 7.0±0.8 6.7±0.8 S6 6.4±0.8
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表 4 桃斯托河西北岸探槽14C样品测试结果
Table 4. Test results of 14C sample from trench on the north west bank of taosto river
实验室编号 样品号 取样位置 测年物质 常规放射性碳年代/a BP 树轮校正2σ/Cal a BP Beta-536481 DLT1-C2 U4地层 泥炭 4 820±30 5 533±41 Beta-536483 DLT1-C4 U5地层 泥炭 7 600±30 8 397±21
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表 5 G109国道以西探槽OSL样品测试结果
Table 5. Test results of OSL sample trench from the trench to west of G109 national highway
实验室编号 样品号 取样位置 环境剂量率/（Gy·ka−1） 测年物质 等效剂量/Gy 年龄/ka — DLT2-1 U3地层 — 未取得测试数据 — — 2020_1_22 DLT2-2 U3地层 3.646±0.160 粉质黏土 17.58±1.97 4.8±0.6 2020_1_23 DLT2-3 U3地层 3.653±0.162 细砂 19.41±1.44 5.3±0.5
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表 6 G109国道以西探槽14C样品测试结果
Table 6. Test results of 14C sample from the trench to the west of G109 national highway
实验室编号 样品号 取样位置 测年物质 常规放射性碳年代/a BP 树轮校正2σ/Cal a BP Beta-570283 DLT2-C1 U4地层 泥炭 5 710±30 6 497±51 Beta-570284 DLT2-C2 U2地层 泥炭 2 820±30 2 922±44
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