基于Davidenkov本构模型的三维沉积盆地非线性地震动谱元法模拟

巴振宁; 赵靖轩; 桑巧稚; 梁建文

doi:10.11779/CJGE20230582

基于Davidenkov本构模型的三维沉积盆地非线性地震动谱元法模拟 English Version

巴振宁^{1, 2, 3,},
赵靖轩³,
桑巧稚⁴,
梁建文^{1, 2, 3}

1.
滨海土木工程结构与安全教育部重点实验室, 天津 300350
2.
天津大学中国地震局地震工程综合模拟与城乡抗震韧性重点实验室, 天津 300350
3.
天津大学土木工程系, 天津 300350
4.
同济大学地下建筑与工程系, 上海 200092

基金项目:

国家自然科学基金项目 52178495

国家自然科学基金地震科学联合基金（重点）项目 U2139208

详细信息

作者简介:
巴振宁(1980—)，男，博士，教授，主要从事大尺度复杂场地宽频地震动模拟方面的研究工作。E-mail: bazhenning_001@163.com

中图分类号: TU435
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出版历程
- 收稿日期: 2023-06-24
- 网络出版日期: 2024-07-11
- 刊出日期: 2024-06-30

Nonlinear ground motion simulation of three-dimensional sedimentary basin based on Davidenkov constitutive model and spectral element method

BA Zhenning^{1, 2, 3,},
ZHAO Jingxuan³,
SANG Qiaozhi⁴,
LIANG Jianwen^{1, 2, 3}

1.
Key Laboratory of Coast Civil Structure Safety of Ministry of Education (Tianjin University), Tianjin 300350, China
2.
Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration (Tianjin University), Tianjin 300350, China
3.
Department of Civil Engineering, Tianjin University, Tianjin 300350, China
4.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 为研究三维沉积盆地内低波速土体非线性反应对近断层地震动的影响，实现基于物理的全过程（震源破裂-地震波传播-复杂场地效应-近地表土体非线性反应）三维复杂场地地震动模拟，在谱元SPECFEM3D程序中进行二次开发，采用目前具有丰富工程应用且适用于不同土类的三参数Martin-Seed-Davidenkov本构模型，结合已有的不规则加卸载准则，通过在程序中修改每个显式时间步下的应力增量，实现了土体剪切模量的实时更新和加卸载拐点的有效识别，将土体的非线性特性纳入到三维复杂场地地震动模拟中。首先将建立的三维模型通过施加合理边界退化至一维，与一维非线性动力分析软件DEEPSOIL的结果进行了对比，验证了开发的正确性；进而将开发的程序应用于中国滇西南地区施甸盆地的非线性地震动模拟，并与相应的线性结果进行了对比。结果显示，受土体非线性的影响，施甸地区PGA和PGV较线性结果峰值均降低，且非线性土体对PGV的影响更加明显，较线性结果最大降低约30%；沉积非线性使沉积内部观测点的速度及其反应谱幅值降低，且特征频率向长周期方向移动。
- 非线性地震反应 /
- 三维沉积盆地 /
- Davidenkov本构模型 /
- 谱元法
Abstract: In order to study the influences of nonlinear response of low-wave velocity soil on near-fault ground motion in three-dimensional sedimentary basin, and realize the simulation of three-dimensional complex site ground motion based on the whole process of physics (source rupture-seismic wave propagation-complex site effect-near-surface soil nonlinear response), the secondary development is carried out in the spectral element method code-SPECFEM3D. The three-parameter Martin-Seed-Davidenkov constitutive model with generous engineering applications and suitable for different soil types is adopted. Based on the existing irregular loading and unloading criteria, the real-time updating of shear modulus of soil and the effective identification of loading and unloading inflection points are realized by modifying the stress increment at each explicit time step in the code. The nonlinear characteristics of soil are incorporated into the three-dimensional complex site ground motion simulation. The established three-dimensional model is first degenerated to one-dimensional one by applying a reasonable boundary, and compared with the results of one-dimensional nonlinear dynamic analysis software DEEPSOIL to verify the correctness of the development. Furthermore, the developed code is applied to the nonlinear ground motion simulation of the Shidian Basin in southwestern Yunnan province, China, and compared with the corresponding linear results. The results show that the peak values of acceleration and velocity in Shidian area are lower than those of linear results, and the influences of nonlinear soil on PGV are more obvious, which is about 30% lower than that of linear results. The deposition nonlinearity reduces the velocity and amplitude of response spectra of the receivers inside the deposition, and the characteristic frequency moves to the long period direction.
- nonlinear seismic response /
- three-dimensional sedimentary basin /
- Davidenkov constitutive model /
- spectral element method

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致谢: 感谢中国地震局工程力学研究所为本研究提供了2001年4月12日施甸5.9级地震近场区域的地震观测记录。

图 1 谱元法中非线性本构开发流程

Figure 1. Development process of nonlinear constitutive in spectral element method

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图 2 与DEEPSOIL对比验证的SPECFEM3D三维模型和入射Ricker波形

Figure 2. SPECFEM3D 3D model verified by comparison with DEEPSOIL (a) and incident Ricker waveform (b)

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图 3 给定应变路径下基于Masing准则和本文不规则加卸载准则的滞回曲线对比

Figure 3. Comparison of hysteresis curves based on Masing criterion and irregular loading and unloading criterion under given strain path

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图 4 不同强度地震动下SPECFE3D和DEEPSOIL的地表原点处水平加速度对比

Figure 4. Comparison of horizontal acceleration of SPECFE3D and DEEPSOIL under different intensity ground motions

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图 5 施甸盆地模拟研究区域

Figure 5. Simulation study area of Shidian Basin

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图 6 场地土的动剪切模量比与阻尼比曲线

Figure 6. Curves of shear modulus ratio and damping ratio of site soils

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图 7 2001年施甸5.9级地震震源时空分布

Figure 7. Spatial-temporal distribution of 2001 Shidian 5.9 earthquake

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图 8 地震动时程、反应谱模拟结果与观测记录对比

Figure 8. Comparison among simulated ground motion time history, Fourier amplitude spectra and ground motion records

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图 9 地表EW水平方向速度波场快照（每时刻第一和第二行分别对应线性和非线性结果）

Figure 9. Snapshot of surface EW velocity wave field (first and second lines correspond to linear and nonlinear results respectively at each moment)

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图 10 模拟区域以及盆地范围内的地表PGA结果（左图为线性结果，右图为非线性结果）

Figure 10. PGA results in simulated area and basin (left figure is a linear result, and right figure is a nonlinear result)

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图 11 模拟区域以及盆地范围内的地表PGV结果（左图为线性结果，右图为非线性结果）

Figure 11. PGV results in simulated area and basin (left figure is a linear result, and right figure is a nonlinear result)

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图 12 盆地内地表点^#1~^#6处速度三分量时程（图 5中对应盆地内地表观测点^#1~^#6）

Figure 12. Three-component time histories of velocity at surface points ^#1~^#6 in basin (Figure 5 corresponds to surface receivers ^#1~^#6 in basin)

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图 13 盆地内地表点^#1~^#6处速度反应谱（图 5中对应盆地内地表观测点^#1~^#6）

Figure 13. Response spectral velocities of surface points ^#1~^#6 in basin (Figure 5 corresponds to surface receivers ^#1~^#6 in the basin)

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表 1 施甸盆地覆盖层及地壳层材料参数

Table 1 Wave velocity structure of Shidian Basin and crustal layers

深度/km	${v_{\text{P}}}$ /(m·s^-1)	${v_{\text{s}}}$ /(m·s^-1)	密度/(kg·m^-3)	${Q_{\text{P}}}$	${Q_{\text{S}}}$
沉积	1100	500	1800	100	50
3	4570	2670	2300	534	267
5	4626	2868	2572	574	287
8	5577	3278	2600	654	327
10	5898	3500	2676	700	350
15	6013	3509	2750	716	358
20	6288	3654	2803	732	366

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表 2 施甸5.9级地震全局震源参数

Table 2 Global source parameters of Shidian M5.9 earthquake

走向/(°)	倾角/(°)	滑动角/(°)	断层面长度/km	断层面宽度/km	震中深度/km	破裂方式
161	65	-150	8.1	7.9	7.5	中心破裂

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表 3 施甸5.9级地震局部震源参数

Table 3 Local source parameters of Shidian M5.9 earthquake

局部参数	单位	定标律	参数值
面积S_m	km²	lgS_m=lgS–0.80	9.10
平均错动量D_m	cm	lgD_m=lgD+0.39	46.66
长度L_m	km	lgL_m=lgL–0.45	2.68
宽度W_m	km	W_m=S_m/L_m	3.40
沿走向中心X_m	km	lgX_m=lgL–0.31	3.79
沿倾向中心Y_m	km	lgY_m=lgW–0.35	3.79

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