Newmark位移预测模型改进及同震滑坡危险性评估研究

黄健航; 刘甲美; 王涛

doi:10.11899/zzfy20250039

Newmark位移预测模型改进及同震滑坡危险性评估研究

doi: 10.11899/zzfy20250039

黄健航^{1, 2, 3,},
刘甲美^{1, 2, 3, ,},
王涛^{1, 2, 3}

1.
中国地质科学院地质力学研究所, 北京 100081
2.
自然资源部活动构造与地质安全重点实验室, 北京 100081
3.
自然资源部陕西宝鸡地质灾害野外科学观测研究站, 陕西宝鸡 721000

基金项目: 国家重点研发计划（2022YFC3003505、2022YFC3003503）；自然科学基金项目（41572313）；中国地质调查项目（DD20221738）；中国地质科学院地质力学研究所科研项目（所科研86）

详细信息

作者简介:
黄健航，男，生于1995年。博士。主要从事地震滑坡危险性评价方面的工作。E-mail：863621345@qq.com

通讯作者:
刘甲美，男，生于1987年。副研究员，硕士生导师。主要从事地质灾害风险定量评估方面的研究。E-mail：ljm19870918@126.com

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出版历程
- 收稿日期: 2025-03-10
- 录用日期: 2025-04-28
- 修回日期: 2025-04-16
- 网络出版日期: 2025-09-19

Improvement of the Newmark Displacement Model and Coseismic Landslides Hazard Assessment

Huang Jianhang^{1, 2, 3
,},
Liu Jiamei^{1, 2, 3
, ,},
Wang Tao^{1, 2, 3}

1.
Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
2.
Key Laboratory of Active Tectonics and Geological Safety, Ministry of Natural Resources, Beijing 100081, China
3.
Observation and Research Station of Geological Disaster in Baoji, Ministry of Natural Resources, Baoji, Shaanxi 721000, China

摘要

摘要: 基于Newmark累积位移模型的区域地震滑坡危险性评估是目前国内外主流的定量评估方法之一，而Newmark位移模型是应用该方法的关键。本文利用2008年汶川M_S8.0地震强震动数据，优化改进并建立了基于临界加速度、Arias 强度参数的线性和二次函数2种形式的Newmark位移模型，同时与已有位移预测模型在拟合优度上进行对比。利用2013年芦山M_S7.0地震强震动数据进行对比分析，验证了改进模型的精度和有效性。基于改进模型及前人模型，开展了2017年九寨沟M_S7.0地震诱发同震滑坡危险性评估分析，预测位移与实际地震滑坡分布对比显示，改进模型的ROC曲线成功率（S_AUC=0.913）略高于前人模型，表明其对地震滑坡高危险区的评估效果更佳，可为青藏高原东缘等类似地区的同震滑坡识别提供参考。
- Newmark /
- 临界加速度 /
- Arias强度 /
- 地震滑坡 /
- 汶川地震 /
- 九寨沟地震
Abstract: Regional seismic landslide hazard assessment based on the Newmark cumulative displacement model is one of the mainstream assessment methods at home and abroad. The Newmark displacement prediction model is the key to applying this method. In this paper, two forms of Newmark displacement models (linear and quadratic functions) were established with the strong motion data of the 2008 Wenchuan M_S8.0 earthquake, based on the critical acceleration and Arias intensity parameters. By comparing with the fitting goodness of previous displacement prediction models, it is shown that the proposed models in this paper have great improvement in the displacement prediction ability. Using the strong motion data of the 2013 Lushan M_S7.0 earthquak, the accuracy and validity of the proposed models were verified. Based on the improved models and previous models, a comparative analysis of the seismic landslides hazard assessment in the 2017 M_S7.0 Jiuzhaigou earthquake was carried out. By comparing the predicted displacements with the actual distribution of earthquake-induced landslides, the results of the ROC curve comparison show that the success rate AUC of earthquake-induced landslides in proposed models is 0.913, which is higher than that of other models. Its identification effect on high hazardareas of earthquake-induced landslides is better. The proposed models provide enhanced theoretical support for coseismic landslide identification in analogous regions such as the eastern margin of the Qinghai-Tibet Plateau.
- Newmark /
- Critical acceleration /
- Arias intensity /
- Seismic landslide /
- Wenchuan earthquake /
- Jiuzhaigou earthquake

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图 1 研究震例及数据分布

Figure 1. The distribution of earthquake events and data

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图 2 Newmark累积位移计算原理（修改自Jibson（2007））

Figure 2. Principle of newmark cumulative displacement calculation （Modified from Jibson （2007））

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图 3 I_a与D_n拟合关系图

Figure 3. Fitting relationship diagram between I_a and D_n

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图 4 不同临界加速度下I_a-D_n二次函数关系拟合

Figure 4. Quadratic relationship between I_a and D_n for different a_cvalues

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图 5 不同Arias强度下logD_n随临界加速度a_c的变化

Figure 5. The variation of logD_n with the a_c under different Arias intensities

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图 6 参数c随I_a变化关系

Figure 6. Relationship between parameter c and I_a

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图 7 不同位移预测模型拟合效果对比

Figure 7. Comparison of fitting performance of different displacement models under various a_c values

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图 8 不同位移模型预测曲线与芦山地震数据散点对比

Figure 8. Comparison between prediction of displacement models and scatter plot of Lushan data

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图 9 区域主要地层年代

Figure 9. Main stratigraphic ages in the region

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图 10 临界加速度a_c

Figure 10. Distribution of a_c

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图 11 地震动峰值加速度a_max

Figure 11. Distribution of a_max

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图 12 基于线性模型的地震滑坡危险性评估结果

Figure 12. Seismic landslide hazard assessment based on the line model

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图 13 基于二次函数模型的地震滑坡危险性评估结果

Figure 13. Seismic landslide hazard assessment based on the quadratic model

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图 14 基于徐光兴等（2012）模型的地震滑坡危险性评估结果

Figure 14. Seismic landslide hazard assessment based on Xu model （Xu et al.，2012）

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图 15 徐光兴等（2012）模型与本文二次函数模型效果对比

Figure 15. Comparison between the result of Xu model （Xu et al.，2012） and our quadratic model

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图 16 九寨沟地震不同位移模型诱发滑坡评估结果 ROC曲线

Figure 16. ROC curves of different displacement models in the Jiuzhaigou earthquake

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表 1 基于Arias强度和a_max的主流Newmark累积位移预测模型

Table 1. The mainstream Newmark displacement prediction models based on Arias intensity and a_max

序号	位移预测模型	参考文献
1	$ \mathrm{l}\mathrm{o}\mathrm{g}{D}_{n}=1.460\mathrm{l}\mathrm{o}\mathrm{g}{I}_{\mathrm{a}}-6.642{a}_{c}+1.546\pm 0.409 $	Jibson（1993）
2	$ \mathrm{l}\mathrm{o}\mathrm{g}{D}_{n}=1.521 {\mathrm{log}}{I}_{\mathrm{a}}-1.1993 {\mathrm{log}}{a}_{c}-1.546\pm 0.375 $	Jibson等（2000）
3	$ {\mathrm{log}}{D}_{n}=0.194+{\mathrm{log}}\left[{\left(1-\dfrac{{a}_{\mathrm{c}}}{{a}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\right)}^{2.262}{\left(\dfrac{{a}_{\mathrm{c}}}{{a}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\right)}^{-1.754}\right]\pm 0.371 $	徐光兴等（2012）
4	$ {\mathrm{log}}{D}_{n}=0.405 {\mathrm{log}}{I}_{\mathrm{a}}-4.756\dfrac{{a}_{\mathrm{c}}}{{a}_{\mathrm{m}\mathrm{a}\mathrm{x}}}+2.276\pm 0.423 $	徐光兴等（2012）
5	$ {\mathrm{log}}{D}_{n}=1.147 {\mathrm{log}}{I}_{\mathrm{a}}-13.664{a}_{c}+9.673{a}_{c}{\mathrm{log}}{I}_{\mathrm{a}}+13.96 $	Yuan等（2016）

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表 2 不同临界加速度时logI_a-logD_n的线性及二次函数关系R²值

Table 2. R² values of the linear and quadratic relationships between logI_a - logD_n for different a_c

a_c	函数关系 R²		a_c	函数关系 R²
a_c	线性函数	二次函数	a_c	线性函数	二次函数
0.01g	0.86	0.92	0.1g	0.81	0.82
0.02g	0.88	0.94	0.12g	0.85	0.85
0.03g	0.87	0.94	0.14g	0.84	0.84
0.04g	0.86	0.93	0.16g	0.79	0.79
0.05g	0.88	0.93	0.18g	0.81	0.83
0.06g	0.88	0.92	0.20g	0.78	0.79
0.07g	0.87	0.90	0.30g	0.65	0.66
0.08g	0.86	0.89	0.40g	0.70	0.70
0.09g	0.84	0.86	平均	0.83	0.85

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表 3 不同Arias强度I_a时a_c-logD_n线性关系R²值

Table 3. R² values of the linear relationship between a_c-logD_n for different I_a

I_a/(m·s⁻¹)	R²	I_a/(m·s⁻¹)	R²	I_a/(m·s⁻¹)	R²	I_a/(m·s⁻¹)	R²	I_a/(m·s⁻¹)	R²
0.830	0.976	1.251	0.994	0.286	0.999	0.627	0.992	5.037	0.993
0.467	0.982	0.929	1	0.141	0.997	1.104	0.956	3.936	0.996
0.075	0.993	0.667	0.986	1.862	0.915	0.124	0.993	2.583	0.996
0.842	0.988	0.629	0.992	1.291	0.996	0.188	0.994	4.189	0.979
1.073	0.999	0.206	0.995	0.618	0.991	0.249	0.999	1.275	0.943
0.282	0.999	0.199	0.983	0.178	0.973	0.875	0.991	4.134	0.997
0.309	0.999	0.079	0.999	0.137	0.998	0.972	0.943	4.056	0.997
0.151	0.997	0.301	0.993	0.057	0.995	0.176	0.993	2.350	0.987
0.469	0.993	0.410	0.998	0.420	0.961	0.134	0.997	0.556	0.977
0.116	0.999	0.280	0.968	0.490	0.989	0.134	1	0.723	0.993
1.907	0.966	2.735	0.999	0.124	0.978	0.845	0.975	0.190	0.995
1.785	0.994	3.378	0.995	0.449	0.965	6.537	0.949	0.909	0.985
0.627	0.993	1.625	0.997	0.425	0.969	4.854	0.996	0.773	1
16.651	0.984	3.222	0.980	0.082	0.997	3.214	0.993	0.150	1
16.425	0.981	4.502	0.968	0.574	0.998	5.080	0.994	2.309	0.98
7.154	0.993	0.683	0.996	0.671	0.983	5.501	0.997	2.461	0.912
1.277	0.996	3.344	0.994	0.152	0.999	7.385	0.996	0.289	0.999
1.323	0.997	3.346	0.996	8.575	0.990	1.393	0.996	1.815	0.984
0.151	0.998	0.055	0.997	4.199	0.981	1.717	0.993	1.926	0.991
1.437	0.995	0.878	0.992	3.586	0.991	1.497	0.996	0.554	0.917
0.414	1	0.752	0.998	11.241	0.995	11.812	0.984	0.344	0.995
1.202	0.985	0.382	0.992	6.935	0.986	11.326	0.973	0.530	0.996
0.976	0.997	0.361	0.999	1.379	0.990	4.591	0.987	0.465	0.996
0.104	1	0.319	0.999	2.813	0.988	0.550	0.988	0.123	0.997
4.032	0.981	0.142	0.994	3.127	0.997	0.150	0.999	0.100	0.992
2.565	0.967	0.372	0.998	1.185	0.981	0.655	0.985	0.045	0.997
0.719	0.982	0.365	0.994	13.227	0.969	0.617	0.992	0.850	0.988
0.226	0.996	0.251	0.998	10.768	0.991	0.185	0.989	1.232	0.986
0.225	0.993	0.607	0.994	10.146	0.992	1.662	0.998	0.527	0.997
0.066	0.998	0.639	0.996	0.378	0.963	1.502	0.943	0.443	0.986
0.383	0.993	0.071	0.959	0.360	0.998	0.264	0.994	0.389	0.995
0.311	0.992	1.203	0.998	0.128	0.998	5.105	0.973	0.164	0.974
0.119	0.999

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表 4 工程岩土体物理力学参数表

Table 4. Physical and mechanical parameters of engineering rock and soil mass grouping

主要岩性组成	粘聚力/kPa	内摩擦角/(°)	重度/(kN·m⁻³)
石英砂岩等	37	39	24
白云岩、灰岩等	34	36	23
砂岩、粉砂岩	33	35	24
板岩	27	32	21
砾石、砂土和黏土层等	17	20	17

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