双级模块式加筋土挡墙动力响应数值分析

祁高; 李思汉; 蔡博渊; 蔡晓光; 黄鑫; 王磊

doi:10.11899/zzfy20250062

双级模块式加筋土挡墙动力响应数值分析

doi: 10.11899/zzfy20250062

祁高^1,,
李思汉^{2, 3, 4, ,},
蔡博渊²,
蔡晓光^{3, 4, 5},
黄鑫^{2, 3, 4},
王磊⁶

1.
江苏省地质局第一地质大队, 南京 210041
2.
防灾科技学院, 防灾减灾工程学院, 河北廊坊 065201
3.
河北省地震灾害防御与风险评价重点实验室, 河北廊坊 065201
4.
廊坊市加筋土结构研发与应用重点实验室, 河北廊坊 065201
5.
中国地震灾害防御中心, 北京 100029
6.
江苏南京地质工程勘察院, 南京 210041

基金项目: 江苏省地质工程环境智能监控工程研究中心开放基金（2023-ZNJKJJ-06）；地震科技星火计划青年项目（XH23067 YA）；河北省高等学校科学研究青年拔尖人才计划项目（BJK2024034）

详细信息

作者简介:
祁高，男，生于1992年。工程师。主要从事地质工程方面的工作。E-mail：294990420@qq.com

通讯作者:
李思汉，男，生于1992年。副教授。主要从事岩土地震工程方面的教学和研究工作。E-mail：lisihan@st.cidp.edu.cn

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出版历程
- 收稿日期: 2025-04-28
- 录用日期: 2025-05-14
- 修回日期: 2025-04-28
- 网络出版日期: 2025-07-23

Numerical Analysis of Dynamic Response of Two-tiered Modular Reinforced Soil Retaining Wall

Qi Gao^1
,,
Li Sihan^{2, 3, 4
, ,},
Cai Boyuan²,
Cai Xiaoguang^{3, 4, 5},
Huang Xin^{2, 3, 4},
Wang Lei⁶

1.
The First Geological Brigade of Jiangsu Geological Bureau, Nanjing 210041, China
2.
College of Disaster Prevention and Mitigation Engineering, Institute of Disaster Prevention, Langfang 065201, Hebei, China
3.
Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment, langfang 065201, Hebei, China
4.
Langfang City Key Laboratory of Research and Application of Geosynthetic Reinforced Soil Structure, Langfang 065201, Hebei, China
5.
China Earthquake Disaster Prevention Center, Beijing 100029, China
6.
Jiangsu Nanjing Geological Engineering Investigation Institute, Nanjing 210041, China

摘要

摘要: 针对地震作用下双级加筋土挡墙临界台阶宽度不明、上下阶墙高选取随意，不利于加筋土挡墙推广应用的情况，基于双级模块式加筋土挡墙的振动台试验结果，建立FLAC 3D数值模型，研究了不同台阶宽度（10、20 、30、40、50、60 cm）、不同墙高比（上下阶墙体分别为3/7、4/6、1/1、6/4、7/3）下加筋土挡墙的墙面位移、加速度响应及地震土压力分布情况。结果表明，面板位移随台阶宽度的增加先减小后增大，最小值出现在台阶宽度为50 cm工况中；加速度放大系数沿墙高非线性递增，上阶挡墙在台阶宽度为40 cm和60 cm时出现加速度响应衰减；下阶墙体土压力在台阶宽度为50 cm时数值最小；上下阶挡墙墙高比为4/6时，墙面峰值位移最小；墙高比为6/4时，上阶挡墙的加速度放大系数最大，墙高比为1/1时，下阶挡墙的加速度放大系数最大；墙高比为7/3时，上阶挡墙的地震土压力值最大，墙高比为1/1时，下阶挡墙的地震土压力值最大。综合分析可知，墙高比为1/1时，临界台阶宽度在50 cm附近；当台阶宽度为20 cm时，上下阶墙体高度应有所区别，不宜均分，也不宜差距过大。研究成果可为双级加筋土挡墙工程设计中台阶宽度和上下阶墙高设置提供数据支撑。
- 双级加筋土挡墙 /
- 振动台试验 /
- 数值模拟 /
- 台阶宽度 /
- 墙高比
Abstract: In view of the unclear critical tier width and random height selection of upper and lower walls in two-tiered reinforced soil retaining walls under seismic loads, which hinders their application, a FLAC 3D model was built based on shaking table tests of two-tiered modular reinforced soil retaining walls. It analyzed face displacement, acceleration response, and seismic earth pressure distribution under different tier widths (10, 20, 30, 40, 50, 60 cm) and height ratios (3/7, 4/6, 1/1, 6/4, 7/3). Results revealed that facing displacement first decreased and then increased with tier width, hitting the minimum at 50 cm. The acceleration amplification factor rose nonlinearly with wall height, with attenuation in the upper wall at 40 and 60 cm widths. The lower wall's earth pressure was smallest at a 50 - cm tier width. The peak facing displacement was minimized when the height ratio was 4/6. The upper wall's maximum acceleration amplification occurred at a 6/4 ratio, while the lower wall's was at 1/1. The upper wall's seismic earth pressure was highest at 7/3, and the lower wall's at 1/1. Comprehensive analysis showed a critical tier width near 50 cm at a 1/1 ratio. At a 20 cm tier width, upper and lower wall heights should differ moderately. These findings offer data support for the design of two-tiered reinforced soil retaining walls, aiding in tier width and height configuration.
- Two-tiered reinforced soil retaining wall /
- Shaking table test /
- Numerical simulation /
- Offset distance /
- Wall height ratio

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图 1 试验测试装置

Figure 1. Test device

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图 2 双级挡墙模型设计

Figure 2. Two-tiered retaining wall model design

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图 3 归一化5 Hz正弦波及傅氏谱

Figure 3. Normalized 5 Hz sine wave and Fourier spectrum

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图 4 双级数值模型

Figure 4. Two-tiered numerical model

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图 5 双级挡墙对比验证

Figure 5. Comparative verification of two-tiered retaining wall

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图 6 D=20 cm时各测点响应情况

Figure 6. The response of each measuring point when D = 20 cm

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图 7 不同台阶宽度动力响应对比

Figure 7. Comparison of dynamic response of different step widths

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图 8 不同分级墙高比动力响应对比

Figure 8. Comparison of dynamic response of different grading wall height ratio

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表 1 模型相似关系参数

Table 1. Model similarity relation parameters

变量	参数	相似关系	相似常数（原型/模型）
长度	L	${C_{\text{L}}}$	10
弹模	E	${C_{\text{E}}}$	1
密度	$\rho $	$ {C}_{\rho }=1 $	1
应力	$\sigma $	$ {C}_{\sigma }={C}_{E}=1 $	1
时间	$t$	${C_{\text{t}}} = C_{\text{L}}^{{\text{0}}{\text{.5}}}$	3.16
速度	$v$	${C_{\text{v}}} = C_{\text{L}}^{{\text{0}}{\text{.5}}}$	3.16
加速度	$a$	${C_{\text{a}}} = 1$	1
重力	$g$	${C_{\text{g}}} = 1$	1
频率	$\omega $	$ {C}_{\omega }={C}_{L}^{-0.5} $	0.316

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表 2 实体单元材料参数

Table 2. Material parameters of solid element

组成部分	本构	密度/(kg·m⁻³)	体积模量/Pa	剪切模量/Pa	摩擦角/(°)	黏聚力/Pa
地基土	M-C	1820	6.667×10⁷	3.077×10⁷	41	1×10⁶
回填土	M-C	1820	6.667×10⁷	3.077×10⁷	41	1×10³
基础	弹性	2200	1.095×10¹⁰	1×10¹⁰	—	—
面板	弹性	2200	1.095×10¹⁰	1×10¹⁰	—	—
海绵垫	弹性	120	1.1×10⁶	8.35×10⁵	—	—

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表 3 结构单元材料参数

Table 3. Material parameters of structural units

弹性模量/Pa	泊松比	密度/(kg·m⁻³)	厚度/m	耦合弹簧的切向刚度/Pa	耦合弹簧的粘聚力/Pa	耦合弹簧的摩擦角/(°)
2.6×10⁹	0.33	300	1×10⁻³	2×10⁷	1.48×10⁴	32

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表 4 接触面单元计算参数

Table 4. Calculation parameters of contact surface element

接触面	法向刚度k_n	切向刚度k_s	界面摩擦角/(°)	界面黏聚力/Pa
面板-面板	1×10⁹	4×10⁷	36	5.8×10⁴
面板-基础	1×10⁹	4×10⁷	36	5.8 e×10⁴
面板-土体	1×10⁸	1×10⁶	25	2.5×10³

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