Comparative Analysis of Calculation Methods for Natural Vibration Frequency of Reinforced Soil Retaining Walls

doi:10.11988/ckyyb.20240043

Abstract

Abstract:

Natural vibration frequency is a crucial parameter in the seismic design of reinforced soil retaining walls. To date, there is no consensus on the calculation methods for the natural vibration frequency of non-monolithic reinforced soil retaining walls. This paper reviews seven existing methods for calculating the natural vibration frequency. Taking the modular reinforced soil retaining wall (hereinafter referred to as the modular type) and the composite gabion geogrid reinforced soil retaining wall (hereinafter referred to as the composite type) as research subjects, we assess the effectiveness of these existing calculation methods by comparing the accuracy coefficient and the absolute percentage error between the measured and calculated results. The analysis reveals that the natural vibration frequencies of the modular and composite models are generally consistent at different heights. Wu Yongsheng’s calculation method shows the closest agreement with the actual measurements. Ghanbari’s method can more effectively mitigate the influence of parameter changes on the analytical calculation, thus demonstrating stronger adaptability. Xu Peng’s method has certain advantages in terms of accuracy and adaptability, with a wider application scope. In seismic design, we recommend that engineers evaluate the natural vibration frequency of the reinforced soil retaining wall before and after construction and consider the horizontal displacement of the panels as an indicator to measure the structural damage state.

Key words: geosynthetic materials, reinforced soil retaining wall, natural frequency, shake table test, comparative analysis

CLC Number:

TU476

CAI Xiao-guang, CAI Bo-yuan, LI Si-han, HUANG Xin, XU Hong-lu, ZHU Chen. Comparative Analysis of Calculation Methods for Natural Vibration Frequency of Reinforced Soil Retaining Walls[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 120-126.

Figures/Tables 11

Table 1 Similarity constants of shaking table model test

物理量	相似常数	比例因子(模型/原型)
		模块式		复合式
		1∶2	1∶4	1∶2.5	1∶5
长度L	$C L$	2	4	2.5	5
弹性模量E	$C E$	1	1	1	1
密度 $ρ$	$C ρ = 1$	1	1	1	1
应力 $σ$	$C σ = C E = 1$	1	1	1	1
时间 $t$	$C t = C L 0.5$	1.4	2	1.6	2.2
速度 $v$	$C v = C L 0.5$	1.4	2	1.6	2.2
加速度 $a$	$C a = 1$	1	1	1	1
重力加速度 $g$	$C g = 1$	1	1	1	1
频率 $ω$	$C w = C L - 0.5$	0.7	0.5	0.6	0.5

Table 1 Similarity constants of shaking table model test

物理量	相似常数	比例因子(模型/原型)
		模块式		复合式
		1∶2	1∶4	1∶2.5	1∶5
长度L	$C L$	2	4	2.5	5
弹性模量E	$C E$	1	1	1	1
密度 $ρ$	$C ρ = 1$	1	1	1	1
应力 $σ$	$C σ = C E = 1$	1	1	1	1
时间 $t$	$C t = C L 0.5$	1.4	2	1.6	2.2
速度 $v$	$C v = C L 0.5$	1.4	2	1.6	2.2
加速度 $a$	$C a = 1$	1	1	1	1
重力加速度 $g$	$C g = 1$	1	1	1	1
频率 $ω$	$C w = C L - 0.5$	0.7	0.5	0.6	0.5

Fig.1 Panel form comparison

Fig.2 Front view and side view of model brick

Fig.3 Gabion cage

Table 2 Related parameters of backfill soil

粒径/mm			内摩擦角 $φ$ /(°)	不均匀系数 C_u	曲率系数 C_c
$d 10$	$d 30$	$d 60$	内摩擦角 $φ$ /(°)	不均匀系数 C_u	曲率系数 C_c
0.18	0.29	0.37	41	2.055	1.262

Table 2 Related parameters of backfill soil

粒径/mm			内摩擦角 $φ$ /(°)	不均匀系数 C_u	曲率系数 C_c
$d 10$	$d 30$	$d 60$	内摩擦角 $φ$ /(°)	不均匀系数 C_u	曲率系数 C_c
0.18	0.29	0.37	41	2.055	1.262

Fig.4 Design diagrams of modular model and composite model[21-22]

Fig.5 Time history curve of white noise acceleration[17]

Fig.6 Modular Fourier spectrum

Table 3 Comparison of natural vibration frequency between calculation and measurement

序号	计算方法	自振频率计算结果/Hz
序号	计算方法	模块式	复合式
1	Bathurst等^[14-15]	21.17	19.05
2	伍永胜^[16]	21.51	19.40
3	Sarbishei等^[9]	16.45	6.48
4	Ghanbari等^[10]	37.60	35.53
5	Ramezani等^[11]	116.42	119.80
6	Darvishpour等^[6]	2.76	1.95
7	徐鹏等^[12-13]	19.80	15.44
8	振动台试验实测	22.43	22.61

Table 4 Error analysis of calculation methods for natural vibration frequency

序号	计算方法	$κ$		绝对百分比误差/%
序号	计算方法	模块式	复合式	模块式	复合式
1	Bathurst等^[14-15]	0.06	0.16	37.13	38.73
2	伍永胜^[16]	0.04	0.14	36.12	37.61
3	Sarbishei等^[9]	0.27	0.71	51.15	79.15
4	Ghanbari等^[10]	-0.68	-0.57	11.66	14.27
5	Ramezani等^[11]	-4.19	-4.30	245.74	285.29
6	Darvishpour等^[6]	0.88	0.91	91.80	93.73
7	徐鹏等^[12-13]	0.12	0.32	41.20	50.34

Table 4 Error analysis of calculation methods for natural vibration frequency

序号	计算方法	$κ$		绝对百分比误差/%
序号	计算方法	模块式	复合式	模块式	复合式
1	Bathurst等^[14-15]	0.06	0.16	37.13	38.73
2	伍永胜^[16]	0.04	0.14	36.12	37.61
3	Sarbishei等^[9]	0.27	0.71	51.15	79.15
4	Ghanbari等^[10]	-0.68	-0.57	11.66	14.27
5	Ramezani等^[11]	-4.19	-4.30	245.74	285.29
6	Darvishpour等^[6]	0.88	0.91	91.80	93.73
7	徐鹏等^[12-13]	0.12	0.32	41.20	50.34

Fig.7 Main control index and auxiliary control index

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