不同概率水准下动剪切模量比与阻尼比上、下限的计算

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摘要采用试验方法，研究不同概率水平下常规土类动剪切模量比和阻尼比非线性曲线上限和下限变化范围，提出典型剪应变下黏性土和无黏性土动剪切模量比和阻尼比落在不同区间概率大小的计算方法和计算公式。计算方法形成的基本思路为：将试验资料整理成标准结果，利用频数分布图、概率纸法检验图和SAS软件得到典型剪应变下2个参数变异性分布形态，根据不同分布形态采用2种不同方法计算典型剪应变下2个动力参数上、下限概率参考值。分析结果表明：不同剪应变下动剪切模量比和阻尼比上、下限值随概率水准的变化具有规律性，不同剪应变下2个动力参数的上限和下限与其出现的概率之间均满足Boltzmann方程，但方程中参数随剪应变和土类而变化；所有概率水平下不同剪应变的动剪切模量比上、下限区间大小均有明显差异，剪应变在10－4～10－3范围内的动剪切模量比上、下限范围最大；同一概率水平下阻尼比上、下限区间大小随剪应变增大而明显增大。提出的2个动力参数的概率计算公式为土动力学和地震工程可靠性理论研究奠定一定基础，也为工程结构的抗震设计和地震安全的风险评估提供直接的技术支持。

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	袁晓铭1
	孙锐1
	陈红娟2

关键词 ：土力学, 动剪切模量比, 阻尼比, 变异性, 上下限, 概率

Abstract：：By using experimental results，the upper and lower limits of the nonlinear curves of the dynamic shear modulus ratio and damping ratio for conventional soils under different probabilities are investigated. The method and formula for calculating the probabilistic zones of the two dynamic parameters for the cohesive and cohesionless soils under the typical shear strains are presented. The approach is that the experimental results are ordered by the standard way，and the distribution form of variability of two dynamic parameters is obtained by the frequency distribution diagram，the tests of normality diagram and the SAS software. According to different distribution forms，the probabilities of the upper and lower limits of the two parameters under typical shear strains are calculated. The results indicate that the relation between the upper and lower limits of the two dynamic parameters and their probabilities can be described by the Boltzmann equation，in which the parameters depend on the soil type and the shear strain. For all probabilities，the ranges of the shear modulus ratio for different shear stains are obviously different while the most ones appear at 10－4–10－3 of the shear strain. For the same probability，the range of the damping ratio increases with increasing shear strain. The proposed formula for calculating the probabilistic zones of the two dynamic parameters lays a foundation for the reliability theory in soil dynamics and earthquake engineering to some extent；and it also can directly supply the technical support to the risk evaluation of a seismic design and seismic safety of engineering structures.

Key words： soil mechanics dynamic shear modulus ratio damping ratio variability upper and lower limits probability

引用本文:

袁晓铭1，孙锐1，陈红娟2. 不同概率水准下动剪切模量比与阻尼比上、下限的计算[J]. 岩石力学与工程学报, 2010, 29(S2): 3930-3940.
YUAN Xiaoming1，SUN Rui1，CHEN Hongjuan2. CALCULATION FOR UPPER AND LOWER LIMITS OF DYNAMIC SHEAR MODULUS RATIO AND DAMPING RATIO UNDER DIFFERENT PROBABILITIES. , 2010, 29(S2): 3930-3940.

链接本文:

https://rockmech.whrsm.ac.cn/CN/Y2010/V29/IS2/3930

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