Influences of integral displacement methods on inverse analysis of accelerograph arrays for cyclic shear stress-strain response
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摘要: 基于加速度阵列的循环剪应力–剪应变反演分析方法被广泛用于原位场地观测和物理模型试验，但积分位移方法、分布函数等关键因素的影响尚缺少认识。选取4种代表性一维剪切梁分布函数，利用一组动力离心模型试验，探讨了积分位移方法对反演剪应力、剪应变的影响特征与规律，并分析了滞回圈和模量阻尼比的变化趋势。结果表明：①积分位移方法对反演剪应力和剪应变影响显著，采用积分位移方法处理后的加速度时程求取剪应力是有效保障滞回圈光滑性和闭合性的重要条件；ARI与USGS方法相比，后者对原加速度时程相位和幅值的影响不可忽略。②线性、三次样条、加权残差等3种剪切梁分布函数取得剪应力、剪应变结果十分吻合，可忽略分布函数的影响，而余弦法分布函数获得结果离散性较大，不宜选取。③积分位移方法对剪切模量具有略微影响，但对阻尼比影响较为显著，ARI法获得阻尼比发展趋势符合一般规律认识，而USGS法与之相悖。研究方法和结论，为有效可靠获取原位场地、土工物理试验等循环剪应力–剪应变响应和验证本构关系模型，提供了重要指导依据和方法支撑。Abstract: The inverse analysis of accelerograph arrays for cyclic shear stress-strain response is widely used in in-situ monitoring and physical model tests, but the influences of the key factors such as integral methods and distribution functions still lack knowledge. Four representative one-dimensional shear beam distribution functions are selected, and a set of dynamic centrifugal model tests are used to clarify the influences of the integral methods and distribution functions on the inverse analysis of shear stresses and shear strains, and the features of the acquired hysteresis loops and modulus damping ratios are further analyzed. The results show: (1) The integral methods exhibit a visible impact on the inversion of the shear stresses and shear strains, and using the acceleration curves processed by the integral methods to obtain the shear stresses is an important condition for effectively ensuring the smoothness and closure of the hysteresis loops. Compared with the ARI method, the USGS method has a non-negligible influence on the phase and amplitude of the original acceleration curves. (2) The shear stresses and shear strains obtained by the three shear beam distribution functions of linear, cubic spline and weighted residuals are very consistent, and the influences of the distribution functions can be ignored. However, the results obtained by the cosine method distribution function are relatively discrete, which is not suitable for selection. (3) The dependence of the shear modulus on the integral methods is slight, but the damping ratios are evidently affected. The development trend of the damping ratios obtained by the ARI method conforms to the general understanding, while the USGS method is contrary to it. The research methods and conclusions may provide important guidance and method support for effectively and reliably obtaining the cyclic shear stress-strain response of in-situ site and geophysical tests and verifying the constitutive relationship models.
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图 1 基于加速度阵列的一维剪切梁模型示意图
Figure 1. Schematic diagram of one-dimensional shear beam model based on accelerograph arrays
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图 2 UC Davis半径9.1 m大型动力离心机
Figure 2. 9.1 m-radius large dynamic centrifuge at UC Davis
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图 5 叠层梁的积分位移与实测位移对比
Figure 5. Comparison between integral displacements and measured displacements of laminated beam
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图 6 积分位移数据处理方法对反演剪应力时程影响
Figure 6. Influences of integral displacement methods on inverse analysis of shear stress time series
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图 7 积分位移数据处理方法对反演剪应力沿深度分布影响
Figure 7. Influences of integral displacement means on inversely calculated shear stress distribution along depth
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图 8 一维剪切梁分布函数对反演剪应力的时程影响
Figure 8. Influences of one-dimensional shear beam distribution functions on inversely calculated shear stress time series
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图 9 一维剪切梁分布函数对反演剪应力沿深度的分布影响
Figure 9. Influences of one-dimensional shear beam distribution functions on inversely calculated shear stress distribution with depth
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图 10 一维剪切梁分布函数对反演剪应变的时程影响
Figure 10. Dependence of inversely calculated shear strain time series on one-dimensional shear beam distribution functions
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图 11 一维剪切梁分布函数对反演剪应变随深度的分布影响
Figure 11. Sensitivity of inversely calculated shear strain along depth to one-dimensional shear beam distribution functions
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图 12 积分位移方法对反演剪应变的时程影响
Figure 12. Dependence of inversely calculated shear strain time series on integral displacement methods
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图 13 积分位移方法对反演剪应变沿深度的分布影响
Figure 13. Sensitivity of inversely calculated shear strain along depth to integral displacement methods
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图 14 积分位移方法对反演滞回圈的特征影响(箭头为起点)
Figure 14. Influences of integral displacement methods on characteristics of inversely calculated hysteresis loops
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图 15 积分位移方法对剪切模量的影响及拟合曲线
Figure 15. Dependence of inversely calculated shear modulus and fitting curves of integral displacement methods
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