土石坝料的变参数R-O模型及其热力学解释
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摘要
坝料动力特性是土石坝动力分析的重要参数,直接关系大坝的地震反应分析结果,并影响其抗震设计。工程实践中,对大型土石坝工程一般是直接进行坝料的动力试验,确定动力参数；而中小型土石坝工程,大多采用工程类比方法确定动力参数。土石坝料动力试验的影响因素众多,试验成果有一定的离散性。即使是进行试验的大型土石坝工程,由于坝料设计干密度的变化及现场施工条件的复杂性等,再加上大型动三轴试验周期长、成本高、试验组数有限等特点,因此室内试验得到的动参数反映实际的程度较难评估。所以,大中型工程一般均需要进行土石坝动力参数的敏感性分析。土体动力参数包含两部分,一是最大动剪模量参数,再就是模量比及阻尼比随动剪应变的变化规律。本文在对现有的国内外试验成果进行系统整理与分析的基础上,给出了堆石料、心墙土料和反滤料的等效动剪切模量和等效阻尼比随动剪应变非线性变化的统一数学表达式,并对归一化的阻尼比随归一化的动剪模量的变化进行了讨论,给出了建议公式。这些公式可用于判定坝料动力试验成果的合理性,也可直接用作坝体动力参数敏感性分析及中小型土坝的坝料动参数。
以200m级心墙堆石坝二维有限元为计算分析模型为例,探讨了坝料在不同的动力特性情况下对动力结果的影响。计算中,将堆石料、心墙料和反滤料的模量、阻尼均值曲线和上、下2倍均方差曲线的不同组合作为计算工况,进行了坝料动力特性敏感性分析。计算结果表明,坝料不同的模量、阻尼曲线对土石坝地震动力分析成果不同。
为建立堆石料、心墙土料和反滤料的模量、阻尼比均值曲线的动力本构模型。以新莲料在不同围压下的动力参数为例,阐述了参考剪应变的二种计算方法,提出了参考剪应变的第三种方法,讨论了参考剪应变三种计算方法的特点与适应性。并以拟合优度为指标,比较了参考剪应变对坝料动力参数的归一程度。最后采用归一程度最佳的计算方法计算堆石料、心墙土料和反滤料三种坝料均值曲线的参考剪应变,并建立了与各自均值曲线相适应的动态本构方程,即变参数的Ramberg-Osgood模型。
以变参数的Ramberg-Osgood模型为研究对象,建立了与三种坝料均值曲线方程相适应且以剪应变为自变量的参数R(γ)与α(γ)表达式,探讨了其适用条件。再以变参数Ramberg-Osgood模型为基础,从热力学基本定律出发,对塑性中心移动为直线时,构造了三种坝料的自由能函数和耗散函数。研究了各自动力耗散特征及动力变形机理,绘制其耗散应力空间和真实应力空间屈服曲线,得出各自门槛应变。
The dynamic characteristics of dam materials are important parameters for dynamic analysis of dam, it is directly related to results of dam's seismic. response and affect the seismic design. In engineering practice, a direct dynamic test was taken to determine the dynamic parameters in the large scale dam project, but in the other hand, analogy method was used in the middle-small scale dam project. It is many influence factors in dynamic test of dam materials and test results have certain discrete. Even though the test of the large-scale dam project is conducted, due to the change of dry density of dam design material and the complexity of site construction conditions, even the characteristics of large-scale cyclic triaxial tests are long period, high cost and limited number of test group, thus parameters from laboratory test are also difficult to reflect the actual fully. Therefore, the larger-middle scale dam project usually needs sensitivity analysis of dynamic parameters. Soil dynamic parameters include two parts, one is the maximum dynamic shear modulus parameter and the other is the variation of the modulus ratio and damping ratio with the variation of dynamic shear strain. On the basis of existing test data which were systematically analyzed again and summarize both at home and abroad, then establish unified mathematical expressions for their relative curves, which are nonlinear variation about dynamic equivalent shear modulus and dynamic damping ratio with shear strain on dam materials,including rockfill materials, core materials and anti-filter materials. In addition, discussed the normalized dynamic damping ratio relating to the normalized dynamic equivalent shear modulus, and provided modification of recommended formulas. These formulas can be used to determine the reasonableness of the dynamic test results and also can be directly used as dynamic parameters of the sensitivity analysis of the dam and the dynamic parameters of the middle-small scale dam project.
Based on 2D-FEM analytical model of 200m high core dam, the dynamic results of the dam materials in the different dynamic properties is discussed. In process of calculation, taking different combinations of average curve and double standard variances of up-down curves about the dynamic damping ratio and the dynamic equivalent shear modulus of rockfill materials, core materials and anti-filter materials as working conditions of dam materials, analyze the sensitivity of the dynamic properties of dam. The results show that the dynamic characteristics of dam materials are the key factors to describe all dynamically analyzed during a seismic design of embankment dam.
For establishing dynamic constitutive model of the modulus and damping mean curve about rockfill materials, core materials and anti-filter materials, take the dynamic parameters of Xinlian material in different confining pressures as an example. Described three solution methods for reference shear strain of different values, and discussed their application characteristics of the three methods. To compare the result of calculating the reference shear strain of the three methods, make the goodness of fit as an indicator to measure the level of the respective normalized of the reference shear strain on the dynamic parameters after the normalization. Finally, Calculate reference shear strain of three kinds of the mean curve about dam materials, rockfill materials, core materials and anti-filter materials, by the highest degree of normalization calculation method. And establish dynamic constitutive equation, adapting their mean curves, which is the Ramberg-Osgood constitutive model with variable parameters.
By taking the Ramberg-Osgood constitutive model with variable parameters as the research object, establish expression of parameters R (y) and (y) with the independent variable shear strain, relating to the mean curve equation of three dam materials, and discuss their applicable conditions. Then base on the Ramberg-Osgood constitutive model with variable parameters, start from the basic laws of thermodynamics, constructed the free energy function and the dissipation function of three materials when the plastic movement of the center of a straight line. Research their dynamic dissipation characteristics and mechanisms of dynamic deformation, draw the dissipative stress space and the real stress space of the yield curve and reached their threshold strain.The calculation method is improved On the basis of the past, compared with the usual, with a more adaptive, and can be applied to different dam material.
以200m级心墙堆石坝二维有限元为计算分析模型为例,探讨了坝料在不同的动力特性情况下对动力结果的影响。计算中,将堆石料、心墙料和反滤料的模量、阻尼均值曲线和上、下2倍均方差曲线的不同组合作为计算工况,进行了坝料动力特性敏感性分析。计算结果表明,坝料不同的模量、阻尼曲线对土石坝地震动力分析成果不同。
为建立堆石料、心墙土料和反滤料的模量、阻尼比均值曲线的动力本构模型。以新莲料在不同围压下的动力参数为例,阐述了参考剪应变的二种计算方法,提出了参考剪应变的第三种方法,讨论了参考剪应变三种计算方法的特点与适应性。并以拟合优度为指标,比较了参考剪应变对坝料动力参数的归一程度。最后采用归一程度最佳的计算方法计算堆石料、心墙土料和反滤料三种坝料均值曲线的参考剪应变,并建立了与各自均值曲线相适应的动态本构方程,即变参数的Ramberg-Osgood模型。
以变参数的Ramberg-Osgood模型为研究对象,建立了与三种坝料均值曲线方程相适应且以剪应变为自变量的参数R(γ)与α(γ)表达式,探讨了其适用条件。再以变参数Ramberg-Osgood模型为基础,从热力学基本定律出发,对塑性中心移动为直线时,构造了三种坝料的自由能函数和耗散函数。研究了各自动力耗散特征及动力变形机理,绘制其耗散应力空间和真实应力空间屈服曲线,得出各自门槛应变。
The dynamic characteristics of dam materials are important parameters for dynamic analysis of dam, it is directly related to results of dam's seismic. response and affect the seismic design. In engineering practice, a direct dynamic test was taken to determine the dynamic parameters in the large scale dam project, but in the other hand, analogy method was used in the middle-small scale dam project. It is many influence factors in dynamic test of dam materials and test results have certain discrete. Even though the test of the large-scale dam project is conducted, due to the change of dry density of dam design material and the complexity of site construction conditions, even the characteristics of large-scale cyclic triaxial tests are long period, high cost and limited number of test group, thus parameters from laboratory test are also difficult to reflect the actual fully. Therefore, the larger-middle scale dam project usually needs sensitivity analysis of dynamic parameters. Soil dynamic parameters include two parts, one is the maximum dynamic shear modulus parameter and the other is the variation of the modulus ratio and damping ratio with the variation of dynamic shear strain. On the basis of existing test data which were systematically analyzed again and summarize both at home and abroad, then establish unified mathematical expressions for their relative curves, which are nonlinear variation about dynamic equivalent shear modulus and dynamic damping ratio with shear strain on dam materials,including rockfill materials, core materials and anti-filter materials. In addition, discussed the normalized dynamic damping ratio relating to the normalized dynamic equivalent shear modulus, and provided modification of recommended formulas. These formulas can be used to determine the reasonableness of the dynamic test results and also can be directly used as dynamic parameters of the sensitivity analysis of the dam and the dynamic parameters of the middle-small scale dam project.
Based on 2D-FEM analytical model of 200m high core dam, the dynamic results of the dam materials in the different dynamic properties is discussed. In process of calculation, taking different combinations of average curve and double standard variances of up-down curves about the dynamic damping ratio and the dynamic equivalent shear modulus of rockfill materials, core materials and anti-filter materials as working conditions of dam materials, analyze the sensitivity of the dynamic properties of dam. The results show that the dynamic characteristics of dam materials are the key factors to describe all dynamically analyzed during a seismic design of embankment dam.
For establishing dynamic constitutive model of the modulus and damping mean curve about rockfill materials, core materials and anti-filter materials, take the dynamic parameters of Xinlian material in different confining pressures as an example. Described three solution methods for reference shear strain of different values, and discussed their application characteristics of the three methods. To compare the result of calculating the reference shear strain of the three methods, make the goodness of fit as an indicator to measure the level of the respective normalized of the reference shear strain on the dynamic parameters after the normalization. Finally, Calculate reference shear strain of three kinds of the mean curve about dam materials, rockfill materials, core materials and anti-filter materials, by the highest degree of normalization calculation method. And establish dynamic constitutive equation, adapting their mean curves, which is the Ramberg-Osgood constitutive model with variable parameters.
By taking the Ramberg-Osgood constitutive model with variable parameters as the research object, establish expression of parameters R (y) and (y) with the independent variable shear strain, relating to the mean curve equation of three dam materials, and discuss their applicable conditions. Then base on the Ramberg-Osgood constitutive model with variable parameters, start from the basic laws of thermodynamics, constructed the free energy function and the dissipation function of three materials when the plastic movement of the center of a straight line. Research their dynamic dissipation characteristics and mechanisms of dynamic deformation, draw the dissipative stress space and the real stress space of the yield curve and reached their threshold strain.The calculation method is improved On the basis of the past, compared with the usual, with a more adaptive, and can be applied to different dam material.
引文
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[2]韩国城,孔宪京.混凝土面板堆石坝抗震研究进展[J].大连理工大学学报,1996,(6)：708-719.
[3]刘小生,王钟宁,赵剑明,刘启旺.面板堆石坝振动模型试验及动力分析研究[J].水利学报,2002,(2)：29-35.
[4]Robert D S, Lembit K. Threshold of dilation under cyclic loading [J]. Journal of the Geotechnical Engineering Division, ASCE,1977,103(GT10):1174-1178.
[5]Richard P R, Richard D W. Modulus and damping due to uniform and variable cyclic loading [J]. Journal of Geotechnical Engineering,1988,114(8):861-876.
[6]Vucetic M. Cyclic threshold shear strains in core materials [J]. Journal of Geotechnical Engineering,1994,120(12):2208-2229.
[7]Hsu C C, Vucetic M. Volume threshold shear strain for cyclic settlement [J]. Journal of Geotechnical Engineering,2004,130(1):58-70.
[8]Drnevich V P. Long-tor resonant column apparatus operating manual [S]. Ine USA,1984.
[9]祝龙根,吴晓峰.饱和反滤料和低塑粘土临界应变的研究闭[J].大坝观测与土工侧试,1988,12(1)：27-33.
[10]DobryR, Swiger WF. Threshold strain and cyclic behavior of cohesionless [J]. Austin T X,1979:521-525.
[11]Lanzo G, Vucetic M, Doroudian M. Reduction of shear modulus at small strains in simple shear [J]. Journal of Geotechnical and Geoenvironmental Engineering,1997, 123:1035-1042.
[12]Hsu C C, Vucetic M. Threshold shear strain for cyclic pore-water pressure in cohesive core materials [J]. Journal of Geotechnical and Geoenvironmental Engineering,2006, 132:1325-1335.
[13]郭晓霞,迟世春,林皋.基于热力学定律的土体动力Hardin-Drnevich模型再认识[J].岩土力学,2008,(9)：2335-2340.
[14]郭晓霞.热力学方法在土体本构模型中的应用研究[D].大连理工大学,2009.
[15]郭晓霞,迟世春,杨峻,林皋.基于热力学原理的土体动力模型阈值应变研究[J].水利学报,2008,(9).
[16]迟世春,郭晓霞,杨峻,林皋.土的动力Hardin-Drnevich模型小应变特性及其阈值应变研究[J].岩土工程学报,2008,(2).
[17]孔宪京,娄树莲,邹德高,贾革续,韩国城.筑坝堆石料的等效动剪切模量与等效阻尼比[J].水利学报,2001,(8).
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