地震液化的突变模型研究
摘要
能量和标准贯入击数是用于液化评价的两个综合性指标。以经过持时修正的能量函数和经过粘粒及上覆压力修正的标贯击数为控制变量,以振动孔隙水压力增长为状态变量, 根据液化的物理意义、室内试验所得到的孔压发展曲线的特点和国内外实测液化资料,建立了基于修正Zeeman 突变方程的孔压发展模型。与目前广泛使用的传统尖点突变模型相比,修正模型增加了一项和三个系数,这样做既保留了原方程中状态变量与其中一个控制变量成线性关系这一优良性质,又能够适应于准确模拟孔压与液化发展。在此基础上,利用液化资料,基于统计学中控制“弃真”概率的方法,运用Matlab 逐步逼近确定了所有的六个待定未知量, 确定了分叉曲线和新旧坐标之间的转换关系。检验结果表明了所建议模型的合理性。
The shaking-induced vibration energy and below count of standard penetration tests are two key factors for evaluating the liquefaction potential of sand. A revised model based on Zeeman equation of cusp catastrophe, which can display the development of liquefaction, is established. In the proposed model, the ratio of shaking-induced pore water pressure with effective confining pressure is taken as the state variable while the earthquake-induced energy function modified by earthquake duration and the below count of SPT corrected by the ——————————————— clay content and overburden confining pressure are taken as two individual controlling variables. In the study, triggering condition of liquefaction based on pore water pressure, development pattern of pore water pressure induced by cyclic loading under undrained condition achieved by experimental tests and seismically-incuced damage records of liquefaction observed in previous earthquakes are taken into account. Compared with the conventional cusp model widely employed in engineering practice, an additional term and three non-unity coefficients are included in the revised model. Therefore the fundamental feature of Zeeman equation and the linear correlation between two independent variables are fully contained in the proposed model and furthermore the model can adequately simulate the liquefaction development. Based on the proposed model, the statistical method based on the validation hypothesis for controlling first type of error is used to define the related parameters, bifurcated curve and transformation relationship between the two coordinate systems. The proposed model is verified by the test results. It is shown that the proposed model is reasonable and can be used to predict liquidation potential of sites in practice.
The shaking-induced vibration energy and below count of standard penetration tests are two key factors for evaluating the liquefaction potential of sand. A revised model based on Zeeman equation of cusp catastrophe, which can display the development of liquefaction, is established. In the proposed model, the ratio of shaking-induced pore water pressure with effective confining pressure is taken as the state variable while the earthquake-induced energy function modified by earthquake duration and the below count of SPT corrected by the ——————————————— clay content and overburden confining pressure are taken as two individual controlling variables. In the study, triggering condition of liquefaction based on pore water pressure, development pattern of pore water pressure induced by cyclic loading under undrained condition achieved by experimental tests and seismically-incuced damage records of liquefaction observed in previous earthquakes are taken into account. Compared with the conventional cusp model widely employed in engineering practice, an additional term and three non-unity coefficients are included in the revised model. Therefore the fundamental feature of Zeeman equation and the linear correlation between two independent variables are fully contained in the proposed model and furthermore the model can adequately simulate the liquefaction development. Based on the proposed model, the statistical method based on the validation hypothesis for controlling first type of error is used to define the related parameters, bifurcated curve and transformation relationship between the two coordinate systems. The proposed model is verified by the test results. It is shown that the proposed model is reasonable and can be used to predict liquidation potential of sites in practice.
引文
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[8]张业民,宋长清.软粘土流动性的尖顶突变模型分析[J].岩土工程学报,1995,17(4):67-70.ZhangYemin,SongChangqing.Analysis of flowing rule for soft clay with cusp catastrophe model[J].ChineseJournal ofGeotechnicalEngineering,1995,17(4):67-70.(inChinese)
[9]凌复华译.突变理论及其应用[M].上海:上海交通大学出版社,1987.LingFuhua(translated).Theory andApplication ofCatastrophe[M].Shanghai:ShanghaiJiaotongUniversityPress,1987.(inChinese)
[10]李顺群.压力超过分叉荷载时中点屈曲位移的确定[J].哈尔滨工业大学学报,2003,35(4):495-501.LiShunqun.Computation of buckling displacement ofEuler bar’s mid-point[J].Journal ofHarbinInstitute ofTechnology,2003,35(4):495-501.(inChinese)
[11]何广讷.土工的若干新理论研究与应用[M].北京:水利电力出版社,1994.HeGuangna.New theories and application for soil[M].Beijing:ChinaWaterConservancy andHydropowerPress,1994.(inChinese)
[12]钟龙辉.轻亚粘土地震液化判别方法的分析[J].岩土工程学报,1980,2(3):113-122.ZhongLonghui.Analysis of evaluating liquefaction of low plasticity clay during earthquake[J].ChineseJournal ofGeotechnicalEngineering,1980,2(3):113-122.(inChinese)
[13]李顺群.土液化的突变模型研究[D].锦州:辽宁工学院,2002.LiShunqun.Study of catastrophe model for predicting earthquake-induced liquefaction of sand[D].Jinzhou:LiaoningInstitute ofTechnology,2002.(inChinese)
[2]钱家欢,殷宗泽.土工原理与计算[M].北京:水利电力出版社,1996.QianJiahuan,YinZongze.Principle andCalculation ofSoilEngineering[M].Beijing:ChinaWaterConservancy andHydropowerPress,1996.(inChinese)
[3]SeedH B.Dynamic analysis of the slide in the lowerSanFernando dam during the earthquake ofFeb.91971[J].Journal of theGeotechnicalEngineeringDivision,ASCE,1976,101(GT9):66-78.
[4]SeedH B.Evaluation ofSoilLiquefactionEffects onLevelGroundDuringEarthquake[A].LiquefactionProblems inGeotechnicalEngineering[C].ASCE NationalConvention,1976.1-104.
[5]SeedH B andLeeK L.Liquefaction ofSaturatedSandsDuringCyclicLoading[J].Journal ofSoilMechanics andFoundationEngineeringDivision,ASCE,1966,(SM6):105-134.
[6]何广讷,张业民.土本构关系的尖点突变模式[J].固体力学学报,1991,12(3):109-206.HeGuangne,ZhangYemin.Cusp-catastrophe model for constitutional relationship of soil[J].ActaMechanicaSolidaSinica,1991,12(3):109-206.(inChinese)
[7]刘军.缓倾角层状岩体失稳的尖点突变模型研究[J].岩土工程学报,2001,23(1):42-44.LiuJun.Study of catastrophic model with cusp point for failure of stratified rock mass with gentle inclination[J]. ChineseJournal ofGeotechnicalEngineering,2001,23(1):42-44.(inChinese)
[8]张业民,宋长清.软粘土流动性的尖顶突变模型分析[J].岩土工程学报,1995,17(4):67-70.ZhangYemin,SongChangqing.Analysis of flowing rule for soft clay with cusp catastrophe model[J].ChineseJournal ofGeotechnicalEngineering,1995,17(4):67-70.(inChinese)
[9]凌复华译.突变理论及其应用[M].上海:上海交通大学出版社,1987.LingFuhua(translated).Theory andApplication ofCatastrophe[M].Shanghai:ShanghaiJiaotongUniversityPress,1987.(inChinese)
[10]李顺群.压力超过分叉荷载时中点屈曲位移的确定[J].哈尔滨工业大学学报,2003,35(4):495-501.LiShunqun.Computation of buckling displacement ofEuler bar’s mid-point[J].Journal ofHarbinInstitute ofTechnology,2003,35(4):495-501.(inChinese)
[11]何广讷.土工的若干新理论研究与应用[M].北京:水利电力出版社,1994.HeGuangna.New theories and application for soil[M].Beijing:ChinaWaterConservancy andHydropowerPress,1994.(inChinese)
[12]钟龙辉.轻亚粘土地震液化判别方法的分析[J].岩土工程学报,1980,2(3):113-122.ZhongLonghui.Analysis of evaluating liquefaction of low plasticity clay during earthquake[J].ChineseJournal ofGeotechnicalEngineering,1980,2(3):113-122.(inChinese)
[13]李顺群.土液化的突变模型研究[D].锦州:辽宁工学院,2002.LiShunqun.Study of catastrophe model for predicting earthquake-induced liquefaction of sand[D].Jinzhou:LiaoningInstitute ofTechnology,2002.(inChinese)
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