基于双向地震作用下边坡共振特性与固有频率研究
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摘要
避共振是工程抗震设计中的重要课题,目前在边坡工程中鲜见这方面的研究。本文运用有限元法研究了边坡在双向地震作用下的共振规律及其固有频率。研究结果表明:边坡虽然有多阶固有频率,但只有前三阶固有频率处共振峰明显,其中尤以第一阶频率处的共振峰值最为突出,其他频率处则无明显共振现象;边坡在双向地震作用下的共振响应存在垂直放大和临空面放大作用;阻尼越大共振峰值越小,共振曲线越平缓;对影响边坡固有频率的主要因素进行深入研究,通过回归分析建立了边坡固有频率的经验公式,经检验该公式的计算误差较小。
One of the most important issues in seismic design is to avoid resonance,and presently there were few studies about this issue in slope engineering.In this paper,the resonance law and natural frequency of slope under bi-directional seismic were studied by Finite Element Method.The results showed that although the slope had multiple natural frequencies,only the resonance peak of first three order natural frequency is most prominent,especially the first order frequency resonance peak,and there was no obvious resonance in other frequency.Resonance response of the slope under bi-directional seismic had the action of vertical amplification and free surface amplification.The resonance peak was declining with the increasing of damping,and resonance curve was gradually gentle.The chief influential factors of natural frequency of the slope were studied deeply.The natural frequency formula of slope was established by regression analysis,of which error calculation was lower after testing.
One of the most important issues in seismic design is to avoid resonance,and presently there were few studies about this issue in slope engineering.In this paper,the resonance law and natural frequency of slope under bi-directional seismic were studied by Finite Element Method.The results showed that although the slope had multiple natural frequencies,only the resonance peak of first three order natural frequency is most prominent,especially the first order frequency resonance peak,and there was no obvious resonance in other frequency.Resonance response of the slope under bi-directional seismic had the action of vertical amplification and free surface amplification.The resonance peak was declining with the increasing of damping,and resonance curve was gradually gentle.The chief influential factors of natural frequency of the slope were studied deeply.The natural frequency formula of slope was established by regression analysis,of which error calculation was lower after testing.
引文
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[2]周德培,张建经,汤涌.汶川地震中道路边坡工程震害分析[J].岩石力学与工程学报,2010,29(3):565-576.[ZHOU D P,ZHANG J J,TANGY.Seismic damage analysis of road slopes inwenchuan earthquake[J.]Chinese Journal of RockMechanics and Engineering,2010,29(3):565-576.(in Chinese)]
[3]郑黎明.铁路边坡岩体的振动特性和机理[J.]岩石力学与工程学报,1994,13(1):69-78.[ZHENG L M.Specific vibration property andmechanism of rockmass in railway slopes[J.]ChineseJournal of Rock Mechanics and Engineering,1994,13(1):69-78.(in Chinese)]
[4]胡聿贤.地震工程学[M.]北京:地震出版社,2006.[HU Y X.Earthquake Engineering[M.]Beijing:Seismological Press,2006.(in Chinese)]
[5]Marco Mucciarelli,Angelo Masi,Maria RosariaGallipoli,et al.Analysis of RC Building DynamicResponse and Soil-Building Resonance Based on DataRecorded during a Damaging Earthquake(Molise,Italy,2002)[J.]Bulletin of the Seismological Societyof America,2004,94(5):1943-1953.
[6]张鲁渝,郑颖人,赵尚毅,等.有限元强度折减系数法计算土坡稳定安全系数的精度研究[J.]水利学报,2003(1):21-26.[ZHANG L U,ZHENG Y R,ZHAO S Y,et al.The feasibility study of strength-reduction method with FEM for calculating safetyfactors of soil slope stability[J].Journal of HydraulicEngineering2,003(1):21-26.(in Chinese)]
[7]赵振军,王颖,宁建国.基于结构动力学的框架结构固有频率估算方法[J.]力学与实践,2006,28(2):41-43.[ZHAO Z J,WANG Y,NING J G.Natural frequency estimation for a frame structureusing structural dynamics[J.]Mechanics inEngineering2,0062,8(2):41-43.(in Chinese)]
[8]瞿志豪,刘莹.超大型结构固有频率实验模拟方法[J.]实验力学,2006,21(2):253-257.[QU ZH,LIU Y.An experimental simulation method of theinherent frequency for a super big structure[J.]Journal of Experimental Mechanics,2006,21(2):253-257.(in Chinese)]
[9]朱建新,赵崇友,胡火焰,等.铲斗振动掘削岩土分析与岩土固有频率的估测方法[J.]中南大学学报,2007,38(3):507-511.[ZHU J X,ZHAO C Y,HU H Y,et al.Analysis of bucket vibratory excavaterock and measuring method of rock’s naturalfrequency[J.]Journal of Central South University,2007,38(3):507-511.(in Chinese)]
[10]宋光明,史秀志,张劲松,等.利用爆破振动观测求解边坡自振频率[J.]金属矿山,2001(3):4-6.[SONG G M,SHI X Z,ZHANG J S,et al.Workingout the natural frequency of slope on the basis of blastvibration monitoring[J].Metal Mine,2001(3):4-6.(in Chinese)]
[11]陈玲玲,高鸣安,钱胜国.边坡稳定性判别新理念——固有频率判别法[J.]岩土力学,2006,27(S2):1219-1222.[CHEN L L,GAO M A,QIAN SG.New theory of distinguishing slope stability-inherent frequency discrimination[J.]Rock and SoilMechanics,2006,27(S2):1219-1222.(inChinese)]
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