土体动力特性、复杂场地非线性地震反应及其方法研究
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摘要
土体动力特性、复杂场地非线性地震反应分析及其方法研究是近二十多年地震工程学和岩土地震工程中非常活跃的前沿领域。该课题涉及面广、关键环节多、方法也不够成熟,虽成果丰硕但仍存在强于试验、弱于观测、研究角度及分析方法单调、物理机制理解不够等显著不足。因此,论文首先总结了国内外的研究现状,阐述了该课题的理论及工程实际意义。
基于大量高质量强震观测及钻井台阵资料,对土体线性、非线性动力参数反演、土动非线性及软土本构、时域积分方法、竖向地震动对斜坡场地非线性地震反应的影响、近断层速度大脉冲地震动下复杂场地双重非线性反应分析等核心问题进行了与前人不同的研究,主要工作及创新如下:
1.土体动力一维非线性本构关系是场地及地基动力响应、土工数值分析的关键。回顾和总结了国内外的发展状况及研究进展,对其分析方法、由等幅循环荷载到不规则荷载的扩展及应用规则、试验阻尼比的等效、滞回曲线形状等核心问题进行剖析、评价和探讨,对各种模型的优缺点进行了比较和讨论,指出了影响场地非线性地震动波形-土体滞回本构曲线形状及曲率变化规律是当今本构研究的热点。
2.通过基岩覆盖单粘土层场地、Los Angeles Obregon Park多覆盖层场地、台湾Lotung DHB钻井台阵试验场对Pyke方法、“阻尼比退化系数”模型、非Masing准则模型一和非Masing准则模型二、“隐式应力阻尼等效”模型这五种常用动力本构进行了细致对比,说明了各模型有效合理的相对性,以及与强震观测相差异的客观性。
针对上述问题及试验中滞回本构曲线形状时常表现为先平缓然后变化剧烈等特征,提出了“考虑试验阻尼效应的一种土体动力双型抛物线本构模型”,建立了不规则荷载下灵活变化的本构规则,并给出了A型和B型抛物线的函数表达及调制因子Ad的施加过程。通过对试验阻尼比的模拟,说明了九种土体本构的差异及加卸载准则。针对台湾LotungDHB钻井台阵试验场地,等效线性化方法SHAKE91、LSSRLI-1,时域非线性方法DESRA-2(Huang等)、以及上述五种方法共计九种方法进行了非线性地震反应分析。结果表明:双型抛物线本构模型计算的复合加速度地震动的峰值大小、波形大小相对关系及后续波形,与实际地震记录较为一致,说明了模型的合理性以及应用于工程实际的可行性。
基于调制因子Ad对滞回本构曲线加以调制的思想,对“阻尼比退化系数模型”进行了扩展和修正,给出了“广义阻尼比退化系数模型”的理论表达式,并由钻井台阵试验场说明了其合理性。最后,将上述所有时域本构模型统一编制为出平面非线性波动程序APNWP_1D。
3.如何合理有效地刻画软土场地非线性地震响应已成为岩土工程中的重要课题之一。对循环荷载下软土刚度退化、动强度降低及残余应变势的研究现状作了探讨,针对动三轴、动简剪、动扭剪试验研究结果,提出了多项式形式的动态残余应力势模型,分别给出了等幅循环荷载的相对残余应力势及不规则荷载的局部相对残余应力势的概念,并通过试验结果加以验证;阐述了残余应力势与残余应变势的密切关系,以及残余应力势在不规则荷载作用下的应用规则;动态残余应力势模型在厦门白鹭洲软弱场地分析中得以应用,其永久位移、应力应变动态范围、淤泥层隔振效应、竖向及剪切地震响应的差异等,均符合人们对残余应力特性及非线性场地反应的认识,进一步说明了模型的合理性及实用性。
4.着重分析了以土工试验资料的归纳提炼为基础的经验关系模型,在剖析以往二维土动弹塑性本构模型之后,提出了土体动力单、双滞回非线性本构模型,给出了具体实现过程及步骤,并设计了两个数值实验实例加以验证,通过计算二维场地非线性动力反应及滞回本构曲线,与一维情形的比较,说明了两类本构模型的合理性。
5.为了认识钻井台阵场地在中小地震动、强地震动下的土体线性、非线性动力特征,校验工程钻探方法及现场测试技术,提高土工试验精度。首先,阐述了线性成层介质场地反应P-SV、SH斜入射波动分析方法,其层转换矩阵元素总为实数。编制了斜入射线性波动场地反应程序SSRA,以均匀弹性半空间波动分析验证了程序的正确性。然后,在其他学者的基础上给出了遗传算法-单纯形法结合形成的全局-局部混合优化方法及设计步骤。最后,针对响嘡老井2#钻井台阵的中小地震记录,提供了以往研究中没有涉及的P波波速值、阻尼比值及与频率有关的阻尼频率因子b值。结果表明:反演的响嘡 2#剪切波速值大于94年单孔原位波速测试结果,而更接近于距其200多米的3#的剪切波速结果。并发现在峰值加速度60gal量级的地震作用中就存在反演可以察觉的土体非线性。另外,对响嘡 2#场地效应特性及应力传递函数进行了分析。
针对强地震动钻井台阵记录,尝试性地给出了时域滞回非线性场地土体动力特性的反演方法,并以日本Kik-net强地震动台网的TKCH07钻井台阵观测资料进行了实践分析,得到的结果基本属于国际公认的砂土及粘性土土工实验范围,说明了其可靠性。
6.目前波动显式有限元分析多以位移和(或)速度作为输入,而加速度记录更直接地保留了地震波的原始信息。为此,发展了一种直接以地震加速度作为输入的显式算法,该算法以中心差分和Newmark-β法结合,并通过平衡方程约简得到。采用水塔及框架结构为例,与现有振型分解联合Duhamel积分方法、Newmark-β隐式解法及五种显式算法进行了对比分析。结果表明:该算法可以在保证计算效率的前提下,得到与振型分解联合Duhamel积分方法、Newmark-β隐式解法相吻合的加速度反应。
另外,对非传统方法-即基于时域数字滤波器传递函数的实时处理方法进行了简要归纳,并推荐了一套初值计算公式。
7.国内外规范推荐或强制规定竖向地震动取为剪切反应谱的1/2-2/3,但该规定如何改进使之更合理已成为一个重要课题。首先对研究现状进行了简单总结,编制了可处理辐射阻尼、地震动相位特性、计算高效的二维波动显式有限元等效线性化程序ELPSV。初步研究表明:竖向地震动强度对周期在0.3秒以下的地表剪切反应谱有一定的影响,而高于0.3秒部分影响轻微。竖向地震动强度对斜坡场地的竖向地震反应及地表竖向反应谱的影响显著,按规范取值将偏于不安全。受地形条件影响,坡顶剪切地震反应会比坡脚反应要大,而竖向地震反应却并不明显。土层交界面的地震反应要比周围反应要低,交界面效应明显。软斜坡场地除竖向地震反应略有差别外,其它情形与硬斜坡场地的规律基本一致。该结果定量反映了竖向地震动的影响程度,为斜坡场地上考虑竖向地震动的建(构)筑结构的抗震设计提供了有益基础。8.利用日本小田原场地强震观测资料,对两个较大的单双滞回非线性波动模拟程序PSVNWA_2D和SHNWA_2D进行了细致校核,不仅分析出平面SH型非线性波动的模拟,而且进行了平面内P-SV型非线性波动的模拟。不但给出了观测点的理论地震图,而且还预测了相应的地震动速度、位移和永久位移。甚至给出了典型单元的单双滞回非线性动力本构曲线。
针对绥棱缓斜坡场地,利用PSVNWA_2D程序计算了Northridge、Turkey两次地震作用,分别输入强弱地震动两种情形,计算了地表点和第二层交界面点加速度和位移反应,说明了各点的地震动变化、滞回曲线变化规律以及两次地震强弱情形的非线性地震反应的差别,分析了传递函数的频谱变化、放大倍数、以及剪切反应引起的竖向地震动。研究中发现了随着地震动输入强度的增大,观测点的非线性反应放大倍数反而增大的现象,文中阐述了原因,并在强震观测和震源机制中获得支持。同时还发现了等效线性化方法与时域非线性方法计算的位移、速度、和加速度传递函数的本质差别。另外,也进行了Loma Prieta地震动作用的分析。
在Kobe地震动作用下,对类西雅图盆地进行了出平面和平面内两种情形的非线性反应分析,其中也进行了线性反应的对比。结果表明:平面内非线性波动模拟结果与出平面情形结果差别显著,尤其是对于位移反应和永久位移值。平面内非线性波动模拟结果中可发现典型的“盆地聚焦效应”,而出平面情形并不明显。但是,两种情形中可以发现明显的“盆地底边边缘效应”。这两种效应,会使位于场地剖面不同位置点的地震动差别很大。这些非线性场地地震反应的特点和规律,有益于重大工程考虑场地非线性的设计地震动的预测与估计,有助于重要建筑结构的非线性抗震设计。
9.通过近断层单向、双向速度大脉冲输入的自检验分析,指出了工程中传统等效线性化方法的适用条件及局限性。提出了既考虑物理(本构)非线性又考虑几何非线性的一维场地时域显式双重非线性动力反应分析方法,并将该方法增加到APNWP_1D程序中,设置单独开关加以控制。
将近断层速度大脉冲地震动输入分解为两种独立机制-弹性大变形机制和双重非线性(弹塑性大变形)机制。提出了双机制分合法和统一法。对于二维复杂场地,针对近断层单向和双向速度大脉冲地震动,结合地震动分解策略,提出了动力弹塑性理论有机结合几何非线性-即动力弹塑性大变形机制分析方法,编制了较大的二维双重非线性动力计算程序软件DNDYN_2D。在TCU068单向速度脉冲和Northridge NWPCR双向速度脉冲作用下,对华林路农科院复杂场地的双重非线性动力反应进行了分析。结果表明:单向速度脉冲地震动作用时,双机制分合法比双机制统一法更合理,双机制统一法更宜于分析双向速度脉冲作用。定量给出了华林路农科院场地的的永久位移、加速度时程及峰值结果。
该方法可用于基岩处几米永久位移的强地震动(PGA大于400gal)作用下,近断层成层场地的强非线性地震反应分析;也可得到工程中较为满意的二维场地双重非线性地震反应解答。
最后,对研究工作简要总结,并指出了另外尚需研究的工作。
Recent twenty years, study on soil dynamic characteristics, nonlinear seismic response of complex site and its methods have become very active research areas, both in earthquake engineering and geotechnical earthquake engineering. This research needs deal with a great many keys and its method is not mature, although the results are much more abundant, it is obvious insufficient and inadequate for monotonous methods and impercipient physical mechanism etc. As a result, firstly, the author has expounded theoretical and practical significance of this reaearch, reviewed the current advancements at home and abroad in this field.
Secondly, based on plenty of high quality strong motion observations and borehole array observations, the core problems: inversions of soil linear and nonlinear dynamic parameters, nonlinear constitutive relastions and soft soil’s, numerical integration methods in time domain, effects of vertical strong motion on nonlinear seismic response of slope site, diploid nonlinear seismic response of complex site during the velocity pulse type strong motion of near fault, are analyzed. The following are main contents and innovative achievements.
1. Soil dynamic 1D nonlinear constitutive relation is the key to numerical method and dynamic response of site and foundation. Firstly, the development and research advancement are summarized. Then, the important problem, which are analysis methods, the application rules of from equal amplitude cyclic load process to irregular load’s, equivalent methods of test hysteretic damping, curve shapes of hysteretic constitutive etc. are analyzed, evaluated and discussed. The advantages and disadvantages of models are compared with each other. Finally, the shape of hysteretic constitutive curve can affect waveform of nonlinear strong motion in site response, which is pointed out especially.
2. By analyzing nonlinear response of clay layer mantled base rock site, Los Angeles Obregon Park multi-mantled layer site, Taiwan Lotung DHB borehole array site, 5 types models, which are Pyke method, damping degradation coefficient model, Non-Masing rule model ONE and model TWO, implicit stress damping equivalent model are compared detailedly with each other. It is objective that some discrepancy between theoretical results and the strong motion observations. Each model is relatively rational and effective.
Considering previous questions and the characteristics of reverse load or unload curves sometimes change more flatly at first and then acutely in soil test. First, the rules of adjustable double-parabola hysteretic constitutive curves in irregular load history are established, and function expression and implement course of A type and B type parabola are expounded. Second, by comparisons of 9 methods simulated results of soil test damping, the load and unload rules of double-parabola model accord with the test results, especially accord with the value of soil test damping. Because of the adjustment coefficient Ad can be changed, the model has more powerful capability of simulation the shape of constitutive relationship curves. Third, using the borehole array records of Taiwan Lotung DHB field test, the nonlinear seismic response of DHB site are analyzed by equivalent linear method SHAKE91, LSSRLI-1; nonlinear method in time domain - DESRA-2, Pyke model, Non-Masing rule model ONE, implicit stress damping equivalent model, damping degradation coefficient model, Non-Masing rule model TWO and double-parabola constitutive model respectively. After compared all the synthesize acceleration ground motions with the observation records, we found that the PGA of double-parabola model are almost equal to the observation value, the comparative size relations of strong motion waveform, subsequence waveform are agree well with the records. As a result, the rationality of double-parabola constitutive model and the feasibility in practical engineering application are manifested.
Similarly, the idea of adjustment coefficient Ad can change the shape of hysteretic constitutive cure, which is applied in previous damping degradation coefficient model. Generalized damping degradation coefficient constitutive model is gained. The function expression and implement course are expounded too, and its rationality is also manifested by borehole array site. At last, all of constitutive models are organized into AntiPlane Nonlinear Wave Propagation program APNWP_1D.
3. How to effectively and rationally describe the nonlinear response of soft soil site is one of the most important tasks in geotechnical engineering. Firstly, stiffness degradation of soft soil, dynamic stress decrease and residual strain potential in cyclic loads are discussed. Dynamic Residual Stress Potential(RSP) in polynomial type are brought forward after detailed analyzing the results of triaxial test, cyclic simple shear test and torsional test. The conceptions of relative RSP and local relative RSP for regular cyclic and irregular load respectively are presented. Simultaneously, RSP are verified by all test data. Secondly, the affinity of RSP and residual strain potential, the application rule of RSP in irregular loads are explained. At last, dynamic RSP is successfully used in seismic response of Xiamen Bailuzhou site. The results of permanent displacement, dynamic range of stress and strain, isolation vibration effect of silt layer and the difference of shear and vertical strong motion, which accord with the knowledge of residual stress characteristic and site nonlinear seismic response, and the model is proved rationality and practicability again.
4. This paper emphatically analyze experiential relation model, which is abstracted from a lot of experiment data. After drastically studied two-dimensional plastic constitutive model, we put forward single hysteretic nonlinear constitutive model and double hysteretic nonlinear constitutive model of soil. The accomplished processes and steps are presented, and two numerical examples are designed for validating these methods. Through the contrast of not only the one-dimensional and two-dimensional nonlinear hysteretic constitutive curve, but also the nonlinear dynamic response, it can be seen that the two type modle are rational.
5. In order to understand the soil linear and nonlinear characteristics of borehole array site not only in the small and moderate earthquake but also in the strong earthquake, verifying and improving the precision of field test and laboratory test. Firstly, the paper expounds the linear horizontal stratified site’s P- SV, SH inclined incidence wave propagation method, whose Layer Transform Array is always real. The SSRA procedure is made, and its right is proved by an example of homogeneous elastic halfspace analysis. Secondly, Inversion methods, SSRA combining a global-local optimization algorithm, which is genetic algorithm (GA) - Simplex Method, are brought forward. At last, using 3 moderate and weak seismic events at Xiangtang borehole array (2#) site, soils dynamic characteristic parameters, including P velocity, damping value, frequency- dependent coefficient b, which are no dealing with in previous literatures, are calculated. S velocities of Xiangtang 2# site are on the whole greater than 1994’s field test results, and are close to the 3# which is 200m far away. At the same time, perceptible soil nonlinear behavior in 60gal magnitude earthquake is detected by inversion analysis. In addition, the displacement and stress transfer function of Xiangtang 2# site are also analyzed.
For the records of borehole array, we tentatively present an inversion method of hysteretic nonlinear in time domain for dynamic characteristic parameters of site soil. Then taking this method in practice by TKCH07 borehole array data in Japan Seismic monitoring Network Kik-net, the result is proved reliable, because it is almost in the test scope of sand and clay, which are accepted by international.
6. Displacement and/or velocity often be inputted in wave motion explicit FEM at present, while acceleration record directly reflects original information of seismic wave. As a result, an explicit integration formula, which is based on both center difference method and Newmark -βmethod, and is reduced by equilibrium equation, is proposed. Water tower and framework structure dynamic analysis indicated that, the acceleration response of the formula is agree well with that of mode analysis associating with Duhamel integral method and Newmark -βimplicit method, when the efficiency of calculating is firstly ensured. In addition, we concisely summarize the real time processing method, which is unconventional method, based on transfer function of numeric filter in time domain, and the first step’s initial value formula are recommended.
7. It isn’t enough in study of vertical strong motion influencing on nonlinear seismic response of slope site for its complicated strong motion input, soil nonlinearity, slope topographty condition and interface effects etc. The methods of taking half or 2/3 of shear response spectrum as vertical seismic action, recommended or prescribed compulsorily in many engineering codes at home and abroad, are used to design buildings. But how to rationally consider this effect is one of the most important tasks. Firstly, these research advancements are reviewed. The necessary of equivalent linear method of 2D wave motion explicit FEM ELPSV program with characteristic of high efficiency, real phase, actual radiation damping, is discussed. Then, strength of vertical strong motion influencing on response spectrum of slope site surface, equivalent response history and PGD and PGV in site section, seismic response of soft slope site are analyzed, and draw some primary conclusions as following: There are certain influences on shear seismic response spectrum when the period less than 0.3s, but it is very light over 0.3s. Vertical seismic response of slope site was distinctly changed by vertical strong motion. Moreover, value of vertical seismic action in code for seismic design for buildings is apt to unsafety. Simultaneously, vertical response of the right site is great than the left’s. The slope top’s shear response is much stronger than slope feet’s for slope topography condition, while vertical seismic response is not obvious. Magnified effect in strong motion is more than in weak motion when ratio of horizontal to vertical component(av/ah) is 2/3, which agrees with the knowledge of nonlinear response. Interestingly, Interface effects make the response is lower than ambient site response. And soft site response is essentially consistent with phenomena of the hard site, except for vertical seismic response is increased previously and then decreased from site bottom to the top. At last, concise epilogue is given. All of conclusions and study results reflected quantitatively effect extent of vertical strong motion, provide beneficial basement for rational considering vertical strong motion in aseismic design of buildings and constructions in slope site.
8. Using the strong earthquake observations at Ashigara Valley in Japan, the two much great single-double hysteretical nonlinear wave motion simulation program-PSVNWA_2D and SHNWA_2D are roundly checked, the author simulate not only SH nonlinear wave motion, but also P-SV nonlinear wave motion. The analysis results not only provide the theoretical strong motion of observation station, but also forecast the earthquake velocity, displacement and permanent displacement correspondingly, even, educe the single - double hysteretic nonlinear dynamic constitutive relation curves.
Aiming at Suiling little slope site, we use PSVNWA_2D program to calculate the displacement and acceleration response of the surface and interface between the first layer and the second layer, when strong and weak type of Northridge and Turkey earthquake as input. The results show not only the changes of every earthquake motion and hysteretic curves, but also the nonlinear earthquake response difference between the strong motion and the weak motion in each earthquake, also difference between the two earthquake. Simultaneously, we analyze the spectrum change of transfer function, amplification coefficient and vertical earthquake motion derived from the shear response. In the research, it is sometimes found that amplification coefficient of nonlinear response at site observation station increase with the earthquake strong motion enhanced. The reason of phenomena is expatiated, and the case is proved by the strong earthquake observation and earthquake mechanism. At the same time, the paper pointed out essential difference of the transfer function of displacement, velocity and acceleration in equivalent linearization and time domain nonlinear technique. In addition, nonlinear seismic response during Loma Prieta earthquake is also analyzed.
Under Kobe earthquake action, nonlinear seismic response of Quasi- Seattle- Basin site at in-plane and anti-plane cases is analyzed. The results indicated that the difference is remarkable between the nonlinear wave motion simulation of in-plane and that of anti-plane, in particular for the displacement response and permanent displacement. In the plane, the‘basin focusing effect’of the nonlinear wave motion simulation is obvious, while the situation in anti-plane. is not enough. But‘the basin basement edge effect’is distinct in two kinds of situations.
These two effects can cause great difference of the seismic motion on the site section. The characteristics and the rules of the nonlinear seismic response are not only beneficial to the forecast and the estimate of seismic motion of important engineering, but also helpful to nonlinear aseismic design of the important construction structure.
9. Inputting the near fault unidirectional and bidirectional velocity big pulse, complex site response is calculated by equivalent linearization method, the result is examined by itself. Rational condition and limitation of the traditional equivalent linearization method in this project are pointed out. In view of shortcomings, dynamic diploid nonlinear anlaysis explicit method in time domain for 1D site seismic response, which taking both physical nonlinear and geometrical nonlinear into account, is put forward. Then this method is taken to the APNWP_1D procedure, and establishing independent switch to control it. We decompose the input motion of near fault velocity big pulse into two kind of independent mechanisms - the elasitc big deformation mechanism and the diploid nonlinearity (elast-plastic big deformation) mechanism. At the same time, the parted and unitive double-mechanisms are proposed. For the two-dimensional complex ground, in view of the near fault seismic motion decomposition strategy, which are used to unidirectional and bidirectional velocity big pulse seismic motion analysis, the method of dynamical plastic theory combined big deformation mechanism is proposed. It has established bigger two-dimensional diploid nonlinear dynamical procedure software DNDYN_2D. Under TCU068 unidirectional pulse and Northridge NWPCR bidirectional pulse action, The diploid nonlinear dynamic response of complex site at Institute of Agricultural Sciences on the Hualin road was analysed. The result indicated that, when seismic motion was unidirectional velocity pulse, the parted diploid- mechanism was more reasonable than unitive diploid-mechanism. However the unitive diploid-mechanism is more suitable for the analysis of bidirectional velocity pulse action. The result also quantitatively present the permanent displacement, acceleration time history and peak value of site at Institute of Agricultural Sciences on Hualin road.
This method may use for strong nonlinear seismic response of near fault stratified site, even on condition of seismic strong motion with several metres permanent displacement (PGA almost greater than 400gal) at bedrock as input. At the same time, more satisfactory answer in diploid nonlinear seismic response of 2D site for engineering also can be obtained.
In the end, existing problems are pointed out and the research problems, which need to be done in future, are suggested.
基于大量高质量强震观测及钻井台阵资料,对土体线性、非线性动力参数反演、土动非线性及软土本构、时域积分方法、竖向地震动对斜坡场地非线性地震反应的影响、近断层速度大脉冲地震动下复杂场地双重非线性反应分析等核心问题进行了与前人不同的研究,主要工作及创新如下:
1.土体动力一维非线性本构关系是场地及地基动力响应、土工数值分析的关键。回顾和总结了国内外的发展状况及研究进展,对其分析方法、由等幅循环荷载到不规则荷载的扩展及应用规则、试验阻尼比的等效、滞回曲线形状等核心问题进行剖析、评价和探讨,对各种模型的优缺点进行了比较和讨论,指出了影响场地非线性地震动波形-土体滞回本构曲线形状及曲率变化规律是当今本构研究的热点。
2.通过基岩覆盖单粘土层场地、Los Angeles Obregon Park多覆盖层场地、台湾Lotung DHB钻井台阵试验场对Pyke方法、“阻尼比退化系数”模型、非Masing准则模型一和非Masing准则模型二、“隐式应力阻尼等效”模型这五种常用动力本构进行了细致对比,说明了各模型有效合理的相对性,以及与强震观测相差异的客观性。
针对上述问题及试验中滞回本构曲线形状时常表现为先平缓然后变化剧烈等特征,提出了“考虑试验阻尼效应的一种土体动力双型抛物线本构模型”,建立了不规则荷载下灵活变化的本构规则,并给出了A型和B型抛物线的函数表达及调制因子Ad的施加过程。通过对试验阻尼比的模拟,说明了九种土体本构的差异及加卸载准则。针对台湾LotungDHB钻井台阵试验场地,等效线性化方法SHAKE91、LSSRLI-1,时域非线性方法DESRA-2(Huang等)、以及上述五种方法共计九种方法进行了非线性地震反应分析。结果表明:双型抛物线本构模型计算的复合加速度地震动的峰值大小、波形大小相对关系及后续波形,与实际地震记录较为一致,说明了模型的合理性以及应用于工程实际的可行性。
基于调制因子Ad对滞回本构曲线加以调制的思想,对“阻尼比退化系数模型”进行了扩展和修正,给出了“广义阻尼比退化系数模型”的理论表达式,并由钻井台阵试验场说明了其合理性。最后,将上述所有时域本构模型统一编制为出平面非线性波动程序APNWP_1D。
3.如何合理有效地刻画软土场地非线性地震响应已成为岩土工程中的重要课题之一。对循环荷载下软土刚度退化、动强度降低及残余应变势的研究现状作了探讨,针对动三轴、动简剪、动扭剪试验研究结果,提出了多项式形式的动态残余应力势模型,分别给出了等幅循环荷载的相对残余应力势及不规则荷载的局部相对残余应力势的概念,并通过试验结果加以验证;阐述了残余应力势与残余应变势的密切关系,以及残余应力势在不规则荷载作用下的应用规则;动态残余应力势模型在厦门白鹭洲软弱场地分析中得以应用,其永久位移、应力应变动态范围、淤泥层隔振效应、竖向及剪切地震响应的差异等,均符合人们对残余应力特性及非线性场地反应的认识,进一步说明了模型的合理性及实用性。
4.着重分析了以土工试验资料的归纳提炼为基础的经验关系模型,在剖析以往二维土动弹塑性本构模型之后,提出了土体动力单、双滞回非线性本构模型,给出了具体实现过程及步骤,并设计了两个数值实验实例加以验证,通过计算二维场地非线性动力反应及滞回本构曲线,与一维情形的比较,说明了两类本构模型的合理性。
5.为了认识钻井台阵场地在中小地震动、强地震动下的土体线性、非线性动力特征,校验工程钻探方法及现场测试技术,提高土工试验精度。首先,阐述了线性成层介质场地反应P-SV、SH斜入射波动分析方法,其层转换矩阵元素总为实数。编制了斜入射线性波动场地反应程序SSRA,以均匀弹性半空间波动分析验证了程序的正确性。然后,在其他学者的基础上给出了遗传算法-单纯形法结合形成的全局-局部混合优化方法及设计步骤。最后,针对响嘡老井2#钻井台阵的中小地震记录,提供了以往研究中没有涉及的P波波速值、阻尼比值及与频率有关的阻尼频率因子b值。结果表明:反演的响嘡 2#剪切波速值大于94年单孔原位波速测试结果,而更接近于距其200多米的3#的剪切波速结果。并发现在峰值加速度60gal量级的地震作用中就存在反演可以察觉的土体非线性。另外,对响嘡 2#场地效应特性及应力传递函数进行了分析。
针对强地震动钻井台阵记录,尝试性地给出了时域滞回非线性场地土体动力特性的反演方法,并以日本Kik-net强地震动台网的TKCH07钻井台阵观测资料进行了实践分析,得到的结果基本属于国际公认的砂土及粘性土土工实验范围,说明了其可靠性。
6.目前波动显式有限元分析多以位移和(或)速度作为输入,而加速度记录更直接地保留了地震波的原始信息。为此,发展了一种直接以地震加速度作为输入的显式算法,该算法以中心差分和Newmark-β法结合,并通过平衡方程约简得到。采用水塔及框架结构为例,与现有振型分解联合Duhamel积分方法、Newmark-β隐式解法及五种显式算法进行了对比分析。结果表明:该算法可以在保证计算效率的前提下,得到与振型分解联合Duhamel积分方法、Newmark-β隐式解法相吻合的加速度反应。
另外,对非传统方法-即基于时域数字滤波器传递函数的实时处理方法进行了简要归纳,并推荐了一套初值计算公式。
7.国内外规范推荐或强制规定竖向地震动取为剪切反应谱的1/2-2/3,但该规定如何改进使之更合理已成为一个重要课题。首先对研究现状进行了简单总结,编制了可处理辐射阻尼、地震动相位特性、计算高效的二维波动显式有限元等效线性化程序ELPSV。初步研究表明:竖向地震动强度对周期在0.3秒以下的地表剪切反应谱有一定的影响,而高于0.3秒部分影响轻微。竖向地震动强度对斜坡场地的竖向地震反应及地表竖向反应谱的影响显著,按规范取值将偏于不安全。受地形条件影响,坡顶剪切地震反应会比坡脚反应要大,而竖向地震反应却并不明显。土层交界面的地震反应要比周围反应要低,交界面效应明显。软斜坡场地除竖向地震反应略有差别外,其它情形与硬斜坡场地的规律基本一致。该结果定量反映了竖向地震动的影响程度,为斜坡场地上考虑竖向地震动的建(构)筑结构的抗震设计提供了有益基础。8.利用日本小田原场地强震观测资料,对两个较大的单双滞回非线性波动模拟程序PSVNWA_2D和SHNWA_2D进行了细致校核,不仅分析出平面SH型非线性波动的模拟,而且进行了平面内P-SV型非线性波动的模拟。不但给出了观测点的理论地震图,而且还预测了相应的地震动速度、位移和永久位移。甚至给出了典型单元的单双滞回非线性动力本构曲线。
针对绥棱缓斜坡场地,利用PSVNWA_2D程序计算了Northridge、Turkey两次地震作用,分别输入强弱地震动两种情形,计算了地表点和第二层交界面点加速度和位移反应,说明了各点的地震动变化、滞回曲线变化规律以及两次地震强弱情形的非线性地震反应的差别,分析了传递函数的频谱变化、放大倍数、以及剪切反应引起的竖向地震动。研究中发现了随着地震动输入强度的增大,观测点的非线性反应放大倍数反而增大的现象,文中阐述了原因,并在强震观测和震源机制中获得支持。同时还发现了等效线性化方法与时域非线性方法计算的位移、速度、和加速度传递函数的本质差别。另外,也进行了Loma Prieta地震动作用的分析。
在Kobe地震动作用下,对类西雅图盆地进行了出平面和平面内两种情形的非线性反应分析,其中也进行了线性反应的对比。结果表明:平面内非线性波动模拟结果与出平面情形结果差别显著,尤其是对于位移反应和永久位移值。平面内非线性波动模拟结果中可发现典型的“盆地聚焦效应”,而出平面情形并不明显。但是,两种情形中可以发现明显的“盆地底边边缘效应”。这两种效应,会使位于场地剖面不同位置点的地震动差别很大。这些非线性场地地震反应的特点和规律,有益于重大工程考虑场地非线性的设计地震动的预测与估计,有助于重要建筑结构的非线性抗震设计。
9.通过近断层单向、双向速度大脉冲输入的自检验分析,指出了工程中传统等效线性化方法的适用条件及局限性。提出了既考虑物理(本构)非线性又考虑几何非线性的一维场地时域显式双重非线性动力反应分析方法,并将该方法增加到APNWP_1D程序中,设置单独开关加以控制。
将近断层速度大脉冲地震动输入分解为两种独立机制-弹性大变形机制和双重非线性(弹塑性大变形)机制。提出了双机制分合法和统一法。对于二维复杂场地,针对近断层单向和双向速度大脉冲地震动,结合地震动分解策略,提出了动力弹塑性理论有机结合几何非线性-即动力弹塑性大变形机制分析方法,编制了较大的二维双重非线性动力计算程序软件DNDYN_2D。在TCU068单向速度脉冲和Northridge NWPCR双向速度脉冲作用下,对华林路农科院复杂场地的双重非线性动力反应进行了分析。结果表明:单向速度脉冲地震动作用时,双机制分合法比双机制统一法更合理,双机制统一法更宜于分析双向速度脉冲作用。定量给出了华林路农科院场地的的永久位移、加速度时程及峰值结果。
该方法可用于基岩处几米永久位移的强地震动(PGA大于400gal)作用下,近断层成层场地的强非线性地震反应分析;也可得到工程中较为满意的二维场地双重非线性地震反应解答。
最后,对研究工作简要总结,并指出了另外尚需研究的工作。
Recent twenty years, study on soil dynamic characteristics, nonlinear seismic response of complex site and its methods have become very active research areas, both in earthquake engineering and geotechnical earthquake engineering. This research needs deal with a great many keys and its method is not mature, although the results are much more abundant, it is obvious insufficient and inadequate for monotonous methods and impercipient physical mechanism etc. As a result, firstly, the author has expounded theoretical and practical significance of this reaearch, reviewed the current advancements at home and abroad in this field.
Secondly, based on plenty of high quality strong motion observations and borehole array observations, the core problems: inversions of soil linear and nonlinear dynamic parameters, nonlinear constitutive relastions and soft soil’s, numerical integration methods in time domain, effects of vertical strong motion on nonlinear seismic response of slope site, diploid nonlinear seismic response of complex site during the velocity pulse type strong motion of near fault, are analyzed. The following are main contents and innovative achievements.
1. Soil dynamic 1D nonlinear constitutive relation is the key to numerical method and dynamic response of site and foundation. Firstly, the development and research advancement are summarized. Then, the important problem, which are analysis methods, the application rules of from equal amplitude cyclic load process to irregular load’s, equivalent methods of test hysteretic damping, curve shapes of hysteretic constitutive etc. are analyzed, evaluated and discussed. The advantages and disadvantages of models are compared with each other. Finally, the shape of hysteretic constitutive curve can affect waveform of nonlinear strong motion in site response, which is pointed out especially.
2. By analyzing nonlinear response of clay layer mantled base rock site, Los Angeles Obregon Park multi-mantled layer site, Taiwan Lotung DHB borehole array site, 5 types models, which are Pyke method, damping degradation coefficient model, Non-Masing rule model ONE and model TWO, implicit stress damping equivalent model are compared detailedly with each other. It is objective that some discrepancy between theoretical results and the strong motion observations. Each model is relatively rational and effective.
Considering previous questions and the characteristics of reverse load or unload curves sometimes change more flatly at first and then acutely in soil test. First, the rules of adjustable double-parabola hysteretic constitutive curves in irregular load history are established, and function expression and implement course of A type and B type parabola are expounded. Second, by comparisons of 9 methods simulated results of soil test damping, the load and unload rules of double-parabola model accord with the test results, especially accord with the value of soil test damping. Because of the adjustment coefficient Ad can be changed, the model has more powerful capability of simulation the shape of constitutive relationship curves. Third, using the borehole array records of Taiwan Lotung DHB field test, the nonlinear seismic response of DHB site are analyzed by equivalent linear method SHAKE91, LSSRLI-1; nonlinear method in time domain - DESRA-2, Pyke model, Non-Masing rule model ONE, implicit stress damping equivalent model, damping degradation coefficient model, Non-Masing rule model TWO and double-parabola constitutive model respectively. After compared all the synthesize acceleration ground motions with the observation records, we found that the PGA of double-parabola model are almost equal to the observation value, the comparative size relations of strong motion waveform, subsequence waveform are agree well with the records. As a result, the rationality of double-parabola constitutive model and the feasibility in practical engineering application are manifested.
Similarly, the idea of adjustment coefficient Ad can change the shape of hysteretic constitutive cure, which is applied in previous damping degradation coefficient model. Generalized damping degradation coefficient constitutive model is gained. The function expression and implement course are expounded too, and its rationality is also manifested by borehole array site. At last, all of constitutive models are organized into AntiPlane Nonlinear Wave Propagation program APNWP_1D.
3. How to effectively and rationally describe the nonlinear response of soft soil site is one of the most important tasks in geotechnical engineering. Firstly, stiffness degradation of soft soil, dynamic stress decrease and residual strain potential in cyclic loads are discussed. Dynamic Residual Stress Potential(RSP) in polynomial type are brought forward after detailed analyzing the results of triaxial test, cyclic simple shear test and torsional test. The conceptions of relative RSP and local relative RSP for regular cyclic and irregular load respectively are presented. Simultaneously, RSP are verified by all test data. Secondly, the affinity of RSP and residual strain potential, the application rule of RSP in irregular loads are explained. At last, dynamic RSP is successfully used in seismic response of Xiamen Bailuzhou site. The results of permanent displacement, dynamic range of stress and strain, isolation vibration effect of silt layer and the difference of shear and vertical strong motion, which accord with the knowledge of residual stress characteristic and site nonlinear seismic response, and the model is proved rationality and practicability again.
4. This paper emphatically analyze experiential relation model, which is abstracted from a lot of experiment data. After drastically studied two-dimensional plastic constitutive model, we put forward single hysteretic nonlinear constitutive model and double hysteretic nonlinear constitutive model of soil. The accomplished processes and steps are presented, and two numerical examples are designed for validating these methods. Through the contrast of not only the one-dimensional and two-dimensional nonlinear hysteretic constitutive curve, but also the nonlinear dynamic response, it can be seen that the two type modle are rational.
5. In order to understand the soil linear and nonlinear characteristics of borehole array site not only in the small and moderate earthquake but also in the strong earthquake, verifying and improving the precision of field test and laboratory test. Firstly, the paper expounds the linear horizontal stratified site’s P- SV, SH inclined incidence wave propagation method, whose Layer Transform Array is always real. The SSRA procedure is made, and its right is proved by an example of homogeneous elastic halfspace analysis. Secondly, Inversion methods, SSRA combining a global-local optimization algorithm, which is genetic algorithm (GA) - Simplex Method, are brought forward. At last, using 3 moderate and weak seismic events at Xiangtang borehole array (2#) site, soils dynamic characteristic parameters, including P velocity, damping value, frequency- dependent coefficient b, which are no dealing with in previous literatures, are calculated. S velocities of Xiangtang 2# site are on the whole greater than 1994’s field test results, and are close to the 3# which is 200m far away. At the same time, perceptible soil nonlinear behavior in 60gal magnitude earthquake is detected by inversion analysis. In addition, the displacement and stress transfer function of Xiangtang 2# site are also analyzed.
For the records of borehole array, we tentatively present an inversion method of hysteretic nonlinear in time domain for dynamic characteristic parameters of site soil. Then taking this method in practice by TKCH07 borehole array data in Japan Seismic monitoring Network Kik-net, the result is proved reliable, because it is almost in the test scope of sand and clay, which are accepted by international.
6. Displacement and/or velocity often be inputted in wave motion explicit FEM at present, while acceleration record directly reflects original information of seismic wave. As a result, an explicit integration formula, which is based on both center difference method and Newmark -βmethod, and is reduced by equilibrium equation, is proposed. Water tower and framework structure dynamic analysis indicated that, the acceleration response of the formula is agree well with that of mode analysis associating with Duhamel integral method and Newmark -βimplicit method, when the efficiency of calculating is firstly ensured. In addition, we concisely summarize the real time processing method, which is unconventional method, based on transfer function of numeric filter in time domain, and the first step’s initial value formula are recommended.
7. It isn’t enough in study of vertical strong motion influencing on nonlinear seismic response of slope site for its complicated strong motion input, soil nonlinearity, slope topographty condition and interface effects etc. The methods of taking half or 2/3 of shear response spectrum as vertical seismic action, recommended or prescribed compulsorily in many engineering codes at home and abroad, are used to design buildings. But how to rationally consider this effect is one of the most important tasks. Firstly, these research advancements are reviewed. The necessary of equivalent linear method of 2D wave motion explicit FEM ELPSV program with characteristic of high efficiency, real phase, actual radiation damping, is discussed. Then, strength of vertical strong motion influencing on response spectrum of slope site surface, equivalent response history and PGD and PGV in site section, seismic response of soft slope site are analyzed, and draw some primary conclusions as following: There are certain influences on shear seismic response spectrum when the period less than 0.3s, but it is very light over 0.3s. Vertical seismic response of slope site was distinctly changed by vertical strong motion. Moreover, value of vertical seismic action in code for seismic design for buildings is apt to unsafety. Simultaneously, vertical response of the right site is great than the left’s. The slope top’s shear response is much stronger than slope feet’s for slope topography condition, while vertical seismic response is not obvious. Magnified effect in strong motion is more than in weak motion when ratio of horizontal to vertical component(av/ah) is 2/3, which agrees with the knowledge of nonlinear response. Interestingly, Interface effects make the response is lower than ambient site response. And soft site response is essentially consistent with phenomena of the hard site, except for vertical seismic response is increased previously and then decreased from site bottom to the top. At last, concise epilogue is given. All of conclusions and study results reflected quantitatively effect extent of vertical strong motion, provide beneficial basement for rational considering vertical strong motion in aseismic design of buildings and constructions in slope site.
8. Using the strong earthquake observations at Ashigara Valley in Japan, the two much great single-double hysteretical nonlinear wave motion simulation program-PSVNWA_2D and SHNWA_2D are roundly checked, the author simulate not only SH nonlinear wave motion, but also P-SV nonlinear wave motion. The analysis results not only provide the theoretical strong motion of observation station, but also forecast the earthquake velocity, displacement and permanent displacement correspondingly, even, educe the single - double hysteretic nonlinear dynamic constitutive relation curves.
Aiming at Suiling little slope site, we use PSVNWA_2D program to calculate the displacement and acceleration response of the surface and interface between the first layer and the second layer, when strong and weak type of Northridge and Turkey earthquake as input. The results show not only the changes of every earthquake motion and hysteretic curves, but also the nonlinear earthquake response difference between the strong motion and the weak motion in each earthquake, also difference between the two earthquake. Simultaneously, we analyze the spectrum change of transfer function, amplification coefficient and vertical earthquake motion derived from the shear response. In the research, it is sometimes found that amplification coefficient of nonlinear response at site observation station increase with the earthquake strong motion enhanced. The reason of phenomena is expatiated, and the case is proved by the strong earthquake observation and earthquake mechanism. At the same time, the paper pointed out essential difference of the transfer function of displacement, velocity and acceleration in equivalent linearization and time domain nonlinear technique. In addition, nonlinear seismic response during Loma Prieta earthquake is also analyzed.
Under Kobe earthquake action, nonlinear seismic response of Quasi- Seattle- Basin site at in-plane and anti-plane cases is analyzed. The results indicated that the difference is remarkable between the nonlinear wave motion simulation of in-plane and that of anti-plane, in particular for the displacement response and permanent displacement. In the plane, the‘basin focusing effect’of the nonlinear wave motion simulation is obvious, while the situation in anti-plane. is not enough. But‘the basin basement edge effect’is distinct in two kinds of situations.
These two effects can cause great difference of the seismic motion on the site section. The characteristics and the rules of the nonlinear seismic response are not only beneficial to the forecast and the estimate of seismic motion of important engineering, but also helpful to nonlinear aseismic design of the important construction structure.
9. Inputting the near fault unidirectional and bidirectional velocity big pulse, complex site response is calculated by equivalent linearization method, the result is examined by itself. Rational condition and limitation of the traditional equivalent linearization method in this project are pointed out. In view of shortcomings, dynamic diploid nonlinear anlaysis explicit method in time domain for 1D site seismic response, which taking both physical nonlinear and geometrical nonlinear into account, is put forward. Then this method is taken to the APNWP_1D procedure, and establishing independent switch to control it. We decompose the input motion of near fault velocity big pulse into two kind of independent mechanisms - the elasitc big deformation mechanism and the diploid nonlinearity (elast-plastic big deformation) mechanism. At the same time, the parted and unitive double-mechanisms are proposed. For the two-dimensional complex ground, in view of the near fault seismic motion decomposition strategy, which are used to unidirectional and bidirectional velocity big pulse seismic motion analysis, the method of dynamical plastic theory combined big deformation mechanism is proposed. It has established bigger two-dimensional diploid nonlinear dynamical procedure software DNDYN_2D. Under TCU068 unidirectional pulse and Northridge NWPCR bidirectional pulse action, The diploid nonlinear dynamic response of complex site at Institute of Agricultural Sciences on the Hualin road was analysed. The result indicated that, when seismic motion was unidirectional velocity pulse, the parted diploid- mechanism was more reasonable than unitive diploid-mechanism. However the unitive diploid-mechanism is more suitable for the analysis of bidirectional velocity pulse action. The result also quantitatively present the permanent displacement, acceleration time history and peak value of site at Institute of Agricultural Sciences on Hualin road.
This method may use for strong nonlinear seismic response of near fault stratified site, even on condition of seismic strong motion with several metres permanent displacement (PGA almost greater than 400gal) at bedrock as input. At the same time, more satisfactory answer in diploid nonlinear seismic response of 2D site for engineering also can be obtained.
In the end, existing problems are pointed out and the research problems, which need to be done in future, are suggested.
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