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chapter 5 static and dynamic stress analysis 第五章 静态和动态应力分析 5-1. stress analysis 5-1.应力分析 a. general. (1) a stress analysis of gravity dams is performed to determine the magnitude and distribution of stresses throughout the structure for static and dynamic load conditions and to investigate the structural adequacy of the substructance and foundation. load conditions usually investigated are outlined in chapter 4. (2) gravity dam stresses are analyzed by either approximate simplified methods or the finite element method depending on the refinement required for the particular level of design and the type and configuration of the dam. for preliminary designs, simplified methods using cantilever beam models for two-dimensional analysis or the trial load twist method for three-dimensional analysis are appropriate as described in the us bureau of reclamation (usbr), “design of gravity dams” (1976).the finite element method is ordinarily used for the feature and final design stages if a more exact stress investigation is required. a.普通方法 (1)重力坝的应力分析是用以确定在静态和动态荷载作用下结构的应力分布和大小情况以及 验证下部和基础的结构强度，荷载条件通常在第四章作了概述。 (2)重力坝的应力分析通过基于满足坝体类型、构造和设计精度要求的近似的简化方法或有 限单元法。初步设计时，根据美国垦务局（usbr）颁布的“重力坝设计规范（1976） ” ， 可以使用二维的悬臂梁模型或者三维的模型试验的简化方法。有限单元法通常用于对应力 精度要求更高的详细和最终设计阶段。 b. finite element analysis. (1) finite element models are used for linear elastic static and dynamic analyses and for nonlinear analyses that account for interaction of the dam and foundation.the finite element method provides the capability of modeling complex geometries and wide variations in material properties. the stresses at corners, around openings, and in tension zones can be approximated with a finite element model. it can model concrete thermal behavior and couple thermal stresses with other loads.an important advantage of this method is that complicated foundations involving various materials, weak joints on seams, and fracturing can be readily modeled. special purpose computer programs designed specifically for analysis of concrete gravity dams are cg-dams (anatech 1993), which performs static, dynamic, and nonlinear analysis and includes a smeared crack model, and merlin (saouma 1994), which includes a discrete cracking fracture mechanics model. b.有限元分析 (1) 有限元模型用于线性弹性的静态和动态分析以及坝体与基础相互影响的非线性分析。 有限元方法具有模拟具有复杂几何形状和不同材料性能的能力。角落处，开口处和有张力 处的应力可以用有限元模型来近似。它可以模拟混凝土的热行为和由其他荷载引起的温度 应力。此方法的重要优点是对于涉及各种材料的复杂的基础，接缝薄弱处和断裂面能很容 易模拟。专门设计用来对混泥土重力坝分析的专用计算机程序是 cg- dams（anatech1993 年） ，它执行静态，动态和非线性分析，并包括一个弥散裂缝模型， 梅兰（萨乌马 1994 年） ，其中包括离散裂缝断裂力学模型。 (2) two-dimensional, finite element analysis is generally appropriate for concrete gravity dams. the designer should be aware that actual structure response is three-dimensional and should review the analytical and realistic results to assure that the two-dimension approximation is acceptable and realistic. for long conventional concrete dams with transverse contraction joints and without keyed joints, a two-dimensional analysis should be reasonably correct. structures located in narrow valleys between steep abutments and dams with varying rock moduli which vary across the valley are conditions that necessitate three-dimensional modeling. (2) 二维的有限元分析一般用于混凝土重力坝。但是设计者应该知道，实际的结构响应是 三维的，应审查理论值和真实值以保证这二维近似方法是合理和有效的。对于较长的并设 有横缝的常规混凝土大坝，二维的分析应是相当正确的。当结构位于陡峭的桥台之间的狭 窄山谷和大坝在各处有不同的岩石模量时则需要使用三维建模。 (3) the special purpose programs earthquake analysis of gravity dams including hydrodynamic interaction(eadhi)(chakrabarti and chopra 1973) and earthquake response of concrete gravity dams including hydrodynamic and foundation interaction effects (eagd84)(chopra, chakrabarti, and gupta 1980) are available for modeling the dynamic response of linear two- dimensional structures. both programs use acceleration time records for dynamic input. the program sdofdam is a two-dimensional finite element model (cole and cheek 1986) that computes the hydrodynamic loading using chopras simplified procedure.the finite element programs such as gtstrudl, sap, ansys, adina, and abaqus provide general capabilities for modeling static and dynamic responses. (3)一些专用的程序如重力坝地震分析及水动力作用（eadhi） （查克拉巴蒂和乔普拉 1973） 、流体作用下的混凝土重力坝的地震响应分析和地基交互影响（eagd84） （乔普拉， 查克拉巴蒂，和 gupta1980 年）可用于模拟线性二维结构的动力响应。这两个程序都对与 动态输入使用加速度时间记录。sdofdam 程序是用乔普拉简化程序计算水动力荷载的一 个二维有限元模型。一些有限元程序如 gtstrudl, sap, ansys, adina, 和 abaqus 提供了模拟静态和动态响应的能力。 5-2. dynamic analysis the structural analysis for earthquake loadings consists of two parts: an approximate resultant location and sliding stability analysis using an appropriate seismic coefficient(see chapter 4) and a dynamic internal stress analysis using site-dependent earthquake ground motions if the following conditions exist: 5-2 动态分析 地震荷载的结构分析包括两部分：一个使用适当的抗震系数（见第 4 章）的位移和抗滑稳 定的近似结果和一个满足下列条件的基于地震动的动态内应力分析： a. the dam is 100 feet or more in height and the peak ground acceleration (pga) at the site is greater than 0.2 g for the maximum credible earthquake. a. 大坝高 100 英尺以上以及一点对于地震幅度的峰值加速度（pga）大于 0.2g。 b. the dam is less than 100 feet high and the pga at the site is greater than 0.4 g for the maximum credible earthquake. b. 大坝高度低于 100 英尺且一点相对于地震幅度的峰值加速度 pga 大于 0.4g。 c. there are gated spillway monoliths, wide roadways, intake structures, or other monoliths of unusual shape or geometry. c. 有门控泄洪坝段，宽的通道，进水口，或其他有不寻常的几何形状的坝段。 d. the dam is in a weakened condition because of accident, aging, or deterioration. the requirements for a dynamic stress analysis in this case will be decided on a project-by-project basis in consultant and approved by cecw-ed. d.大坝由于意外情况，老化，或恶化而处于性能衰减的状况。在这种情况下的动态应力分 析的要求将决定于专家的且被 cecw-ed 认可的项目标准。 5-3. dynamic analysis process the procedure for performing a dynamic analysis include the following: a. review the geology, seismology, and contemporary tectonic setting. b. determine the earthquake sources. c. select the candidate maximum credible and operating basis earthquake magnitudes and locations. d. select the attenuation relationships for the candidate earthquakes. e. select the controlling maximum credible and operating basis earthquakes from the candidate earthquakes based on the most severe ground motions at the site. f. select the design response spectra for the controlling earthquakes. g. select the appropriate acceleration-time records that are compatible with the design response spectra if acceleration-time history analyses are needed. h. select the dynamic material properties for the concrete and foundation. i. select the dynamic methods of analysis to be used. j. perform the dynamic analysis. k. evaluate the stresses from the dynamic analysis. 5-3 动态分析过程 执行动态分析的过程包括以下内容： a.调查其地质学，地震学及当代构造环境。 b.确定地震的来源。 c.确定设计值、地震震级和位置。 d.确定地震的衰减关系。 e.确定基于最严重的地面运动的设计地震的最大可控值和操作标准。 f.确定用于控制地震的设计反应谱。 g.如果需要进行加速度-时间时程分析时，确定合适的满足设计反应谱的加速度-时间记录。 h.确定混凝土和基础的动态材料属性。 i.确定用来进行动力学分析的方法。 j.进行动力学分析。 k.通过动力学分析求得应力值。 5-4. interdisciplinary coordination a dynamic analysis requires a team of engineering geologists, seismologists, and structural engineers. they must work together in an integrated approach so that elements of conservatism are not unduly compounded. an example of undue conservatism includes using a rare event as the mce, upper bound values for the pga, upper bound values for the design response spectra, and conservative criteria for determining the earthquake resistance of the structure. the steps in performing a dynamic analysis should be fully coordinated to develop a reasonably conservative design with respect to the associated risks. the structural engineers responsible for the dynamic structural analysis should be actively involved in the process of characterizing the earthquake ground motions (see paragraph 5-6) in the form required for the methods of dynamic analysis to be used. 5-4.各学科之间的相互配合 动态分析需要工程地质学家，地震学家和结构工程师的合作。他们必须相互协调的工作在 一起以便少部分的保守主义不会过度的复杂化。过分保守的例子包括使用如 mce 的一个 罕见事件，上界的 pga 值，上界值的设计反应谱，以及确定结构抗震的保守标准。在进 行动态分析的步骤应充分配合以得出在相关风险下相当保守的设计。负责结构动力分析的 结构工程师应积极参与到所用的动态分析方法对地震地面运动特征（见第 5-6）的形式要 求的过程中。 5-5. performance criteria for response to site-dependent earthquakes a. maximum credible earthquake. gravity dams should be capable of surviving the controlling mce without a catastrophic failure that would result in loss of life or significant damage to property. inelastic behavior with associated damage is permissible under the mce. b. operating basis earthquake. gravity dams should be capable of resisting the controlling obe within the elastic range, remain operational, and not require extensive repairs. 5-5.某点的地震响应性能判别标准 a.可信地震最大值。重力坝应具有继续控制 mce 的能力而不会造成人员死亡或重大财产损 失等灾难性后果。 b.地震控制标准。重力坝应具有在弹性范围内抵抗控制 obe，保持运行且不用大修的能力。 5-6. geological and seismological investigation a geological and seismological investigation of all damsites is required for projects located in seismic zones 2 through 4. the objectives of the investigation are to establish controlling maximum and credible operating basis earthquakes and the corresponding ground motions for each and to assess the possibility of earthquake-induced foundation dislocation at the site. selecting the controlling earthquakes is discussed below. additional information is also available in tm 5-809-10-1. 5-6. 地质和地震调查 关于所有水库所在地地质和地震调查需要在地震带 2 到 4 个调查项目。调查的目的是为了 对每个点建立控制最大值和可信的地震控制标准和相应的地震地面运动，并评估在当地由 地震引起的地基错位的可能性。下面讨论了确定控制地震。其他信息也可在 tm5-809-10- 1 找到。 5-7. selecting the controlling earthquakes a. maximum credible earthquake. the first step for selecting the controlling mce is to specify the magnitude and/or modified mercalli (mm) intensity of the mce for each seismotectonic structure or source area within the region examined around the site. the second step is to select the controlling mce based on the most severe vibratory ground motion within the predominant frequency range of the dam and determine the foundation dislocation, if any, capable of being produced at the site by the candidate mces. if more than one candidate mce produce the largest ground motions in different frequency bands significant to the response of the dam,each should be considered a controlling mce. 5-7.确定控制地震 a. 可信地震最大值。用于确定控制 mce 的第一步是为在工地附近的检查区域内 的每个地震构造结构或水源区指定 mce 的大小和/或修改其麦加利（毫米）强 度。第二步是选择建立在大坝内主要频率范围内最严重的地震动的控制 mce，并确定基 础错位，即此处 mce 的延展能力。如果有不止一个预选的 mce 产生对大坝响应重大的在 不同频段的最大地面运动，则每个都应看作一个控制 mce. b. operating basis earthquake. (1) the selection of the obe is based upon the desired level of protection for the project from earthquake-induced damage and loss of service project life.the project life of new dams is usually taken as 100 years. the probability of exceedance of the obe during the project life should be no greater than 50 percent unless the cost savings in designing for a less severe earthquake outweighs the risk of incurring the cost of repairs and loss of service because of a more severe earthquake. b.地震设防标准。 (1) obe 的确定是建立在工程在遭受地震破坏及超过使用年限时对工程期望得到的保护水 平的基础之上的。新建的大坝的工程使用年限一般取为 100 年。在使用期限内的 obe 的超 越概率应不大于 50%，除非在设计时冒花钱在修理上而降低防震要求以及由于更多的地震 而丧失使用功能的风险节约成本。 (2) the probabilistic analysis for the obe involves developing a magnitude frequency or epicentral intensity frequency (recurrence) relationship of each seismic source; projecting the recurrence information from regional and past data into forecasts concerning future occurrence; attenuating the severity parameter, usually either pga of mm intensity, to the site; determining the controlling recurrence relationship for the site; and finally,selecting the design level of earthquake based upon the probability of exceedance and the project life. (2) 对 obe 的概率分析涉及到对每个震源研究其震级频率与震中频率（复发）之间的关系； 通过对当地过去地震信息来预测将来的情况；当地的某些参数，通常是 mm 强度的 pga 的衰减程度；确定此处的控制复发的关系；最后，依据超越频率及使用寿命确定抗震设防 水平。 5-8. characterizing ground motions a. general. after specifying the location and magnitude (or epicentral intensity) of each candidate earthquake and an appropriate regional attenuation relationship, the characteristics of vibratory ground motion expected at the site can be determined. vibratory ground motions have been described in a variety of ways, such as peak ground motion parameters, acceleration-time records (accelerograms), or response spectra (hayes 1980, and krinitzsky and marcuson 1983). for the analysis and design of concrete dams, the controlling characterization of vibratory ground motion should be a site-dependent design response spectra. 5-8. 表征地震动 a. 一般地。当指定了位置以及每个预设地震的震级（或震中强度）且一个适当区域的衰减 关系，则此处地面运动的震动特征即可确定。地震运动已经用很多方式进行了描述，如地 面运动参数的峰值，加速度-时间记录（加速度） ，或反应谱（海斯 1980 年，krinitzsky 和 马库森 1983） 。对于混凝土坝的分析和设计，对地震动的控制特征应基于此地的设计反应 谱。 b. site-specific design response spectra. (1) wherever possible, site-specific design response spectra should be developed statistically from response spectra of strong motion records of earthquakes that have similar source and propagation path properties as the controlling earthquake(s) and are recorded on a foundation similar to that of the dam. important source properties include magnitude and, if possible, fault type and tectonic environment. propagation path properties include distance, depth, and attenuation. as many accelerograms as possible that are recorded under comparable conditions and have a predominant frequency similar to that selected for the design earthquake should be included in the development of the design response spectra. also, accelerograms should be selected that have been corrected for the true baseline of zero acceleration, for errors in digitization, and for other irregularities (schiff and bogdanoff 1967). b. 特殊地点的设计反应谱 在任何可能的地方，特殊地点的设计反应谱都应从与控制地震一样有相似来源和传播途径 的以及在与大坝相似的基础上记录下的强烈的地震运动记录的反应谱进行统计学的研究。 重要的来源属性包括震级，如果可能的话，还包括断层类型和地质环境。传播路径属性包 括距离，深度和衰减。在可比的条件下记录的且与设计地震有相似主频的尽可能多的加速 度值应包括在设计反应谱的研究中。此外，应选择对真正的加速度基准线，对数字误差和 对其他不规范的行为进行校正后的加速度值（schiff 和 bogdanoff1967） 。 (2) where a large enough ensemble of site-specific strong motion records is not available, design response spectra may be approximated by scaling that ensemble of records that represents the best estimate of source, propagation path, and site properties. scaling factors can be obtained in several ways. the scaling factor may be determined by dividing the peak or effective peak acceleration specified for the controlling earthquake by the peak acceleration of the record being rescaled. the peak velocity of the record should fall within the range of peak velocities specified for the controlling earthquake, or the record should not be used. spectrum intensity can be used for scaling by using the ratio of the spectrum intensity determined for the site and the spectrum intensity of the record being rescaled (usbr 1978). acceleration attenuation relationships can be used for scaling by dividing the acceleration that corresponds to the source distance and magnitude of the controlling earthquake by the acceleration that corresponds to the source distance and magnitude of the record being rescaled (guzman and jennings 1970). because the scaling of accelerograms is an approximate operation at best, the closer the characteristics of the actual earthquake are to those of the controlling earthquake, the more reliable the results. for this reason, the scaling factor should be held to within a range of 0.33 to 3 for gravity dam. (2) 某地足够大的强震集合是不可能的，设计反应谱可能通过换算最具代表性的资料，传 播路径，以及地貌的记录近似取得。换算因素包括多个方面。比例因数可通过区分峰值或 由重新调整的记录的峰值加速度产生的为控制地震规定的有效加速度峰值确定。记录的速 度峰值应在为控制地震而确定的速度峰值范围内，否则此记录是不能使用的。频谱强度能 通过用某地的频谱强度与被重新评估的记录的频谱强度的比率来换算的到(usbr 1978)。通 过区分与换算后记录的震源矩和震级一致的加速度得到的控制地震的与换算后记录的震源 矩和震级一致的加速度，加速度衰减关系可用来换算(guzman and jennings 1970)。由于加 速度按比例缩放充其量是一个近似运算，对于控制地震来说越接近实际地震的特点意味着 更可靠的结果。因此，重力坝的比例因子的取值应在 0.333 的范围内。 (3) guidance for developing design response spectra,statistically, from strong motion records is given in vanmarcke (1979). (3)从强震记录统计得到的设计反应谱的研究指导可参见 vanmarcke (1979)。 (4) site-dependent response spectra developed from strong motion records, as described in paragraphs 5-8b,should have amplitudes equal to or greater than the mean response spectrum for the appropriate foundation given by seed, ugas, and lysmer (1976), anchored by the pga determined for the site. this minimum response spectrum may be anchored by an effective pga determined for the site, but supporting documentation for determining the effective pga will be required (newmark and hall 1982). (4)如在 5-8 段描述的那样，某地由强震记录得到的反应谱应该有振幅大于或等于 seed, ugas, and lysmer (1976)所提出的恰当选择的且由对某点确定的 pga 的固定基础的平均反 应谱。反应谱的最小值可通过一个为某点确定的有影响的 pga 值标记，但是必要条件是要 有确定有影响的 pga 值的文档(newmark and hall 1982)。 (5) a mean smooth response spectrum of the response spectra of records chosen should be presented for each damping value of interest. the statistical level of response spectra used should be justified based on the degree of conservatism in the preceding steps of the seismic design process and the thoroughness of the development of the design response spectra. if a rare event is used as the controlling earthquake and the earthquake records are scaled by upper bound values of ground motions, then use a response spectrum corresponding to the mean of the amplification factors if the response spectrum is based on five or more earthquake records. (5)一个从反应谱记录中选择的平滑的反应谱应能反应每个相关的阻尼值。反应谱的统计水 平常应根据前面的抗震设计步骤和设计反应谱的所有情况的保守水平进行适当调整。如果 一个罕见事件用来代表控制地震和由地震动的上限值换算得到的地震记录，那么当反应谱 是根据五个或更多的地震记录得出的时要用一个与平均放大因子相适应的反应谱值。 c. accelerograms for acceleration-time history analysis. accelerograms used for dynamic input should be compatible with the design response spectrum and account for the peak ground motions parameters, spectrum intensity, and duration of shaking. compatibility is defined as the envelope of all response spectra derived from the selected accelerograms that lie below the smooth design response spectrum throughout the frequency range of structural significance. c.加速度-时间的加速度时程分析。用于动态输入的加速度应与设计反应谱和地震动峰值、 光谱强度、震动持续时间的所占比例相匹配。匹配度是指由所有来源于比依照结构重要性 确定的设计反应谱稍低而选择的加速度的反应谱的包络线。 5-9. dynamic methods of stress analysis a. general. a dynamic analysis determines the structural response based on the characteristics of the structure and the nature of the earthquake loading. dynamic methods usually employ the modal analysis technique.this technique is based on the simplifying assumption that the response in each natural mode of vibr