Static and Dynamic Stress Analysis(静态和动态应力分析)

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 Chopra’s 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