Design of Gravity Dams.doc

Design of Gravity DamsConcrete dams may be categorized into three principal types according to their particular physical form and the features of their design. The three types are: arch, gravity, and buttress.A gravity dam is a concrete structure which resists the imposed forces by its weight and section without relying on arch and beam action.In its common usage the term is restricted to solid masonry or concrete dams which are straight or slightly curved in plan. The downstream face of gravity dam is usually of uniform slope which if extend, would intersect the upstream face at or near the maximum reservoir level. The upstream face is normally vertical excepting for steep batter near the heel. The upper portion is usually thick enough to resist the impact of loading objects and accommodate a roadway. The thickness of section at any elevation is adequate to resist sliding and to ensure compressive stresses at the heel under different conditions of loading.For a gravity dam to be stable , the following criteria should be satisfied:1) resultant of static and pseudo-static forces should lie within the middle third lines or the kern of the dam at all section. This ensures a factor of safety of about 2 against overturning and eliminates tensile stress at the heel and the toe of the dam.2) The dam should provide adequate factor of safety against sliding at the construction joints, the base of the dam, and any planes of weakness within the foundation.3) Maximum stresses in the dam section and the foundation should be within the permissible stresses of the concrete used in the dam section and the foundation rock respectively.Gravity dams can be analyzed by the Gravity Methods, Trial-load Twist Analysis, or the Beam and Cantilever Method, / depending upon the configuration of the dam, continuity between the blocks, and the degree of refinement required. 1.Concrete Gravity Dams on Rock FoundationsThe designer of any dam must make basic assumptions regarding site conditions and their effects on the proposed structure. Site investigations provide the engineer with much of the information to evaluate these assumptions, the bases for safe dam design. Some important assumptions for small dam design involve uplift pressure, seepage control measures, channel degradation and downstream toe erosion, foundation conditions, and quality of construction. Additional assumptions should involve silt loads, ice pressures, earthquake accelerations, and wave forces.Safety factors should be considered in the light of economic conditions. Large safety factors result in a more costly structure: however, low safety factors may result in failure, which could also lead to high cost. Proper safety factors result only from an adequate determination of sliding, overturning, and overstressing forces within and acting on the dam. 2.OverturningOrdinarily，the safety factor against overturning is between 2 and 3. In smaller dams it is often larger. If the computed safety factor falls below 2, the section of the dam should be modified to increase the safety margin. A gravity dam rarely fails from over turning since any tendency to overturn provides greater opportunity for a sliding force to create the failure. The safety factor against overturning is the ratio of the righting moment to the overturning moment about the toe of the dam. This can be expressed as: （1）In which =force due to weight of concrete =force due to weight of water on inclined surfaces P=force of water acting to displace dam downstream U=uplift force L=length of moment arm for respective forcesAlso,if the uplift pressure at the upstr am face exceeds the vertical stress at any horizontal section without uplift, the uplift forces greatly increase the tendency for overturning about the downstream toe at that assumed horizontal plane. The dam may still be considered safe if the tension stresses devdloped are less than the allowable stresses in the concrete and in the foundation material. This assumption is based on good workmanship and development of a tensile strength within the structure on all horizontal planes.3.Dam SlidingThree approaches are used by engineers in evaluating the safety of a dam from being displaced downstream. Each has merit and generally involves the same relationship of forces. Although the computed values are safe, they are comsiderably different. The three approaches are(1)a safe sliding factor, (2)a safety factor, and (3)a shear-friction safety factor .Clear distinction must bu made among these three approaches. The primary purpose of each is to obtain a safe coefficient that when exceeded would put the dam in jeopardy of biing pushed downstream. The sliding factor of a gravity dam with a horizontal base equals the tangent of the angle between the perpendicular to the base and the resultant foundation reaction. The sliding factor for small dams is computed by taking the ratio of the summation of horizontal forces P,to the summation of vertical forces. （2）If f, computed in this manner, is equal to or less than the static friction coefficient , , the dam is considered safe. A unit width of 1 ft. is assumed for these calculations. Safe values for the sliding factor coefficient are given in Table 1 for various foundation materials. Table 1 ALLOWABLE SLIDING FACTORS FOR VARIOUS FOUNDATION CONDITIONS (3)The factor of safety, fs, against silding is defined as the ratio of the coefficient of static friction, *, to the tangent of the angle between a perpendicular to the base and the direct foundation reaction,expressed as : This approach also assumes shear forces as added safety measures. The safety factor against sliding is usually between 1 and 1.5 for gravity dams on rock utilizing a conservative cross-section. The inclusion of uplift and seismic forces in the calculations may reduce the safety factor to about unyit. These values are for safety against sliding on a horizontal plane;if the forndation slopes downstream, the safety factors against sliding on the plane of the base are correspondingly reduced. Designers often use concrete placed into cutoffs or rock foundations to decrease the sliding tendency of the dam. Another approach, favored by many engineers, includes the evaluation of shear into the safety factor. The shear-friction relationship is : （4）In which b=base length at plane of shear being studied ,=allowable working shear stress of material or materials at plane of shear.Safety factors computed in this manner should approach values used in normal structural computations. Static friction values often assumed for concrete moving rock or concrete on concrete surfaces varies from 0.65to 0.75.The working shear stress,of concrete is related to the compressive strength of concrete. The unit shearing strength of concrete is about one-fifth the compression breaking stress from standard cylinders. This indicates a strength of 400 to 800 psi for concrete in dams. It also provides a safety factor of 4 if the unit working stresses used in computations are 100 to 200 psi. Greater working stresses are not recommended unless the concrete for the smaller dams is actually pretested.要求：翻译成中文重力坝设计根据混凝土大坝的具体物理结构和设计特点，分为三种类型：分别为拱坝，重力坝，支墩坝。重力坝是通过自身重力来抵抗外界施加的压力的混凝土结构，并且剖面不是拱和梁型式的。在通用的惯例中限制于实心砌体和在计划中垂直或曲线的混凝土坝。重力坝的下游面通常是均匀的斜坡，如果该斜面延伸，将会使坝体上游面和接近水库最高水位的地方相交。除了在上游坡脚处有倾角外，上游面都是垂直的。大坝的上半部分足够厚以抵制客观荷载的冲击和方便修建道路。在一些剖面图中，剖面的厚度是能足够抵抗重力滑动和确保不同工况荷载作用下的压缩应力的。重力坝要保持稳定，必须满足以下条件：1）产生的静态和动态的力量应集中在中间的第三坝段或所有大坝剖面部分的核心。这确保了大坝在坝踵和坝趾处的抗垮台和消除拉应力的安全因素。2）大坝应该提供足够的安全因子在施工缝，大坝基础以及任何软弱地基。3)在大坝剖面和地基的最大应力应在混凝土的允许应力之内，此混凝土允许应力被分别用于大坝部分和基岩。重力坝可以通过重力法、试验负荷扭转分析或者梁和连续的方法，而这些方法是基于大坝的结构和大坝与所需细化程度的衔接。1、岩基上的混凝土重力坝任何大坝的设计者一定会做基本假设以考虑地利条件及其对合适结构的影响。地利考察可以为工程师提供更多的信息以求证假设，这样是为了保证安全大坝的设计。对小坝设计的一些重要假设包括扬压力、渗流控制措施、河道冲刷和下游坝址侵蚀、基础条件以及建筑物的质量。还有一些假设应该包括泥沙压力、冰压力、地震加速度以及浪压力。安全因子应该考虑少量的经济状况。重大的安全因子会导致昂贵的结构，但是微不足道的安全因素也可能导致失败，即带来重大的损失。合适的安全因素只出自充分的决定，这个决定包括滑坡、倾覆、作用在大坝及附近的超荷载。2、倾覆一般地抗倾覆因子在二到三之间。相对较小的大坝反而需要较大的安全因子。如果计算的安全因子小于二，大坝部分应该增大它的安全边缘。自从任何的倾覆趋势为产生抗滑力提供了更多的机会，大坝几乎不可能倾覆。抗倾覆安全因子是对于坝踵恢复力矩与倾覆力矩的比值。如下描述：FS0=Wcl1+Wwl2Pl3+Ul4 (1)式中Wc表示大坝自重；Ww表示静水压力；P表示下游水压力；U表示扬压力；L表示各种力的力臂长度；如果在上游面的扬压力超过除了向上的任意水平部分的垂直应力，扬压力则