岩基上的混凝土重力坝

重力坝具有水平地基面时，其滑动系数等于基面垂线和地基反力合力之间夹角的正切。在小坝上，滑动系数的计算可以取水平力总 和和垂直力总和 （包括扬压力 ），或
如果这种方法求得的 值等于或小于静摩擦系数 ，则认为坝是安全的。计算中假定取单位宽度为1英尺。各种地基材料的滑动系数安全值列表于13.1中。
The factor of safety,, against sliding 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
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.安全系数应根据经济情况来考虑。安全系数大，导致结构费用昂贵；而安全系数小则可能引起失事，也会导致很大的经济损失。
2 overturning倾覆
Ordinarily, the safety factor against overturning is between 2 and 3. 一般来说（通常），抗倾覆安全系数在2～3之间。
In small dams it is often larger.较小的坝通常取较大的值
A gravity dam rarely fails from overturning since any tendency to overturn provides greater opportunity for a sliding force to create the failure. 重力坝很少因倾覆而破坏。因为任何一种倾覆的趋势，都更可能引起滑动而导致破坏。
Clear distinction must be made among these three approaches. 必须将这三种方法区别清楚。
The primary purpose of each is to obtain a safe coefficient that when exceeded would put the dam in jeopardy of being pushed downstream.每种方法的基本目的都是要求得一个安全系数，当越出此安全系数范围时，坝就有向下游滑动的危险。
Site investigations provide the engineer with much of the information to evaluate these assumptions, the bases for safe dam design. 坝址的查勘为工程师拟定这些假定提供了许多资料。这些假定是安全设计的基础。
Proper safety factors result only from an adequate determination of sliding, overturning, and overstressing forces within and acting on the dam.只有在适当地确定坝内和作用在坝体上的滑动、倾覆以及应力超限的作用力之后，才能得到合适的安全系数。
Additional assumptions should involve silt loads, ice pressures, earthquake accelerations, and wave forces.其它一些附加假定应包括泥沙荷载、冰压力、地震加速度和波浪力。
1 safety factors 安全系数
抗倾覆安全系数是绕坝址的复位力矩（扶正力矩restoring couple）和倾覆力矩的比值，可以用公式表示为：
式中： 为混凝土的重量； 为斜面上的水重； 为水对坝体向下游的推力； 为扬压力； 为各力的力臂。
Also, if the uplift pressure at the upstream 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.此外，如果上游面的扬压力超过任一水平断面上不计扬压力算得的垂直应力，则扬压力将使绕坝所假定的水平断面下游点倾覆趋势大大增加。
Lesson 13 concrete gravity dam on rock foundations 岩基上的混凝土重力坝
The designer of any dam must make basic assumptions regarding site conditions and their effects on the proposed structure. 设计人员在设计任何坝时，都必须对有关坝址的情况及其对结构物的影响做出一些基本假定。
Which： is force due to weight of concrete; is force due to weight or water on inclined surfaces; is force of water acting to displace dam downstream; is uplift force; is length of moment arm for respective forces.
The safety factor against overturning is the ration of the righting moment to the overturning moment about the toe of the dam. This can be expressed as
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. 有关小坝设计的一些主要假定包括：扬压力，渗流控制措施，河槽冲刷深度以及下游坝趾的冲蚀，坝基条件和施工质量。
3 sliding 滑动
Three approaches are used by engineers in evaluating the safety of a dam from being displaced downstream. 工程师们衡量向下游移动的安全性有三种方法。
Each has merit and generally involves the same relationship of forces. 每一种都有优点，并且所考虑作用力之间的关系大体上都相同。
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, to the summation of vertical forces, including the uplift, or
抗滑安全系数 的定义是静摩擦系数 和地基面垂线与地基反力夹角的正切之间的比值，即
This approach also assumes shear forces as added Байду номын сангаасafety measure. 这个方法也假定剪力为附加安全度。
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 unity. 对于岩基上断面偏保守的重力坝，抗滑安全系数一般在1～1.5之间。计算中记入扬压力和地震力后，安全系数可降低到接近1。
If the computed safety factor falls below 2, the section of the dam should be modified to increase the safety margin. 如果算出的安全系数小于2（在2以下），应修改坝的断面以提高安全度。
The dam may still be considered safe if the tension stresses developed 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.在这种情况下，如果引起的拉应力小于混凝土内和地基材料的允许应力，则该坝仍可认为是安全的。这个假定是基于施工工艺良好和结构内所有平面上都具有抗拉强度做出的。