重力坝抗震设计理论

The PGA at the foundation was 0.38, 0.29 and 0.27 g in the upstream to downstream direction, the cross-canyon direction, and the vertical direction, respectively Peak accelerations at the crest in the same directions were 1.79, 2.04 and 1.33 g, respectively.
日本Gohonmatsu
Dam（五本松坝）

Was built in 1900 of concrete rubble masonry The dam has a structural height of 108 feet (33 m) and a crest length of 361 feet (110m)

动水压力作用方向

与坝面正交 与加速度方向相反

迎水坝面倾斜

动水压力折减系数
η c=θ /90

θ —坝面与水平面夹角

日本Takou

Dam

252 foot (77 m) high, concrete gravity dam with a crest length of 1056 feet (322 m) March 11, 2011 Tohoku Earthquake M 9.0
An aftershock of magnitude M 7.1 occurred on March 17
The dam showed no damage

2.2 拟静力法

水平向设计地震加速度 ah 7 8 9 设计烈度 ah 0.1g 0.2g 0.4g

地震作用

地震惯性力 地震动水压力 地震动土压力
2.2.1地震惯性力




质点i的水平地震惯性力 Fi ah GEi i / g ξ—地震作用效应折减系数， 取0.25 GEi—集中在i点的重力 4 1 4( h / H ) i GE—总重力 i 1.4 n G αi —重力坝沿高度的动态 1 4 Ej (h j / H ) 4 分布系数 j 1 GE H—坝高 n—坝体计算质点总数

坝长853m，最大坝高103m 坝顶宽度14.8m，底宽70.2m 装机容量192 万千瓦。

1967年12月11日印度Koynanagar Earthquake M6.5（ M7.0 ） 级地震

震中距坝址约15km 地震时实测地面最大加速度

坝轴向0.63g，顺河向0.49g，竖向0.34g。

重力坝地震反应加速度沿坝高的分布规律

沿坝高放大 坝顶放大倍数5.0 沿坝高按1+4(h/H)4变化
2.2.2地震动水压力

单位宽度坝面的总地震动水压力 F=0.65ahξ ρ wH02

H0—水深；ρ w—水的质量密度 合力作用点在水面以下0.54H0处

水深h处地震动水压力
p(h)=ahξ ψ (h)ρ wH0 ψ (h)—水深h处地震动水压力分布系数（规范表）

PHGA during the main shock is estimated 0.4 g The water level during main shock was 108 feet (33 m) below the crest elevation.


The wall of the gate house was cracked and there was an offset in the dam’s parapet wall


Peak accelerations of 0.54 g horizontal and 0.49 g vertical were measured in the lower inspection gallery Peak accelerations of 2.09 g at the crest of the dam.

坝高21.4m ,长352m 泄洪闸18孔，宽12.8m、高8.0m 弧形闸门

车笼埔断层在石冈坝下游3km处通过


地震后经测量发现，在坝址上下游附近新产生了8 条次 断层 其中一条次断层恰好通过石冈坝

断层上盘上升了约10.0m ，下盘上升只有2.2m

坝体两侧产生约7.8m 的垂直错动 活断层通过处，坝体完全被毁 断层两边坝顶高程相差7.8m ，三扇弧形闸门完全毁坏
2 重力坝抗震设计理论（一）



重力坝震害 拟静力法计算重力坝地震作用 动力法重力坝地震反应分析 重力坝抗震措施
2.1 重力坝震害
印度Koyna重力坝

Koyna坝位于印度西南部Maharashtra 邦，建成于 1963 年 材料为蛮石混凝土重力坝（rubble concrete）

日本Kasho

Dam


Completed in 1990 152 ft (46.4 m) high concrete gravity dam October 6, 2000 Western Tottori earthquake (M7.3) in Japan.

The epicenter of the earthquake was about 1.9 miles (3 km) from the dam.





The dam was shaken by the magnitude M 8.3 San Francisco Earthquake on April 18, 1906 with an estimated PHGA of 0.52 to 0.68 g The dam is located about 0.25 miles (300 to 400 m) from and nearly parallel to the San Andreas Fault where the ground moved horizontally 8 feet (2.4 m) There reportedly was not the slightest crack in the dam.
台湾石岗重力坝

1999 年9 月21 日台湾百年来规模最大的强 烈地震。震中位于日月潭西南方12.5km， 南投县集集镇，因此名为集集地震
震源深度8.0km，震级7.3，本次地震释放 的能量相当于40颗1945年投掷在日本广岛 原子弹的威力


石冈混凝土重力坝位于大甲溪下游，1977 年建成

附近地震台实测最大加速度

东西向570gal ,南北向410gal ,垂直向480gal

到目前为止全世界唯一的被地震完全摧毁 的混凝土坝

ຫໍສະໝຸດ Baidu
经过地震,该坝平均向北位移7.0m ,向西位移 0.98m

除坝体外，在坝址上游400m 及1500m 处， 河床也分别隆起了约6m 及3.5m，并在河床 中形成了瀑布的奇观



The epicenter of the January 17, 1995 Kobe Earthquake was 9.3 miles (15 km) away from the dam The PHGA was 0.83g

The only damage was hairline cracks in the concrete capping of the parapet on the crest of the dam

地震造成坝体水平裂缝

上游面裂缝18条，下游面裂缝7条 裂缝主要集中于629m 高程的坝坡改变处


美国Lower Crystal Springs Dam
Completed in 1890 Located about 20 miles (32 km) south of San Francisco, California The dam has a structural height of 154 feet (47 m), a crest width of 25 feet, and a crest length of 600 feet (183 m).


The main shock produced a relative displacement of 1.1 inches (28 mm) toward the right abutment and 0.28 inches (0.7 mm) in the upstream direction There was basically no damage to the concrete gravity dam The walls at the base of the control room, a reinforced concrete structure cantilevering upstream from the crest of the dam, were cracked