Analysis of Gravity Dam _ Advance Engineering Mathematics Review

Analysis of Gravity Dam Tags: eccentri eccen tricit city y rig righti hting ng mom oment ent over overtur turni ning ng mom omen entt foun founda dati tion on pre pressure ssure hydr hydrosta ostati tic c force facto factorr of of safety safety overtur over turni ning ng Factor Factor of safety ag agai ainst nst sli slidi ding ng fricti friction on hydr hydrosta ostati tic c upl uplift ift sli slidi ding ng

factorr of facto of safety safety agai against n st

Dams are structures whose purpose is to raise the water level on the upstream side of river, stream, or other waterway. The rising water will cause hydrostatic force which will tend the dam to slide horizontally and overturn about its downstream edge or toe. The raised water level on the upstream edge or heel will also cause the water to seep under the dam. The pressure due to this seepage is commonly called hydrostatic uplift and will reduce the stability of the dam against sliding and against overturning.

Grav ity Dam Analysis Analysis The weight of gravity dam will cause a moment opposite to the overturning moment and the friction on the base will prevent the dam from sliding. The dam may also be prevented from sliding by keying its base into the bedrock.

Step 1 Consider 1 unit length (1 m length) of dam perpendicular to the cross section. Step 2  Determine all the forces acting:

1. Vertical forces = Weight of dam = Weight of water in the upstream side (if any) = Hydrostatic uplift Weight of permanent structures on the dam 2. Horizontal Horizontal forces = Horizontal component of total hydrostatic force Wind pressure, wave action, floating bodies, earthquake load, etc.

Step 3

Solve for the reaction 1. Horizontal component of the reaction 2. Vertical component of the reaction

Step 4 Moment about the toe

1. Righting moment, = Sum of all rotation towards the upstream side 2. Overturning moment, = Sum of all rotation towards the downstream side

Step 5  Location of

as measured from the toe

Factors of Safety Factor of safety against sliding,

Factor of safety against overturning,

Where

= coefficient of friction between the base of the dam and the foundation.

Foundation Pressure Eccentricity,

If

,

is within the middle third and the foundation pressure is trapezoidal (triangular if

is exactly

) acting from heel to toe.

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