Civil Engineering: What is Dam | Arch Dam | Earths Dam | how to build

Arch Dams

Arch dams are curved in plan so that they transmit part of the water pressure to the canyon walls of the valleys in which they are built. The arch action requires a uniﬁed monolithic concrete structure. Arch dams are classiﬁed as thin if the ratio of their base thickness to their structural height is less than 0.2 and thick if that ratio is larger than 0.3. The upstream side of an arch dam is called the extra_dos and the downstream side is the intra_dos (See Arch Dams fig below).

The structural analysis of arch dams assumes that it can be considered as a series of horizontal arch ribs and a series of vertical cantilevers. The load is distributed among these two actions in such a way that the arch and cantilever deﬂections are equal. This analysis is a specialized subject of structural engineering. The US Department of the Interior, Bureau of Reclamation (1977) has published an extensive book on the subject. only the simpliﬁed cylinder theory is summarized below.

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The forces acting on an arch dam are the same as on a gravity dam, but their relative importance is not the same. The uplift is less important because of the comparatively narrow base and the ice pressure is more important because of the large cantilever action. If the arch has a radius r and a central angle q, the horizontal hydro-static force due to a head h is

Hh = g h 2r sin (q/2)

This force is balanced by the abutment reaction in the upstream direction

Ry = 2R sin (q/2)

By equating the two forces the abutment reaction (Fig.)

Becomes R = g hr

If the working stress of the concrete is sw, the thickness of the arch rib is

t = g hr/sw

It is seen that with this simpliﬁed theory the thickness increases linearly with the depth. The volume of a single arch rib with a cross section

A is V = rAq

Where q is in radians.

Because of the relationship between the thickness t and the radius, the angle that minimizes this volume of concrete can be shown to be

q = 133o34¢

For this angle the radius r of the arch in a valley of width B is

r = (B/2) sin (66o47¢) = 0.544 B

One could select an arch of constant radius with an average angle around 133o34¢.

The angle would be larger at the top and smaller at the base. Alternatively one could select a ﬁxed angle and determine the valley width B at various depths and calculate the radius r required and then the necessary thickness t. A compromise between these two cases consists in keeping the radius ﬁxed for a few sections and varied in others.

Earth Dams:

Rolled-ﬁll earth dams are constructed in lifts of earth having the proper moisture content.

Each lift is thoroughly compacted and bonded to the preceding layer by power rollers of proper design and weight.

Rolled-ﬁll dams are of three types: homogeneous, zoned and diaphragm.

Early earth dams were homogeneous simple embankments as are many levees today.

Most earth dams are zoned embankments. They can have an impermeable core made out of clay or a combination of clay, sand and ﬁne gravel. This core can be ﬂanked on the upstream and downstream sides by more previous zones or shells.

These zones support and protect the impervious core. The upstream zone provides stability against rapid draw down while the downstream zone controls the seepage and the position of the lower phreatic surface. In addition there can be ﬁlters between the impervious zone and the downstream shell and a drainage layer below.