Truncated Boundary of the Reservoirs Far End

The Sharan boundary condition, which was already described, at the far-end truncated boundary can be written as:

On 2hp C

Implementation of the truncated boundary condition in the finite element model, can be done by separating the force vector {F} in equation 3.7 into two components:

where {FF1} is the component of the force due to acceleration at the boundaries of the dam-reservoir and reservoir-foundation while {FF2} is due to truncation at the far boundary and can be written as:

where Dj = Dj and Dj is defined as:

In equation 3.10, ¿T is the side of the element on the truncated boundary. Substituting equations 3.8 and 3.9 into equation 3.7 results in:

[G]{P} + C [D] {P} + ([H] + - [D]){p} = {FFi} (3.11)

In general form, we can write the finite element form of the equation of the reservoir as:

[G]{p} + [C]{P} + [K 0}{p} = {F} — p[Q]T ({U} + {Ua }) = {F2} — p[Q]T {U}

Putting equation 3.11 in the format of the above equation, the following relationships are obtained:

Where {F2} is forces due to ground acceleration on the dam-reservoir boundaries and total acceleration on the rest of the boundaries.

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