Transient pressures in hydrotechnical tunnels .pdf

  • View
    221

  • Download
    1

Embed Size (px)

Text of Transient pressures in hydrotechnical tunnels .pdf

  • 8/11/2019 Transient pressures in hydrotechnical tunnels .pdf

    1/17

    EARTHQUAKE ENGINEERING A N D STRUCTURAL DYNAM ICS, VOL. 16, 523-539 (1988)

    TRANSIENT PRESSURES IN HYDROTECHNICAL TUNNELS

    DURING EARTHQUAKES

    SLOBODAN B. KOJIC*

    University of Southern California, Los Angeles, C A , U.S.A. , and Energoproject Co. , Belgrade, Yugoslavia

    A N D

    MIHAILO

    D.

    TRIFUNAC?

    Department of Civil Engineering, University of Southern California, Los Anyeles , CA, U . S . A .

    SUMMARY

    Transient pressures generated by earthquake shaking in hydrotechnical tunnels are evaluated by the discrete Fourier

    transform technique. The effects

    of

    the horizontal ground motion accelerating the closed dow nstream tunnel gate, as well

    as the upstream dam face, and the influence of the vertical motion of the reservoir floor are considered in this analysis.A n

    example

    of

    a typical bottom outlet

    is

    analysed by subjecting

    it to

    several computed accelerogram s.

    It

    is shown that

    high

    hydrodynamic pressures can be developed, several times larger

    than

    the hydrostatic pressure.

    I N T R O D U C T I O N

    Hydrotechnical tunnels, penstock and bottom outlets are common elements in many dam projects. Their

    functions are to provide efficient and economical means of releasing the water from the reservoir according to

    the desired dow nstream use for irrigation or

    for

    power generation. The conduits which lead the water to the

    turbines are usually designed to withstand high hydraulic transient pressures arising in various turbine

    operations. Surge tan ks are frequently used to protect the upstream par t of the conduit. For such systems there

    is little need for analysis of hydrodynamic pressures due to earthquakes, althou gh som e pressure increase may

    be expected. However, hydrotechnical tunnels and bottom outlets for irrigation purposes usually are not

    designed for waterhammer effects like the turbine penstocks. In mo st cases such tunnels d o no t have surge

    tanks or other openings, which would da m p the transient pressures caused by an earthquake . Usually, they

    may have valves or gates located at the upstream intake, at an intermediate point an d at the downstream end.

    Owing to various downstream demands, it may happen that the intermediate or the end gates are closed fo r

    long periods of time, leaving the upstream condu it part u nder a full reservoir pressure. Under such conditions

    in seismically active regions, an ear thq uak e may cause the water pressure to increase or decrease w ith respect to

    the hydrostatic pressure or steady pressure conditions. Un derstanding of the transient hyd rodynam ic pressure

    caused by earthquakes is of interest for the proper design approach

    to

    these structures. Failure of the

    hydrotechnical tun nel during a n earth qua ke can initiate erosion of su rrou nd ing material and consequently,

    depending where a break occurs, it may cause increased uplift un de r the dam , dam abu tm ent failure, stilling

    basin

    or

    spillway damage, hydroelectric power plant break

    or

    a crash

    of

    any o ther vital component

    of

    the dam

    system. Any of these events can be a starting point for a dam collapse.

    Zienkiewicz' was am on g the first to point out the resonant effects in the bottom outlets due to harmonic

    horizontal motion

    of

    the downstream gate. On a specific project O bradoviC2 carried out an e arth qu ake

    *

    Research Fellow, University of Southern California, and Staff Member, Energoproject Co.

    Professor of Civil Engineering.

    0098-8847/88/040523-17$08.50

    988

    by John Wiley

    &

    Sons, Ltd.

    Received

    13

    Ma y

    1987

    Revised 6 October

    1987

  • 8/11/2019 Transient pressures in hydrotechnical tunnels .pdf

    2/17

    524

    S.

    B. KOJIC AN D

    M.

    . TRIFUNAC

    response analysis of water in the bottom outlet. His model has included only horizontal downstream gate

    motion in the generation of hydrody namic pressures due to earth quak es. The m ethod used in his analysis is the

    method of characteristics. The results showed that high hyd rodynam ic pressures can be developed during an

    earthquake and that these depend on earthquake amplitude and frequency content.

    The present analysis has the following objectives.

    (a) To illustrate the additional effects

    of

    upstream bound ary conditions, i.e. the influence of hydrody nam ic

    pressures developed during earthquake response of dam and reservoir

    floor

    on generation of transient

    pressures along the bottom outlet.

    For

    simplicity, the da m will be con sidered a s rigid, althou gh, in so m e cases,

    its flexibility may not be igno red. Inclusion of the d am flexibility is possible via finite elemen t discretization of

    the da m, for example, but it will not be studied here. The reservoir and the water in the condu it are assumed to

    be compressible. The downstream boundary condition, horizontally moving gate, has been included also.

    (b) To demonstrate the possibility of using the method of discrete Fourier transform in a hydraulic

    transient problem via the fast Fourier transform algorithm.

    (c) To examine the capabilities of the mathematical model an d of the p roposed numerical technique on a

    realistic bottom outlet mo del.

    DES CRIP TION OF T H E B O T T O M O U T L E T

    The bo ttom outlets carry water from the reservoir to the river

    or

    to the irrigation channels downstream.

    A

    simplified schematic of this structure, with the dam and the stilling basin, is shown in F igure 1 . The bottom

    , - I N T A K E GATE

    CLOSED

    D O W N S T R E A M GATE

    x 2 , f

    BOTTOM

    OUTLET

    BOTTOM

    ; HYP OCENTER

    ( a ) S E C T I O N

    A - A

    /

    /

    t EP I CENTER

    ( b ) L A Y O U T

    Figure 1 .

    Bottom

    outlet, dam and reservoir with earthquake ground accelerations: u; and a:

  • 8/11/2019 Transient pressures in hydrotechnical tunnels .pdf

    3/17

    HYDROTECHNICAL TUNNELS DURING EARTHQUAKES 525

    outlet intake is usually located at the b ottom of the reservoir close to the d am upstream face. The intak e sliding

    gate stops water flow when the b ot tom outlet is serviced or rep aired. An inte rme diate valve helps in closing of

    the intake gate. The downstream gate regulates the water discharge according to the downstream

    requirements. Before entering into the river the water is passed through the stilling basin whose role is to

    decrease the water velocity. The cross section of the conduit is usually circular and it is made of reinforced

    concrete. The conduit may be lined by steel,

    if

    water velocities and pressures a re high.

    Th e gates, concrete a nd steel lining are, in general, dimen sioned t o withstand the full reservoir pressure. O nly

    the intermediate valve is checked fo r hydrod ynam ic effects to en able its closure in th e flowing water with high

    velocity

    .

    If the dam is located in a seismically active region, it is of interest for the gene ral da m safety to de termine the

    hydrodynamic, transient pressure along the bottom outlet during an earthquake. The case when the

    downstream gate is closed and the bottom outlet is under the full reservoir pressure will be considered.

    Without loss of generality the bot tom outlet axis is assumed to be perpendicular to the da m upstream face.

    Under these conditions the whole system, the dam, the reservoir bottom and the downstream gate, is

    exposed to the ground motion.

    T H E M A T H E M A T IC A L M O D E L A N D T H E S O L U T I O N P R O C E D U R E

    One-dimensional wave equation for viscous po w

    water assumed to be linearly compressible and viscous, is described by the following wave e q ~ a t i o n : ~

    The hydrodynamic pressure associated with small amplitude, irrotational, one-dimensional mo tion, and for

    where p ( s , r is the hydrodynamic pressure, in excess of hydrostatic pressure, alo ng the b otto m outlet, as a

    function of the space coo rdin ates and time r , c is com pression wave velocity in water, and R describes friction

    losses.

    Equation (1) is called the waterhammer equation and it is used in hydraulic engineering for analysis

    of

    unsteady, transient flow through closed

    conduit^.^

    The friction

    R

    is assumed to be the same as fo r the steady-

    state

    flow

    in con duits, i.e. the D arcy-Weisbach formula is used for comp uting th e friction losses.

    R will

    be

    presented in this transient problem, caused by an earthquak e, in a somew hat different form t o that which is

    normally used in waterhammer analysis (mean discharge3 is assumed to be equal t o zero). Fo r laminar flow, R

    can be shown to be

    and for turbulent flow,

    fc

    R = - -

    c 2D

    (3)

    where v = p/p , the kinematic viscosity, p is the absolute water viscosity, p is the water mass density,

    D

    is the

    condu it diameter,f'is the friction factor dependent on the conduit roughness and Reynolds number i t can be

    determined from the M oody diagram4), and v is the water particle velocity in the cond uit. Th us, the hyp erbolic

    partial differential equation (1) is linear for laminar flow an d non-linear for turbu lent flow.

    The w ater particle velocity u is assumed

    to