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

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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

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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:

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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