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Evaluation of Cavitation Occurrence Based on Reliability in Chute Spillways by Using First Order Reliable Method and Monte Carlo Simulation Method from 18 Spillways Laboratory Models, Iran

  • Hydraulic Engineering
  • Published:
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Abstract

Controlling cavitation occurrence is one of the most important factors in chute spillways designing due to high velocity and the negative pressure of flow. A probabilistic design approach was implemented in the present study to estimate the probability of cavitation occurrence on chute spillways. In addition, the uncertainty presence of the effective parameters in the limit state function related to the cavitation occurrence was highlighted in the present design. The probability of cavitation occurrence was studied based on the reliability of first order reliable method (FORM) and it was controlled by Monte Carlo simulation method. The data was extracted from eighteen spillways laboratory models built by the Iranian Water Research Institute, among which ten were aerated and eight were without aerator. Accordingly, as a result of the performance of these spillways and the cavitation occurrence in the prototype, a graph and its relationship was found for controlling the cavitation occurrence and its failure probability based on the mean velocity and flow mean pressure along the chute spillway. According to the results of this study as a new method for designing based on reliability, it could be controlled the probability of cavitation occurrence.

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Abbreviations

CX :

variance-covariance matrix of the X random variables

\({F_i}(x_i^*)\) :

cdf of the random variable Xi in \(x_i^*\)

\({f_i}(x_i^*)\) :

pdf of the random variable Xi in \(x_i^*\)

FW(.):

cumulative distribution function

g :

gravity acceleration (m/s2)

g(XL):

load function

h :

flow depth (m)

h(XR):

resistance function

i :

number of random variable

L :

external loading of an engineering system

l :

Chute length along slope (m)

P :

pressure on spillway floor (pa)

P atm :

atmospheric pressure (pa)

p f :

probability of failure

p s :

probability of safe

P V :

vapor pressure of the water (pa)

q :

flow discharge per unit width (m2/s)

r :

number of repetitions in Hasofer and Lind model

R :

resistance or strength of an engineering system

SX :

vector of sensitivity coefficient of limit state function at the design point of x*

[T]t :

transitive matrix of the Eigenvector matrix of the variance-covariance matrix (CX)

V:

flow velocity along slope (m/s)

W :

limit state function

W′:

standardized limit state function

X :

random variable

x′*:

design point (The point on the limit state function which has the lowest reliability in gaussian standardized space)

x*:

design point (The point on the limit state function which has the lowest reliability in non-gaussian space)

z :

altitude from the sea level (m)

β :

reliability index

γ :

specific weight of water (N/m3)

ε f :

surface roughness (m)

θ :

chute floor angle to the horizon

\(\mu _{i{\,_e}}^*\) :

equivalent gaussian value of mean for random variable of i in Xi = xi* (pa.s)

μ W :

mean value of the limit state function (pa.s)

μW :

water dynamic viscosity (pa.s)

\({\mu _{{X_i}}}^m\) :

modified values of mean for random variable of Xi (pa.s)

ρ :

curvature radius of the vertical arc on chute spillway (m)

ρ w :

water density (kg/m3)

σ :

cavitation index

σ′ :

surface tension between air and water (N/m)

σ cr :

critical cavitation index

σ w :

standard deviation of the limit state function

\(\rho _{{i_e}}^*\) :

equivalent gaussian value of standard deviation for random variable of i in \({X_i} = x_i^*;\)

\({\sigma _{{X_i}}}^m\) :

modified values of standard deviation for random variable of Xi

\(\Phi (z_i^*)\) :

cdf of the standard gaussian variable of \(z_i^*\,:_i^* = (x_i^* - \mu _{i\;e}^*)/\sigma _{i\;e}^*\)

\(\emptyset (z_i^*)\) :

pdf of the standard gaussian variable of \(z_i^*\;:z_i^* = (x_i^* - \mu _{i\;e}^*)/\sigma _{i\,e}^*\).

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Acknowledgements

The authors would like to express their sincere thanks to the hydraulic structures group of Iranian Water Research Institute especially Reza Roushan and Ali Khorasanizadeh for their cooperation and support.

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Correspondence to Mehdi Azhdary Moghaddam.

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Moghaddam, M.A., Shahrabadi, A.H. Evaluation of Cavitation Occurrence Based on Reliability in Chute Spillways by Using First Order Reliable Method and Monte Carlo Simulation Method from 18 Spillways Laboratory Models, Iran. KSCE J Civ Eng 24, 1169–1182 (2020). https://doi.org/10.1007/s12205-020-2170-z

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