ABSTRACT
If Z > 0, the structure is reliable; if Z = 0, the structure is in the limit state; if Z < 0, the structure is failure.
If the random variables x1,x2,…,xn are distributed normally, its mean and standard deviation are μ μ μx xn1 2x , ,… and σ σ σx xn1 2x , ,… respectively. Therefore, the performance function of structure Z g x xn( ,x , , )1 2 is a normal random variable also, and its mean μz and standard deviation σ z can be expressed as follow:
μ μ μz xμ xn( , )1 2x
σ σ μ
n g x
∂ ∂
⎛ ⎝ ⎜⎜
⎞ ⎠ ⎟⎟
The probability density of Z can be expressed as follow:
f z z
z ) exp ( )z= −
⎛ ⎝⎜
⎞ ⎠⎟
1 2 2
2πσ μ
σ
Convert the normal distribution of Z into standard normal distribution, so the failure probability of Z can be expressed as follow:
Pf z z= Φ=Φ )(− (− )β β= − Φ) (
1 INTRODUCTION
At present, hydraulic structure design use empirical constant value method. Take the gravity dam stability analysis as an example, in the Chinese gravity dam design code, we have made a different control index of anti-sliding stability safety factor by pure friction resisting equation and shearing resisting equation, but the difference are enormous, both of which are empirical value, and stands the design index of gravity dam anti-sliding stability safety index only. In recent years, domestic and foreign scholars have made many researches on reliability theory of gravity dam design [1-2], and important achievements have been made. This paper has made a study on reliability of gravity dam single slope deep anti-sliding stability, and provides preferences for using reliability degrees theory to study deep anti-sliding stability.
