Table 1 Basic random variables and fuzzy variables of dam body and foundation
From: Risk analysis of gravity dam instability using credibility theory Monte Carlo simulation model
Variables | Variable type | Parameter |
|---|---|---|
Upstream depth \(H_{1} \left( {\text{m}} \right)\) | Random | \(\mu_{{H_{1} }} = 118,\;\sigma_{{H_{1} }} = 2.2\) |
Downstream depth \(H_{2} \left( {\text{m}} \right)\) | Random | \(\mu_{{H_{1} }} = 8,\;\sigma_{{H_{1} }} = 0.8\) |
Volume weight of dam concrete \(\gamma_{c} \left( {{\text{kN/m}}^{ 3} } \right)\) | Random | \(\mu_{{f^{{\prime }} }} = 24.0, \;\sigma_{{f^{{\prime }} }} = 0.5\) |
Shearing friction coefficient of dam foundation surface \(f^{{\prime }}\) | Fuzzy | \(\left[ {0.9,1,1,1} \right]\) |
Shearing cohesion of dam foundation surface \(c^{{\prime }} \left( {\text{MPa}} \right)\) | Fuzzy | \(\left[ {0.8,0.9,1.0} \right]\) |
Uplift pressure reduction coefficient of upstream curtain \(\alpha_{1}\) | Fuzzy | \(\left[ {0.16,0.20,0.38} \right]\) |
Uplift pressure reduction coefficient of downstream curtain \(\alpha_{2}\) | Random | \(\mu_{{\alpha_{2} }} = 0.30,\;\sigma_{{\alpha_{2} }} = 0.03\) |