Table 9 Fuzzy random sensitivity of soil depth.

From: Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model

Mine

Deep/m

Conventional mean sensitivity

Conventional standard deviation sensitivity

Fuzzy random mean sensitivity

Fuzzy random standard deviation sensitivity

\(\mathop {\left( {\frac{{\partial \tilde{P}_{f} }}{{\partial \tilde{\mu }_{{x_{i} }} }}} \right)}\nolimits_{\alpha }^{ - }\)

\(\mathop {\left( {\frac{{\partial \tilde{P}_{f} }}{{\partial \tilde{\mu }_{{x_{i} }} }}} \right)}\nolimits_{\alpha }^{ + }\)

\(\mathop {\left( {\frac{{\partial \tilde{P}_{f} }}{{\partial \tilde{\sigma }_{{x_{i} }} }}} \right)}\nolimits_{\alpha }^{ - }\)

\(\mathop {\left( {\frac{{\partial \tilde{P}_{f} }}{{\partial \tilde{\sigma }_{{x_{i} }} }}} \right)}\nolimits_{\alpha }^{ + }\)

Main shaft

391–430

− 0.1147

− 0.0311

− 0.0932

− 0.1435

− 0.0273

− 0.0339

430–490

− 0.1352

− 0.0272

− 0.1023

− 0.1638

− 0.0242

− 0.0293

490–545

− 0.1517

− 0.021

− 0.124

− 0.1874

− 0.0186

− 0.0247

400–420

− 0.1381

− 0.0334

− 0.1067

− 0.1682

− 0.0305

− 0.0362

Auxiliary shaft

420–480

− 0.1528

− 0.0276

− 0.1282

− 0.1846

− 0.0246

− 0.0312

480–544

− 0.1816

− 0.0218

− 0.1558

− 0.218

− 0.0183

− 0.0246

400–430

− 0.1045

− 0.0331

− 0.082

− 0.1352

− 0.0309

− 0.0357

Air shaft

430–490

− 0.1289

− 0.0293

− 0.1045

− 0.1574

− 0.0267

− 0.0325

490–538

− 0.1463

− 0.0256

− 0.1193

− 0.1737

− 0.0225

− 0.0284