Table 8 Fuzzy random sensitivity of calculation model uncertainty coefficient.

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

0.2224

0.0557

0.1808

0.2534

0.0535

0.0597

430–490

0.2516

0.0471

0.2222

0.2811

0.0459

0.0537

490–545

0.2722

0.0396

0.2431

0.3130

0.0371

0.0461

400–420

0.2461

0.0522

0.2163

0.2738

0.0503

0.0582

Auxiliary shaft

420–480

0.2654

0.0485

0.2377

0.2879

0.045

0.0576

480–544

0.2876

0.0425

0.2469

0.3228

0.0356

0.0475

400–430

0.2210

0.0683

0.1914

0.2436

0.0649

0.0769

Air shaft

430–490

0.2564

0.0644

0.2232

0.2739

0.0609

0.0708

490–538

0.2749

0.0607

0.2438

0.3200

0.0562

0.0684