Study Evaluation of Random Set Method on Results from Reliability analysis of Finite Element in Deep Excavation Article Code: 443 Presenter Mehdi Poormousavian Other Authors Ali Fakher

Outline Basic concepts Random set Finite Element procedure Application to deep excavation Results from Random set Analysis Comparison with Point estimate method Conclusion

Overall Geotechnical Design process Concept RS-FEM Deterministic model the material properties are well known, none of them is random Case Study Result When a river or stream reaches to a plain, estuary etc., the flow velocity is decreased and suspension materials are deposited onto the bed. These deposits or sediments are consolidated under the self-weight of the soil particles. Soil structures, especially fine grained soils, is formed during settling conditions and sedimentation process carried through water. Sedimentation process is a physico-chemical process in the nature because fine grain soils are composed of active clay minerals. Point Estimate Conclusion

Overall Geotechnical Design process Concept RS-FEM Non-Deterministic model is for the purpose of estimating the probability of outcomes within a forecast to predict what conditions might be like under different situations. Case Study Result When a river or stream reaches to a plain, estuary etc., the flow velocity is decreased and suspension materials are deposited onto the bed. These deposits or sediments are consolidated under the self-weight of the soil particles. Soil structures, especially fine grained soils, is formed during settling conditions and sedimentation process carried through water. Sedimentation process is a physico-chemical process in the nature because fine grain soils are composed of active clay minerals. Point Estimate Conclusion

Factor of safety and probability of failure Concept RS-FEM Case Study Result Point Estimate Conclusion

Reliability methods Concept RS-FEM Case Study Result Point Estimate There aren’t enough point data, instead interval information are applied. RS-FEM Wide range of point input data from soil tests are at engineer disposal. Case Study Result When a river or stream reaches to a plain, estuary etc., the flow velocity is decreased and suspension materials are deposited onto the bed. These deposits or sediments are consolidated under the self-weight of the soil particles. Soil structures, especially fine grained soils, is formed during settling conditions and sedimentation process carried through water. Sedimentation process is a physico-chemical process in the nature because fine grain soils are composed of active clay minerals. Point Estimate Conclusion

Random Set Finite Element Method Concept RS-FEM Random set method Introduce by Dempster 1967, Continue by Kendall 1974, Matheron 1975 ,Shafer 1976, Godman 1985 Random set method combine Finite element method(RS- FEM) Both concepts were integrated by Tonon et al 1996 for reliability analysis of a tunnel lining Peschl 2004 and Schweiger 2007 illustrated RS-FEM Nasekhian 2011 used RS-FEM for reliability analysis of tunnel(Case study) Ghazian and Fakher 2014 used RS-FEM in reliability analysis of excavation and horizontal displacement of excavated wall was gained between 17 and 118 mm, which wasn’t practical. Case Study Result Point Estimate Conclusion

Concept RS-FEM Case Study Result Point Estimate Conclusion

Saba Project Northern wall particulars: Depth: 27 m Concept RS-FEM Northern wall particulars: Depth: 27 m Anchor: 6 in height, 6 m bond length Soil: touched soil(0-2)m, sand layer(2-10)m, sand layer(10-27)m Case Study Result Point Estimate Conclusion

First step of RS-FEM Definition of Geometry or geometrics Concept RS-FEM Definition of Geometry or geometrics Software: Plaxis V8.5 2D Soil behavior model: Hardening-soil Case Study Result Point Estimate Conclusion

First step of RS-FEM Definition of Geometry or geometrics Concept RS-FEM Definition of Geometry or geometrics Software: Plaxis V8.5 2D Soil behavior model: Hardening-soil Case Study Soil Depth(m) water ɤ (KN/m3) c (KN/m2) ϕ (°) Ψ (°) E50 (KN/m2) Eur (KN/m2) m K0nc (KN/m2) Touched 0-2 Drained 16.5 5 27 15000 45000 0.5 0.546 Sand 2-10 19 35 34 4 68000 204000 0.78 0.441 sand 10-27 drained 20.7 65 38 8 130000 390000 0.384 Result Point Estimate Conclusion

Second step of RS-FEM Concept RS-FEM Selection of input parameters that should be considered as basic variables in the RS analysis providing the expected ranges from two different sources. Case Study soil probability c (KPa) ϕ degree E (MPa) ɤ (KN/m3) Ψ m anchor loading (KPa) Touched Set 1 0.5 6-11 24-32 10-22 13.5-16.5 1-8 0.44-0.64 7-27 6-16 Set 2 12-22 27-37 14-28 15.5-18.5 4-11 0.56-0.76 13-33 9-19 sand 26-36 26-33 56-92 18-21.6 0.45-0.75 30-41 29-37 79-110 20-23.5 0.65-0.95 48-71 31-41 105-135 17-20.7 0.35-0.65 73-94 40-45 124-155 19.4-23.3 0.55-0.85 Result Point Estimate Conclusion

Third and fourth steps of RS-FEM Concept RS-FEM Reduce uncertainty via Variance reduction technique by Vanmarcke Sensitivity analysis Case Study Result Point Estimate Conclusion

Result from Sensitivity analysis Concept secondary compound Cohesion of second sand layer Friction of second sand layer loading Main compound Cohesion of second sand layer Friction of second sand layer Density of first sand layer RS-FEM Case Study Result Point Estimate Conclusion

Random Set Model 2n analysis 64 Concept RS-FEM 2n analysis Lower and upper cumulative distribution functions or p-box Classify from the lowest value to highest value Range of most likely values 64 Case Study Result Point Estimate Conclusion

Main compound result from RS-FEM Concept RS-FEM Case Study 18-40 RS-FEM Result Designed Observed Point Estimate Conclusion

Secondary compound result from RS-FEM Concept RS-FEM Case Study 18-40 RS-FEM Result Allowable Designed Observed Point Estimate Conclusion

Main compound result from RS-FEM Concept RS-FEM RS-FEM Designed Best fitted: Rice distribution PF=1.7E-06 Case Study Best fitted: Lognormal distribution PF=1.19E-15 1.52-2.08 Result Point Estimate Conclusion

Secondary compound result from RS-FEM Concept RS-FEM Case Study 1.57-2.1 Result Point Estimate Conclusion

Compare RS-FEM and Point estimate method Concept RS-FEM Case Study Result 1.8σ Observed PEM Point Estimate Conclusion

conclusion Concept RS-FEM The number of finite element analysis by RS-FEM and PEM are 64 and 19 respectively, which are much lower than a Monte Carlo method relatively. 20 initial parameters are considered for sensitivity analysis, so many uncertainties are enter to design that logical and practical range is gained. horizontal displacement of excavated wall is gained between 18 and 40 mm, which versatile with field measurements (15 to 30 mm). Using RS-FEM before starting excavation leading to assurance for employers to be aware of displacements so that cost could reduced and designs are optimized. Case Study Result Point Estimate Conclusion

“doubt is an uncomfortable condition, but certainty is a ridiculous one.” Introduction Literature review Voltaire (1694-1778) Purpose Material and sample preparation Results and discussion Conclusion