Chapter 3: Application of Reliability Based Design to everyday geotechnical problems

What did we do ? Why did we do it ? What did we find ? Practical RBD

What did we do ? What did we do ? Chose 7 simple structures (Orr, 2005) One soil type (sand, f’k = 32o, gk = 20kN/m3) Found Eurocode-compliant solution Determined b (FORM and Monte Carlo) Calculated FoS (Mean & characteristic values) Repeated for range of parameters & CoV What did we do ?

Footings Single pile Retaining walls 4 3 5 What did we do ? 1 2 6

What did we do ? Soil Type Non-cohesive sand: f’k = 32o, log-normal, CoV=0.1 gk = 20kN/m3, normal, CoV=0.05 rf,g = 0.2 What did we do ?

What did we do ? Loading: Gk fixed value, = mean Qk log-normal CoV = 0.25 Wk Gumbel CoV = 0.50 What did we do ?

Why did we do it ? Why did we do it ? Ease of application of RBD methods Check reliability of Eurocode compliant designs Variation in reliability index with: variation in parameters f’ and g variation in CoV Compare with working stress design Why did we do it ?

What did we find ? What did we find ? b Reliability Ind. b values 3.2 – 3.7 (< 3.8) b FORM ~ b M/C b reasonably constant for all types of structure Global FoS FORM M/C Mean Char 0. Strip vertical load 3.49 3.45 5.18 2.50 1. Square vertical load 3.51 3.46 4.86 2.40 2. Square inclined load 3.69 3.58 6.58 2.60 3. Pile 3.36 3.35 2.76 1.73 4. Gravity wall 3.33 3.3 6.88 3.12 5. Cantilever wall 3.40 3.39 2.34 1.63 6. Anchored wall 3.24 3.23 1.43 1.25 What did we find ?

What did we find ? What did we find ? FoS determined using mean values too high FoS using charac-teristic values about right b Reliability Ind. Global FoS FORM M/C Mean Char 0. Strip vertical load 3.49 3.45 5.18 2.50 1. Square vertical load 3.51 3.46 4.86 2.40 2. Square inclined load 3.69 3.58 6.58 2.60 3. Pile 3.36 3.35 2.76 1.73 4. Gravity wall 3.33 3.3 6.88 3.12 5. Cantilever wall 3.40 3.39 2.34 1.63 6. Anchored wall 3.24 3.23 1.43 1.25 What did we find ?

What did we find ? FORM gives similar results to Monte Carlo b values bit low but generally OK b values consistent for all problem types FoS highly variable – poor measure What did we find ?

What did we find ? Characteristic values: FORM design point values: QHk = 638 kN QVk = 1 306 kN QHk = 400 kN GVk = 3 000 kN + 310 kN QVk = 2 000 kN What did we find ?

What did we find ? FORM gives similar results to Monte Carlo b values bit low but generally OK b values consistent for all problem types FoS highly variable – poor measure DA B* will give different eccentricity to DA1 What did we find ?

Effect of varying f’ and g What did we find ?

Effect of varying CoV What did we find ?

What did we find ? FORM gives similar results to Monte Carlo b values bit low but generally OK b values consistent for all problem types FoS highly variable – poor measure DA B* will give different eccentricity to DA1 b values consistent for range of material properties b values below target for high CoV of material properties Designing for normal FoS may be unreliable What did we find ?