1. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIXOUTLINE OUTLINE 1.There is significant spatial variability of soil properties, even in so-called homogeneous layers SPATIAL VARIABILITY 3.Monte Carlo simulation method for analyzing the effects of spatial variability MONTE CARLO SIMULATIONS 2.How soil heterogeneity affects the bearing capacity of shallow foundations EFFECTS 4.How each probabilistic characteristic of spatial variability influences the structural response FRAGILITY CURVES 5. Implications for geotechnical design DESIGN RECOMMEND

2. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX SPATIAL VARIABILITY OF SOIL PROPERTIES Cone tip resistance recorded at Tarsiut P-45 Average values (spatial trends) Fluctuations: standard deviation probability distribution correlation structure SPATIAL VARIABILITY

3. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX SPATIAL VARIABILITY OF SOIL PROPERTIES SPATIAL VARIABILITY Average values (spatial trends) and percentile values of cone tip resistances recorded at Tarsiut P45 (Molikpaq core)

4. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX SPATIAL VARIABILITY OF SOIL PROPERTIES SPATIAL VARIABILITY

5. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX SPATIAL VARIABILITY OF SOIL PROPERTIES SPATIAL VARIABILITY The correlation structure for the fluctuations of recorded cone tip resistance, based on the sample correlation functions correlation function in vertical direction sample cross-correlation between q c and I c

6. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX Predicted deformed shape and contours of plastic shear strain for a uniform soil BEARING CAPACITY OF SHALLOW FOUNDATIONS Pressure-settlement relation Vertical pressure (kPa) Settlements (m) 00.10.20.30.40.5 0 100 200 300 400 500 600 700 ultimate bearing capacity Uniform Soil EFFECTS BEARING CAPACITY: Load carrying capacity of foundations Based on criteria of shear failure

7. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX One sample function for cohesion (kPa) 50 100 150 Actual failure surface deviates from its “theoretical position” to pass through weaker material Average mobilized strength is, in general, lower than the actual average strength BEARING CAPACITY OF SHALLOW FOUNDATIONS Heterogeneous Soil – EFFECT OF LOOSE ZONES EFFECTS

8. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX  =0.1 Max. shear strain (%) 0 1 10 20 Initial soil level  =0.1 B=4m Max. shear strain (%) 0 1 10 20 a. c. b. 150 100 50 c u (kPa) d. Settlement  (m) Spatially varying soil shown in Fig. 1b Uniform soil (deterministic) Normalized pressure q/c u av 00.10.20.30.40.5 0 2.0 4.0 6.0

9. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX B 7.5 x B 2.5 x B F OC clay long, rigid structure plane strain analysis undrained loading elastic-perfectly plastic behaviour large deformations interface with Coulomb friction Soil properties undrained shear strength, c u,  STOCHASTIC PARAMETER deformation modulus, E = (300 to 1500) c u coefficient of variation of c u : CV = 10% to 40% probability distributions: Gamma and Beta separable correlaton structure with  H =  V FINITE ELEMENT ANALYSES WITH STOCHASTIC INPUT Bearing Capacity – ABAQUS/STANDARD MONTE CARLO SIMULATIONS

10. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX Pressure-settlement curves ( Gamma distribution; C V = 40%) Monte Carlo simulation results Vertical pressure (kPa) Settlements (m) 00.10.20.30.40.5 0 100 200 300 400 500 600 700 Deterministic analysis results BEARING CAPACITY OF SHALLOW FOUNDATIONS Heterogeneous Soil – MONTE CARLO SIMULATONS MONTE CARLO SIMULATIONS TWO EFFECTS: 1. Response variability 2. Reduction in average bearing capacity

11. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX 20100 20 0 125 250 375 500 625 750 Footing rotation (%) Vertical pressure (kPa) Footing rotations under centered vertical loads FRAGILITY CURVES – BEARING CAPACITY FRAGILITY CURVES: Express the probability of exceeding a certain damage level as a function of the load intensity DAMAGE LEVELS: Describe discrete serviceability limit states, and can include the ultimate limit state (failure) Damage levels in terms of footing rotations (along the lines of Grant et al. 1974) minor damage: 1/500 medium damage: 1/300 major damage: 1/150 FRAGILITY CURVES

12. OUTLINE SPATIAL VARIABILITY FRAGILITY CURVES MONTE CARLO SIMULATIONS CONCLUSIONS EFFECTS DESIGN RECOMMEND BEARING CAPACITY OF HETEROGENEOUS SOILS APPENDIX FRAGILITY CURVES – BEARING CAPACITY FRAGILITY CURVES: Express the probability of exceeding a certain damage level as a function of the load intensity DAMAGE LEVELS: Describe discrete serviceability limit states, and can include the ultimate limit state (failure) 0.40.60.811.2 0 0.2 0.4 0.6 0.8 1 normalized bearing pressure (q/q u det ) probability of damage minor damage medium damage major damage failure b. Fragility curves for a strip foundation on heterogeneous soil: CV = 40%  H /B = 1.25 E/c u = 1500 Gamma distribution P f = 5% Estimating the Nominal value – q n FRAGILITY CURVES