baltimore_soils
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OUTLINE OUTLINE SPATIAL VARIABILITY 1. There is significant spatial variability of soil properties, even in so-called homogeneous layers EFFECTS 2. How soil heterogeneity affects the bearing capacity of shallow foundations MONTE CARLO SIMULATIONS 3. Monte Carlo simulation method for analyzing the effects of spatial variability 4. How each probabilistic characteristic of spatial variability influences the structural response FRAGILITY CURVES DESIGN 5. RECOMMEND Implications for geotechnical design CONCLUSIONS APPENDIX BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY EFFECTS MONTE CARLO SIMULATIONS FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS SPATIAL VARIABILITY OF SOIL PROPERTIES Cone tip resistance recorded at Tarsiut P-45 Average values (spatial trends) Fluctuations: • standard deviation • probability distribution • correlation structure APPENDIX BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY SPATIAL VARIABILITY OF SOIL PROPERTIES Average values (spatial trends) and percentile values of cone tip resistances recorded at Tarsiut P45 (Molikpaq core) EFFECTS MONTE CARLO SIMULATIONS FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY OF SOIL PROPERTIES SPATIAL VARIABILITY EFFECTS MONTE CARLO SIMULATIONS FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY EFFECTS MONTE CARLO SIMULATIONS SPATIAL VARIABILITY OF SOIL PROPERTIES The correlation structure for the fluctuations of recorded cone tip resistance, based on the sample correlation functions correlation function in vertical direction FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX sample cross-correlation between qc and Ic BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY BEARING CAPACITY OF SHALLOW FOUNDATIONS BEARING CAPACITY: • Load carrying capacity of foundations • Based on criteria of shear failure EFFECTS Uniform Soil MONTE CARLO SIMULATIONS Predicted deformed shape and contours of plastic shear strain for a uniform soil FRAGILITY CURVES DESIGN RECOMMEND 700 600 500 400 APPENDIX 300 200 100 Vertical pressure (kPa) CONCLUSIONS Pressure-settlement relation ultimate bearing capacity Settlements (m) 0 0 0.1 0.2 SOILS 0.3 0.4 BEARING CAPACITY OF HETEROGENEOUS 0.5 OUTLINE BEARING CAPACITY OF SHALLOW FOUNDATIONS SPATIAL VARIABILITY EFFECTS Heterogeneous Soil – EFFECT OF LOOSE ZONES 150 One sample function for cohesion (kPa) 100 MONTE CARLO SIMULATIONS 50 FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX 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 HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY a. B=4m d/B=0.1 Initial soil level Max. shear strain (%) 0 1 10 20 EFFECTS b. MONTE CARLO SIMULATIONS FRAGILITY CURVES cu (kPa) 150 100 50 c. d/B=0.1 CONCLUSIONS APPENDIX Max. shear strain (%) 0 Normalized pressure q/cuav DESIGN RECOMMEND 1 10 20 d. 6.0 4.0 Uniform soil (deterministic) Spatially varying soil shown in Fig. 1b 2.0 0 0 Settlement d (m) 0.1 0.2 0.3 0.4 0.5 BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY EFFECTS FINITE ELEMENT ANALYSES WITH STOCHASTIC INPUT B long, rigid structure Bearing Capacity – ABAQUS/STANDARD F OC clay 2.5 x B MONTE CARLO SIMULATIONS FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX 7.5 x B • plane strain analysis • undrained loading • elastic-perfectly plastic behaviour • large deformations • interface with Coulomb friction Soil properties • undrained shear strength, cu, STOCHASTIC PARAMETER • deformation modulus, E = (300 to 1500) cu • coefficient of variation of cu: CV = 10% to 40% • probability distributions: Gamma and Beta • separable correlaton structure with qH = qV BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE BEARING CAPACITY OF SHALLOW FOUNDATIONS SPATIAL VARIABILITY Heterogeneous Soil – MONTE CARLO SIMULATONS EFFECTS Pressure-settlement curves (Gamma distribution; CV = 40%) MONTE CARLO SIMULATIONS DESIGN RECOMMEND CONCLUSIONS TWO EFFECTS: Vertical pressure (kPa) FRAGILITY CURVES 700 600 500 1. Response variability 400 2. Reduction in average bearing capacity 300 200 Monte Carlo simulation results 100 0 APPENDIX Deterministic analysis results 0 0.1 0.2 0.3 Settlements (m) 0.4 0.5 BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE SPATIAL VARIABILITY EFFECTS MONTE CARLO SIMULATIONS 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) Footing rotations under centered vertical loads DESIGN RECOMMEND CONCLUSIONS APPENDIX Vertical pressure (kPa) FRAGILITY CURVES 750 625 Damage levels in terms of footing rotations (along the lines of Grant et al. 1974) 500 375 250 125 0 20 10 0 10 Footing rotation (%) 20 • minor damage: 1/500 • medium damage: 1/300 • major damage: 1/150 BEARING CAPACITY OF HETEROGENEOUS SOILS OUTLINE EFFECTS MONTE CARLO SIMULATIONS FRAGILITY CURVES DESIGN RECOMMEND CONCLUSIONS APPENDIX 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) 1 probability of damage SPATIAL VARIABILITY FRAGILITY CURVES – BEARING CAPACITY b. minor damage medium damage major damage failure 0.8 0.6 Fragility curves for a strip foundation on heterogeneous soil: • CV = 40% • qH/B = 1.25 • E/cu = 1500 • Gamma distribution 0.4 0.2 Pf = 5% 0 0.4 0.6 0.8 1 normalized bearing pressure (q/qu 1.2 Estimating the Nominal value – qn det) BEARING CAPACITY OF HETEROGENEOUS SOILS
