DGF Seminar in Cooperation with DONG Energy Wind Power DONG Energy Gentofte 1 April 2014 12:00 21:00 PROBABILISTIC APPROACH TO DETERMINING SOIL PARAMETERS Lars Vabbersgaard Andersen, John Dalsgaard Sørensen, Sarah Firouzianbandpey & Mohammad Javad Vahdatirad Aalborg University Department of Civil Engineering
01/04/2014 Probabilistic Approach to Determining Soil Parameters 2 INTRODUCTION Treatment of uncertainties in design of foundations
01/04/2014 Probabilistic Approach to Determining Soil Parameters 3 Introduction: Overall design approach Status for the design of foundations for offshore wind farms Geotechnical field measurements carried out at the location of each turbine (usually CPT) Characteristic values of the material properties are determined (usually as 5% quantile values or cautious estimates ) The soil is assumed to consist of a number of well defined layers Within each detected layer the soil is regarded as a homogeneous material The application of partial safety factors provides design values, and deterministic design of each foundation is performed
01/04/2014 Probabilistic Approach to Determining Soil Parameters 4 Introduction: Overall design approach Suggested approach for future applications
01/04/2014 Probabilistic Approach to Determining Soil Parameters 5 Introduction: Stochastic models Types of uncertainties Aleatory uncertainty (physical) Epistemic uncertainty (statistical, model, measurement) Models for each uncertain parameter Recommended distribution types Coefficients of variation Statistical dependencies (correlation / conditional distributions) Guidelines and recommendations ISO 2394: General principles Background documents for IEC standards,, Eurocodes Recommendations from various committees ISO 19900 (offshore structures) JCSS (Joint Committee of Structural Safety) ISO: Guide to the expression of uncertainty in measurements)
01/04/2014 Probabilistic Approach to Determining Soil Parameters 6 Introduction: Stochastic models The position (depth) of interfaces: Stochastic variables Inclination of layer interfaces: Stochastic variables Strength and stiffness of each layer: Stochastic fields
01/04/2014 Probabilistic Approach to Determining Soil Parameters 7 Introduction: Target reliability index Target reliability index optimal reliability level Building codes: e.g. Eurocode EN1990:2002: annual P F = 10-6 or β = 4.7 Fixed steel offshore structures: e.g. ISO 19902:2004 manned: annual P F ~ 3 10-5 or β = 4.0 unmanned: annual P F ~ 5 10-4 or β = 3.3 IEC 61400-1: land-based wind turbines IEC 61400-3: offshore wind turbines annual P F ~ 5 10-4 or β = 3.3 Observation of failure rates for wind turbines 1984-2000 Failure of blades: approx. 2 10-3 per year (decreasing) Wind turbine collapse: approx. 0.8 10-3 per year (decreasing)
01/04/2014 Probabilistic Approach to Determining Soil Parameters 8 Introduction: Assumed resistance model Load bearing capacity / stiffness of soil estimated by Y = b δ R(X,W) where X: vector of random variables (soil strength / stiffness parameters) W: vector of deterministic parameters (e.g. foundation width) R( ): model for resistance (capacity / stiffness) b: bias associated with the resistance model (often assumed to be 1.0) δ: model uncertainty associated with the resistance model (modelled as LogNormal distributed with unit mean and coefficient of variation equal to V δ )
01/04/2014 Probabilistic Approach to Determining Soil Parameters 9 Introduction: Soil strengths / stiffnesses Stochastic fields in the form X(x,y,z) Statistically homogeneous in horizontal and vertical directions with aleatory uncertainty assuming Mean value is a function of the depth: μ X (z) (e.g. a polynomial of z) Standard deviation (vertical): σ X,z (z) (depth dependent) Standard deviation (horizontal): σ X,h (z) (depth dependent) Correlation length (vertical): δ X,z Correlation length (horizontal): δ X,h Each field is discretized into a set of stochastic variables Soil parameters (e.g. Young s modulus E and undrained shear strength s u ) are typically correlated Each statistical parameter is subject to epistemic uncertainty (statistical / model uncertainty)
01/04/2014 Probabilistic Approach to Determining Soil Parameters 10 GEOTECHNICAL SITE ASSESSMENT BY CPT Identification of soil types and geotechincal properties based on cone-penetration tests
01/04/2014 Probabilistic Approach to Determining Soil Parameters 11 Site assessment by CPT: Classification of soil There have been lots of efforts on in-situ techniques to classify soils and predicting the important engineering parameters Example site is at the offshore wind farm London Array located in the south eastern offshore area in England 2 PCPT tests (with pore pressure measurements) and 1 borehole test have been carried out to 55 m depth Different CPT-based classification methods by Robertson et al. (1986), Robertson et al. (1990), Ramsey (2002), Eslami (2004) and Schneider (2008) have been considered for the purpose of interpretation and comparison of soil types of the region
Normalized Cone resistance q t (Mpa) 01/04/2014 Probabilistic Approach to Determining Soil Parameters 12 Site assessment by CPT: Robertson et al. 1990 10 3 SBT after Robertson et al., 1990 7 10 2 6 5 4 10 1 3 1 2 10 0-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Pore pressure ratio
01/04/2014 Probabilistic Approach to Determining Soil Parameters 13 Site assessment by CPT: Robertson et al. 1990
Normalized Cone resistance q t (Mpa) 01/04/2014 Probabilistic Approach to Determining Soil Parameters 14 Site assessment by CPT: Ramsey 2002 SBT after Ramsey, 2002 10 3 5 5 9 10 2 8 4 7 4 10 1 6 3 1 2 10 0-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Pore pressure ratio
01/04/2014 Probabilistic Approach to Determining Soil Parameters 15 Site assessment by CPT: Ramsey 2002
01/04/2014 Probabilistic Approach to Determining Soil Parameters 16 Site assessment by CPT: Classification of soil Most CPT classification methods, in general, are reliable for classifying the soil with an acceptable accuracy Nevertheless some of methods are more confident with high certainties in some particular soil types and others are less confident Different methods have different capabilities in identifying correctly various soil types This is possibly due to the differences in the development processes behind the charts, i.e. the various CPT-based classification charts rely on different background data Also the results show that some of the methods are unexpectedly unreliable regarding the prediction of soil types
01/04/2014 Probabilistic Approach to Determining Soil Parameters 17 Site assessment by CPT: Soil properties Empirical models for fine-grained soils Undrained shear strenght (s u ) usually found from cone resistance For very soft clay, s u may be found from excess pore pressure Over-consolidation ratio (OCR) Constrained modulus (M) Empirical models for coarse-grained soils Drained conditions during penetration (no excess pore pressure) Properties found from cone resistance and sleeve friction Relative density (I D ) Effective friction angle (φ ) based on I D or cone resistance Constrained modulus (M) and Young s modulus (E) Small strain shear modulus (G 0 ) and shear wave velocity (V S )
01/04/2014 Probabilistic Approach to Determining Soil Parameters 18 Site assessment by CPT: Soil properties Example comparisons of models and measurements Large model uncertainties are observed Models are often biased
01/04/2014 Probabilistic Approach to Determining Soil Parameters 19 Site assessment by CPT: Seismic CPT Accelerations are measured Arrival times Wave speeds Shear moduli
01/04/2014 Probabilistic Approach to Determining Soil Parameters 20 Variation of soil properties: Seismic CPT Shear moduli for sandy site Shear moduli for clayey site
01/04/2014 Probabilistic Approach to Determining Soil Parameters 21 VARIATION OF SOIL PROPERTIES Formulation of a stochastic model for soil with statistical properties based on cone-penetration tests
01/04/2014 Probabilistic Approach to Determining Soil Parameters 22 Variation of soil properties: 1-dimensional model Soil properties vary with spatial location due to geologic, environmental, and physical-chemical processes This inherent soil variability can be represented using statistical parameters and models Auto-covariance function for one-dimensional process Cov X t, X t = E X t μ X X t μ X where s and s are locations of two points Auto-correlation function Cov X t, X t ρ τ = Var X where τ = t t is the distance between t and t
01/04/2014 Probabilistic Approach to Determining Soil Parameters 23 Variation of soil properties: 1-dimensional model Example models for the auto-correlation 1. Exponential: ρ τ = exp τ D (this model is usually assumed) 2 2. Quadratic exponential (Gaussian): ρ τ = exp τ D Scale of fluctuation (or correlation length) 1. Exponential: δ = 2D δ = 2 0 2. Quadratic exponential: δ = D π ρ τ dτ τ < δ: strong correlation between two values X t, X t τ > δ: weak correlation between two values X t, X t
01/04/2014 Probabilistic Approach to Determining Soil Parameters 24 Variation of soil properties: Example test sites Two sites: Frederikshavn and Aalborg Soil is assumed to be statistically homogeneous Statistically homogeneous subsets (soil layers) must be identified For in situ tests with no direct soil samples (e.g. CPT) indirect means must be used for identification
01/04/2014 Probabilistic Approach to Determining Soil Parameters 25 Variation of soil properties: Frederikshavn site Plan of CPT soundings
01/04/2014 Probabilistic Approach to Determining Soil Parameters 26 Variation of soil properties: Aalborg site Plan of CPT soundings and borehole tests
01/04/2014 Probabilistic Approach to Determining Soil Parameters 27 Variation of soil properties: Cross correlation Horizontal and vertical cross correlation
Vertical correlation coefficient 01/04/2014 Probabilistic Approach to Determining Soil Parameters 28 Variation of soil properties: Aalborg site Vertical correlation coefficient of the cone resistance 1 CPT No. 1-9 Exponential fit 0.5 0-0.5 0 0.5 1 1.5 2 2.5 3 3.5 Distance (m)
Horizontal correlation coefficient 01/04/2014 Probabilistic Approach to Determining Soil Parameters 29 Variation of soil properties: Aalborg site Horizontal correlation coefficient of the cone resistance 1 0.8 Exponential fit CPT No. 1-8 0.6 0.4 0.2 0-0.2-0.4 0 5 10 15 20 25 30 35 40 45 Distance (m)
Vertical correlation length (m) 01/04/2014 Probabilistic Approach to Determining Soil Parameters 30 Variation of soil properties: Correlation lengths Main results from the Frederikshavn and Aalborg sites 0.8 0.7 Aalborg site Frederikshavn site 0.6 0.5 0.4 0.3 0.2 0.1 0 10 1 10 2 10 3 Mean (q c1n )
Y (m) Estimated q c1n (Mpa) Y (m) Estimated q c1n (Mpa) 01/04/2014 Probabilistic Approach to Determining Soil Parameters 31 Variation of soil properties: Kriging Low correlation High correlation Depth: 2 m below surface δ h = 2 m, δ v = 0.45 m Mean value dominates the result in desolate areas Depth: 2 m below surface δ h = 10.5 m, δ v = 0.45 m Less influence of the mean value even at the corners 0 140 0 150-2 -4-6 -8-10 -12 130 120 110 100 90-2 -4-6 -8-10 -12 140 130 120 110 100 90-14 -5-4 -3-2 -1 0 1 2 3 X (m) 80-14 -5-4 -3-2 -1 0 1 2 3 X (m) 80
01/04/2014 Probabilistic Approach to Determining Soil Parameters 32 INFLUENCE ON DESIGN Stochastic analysis of foundation response using simple models or advanced nonlinear finite-element models
Probability Density 01/04/2014 Probabilistic Approach to Determining Soil Parameters 33 Simple models: Surface footing on layered soil First natural frequency of wind turbine including springs representing the foundation and soil response 70 60 Deterministic value for design Histogram 50 40 30 20 10 0 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 Natural frequency (f n ), Hz The tales of the distribution are important for design
Probability Density Probability Density Probability Density Probability Density 01/04/2014 Probabilistic Approach to Determining Soil Parameters 34 Simple models: Monopile foundation in clay Eigen frequency obtained from p y curves 3.5 x 10-8 3 2.5 2 (a) Histogram Lognormal distribution (b) (b) x 10 x 10-10 -10 Histogram 0.9 0.9 Lognormal distribution 0.8 0.8 0.7 0.7 0.6 0.6 80 70 60 50 Histogram 0.5 0.5 40 1.5 0.4 0.4 30 1 0.5 0 0 5 10 10 15 15 Impedance (horizontal), N/m x x 10 10 7 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Impedance (rotational), N.m/rad x 10x 10 10 10 20 10 0 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 Natural frequency (f n ), Hz
01/04/2014 Probabilistic Approach to Determining Soil Parameters Nonlinear FEA: 2-D model of surface footing Comparison of two FE models with deterministic design RFEM by Griffiths and Fenton (Colorado School of Mines) ABAQUS / Matlab... by Vahdatirad et al. (Aalborg University) Deterministic design by DNV-OS-J101 (2013) 35
01/04/2014 Probabilistic Approach to Determining Soil Parameters 36 Nonlinear FEA: 2-D model of surface footing Comparison with the stochastic FEA models can provide insight into the bias related to the simple DNV method A recent study indicates the posibility of 10 20% savings Correlation length δ x = 0.5 b eff Correlation length δ x = 8 b eff Bias in the resistance, r 2.2 2 1.8 1.6 1.4 1.2 1 = 2.33 = 3.10 = 3.30 = 3.70 0.8 1 1.2 1.4 1.6 1.8 2 Bias in the strength parameter, cu Bias in the resistance, r 2 1.8 1.6 1.4 1.2 1 0.8 = 2.33 = 3.10 = 3.30 = 3.70 1 1.2 1.4 1.6 1.8 2 Bias in the strength parameter, cu
01/04/2014 Probabilistic Approach to Determining Soil Parameters Nonlinear FEA: 3-D model of a monopile Sample random field simulation results Mapping of the three-dimensional random field in the finite-element model Plastic strains at fully developed failure mechanism 37
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