The document discusses risk evaluation methods for pile foundation design according to standards. It describes how pile foundation design involves many limitations and uncertainties related to limited calculation models, ground investigation, and variability in ground parameters. Probabilistic methods like reliability-based design (RBD) are recommended to formally account for these uncertainties using probability theory and target acceptable probability of failure levels. The document outlines reliability index calculation methods and how codes like Eurocode calibrate partial safety factors to achieve target reliability levels based on probabilistic characteristics of load and resistance variables.
- Evolution of the design standards
- Composition and links between Eurocodes
- Fundamental requirement in Eurocodes
- Eurocode 0 : BASIS OF STRUCTURAL DESIGN
- Partial Factor method - probabilism
- Limit states
- Eurocode 1 - Actions and combinations
- Evolution of the design standards
- Composition and links between Eurocodes
- Fundamental requirement in Eurocodes
- Eurocode 0 : BASIS OF STRUCTURAL DESIGN
- Partial Factor method - probabilism
- Limit states
- Eurocode 1 - Actions and combinations
This paper develops a novel approach to characterize the uncertainty in the accuracy of surrogate models. This technique segregates the design domain based on the level of cross-validation errors; the overall framework is called Domain Segmentation based on Uncertainty in the Surrogate (DSUS). The estimated errors are classified into physically meaningful classes based on the user’s understanding of the system and/or the accuracy requirements for the concerned system analysis. In each class, the distribution of the cross-validation errors is estimated to represent the uncertainty in the surrogate. Support Vector Machine (SVM) is implemented to determine the boundaries between error classes, and to classify any new design (point) into a meaningful class. The DSUS framework is illustrated using two different surrogate modeling methods: (i) the Kriging method, and (ii) the Adaptive Hybrid Functions (AHF). We apply the DSUS framework to a series of standard problems and engineering problems. The results show that the DSUS framework can successfully classify the design domain and quantify the uncertainty (prediction errors) in surrogates. More than 90% of the test points could be accurately classified into its error class. In real life engineering design, where we use predictive models with different levels of fidelity, the knowledge of the level of error and uncertainty at any location inside the design space is uniquely helpful.
To those who may have an interest in how Bayes has inspired and influenced my research and industrial activities. What you will see is indeed only selected parts of the works of my student and colleagues in academia and industry - over more than 30 years. There is much more - and much more to come.
Reliability Analysis of Slope Stability by Central Point MethodIJERA Editor
Given uncertainty and variability of the slope stability analysis parameter, the paper proceed from the perspective of probability theory and statistics based on the reliability theory. Through the central point method of reliability analysis, performance function about the reliability of slope stability analysis is established. What’s more, the central point method and conventional limit equilibrium methods do comparative analysis by calculation example. The approach’s numerical results are consistent with the traditional limit equilibrium method and meet the objective reality. The accuracy and practicality of reliability analysis is confirmed in order to provide reliability theory a scientific basis for the feasibility of slope stability analysis.
STRUCTURAL RELIABILITY ASSESSMENT WITH STOCHASTIC PARAMETERSP singh
The performance of a structure [23] is assessed by its safety [1], serviceability [1] and economy [1]. Since we do not know the exact details of loads [4] acting on a structure at any time, there is always some uncertainty about the total loads on structure. Thus random variables (means stochastic variable) of loads and other parameters are the main criteria of design variables [18]. They vary with space and time. The input variables is never certain and complete. The safety factor provided in the existing codes and standers primarily based on practice, judgment and experience, may not be adequate and economical. Using the techniques presented earlier, we can design or analyze individual members in the contest of structural reliability [2][3][22][24]. However we are not examined how the system performs [23] or how to calculate the reliability of the structure as a whole.
Soil-structure interaction uncertainties and their effects on the development...Ali Saeidi
The extraction of ore and minerals by underground mining or other underground workings often cause ground subsidence phenomena. In urban regions, these phenomena may induce small to severe damage to buildings. We have developed vulnerability functions for determining damage to building in subsidence regions. The methodology uses Monte Carlo simulations, and existing analytical methods based on the beam theory for the evaluation of damage in the subsidence area. It allows taking into account uncertainties both on the geometrical and mechanical parameters of buildings, and on the phenomena of soil structure interaction for analytical methods. This paper focuses on uncertainties on soil-structure interaction. The determination of damage with analytical methods requires values of the horizontal strain and the deflection transmitted to buildings. But the available geotechnical parameters are the horizontal ground strain and the ground curvature; soil structure interaction parameters are then required to determine how these geotechnical strains are transmitted to buildings. The value of these later parameters are dependent on several factors, such as the soil and the building rigidity, the building type, the mine or tunnel depth, the localisation of building in a subsidence basin. All of these factors increase the uncertainties in building vulnerability functions, and must be considered in the development of these functions. We observed that low values of ground curvature coefficient (KΔ) lead to a flattening of the vulnerability curve (low vulnerability), and that low values of horizontal strain soil-struction interaction coefficient (Kε) lead to a shift of the vulnerability curve to the right (reduced vulnerability). Finally, it
Optimum penetration depth of cantilever sheet pile walls in dry granular soil Ahmed Ebid
in Cantilevered sheet
pile walls are commonly used in shoring systems of deep excavation down to about 5.00 m. The most common design procedure for this type
of flexible retaining structures is to determine the required penetration depth for stability and then increasing the calculated penetration
depth by 20% to 40% to achieve a factor of safety of about 1.5 to 2.0. This procedure has two disadvantages; first, the procedure does not
give accurate values for penetration depth or corresponding factor of safety, second, it ignores the effect of uncertainty in the used
geotechnical parameters. The first aim of this study is to overcome those two disadvantages by introduce an alternative formula to
determine the optimum penetration depth of cantilever sheet pile walls in dry granular soil based on reliability analysis concept, while, the
second aim is to study the impact of using the optimum depth on the cost of the shoring system. The study results assure the validity of
provision of increasing the calculated penetration depth by (20% to 40%) and introduced a formula to calculate the required penetration
depth to achieve probability of failure of 0.1% and proved that using this optimum depth can reduce the direct cost of the shoring system by
5% to 10% based on internal friction angle of soil.
Adaptive response surface by kriging using pilot points for structural reliab...IOSR Journals
Structural reliability analysis aims to compute the probability of failure by considering system uncertainties. However, this approach may require very time-consuming computation and becomes impracticable for complex structures especially when complex computer analysis and simulation codes are involved such as finite element method. Approximation methods are widely used to build simplified approximations, or metamodels providing a surrogate model of the original codes. The most popular surrogate model is the response surface methodology, which typically employs second order polynomial approximation using least-squares regression techniques. Several authors have been used response surface methods in reliability analysis. However, another approximation method based on kriging approach has successfully applied in the field of deterministic optimization. Few studies have treated the use of kriging approximation in reliability analysis and reliability-based design optimization. In this paper, the kriging approximation is used an alternative to the traditional response surface method, to approximate the performance function of the reliability analysis. The main objective of this work is to develop an efficient global approximation while controlling the computational cost and accurate prediction. A pilot point method is proposed to the kriging approximation in order to increase the prior predictivity of the approximation, which the pilot points are good candidates for numerical simulation. In other words, the predictive quality of the initial kriging approximation is improved by adding adaptive information called “pilot points” in areas where the kriging variance is maximum. This methodology allows for an efficient modeling of highly non-linear responses, while the number of simulations is reduced compared to Latin Hypercubes approach. Numerical examples show the efficiency and the interest of the proposed method.
Presentation by Tony Limas of Granite Construction titled "Quantifying Risk of End Result Specifications," delivered at the California Asphalt Pavement Association (CalAPA) Spring Asphalt Pavement Conference April 25-26, 2018 in Ontario, CA.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models.
This paper develops a novel approach to characterize the uncertainty in the accuracy of surrogate models. This technique segregates the design domain based on the level of cross-validation errors; the overall framework is called Domain Segmentation based on Uncertainty in the Surrogate (DSUS). The estimated errors are classified into physically meaningful classes based on the user’s understanding of the system and/or the accuracy requirements for the concerned system analysis. In each class, the distribution of the cross-validation errors is estimated to represent the uncertainty in the surrogate. Support Vector Machine (SVM) is implemented to determine the boundaries between error classes, and to classify any new design (point) into a meaningful class. The DSUS framework is illustrated using two different surrogate modeling methods: (i) the Kriging method, and (ii) the Adaptive Hybrid Functions (AHF). We apply the DSUS framework to a series of standard problems and engineering problems. The results show that the DSUS framework can successfully classify the design domain and quantify the uncertainty (prediction errors) in surrogates. More than 90% of the test points could be accurately classified into its error class. In real life engineering design, where we use predictive models with different levels of fidelity, the knowledge of the level of error and uncertainty at any location inside the design space is uniquely helpful.
To those who may have an interest in how Bayes has inspired and influenced my research and industrial activities. What you will see is indeed only selected parts of the works of my student and colleagues in academia and industry - over more than 30 years. There is much more - and much more to come.
Reliability Analysis of Slope Stability by Central Point MethodIJERA Editor
Given uncertainty and variability of the slope stability analysis parameter, the paper proceed from the perspective of probability theory and statistics based on the reliability theory. Through the central point method of reliability analysis, performance function about the reliability of slope stability analysis is established. What’s more, the central point method and conventional limit equilibrium methods do comparative analysis by calculation example. The approach’s numerical results are consistent with the traditional limit equilibrium method and meet the objective reality. The accuracy and practicality of reliability analysis is confirmed in order to provide reliability theory a scientific basis for the feasibility of slope stability analysis.
STRUCTURAL RELIABILITY ASSESSMENT WITH STOCHASTIC PARAMETERSP singh
The performance of a structure [23] is assessed by its safety [1], serviceability [1] and economy [1]. Since we do not know the exact details of loads [4] acting on a structure at any time, there is always some uncertainty about the total loads on structure. Thus random variables (means stochastic variable) of loads and other parameters are the main criteria of design variables [18]. They vary with space and time. The input variables is never certain and complete. The safety factor provided in the existing codes and standers primarily based on practice, judgment and experience, may not be adequate and economical. Using the techniques presented earlier, we can design or analyze individual members in the contest of structural reliability [2][3][22][24]. However we are not examined how the system performs [23] or how to calculate the reliability of the structure as a whole.
Soil-structure interaction uncertainties and their effects on the development...Ali Saeidi
The extraction of ore and minerals by underground mining or other underground workings often cause ground subsidence phenomena. In urban regions, these phenomena may induce small to severe damage to buildings. We have developed vulnerability functions for determining damage to building in subsidence regions. The methodology uses Monte Carlo simulations, and existing analytical methods based on the beam theory for the evaluation of damage in the subsidence area. It allows taking into account uncertainties both on the geometrical and mechanical parameters of buildings, and on the phenomena of soil structure interaction for analytical methods. This paper focuses on uncertainties on soil-structure interaction. The determination of damage with analytical methods requires values of the horizontal strain and the deflection transmitted to buildings. But the available geotechnical parameters are the horizontal ground strain and the ground curvature; soil structure interaction parameters are then required to determine how these geotechnical strains are transmitted to buildings. The value of these later parameters are dependent on several factors, such as the soil and the building rigidity, the building type, the mine or tunnel depth, the localisation of building in a subsidence basin. All of these factors increase the uncertainties in building vulnerability functions, and must be considered in the development of these functions. We observed that low values of ground curvature coefficient (KΔ) lead to a flattening of the vulnerability curve (low vulnerability), and that low values of horizontal strain soil-struction interaction coefficient (Kε) lead to a shift of the vulnerability curve to the right (reduced vulnerability). Finally, it
Optimum penetration depth of cantilever sheet pile walls in dry granular soil Ahmed Ebid
in Cantilevered sheet
pile walls are commonly used in shoring systems of deep excavation down to about 5.00 m. The most common design procedure for this type
of flexible retaining structures is to determine the required penetration depth for stability and then increasing the calculated penetration
depth by 20% to 40% to achieve a factor of safety of about 1.5 to 2.0. This procedure has two disadvantages; first, the procedure does not
give accurate values for penetration depth or corresponding factor of safety, second, it ignores the effect of uncertainty in the used
geotechnical parameters. The first aim of this study is to overcome those two disadvantages by introduce an alternative formula to
determine the optimum penetration depth of cantilever sheet pile walls in dry granular soil based on reliability analysis concept, while, the
second aim is to study the impact of using the optimum depth on the cost of the shoring system. The study results assure the validity of
provision of increasing the calculated penetration depth by (20% to 40%) and introduced a formula to calculate the required penetration
depth to achieve probability of failure of 0.1% and proved that using this optimum depth can reduce the direct cost of the shoring system by
5% to 10% based on internal friction angle of soil.
Adaptive response surface by kriging using pilot points for structural reliab...IOSR Journals
Structural reliability analysis aims to compute the probability of failure by considering system uncertainties. However, this approach may require very time-consuming computation and becomes impracticable for complex structures especially when complex computer analysis and simulation codes are involved such as finite element method. Approximation methods are widely used to build simplified approximations, or metamodels providing a surrogate model of the original codes. The most popular surrogate model is the response surface methodology, which typically employs second order polynomial approximation using least-squares regression techniques. Several authors have been used response surface methods in reliability analysis. However, another approximation method based on kriging approach has successfully applied in the field of deterministic optimization. Few studies have treated the use of kriging approximation in reliability analysis and reliability-based design optimization. In this paper, the kriging approximation is used an alternative to the traditional response surface method, to approximate the performance function of the reliability analysis. The main objective of this work is to develop an efficient global approximation while controlling the computational cost and accurate prediction. A pilot point method is proposed to the kriging approximation in order to increase the prior predictivity of the approximation, which the pilot points are good candidates for numerical simulation. In other words, the predictive quality of the initial kriging approximation is improved by adding adaptive information called “pilot points” in areas where the kriging variance is maximum. This methodology allows for an efficient modeling of highly non-linear responses, while the number of simulations is reduced compared to Latin Hypercubes approach. Numerical examples show the efficiency and the interest of the proposed method.
Presentation by Tony Limas of Granite Construction titled "Quantifying Risk of End Result Specifications," delivered at the California Asphalt Pavement Association (CalAPA) Spring Asphalt Pavement Conference April 25-26, 2018 in Ontario, CA.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models.
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Risk evaluation according to standards cristina de hc tsuha
1. Cristina de H.C. Tsuha & Nelson Aoki
University of São Paulo / Brazil
RISK EVALUATION ACCORDING TO STANDARDS
2. Risk
“The term risk implies a combination (the product) of the
probability of an event occurring and the consequences
of the event should it occur”
“Probability of failure is a measure of risk only if all failure modes
result in the same consequences”
Lacasse & Nadim (1998)
Probability and costs of foundation problems
Their impacts
Labor, Materials , Equipment,
Business Costs, Environmental
Costs , Social Costs , Deaths, etc.
Risk cost = x
• Structural collapse
• Excessive settlements
probability of failure cost of failure
1
3. Risks associated with pile foundation
Design of pile foundations involves many
limitations and uncertanties
DESIGN PROBLEM
GOAL : minimize the risks
(acceptable level/ economical)
Limited calculation models
Limited ground investigation
Uncertanties in ground parameters
Spatial variability
Bauduin (2003)
2
4. R1
Rn
Ri
R4
R3
R2
Variability of pile resistance in a construction project
Resistance (kN)
Example of a
construction project
R mean = 3295 kN
Standard deviation = 483 kN
Coefficient of variation = 14,7 %
Dynamic measurements
(CAPWAP) on 74 piles
Frequency(%)
3
6. R-E should be > 0
Mathematically:
pile does not fail
Margin of safety (M = R-E)
M
σM
mM
pf
y
0
Probability of failure and Reliability index β
β = µZ / σZ
22
ER
ER
Normally distributed random variable
5
β
7. Lognormal distribution
)1(1ln
1
1
ln
22
2
2
RE
R
E
E
R
vv
v
v
6
Probability of failure and Reliability index β
8. Formulations (Freudenthal) involved convolution functions
(R and E distribution) to obtain pf
Probability of failure and Reliability index β
7
Probabilistic Deterministic
10. Safety factor and probability of failure
The factor of safety is therefore not a sufficient indicator of safety margin because the
uncertainties in the analysis parameters affect probahility of failure
uncertainties do not interven in the deterministic calculation of safety factor.
9
Lacasse & Nadim (1998)
11. Reliability levels of a construction project
Level zero: deterministic methods
random variables are taken as deterministic and uncertainties are taken into
account by a global safety factor (based on past experience)
Level I: semi-probabilistic methods
deterministic formulas are applied to representative values of RVs multiplied by
partial SFs. The characteristic values are calculated based on statistical
information/ the partial SFs are based on level II or level III reliability methods
Level II: approximate probabilistic methods
RVs are characterised by their distribution and statisticalparameters probabilistic
evaluation of safety achieved using approximate numerical techniques
Level III: full probabilistic methods
Techniques that take into account all of the probabilistic characteristics of the RVs
Level IV: risk analysis
probabilistic characteristics & consequences of failure are taken into account
The level of accuracy depends on the way that uncertainties are considered in the design
(Teixeira et al. 2012)
10
12. Load and Resistance Factor Design (LRFD)
LRFD is appropriate for geotechnical designs because:
the variabilities and uncertainties associated with natural systems (the ground in this
case) are much greater than those associated with well-controlled engineered
systems
The specifications were calibrated based on a combination of simplistic reliability
analysis, fitting to WSD and engineering judgment.
11
Lacasse & Nadim (1998)
(Paikowsky 2004)
Load and Resistance factor design
Separate uncertanties in loading from uncertanties in resistance
Use procedures from probability theories
LRFD requires a selection of a set of target reliability levels (β)
13. LRFD formulation – Pile foundations
12
Traditional design
E
R
F calc
S
Single (Global) Safety Factor
(margin for error and uncertainty in actions and resistances)
Design value of
action effect
LRFD, Partial factor method (Eurocode 7)
Limit state design concept with partial factors and
characteristics values
Ed Rd
Design value of
resistance
to obtain appropriate levels
of reliability (RBD methods)
related to a specific
calculation model
14. LRFD equations – Pile Foundations
13
Ed Rd
Compressive resistance
. " " .
partial factor
on pile
resistance
(European)
characteristic pile
resistance
partial factors of permanent and variable
action effect
;
+ ;
base shaftCharacteristic pile resistance Rk:
• Uncertanties related to calculation method
• Variability over the construction site
∅ .
reduction
factor
(other codes)
16. Partial factors linked to reliability index β
15
Low probability
of failure
Ex: β = 3.8, Pf = 7.2 x 10-5
Partial factors (gvalues)
Reliability levels for representative structures as
close as possible to the target reliability index bT
reliability index β
Related to a probability of failure
Quantity to evaluate “safety”
Density functions
of R and E
E, E , vE
R, R , vR
17. Partial factors linked to reliability index β
16
FOSM reliability formulas
Lognormal distribution is often used:
Sensitivity factors
E and vE ?
R and vR ?
18. Partial factors linked to reliability index β
17
R = P . Rcal
Bias of the resistance funcion
E = E . Ek
Bias for the actionVE and VR ?
Model uncertainty (P and Vp )
Variability of R over the site ( )
Variability of effects of execution (monitoring)
19. Model uncertanty
18
Bauduin (2003)
Model uncertanty
Random variable B
VB
mB
R = P . Rcal
coefficient of variation
calculated resistance
If load tests were performed
p% of measured would be lower
than prediction
Model factor m
Reliability of the calculation model
21. Partial factors (calculation model uncertanty)
20
Design value of resistance Rd
.
;
+ ;
;
+
;
.
1
mod
P and Vp (different types of pile in different types of ground)
23. Stiffness of the structure and monitoring
22
stiffness
Bauduin (2003)
transfer loads from weaker to stronger piles
Favorable effect
monitoring
Reduce uncertanty related to installation effects
25. Partial factors linked to reliability index β
24
FOSM
Target
reliability
ULS ocurrence: Ed = Rd
VE VR
reduction
factor
(AASHTO)
∅ .
26. Brazilian code: NBR 6122 (2010)
Recognize the risks involved in Foundations
Introduces the concept of correlation factor (static load tests &
ground tests) to deal with the spatial variability of pile resistance
25
Static load tests (number and type of piles)
5 dynamic
(CAPWAP)
for 1 static
27. Estimation of vR using the Brazilian code
Correlation factors
(static tests)
4
min,
3
,
,
)(
,
)(
mcmeanmc
kc
RR
MinR
Variability of pile resistance (vR or R)
645.1
)( ,, kcmeanmc
R
RR
Reliability index
pf = 1-()Probability of failure
22
ER
ER
simple closed form
normal reliability
calculation formula
E and R assumed to be normally distributed
uncertanty of calculations models (based on SPT test) ? ? ?
“ No information about bias of calculation models”
Estimation of β and Pf
26
P ???
28. R density distribution
27
R
Obtain R density distribution from:
static tests, dynamic tests, dynamic formula, etc.VR
Example
Resistance (kN)
R measured
Number
of piles
mean
(kN)
COV (%)
Static tests 4 3756 12,3
Capwap 74 3295 14,7
Dynamic formula 2506 3231 16,0
Best fit distribution for R
Formulations (Freudenthal) involved
convolution functions (R and E distribution)
to obtain and Pf
Update during and after construction
(normal, lognormal, beta, etc.)
29. Christian 2004, Baecher & Christian 2005, Phoon et al 1995, and Phoon et al. 2003):
• The uncertainties in geotechnical engineering are largely inductive: starting from
limited observations, judgment, knowledge of geology, and statistical reasoning are
employed to infer the behavior of a poorly-defined universe.
• The probabilistic methods help to relieve the foundation engineer from the ill-suited
task of assessing the complex relationship between uncertainties and risks intuitively,
while at the same time emphasizing the importance of engineering judgment and
experience on the other design aspects that are currently beyond the scope of
mathematical analysis.
• The geotechnical engineer’s role is not solely to provide judgment on selection of
parameters, methods of calculations and resulting safety, but also to take an active
part in the evaluation of hazard, vulnerability and risk.
• Communication of risk within a transparent and rational framework is necessary in
view of increasing interest in code harmonization public involvement in defining
acceptable risk levels, and risk-sharing among client, consultant, insurer, and financier.
Advantages of employing RBD
• The probability theory can provide a formal framework for developing design criteria
that would ensure that the probability of "failure" (to refer to exceeding of any
prescribed limit state) is acceptably small.
28
