Modification of partial safety factors for a semi-probabilistic evaluation of existing timber structures

Structural Design Practice has transformed from conventional Working Stress Method to Limit State Method—Load and Resistance Factor Design (ACI) or Partial Safety Factor approach (IS Code). Geotechnical Design Philosophy is in the transformation stage to implement Load and Resistance Factor Design (LRFD). Eurocode-7 accommodates three design approaches (DAs) that allow partial factors to be introduced at the beginning of the calculations (strength partial factors) or at the end of the calculations (resistance partial factors), or some intermediate combinations thereof. IS 6403 provides guideline to calculate ultimate bearing capacity for shallow foundations. It gives bearing capacity factors and other factors, viz., inclination factors, depth factors, shape factors, etc., and accounts for the effect of water table. To calculate allowable bearing pressure a Factor of Safety 2.50 is recommended separately by IS 1080. Eurocode 7 provides guideline for proportioning shallow foundations using partial safety factors for Action, Material Parameters, and Resistance. The Action includes Dead Loads as well as Imposed Loads. Material Parameters includes shear parameters “c” and “φ” in drained and/or undrained state. The Resistance Factors are assigned based on the design methods used. For shallow foundations three design approaches are considered for which partial safety factors are given. Parametric study is carried out to compare the ratio of capacity obtained from IS Code WSM and EC7 LSM for different soil type (c-soil, phi—soil, and c-phi soil) keeping other parameters constant.

This study addresses the partial safety factors used in structural design codes. The study is based on the theory of structural reliability, which allows an explicit consideration of the uncertainties in material strengths and load actions, and results in a quantitative measure of structural safety: the reliability index. A calibration methodology is considered, which allows one to find a set of partial safety factors that minimizes the variations on reliability indexes, for all structures designed within a code, with respect to a pre-selected target reliability. An initial calibration is performed for a target reliability index 3,0, but other target reliabilities are also considered. The analysis is limited to steel structural members. The calibration is made for two distinct code formats. In the ANSI/AISC code format, a set of partial factors is obtained for each load combination expression. In the Brazilian and European code formats, one single set of partial (and load combination) factors is obtained, for a single load combination expression. Partial safety factors obtained for both code formats are compared with partial factors used in National Brazilian code ABNT NBR8800:2008. The resulting reliability indexes are also compared, for the distinct load combination expressions, in terms of the proportionality ratios between the distinct actions. Results obtained in the study show that the partial safety factors used in ABNT NBR8800:2008 lead to significant variation on reliability indexes. Another set of partial safety factors is obtained in the study, which provides greater uniformity of reliability indexes. These results suggest that a revision of partial safety factors adopted in ABNT NBR8800:2008 might be recommended. This recommendation, however, is dependent on a deepening of the investigation started in this study, which does not reflect all design situations covered by the design code.

Enhanced knowledge from a qualified survey in situ can help to model the load-bearing behaviour of an existing structures more realistically by considering specific knowledge on material parameters and conditions. A semi-probabilistic evaluation format with partial safety factors is used in common practice. Standardised options to include specific information into the design concept have to be worked out. These are improved strength grading using non-/semi-destructive means and adjustments within the safety concept itself. However, for everyday practice two problems arise. It is often not possible to determine strength parameters but reference properties like Young’s modulus or density. Besides, an exhaustive determination of material parameters is cost-intensive and therefore often not possible for smaller projects. This contribution presents a procedure to include data gained in a qualified survey in situ into the design concept for the verification of load-bearing capacities of existing timber structures. The level of detail of the design format is increased stepwise considering the level of detail of the survey. These levels are named Knowledge Levels in accordance with the Science and Policy Report of the Joint Research Centre (JRC) from 2015. Knowledge Level 1 includes the evaluation based on current Eurocodes without adjustments. Knowledge Level 2 is divided into three sub-levels including adjustments of partial safety factors for target values derived for existing structures, an improved strength grading based on non-/semi-destructive technical means and the updated of the partial safety factor for the material strength based on measured reference properties. Knowledge Level 3 includes a probabilistic evaluation comparing the actual reliability of the current design situation with and without parameter update.KeywordsTimberExisting structuresEvaluation procedureSemi-probabilistic safety conceptPartial safety factors

Steels for the transporting of fossil energy sources - offshore, ships, tanks, electrical sheet : Heller, T. et al. Stahl und Eisen, 2002, 122, (5), 39–46. (In German)

Reliability-based calibration of fatigue design guidelines for ship structures

Partial Safety Factors (PSFs) are scaling factors which are used to modify the input parameters to a deterministic fracture mechanics assessment in order to consider the effects of variability or uncertainty in the values of the input parameters. BS7910 and SINTAP have adopted the technique, both of which use the First Order Reliability Method (FORM) to derive values for PSFs. The PSFs are tabulated, varying with the target probability of failure, p(F), and the Coefficient of Variance (COV) of the variable. An accurate assessment of p(F) requires a probabilistic method with enough simulations. This has previously been found to be time consuming, due to the large number of simulations required. The PSF method has been seen as a quick way of calculating an approximate, conservative value of p(F). This paper contains a review of the PSF method, conducted using an efficient probabilistic method called the Hybrid probabilistic method. The Hybrid probabilistic method is used to find p(F) at a large number of assessment points, for a range of different PSFs. These p(F) values are compared to those obtained using the PSF method. It is found that the PSF method was usually, and often extremely, conservative. However there are also cases where the PSF method was non-conservative. This result is verified by a hand calculation. Modifications to the PSF method are suggested, including the establishment of a minimum PSF on each variable to reduce non-conservatisms. In light of the existence of efficient probabilistic techniques, the non-conservatisms that have been found in the PSF method, coupled with the impracticality of completely removing these non-conservatisms, it is recommended that a full probabilistic assessment should generally be performed.

When there are uncertainties in the input random variables, or scatter in the material properties, probabilistic assessment is a useful tool for decision making in the field of safety analysis. The partial safety factor (PSF) method was aimed on ensuring that the failure probability did not exceed a target value. In order to be conservative the input value for each random variable during the assessment procedure should be multiplied by the partial safety factors. So it is essentially a deterministic assessment using conservative values of the input random variables and a relatively simple and independent method of assessing failure probabilities using R6 failure assessment diagram. The application of partial safety factors is an important breakthrough of assessment in structures containing defects. In recent years, sets of PSFs for load, defect size, fracture toughness and yield stress had been given in two standards, BS7910 and API579. However, the recommended PSFs in both standards were larger than the original PSFs in PD6493 which was replaced by BS7910. It is therefore a new method of calculating PSFs should be found to prove which is more appropriate and convenient for engineering application. In the case of the partial safety factor method target reliabilities in the range from 0.001 to 0.00001 were considered and new series of PSFs were derived from the results of reliability analysis for the linear elastic fracture mode and elastic-plastic fracture mode. After comparing with the PSFs in BS7910 and API 579, it is concluded that the partial safety factors were generally conservative compared to our research work.

The use of fibre reinforced concrete (FRC) to produce segmental linings of TBM-constructed tunnels is an increasing tendency. So far, more than 50 tunnels have been constructed with this structural material, in some of these even using solely fibres as reinforcement. Moreover, several design guidelines (e.g., fib Model Code 2010) already include the FRC as structural material. There also exist specific guidelines for the design of FRC precast segment linings (e.g., ITAtech Report/7-15 and ACI 544.7R-16). These guidelines deal with the design of FRC considering the traditional limit state safety format. Therefore, partial safety factors for both the loads (γ L ) and material strengths (γ M ) must be considered. In particular, the magnitude of γ M considered for compressive and tensile FRC strengths are assumed to be the same. Nonetheless, this assumption can be unrealistic, particularly in terms of flexural residual strength (f R ) since this property present higher scatter than the compressive strength (f c ). This is particularly true for elements with a reduced cracking surface (e.g., beams) due to the higher impact that uncertainties like fibre orientation and distribution have on the variability of f R . Therefore, this assumption can lead to lower reliability indexes (β) than those established for traditional reinforced concrete structures. However, this variability tends to decrease with the increase of the width of the cracked sections (e.g., slabs). The results of a structural reliability analysis carried out to calibrate partial safety factors for f R is presented. Full-scale bending tests on precast segments with different dimensions, amounts and type of fibers were considered. This partial safety factors could be used in the design of future precast FRC tunnel linings.

In structure design, for expressions with partial safety factors, partial safety factors and nominal value of loads are calculated based on the presupposition that the design reference period is 50 years. When the design reference period is not 50 years, it would cause unclear reliability of building structure by using expressions with partial safety factors following correlative codes yet. It may lead to hidden dangers in that way. In order to derive expressions with partial safety factors suitable for any design reference period, two useful methods are shown in this paper, modification of partial safety factors and modification of importance factor of structures. From results of analysis, we get the conclusions that it can assure the reliability index of the expression using the method of modification of partial safety factors, and the method of modification of importance factor of structures is very simple, but cannot assure the reliability index of the expression.

Valsangkar and Schriver have contributed to furthering the use of limit state design methods in geotechnical engineering. The title of the paper implies partial safety factors for anchored bulkhead design, but the only limit state that was examined was kickout. Design of the bulkhead requires examination of a number of other limit states including anchor rod capacity, sheet pile yield, wale yield, and anchorage capacity (Navfac 1986), and all of these use soil and water pressures in their formulation. It would be desirable to use, for example, the same resistance factor for the soil friction angle for each limit case. To establish the adequacy of the recommended partial safety factors, the other limit states for an anchored bulkhead should also be compared with conventional design. An interesting outcome of this paper is that with the proposed partial safety factors for limit state design, the sequence of solving of statics problem, i.e., how water pressures are introduced into the moment equation, affects the design. The authors recommend that commentary be included in the Canadian Foundation Engineering Manual (Canadian Geotechnical Society 1985) to clarify this point. The partial safety factors discussed by the authors are applied to the loads and resistances in the design and are used to account for uncertainties in these values. However, implicit in these factors are components that account for uncertainties in the dimensions and method of analyses used. Water has no shear strength and virtually no variability of unit weight. The quantity that causes variability in the water pressures is the water level difference, i.e., a dimension. In some cases, such as this water level difference, should a separate factor be considered that would be applied directly to the dimension before being used in the limit state equation? If applied in this case, the sequence of incorporating water pressures in the moment equation would not change the design. For anchored bulkheads in particular, another dimension that should be considered for a separate factor is the dredge depth in front of the bulkhead. Dredging, which often occurs on a regular basis during the life of a bulkhead, may give a higher variability to the passive pressure than would normally be experienced with passive pressure being used in other types of design. Terzaghi (1954), Tschebotarioff (1973), and Navfac (1986), among others, recommend an increase in the embedment depth to account for this. Since this type of partial safety factor is thus used by many in conventional design, more widespread use of a partial safety factor applied to dimensions in limit state design should perhaps be considered.

International design codes for seagoing steel ships of today are in the process of testing a new safety format with load factors separately multiplied with nominal (code) values of still water and wave loads. This leads to two design values of these loads, the sum of which must not exceed a design value of the strength of the ship structure, which is again a nominal (code) value of strength, this time divided by a strength factor. Such load and strength factors are generally termed partial safety factors. In the paper, vertical still water and wave bending moments of containerships are considered as loads. The partial safety factors are determined on the basis of reliability analysis, i.e., the sum of the design values of the loads will not exceed a design serviceability limit state of the ship’s structure with given probability. To enable reliability analysis, distribution density of the ship’s strength to resist bending moments is based on a stochastic interpretation of nominal (code) values used in the conventional safety format. The probability density of the still water bending moment is obtained from recently published statistical data. The probability density of the wave bending moment is calculated using advanced hydrodynamic and spectral analysis, including long-term statistics of the (North Atlantic) seaway. Reliability and related design values are estimated using the FORM algorithm with due consideration of the different repetition numbers for which the stochastic models of the two bending moments are valid. The results are presented as nonlinear regression formulas and as diagrams that specify partial safety factors related to length and beam of containerships. The nominal values of bending moments to be used with these partial safety factors are given as functions of length, beam, and block coefficient of those ships.

New framework for calibration of partial safety factors for fatigue design

The partial safety factors are calculated for three double hull tankers of different size, designed according to the new IACS Common Structural Rules and based on load models estimated from the rule design values. The ultimate strength is calculated using progressive collapse method based on the net scantlings +50% of the corrosion addition, tnet+50, and applying the failure modes defined in the new rules defined in the Common Structural Rules. For one of the tankers the load models are calculated based on the actual load manual data. The still water bending moment is calculated for full load condition and the wave bending moment is based on direct calculations of wave induced load, determining the extreme value. The calculated loads are compared with the rule design values. Another load modeling based on the rule design values is calculated. The reliability and partial safety factors are calculated for both cases to show how the load models affect the values of partial safety factors. Sensitivity analysis is made to study the importance of the variables. The reliability of the three takers is calculated based on the rule design values and the corresponding partial safety factors are assessed. To achieve a certain pre defined level of reliability, a design modification factor is applied to the deck plating to adjust the ultimate strength. The loads are assumed to remain unchanged by the design modification factor.

Design optimisation of wind turbine towers with reliability-based calibration of partial safety factors

This paper investigates the priorities as well as the safety factors of each assessment variable for a defective pipeline based on a partial safety factor concept considering the target failure probabilities during operating period of components of interest. For this, firstly wall-thinned pipeline under internal pressure is considered, which is important in fitness-for-service assessment of corroded pipeline. For the analysis, scatters in the applied pressure, mechanical properties and geometries of wall-thinned pipeline are considered using normal and log-normal distributions. In addition, partial safety factors of a circumferential through-wall cracked pipeline subjected to global bending moment are also evaluated based on the elastic-plastic fracture mechanics. In this case, scatters in the applied bending moment, mechanical and fracture properties are considered based on normal and log-normal distributions. More importantly, two different deterministic integrity assessment methods are applied to wall-thinned pipeline and two different estimation methods of elastic-plastic J-integral are applied to circumferential through-wall cracked pipeline to evaluate the partial safety factors. Resulting values of partial safety factors are calculated using both the advanced first-order second moment method (AFOSM) and the second-order reliability method (SORM). Moreover, the effects of statistical distributions and variations of standard deviations of assessment variables on the partial safety factors are also demonstrated.