Resistance Factor Design Research Articles

Design of MSE Wall with geotextile reinforcement for temporary mitigation of landslide in Padang Panjang – Sicincin road section (STA 64+100)

The Padang Panjang - Sicincin roads section was cut off due to a flash flood on Saturday, 11 May 2024. This caused a landslide in the area resulting in the national road access being cut off, and traffic flow was forced to be diverted to several alternative routes. The study aims to obtain the total length of geotextile at any depth (L), the vertical spacing of the layers (Sv), and the lap length (l1) in MSE wall heights at STA 64 + 100. The computation method for external and internal stability (pull out and break), uses the Load Resistance Factor Design (LRFD). From the calculation results for the effective height (He) of the MSE wall of 8 m, the reinforcement length is 6 m, the embedment depth is 0.6 m, the vertical spacing (Sv) is 0.8 m from the internal stability, and the fold length (l1) is 1 m. The design results obtained MSE wall dimensions that are safe for external and internal stability. These dimensions can be used for temporary landslide handling but not long-term. For long-term stability, adding facing elements like secant piles, cantilever walls, and other forms is recommended to avoid erosion due to river water flow.

Analysis of the Space Frame Structure of the Cileungsi Fly Over Tower Bogor Regency

This research is part of the plan of the Bogor Regency government, especially Cileungsi District, in arranging the Cileungsi flyover which is currently filled with garbage and used as a shadow terminal, making the area look slum. The arrangement effort is made to create a comfortable, neat flyover that can become an icon of Bogor Regency. The research aims to produce a portal tower flyover design that is aesthetic, unique, sturdy, and meets the strength and stability standards of the structure according to local conditions. The analysis was carried out using SAP2000 software to model the three-dimensional space structure and identify the strength, stability, and deflection of the structure. The LRFD (Load Resistance Factor Design) method is used in calculating the bearing capacity of the structure. The results of the analysis show that the space frame structure made of steel pipes has stable and rigid behavior, meeting all work loads, including dead loads, live loads, wind, and earthquakes. The design of the 13-meter deep pile foundation has also been proven to be able to withstand loads safely. The design of the space frame structure made of steel pipes for the Cileungsi flyover portal tower is declared strong, stable, and safe to implement. This structure can be used as a new icon for Bogor Regency, especially Cileungsi District. The implementation of this design requires detailed depiction as a construction guideline in the field.

An ULS reliability-based design method for mooring lines using an efficient full long-term approach

In the long-term scenario, the environmental actions to which floating offshore structures are subjected to, such as waves, wind and current, are non-stationary stochastic processes. However, this long-term behavior is usually modeled as a series of short-term stationary conditions. In a full long-term analysis approach, an estimate of the N-year response can be obtained through a multi-dimensional integration over expected short-term environmental conditions. An innovative and more efficient long-term integration approach based on the Importance Sampling Monte Carlo Simulation (ISMCS) method is presented, where the uniform distribution over an environmental contour is used as the sampling function. In parallel, a multi-dimensional joint environmental model that statistically describes all relevant environmental parameters is employed, contemplating linear and directional variables, and thoroughly accounting for the occurrences of wind waves and swell. The methodology is applied to two FPSOs systems installed in Brazilian ultradeep waters. Ultimately, a design-oriented procedure based on the developed methodologies is provided, using an Ultimate Limit State (ULS) reliability-based design with calibrated safety factors in an LRFD (Load and Resistance Factors Design) format. It is shown that the developed procedures can be powerful tools to account for the simultaneous occurrence of wind sea and swell waves in offshore system response evaluations required in the design and life extension analyses.

Evaluation of Minimum Web Reinforcement Requirements for Slender and Non-Slender Beams

Prescriptive shear requirements in the U.S. from the American Concrete Institute (ACI) 318 (2019), the American Association of State Highway and Transportation Officials Load and Resistance Factor Design (AASHTO LRFD) Bridge Design Specifications (2020), and the fédération international du béton Model Code ( fib MC) (2010) include a minimum web reinforcement requirement. In general, slender beams require a minimum area of web reinforcement equal to 0.08% of the cross-section, while non-slender beams require up to 0.30%, or roughly three times more than the slender beam requirement. This investigation aims to evaluate the discrepancy between these requirements in relation to the strength and serviceability behavior of experimental test data. This is carried out through an analysis of existing and peer-reviewed databases. The results show that the minimum web reinforcement needed to ensure shear strength is consistent with code requirements for slender beams, but not non-slender beams. The minimum web reinforcement needed to restrain crack widths is consistent with code requirements for non-slender beams, but not slender beams. Thus, the prescriptive web reinforcement requirements for slender and non-slender beams do not appear to be derived from the same criteria. The requirement for slender beams is derived based on these members achieving their predicted strength, while the requirement for non-slender beams is derived based on the width of in-service cracks.

Explicit consideration of geomaterial uncertainties in the load resistance factor design of piles driven into rock-based intermediate geomaterials

The study presents a method for estimating the end bearing of piles driven into rock-based intermediate geomaterials (IGMs). Existing design methods, rooted in soil mechanics, often fall short when applied to IGMs. Moreover, the geomaterial (geological and ground properties) uncertainties are neglected and the piles are designed based on subsurface information from distant boreholes. To address this gap, the study introduces an approach that explicitly considers geomaterial uncertainties by combining empirical models and geostatistical simulation to predict end bearing. Using data from 87 piles driven into various rock-based IGMs with dynamic load testing as the construction control technique, this study introduces the Proposed Design Method (PDM) for the prediction of end bearing. PDM is compared to the Current Design Method (CDM), which is based on traditional soil-mechanics methods. Predictions from these methods are subsequently evaluated against the measured end bearings. The results demonstrate that while the PDM yields comparable predictions to the CDM, it offers a more robust consideration of geomaterial uncertainties. The PDM leads to an approximate 13.60% to 19.35% increase in uncertainties compared to CDM across various IGMs. These findings advance the understanding of pile behavior in the presence of geomaterial uncertainties and inherent variability.

A Reliability-Based Design Approach for the Flexural Resistance of Compression Yielded Fibre-Reinforced Polymer (FRP)-Reinforced Concrete Beams

Fibre-reinforced polymer (FRP) reinforcement has been employed as an alternative to conventional steel reinforcement in concrete structures, which is attributed to its excellent strength and corrosion resistance. However, one drawback is that FRP reinforcements are brittle and affect the ductility of concrete structures. One of the recent effective techniques proposed to overcome ductility issues is the compression yielding (CY) concept. The CY mechanism allows the structure to fail differently than the conventional FRP-reinforced concrete structure. Thus, the existing design recommendations as per the current codes for FRP-reinforced concrete structures are not appropriate. Hence, reliability studies are crucial for the development of a functional CY beam design in order to emphasise the structure’s lifetime performance and to guarantee safety requirements. In this study, a reliability-based design approach is developed for a compression-yielded FRP-reinforced concrete beam (CY beam) using load and resistance factor design (LRFD). Firstly, the flexural failure modes of CY beams are discussed. The uncertainties involved in the development of the probabilistic model for the CY beam are defined. A case study is consequently conducted for a CY beam with random variables that are associated with the statistical characteristics of material properties and load. The reliability analysis method employed in this research is the Hasofer–Lind method. The results suggest the importance of choosing appropriate design variables and stochastic parameters for CY blocks that contribute to a higher level of reliability. The reliability index and resistance factors of a CY beam are then evaluated using the Monte Carlo Simulation computational method. The reliability index value of 3.336 is obtained from the simulation, which indicates that the CY beam demonstrates ductile behaviour. The results not only demonstrate ductile behaviour but also contribute to a possible reduction in material costs and a substantial safety margin. When compared to conventional FRP-reinforced concrete beams, for different load ratios, CY beams showed higher resistance and better reliability levels.

Calibrating resistance factors of pile groups based on individual pile proof load tests

Pile load tests have been utilized to reduce the uncertainty of pile resistance, thus leading to a higher resistance factor used in the Load and Resistance Factor Design (LRFD). Previous studies have primarily focused on calibrating resistance factors for single piles based on load tests. This calibration hinges upon the resistance bias factor of single piles, defined as the ratio of measured resistance to predicted resistance. Due to the redundancy in the pile group system, it is conventionally assumed that if the individual piles within the group achieve a lower reliability index (e.g., 2.0–2.5), the pile group as a whole attains the target reliability index of 3. However, the approach is empirical as it does not consider system redundancy directly. Moreover, this empirical approach disregards the correlation between resistance bias factors of individual piles, which is inherently influenced by the spatial variability of soils. In this study, the random finite difference method (RFDM) is employed to evaluate the correlation between resistance bias factors of individual piles in spatially variable soils. The resultant correlation matrix is subsequentially employed in Bayes’ theorem to update resistance bias factors using individual pile load test results and their corresponding test locations. The updated resistance bias factors are then used for the direct calibration of resistance factors for pile groups within the framework of LRFD. A pile group subject to vertical loading in undrained clays is adopted for illustration. Comparative analyses between the proposed approach and the empirical approach demonstrate that the latter tends to overestimate the resistance factor. Furthermore, the proposed approach enables the determination of optimal locations for conducting subsequent load tests based on previous test results.

Experimental evaluation and design of fillet welds under in-plane eccentric loads

The principal objective of this investigation is to furnish equations to compute the design strength of fillet welds under in-plane eccentric loads suitable for load and resistance factor design (LRFD) applications. Over the years, experimental and analytical techniques have been used to arrive at safe estimates for the strength of such welds in common practical applications. The conventional elastic design (ED) method is very conservative and is not compatible with the LRFD design philosophy. In addition, the ED method neglects the weld group's ductility and strain compatibility. On the other hand, the instantaneous center of rotation (IC) method considers the above parameters but requires complex calculations. In the present study, a method for designing fillet welds under eccentric loading is introduced called the plastic design (PD) method. This method considers the inelastic properties of the welds in a simple manner while providing an accurate prediction of the weld group's capacity. The performance of the proposed PD method was compared with the IC method for several cases. The ultimate loads obtained were mostly within 10% difference on the conservative side and only marginally different for a few. Additionally, the fillet weld group's resistance under in-plane eccentric loads was evaluated experimentally using 12C-shaped specimens with the load applied at different angles of 0, 45, and 75°. The test results also confirmed the efficacy of the proposed PD method in evaluating the design strength of such weld groups.

Advanced analysis of intact, fire-damaged, and CFRP retrofitted bridge pier columns under vehicle collisions: Empirical equivalent static force equation and framework

A series of numerical simulations were completed to investigate the behavior of intact, fire-damaged, and Carbon Fiber-Reinforced Polymers (CFRP) retrofitted reinforced concrete (RC) bridge columns of varying sizes subjected to vehicle collisions. Three-dimensional finite element models of isolated RC columns and their foundation systems surrounded by soil volumes were developed using LS-DYNA. A comprehensive parametric study was carried out to investigate the effects of nine demand and design parameters on the performance of bridge columns. Studied parameters included: column diameter, column height, unconfined compressive strength, steel reinforcement ratio, fire duration, CFRP wrap thickness, wrapping configuration, vehicle’s mass, and vehicle’s speed. For each studied scenario, Peak Twenty-five Milli-second Moving Average (PTMSA) was employed to estimate the Equivalent Static Force (ESF) corresponding to each vehicle collision scenario. Resulting ESFs were then utilized to assess effectiveness of the current ESF approach available in the American Association of State Highway and Transportation Officials Load and Resistance Factor Design (AASHTO-LRFD) Bridge Design Specification for analyzing and helping design bridge columns under vehicle collision. Multivariate nonlinear regression analyses were used to derive an empirically based, simplified equation to predict the ESF that corresponds to a vehicle collision. Rather than constant design force, this equation established a correlation between ESF and kinetic energy, column axial capacity, and column height. Results indicated that the proposed equation is reliable and can accurately predict ESFs over a diverse range of collision scenarios that included intact, fire damaged, and CFRP retrofitted columns. To facilitate realistic implementation of the derived equation, an ESF assessment framework was also devised.

Seismic design optimization of space steel frame buildings equipped with triple friction pendulum base isolators

To increase the seismic resilience of structures, it is necessary to utilize seismic isolation to increase structural periods and reduce story drifts. When seismic isolation is implemented, structures are capable of deforming by remaining within safe limits. Thus, more seismically resilient designs are achieved compared to conventional fixed-based structures since lighter structural design weights are attained. The principal aim of this study is to achieve the comparative design optimization of space steel frame buildings equipped with seismic base isolation and to examine the effect of seismic base isolation on optimum structural design weight by comparing the same structures with conventional rigid-based ones. For seismic base isolation, triple friction pendulums are implemented into steel frame buildings. For this aim, four different space steel frame buildings with 4-, 6-, 8-, and 10-story are treated as design examples. A novel design optimization algorithm is encoded, which includes nature-inspired metaheuristic artificial bee colony, crow search, and Archimedes optimization algorithms to achieve design optimizations of triple friction pendulums equipped with seismic-isolated space steel frame buildings. The practice code provisions of load and resistance factor design specification for structural steel buildings have been applied to control the structural design constraints of inter-story drift, top-story drift, strength, displacement, and connections geometry of beams and columns. Eventually, it has been remarked that seismic base isolation significantly reduces the structural optimal design weight of space steel frame buildings.

System reliability-based design of composite frames with concrete – filled steel plate shear walls

Nowadays, many high-rise buildings are constructed from concrete-filled steel tubular (CFST) columns and concrete-filled steel plate (CFSP) shear walls due to their superior merits. However, these composite buildings are still designed by traditional load and resistance factor design (LRFD) approach which is conservative and impossible to explicitly capture the complex behaviour of CFST structures. Hence, this paper develops an efficient framework for the system design of CFST structures utilizing nonlinear simulation and reliability analysis. Firstly, a C+ + source code for a new material model is developed in OpenSees to capture the behaviour of semi-rigid connections. This material is implemented into the numerical model of CFST structures. Secondly, a framework based on subset simulation is developed for the reliability analysis. This code rigorously considers uncertainties of variables such as numerical model, geometric and material properties or applied loads of both American (US) and Australian (AS) standards. Finally, case study and parametric study are conducted by using the developed framework to propose resistance reduction factors for the investigated frames. The results of the study show that the resistance reduction factor can be taken as 0.8 for both AS and US codes. This proposed factor can be a great source of reference for the system design of CFST buildings with composite shear walls.

Improved Wave Equation Analysis for Piles in Soil-Based Intermediate Geomaterials with LRFD Recommendations and Economic Impact Assessment

The Wave Equation Analysis of Pile Driving (WEAP) has been widely used to determine drivability, predict static resistance, and assure the integrity of piles in soils. Assigning static and dynamic properties of Soil-based Intermediate Geomaterials (S-IGMs) remains a challenge in WEAP, partly attributed to IGMs that act as transition geomaterials between soil and hard rock. Furthermore, reliable static analysis methods for unit resistance predictions are rarely available for driven piles in S-IGMs in the default WEAP method. To alleviate these challenges, this study presents improved WEAP methods for steel piles driven in S-IGMs, including proposed damping parameters and Load and Resistance Factor Design (LRFD) recommendations based on newly developed static analysis methods and the classification of S-IGMs. A back calculation approach is used to generate the appropriate damping parameters for S-IGMs for three distinct subsurface conditions utilizing a database of 34 steel H- and pipe piles. Newly developed WEAP and LRFD procedures are also recommended. Additional independent 22 test pile data are used to compare and evaluate the accuracy and efficiency of the proposed WEAP methods with the default WEAP method. Compared with the default WEAP, bearing graph analysis results revealed that the selected proposed WEAP method, on average, reduces the underprediction of pile resistances by 6% and improves the reliability with a 43% reduction in the coefficient of variation (COV). Calibrated resistance factors for the proposed WEAP method increase to as high as 0.75 compared to the current AASHTO recommendation of 0.50. An economic impact assessment reveals that the proposed WEAP method is more efficient than the default WEAP method as the average difference in steel weight for 32 test piles is 0.06 kg/kN, almost close to zero, reducing the construction challenges in the current engineering practice.

Resistance Factor Spectra for the Ultimate Limit State of the National Building Code of Canada

Over the years, structural engineering codes and specifications in Canada and elsewhere have moved from an allowable stress design (ASD) approach to a load and resistance factor design (LRFD) philosophy. LRFD methodology takes better account of the inherent variability in both loading and resistance by providing different factors of safety for loads of distinct natures with regard to their probability of overload, frequency of occurrences and changes in point of application. The method also results in safer structures because it considers the behavior at collapse. While resistance factors for traditional construction materials based on LRFD in the National Building Code (NBC) of Canada are available, they cannot be used for non-conventional ones. This is because the resistance of such materials due to various load effects has unique bias factors (λR) and coefficients of variation (VR), which greatly impact their reliability index (β). In this study, relationships between the resistance factor ϕ and critical load effects from the NBC load combinations at ultimate limit states are developed for a wide range of resistance bias factors and coefficients of variation. The relationships are presented in the form of charts that are useful for researchers and code-writing professionals who have expertise in the various fields of structural engineering but lack proper background in reliability theory. The developed spectra showed that for the same ϕ, β increases with an increase in the live-to-dead load (L/D) ratio until it reaches 1; thereafter, the shape of the relationship will depend on the statistics of the resistance as well as on the magnitude of ϕ. For a small ϕ and VR, β will keep increasing with an increase in the L/D ratio from 1 until 3, albeit at a lesser rate. For L/D > 3, the relationship between the critical β and applied load is just about constant. This finding is also true for load combinations involving snow and wind. Application of the method is illustrated by a practical example involving the shear strength of a corrugated web steel beam.

Resistance factors for reliability based-design of geogrid reinforced soil foundations against ultimate and serviceability limit state

In the recent decades, the use of geosynthetics to improve the overall soil’s bearing capacity and settlement behavior under shallow foundations has become a major topic. Despite several studies that have been carried out on Reinforced Soil Foundations (RSF), no design specifications have been set to design RSF against the Ultimate and Serviceability Limit State (ULS and SLS) in any of the established codes. This paper presents the development of resistance factors based on the Load and Resistance Factor design (LRFD) approach against the ULS and SLS for strip footing resting on C−ϕ soils. The resistance factors are developed using a spreadsheet-based reliability model based on the First Order Reliability Method (FORM) to be consistent with the ASCE-7 load factors. The resistance factors are calibrated at a targeted probability failure (Pf) of 0.13499% and 0.00317% for ULS and 2.27%, for SLS. A Finite Element Model (FEM) is developed to validate three analytical solutions to establish the reliability model. The FEM results showed an agreement with the analytical solutions. For ULS the developed resistance factors at Pf= 0.13499% ranged from 0.33 to 0.9 assuming lognormally distributed variables and 0.25 to 0.89 assuming normally distributed variables. The resistance factors against SLS at Pf= 2.27%. ranged from 0.39 to 0.85 considering lognormally distributed variables and 0.35 to 0.83 considering normally distributed variables.

A reliability-based assessment framework for drag anchors

Drag anchors are often employed in offshore floating facility moorings. The standard drag anchor design approach is based on a deterministic load and resistance factor design (LRFD) framework that considers characteristic design “low” and “high” estimates of soil strength and other geotechnical parameters, combined with code-specified partial factors. A disadvantage of this approach is that the resulting anchor designs may not achieve a consistent level of reliability. This paper describes a study that addresses this limitation by developing and demonstrating a generalised drag anchor probability of failure analysis framework for inclusion in a reliability-based assessment (RBA) of a mooring. A feature of the study is the inclusion of consolidation and cyclic loading effects in the anchor analysis. The study highlights the benefits an RBA approach can offer to the drag anchor design process, including reduced anchor size and preloading requirements, and increased confidence in the anchor design and estimate of anchor performance. For temporarily moored facilities, this approach offers the potential to exploit expanded weather windows for operations. For permanently moored floating offshore wind developments, this approach may allow adoption of reduced levels of target reliability, thereby reducing costs for systems with a large number of anchors.

Comparative study on semi-probabilistic design methods to calibrate load and resistance factors for sliding stability design of caisson breakwaters

The partial safety factor method commonly necessitates a set of multiplying factors (MFs) to modify the basic variables; hence, when multiple variables are included, it is complicated for design practice. Conversely, the load and resistance factor design (LRFD) format is more practical since it utilizes fewer factors to adjust loads and resistance. This study carries out a comparative study of the two semi-probabilistic design formats and four calibration methods to determine the more suitable design approach and establish associated factors for sliding stability designs of caisson breakwaters under wave and seismic conditions. To fulfill the aforementioned purposes, 12 perforated caisson breakwaters are first selected; thereafter, four calibration methods, which include a closed-form solution and three scenarios based on Monte Carlo simulation (MCS), are executed to determine individual MFs for each case. The final single set of MFs for design practice is calibrated via an optimization process. The present study shows that the two design formats can provide similar solutions. Hence, the LRFD-based concept is recommended to be applied owing to its easier implementation in code calibrations and design practices. Moreover, the performance of the shifting-technique-MCS-based calibration (the simplest simulation) is thoroughly investigated, and it is then found that this approach must be used with care if the target safety considerably varies from the initial safety level. In the present work, an efficient and accurate approximation method to specify the final MFs set is proposed because the optimization-based calibrations to determine the final set of MFs are time-consuming and expensive to evaluate.

Estimation of confidence in the calculated resistance factor for simple limit states with limited data for load and resistance model bias

The estimation of the resistance factor in load and resistance factor design (LRFD) calibration for simple soil–structure limit states is most often based on model bias data of limited size. Frequently, the bias data are only available or required for the resistance term. In this study, the confidence in the estimate of the mean of the resistance factor is computed for the case of one resistance factor and one load factor where limited model bias data are available for both load and resistance terms. The bootstrap method is used to compute synthetic load and resistance bias data sets from which confidence intervals on the point (mean) estimate of the resistance factor and load factor are computed. A closed-form solution is used to calculate the resistance factor for a single prescribed load factor and target reliability index, bias data, and nominal load and resistance variables that are lognormally distributed. However, the approach is general using Monte Carlo simulation. The method is demonstrated using the case of the internal stability pullout limit state for steel strip mechanically stabilized earth walls. The example demonstrates the quantitative influence on pullout design using upper and lower 95% confidence interval limits for load and resistance factors.

Derivation of stainless steel material factors for European and U.S. design standards

Modern structural design standards are based on the Limit State Design (LSD) philosophy, also known as Load and Resistance Factor Design (LRFD), which involves the use of resistance functions with accompanying safety factors that are based on a statistical evaluation of relevant experimental data, carried out within the framework of a probabilistic reliability theory. This paper presents the derivation of material factors for the yield strength and ultimate tensile strength of austenitic, duplex and ferritic stainless steels, and their associated coefficients of variation (COV) for use in evaluating the safety factors for the European design code EN 1993-1-4 and the American design codes Specification for Structural Stainless Steel Buildings (ANSI/AISC 370–21) and Specification for the Design of Cold-Formed Stainless Steel Structural Members (ASCE/SEI 8–22). Separate material factors and associated COV values are required for the U.S. and European design codes due to the different minimum specified strength values that are given in the respective product standards. The material factors were derived by analysing a large amount of material data provided by different stainless steel producers, which encompassed a wide range of stainless steels and material thicknesses.

ASD and LRFD: Reliability comparison for designs subjected to wind loads

Current design practice in the United States allows engineers to use either Allowable Strength Design (ASD) or Load and Resistance Factor Design (LRFD) method, under the assumption that both methods provide similar levels of economy (available design strengths) and safety (probabilities of failure and reliability indices) regardless of the design conditions. Recent studies have demonstrated that significant differences in economy can arise between ASD- and LRFD-based designs subjected to combinations of gravity and wind loads, suggesting inconsistencies between the safety levels. This study investigates the safety levels provided by the ASD and LRFD methods for such design cases. The safety levels were estimated using a formal reliability analysis with consideration of geometrically non-linear second-order effects. The reliability analysis was performed using Monte Carlo simulations with appropriate probability distributions for the random variables associated with both resistance and loads. The findings of this study indicate that generally accepted uniformity of reliabilities achieved by the ASD and LRFD methods does not hold for design cases governed by wind loads. The safety levels achieved by using the ASD method are less consistent than those achieved by using the LRFD method. The use of the ASD method generally entails the acceptance of failure risks many times greater than for those of the LRFD method, and target safety levels lower than those stipulated by the ASCE 7 Standard. These results highlight the need for a reevaluation of the current design practices to ensure that the required target levels of structural safety are consistently met.

Reliability-based factor of safety for bearing capacity of square foundations on 3D cohesive-frictionless soils considering samples

Reliability-based design concepts have been widely adopted in structural engineering but remain less prevalent in geotechnical practice due to the challenges of characterising ground uncertainties. To facilitate the unification of structural and geotechnical designs in complex engineering systems, we focus on square shallow foundations as crucial elements. Before a complete transition to load and resistance factor design, understanding the reliability of foundations designed using traditional factors of safety is essential. This paper presents a simplified analytical method for evaluating the probability of failure of square shallow foundations on 3D cohesive soils, utilising local average theory. The approach efficiently computes local averages and covariances of soil properties without the need for time-consuming 3D finite element computations. Verified against random finite element analysis, the method accurately determines required factors of safety for bearing capacity designs. Site-specific parameters, including sample location, shear strength coefficient of variation, and spatial variability fluctuation scale, influence the derived factors of safety. We advocate a pragmatic approach that calibrates traditional factor of safety methods with rigorous reliability theories, easing the transition to reliability-based design for practicing engineers. Moreover, the determined factors of safety can aid in establishing appropriate resistance factors by considering suitable load factors.