Geo-Trends Review

You can visit the link below to access my article publication related to what you seek. I hope this helps.

https://doi.org/10.17576/jkukm-2023-35(3)-19

A very interesting question Fayrouz, and one that is worthy of discussion because there is a lot of misundertsanding around the issues.

First we need to clarify that you are talking about Lumped Factors of Safety. I often refer to these as "magic numbers", becasue of the range of things that we expect them to cover, which include in general:

• Dead load uncertainty
• Live load uncertainty
• Load combination uncertainty
• Spatial variation of geotechnical parameters within a unit
• Spatial variation of geometry of a unit
• Soil sampling disturbance
• Laboratory testing uncertainty
• Anisotropy
• Geostructure intallation disturbance
• Model uncertainty
• Acceptable settlement at working loaad

When you realise that you are expecting all of these things to be covered by one simple lumped factor, it should help you to realise why the numbers vary. You have given two examples, of slope stability and bearing capacity, so let's look quickly at those. In the list we included "model uncertainty", and when we analyse slope satbility we usually use the method of slices. This is a limit equilibrium approach which requires that all points on the failure surface meet their peak strength at the same displacement, but this is not likely to happen in practice. A slope failure will ususally initiate near the toe, and the failure surface will progressively develop up to the crest, so that uncertainty needs to be allowed for. We also included "acceptable settlement at working load", and must note that the movements associated with bearing capacity failure of a surface footing are large, much too large to be acceptable for a building foundation, hence a larger "Factor of Safety" is required.

All of this leads to the preferred use of Limit State Design, because this breaks the Lumped Factor of Safety down into many separate Partial Factors, which can be allocated based on the uncertainty and influence of the different parts of the calculation. Most obviously, Permanent Loads are generally better known, through dimensions and known weights of materials, than Imposed Loads (or Live Loads) which can be very variable, such as wind or traffic. Therefore the Imposed Loads have higher Partial Factors. Similarly it is recognised that we can measure the angle of friction more relaibly than the apparent cohesion (which varies with confining pressure), so the partial reduction factors applied to tan phi' are nearer to 1 than those applied to c'. When it comes to allowable settlement this is dealt with quite separately at the Serviceability Limit State, usually using unfactored loads so that settlement is estimated at the working load, but it does attempt a realistic calculation of settlement so requires you to know deformation parameters and not just strength parameters.

Finally, the Partial Factors are selected such that there is an acceptably low Probability of Failure of the designed system. It is a fact that again is not well understood, that there is an inherent assumption in civil engineering that failure could occur, such as by an extreme natural event like a flood, tornado or earthquake for example, or an extreme truck load going over a bridge. We have to make estimates of the likelihood of an extreme event, and then look at the likely damage, and balance that against the cost of preventing failure, for example by building a dam higher, remembering that with a triangular shape, raising tjhe crest by 1 m involves a huge increase in the volume of the dam. People don't like talking about failure, or Probability of Failure, so we tend to use the Reliability Index, which is related by a mathematical formula. Partial Factors in LSD are then selected to achieve a given Reliability Index, and these are chosen by Governments through national standards.

I hope that helps you to understand.

Stephen

This is an excellent question regarding the fundamental principles underlying factor of safety selection in geotechnical practice. The differentiation between slope stability factors (typically 1.5) and bearing capacity factors (typically 3.0) reflects sophisticated risk assessment methodologies rooted in probabilistic analysis, failure consequences, and uncertainty quantification.

I'll present a comprehensive theoretical foundations, regulatory frameworks, and empirical methodologies that govern these critical design parameters, as follows.

Factor of Safety Fundamentals in Geotechnical Design

The theoretical and practical foundations governing factor of safety selection in geotechnical engineering reveal a sophisticated framework where slope stability analyses typically use factors of 1.3-1.5 while bearing capacity calculations require 2.5-3.0, reflecting fundamental differences in failure mechanisms, risk characteristics, and design objectives. This disparity stems from rigorous engineering principles rather than arbitrary convention, with modern practice increasingly adopting risk-based approaches that explicitly account for uncertainty, consequences, and reliability targets.

Theoretical foundations driving safety factor differences

The fundamental distinction between slope stability and bearing capacity safety factors originates from limit state design theory and the specific failure mechanisms each analysis addresses. Slope stability focuses primarily on the Ultimate Limit State (ULS) - preventing catastrophic mass movement through limit equilibrium analysis where the factor of safety represents the ratio of available shear strength to mobilized shear stress along a failure surface. These analyses benefit from progressive failure characteristics that often provide observable warning signs and allow time for intervention.

In contrast, bearing capacity calculations must satisfy both Ultimate Limit State and Serviceability Limit State (SLS) requirements simultaneously. The critical insight is that settlement control, not shear failure prevention, drives the higher safety factors used in foundation design. Research from the University of West England confirms that "a value for Fs of 2.5-3.0 is sufficiently high to empirically limit settlement" - the primary reason bearing capacity factors exceed slope stability values.

This theoretical framework explains why different failure mechanisms require different safety margins. Slope failures typically involve large displacement only at failure with clear failure criteria, while bearing capacity failures can involve significant settlements well before shear failure occurs. The dual criteria requirement in foundation design - preventing both shear failure and controlling settlement - necessitates the higher safety factors observed in practice.

Historical development and scholarly evolution

The foundation of modern geotechnical safety factors traces directly to Karl Terzaghi's seminal 1943 work "Theoretical Soil Mechanics," which established the values still used today. The New Zealand Geotechnical Society documents that "Terzaghi presents a target FoS of 1.5 for slope stability" and simultaneously established 2.5-3.0 for bearing capacity, creating the fundamental framework through empirical observation and engineering judgment.

The golden age of method development (1950s-1960s) saw systematic refinement by pioneers including Bishop (1955), Morgenstern and Price (1965), Spencer (1967), and Janbu (1973), who developed the rigorous analytical methods supporting these safety factor values. Throughout this period, the 1.5 factor for slope stability became increasingly standardized while bearing capacity factors remained higher due to settlement control requirements.

Major geotechnical failures profoundly shaped safety factor evolution. The 1963 Vajont Dam disaster killed approximately 2,000 people and became a watershed moment, highlighting the need for thorough geological investigations and more rigorous slope stability analyses. This tragedy and similar events led to enhanced emphasis on geological uncertainty and the development of observational methods and monitoring systems.

The transition from allowable stress design to limit state design (1970s-present) marked a fundamental philosophical shift. The introduction of Load and Resistance Factor Design (LRFD) in the 1980s brought separate treatment of load and resistance uncertainties, while the emergence of reliability-based design in the 1970s-1990s provided mathematical frameworks for probabilistic factor selection. This evolution demonstrates the maturation of geotechnical engineering from empirical art to probabilistic science.

Regulatory standards and international approaches

Modern geotechnical design codes employ sophisticated approaches to safety factor specification, with Eurocode 7 leading the transition to partial factor methodology. Rather than single global factors, Eurocode 7 employs separate factors for Actions (A), Materials (M), and Resistance (R) with values ranging from 1.0 to 1.5 applied to different uncertainty sources. This approach acknowledges that different uncertainties require different treatment, providing more rational design than traditional global factors.

AASHTO LRFD Bridge Design Specifications implements Load and Resistance Factor Design with resistance factors typically ranging from 0.35 to 0.8 depending on soil type, analysis method, and property variability. The system targets probability of failure of 0.0003 (1 in 3,500 structures) through statistical calibration of factors to regional geology and construction practices.

International standards reveal fascinating variations in approach. Australian Standards (AS 2159) employs risk-based geotechnical reduction factors ranging from 0.40 to 0.90 based on Individual Risk Rating (IRR) and Average Risk Rating (ARR) systems. Germany selected Design Approach 2 Modified (DA2)* for Eurocode 7 implementation because it best maintains their traditional safety levels while providing economic design.

The International Building Code (IBC) maintains traditional prescriptive approaches with minimum factor of safety of 1.5 for retaining walls and 3.0 for uplift capacity in deep foundations, prioritizing simplicity and proven performance over sophisticated probabilistic methods.

Probabilistic foundations and uncertainty quantification

The mathematical relationship between reliability indices and safety factors provides the scientific foundation for factor selection. For lognormal distributions common in geotechnical applications, the reliability index = ln(_FS) / [ln(1 + V²)], where V represents the coefficient of variation of the safety factor. Modern codes typically target reliability indices of 3.2-3.8 for ultimate limit states (probability of failure 10 to 10) and 2.3-3.0 for serviceability limit states (10² to 10³).

Uncertainty quantification reveals fundamental differences between slope stability and bearing capacity problems. Slope stability uncertainties primarily involve shear strength parameters (COV = 15-30%) and spatial variability effects, with large failure surfaces averaging spatial variability. Bearing capacity faces bearing capacity equation uncertainty, local soil conditions, and model uncertainty that can be more significant than parameter uncertainty.

Spatial variability profoundly affects reliability calculations. Research demonstrates that correlation length affects reliability significantly, with larger failure surfaces averaging out spatial variability more effectively. Random field analysis shows that coefficient of variation in resistance can be reduced from 0.5 to 0.3 with adequate site investigation, directly impacting appropriate safety factor selection.

Monte Carlo simulation and First-Order Reliability Method (FORM) enable sophisticated uncertainty propagation and reliability analysis. These methods reveal that current LRFD implementations don't necessarily provide more consistent reliability than traditional methods, with dispersion in design failure probabilities spanning 5-7 orders of magnitude.

Practical implementation and real-world considerations

Modern geotechnical practice increasingly employs consequence classification systems that link safety factors to potential failure impacts. The New Zealand Geotechnical Society's risk-based approach categorizes consequences from Minor-Low (no fatalities, 0-2 houses damaged) to Disastrous (>100 fatalities, >1000 houses damaged), with corresponding safety factors ranging from 1.2-1.5 for minor consequences to 1.6-2.5 for catastrophic consequences.

Load type considerations require different safety factor approaches. Static loading typically requires factors of 1.5-2.0 for long-term conditions, while seismic conditions often use factors of 1.0-1.2 through pseudo-static analysis. Dynamic loading and high groundwater conditions introduce additional complexity requiring specialized factor selection based on return periods and consequence classification.

Construction method considerations significantly impact safety factor selection. Temporary structures (excavation support, construction platforms) justify lower factors of 1.2-1.6 due to limited exposure time, while permanent structures require higher factors reflecting long-term performance requirements. Construction quality control directly influences achieved reliability, with higher quality control justifying lower design safety factors while maintaining equivalent safety levels.

The Level of Engineering (LoE) concept provides a systematic framework for adjusting safety factors based on investigation quality. LoE I (best practice) with continuous sampling and extensive testing allows factors of 1.2-1.6, while LoE IV (poor practice) requires factors of 1.8-2.5 to achieve equivalent risk levels.

Economic optimization and risk management

Economic optimization reveals that optimal safety factors result from balancing investigation costs, construction costs, and expected failure costs. Research demonstrates that routine structures achieve good cost-benefit ratios with factors of 1.5-2.0, while critical structures justify higher factors of 2.0-3.0 based on failure consequences. Temporary works appropriately use lower factors of 1.2-1.5 due to limited exposure periods.

Probabilistic approaches increasingly replace deterministic methods for critical projects, providing better risk quantification and communication. Case studies using Rocscience analysis demonstrated that single factor of safety values can be misleading, with probabilistic analysis revealing probability of failure of 6.4% despite a mean factor of safety of 1.34.

Performance-based design integrates monitoring and feedback systems, allowing lower initial safety factors when combined with observational methods. This approach requires clear performance criteria, real-time monitoring, predetermined corrective actions, and qualified personnel for data interpretation.

Professional guidance and authoritative sources

The research reveals extensive documentation in peer-reviewed academic literature supporting these safety factor values. Key theoretical foundations appear in classic texts by Terzaghi (1943), Bishop (1955), Duncan & Wright, and Bowles, while modern developments are documented in journals including the Journal of Geotechnical and Geoenvironmental Engineering, Géotechnique, Canadian Geotechnical Journal, and Engineering Geology.

Professional society publications from ASCE, ICE, CGS, and NZGS provide comprehensive guidance on practical implementation, while regulatory standards including Eurocode 7, AASHTO LRFD, IBC, and Australian Standards specify detailed requirements with technical justifications.

Industry best practices emphasize matching investigation level to project consequences, using probabilistic methods for critical projects, considering construction quality in factor selection, and implementing monitoring systems. Common pitfalls include using fixed factors without considering uncertainty, inadequate site investigation, and poor risk communication to stakeholders.

Conclusion

The apparent disparity between slope stability (1.3-1.5) and bearing capacity (2.5-3.0) safety factors reflects sophisticated engineering principles rather than arbitrary convention. Settlement control requirements drive higher bearing capacity factors, while progressive failure characteristics in slope stability allow lower factors with appropriate risk management. The evolution from empirical approaches to probabilistic methods demonstrates the maturation of geotechnical engineering, providing mathematical frameworks for rational factor selection based on uncertainty quantification, consequence assessment, and reliability targets.

Modern practice increasingly adopts risk-based approaches that explicitly account for failure consequences, load characteristics, soil variability, construction methods, and economic optimization. This evolution enables more rational and cost-effective designs while maintaining appropriate safety levels through systematic consideration of uncertainty and risk rather than reliance on traditional fixed values.

The research confirms that factor of safety selection in geotechnical design is grounded in rigorous theoretical foundations, supported by extensive academic literature, professional guidance, and regulatory standards that provide comprehensive frameworks for practical implementation. The continuing evolution toward probabilistic methods and risk-based design represents a significant advancement in engineering practice, enabling optimized designs that balance safety, economy, and performance through explicit consideration of uncertainty and consequences.

A very comprehensive reply Dr Costas, but I would like to take issue with two points, the first of which I find is a common misundertsanding and can be dangerous. You refer to "Temporary works appropriately use lower factors of 1.2-1.5 due to limited exposure periods.", but this is only relevant when your analysis includes time based parameters, such as rainfall for example. It does not apply when we are only concerned with spatial variation, and where life safety is concerned which is true of many temporary works situations. I am very much involved with working platforms for tracked plant, where the concequences of failure could be horrendous, and there is no justiifctaion for the use of reduced Factors of Safety and Partial Factors.

The second is the mixing up of the terms Factor of Safety and Partial Factors. These are quite different, and it is much safer for those with less experience to keep them separate. Taking an example, again from working platforms, there is a widely accepted method which uses empirical loading factors in a working stress design, but these are too often used as Factors of Safety in quite different methods.

Cheers

Thank you for the detailed insights. Here's my brief perspective. 
Safety factors reflect the nature of failure and uncertaintyFS 1.5 for slopes due to progressive failure with warning, while FS 3.0 for bearing capacity accounts for sudden, brittle collapse. 

Thanks a million Professor Buttling and Professor Sachpazis for your comprehensive, rich, and insightful response. It really enhanced my knowledge and gave me another perspective. 

Thank you so much Noman, this is concise and determenstic.