Understanding the Factor of Safety (FoS) in soil and rock mechanics

Introduction

Factor of Safety (FoS) is the most common quantitative measure of a slope’s stability. The most widely used definition for slope stability FoS is that it is the ratio of the shear strength of the soil to the shear stress required for equilibrium (Duncan, 2000). The safety factor is an important parameter that needs to be considered when dealing, for example, with the stability of slopes in open-cast mines or walls in underground mines. Terzaghi, in his 1943 “Theoretical Soil Mechanics”, presents a target FoS of 1.5 for slope stability, without a detailed discussion of why this value was selected (Schnaid et al., 2020). In this article, we will first present the different interpretations that can be made of FoS values, then the applications and finally the methods that can be used to increase the safety factor.

Interpretation of FoS values

First of all, let’s remember that, in rock mechanics, the FoS is a measure of how stable a rock mass or structure is under given conditions. It is defined as a ratio of the resisting forces (shear strength of the rock) to the driving forces (stresses or loads acting on the rock). It is expressed by the formula below:

FoS = Shear Strength / Shear Stress

• Shear strength or resisting forces include soil cohesion, frictional strength, and stabilizing structural measures.
• Shear stress or driving forces are primarily due to the weight of the slope and external loads, such as water infiltration and seismic activities.

The safety factor has characteristic values, each of which is interpreted in a different way, as summarised in Table 1.

Table 1: interpretation of FoS values

Applications of FoS in rock Mechanics

The measurement of the safety factor has applications in several branches of rock mechanics. Without going into too much detail, in this section we present a few uses for this tool.

• Slope Stability Analysis: ensures open-pit slopes remain stable against failure.
• Underground Support Design: determines the required support for tunnels and stopes.
• Pillar Design: helps evaluate if a pillar can support the overlying load safely.
• Rockslide and Collapse Prediction: used in assessing natural rock slopes or engineered excavations.

Methods for increasing the Factor of Safety

There are several proven methods to increase the FoS of slopes in soils. Below are some common strategies ((6) Methods for Increasing the Factor of Safety of Slopes in Soils | LinkedIn, n.d.):

Soil Reinforcement

Soil reinforcement is a powerful method for stabilizing slopes by enhancing the mechanical properties of soil. This technique increases the soil’s shear strength, thereby boosting the Factor of Safety (FoS). It is very effective in steep slopes, excavations, and areas where conventional methods may not be feasible.

• Soil Nailing: Soil nailing involves inserting steel bars (referred to as nails) into the slope at regular intervals. These nails are typically grouted to form a strong bond with the surrounding soil, significantly increasing its shear strength.

This technique is commonly used in stabilizing steep excavations, highway cuttings, and embankments.

This method is cost-effective and can be installed with minimal disturbance to the existing landscape, making it ideal for urban environments or restricted spaces.

• Geosynthetics Reinforcement: Geosynthetics, such as geogrids, geotextiles, and geomembranes, are synthetic materials strategically placed within soil layers to enhance structural integrity and increase tensile strength. By integrating these materials into the soil, engineers can improve load distribution, reduce settlement, and significantly enhance slope stability, especially in weak or loose soils, thereby increasing the Factor of Safety. Geosynthetics are commonly used in reinforced soil walls, embankments, slopes, erosion control, and drainage systems and can be combined with other stabilization methods like retaining walls for added effectiveness. These materials are lightweight, durable, and easy to install, making them a cost-effective solution for challenging geotechnical conditions while also promoting sustainability by reducing the reliance on traditional construction materials.

Retaining Structures

Retaining structures are essential in providing lateral support to slopes, preventing soil movement, and enhancing stability, especially in areas with limited space such as urban environments. These structures resist lateral earth pressures, making them effective in safeguarding infrastructure and preventing landslides.

• Retaining Walls: These walls provide strong lateral resistance to unstable slopes. Common types include: Reinforced Concrete Walls: Offer robust support for steep slopes and are highly durable. Gabions: Wire mesh baskets filled with rocks that provide flexibility and drainage, ideal for slope stabilization and erosion control. Mechanically Stabilized Earth (MSE): These walls use layers of compacted soil reinforced with geosynthetics, providing both strength and flexibility.

They enhance the slope’s overall stability by distributing loads more evenly and preventing erosion.

Drainage Control

Effective drainage control is vital for maintaining slope stability, as water infiltration can significantly weaken soil strength and increase the driving forces that lead to slope failures. Proper management of surface and subsurface water reduces pore water pressure, enhances soil strength, and minimizes the risk of landslides.

• Surface Drains: Channels, ditches, and contour drains are designed to divert surface water away from the slope, preventing excessive infiltration. By guiding runoff, these drains reduce soil saturation and erosion, protecting the slope’s surface integrity.
• Subsurface Drains: Installing perforated pipes, gravel trenches, or French drains below the surface helps intercept and redirect groundwater flow. These systems lower the water table and reduce pore water pressure within the soil, thus enhancing the overall stability of the slope.

Grading and Slope Reshaping

Grading and reshaping slopes is an effective way to improve stability by modifying the natural terrain. By reducing the slope angle or incorporating benches, this method decreases the driving forces that contribute to slope failures. It is often combined with vegetation to further stabilize the surface and prevent erosion. Common methods include.

• Cut-and-Fill Operations: This technique involves removing soil from steeper sections (cut) and filling lower areas to achieve a gentler, more stable gradient. It helps redistribute the soil mass, reducing the risk of landslides.
• Terracing: Creating horizontal steps or terraces along a slope reduces the overall effective slope angle. This not only decreases the gravitational force acting on the slope but also helps manage surface runoff, minimizing erosion.

Vegetation and Bioengineering

Vegetation and bioengineering techniques are sustainable, eco-friendly solutions for enhancing slope stability. The deep roots of plants help anchor soil particles, significantly reducing surface erosion and controlling runoff. By establishing a dense network of roots, vegetation improves soil cohesion and resists shallow slope failures. Additionally, bioengineering practices, such as using live stakes, fascines, or vegetative mats, can provide immediate stabilization while natural vegetation takes root.

While these methods are cost-effective and environmentally beneficial, they require time for the vegetation to mature and become fully effective. However, once established, they offer long-term stability with minimal maintenance and contribute to improved slope resilience against erosion and weathering.

• Grasses and Shrubs: Ideal for shallow slopes.
• Trees: Provide deep root systems for steeper slopes.

Ground Improvement Techniques

Ground improvement methods are employed to enhance the engineering properties of soil, thereby increasing its strength, stability, and resistance to settlement. These techniques are particularly effective in areas with loose or weak soils, ensuring safer and more durable foundations.

• Jet Grouting: This process involves injecting a high-pressure jet of cementitious material into the soil, creating solidified columns. These columns increase shear strength and reduce permeability, making the ground more stable and less prone to settlement.
• Stone Columns: By inserting compacted gravel columns into the ground, this technique improves soil density and bearing capacity. Stone columns help in reinforcing weak soils, enhancing their drainage, and reducing the risk of liquefaction during seismic events.
• Vibro-Compaction: In this method, a vibrating probe is used to densify granular soils, particularly sands, by rearranging soil particles into a more compact state. This increases soil strength, reduces compressibility, and enhances load-bearing capacity.

Conclusion

The safety factor is a fundamental parameter used in rock mechanics to assess the stability of structures such as slopes. Depending on its value, it can be interpreted in different ways. It applies to a wide range of areas, and several methods, such as soil improvement or even stabilisation through the use of vegetation (bioengineering), can help to improve it, depending on the context and environmental conditions.

Reference

(6) Methods for Increasing the Factor of Safety of Slopes in Soils | LinkedIn. (n.d.). Retrieved March 5, 2025, from https://www.linkedin.com/pulse/methods-increasing-factor-safety-slopes-soils-george-agutu-ghtuf/

Duncan, J. M. (2000). Factors of Safety and Reliability in Geotechnical Engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)

Schnaid, F., Mello, L. G., & Dzialoszynski, B. (2020). Guidelines and recommendations on minimum factors of safety for slope stability of tailings dams. Soils and Rocks, 43(3), 369–395. https://doi.org/10.28927/SR.433369