Global Stability Analysis Methods, Common Pitfalls, and Strategies for Successful Performance

By J.E. Hughes, Ph.D., P.E.¹, Z.K. Boswell, P.E.², B.P. Strohman, P.E., G.E.³

Introduction

Many construction projects incorporate fill or excavated slopes, utilize support of excavation systems, or require retaining walls as part of the necessary site development. These structures create unbalanced loads, requiring a professional engineer to perform global stability analyses (GSA) to evaluate the potential failure surfaces that can develop behind and below the structure due to the unbalanced loading condition (Figure 1). Global stability is often described in terms of the factor of safety against failure along a failure surface. The factor of safety is defined as the ratio of the soil shear strength (resistance) to driving shear stress acting along the failure surface. 

GSAs are a crucial part of the design process for these structures. If performed incorrectly, unexpected movement or potential catastrophic failure can result, posing a significant risk to public safety and adjacent property.

This paper describes some common global stability limit equilibrium analysis methodologies, software considerations and common pitfalls, and strategies for successful performance. Most of the content herein applies to two-dimensional analyses; however, many of the considerations, pitfalls, and strategies are applicable to three-dimensional analyses as well.

Common Limit Equilibrium Analysis Methodologies

The Limit Equilibrium Method (LEM) is one of the most utilized procedures to perform GSAs. Limit equilibrium is a static analysis technique that evaluates force and moment equilibrium conditions assuming the soil and/or structure above the failure surface acts as a rigid body above an assumed failure surface of a given shape (i.e., circular/arc, spiral, noncircular). LEMs utilize the material’s shear strength and do not rely on the soil’s stress-strain behavior. Vertical, horizontal, and moment forces induced along the failure surface (Figure 2) and external loads acting on the rigid body (e.g., structures), live loads (e.g., vehicles), and temporary loads (e.g., construction loads) are typically considered explicitly in these analyses. In global LEM analyses, the mass of the rigid body is divided into slices. 

Various global limit equilibrium analysis methods are frequently used throughout the geotechnical engineering industry, including Ordinary Method of Slices, Simplified Bishop (SB), Spencer, Morgenstern and Price (MP), to name a few of the most common. Each global LEM has limitations that the engineer must consider before selecting one or more methods for use. These limitations can include assumptions or simplifications that are only applicable to isotropic soil conditions, circular failure surfaces, etc. Furthermore, some global LEMs, such as Ordinary Method of Slices or SB, are often over-simplified, inaccurate, or both due to various inherent assumptions. 

GSA Software Considerations, Common Pitfalls, and Strategies for Successful Performance 

Engineers frequently perform GSAs using commercially available, user-friendly limit equilibrium software packages, allowing them to perform multiple analyses quickly and efficiently. Some of these software packages allow engineers to utilize simplified analyses that only partially satisfy force and moment equilibrium (e.g., SB method). Other software packages allow engineers to utilize more robust analyses that are considered complete equilibrium procedures (e.g., Spencer, and MP). Further, these software packages can quickly analyze many failure surfaces and loading conditions for multiple LEMs simultaneously. However, a failure to understand the mechanics of the software combined with a lack of understanding of the inherent assumptions or simplifications of certain LEMs can lead to the use of inappropriate assumptions, unconservative analyses, and potentially unsafe conditions. 

LEM Analysis Methodologies

Many LEM analysis methodologies rely on various simplifying assumptions or limitations that require careful consideration when performing GSAs. For example, one of the more widely utilized analysis procedures is the SB method. This method uses the forces in the vertical direction and the moments about the center of the circular failure surface to evaluate equilibrium conditions of the failure wedge, whereas the shear forces between individual slices are not considered. While many software packages allow the engineer to analyze slopes for noncircular failure surfaces using the SB method, this method is only appropriate for circular failure surfaces. 

Unlike the SB method, the MP and Spencer methods satisfy force and moment equilibrium conditions and are appropriate for both circular and noncircular failure surfaces. In the authors’ experience, methods that satisfy force and moment equilibrium conditions provide more reliable results. When performing these analyses, it is imperative that the engineer understand the benefits and limitations of the available methodologies and evaluate their appropriateness for each project.

Soil and Groundwater Conditions

The soil and groundwater conditions play an important role in determining the global stability of slopes, support of excavation systems, retaining walls, and other structures. Thus, it is essential to utilize and accurately depict the site-specific soil and groundwater conditions for use in the GSAs. The authors recommend the engineer rely on location-specific subsurface investigations and field and laboratory testing, if feasible, to assess the necessary analysis parameters. 

As part of the evaluation of the soil and groundwater conditions, a detailed understanding of the material’s shear strength is required. Drained and undrained strengths are used to define the behavior of soils during shearing. Drained strength is the strength when the soil is loaded slowly or over a long period of time such that no excess porewater pressures develop, or when the excess porewater pressure fully dissipates after the soil is loaded. Undrained strength is the strength when the soil is loaded faster than the porewater can flow in and out of the material during shearing. During undrained shearing, excess porewater pressure develops within the soil. Over time, the excess porewater pressures dissipate and the drained strength is achieved. The construction type (temporary vs. permanent), the design life of the structure, and the soil type impact whether an evaluation of the drained condition, undrained condition, or both is necessary. Further, for sites with loose, saturated sands or sensitive clay soils, an evaluation of the potential for post-peak strength loss during shearing is required.

The groundwater conditions at a site can also directly influence the shear strength of the soil and the driving forces acting on the failure surface. An understanding of the static groundwater levels is necessary and should also consider seasonal groundwater fluctuations and less frequent extreme groundwater events, if necessary. Further, the use of parametric studies to evaluate the sensitivity of the results with respect to the input and analysis parameters is an essential measure to understand the reliability of the analysis results.

External Loading Conditions

External loading conditions can also significantly impact the response of a structure or slope, both during and after construction. For example, during construction, analyses are typically required at various excavation depths, at differing stages of fill placement, or when other unbalanced loads are placed or removed from the areas near the slope or structure. For analysis of the permanent, long-term condition, loads from adjacent structures and seismic loads should be considered.

Of critical importance for GSAs are the magnitude of the load, its location, depth, and extent relative to the structure or slope. Furthermore, the authors recommend that engineers exclude temporary loads in GSAs if those loads have a stabilizing effect. These temporary loads can unconservatively increase shear resistance along the failure surface.

Anisotropic Soil Behavior and Shape of the Failure Surface

Two key considerations that require detailed attention when evaluating the global stability of a structure or slope are soil anisotropy (e.g., soil that has properties that are directionally dependent) and the shape of the critical failure surface. The United States Army Corp. of Engineers (USACE) Engineering and Design Manual for Slope Stability (EM 1110-2-1902), emphasizes the importance of these items, stating, “Stability analyses based on general slip surfaces are now much more common and are useful as a design check of critical slip surfaces of traditional shapes (circular, wedge) and where complicated geometry and material conditions exist. It is especially important to investigate stability with noncircular slip surfaces when soil shear strengths are anisotropic.” 

To consider the effects of anisotropy of the undrained shear strength, different strength zones are often utilized in GSAs: triaxial compression (TXC) behind the slope or structure, direct simple shear (DSS) below the slope or structure, and triaxial extension (TXE) in front of the slope or structure. While the USACE emphasizes the importance of analyzing non circular slip surfaces for anisotropic soil conditions, it is often necessary to analyze both circular and noncircular failure surfaces using appropriate global LEM methodologies to determine the critical failure surface. The authors recommend that engineers evaluate soil anisotropy and the importance of the different modes of shearing (TXC, DSS, and TXE) when performing GSAs.

Evaluation of Failure Surfaces

Most global limit equilibrium software packages allow the engineer to either manually define the failure surfaces, or the program automatically generates the failure surfaces. If the engineer chooses to define the failure surfaces manually, they should have sufficient experience performing GSAs to assess the suitability of the results. For manually defined failure surfaces, it is typically necessary to define multiple failure surfaces, compare the factors of safety, and evaluate the reasonableness of the results. This process is often both monotonous and time-consuming to identify the critical failure surface and factor of safety. In lieu of manual definition of failure surfaces, it is often more common to have the limit equilibrium software automatically generate the failure surfaces utilizing a user-defined search criterion. This approach often results in the analysis of significantly more failure surfaces. For automatically generated failure surfaces, the engineer should still perform a thorough review to evaluate the suitability of the results and slip surfaces.

Engineers performing GSAs either manually or automatically specified failure surfaces should understand how the software defines the failure surface to ensure the critical failure surface and factor of safety are identified. If the program features multiple search algorithms, each algorithm needs to be considered, and the results compared for consistency.

Regardless of the failure surface selection approach (manual or automatic), the use of narrow model extents typically leads to misleading and often unconservative results. For example, if the model’s edges are too close to the structure being analyzed, the program likely will not identify the critical failure surface and factor of safety. To ensure the critical failure surface is not overlooked, the model extents should be at least two times the width of the structure. Refinement of model size and extents can be performed only after the engineer is confident the analysis is capturing the critical failure surfaces and factor of safety (Figure 3).

Software Model Verification

Model verification is a critical aspect for all engineering analyses, but is particularly important when using commercially available software packages. When performing GSAs, a prudent approach is to verify the reasonableness of the results for a simple case or to use a previously validated problem to assist in validating the results. Typically, the model validation uses the same inputs and analysis methodologies, and if the results are inconsistent, the engineer should evaluate the differences and update the analysis. 

Closing Remarks

Global stability analyses are commonly encountered within the geotechnical engineering industry. Background and knowledge of typical analysis methodologies and commonly utilized commercially available software packages are required to achieve reliable results. Unexpected movements or catastrophic failures can occur if these analyses are performed incorrectly. 

While recognizing and avoiding common pitfalls aid in achieving successful GSA performance, the authors recommend the following fundamental strategies, 1) utilize LEMs that are considered complete equilibrium procedures (e.g., Spencer, and Morgenstern and Price), 2) use site-specific information for the subsurface and loading conditions, 3) check the model extents, and 4) verify the analysis software. Following these approaches provides greater reliability in the analysis results.

Jake Hughes, Ph.D., P.E., is a Consulting Engineer at Simpson Gumpertz & Heger. He is experienced in geotechnical and structural engineering. Jake can be reached at jehughes@sgh.com.

Zachary Boswell, P.E., is a Senior Consulting Engineer at Simpson Gumpertz & Heger with experience designing and investigating below-grade construction. He can be reached at zkboswell@sgh.com.

Bryan P. Strohman, P.E., G.E., P.Eng., is an Associate Principal in Simpson Gumpertz & Heger’s Waltham, Massachusetts office and co-leader of SGH’s Heavy Civil and Marine Practice Area. He has diverse experience in geotechnical, civil, and structural engineering, including designing and investigating various below-grade structures. Bryan can be reached at bpstrohman@sgh.com.