Revisiting the Lodalen Slide
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- 4 days ago
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A Forensic Slope Stability Analysis Using the Morgenstern-Price and FEM Methods
Abstract:
The 1954 Lodalen landslide, documented by Sevaldson (1956), provides a critical case study for evaluating slope stability analysis methods. This study reassesses the failure using the Morgenstern-Price limit equilibrium method (LEM) and Finite Element Method (FEM) to compare their accuracy and mechanistic insights. The 17 m high, 2:1 inclined clay slope (ϕ' = 27°, c' = 10 kPa) was modelled in DeepEX - shoring & Tunnels design software under drained conditions with measured pore pressures. LEM analysis produced a factor of safety (FS) of 0.971, while FEM yielded an FS of 1.00, closely matching Sevaldson’s original Bishop method results (FS ≈ 1.0). The FEM further revealed the rotational failure mechanism through displacement patterns, aligning with LEM-derived slip surfaces. The agreement between methods confirms their reliability in forensic analysis, while FEM provides enhanced understanding of progressive failure. This study demonstrates the value of historical case studies in validating modern geotechnical tools and highlights the complementary strengths of LEM and FEM in slope stability assessment.
Keywords: Lodalen landslide, slope stability, Morgenstern-Price method, Finite Element Method, forensic analysis.
Introduction
The Lodalen landslide of October 6, 1954, remains a seminal case study in geotechnical engineering, meticulously documented by Sevaldson (1956) through comprehensive field investigations, laboratory testing, and detailed post-failure analyses. This well-documented event provides a unique opportunity to evaluate the reliability of modern slope stability assessment methods, particularly in forensic geotechnical analysis. By revisiting this case with the Morgenstern-Price method (Morgenstern and Price, 1965) and the Finite Element Method (FEM), this study aims to assess the accuracy of analytical and numerical tools while refining our understanding of slope failure mechanisms. For the present study, the model and all analyses are performed using the software DeepEX in which the Limit Equilibrium Method (LEM) and Finite Element Method are implemented.
At the time of failure, the Lodalen slope stood 17 meters high with a steep 2:1 (H:V) inclination (approximately 26°). The soil profile consisted primarily of clayey soil, with laboratory-derived shear strength parameters indicating an average friction angle (ϕ') of 27° and an effective cohesion (c') of 10 kPa. The pore water pressures were carefully measured and reported in Sevaldson’s study, along with precise pre- and post-failure geometry (Figure 1).
Figure 1 – Cross-section of the failed slope, showing site investigation points, pre- and post-collapse geometry (a), and pore water pressure distribution alongside Bishop method stability analysis (Sevaldson, 1956).
Sevaldson (1956) selected three critical sections for slope stability analysis, computing the average factor of safety (FS) under both ϕu = 0 and drained conditions using the conventional method and Bishop’s method. The results obtained an FS of 1.01 (ϕu = 0), 0.85 (conventional method, drained), and 1.00 (Bishop’s method, drained), highlighting the sensitivity of the analysis to shear strength assumptions.
Model description and framework
In this study, the slope was modelled with explicit consideration of the phreatic surface (water table) and the geometry presented in Figure 2. A deterministic stability analysis was performed using both the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM).
The LEM analysis employed the Morgenstern-Price method, which satisfies both force and moment equilibrium while accounting for variable inter-slice forces. The sliding mass was divided into vertical slices, with normal (E) and shear (T) inter-slice forces related through an assumed side-force function. Through iterative calculations, the factor of safety (FS) was determined, accommodating complex, non-circular failure surfaces (Morgenstern & Price, 1965).
The FEM model utilized a sparse mesh, appropriate for the model scale without compromising accuracy, and applied the Strength Reduction Method (SRM) to assess the safety factor (FSc-ϕ). The FEM-SRM approach systematically reduces soil shear strength parameters (c' and φ') until failure occurs, with the strength reduction factor (SRF) at failure representing the factor of safety. Unlike LEM, FEM-SRM does not require predefined slip surfaces and instead numerically solves stress-strain equilibrium, capturing progressive failure and stress redistribution (Griffiths & Lane, 1999). An exponential constitutive model was incorporated to better represent the nonlinear shear strength degradation and progressive failure behaviour of the soil.
Figure 2 – Slope model for stability analysis, incorporating geometry and hydraulic conditions - DeepEX.
LEM Analysis Results
Figure 3 presents the LEM-derived critical slip surface (delineated in red), with a computed FS of 0.971—marginally below 1.0, indicating imminent instability under the given soil strength and pore pressure conditions. The analysis considered circular slip surfaces, with the most critical mechanism identified.
Figure 3 – LEM results: FS, slip surface, and slice divisions - DeepEX.
FEM Analysis Results
The FEM-SRM was conducted using the same model (Figure 2) and drained c–ϕ parameters as the LEM. Progressive reduction of shear strength parameters (c' and ϕ') until failure provided an FS of 1.0 (Figure 4), aligning closely with Bishop’s method (FS ≈ 1.0) and supporting the robustness of both approaches. Unlike LEM, FEM captures stress redistribution and deformation patterns, offering deeper mechanistic insights.
Figure 4 – FEM results: Displacement contours and strength reduction factor (SRF) - DeepEX.
Figure 5 illustrates the deformed mesh and displacement vectors (red arrows), revealing a rotational failure mechanism initiating at the crest and propagating toward the toe. Displacement magnitudes localize along a curved shear zone, consistent with LEM-predicted slip surfaces. Sparse vectors outside this zone confirm localized movement, typical of drained c–ϕ failures.
Figure 5 – FEM-derived failure mechanism: Deformed mesh and displacement vectors - DeepEX.
Conclusions
The forensic re-evaluation of the Lodalen landslide case using both limit equilibrium (Morgenstern-Price) and finite element methods has provided valuable validation of the original stability assessments while offering enhanced mechanistic understanding of the failure. Key observations from this dual-methodology approach include:
Methodological Validation
The close agreement between the computed factors of safety (FEM: 1.00; LEM: 0.971) and Sevaldson's original Bishop method results (1.00) confirms the reliability of modern analytical techniques when applied to well-documented case histories. This consistency across different solution methods strengthens confidence in slope stability assessment protocols implemented in DeepEX.
Comparative Advantages
The limit equilibrium analysis efficiently identified the critical failure surface and global stability condition.
The finite element approach provided complementary insights into stress redistribution, deformation patterns, and progressive failure development.
The strength reduction technique successfully captured the transition from stable to unstable conditions.
Failure Mechanism Clarification
The FEM results clearly illustrated the rotational failure mode, with displacement vectors and shear strain localization patterns confirming the kinematic behaviour implied by the LEM-derived slip surface. This multi-evidence approach provides more robust failure mechanism interpretation than either method could achieve independently.
Practical Implications
This analysis demonstrates how historical case studies, when properly documented, continue to serve as important benchmarks for:
• Validating new analysis methods.
• Demonstrating the complementary nature of different analysis approaches.
• Enhancing understanding of failure processes in cohesive soils.
Recommendations for Future Work
To build upon these findings, subsequent investigations could:
• Incorporate more sophisticated constitutive models to better represent soil behaviour.
• Evaluate sensitivity to parameter uncertainty through probabilistic analysis.
• Examine the influence of groundwater transient conditions.
This study emphasizes the lasting value of well-documented case histories in geotechnical engineering, while demonstrating how modern computational methods can provide additional insights from classic failures. The Lodalen case continues to serve as both a validation benchmark and a teaching example for slope stability analysis. On the other hand, the results further demonstrate DeepEX's capabilities as a reliable solution for slope stability analysis, accurately reproducing validated failure mechanisms while extending to more complex geotechnical challenges.
References
Griffiths, D. V., & Lane, P. A. (1999). Slope stability analysis by finite elements. Geotechnique, 49(3), 387-403.
Morgenstern, N. R., & Price, V. E. (1965). The Analysis of the Stability of General Slip Surfaces.
Sevaldson, R. A. (1956). The Slide in Lodalen, October 6th, 1954. Géotechnique, 6(4), 167–182. https://doi.org/10.1680/geot.1956.6.4.167
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