Bishop & Janbu Comparative Worked Examples Workbook (Excel + PDF)

This workbook operationalizes two foundational limit equilibrium methods used in geotechnical engineering to evaluate the stability of natural or engineered slopes. The Bishop method assumes a circular failure surface and neglects interslice shear forces while satisfying moment equilibrium about the center of the circle—resulting in a closed-form, iterative solution for factor of safety. In contrast, the Janbu method accommodates non-circular (e.g., polygonal or composite) slip surfaces and enforces horizontal force equilibrium; its simplified version assumes zero interslice shear, whereas the generalized version incorporates an empirical interslice force function (often using the 'Janbu’s correction factor' or 'λ-procedure') to improve accuracy. The workbook implements both methods side-by-side using consistent geometry, soil stratigraphy, pore-water pressure distribution, and loading conditions—allowing direct numerical comparison of FoS, critical slip surface location, and convergence robustness. It includes built-in validation checks (e.g., equilibrium residuals, mass balance), sensitivity tables, and graphical outputs (e.g., FoS vs. trial surface depth, convergence history plots). Pedagogically, it clarifies common misconceptions—such as the erroneous assumption that Bishop always yields conservative results—and demonstrates how method selection impacts design decisions in landslide risk mitigation, cut-and-fill design, and dam embankment evaluation.