Slope Stability
Analyzes slope stability using limit equilibrium methods to establish a factor of safety against sliding.
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Geotechnical Engineering · Soil properties, foundation selection, bearing, settlement, earth pressure and slope stability.
Deliverable: Slope stability analysis with FS by limit equilibrium method for the governing cross-section.
Minimum tables, figures and equations for Slope Stability
Tables — at least 7
- Table — trial sections or sizes considered, with the capacity of each and the selection decision
- Table — final selected geometry for every element: dimensions, thickness, grade, spacing, elevation
- Table — bearing capacity and footing or pile size at each location
- Table — ultimate limit state check summary: demand, capacity, ratio, pass or fail, governing clause
- Table — serviceability check summary: deflection, crack width, settlement, freeboard or velocity against its limit
- Table — factors of safety achieved against the factor required, per failure mode
- Table — settlement (immediate and consolidation) against the tolerable limit
Figures — at least 4
- Figure — free body diagram of each isolated element, fully labelled with loads, reactions, dimensions and axes
- Figure — shear and moment (or pressure and velocity) diagrams for each force-carrying element
- Figure — dimensioned section or plan of each designed element
- Figure — capacity versus demand plot, interaction diagram, or rating curve as applicable
Equations — at least 8
- Equation — equilibrium equations written out for each free body (sum of forces and sum of moments, or continuity and energy)
- Equation — the internal force relations V(x) and M(x), or the momentum/thrust relation, used to compute each element's demand
- Equation — the resulting demand at the critical section of each element, with numeric substitution
- Equation — the capacity expression for each element type, shown with full numeric substitution and units
- Equation — the sizing criterion that sets the final dimension (for example required area, depth or diameter)
- Equation — each limit state check written as demand over capacity with numbers substituted
- Equation — the factor of safety calculation for each failure mode checked
- Equation — sliding, overturning, bearing and global stability factors of safety
Number every table and figure (Table 4.x, Figure 4.x), caption it, and refer to it by number in your text. Number displayed equations and show the substitution with units. These counts are minimums — add whatever else your design needs.
Engineering documentation standard — required in every Chapter 4 subsection
These rules are graded on every subsection. Work that misses them is capped on technical accuracy, exhibits, codes and communication, whatever the quality of the prose.
Code and standard references
- Every requirement, factor, coefficient, limit and allowable you apply cites the governing document AND the exact section, article or sub-article number — e.g. ACI 318-19 §22.5.5.1, AISC 360-22 Chapter J, Section J3.6, AASHTO LRFD 10th Ed. Article 3.6.1.2.2, ASCE 7-22 §12.8.1, ASTM D2487, state DOT manual section, local stormwater manual chapter.
- Give the edition or year of every document the first time it appears, then use a consistent short form.
- Where a code equation is used, quote the equation number (e.g. Eq. 22.5.5.1) next to your displayed equation.
- Where you depart from a code provision, state the clause you are departing from and the engineering justification.
- List every code, standard and manual actually used in a Codes and Standards table at the start of the subsection.
Citations for statements
- Every statement of fact, value taken from elsewhere, material property, soil parameter, rainfall depth, unit cost or published method carries an in-text citation (APA) to its source.
- Field and lab data cite the report, boring log, gauge, survey file or test number and its date.
- Manufacturer data cites the product literature and revision date; software results cite the program, version and model file name.
- Uncited assertions are treated as assumptions and must appear in the assumptions table with a justification.
- Every in-text citation resolves to a full entry in the reference list.
Step-by-step calculations
- Structure every calculation the same way: (1) objective, (2) governing code clause, (3) equation in symbolic form with the equation number, (4) definition of each symbol, (5) numerical substitution, (6) result with units, (7) comparison against the limit and the pass/fail statement.
- Show the substitution line — never jump from the formula to the answer.
- Number displayed equations sequentially (Eq. 4.1, 4.2, …) and refer to them by number in the text.
- State the load or flow combination governing each calculation by name.
- Carry consistent significant figures and round only at the reported result; state the rounding convention once.
- Present repetitive element checks in a calculation table with one row per element and the same column order throughout.
Free body diagrams and figures
- Draw a separate free body diagram for each isolated element — no combined sketches standing in for several members.
- Dimension every FBD: span, depth, thickness, cover, eccentricity, embedment, slope, pipe diameter, wall height — with the dimension lines and values shown.
- Label every force, pressure, reaction and moment with its symbol, magnitude and units, and show the sign convention and coordinate axes.
- Show supports and boundary conditions explicitly (pin, roller, fixed, elastic, buoyant, hydrostatic).
- Accompany each FBD with its shear, moment, thrust, pressure or hydraulic grade diagram at the same scale reference.
- Number and caption every figure (Figure 4.x) and refer to it by number in the narrative; add a scale or north arrow to plans.
Units and notation
- Every number in text, tables, figures and equations carries its unit — no bare numbers.
- Use one unit system throughout (US customary or SI); if both appear, give the converted value in parentheses consistently.
- Check dimensional homogeneity of each equation and say so — the units of both sides must match.
- Provide a nomenclature table defining every symbol with its unit.
Checking and verification
- Every calculation is checked by an independent route — hand check against software, alternative method, order-of-magnitude estimate, or a published worked example — and the check is shown, not just claimed.
- Report demand-to-capacity ratios and factors of safety against the required values, with the source clause for each required value.
- Include a verification/checking table: item, method of check, expected, obtained, difference, accept or revise.
- Sanity-check every result (magnitude, direction, plausibility) and state the conclusion.
- Record who checked the work and on what date; flag anything still unverified as an open item.
- State limitations and the range over which the result is valid.
How to complete this section
Do this next: Read the Slope Stability lecture and the worked example so you know what "Slope stability analysis with FS by limit equilibrium method for the governing cross-section." has to contain.
Not sure how to start or how much depth is expected? Read the fully written model example for this deliverable first — it shows the structure, tables and level of justification your advisor grades against.
Geotechnical Design Office — what this workspace teaches
Soil properties, foundation selection, bearing, settlement, earth pressure and slope stability.
- Reading boring logs and building a design soil profile
- Soil classification, index properties and strength parameters
- Shallow foundation bearing capacity (Terzaghi, Meyerhof) and factors of safety
- Immediate, consolidation and secondary settlement
- Lateral earth pressure: at-rest, active, passive; Rankine and Coulomb
- Retaining wall stability: sliding, overturning, bearing, global
- Deep foundations: pile capacity, skin friction, end bearing, group effects
- Slope stability methods and required factors of safety
- Ground improvement and groundwater control
End-of-term milestones
- Tuesday, November 17, 2026 — Poster printed and ready. 36 in × 48 in poster finalized and printed one week before the November 24 showcase.
- Wednesday, November 18, 2026 — Final document package uploaded for scoring. Chapters 4–5, calculation package, drawings and appendices uploaded in the app for advisor scoring.
- Wednesday, November 18, 2026 — Poster presentation to faculty and industry. Wednesday poster session — printed 36 in × 48 in poster presented in person; industry reviewers score communication and impact.
- Wednesday, November 25, 2026 — Oral presentation and defense (scored). Scored oral presentation and defense held on Wednesday, November 25.
Slope Stability
Analyzes slope stability using limit equilibrium methods to establish a factor of safety against sliding.
Section B
Engineering story
A real project situation that frames this module
It is week 6 of implementation and the geotechnical engineering team has reached slope stability. Analyzes slope stability using limit equilibrium methods to establish a factor of safety against sliding. The geotechnical reviewer for the owner asks one question: what establishes that limit equilibrium methods?
The team treats critical failure surface search (circular and non-circular) as a background assumption instead of an input that must be established and recorded. The result is settlement, bearing failure or slope instability below the finished grade, discovered only after the design of record that drawings, quantities and cost are generated from has already been built on it.
Adjacent property owners, excavation crews and the geotechnical engineer of record carry the consequence. On this module specifically, the exposure runs through effective stress vs, and the cost of correction rises every week the subsurface interpretation and foundation recommendation moves closer to issue.
Decisions the engineer must make
- What record establishes limit equilibrium methods, and is that record in the project data inventory?
- Does NAVFAC DM-7 (DM-7.1), Ch. 7, govern here — and is that the edition adopted by the jurisdiction?
- What is the acceptance criterion for critical failure surface search (circular and non-circular), and was it written before the result was known?
- Is FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα) valid over the parameter range this project actually occupies?
- If the check fails, does the team revise the subsurface interpretation and foundation recommendation or raise a change request against the locked baseline?
Photo 1. Subsurface investigation: SPT samples and the boring log that every geotechnical number traces back to.
Capstone Studio instructional photograph
Section C
Why this matters
Professional
A licensed engineer defending slope stability cites NAVFAC DM-7 (DM-7.1), Ch. 7, and shows the record behind each input. Your slope stability analysis with fs by limit equilibrium method for the governing cross-section. is reviewed the same way — traceability is assessed before arithmetic.
Technical
Limit equilibrium methods is what makes FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα) usable on this project rather than a formula copied from a reference. Get it wrong and every quantity derived from it is wrong by the same factor.
Safety
The failure mode this module guards against is settlement, bearing failure or slope instability below the finished grade. It reaches people through factor of safety acceptance criteria for static and seismic conditions, which is why the safety check is recorded explicitly here rather than inferred from a passing strength or performance check.
Economic
The design of record that drawings, quantities and cost are generated from is priced from this work. Quantities, unit costs and schedule float all trace to limit equilibrium methods; a late correction here is paid for as a change order, not a redline.
Environmental
Environmentally, this module fixes spoil handling, dewatering discharge and groundwater drawdown near the site. Choosing conservatively without justification is not free — the excess shows up as material, energy and land that the project consumes for no measurable gain.
Community
Slope/excavation factor of safety must be checked against the site-specific soil strength, not a generic assumption Neighbors whose structures, utilities and streets sit within the zone of influence live with that outcome long after the semester ends.
Section D
Learning objectives
By the end of this module you will be able to:
- 1.Analyze limit equilibrium methods, using this project's own conditions rather than a textbook case.
- 2.Justify critical failure surface search (circular and non-circular), using this project's own conditions rather than a textbook case.
- 3.Interpret effective stress vs, using this project's own conditions rather than a textbook case.
- 4.Apply seismic (pseudo-static) slope stability with a horizontal seismic coefficient, using this project's own conditions rather than a textbook case.
- 5.Compute the governing quantity from FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα), with a unit audit on every term.
- 6.Apply NAVFAC DM-7 (DM-7.1), Ch. 7, and cite the section that governs your acceptance decision.
- 7.Produce slope stability analysis with fs by limit equilibrium method for the governing cross-section. at a standard the geotechnical reviewer for the owner would accept without a second revision cycle.
Section E
Instructional content
Full lecture notes with figures and governing equations
The engineering content of slope stability
Analyzes slope stability using limit equilibrium methods to establish a factor of safety against sliding. That single sentence hides the substance of the module: limit equilibrium methods, and critical failure surface search (circular and non-circular). Both must be established from project evidence before anything downstream is credible.
In geotechnical engineering, this work is the input to the subsurface interpretation and foundation recommendation. Effective stress vs — which is why this page asks you to record the source of every quantity, not just its value. The design of record that drawings, quantities and cost are generated from depends on it.
- Limit equilibrium methods: Ordinary Method of Slices, Bishop's Simplified, Spencer's method
- Critical failure surface search (circular and non-circular)
- Effective stress vs. total stress slope analysis, drained vs. undrained conditions
- Seismic (pseudo-static) slope stability with a horizontal seismic coefficient
- Factor of safety acceptance criteria for static and seismic conditions
Photo 1. The engineering content of slope stability in practice — Subsurface investigation: SPT samples and the boring log that every geotechnical number traces back to.
Capstone Studio instructional photograph
Governing relationships and how they are applied here
The relationships below govern slope stability. FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα) — each is valid only inside the parameter range this project occupies, so state that range before substituting.
Critical failure surface search (circular and non-circular) sets the values you place into these expressions. Any code-prescribed factor must match NAVFAC DM-7 (DM-7.1); a factor lifted from a different edition silently changes the answer.
FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα)
- Bishop/Fellenius method of slices factor of safety along a trial failure surface
Photo 2. Governing relationships and how they are applied here in practice — Subsurface investigation: SPT samples and the boring log that every geotechnical number traces back to.
Capstone Studio instructional photograph
Constraints, adopted standards and the safety case for slope stability
NAVFAC DM-7 (DM-7.1), Ch. 7, governs this module: Slope stability analysis methods
The safety case is explicit here. The failure mode is settlement, bearing failure or slope instability below the finished grade; the people exposed are adjacent property owners, excavation crews and the geotechnical engineer of record; the control that prevents it is factor of safety acceptance criteria for static and seismic conditions together with an independent check by someone who did not perform the work.
- Controlling criterion for this module: limit equilibrium methods.
- Adopted reference: NAVFAC DM-7 (DM-7.1) — cite Ch. 7 by number.
- Failure mode guarded: settlement, bearing failure or slope instability below the finished grade.
- Evidence produced: Slope stability analysis with FS by limit equilibrium method for the governing cross-section..
Photo 3. Constraints, adopted standards and the safety case for slope stability in practice — Subsurface investigation: SPT samples and the boring log that every geotechnical number traces back to.
Capstone Studio instructional photograph
Where this method stops being valid
Every method has a domain of validity. State the range of geometry, loading, material behaviour or flow regime over which your approach holds, and state what you would do instead beyond it.
For this project, the boundary you are most likely to push is factor of safety acceptance criteria for static and seismic conditions. If you cross it, say so in writing, bound the error, and carry the limitation into your results chapter. A disclosed limitation is professional practice; a silent extrapolation is not.
Photo 4. Where this method stops being valid in practice — Subsurface investigation: SPT samples and the boring log that every geotechnical number traces back to.
Capstone Studio instructional photograph
Section F
Engineering workflow
Steps
- 1. Assemble the inputs this module needs — limit equilibrium methods; critical failure surface search (circular and non-circular) — each with a unit and a source record.
- 2. Confirm NAVFAC DM-7 (DM-7.1) is the adopted edition and locate Ch. 7.
- 3. State the assumptions and the acceptance criterion for limit equilibrium methods.
- 4. Evaluate FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα) term by term, carrying one extra significant figure.
- 5. Test the result against effective stress vs.
- 6. Audit units and run an order-of-magnitude check by hand before the number leaves your desk.
- 7. Obtain an independent check from a teammate who did not perform the work, and record their name and date.
- 8. Assemble slope stability analysis with fs by limit equilibrium method for the governing cross-section. and submit it to the geotechnical reviewer for the owner for review.
Decision points
- Is every input behind limit equilibrium methods traceable? If not — stop and collect the record.
- Does the result satisfy critical failure surface search (circular and non-circular)? If not — revise the work, never the criterion.
- Would the correction change the design of record that drawings, quantities and cost are generated from? If yes — raise a change-control request before proceeding.
Quality checklist
- Documented: limit equilibrium methods
- Documented: critical failure surface search (circular and non-circular)
- Documented: effective stress vs
- NAVFAC DM-7 Ch. 7 cited by section number
- Units audited on every expression
- Acceptance criterion recorded before the result
- Independent check signed and dated
- Slope stability analysis with FS by limit equilibrium method for the governing cross-section. attached and named per the course convention
Section H
Interactive visualization
Slope Stability — step-through
Advance one frame at a time. Each frame adds one engineering decision to the previous state.
Step 1 of 6
Start from the confirmed inputs: geometry, materials, loads or flows, each with a source.
Section I
Applicable codes and standards
NAVFAC DM-7
DM-7.1 · Ch. 7
Adopted design/analysis reference governing this module.
Relevance: Slope stability analysis methods
Reference the section number and edition in your calculation package. Do not reproduce code text.
Section J
Worked examples
Full engineering solution format
Section K
Common mistakes and how to avoid them
- Treating limit equilibrium methods as a given instead of establishing it from a project record.
- Producing slope stability analysis with fs by limit equilibrium method for the governing cross-section. without showing how critical failure surface search (circular and non-circular) was satisfied.
- Substituting into FS = Στ_resist/Στ_driving = Σ[c'·l + (N−u·l)·tanφ']/Σ(W·sinα) outside the range where it is valid, and reporting the number anyway.
- Missing factor of safety acceptance criteria for static and seismic conditions, which is exactly the path to settlement, bearing failure or slope instability below the finished grade.
- Designing to the average condition when the governing condition is the controlling one.
- Freezing a design before the constructability and access review that would have changed it.
- Referencing figures, tables, or sources that never appear in the reference list.
- Carrying an assumption forward after the governing condition changed, without re-checking the result.
- Reporting numbers without units, or mixing US customary and SI inside a single calculation chain.
Section L
Industry case study
Nicoll Highway Excavation Collapse (Singapore, 2004)
Deep excavation slope and retaining system for a rail tunnel
Official findings
- Committee of Inquiry found the design underestimated the soil's driving forces relative to the retaining system's resisting capacity, leading to collapse
Field observations
- The controlling assumption was documented nowhere in the design record.
- No independent check existed at the stage where the error entered the work.
Engineering interpretation
- Interpretation below is student analysis for instructional purposes, not an official finding.
- Map the failure to a step in your own workflow and state where your process would have caught it.
Lessons learned
- Slope/excavation factor of safety must be checked against the site-specific soil strength, not a generic assumption
Source: Summarize the published investigation; cite it in your reference list. Do not reproduce copyrighted report text.
Section M
FE Civil exam connection
Handbook FE Reference Handbook — geotechnical engineering section (record the section number from your handbook edition).
Exam topics
Handbook formulas
- FS = Στ_resist/Στ_driving
Weak results here feed your FE Civil Academy weak-area queue for targeted practice.
Question 1 of 2
Score: 0/2In slope stability, which item must be established BEFORE the analysis is run?
Section N
Apply it to your project — Slope Stability
Complete this using your own capstone project data. Every field is saved to your project record and routed to your advisor with this module's submission.
Inputs and sources
Every value needs a traceable source.
| Quantity | Value | Unit | Source / record |
|---|
Assumptions and consequences
| Assumption | Basis | Consequence if wrong |
|---|
Self-check before submission
Section O
Design challenge
Consulting challenge — Slope Stability
Your firm has been retained to deliver the slope stability scope for a municipal client on a compressed schedule. Produce the technical position your firm would defend at a public meeting.
Client request: The client wants a defensible recommendation, the basis of design, and an honest statement of what remains unresolved.
Constraints
- Adopted local code edition governs; no exceptions without written variance.
- Budget and schedule are fixed; scope changes require change control.
- Public safety and accessibility requirements are non-negotiable.
Deliverables
- One-page basis of design
- Supporting calculation extract
- Risk and limitation statement
Evaluation
- Technical correctness
- Standard compliance
- Clarity of engineering judgment
- Honest treatment of uncertainty
Section P
Documentation workspace
Write the report section for this module in the academic editor
Section Q
File uploads
Accepted: PDF, DOCX, XLSX, CSV, PNG, JPG, ZIP, GeoStudio, PLAXIS
No files uploaded yet.
Section R
Deliverable and advisor review
Slope stability analysis with FS by limit equilibrium method for the governing cross-section.
Submissions route to your assigned faculty advisor and are scored independently by faculty and administrator rubrics.
Reflection
What was the hardest engineering judgment in this module, and how did you resolve it?
Section S
ABET outcome mapping
Slope stability analysis with FS by limit equilibrium method for the governing cross-section. with advisor review and dual scoring.
Assessment: Faculty rubric score and administrator rubric score on this module's submission.
Rubric: Engineering design · Target: 70% of students at or above 'meets expectations'.
Section T
References and further study
NAVFAC DM-7 (DM-7.1)
Adopted reference — cite section numbers, do not reproduce text.
Slope Stability — instructor design procedure
Course template for the calculation package format expected in the final report appendix.
NCEES FE Reference Handbook
Locate the equations used here and note the handbook section for exam recall.
Advisor meeting agenda item
Bring the unresolved decision from this module to your next weekly advisor meeting.