1. Numerical Analysis of slopes
ICL Landslide Teaching Tools　
PPT-tool (b) (1)
Numerical Analysis of slopes
Simon Nelis
Simon NELIS
Formerly at GNS Science (Lower Hutt)

2. Numerical modelling and analysis
ICL Landslide Teaching Tools　
PPT-tool (b) (2)
Numerical modelling and analysis
What is numerical analysis?
Why undertake numerical analysis?
Provides insight into processes and mechanisms controlling stability
Numerical analysis has become much more commonplace in the last 20 years
Commercially available software is cheaply available and complex analyses can be run on desk top PC’s

3. Applicability to slope stability
ICL Landslide Teaching Tools　
PPT-tool (b) (3)
Applicability to slope stability
Ability to define Factor of Safety of a slope
Back analysis to determine material strengths and/or triggering mechanisms
Undertake sensitivity analyses
Material properties
Groundwater
Analyse effects of changes to slope geometry, e.g. Ruapehu dam breach analysis
Investigate the effect of changing static and dynamic loads on stability of the slope
Determine the effectiveness of remedial measures on improving performance of the slope.

4. Software available Limit equilibrium Slide Slope/W
ICL Landslide Teaching Tools　
PPT-tool (b) (4)
Software available
Limit equilibrium
Slide
Slope/W
Finite Element / difference
Phase 2
FLAC2D and FLAC3D
PLAXIS
Discrete / Distinct elements
UDEC
PFC2D and PFC3D

5. Conventional analyses
ICL Landslide Teaching Tools　
PPT-tool (b) (5)
Conventional analyses
Analysis Method
Critical Parameters
Advantages
Limitations
Stereographic and Kinematic
Critical slope and discontinuity geometry; representative shear strength characteristics.
Relatively simple to use; gives initial indication of failure potential; may allow identification and analysis of critical key blocks using block theory; links are possible with limit equilibrium methods; can be combined with statistical techniques to indicate probability of failure.
Only really suitable for preliminary design or design of non-critical slopes; critical discontinuities must be ascertained; must be used with representative discontinuity/joint shear strength data; primarily evaluates critical orientations; neglecting other important joint properties.
Limit Equilibrium
Representative geometry an material characteristics; soil or rock mass strength properties (cohesion and friction); discontinuity shear strength characteristics; groundwater conditions; support and reinforcement characteristics.
Wide variety of commercially available software for different failure modes (plane, wedge, toppling etc.); can analyse Factor of Safety sensitivity to changes in slope geometry and material properties; more advanced codes allow for multiple materials, 3-D, reinforcement and/or groundwater profiles.
Mostly deterministic producing a single Factor of Safety (but increased use of probabilistic analysis); Factor of Safety gives no indication of failure mechanisms; numerous techniques are available all with varying assumptions; strains and intact failure not considered; probabilistic analysis requires well defined input data to allow meaningful evaluation.
Rockfall Simulators
Slope geometry, rock block sizes and shapes; coefficient of restitution.
Practical tool for siting structures; can use probabilistic analysis; 2-D and 3-D codes are available.
Limited experience in use relative to empirical design charts.

6. Examples Conventional analyses
ICL Landslide Teaching Tools　
PPT-tool (b) (6)
Examples Conventional analyses
Rockfall simulation

7. Examples Conventional analyses
ICL Landslide Teaching Tools　
PPT-tool (b) (7)
Examples Conventional analyses
Limit Equilibrium

8. Advanced numerical analyses
ICL Landslide Teaching Tools　
PPT-tool (b) (8)
Advanced numerical analyses
Analysis Method
Critical Parameters
Advantages
Limitations
Continuum Modelling (e.g. finite element, finite difference).
Representative slope geometry; constitutive criteria; (e.g. elastic, elasto-plastic, creep); groundwater characteristics; shear strength of surfaces; in situ stresses.
Allows for material deformation and failure (Factor of Safety concepts incorporated); can model complex behaviour and mechanisms; 3-D capabilities; can model effects of pore water pressures, creep deformation and/or dynamic loading; able to assess effects of parameter variations; computer hardware allow complex models to be solved with reasonable run times.
User must be well trained, experienced and observe good modelling practice; need to be aware of model and software limitations (e.g. boundary effects, meshing errors, hardware memory and time restrictions); availability of input data generally poor; required input parameters not routinely measured; inability to model effects of highly jointed rock; can be difficult to perform sensitivity analysis due to run time constraints.
Discontinuum Modelling (e.g. distinct element, discrete - element).
Representative slope and discontinuity geometry; intact constitutive criteria; discontinuity stiffness and shear strength; groundwater characteristics; in situ stress state.
Allows for block deformation and movement of blocks relative to each other; can model complex behaviour and mechanisms (combined material and discontinuity behaviour coupled with hydro-mechanical and dynamic analysis); able to assess effects of parameter variations on instability.
As above, user required to observe good modelling practice; general limitations similar to those listed above; need to be aware of scale effects; need to simulate representative discontinuity geometry (spacing, persistence, etc.); limited data on joint properties available (e.g. joint normal stiffness, joint shear stiffness).
Hybrid/Coupled modelling
Combination of input parameters listed above for stand-alone models.
Coupled finite-/distinct-element models able to simulate intact fracture propagation and fragmentation of jointed and bedded rock.
Complex problems require high memory capacity; comparatively little practical experience in use; requires ongoing calibration and constraints.

9. Examples advanced numerical analysis
ICL Landslide Teaching Tools　
PPT-tool (b) (9)
Examples advanced numerical analysis
Finite Element modelling

10. Examples advanced numerical analysis
ICL Landslide Teaching Tools　
PPT-tool (b) (10)
Examples advanced numerical analysis
Distinct Element
East-west profile
Equilibrium
13,000 iterations
20,000 iterations
25,000 iterations

11. Limitations and pitfalls numerical analysis
ICL Landslide Teaching Tools　
PPT-tool (b) (11)
Limitations and pitfalls numerical analysis
Numerical analyses are performed on the basis of given input, not on a through understanding of physics of the problem
Errors arise from:
Poor understanding of geological/geotechnical model
Inadequate material testing to define material behaviour
Inadequate zonation forcing the model to behave in a particular way
Results using the same software and input parameters can be user dependant
Models can be sensitive to constitutive models chosen to represent material behaviour
Sensitive to sequence of calculation
Results should be used to gain an insight into physical processes, rather than used as an absolute predictive tool

12. ICL Landslide Teaching Tools　
PPT-tool (b) (12)
Conclusions
Numerical analyses should be carried out, but the results should NEVER be considered an accurate representation of reality
The ability of numerical models to predict mechanisms of behaviour is a major advantage
Analyses can deal with both complex and simple problems
Results from numerical models can be user dependant
Limitations exist with constitutive models used to represent material behaviour in models
An in depth knowledge of soil mechanics is required
Familiarity of the software being used for the analysis is required