Slide (4.0)

A White Paper describing our fully featured

limit equilibrium analysis program for slope

stability with integrated fi nite-element

groundwater analysis capabilities

Geomechanics

software solutions

used worldwide by

geotechnical

engineers

A synopsis of slope stability analysis with Slide

Rocscience is very pleased to announce the release of the latest version of Slide 4.0, which

includes a new integrated groundwater analysis module, major enhancements to support

modelling, and an improved toolkit for annotating fi gures generated in the software.

Introduction to Slide

Slide is a program for two-dimensional slope stability analysis developed by Rocscience. Slide can be used to design and/or analyze natural slopes or man-made (engineered) slopes such as cuts, embankments and fi lls (including earth dams and retaining structures such as tie-back walls, and soil nail structures),

and waste dumps formed from mining or industrial by-products.

Slide has the ability to analyze both a single user-defi ned non-circular failure surface and to search for the minimum non-circular failure surface. Composite surfaces containing both a circular and non-circular component can also be analyzed.

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Slide has an appealing and easy-to-use graphical interface, and provides a wide range of modelling and data interpretation functionalities. It calculates safety factors for circular and non-circular slope failure surfaces, using a number of widely used limit equilibrium analysis approaches such as the Bishop, Janbu, Spencer, Corp Engineers 1&2, Lowe-Karafi ath, and GLE methods.

Slide 4.0 also contains dozens of minor improvements that make the program more usable. The simple-to-use model building and editing tools in Slide

provide very convenient means for performing the parametric studies that underlie sound geotechnical engineering practice. The graphical data interpreter gives users a rich set of tools for viewing and analyzing model results.

As a result of the improvements to Slide, engineers now have a software package created specifi cally for performing the tasks involved in analyzing and designing slopes. This document lays out the philosophy governing the development of Slide, and the engineering toolkit it offers to slope designers.

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Philosophy of Slide: the engineering of slopes

The analysis and design of slopes are not trivial undertakings. Each of the several steps needed to solve this class of problems can consume signifi cant effort and resources. Consequently, a toolkit that simplifi es the performance of the tasks is of great benefi t to engineers. This is especially true when all those tools are assembled into one software package, and organized in an intuitive manner that refl ects how real-world design is done.

To develop a cutting-edge program intended for practical, day-to-day design of slopes, Rocscience software developers consulted practitioners in order to fully appreciate their needs, and combined that knowledge with the most recent advances in slope stability analysis and in computer technology.

Company engineers understood that it would be possible to create an effective software tool for practical design only if the goals and tasks of geotechnical engineers were properly appreciated.

“The sciences do not try to explain, they hardly even try to interpret, they mainly make models.

By a model is meant a mathematical construct which, with the addition of certain verbal

interpretations, describes observed phenomena. The justifi cation of such a mathematical

construct is solely and precisely that it is expected to work” - John von Neumann

Slide was developed to give practicing engineers the opportunity to focus on engineering, leaving the tedious and mundane tasks to the program. In the design environment facilitated by Slide, engineers can spend greater amounts of time studying results from different parameter combinations and creating alternative solutions.

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Goals and Philosophy of PracticalSlope Design and Analysis

Engineers perform slope stability analysis for a variety of reasons. The aims of slope stability analysis identifi ed from literature [References 1 – 2] and from interaction with practitioners include the following:

Assessment of the stability of slopes under specifi ed conditions

Evaluation of the possibilities of the failure of slopes.

Determination of the infl uence of proposed changes on a slope

Comparisons of the effectiveness of alternative remedial or preventive measures

Sensitivity analyses for evaluating the infl uence of variations in critical parameters such as geometry, material properties and groundwater conditions on the stability of slopes

Analysis of failures that have already occurred. This helps understand failure mechanisms and obtain in-situ material properties.

Design of remedial or preventive measures for slopes, and

Assessment of the effects of exceptional loadings such as earthquakes on slopes and embankments

Since the purpose of modelling in geotechnical engineering is to gain understanding and to explore potential trade-offs and alternatives, rather than to make absolute predictions, it was recognized that a practical slope stability program must combine computational speed with model creation swiftness and ease. Such a product would allow engineers to perform sensitivity analysis – a most informing approach in geotechnical modelling – in which the response of models to changes in parameters and assumptions is studied.

In creating Slide, developers ensured that they adhered to the philosophy and methodology behind good geotechnical modelling. Sound geotechnical modelling encourages a cautious approach in which engineers consider wide-ranging scenarios in ways that lead to new knowledge or fresh understanding. A modelling framework of this nature can alert modellers to phenomena, situations, or outcomes not previously considered. As well it can help engineers identify areas where more fi eld data or information is required.

The purpose of

modelling in

geotechnical

engineering is to

gain understanding

and to explore

potential trade-offs

and alternatives.

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Modelling Features in Slide

The stability of a slope is infl uenced by factors such as geological conditions (soil and rock layers,

discontinuities, groundwater conditions, etc.), material properties, and geometry. As a rule many of

these factors cannot be defi ned with much certainty. This uncertainty means that engineers must

analyze various possible scenarios in order to avoid surprises and unexpected behaviour.

For Slide to be a benefi cial program for

routine practical design, it was necessary

to equip the program with a wide range

of analysis methods and strength models,

and with tools that facilitate quick

creation of models, and easy and fast

modifi cation of model input parameters/

assumptions.

In this section we shall be describing the

different analysis methods, shear strength

models, and some of the principal tools

available in the program.

Analysis Methods

Slide incorporates the most widely used and accepted limit-equilibrium approaches based on the method of

slices.

Ordinary

Bishop Simplifi ed

Janbu Simplifi ed

Janbu Corrected

Spencer

Corp Engineers 1 & 2

Lowe-Karafi ath, and

Generalized Limit Equilibrium Method (GLE)

The methods implemented in the program are the:

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A note on the Use of VariousAnalysis Methods

Because the formulation of the stability of a slope in limit equilibrium terms is a statically indeterminate problem (the number of equations is less than the number of unknowns), all approaches based on the method of slices use simplifying assumptions. These assumptions limit the range of application of the different methods. To make the best use of his/her time and of Slide’s capabilities, it is important for the engineer to understand the varying strengths and limitations inherent in different slope stability formulations.

Table 1. Limit equilibrium slope stability methods and the equilibrium equations they satisfy [1].

Method Satisfaction of Force Equilibrium Satisfaction of Moment Equilibrium

Horizontal Vertical

Ordinary Method No No YesBishop Simplifi ed No Yes YesJanbu Simplifi ed Yes Yes NoJanbu Corrected Yes Yes NoCorps of Engineers 1 & 2 Yes Yes NoLowe and Karafi ath Yes Yes NoGLE Yes Yes YesSpencer Yes Yes Yes

In this sub-section we provide guidelines, obtained from literature, on the use of the various analysis methods.

The limit equilibrium methods implemented in Slide fall into three main categories:

Methods that satisfy force equilibrium equations

Methods that satisfy moment equilibrium equations, and

Methods that satisfy both force and moment equilibrium equations.

Table 1 below provides a summary of the groupings of the methods in Slide.

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The method selected for analyzing a specifi ed slope problem must be suitable for the slope

conditions being analyzed. Table 2 below is a summary of the conditions under which the various

methods are most suitable. They were compiled from references [3 – 4].

Analysis Method Shape of Slip Surfaces Limitations and Applications

Ordinary Only circular slip surfaces

Highly inaccurate for effective stress analysis of fl at slopes with high pore pressures.

Perfectly accurate for φ = 0 analysis.

Quite accurate for total stress analysis for circular slip surfaces.

Method does not have numerical stability problems.

Bishop Simplifi ed Only circular slip surfaces

Except when numerical instabilities arise, accurate for all conditions (gives practically the same answers as the methods that satisfy all equations of equilibrium).

Method is numerical unstable under certain conditions.

If for a specifi c slip circle the factor of safety obtained from the method is smaller than the factor of safety from the Ordinary method, then it can be concluded the Bishop method experienced numerical diffi culties. In that case the result from the Ordinary method is the more accurate.

Force Equilibrium Methods:Lowe and Karafi athCorps of Engineers 1 & 2Janbu Simplifi edJanbu Corrected

Any shape of slip surface Computed factor of safety values are sensitive to the assumed inclinations of side forces.

Can experience numerical instabilities.

For slopes in cohesive soils, when side forces are improperly chosen, these methods may yield factor of safety values that are about a third larger than the ‘correct’ value.

Force and Moment Equilibrium Methods:Morgenstern and PriceSpencer

Any shape of slip surface Can be deemed to provide the correct answers to most practical problems.

Accurate for any conditions except when numerical instabilities occur.

Give about the same answers. Variation in answers is slightly increased in problems involving non-homogeneous materials.

Table 2. Analysis methods, situations in which they are most applicable, and limitations.

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Location of Critical Surfaces

One of the most important facets of slope stability analysis is fi nding the slip surface, which has the lowest factor of safety. The developers of Slide implemented proven search techniques for locating both circular and non-circular slip surfaces. They help engineers to ensure they have indeed determined critical surfaces. The techniques in Slide are as follow:

Circular surface grid search

Single circular surface defi ned by a centre and radius or by three points on the surface

Slope Search method (allows users to defi ne slope parts through which circular slip surfaces must pass)

Auto-refi ne search (an iterative technique for locating the minimum slip circle that uses the results of a previous iteration to narrow the search area in the next step)

Non-circular block search using random surface generation, and

Non-circular path search using random surface generation.

Non-circular block search technique

Circular surface grid search technique

Strength Models

The shear strengths of the materials that form a slope have signifi cant impact on stability and are required for all limit equilibrium methods. The following strength models are found in Slide:

Mohr-Coulomb

Hoek-Brown

Generalized Hoek-Brown

Anisotropic strength

Non-Linear shear-normal functions

Undrained (φ = 0)

Zero strength

Infi nite strength

Vertical Stress Ratio

Barton-Bandis

Power Curve, and

Hyperbolic.

In the majority of practical slope problems, the greatest uncertainty is associated with the evaluation of shear strength parameters. As a result engineers often have to assess the infl uence of various assumed strength models and parameters on stability. To facilitate this process signifi cant effort was expended creating simple, quick-to-use means for entering strength parameters into Slide. This goal was realized through the use of intuitively organized dialogs.

Slide can

accommodate slope

models consisting

of multiple materials

as well as tension

cracks. It can also

read data fi les from

other slope stability

analysis packages

such as Slope/W

and XSTABL.

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Model Creation Tools in Slide

The model creation unit (Modeller) in Slide has undergone numerous improvements to make it easier to create and modify models. Unlike most slope stability programs, Slide does not impose severe restrictions on the types of geometries that can be modelled, nor on the manner in which boundaries have to be defi ned. It can readily accommodate complex slope and material boundary geometries. This fl exibility and generality, attained through the use of soil cell technology, allows Slide to be used to model a very wide range of geometric confi gurations. Soil cell technology is an adaptation and improvement of techniques that have been very successful in fi nite element programs.

The geometry of models is entered into Slide using CAD-based graphical data technology. Such an approach allows for the interactive building and editing of models. Slide can also import model geometries from Autocad™ DXF fi les. Additional tools in Slide that facilitate smooth model creation and modifi cation include undo/redo functions.

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Feature for ParametricAnalysis and Interpretationof Multiple Files

In parametric and sensitivity analysis, model geometry and parameters are varied and results of alternative scenarios compared or analyzed. To facilitate the comparison of multiple fi les, Slide is equipped with the two features listed below: Quick-Zoom menu option that

scales all windows to the same coordinate system (the feature is also very useful for producing consistent screen captures). Data-Tips, which bring up relevant

model information as the mouse is moved over different entities in a model. For example, when the mouse is moved over a material, its properties such as cohesion and friction angle pop-up.

Other improvements made to the Modeller’s interface:

Display of coordinates for entities in a model (this feature is invaluable for checking whether a model has been correctly described, and comparing that model with another) Interactive pie chart that makes

entering anisotropic strength functions intuitive Availability of pop-up menus on the different entities of a model (right-clicking on a grid, for example, brings up a dialog that allows you to change grid spacing, or move the grid) Context-sensitive help for all dialogs

in the Modeller Defi nition of specifi ed circular

slip surfaces using three points along the surface, making it easier to place such circles in a model.

Slide is equipped with

a Quick Zoom menu

option and Data-Tips

to facilitate the

comparison of

multiple fi les

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Loading

The loads acting on a slope play a

signifi cant role in stability. The location,

magnitude and direction of loads can

either increase or reduce stability. Slide

allows users to model line loads, and

uniform and triangular distributed

loads. Through the use of the seismic

acceleration coeffi cient, Slide can also

accommodate the modelling of the

impact of earthquakes on slopes. Users

can analyze both horizontal and vertical

loads imposed by earthquakes.

Support

A variety of support measures are

employed by geotechnical engineers

to stabilize slopes. The distribution of

loads along reinforcement elements

differs from one support type to the

other. To enable engineers to design

support systems by modelling them

and comparing their effectiveness, the

following commonly used reinforcement

types are incorporated into Slide:

Grouted Tiebacks End-Anchored Support Soil Nails GeoTextiles Micro-Piles, and User-Defi ned Support

(for complete fl exibility).

Line loads, uniform and triangular distribution

loads can be easily implemented in Slide

Slide 4.0 introduces major enhancements in

support modelling by introducing

several new support types

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Data Interpretation and Report Tools in Slide

The numerical results from slope stability analyses guide engineers in comparing possible

scenarios and adopting design approaches. Tools, therefore, that help with the visualization and

interpretation of results are of great importance to slope designers.

Maximize the insight that can be gained from results

Uncover underlying trends in slope behaviour

Extract model parameters that have the most impact on stability

Detect any anomalous situations or behaviour

Test underlying assumptions on parameters such as shear strength models and groundwater conditions.

These goals were achieved mainly through the use of cutting-edge graphics technology. The graphics techniques in Slide empower users with signifi cant ability to gain fresh and sometimes unexpected insight into slope behaviour.

Slide interpreter

generates minimum

factor of safety

contours and colour

codes critical slip

surfaces by their

ranges of safety

In designing the Data Interpreter in Slide,developers aimed at incorporating approaches that help:

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Slide Features that FacilitateReport Generation

At the end of a modelling or design exercise, engineers have to produce reports on their fi ndings. To facilitate the report generation, Slide can output professional quality fi gures of a model, and results summaries. It also supplies users with tools for dimensioning models, and a toolkit for adding annotations such as text, arrows, lines, and boxes to drawings of models.

Images from Slide can be copied to the Windows clipboard for pasting into reports. As well images can be saved to fi le formats that can be easily imported into Autocad™. The program has a single-click option for converting colour images into grayscale captures. Slide also has simple-to-use functions for exporting data and plots directly to Microsoft Excel™ or other spreadsheet or word processing programs.

Slide supplies

users with tools

for dimensioning

models and a

toolkit for adding

annotations

The data interpretation features in Slide include contouring and plotting facilities, and ability to view multiple plots on a screen. The Interpreter generates minimum factor of safety contours, and colour codes critical slip surfaces by their ranges of factor of safety values. It also has tools for plotting essential model results such as the normal and shear stress distributions, strength distributions and pore pressures along slip surfaces.

The colour coding of critical slip surfaces helps engineers to not only calculate the minimum critical surface, but also identify all surfaces with critical factor of safety values less than a specifi ed threshold. Such knowledge is required, for example, for the determination of lengths of anchors and other stabilization methods. Slide supplies an innovative tool for displaying all such critical slip surfaces.

The Interpreter

tools were grouped

and organized

in ways that

complement the

natural pattern-

recognition

capabilities of

users.

Groundwater Calculations for Slope Stability Analysis

Groundwater conditions in a slope have a signifi cant infl uence on stability. Groundwater affects

stability through effects such as generation of positive and negative pore pressures that alter

stress conditions, and changes to the bulk density of slope materials.

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Typically, traditional slope stability programs incorporate groundwater into analysis through consideration of a ‘hydrostatic line’. Although simple to implement, the ‘hydrostatic line’ approach is conservative in some cases, especially in cases when unsaturated zones can arise. In layered soil problems, the approach overestimates pore water pressures in

some zones, affecting the calculation of shear strength at the bases of slices.

The latest version of Slide, version 4.0, incorporates an integrated steady-state groundwater analysis module. The module uses the fi nite element method to calculate groundwater fl ows, pressures

and gradients.

Pore water pressure

calculated from the

new module can

be automatically

incorporated in

slope stability

analysis by Slide.

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Also the module relies on the same fi nite element and automatic mesh generation technology implemented in Phase 2 (a geotechnical fi nite element stress analysis program developed by Rocscience).

The groundwater module in Slide offers users several types of boundary conditions. This allows users to test different hypotheses on groundwater conditions in a slope. This ability

to test different alternatives makes it possible for engineers to bracket the extents of the infl uence groundwater has on slope behaviour.

Users can seamlessly incorporate computed pore pressures into slope stability analysis in Slide, since the groundwater module is completely embedded in the Modeller. As an added bonus, the module can be used for general groundwater analysis.

Boundary conditions can be easily set by

picking either segments or nodes

Future Advancements

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These include probabilistic analysis, fi nite element analysis, and additional commonly used support models. Plans are also in place for including the Sarma and Generalized Wedge slope stability analysis methods into Slide.

Probabilistic Analysis

Probabilistic analysis is receiving increasing acceptance in several areas of geotechnical engineering. In slope stability analysis it has been recognized that the factor of safety is not necessarily a good indicator of the probability that a slope would fail. A slope can have a factor of safety higher than that of another but still have higher threat of failure. This is due to the fact that factor of safety analysis utilizes average values of parameters and thus can mask the wider variation (uncertainty) in the values of the different parameters affecting stability. With probabilistic analysis engineers will be able to assess the risks of failure associated with different slope and design options.

In addition to Monte Carlo simulation methods, Rocscience intends to implement state-of-the-art reliability methods in upcoming Slide versions.

Finite Element Analysis

With the use of soil cell technology, and the implementation of an integrated fi nite element groundwater analysis module, the current version of Slide has the necessary building blocks used in fi nite element analysis. This method of analysis enjoys certain advantages over limit equilibrium methods. These include the ability to model stresses and deformations, ability to consider the history of formation of a slope (for both natural slopes and engineered slopes such as embankments), and no prior assumptions on shape or location of failure surfaces. The prediction of stress and deformation conditions in a slope is very useful for determining the conditions under which laboratory tests for slope materials should be made. The magnitude of deformations is also a better predictor of stability and behaviour than factor of safety values.

Rocscience strongly

believes that it is

important to extend

the Slide capabilities

to include stress and

deformation analysis.

In response to requests from users and to advancements in slope stability technology, a number of

techniques have been designated for implementation in future versions of Slide.

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Due to these advantages and the existence in Slide of the building blocks of the fi nite element method, Rocscience strongly believes that it is important to extend the program to stress and deformation analysis. Finite element analysis of slopes can be performed in Phase2, the fi nite element geotechnical modelling package developed by the company. However, as the application of the method to slope stability analysis becomes more common, it will be a natural step to include the method in Slide.

Additional Support Models

To expand Slide’s range of design appli-cations, subsequent versions will include more support models. It is the goal of the program’s developers to equip engi-neers with more design tools, in addition to the existing analysis methods.

Sarma and Generalized WedgeAnalysis Methods

The classical slope stability methods, described earlier in the document, are mostly useful for the analysis and design of soil slopes. In rock slopes, however, failure surfaces commonly pass through

pre-existing discontinuities such as joints and faults, or through weak material seams. There are plans therefore to add to Slide’s repertoire of methods, analysis approaches that accommodate the failure modes encountered in rock slopes. Two methods that have been identifi ed for implementation are the Sarma and Generalized Wedge analysis techniques.

The Sarma method is well suited for the analysis of complex non-circular slope stability problems requiring non-vertical slices. It allows the strength properties of slice boundaries to differ from those of the slice material. As a result of this feature discontinuities and failure planes can be explicitly modelled by the method.

The Generalized Wedge method has attributes similar to those of the Sarma method. It differs however in the way it calculates factor of safety values. The Generalized Wedge method uses an iterative approach to compute the factor of safety from force equilibrium considerations of wedges. It also ensures that moment equilibrium is maintained.

Concluding Remarks

The program was designed to free slope designers from mundane tasks to enable them to focus their creative energies on the actual engineering aspects of the design process. It allows users to achieve a most fundamental goal of geotechnical engineering design – multiple analyses of problems that yield insight and fresh understanding. Slide will continue to evolve along these lines.

Slide will also seek to bring recent advancements in slope stability analysis from the realms of academic research to the forefront of practical and everyday analysis and design. This assures users access to state-of-the-art knowledge that enhances their productivity and the safety and economy of their designs.

In creating Slide, developers have been guided by the needs of the practising engineer and the

tasks they typically perform when designing or analyzing slopes.

References

1. Abramson, L.W., L.S. Thomas, S. Sharma and G.M. Boyce. Slope Stability and Stabilization Methods. 2001. John Wiley & Sons. New York.

2. Chowdury, R.N. Slope Analysis. 1978. Elsevier, New York.

3 Duncan, J.M., 1996, “State of the art: limit equilibrium and fi nite element analysis of slopes,” Journal of Geotechnical Engineering, pp 577-596.

4. Duncan, J.M. and S.G. Wright. 1980. “The accuracy of equilibrium methods of slope stability analysis,” Engineering Geology, vol. 16, pp 5-17.

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