RocPlane (2.0)

A White Paper featuring RocPlane, our new

interactive software tool for performing planar rock slope

stability analysis and design

Geomechanics

software solutions

used worldwide in

the geotechnical and

mining industries

RocPlane for planar rock slope stability

Rocscience is very pleased to announce the release of RocPlane 2.0, a new interactive software tool

for performing planar rock slopes stability analysis and design. RocPlane makes it very easy to quickly

create planar models, visualize them in both 2D and 3D, and evaluate analysis results. This document

devotes particular attention to RocPlane’s ability to facilitate good engineering modelling practices.

Introduction to RocPlane

This white paper lays out the intended

role of RocPlane in modelling planar rock

slope stability problems. It will provide a

synopsis of planar slope stability analysis

and outline the different features in Roc-

Plane that facilitate the work of engineers

at different stages of design. The docu-

ment devotes particular attention to Roc-

Plane’s ability to facilitate good modelling

practices, as advocated by leading rock

mechanics authorities. These general prin-

ciples guide Rocscience’s development of

engineering software tools.

RocPlane is designed to assist engineers

in evaluating the stability of planar rock

slopes, and in formulating effective strate-

gies for improving stability.

For many rock slope problems, engineers

are required to assess the stability of slid-

ing masses in very short time. Often

such analyses are based on incomplete

data on conditions in the slopes. Such

circumstances require the prediction of

slope responses to variations in the values

of parameters that infl uence stability. As

well, engineers have to generate reports

that display model information and anal-

ysis results in a lucid and convenient

manner for the benefi t of managers, cli-

ents and colleagues.

RocPlane was designed to make it easy for

slope designers to achieve all their design

and report generation goals. The program

allows users to readily create, compute

and modify models. Its features give

users the opportunity to compare alter-

native remedial measures, allowing them

to opt for the most effective courses of

action. Used in conjectural ways, Roc-

Plane models give engineers a chance to

get the most out of their data.

2

Slope Engineering Design Process

Generally, engineering rock slope design

involves the following aspects:

Collection and analysis of data

Modelling of slopes

Remediation measures, if required,

for increasing stability of sliding

blocks

Writing of reports detailing analysis

results, input data, underlying

assumptions, and recommended

forms of action

For engineers to fully leverage their tech-

nical expertise during the design process,

they require tools that are easy to use and

have the required functionalities. In the

absence of such tools, they are compelled

to devote unwarranted amounts of time

and effort just trying to adapt their tools

to the tasks at hand. This detracts from

the principal design focus - the solution

of a slope stability problem - and reduces

overall productivity. As well, it takes away

time that could be otherwise devoted to

engineering creativity.

Role of RocPlane in DataCollection and Analysis

Rock engineering experts advocate the

use of models at the earliest stages of

a design project. Since there is often

little data available at preliminary design

stages, RocPlane was developed to facili-

tate the quick building and computation

of models, and easy model modifi cation.

Good conceptual modelling is a helpful

tool for testing how data can be collected

and used in the most effective manner. It

also helps engineers to understand occur-

ring phenomena and factors that control

them. RocPlane, because it allows easy

modelling, can contribute to signifi cant

time and money savings, and improved

design. Its use early in a project can help

engineers avoid the trap of investing large

amounts of money and effort without

understanding how effective the invest-

ment will be. Used carefully, RocPlane

can help uncover input parameters of a

rock slope problem that require more

careful consideration than others.

Rocscience therefore developed RocPlane

as a problem-solving tool for which the

ultimate test is not how accurate results

RocPlane was developed

to facilitate the quick building

and computation of models,

and easy modifi cation

3

are, but whether engineers are more

likely to make better decisions with them

than without them. It is designed to facil-

itate the testing of plausible alternative

assumptions and to help assess the conse-

quences of each assumption.

Modelling Methodology

The modelling of rock engineering prob-

lems is generally complex; the interpreta-

tion of data for use in models, the facets

of a problem that must be included in

a model, and the assumptions that are

most appropriate all demand considerable

amounts of professional judgement. This

is why geomechanics modelling is at times

compared to an ‘art’.

For slope design in such an environment,

RocPlane modelling can aid engineers to

gain understanding, and to investigate

potential trade-offs and alternatives.

Although based on a straightforward algo-

rithm, the program’s simplicity ensures

that users have complete intellectual con-

trol of the models they build. Models

are readily understood, and interactions

between important problem parameters

easily evident.

Other Benefi ts of using RocPlane

Combined with the good modelling

methodology that it facilitates, RocPlane

can help slope engineers increase con-

fi dence in their modelling results. The

program’s models, used innovatively, can

forewarn engineers to scenarios or out-

comes not considered beforehand.

RocPlane provides different shear

strength models, groundwater pressure

regimes, and other parameter models that

allow engineers to evaluate the impli-

cations of assumptions they use in anal-

yses. Even when a slope situation is

clearly three-dimensional, RocPlane can

help engineers create models that bracket

the true behaviour of the slope. In many

instances the bounds established in this

fashion are suffi ciently narrow and thus

provide useful information on the actual

real-life situation being modelled.

The program’s simplicity

ensures that users have

complete intellectual control

of the models they build

4

Overview of Planar Slope Stability Analysis

Planar failure is a relatively rare failure mode in rock slopes. This is because the specifi c geometrical

conditions required to produce such a failure are seldom encountered in real slopes. This not withstand-

ing, the study of planar failure mechanisms offers many benefi cial rock slope design insights. This

failure mode is particularly valuable for investigating the sensitivity of slopes to variations in parameters

such as the shear strength of failure surfaces and groundwater conditions.

To facilitate further discussion, the fi gure

to the right shows the primary compo-

nents of a planar failure model, and the

terminology, used in RocPlane.

General Conditions for plane failure

For planar failure to occur in a rock

slope, the following geometrical condi-

tions must be present:

A sliding or failure plane that

strikes parallel or approximately

parallel (within 20o) to the face of

the slope.

The failure plane must daylight

into the face of the slope. This con-

dition occurs when the failure sur-

face dips at angle shallower than the

slope face.

The dip of the failure plane must

be greater than the friction angle of

this plane.

The presence of release surfaces

at the lateral boundaries of the slide

block that have insignifi cant resis-

tance to sliding.

The two-dimensional models in Roc-

Plane analyze the stability of slope slices

that are taken perpendicular to the face

Plane failure problems may or may not involve tension cracks

of the slope, and that have unit thickness.

With this assumption, the area of the sur-

face on which sliding occurs can be rep-

resented by its trace length on a vertical

cross-section through the sliding block,

while the volume of the sliding block can

be represented by the area of the fi gure

created by the vertical section.

5

Assumptions in RocPlane

The models in RocPlane are based on

limit equilibrium analysis of a sliding

block. The factor of safety of the slope

or sliding mass is defi ned as the ratio of

the total forces resisting down-slope slid-

ing to the total forces inducing sliding.

The resisting forces comprise the shear

strength of the sliding surface, artifi cial

reinforcement of the slope or other sta-

bilizing external forces, if present. The

driving forces consist of the down-slope

component of the weight of the sliding

block, forces generated by seismic acceler-

ation, forces due to water pressures acting

on various faces of the block, and external

forces on the upper slope surface.

The limit equilibrium models in Roc-

Plane assume that all forces operating

on a sliding block act through the cen-

troid of the block; they ignore overturn-

ing moments. When an analysis involves

a tension crack, it is assumed that the

tension crack, just as the failure plane,

strikes parallel to the slope face.

Whereas many planar wedge analysis

programs consider only vertical tension

cracks, RocPlane allows for non-vertical

tension cracks as well. Non-vertical ten-

sion cracks in RocPlane can have angles of

inclination from the horizontal that can

exceed 90o.

RocPlane also has the following

capabilites:

A variety of water pressure distribu-

tions including user-defi ned distri-

butions. A simple example of

assumed pressure distributions

available in RocPlane is the case

where water enters a sliding plane

from the bottom of a tension

crack and seeps along the sliding

surface, escaping at atmospheric

pressure where the sliding plane

daylights in the slope face.

Five different shear strength models

for sliding planes, namely the

Mohr-Coulomb, Barton-Bandis,

Hoek-Brown, Generalized

Hoek-Brown and Power Curve

models.

A horizontal or non-horizontal

upper slope surface.

A bench analysis mode for design

ing and analyzing the stability of

individual benches in a benched

slope (e.g. open pit mine slope).

6

RocPlane Features

RocPlane is endowed with many features that provide users with the ability to rapidly build and modify

models, and run them. It also includes functionalities for easily analyzing results, generating fi gures and

charts, and producing convenient summaries of models and results.

The report generation features of Roc-

Plane are especially useful to engineers

when writing reports with high-quality,

and professional-looking drawings and

diagrams. They help slope designers to

readily communicate fi ndings to people

with varying slope engineering knowl-

edge. Major features in RocPlane are des-

ribed next.

Creation and Modifi cation of Models

For beginners, or infrequent users of a

software program, it is very necessary to

use an intuitive tool that allows them

to fi nd the features they need to accom-

plish their task with minimum effort. As

a result, a key development goal of Roc-

Plane was to provide an interface that

users can use without extensive experi-

ence with the software.

Easy discovery of model creating tools in

RocPlane is made possible through the

use of:

User friendly dialogs for defi ning

and modifying slope geometry, and

Easy-to-use dialog for entering

other input data

Functionalities that empower users to

rapidly explore a wide variety of situa-

tions include:

An option in the Input Data dialog

for including or excluding a tension

crack

Deterministic analysis for calculat-

ing the factor of safety of a slope or

sliding mass

Sensitivity analysis for evaluating

the infl uence of individual param-

eters upon the factor of safety

Probabilistic analysis for evaluating

the probability or risk of failure of

a slope

Application of multiple external

forces such as reinforcement loads,

or loads from buildings

Different water pressure distribu-

tions for a failure plane and tension

crack (users also have opportunity

to defi ne custom water pressure

distributions)

Application of seismic accelerations

that can destabilize a slope

An intuitive program, RocPlane gives theuser more confi dencein modelling bymaking functionalityeasy to discover.It focuses on making common tasks easyto preform.

7

Input Data Dialog

Data, including geometrical parameters,

for RocPlane models is entered through

an Input Data dialog. This dialog has

unique properties that make it easy to per-

form parametric analysis, or work simul-

taneously with multiple fi les. It can be

minimized or maximized with simple

mouse clicks. Whenever multiple fi les are

open, it automatically displays input data

for the active fi le.

In the Input Data dialog users can enter

deterministic or probabilistic input, based

on the selected analysis mode.

Wedge View

A sliding block or wedge in a model is dis-

played in a four-view, split screen format

showing TOP, FRONT, SIDE and PER-

SPECTIVE views. This feature enhances

perception of the model.

In the Wedge View, users can,

Rotate a model (in the Perspective

View only)

Move the sliding block out of the

slope (in all views)

Resize or maximize the different

views, and

Zoom in or out of the model

Info Viewer

RocPlane has an Info Viewer option that

displays a convenient summary of model

parameters and analysis results. The infor-

mation listed in the Info Viewer is very

useful for inclusion in a report or for

printing.

2D View of Models

In RocPlane users have the option of

viewing a cross-section, taken through a

model, which displays the geometry of

the model (including dimensions), and

the magnitudes of the force, normal to

the failure plane, and driving force. The

2D View also displays a table that sum-

marizes the values of important quantities

such as the factor of safety, wedge weight,

shear force, etc., computed in an analysis.

The Input Data Dialog in RocPlane in the example shown, the dialog isconfi gured for entering data for a deterministic analysis.

8

Four-view, split display of a planar rock slope medel in RocPlane. By simply clicking and dragging the right mouse button, or rotat-ing the mouse wheel, the block can be made to slide up or down the slope.

The 2D display of a planar slope model in RocPlane

9

Bench Anlaysis

Normally, RocPlane determines a sliding

block size as defi ned by a failure surface

extending from the toe of a slope to

the upper surface of the slope or to a

tension crack. By selecting the bench

analysis option in the Input Data dialog,

however, a user can defi ne an alternative

(smaller) wedge, scaled to the width of a

bench. This option is very useful for the

design of benches in an open-pit.

One of the most critical components of

any slope stability analysis is the deter-

mination of the water pressure distri-

bution within the slope. Current site

investigation methods are unable to pre-

cisely defi ne groundwater fl ow regimes

in a slope or rock mass. As a result a

slope designer must consider a number

of realistic extremes in order to bracket

the range of possible factors of safety,

and to gauge the sensitivity of a slope to

variations in groundwater conditions.

Some of the plausible groundwater pres-

sure distributions that can be modelled

in RocPlane are described next.

Dry slopes: This is the simplest case that

can be found in rock slopes. When using

this case it is assumed that a slope is com-

pletely drained.

Water in slope with no tension crack:

When no tension crack exists at the top

of the slope a reasonable water pressure

distribution has water intersecting the

failure surface at a specifi ed elevation

above the toe of the slope. It is then

assumed that pressures increase linearly

with depth to a maximum value at

half the specifi ed elevation and thereafter

decreases linearly to zero at the toe of

the slope.

Sliding block in the analysis of a slope bench. The block is scaled to the width of the bench. As such the failure plane does not exit at the slope toe.

Sliding block in the analysis of a complete slope. The block is scaled to the height of the slope by assum-ing that the failure plane paases through the slope toe.

Groundwater Pressure Distribution in RocPlane

10

Water pressure distri-bution ina slope with no tension crack. In this particular case it is assured that the pressure disribution on the failure varies linearly with height, reaching a maximum at the mid-height of the slope.

Simplest assumption of water pressure dis-tribution on sliding surface and tension crack. Here the pres-sure distribution in the tension crack increases linearly from the upper level of the column of water to a maximum value at the base. On the fail-ure plane it decreases linearly from the base of the tension crack to a zero value at the slope face.

11

Water in tension crack and on

sliding surface:

There is a range of plausible water pres-

sure distributions, which are likely for

such conditions. In all of the cases

the water pressure in the tension crack

increases linearly from the upper level of

the water column to the base of the ten-

sion crack.

In the simplest assumption, the pressure

distribution along the sliding surface

decreases linearly from the base of the

tension crack to a zero pressure condition

at the point where water exits from the

slope (the intersection of the failure sur-

face and the slope face). Since the actual

pressure distribution in a slope is often

not known, this assumed distribution is as

reasonable as any other made.

RocPlane considers an alternative water

pressure distribution in which pressures

along the failure plane increase linearly

from the tension crack base, reaches a

maximum value at the mid-height point

of the slope, and then decreases linearly

to the intersection of the failure plane and

the slope face.

More extreme case of water in tension crack

and on sliding surface:

If the exit point of water in a slope

became blocked or clogged for some

reason such as freezing of the slope face

in the winter, water pressure at the face

could be due to the full head of water in

slope instead of a zero pressure condition

at face. Such a water pressure distribution

is more dangerous to the stability of a

sliding block.

Custom Pressure:

The Custom Water Pressure option allows

users to independently specify the average

water pressure on a sliding plane, and on

a tension crack if present. This option

allows the greatest fl exibility in specifying

water pressure distributions, and is very

useful if actual water pressure data for

slopes is available.

Critical Tension Crack Location

When it is not possible to determine the

trace of a tension crack on the upper sur-

face or face of a slope (for example when

a tension crack is obscured by an over-

lying structure) it becomes necessary to

consider the worst-case slope stability sce-

nario. In such situations, RocPlane can

be used to search for the location of

the critical tension crack. The critical ten-

sion crack is the tension crack that, for

a particular slope condition, produces the

lowest factor of safety.

Reinforcement of a Slope/Slope

Stabilization Options

If it is established that a particular slope is

unstable, it becomes expedient to stabilize

the sliding mass. Slopes can be stabilized

through drainage, application of external

loads, fl attening or reduction of slope face

angle, reduction of slope height, or a

combination of measures.

12

External forces or loads that can be

applied to stabilize a sliding block

include measures such as rockbolts, cables

anchored into the rock mass behind fail-

ure surface, or the construction of a waste

rock berm to support the toe of slope.

The effect of a waste rock berm can be

accounted for in RocPlane as external

force specifi ed through a magnitude and

direction.

In the case of reinforcement, RocPlane

allows users to evaluate the number,

length and capacity of bolts needed to

stabilize a sliding block. For deterministic

analysis the program immediately calcu-

lates and displays the factor of safety as

users change various bolt parameters. This

makes it possible for users to interactively

modify bolt properties and see the effect

on stability.

Optimization of bolt orientation: Through

the selection of a simple option in Roc-

Plane, users can optimize individual bolts.

This option automatically determines the

bolt orientation that maximizes the factor

of safety.

Bolt load required to attain specifi ed

factor of safety: RocPlane supplies users

with an option that can calculate the bolt

load required to achieve a specifi ed factor

of safety for a sliding block.

Shear Strength Models

A critical assumption in planar slope

stability analysis involves the shear

strength of the sliding surface. There

are several models in rock engineering

that establish the relationship between

the shear strength of a sliding surface

and the effective normal stress acting on

the plane. RocPlane offers the following

widely accepted shear strength models:

Mohr-Coulomb

Barton-Bandis

Hoek-Brown

Generalized Hoek-Brown, and

Power Curve

Miscellaneous Features

Multiple Document Interface: In RocPlane

users can have several fi les open at the

same time. This feature facilitates the

simultaneous, quick and convenient anal-

ysis and comparison of multiple slope

models. It is very useful for evaluating the

merits of various remedial measures.

Internet Auto-Update Feature: Whenever a

user starts RocPlane, the program checks

for a new update at the Rocscience web-

site. If one is available, RocPlane prompts

the user to download the new version

immediately or asks if the user is to be

notifi ed again after a user-specifi ed period.

Interactive dialogfor specifying and modifying theparameters of a bolt. As soon as any bolt parameters are changed, RocPlane immediately recalcu-lates the factor of safety of the sliding block and displays it in the dialog.

13

Sensitivity Analysis and Sensitivity Plots

The effect of uncertainty in the values of a model’s parameters on results can be explored using a

sensitivity analysis. In sensitivity analysis, values of model parameters are varied across a range of likely

values and the effect on computed factors of safety observed.

This exercise helps identify the parameters

that have the most effect on the stability

of a sliding block, and can be used to

compare the effectiveness of various reme-

dial measures.

RocPlane can generate sensitivity plots,

which are plots of factor of safety results

on the basis of percentage changes in

model parameters specifi ed by users. On

sensitivity plots, the gradient of a curve

for a parameter indicates the effect that

parameter has on the factor of safety of

a sliding mass. Steeper rising or falling

curves indicate greater infl uence on the

factor of safety.

Sensitivity plotsshowing the infl uence of changes in slope angle, slope height, cohesion and the depth of tension crack fi lled with water. From the plots it is evident that changes in slope angle exert the strongest infl u-ence on the stability of the sliding block.

14

Uncertainty and Probabilistic/Stochastic Analysis

Probabilistic or stochastic analysis is used whenever it is important to consider the uncertainty in a

slope’s factor of safety. Estimation of this uncertainty helps to assess the probability or risk of failure

of the slope. Stochastic modelling enables engineers to go beyond the mere assessment of best- or

worst-case scenarios; it also makes it possible for them to evaluate outcomes most likely to occur.

RocPlane supplies the tools needed to per-

form true probabilistic analysis. It allows

users to specify statistical distributions

and ranges for input variables, and auto-

matically run hundreds or even thousands

of possible combinations of the variables

in a model.

Since every remedial measure for stabi-

lizing a sliding mass has a price tag,

RocPlane stochastic modelling can help

engineers and managers to weigh costs

against probability of success.

The histogram plot of the factor of safety results for a proba-bilistic analysis. The best-fi t distribution - a lognormal distribu-tion - for this histo-gram is also shown on the plot.

15

Some of the probabilistic analysis capabili-

ties in RocPlane include:

Statistical distributions (normal,

uniform, triangular, beta, exponen-

tial and lognormal probability

distribution functions) for input

data

Goodness-of-fi t tests for output data

distributions, and

Monte Carlo and Latin Hypercube

probabilistic simulation techniques

An option in RocPlane allows engineers

to include the correlation between the

cohesion and friction angle of sliding sur-

faces modelled with the Mohr-Coulomb

strength relationship, since this correlation

can infl uence expected outcomes.

Data and Results Interpretation Tools

for Probabilistic Analysis

RocPlane users have at their disposal

extensive and fl exible graphical capabil-

ities for interpreting and understanding

the behaviour of a planar failure model.

The program offers the following data

interpretation features:

Graphical output such as histograms

and cumulative (S-curve) distribu-

tions for all statistical input data

and quantities, such as wedge

weight and factor of safety, com-

puted in a model

Scatter plots of variables accompa-

nied by the calculation of correla-

tion coeffi cients and parameters of

best fi t lines for plotted data

Viewing of wedges corresponding

to points on histograms

Export of data from a probabilistic

simulation directly to Microsoft

Excel, the clipboard or a text fi le

Users can generate histograms and cumu-

lative plots for data that they select. On

the histogram plot for a selected variable,

RocPlane lists the mean, standard devia-

tion, minimum and maximum values of

the variable.

RocPlane lets users view sliding block

confi gurations that correspond to points

selected on a histogram or scatter plot.

When a user clicks on a part of a histo-

gram or scatter plot, the program updates

all views such as the Wedge View, 2D

View and Info Viewer so that they display

information for the nearest sliding block

model corresponding to the selected point

on the plot. This feature is useful, for

example, for determining the typical slope

conditions that generate sliding blocks of

a specifi ed factor of safety.

The results of a probabilistic simulation

in RocPlane can be displayed in graphs

and charts within the program, or can

be exported to the familiar interface of

Microsoft Excel with the simple click of

a button. They can also be copied to the

clipboard or to a text fi le. This feature

allows users to further process simulation

results using software with more sophisti-

cated statistical functionalities.

The results of aprobabilisticsimulation in RocPlane can bedisplayed in graphs and charts withinthe program, or can be exported to the familiar interface of Microsoft Excel.

16

Reporting Models and Analysis Results

The communication of model results to managers, colleagues, clients, or the public forms an

important part of the work of engineers. In addition to previously described features, the following

are some of the helpful tools RocPlane supplies, which make the communication of model

information and results easy to perform.

Grayscale option

The Grayscale option in RocPlane is a

toggle that automatically converts all the

views of a current document from colour

to grayscale, or vice versa. Toggled on,

the Grayscale option is useful for sending

images to a monochrome printer, or for

capturing monochrome image fi les.

The histogram plot of the factor of safety results for a probabi-listic analysis shown in grayscale.

Printing

The contents of an active view or window

in RocPlane can be readily printed. Print

output is confi gured to have a profes-

sional look and high quality. Users can

preview the look of the page to be

printed, and can customize the print out-

look by changing parameters such as ori-

entation of the page and margins.

17

Clipboard support

An active view can be captured to the

clipboard with a single command. From

the clipboard, images can be pasted

directly into word or image processing

applications.

Screen Capture to Image File

RocPlane has an Export Image File

option that allows users to save an

active view directly to a JPEG (*.jpg) or

Windows Bitmap (*.bmp) graphics fi le

format.

Concluding Statements

The software allows rock slope engineers

to focus on providing creative and innova-

tive solutions to problems by equipping

them with considerable functionality, and

freeing them from laborious and mun-

dane aspects of their design work. Using

RocPlane, slope designers can gain very

good understanding of planar failure slope

behaviour, and examine many plausible

possibilities with minimal effort.

RocPlane is a problem-solving tool created for engineers by engineers. It lays

out its tools in a well-designed and intuitive manner, and allows speedy building,

modifi cation and computation of models. Combined, these attributes facilitate

good modelling and engineering design practices.

RocPlane helps engineers to achieve the

important maxim that rock mechanics

models should never be run only once,

as the sensitivity of the results to changes

in model parameters and assumptions are

most informing.

18