Tutorial_11_Overall_Slope_Reliability.pdf

Overall Slope Reliability Tutorial 11-1

Overall Slope Reliability

This tutorial will demonstrate the Overall Slope probabilistic analysis

method in Slide .

The finished product of this tutorial (file: Tutorial 11 Overall Slope

Reliability.sli ) can be found in the Examples > Tutorials folder in your

Slide installation folder.

Introduction

In Slide , there are two types of Probabilistic Analysis which can be

carried out.

1. Probabilistic Analysis Type = Global Minimum

2. Probabilistic Analysis Type = Overall Slope

With the Global Minimum method, the probabilistic analysis is carried

out ONLY on the deterministic Global Minimum slip surface.

It is assumed that the Probability of Failure (or the Reliability) of the

deterministic Global Minimum slip surface, is representative of the

Probability of Failure for the slope.

This method is a commonly used approach to probabilistic slope stability,

and was demonstrated in Tutorial 08 .

Slide v.5.0

Tutorial Manual

Overall Slope Reliability Tutorial 11-2

Overall Slope Method

The Overall Slope Probabilistic Analysis Type in Slide represents a

different approach to the probabilistic analysis of slope stability.

1. With the Overall Slope method in Slide , the ENTIRE SEARCH for a

Global Minimum slip surface, is repeated N times (where N =

Number of Samples). For each search iteration, a new set of random

variable samples is first loaded, and the search is carried out.

2. A Global Minimum slip surface, FOR EACH SEARCH iteration, is

then determined. This will generally result in the location of

SEVERAL different Global Minimum slip surfaces (for example, 10 to

50 surfaces might typically be located), corresponding to different

values of the sampled input data random variables.

There are two important results which are derived from the Overall

Slope Probabilistic Analysis:

• The Overall Slope Reliability

• The Critical Probabilistic Surface

Overall Slope Reliability

The Overall Slope Reliability is based on the distribution of safety factors

obtained from ALL of the Global Minimum slip surfaces located by the

analysis.

Because multiple Global Minimum slip surfaces will (in general) be

located, the Overall Slope Reliability is not associated with a specific slip

surface, but instead, can be considered truly representative of the entire

slope. Hence the name “Overall Slope” analysis method.

From the Overall Slope analysis, we may calculate both:

• Probability of Failure

• Reliability Index

The definition of the Probability of Failure, for the Overall Slope method,

is the same as for the Global Minimum method. That is, the Probability

of Failure is the number of analyses which result in a safety factor less

than 1, divided by the total Number of Samples. Similarly, the Reliability

Index is calculated using the same equations discussed in Tutorial 08

(Probabilistic Analysis tutorial).

Just remember that the PF and RI calculated for the Overall Slope, are

not associated with a specific slip surface, but include the safety factors of

ALL Global Minimum slip surfaces from the Overall Slope Probabilistic

Analysis.

Slide v.5.0

Tutorial Manual

Overall Slope Reliability Tutorial 11-3

Critical Probabilistic Surface

Another result which follows from an Overall Slope Probabilistic

Analysis, is the Critical Probabilistic slip surface.

The Critical Probabilistic Surface is the individual slip surface which has

the Minimum Reliability Index (and also the maximum Probability of

Failure).

It is important to note that the Critical Probabilistic Surface IS NOT

NECESSARILY THE SAME AS THE CRITICAL DETERMINISTIC

SLIP SURFACE. In general, the Critical Probabilistic Surface and the

Critical Deterministic Surface (i.e. the deterministic Global Minimum

slip surface), can be different surfaces.

Critical Deterministic Surface

During the Overall Slope probabilistic analysis, the program also keeps

track of the Probability of Failure and Reliability Index for the Critical

Deterministic Surface (i.e. the deterministic Global Minimum slip surface

– the slip surface with the minimum safety factor, when all input

parameters are equal to their mean values).

The Probability of Failure and Reliability Index which are calculated for

this surface, are the same as would be calculated by running the Global

Minimum probabilistic analysis method.

Summary of Results

An Overall Slope probabilistic analysis with Slide , therefore provides

THREE distinct sets of results.

We can rank these results from LOWEST Reliability Index to HIGHEST

Reliability Index (OR the equivalent, HIGHEST probability of failure, to

LOWEST probability of failure), as follows:

1. The Overall Slope Results – in general, the Overall Slope Results will

give the LOWEST Reliability Index (and the HIGHEST Probability of

Failure), because “failure” can occur along any surface in the slope.

The analysis is not restricted to a single slip surface.

2. The Critical Probabilistic Surface – the Critical Probabilistic Surface

will (in general), have a HIGHER Reliability Index than the Overall

Slope results (and a lower Probability of Failure).

3. The Critical Deterministic Surface – the Critical Deterministic

Surface will (by definition), have a HIGHER Reliability Index than

the Critical Probabilistic Surface, IF THE TWO SURFACES ARE

DIFFERENT. If the two surfaces are the same, then the results will

of course be equal.

Slide v.5.0

Tutorial Manual

Overall Slope Reliability Tutorial 11-4

The potential advantage of the Overall Slope method, compared to the

Global Minimum method, is that the Overall Slope method does NOT

assume that the Probability of Failure for the slope, is equal to the

Probability of Failure of the Deterministic Global Minimum slip surface.

The interpretation and application of these results for slope design

purposes, is the responsibility of the geotechnical engineer. It is not

possible to make a general statement regarding which Probability of

Failure or Reliability Index should be used, as this may vary

considerably, depending on the model, and the goals of the analysis.

Time to Run Analysis

The Overall Slope method involves a substantially greater computation

time than the Global Minimum method, because the entire slip surface

search is repeated for each set of random samples. Depending on the

Number of Samples, and the complexity of your model, the Overall Slope

Probabilistic Analysis in Slide , can take SEVERAL HOURS to complete.

In general, you may wish to run an Overall Slope probabilistic analysis,

at the end of a day, as an overnight run. Remember that the Slide

Compute Engine can run multiple files in succession, so you can set up

several files for an Overall Slope Probabilistic Analysis, and run the

analyses overnight.

Slide v.5.0

Tutorial Manual

Overall Slope Reliability Tutorial 11-5

Model

For this tutorial, we will read in a file.

Select: File → Open

Open the Tutorial 11 Overall Slope Reliability.sli file, which you will

find in the Examples > Tutorials folder in your Slide installation folder.

The model is already completed, so we will note the following significant

features of the model, and then view the analysis results.

Project Settings

Go to the Project Settings dialog, and select the Statistics tab.

Notice that the Probabilistic Analysis Type = Overall Slope. Select Cancel

or Escape.

Material Statistics

Go to the Material Statistics dialog (in the Statistics menu). Notice that

we have defined the Cohesion and Friction Angle for 3 different

materials, as Random Variables (for a total of 6 Random Variables). All

variables have Normal distributions.

Slide v.5.0

Tutorial Manual

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: