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Field stresses in SIGMA/W can be used to establish the initial stress of the subsurface.

This webinar demonstrates a practical example using the Field Stresses feature in SIGMA/W, as well as some practical tips for simulating initial stress in the subsurface.

Establishing the initial stress in the subsurface is key to conducting stress-strain analyses that captures the behaviour of the physical system. The presence of high in situ stress, for example, can lead to rock bursts or significant deformations in mining and tunnel applications. High stresses environments are common in complex geological systems in which tectonics or other geological processes lead to over-stressed rock, or in geotechnical applications at great depths. This webinar reviews field stresses and how they are used, including a practical example in SIGMA/W and tips for avoiding potential pitfalls.



Vincent Castonguay


22 min

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Video Transcript

<v Instructor>Hello and welcome</v>

to this GeoStudio webinar focusing

on field stresses, one of the recent additions

to our products.

I’m Vincent Castonguay, I work as a research

and development specialist with

the Geoslope engineering team here at Seequent.

Today’s webinar will be approximately 30 minutes long.

Attendees can ask questions using the chat feature.

I will respond to these questions via email

as quickly as possible.

A recording of the webinar will also be available

so participants can move you the demonstration at

a later time.

GeoStudio is as a software package developed

for geotechnical engineers and earth scientists comprise

of several products.

The range of products allow users to solve

a wider array problems that may be encountered

in these fields.

Today’s webinar relate specifically to SIGMA/W.

Those looking to learn more about

the products including background theory, available features

and typical modeling scenarios can find an extensive library

of resources on the Geoslope website.

There you can find tutorial videos, examples

with detailed explanations and engineering books

on each products.

Calculating in situ stresses that applied to a domain

is one of the most important steps

in any stress train numerical analysis.

Large-scale geological processes

such as tectonic plate movements,

can greatly influence field stresses at large depth.

SIGMA/W webinar now offers an in situ analysis type that

can help easily specify these stresses.

Today’s webinar now will be divided into two parts.

We will first review the basics

of field stresses before looking into how

to use SIGMA/W model these.

Interested users are encouraged to download

the underground tunnel excavation practical example

from our website.

Which includes both an explanatory PDF

and a GeoStudio file.

There are three methods one can use

to initialize in situ stresses in a SIGMA/W analysis.

By using the gravity activation method, gravity is applied

to create a vertical stress field using the unit weight

of the soils involved.

Poisson’s coefficient and the geometry of the domain

will then control how a resentful stresses develop

in response to the vertical stresses.

As for the gravity activation,

the K naught procedure uses gravity to initiate

a vertical stress field in the domain.

This time however, horizontal stresses are calculated

by enforcing a defined K naught value.

Users should consult a SIGMA/W manual

for more information about the K naught procedure

and to learn when this procedure should

and should not be used.

The last way to initialize stresses in SIGMA/W

is to proceed via a user specified stress field.

In this case, gravity will be ignored in favor of a set

of stress quantities and directions specified better user.

At large depth, tectonic forces

and other large scale geological processes

can greatly influence institutes stresses producing

what are called locked-in stresses.

These stresses exist within the rock mass and cannot

be calculated by simply considering the unit weight

of the rocks and soils above like we conventionally do

for shallow ground calculations.

Tools such as the world stress map exists to help engineers

and geoscientists estimate the magnitude and orientation

of these locked-in stresses,

at various locations around the globe.

Direct measurement of stresses using stress cells

are indirect methods such as evaluating breakout orientation

in a tunnel arrays, are also use for determining

the in situ stress conditions.

Such tools provide the necessary inputs to specify

its field stressors for a SIGMA/W analysis,

where such stress patterns are expected.

As we will see in greater details later

on in this webinar via practical example, field stresses

are specified in SIGMA/W through the defined dropdown menu.

When defining new field stresses,

the major principle stress sigma one,

the minor principal stress sigma three

and the out of plane stress sigma Z are specified.

In addition, the direction

of the major principles stress alpha must also be specified.

The orientation is taken as positive counter-clockwise

from the x-axis.

The stresses hence defined will be applied uniformly

to each element from the regions that are selected.

Let us look at a few simple application cases.

Imagine this squared represents that domain

to which field stresses are to be applied.

Isotropic stresses of 10,000 kPa are applied here.

With alpha the principal stress direction being zero.

As sigma one is oriented along the x-axis.

By choosing a non-zero value for alpha

for example, minus 35 degrees here

the orientation of the applied stresses is rotated.

Remembered that alpha is positive counter-clockwise.

Here, I have also specified varied values

for the tree stress components, creating

an anisotropic stress field.

Remember that when specifying these stresses

the largest stress should always be sigma one,

the major principles stress.

I will use this stress pattern in the example that follows.

Before we move on to the practical example, let us review

a few important considerations.

The field stresses defined will be uniformly applied

to the whole domain that is selected.

Gravity’s ignored when initializing in situ stresses using

the field stresses method as stresses I specified

by the user.

A proper analysis three sequence using field stresses

will generally start with the

in situ field stresses analysis, followed

by stress correction analysis.

And finally, the load-deformations analysis

that were desired from the start.

This could be an excavation for example.

The stress correction analysis ensures

that no stress state breaches

its yield criterion following

the stress initialization procedure.

Let us now consider a practical example

where field stresses are used in GeoStudio.

Here is the geometry we will be working with.

This represents two tunnels to be excavated at large depth.

I generated the geometry from a DWG drawing

that was imported into Build3D,

the companion software we use with our 3D products

and then export it back into GeoStudio.

Any other methods to create your model geometry

would also work here.

As described a moment ago, the first step for these types

of problems is to add an in situ analysis using

the field stresses method.

The first example is going to use

the Hoek-Brown material model, so let us identify this

in the analysis name.

We didn’t need to specify the pattern

of field stresses we want to apply to our domain.

We then need to specify the pattern

of field stresses we want to apply to our domain.

I will be using the pattern shown earlier

where the major principle stress sigma one is oriented

at an angle of minus 35 degrees from the x-axis,

with a value of 12,000 kPa.

The minor principles sigma three, takes a value

of 8,000 kPa.

And finally, the out of plane stress sigma Z, takes

a value of 10,000 kPa.

I can then draw this field stresses definition

onto my entire domain.

Let us now define the material we will be using

for this analysis.

I chose to hook brown material model to represent

a bedrock we are working with at depth.

This is obviously just an example.

Use whichever material model fits your specific needs.

I then apply this material to every region of my domain,

since I suppose the rock is very homogenous here.

The next step is to apply proper boundary conditions.

These are quite simple for such an analysis, as we will fix

the domain in both X and Y directions on each of its sites,

which is what is required for a field stresses analysis.

Lastly, make sure that secondary nodes are turned

on for better precision and that the size of

the elements is appropriate.

I can now run the analysis and let the solver apply

the field stresses to the domain.

Once the solver is done, I can verify that the stresses

are correctly applied by going into results

and then view result information.

I can set at any element in the domain

and verify that the maximum

and minimum total stresses correctly correspond to the major

and minor in principal stresses sigma one

and sigma three, I had specified earlier.

In this case 12,000 and 8,000 kPa respectively.

The out of plane stress sigma Z,

also correctly indicates 10,000 kPa.

Note here that since our principal stresses were defined at

an angle of 35 degrees, the maximum

and minimum stressors do not coincide with

the horizontal and vertical directions.

Causing the X and Y total stresses to take values in between

the major and minor principles stresses.

Finally, note that I could have chosen any element

in the domain since field stresses

are applied uniformly throughout the domain.

The next step once we verified our stresses

are correctly applied, is to perform

a stress correction analysis to ensure

that no stress point lies in illegal stress space.

Let us go back to define project

and add a stress to distribution analysis using

this stress correction method, that uses

the stresses defined in the previous step as inputs.

After I’ve solved this analysis I can view if there

were indeed some problematic stress points in my domain

by toggling view plastic states on the right side

of the screen.

In this case, all was good since there are no elements

that turned yellow.

In a separate example I will show in a few minutes, we

will see how that looks when stresses have been corrected.

Now that I know I have a correctly defined stress field I

can proceed with the excavation of the first tunnel,

by adding a load information analysis to my analysis tree.

I will make sure to take the reset displacement

and strains tick boxes here to ensure strains

that I’ve occurred in the previous analysis

are not carried forward.

To simulate the excavation I simply removed

the material model that was attributed to the interior

of the tunnel.

I can now launch the solver.

Once the results have computed I

can view various results like

the accumulated displacement field in the domain.

Here we can see that the bottom of the excavation

is bulging up.

By exaggerating the mesh deformation, we can see

this more clearly.

In a sense the large stresses that exists in the domains

are causing the tunnel to close in

on itself following the excavation.

If these deformations or yielding were judged

to be excessive, a bolting pattern might be proposed

to mitigate the situation.

To monitor the formations that occur inside

the tunnel following the excavation I can plot

the total displacement for a specific point at the bottom

of the excavation.

Here we can see that the bottom experienced an uplift

of 75 millimeters following the excavation.

Another interesting set of results to view is the patterns

of horizontal and vertical stresses that

are generated around the excavation.

These stresses started at the values we viewed earlier,

but varied following the excavation

as deformations occurred.

As we proceed with the excavation of the second tunnel,

these modified field stresses will certainly have an impact

on stresses and strains that are generated further on.

Lastly, by toggling on the view plastic states option I

can see that a large portion of the elements surrounding

the excavation reached a hook brown yield criterion we

had fixed, which explains the large deformations we see.

I cannot proceed with the excavation of the second tunnel

by adding a second load deformation analysis as a child

of the first excavation, as we will be using the stresses

from the previous steps as inputs.

This time, I want to leave the reset check boxes off

since I want to display

the accumulated deformations resulting

from both excavations.

Again to simulate the excavation, I simply removed

the soil model from inside of the tunnel geometry

and I launched the analysis.

As you can see, the excavation of the second tunnel modified

the field stresses again,

which caused additional deformations to propagate including

in the first excavated tunnel.

By going back and forth from the first to

the second excavation phases in the analysis tree, I can see

how vertical and horizontal stresses varied

as a result of the second excavation.

As you can expect, the second excavation caused

the region of plastic states to expand even further.

This caused deformations in excess of 110 millimeter

to develop at the base of the first tunnel.

Let us not consider a second example using

the same geometry, but with different materials.

Since this simulation steps I want to perform will be

the same as the previous analysis I can simply right-click

on the first analysis and then select add analysis

and then clone.

And choose to clone the whole analysis branch.

I then update the names of the newly created analysis

to keep my analysis tree well-organized.

I have already created two materials for

this analysis, both using

the Mohr-Coulomb hardening softening material model.

The first material is called Mohr-Coulomb and represents

the good quality bedrock.

It uses functions to define both its effective cohesion

and fiction angle.

These functions define how each parameter will vary as

of yet deviatoric plastic strains develop in

the material during shearing.

The second material is called weak Mohr-Coulomb

and represents a poor quality rock layer

that unfortunately, our two tunnels must pass through.

Similar to the intact Mohr-Coulomb material,

it also uses effective collision and fiction angle functions

to account for softening caused by

the deviatoric plastics strains.

As shown on this plot,

the weak Mohr-Coulomb material only offers approximately

a third of the resistance compared to the intact material,

when subjected to tracks triaxial loading.

I can now draw-up both of these materials

to the appropriate regions of the domain.

I must ensure that I draw these new materials to

the whole analysis tree.

To do this quickly, I can check the apply

to multiple analysis box and select each analysis part

of the second example.

I will then go back to the excavation phases

and remove the materials in the tunnels

as I had done previously.

I can now solve the in situ analysis and verify again that

the field stresses were correctly applied.

I am using the same field stresses definition

as previously here.

I can not perform distress correction analysis

to catch any stress point that would be

in indigo stress space.

Once the analysis is done, by toggling

the plastic states on we can see that every element

where the weak Mohr-Coulomb material was applied is flagged

as being plastic.

This means that the field stresses applied

on the first we’re sufficiently intense to bring

these elements pass their yield criterion.

The stress redistribution algorithm was hence activated

and excess stresses were redistributed

to neighboring elements until no element remained

in indigo stress space.

The contour plots of horizontal

and vertical stresses, now show variations in the domain

as a result of the registration of stresses that occurred.

This showcases the importance of performing

the stress correction analysis

for these types of simulations.

Ideally, you do not want any areas of your domain

to undergo plastic deformation prior to excavation steps,

which is why we do distress redistribution analysis.

If there is plastic deformation prior

to excavating after distress redistribution analysis,

then the material strength or field stresses might need

to be adjusted accordingly.

In our case, stressors were adjusted by around 0.1%

which is quite reasonable.

If very large tress corrections are needed

or if the whole domain is yielding, it should be a red flag

for us to cut reconsider our simulation inputs.

In any case we need to start

from well-defined initial conditions.

Had we not done the stress distribution analysis, we

would have started our subsequent load information analysis

with the wrong stresses, which would have resulted

in larger deformations than what we will have expected.

Now that we have a vetted stress state

in the whole domain, we can go ahead and solve

the load deformation analysis that corresponds

to the excavation of the first tunnel.

This time the shear deformations that are cured within

the domain are a lot more intense than in the first example,

since the weak Mohr-Coulomb material

shows intense plasticity.

We can see that the bottom left corner

of the excavation displays large deformations.

Looking at the same center point in the excavation

as previously, we can now see vertical deformations

that reach almost 200 millimeters.

Finally, that are solved the analysis for the excavation

of the second tunnel.

As expected, the second tunnel

also experiences large deformations especially, toward

its top left part.

Toggling plastic states on reveals

that large plastic zones are developing

in the block mass that surrounds both excavations.

This concludes our webinar

on field stresses in SIGMA/W.

The webinar first reviewed the basics of field stresses

and why such stresses can exist at larger depth.

We then moved on to a practical example,

where field stresses were used

to simulate stress conditions surrounding tunnel excavations

in a mass.

With the example featuring

a weak Mohr-Coulomb material, we saw the importance

of performing a stress correction analysis after

the field stresses have been initialized to ensure

that we start our subsequent load information analysis

with valid stress state.

Don’t forget that you can download a similar example

from our website if you want to give this workload

a try by yourself.

If you’d like some new features and capabilities added

for field stresses in SIGMA/W, don’t hesitate

to make suggestions by submitting support requests.

We have now reached the end of this webinar.

A recording of the webinar will be available to view online.

Please take the time to complete the short survey

that appears on your screen so we know what types

of webinars you are interested in attending in the future.

Thank you very much for joining us and have a great rest

of your day, goodbye.