### The well-known Modified Cam Clay material model is used worldwide to model clays and other soils that exhibit yielding and non-linear elastic-plastic deformaiton patterns.

This webinar will review this material model in SIGMA/W.

The Modified Cam Clay material model in SIGMA/W can be used to simulate clays and other soils that exhibit yielding and non-linear elastic-plastic deformation patterns. This webinar will introduce you to MCC model theory and formulation and step you through the analysis and calibration of a triaxial test in SIGMA/W. A comparison of laboratory data to the SIGMA/W results will also be presented.

### Overview

**Speakers**

**Kathryn Dompierre**

**Duration**

28 min

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Videos## Find out more about Seequent's civil solution

Learn more### Video Transcript

[00:00:06.900]

<v Kathryn>Hello, and welcome to this GeoStudio</v>

[00:00:08.510]

Material Model webinars series on Modified Cam Clay.

[00:00:12.810]

My name is Kathryn Dompierre,

[00:00:14.300]

and I’m a Research and Development Engineer

[00:00:16.300]

with the GEOSLOPE engineering team here at Seequent.

[00:00:19.860]

Today’s webinar will be approximately 30 minutes long

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attendees can ask questions using the chat feature.

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I will respond to these questions via email

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as quickly as possible.

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A recording of the webinar will be available

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so participants can review the demonstration

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at a later time.

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GeoStudio is a software package developed for geotechnical

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engineers and earth scientists comprise of several products.

[00:00:47.210]

The range of products allows users to solve

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a wide array of problems

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that may be encountered in these fields.

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Today’s webinar will focus on SIGMA/W.

[00:00:58.040]

Those looking to learn more about the products,

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including background theory,

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available features and typical modeling scenarios

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can find an extensive library of resources

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on the GEOSLOPE website.

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Here, you can find tutorial videos,

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examples with detailed explanations

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and engineering books on each product.

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To begin this webinar,

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let us consider a soil element

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using both the experimental approach

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and a numerical approach.

[00:01:27.720]

And in experimental approach there’s a real soil sample

[00:01:30.590]

that is used for example, to conduct attracts yield test.

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The responses of this soil sample are measured

[00:01:37.130]

in the laboratory and the soil behavior

[00:01:39.070]

can be studied accordingly.

[00:01:41.960]

And the numerical approach on the other hand,

[00:01:43.770]

it is necessary to perform a calibration process

[00:01:46.490]

for the constituent of model

[00:01:47.890]

as the first step of numerical modeling,

[00:01:51.430]

the measured results from the soil sample

[00:01:53.300]

are required at this step.

[00:01:56.720]

This calibration procedure provides model constants

[00:01:59.500]

for the soil.

[00:02:01.960]

These constants are then used as input parameters

[00:02:04.730]

for a numerical model

[00:02:06.230]

for example in SIGMA/W

[00:02:08.420]

and this simulated results will be obtained

[00:02:10.650]

by solving the numerical model.

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The simulated results can then be compared

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to the corresponding laboratory results

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to verify the accuracy of the numerical modeling.

[00:02:23.040]

In today’s webinar the calibration procedure

[00:02:25.170]

for the modified Cam Clay material model will be provided.

[00:02:29.310]

This process will be applied to a specific type of Clay

[00:02:32.480]

as an example and the numerical values

[00:02:34.630]

of the model constants will be calculated.

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The main steps of modeling attracts yield test

[00:02:40.670]

in SIGMA/W will be reviewed,

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and the simulation results will be compared

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to the experimental and analytical results

[00:02:48.170]

for validation purposes.

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This webinar will begin by reviewing the theory

[00:02:54.370]

of the modified Cam Clay constituent of model.

[00:02:57.660]

Then step-by-step instructions will be provided

[00:03:00.160]

for calibrating this material model

[00:03:01.820]

using attracts field data series.

[00:03:05.350]

A demonstration of the steps of modeling attracts

[00:03:07.900]

yield test and SIGMA/W will be provided.

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And the simulated results will become paired and verified

[00:03:13.240]

using the analytical and laboratory results.

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The modified Cam Clay material model is a critical state

[00:03:21.030]

based non-linear constituent model

[00:03:23.430]

developed by Roscoe and Berlin in 1968.

[00:03:27.580]

In this model the author is modified

[00:03:29.300]

their previous constituent of model

[00:03:31.200]

by changing the geometry of the yield surface

[00:03:33.610]

from a bullet shape service to an ellipse.

[00:03:37.350]

For an isotropic loading condition

[00:03:39.420]

where the stress path is entirely located

[00:03:41.700]

on the horizontal axis.

[00:03:43.790]

The plastic strain increment vector is also horizontal

[00:03:48.010]

note that the plastic strain increment vector

[00:03:50.210]

is perpendicular to the yield surface.

[00:03:53.680]

The soil state is over consolidated

[00:03:55.730]

before reaching the yield surface.

[00:03:58.170]

After that the elliptical surface will be scaled up

[00:04:00.950]

as loading progresses.

[00:04:03.520]

The soil undergoes normal consolidation in this phase.

[00:04:08.870]

The soil response is assumed to be linear

[00:04:11.110]

in V versus lawn P prime space.

[00:04:14.620]

The slope of the normal consolidation line

[00:04:16.610]

is called the Virgin compression index or lambda

[00:04:20.490]

while the over consolidation and unloading, reloading lines

[00:04:23.610]

are assumed to be parallel.

[00:04:26.340]

Their slope is called the swelling index or Kappa.

[00:04:32.350]

In a deviatoric loading condition

[00:04:34.320]

where the vertical principles stress

[00:04:35.880]

is different than the horizontal one.

[00:04:38.090]

The stress path reaches the elliptical yield surface

[00:04:40.820]

at a point away from the horizontal axis.

[00:04:44.020]

This means that the plastic strain increment vector

[00:04:46.520]

contains deviatoric components as well.

[00:04:50.250]

In V versus lawn P prime space

[00:04:52.810]

the over consolidation and unloading, reloading phases

[00:04:56.100]

are still aligned with a slope of kappa.

[00:04:59.240]

However, the normal consolidation phase

[00:05:01.330]

is not necessarily a straight line

[00:05:03.370]

for a general and isotropic loading condition.

[00:05:08.980]

Before moving on to the demonstration,

[00:05:11.010]

we need to review some fundamental formulations.

[00:05:14.900]

As mentioned before the modified Cam Clay material model

[00:05:17.790]

is a critical state based constituent of model.

[00:05:20.460]

So different stress paths

[00:05:22.170]

eventually tend to the critical state line.

[00:05:25.650]

In this model the slope of the critical state line

[00:05:28.950]

or the critical state stress ratio

[00:05:31.400]

can be expressed in terms of the effective friction angle

[00:05:34.130]

in the more coolum failure criteria.

[00:05:38.590]

The yield surface is an ellipse

[00:05:40.360]

that passes through the origin

[00:05:42.060]

and intersects the critical state line

[00:05:44.120]

at its peak point.

[00:05:48.220]

The over consolidation ratio

[00:05:50.050]

is the ratio between the maximum isotropic stress

[00:05:52.840]

experienced by the soil

[00:05:54.280]

and the current isotropic stress of the soil.

[00:05:59.930]

For a stress state inside the yield surface

[00:06:02.300]

the soil response is elastic.

[00:06:04.440]

The compliance matrix is diagonal

[00:06:07.090]

and the bulk and shear modular are both proportional

[00:06:09.730]

to the mean effect of stress, P prime

[00:06:13.000]

and the specific volume V.

[00:06:17.520]

After reaching the yield surface and as it expands,

[00:06:20.640]

the soil response becomes elasto plastic

[00:06:23.630]

and non diagonal coupled components

[00:06:25.710]

appear in the compliance matrix.

[00:06:28.480]

Incremental strains in this condition

[00:06:30.450]

are the summation of elastic and plastic strains.

[00:06:33.530]

And so the current stress ratio plays a key role

[00:06:36.240]

in the soil response.

[00:06:40.690]

According to the framework proposed in the modified

[00:06:42.910]

Cam Clay model, the model constants include

[00:06:46.600]

the slope of the normal isotropic consolidation line

[00:06:49.280]

represented by lambda,

[00:06:51.670]

the slope of the over consolidation line or kappa,

[00:06:55.890]

the effective poisson’s ratio, new prime

[00:07:00.260]

and the effect of critical state friction angle, five-prime.

[00:07:04.700]

These four constants determined the soil type

[00:07:06.940]

based on the modified Cam Clay model.

[00:07:10.100]

Some other parameters will also be needed

[00:07:11.910]

to describe the initial conditions

[00:07:13.640]

of a specific soil sample.

[00:07:16.110]

These include the initial void ratio, the unit weight

[00:07:20.820]

and the over consolidation ratio.

[00:07:26.480]

In order to find the model constant

[00:07:28.140]

corresponding to a specific soil,

[00:07:30.410]

a step-by-step calibration procedure is discussed here

[00:07:33.370]

based on drain tracks, yield test results.

[00:07:36.800]

As the first step, the critical state stress ratio

[00:07:40.350]

M sub C or its equivalent,

[00:07:43.130]

the effect of critical state friction angle

[00:07:45.840]

can be estimated from drain tracks, yield test results.

[00:07:51.090]

According to critical state soil mechanics,

[00:07:53.240]

stress paths of samples

[00:07:54.550]

with different initial confining stresses

[00:07:56.950]

eventually tend to the critical state line

[00:07:59.000]

at their failure point.

[00:08:00.940]

Therefore, the critical state line

[00:08:02.480]

is a straight line that passes through the failure points.

[00:08:06.130]

The critical state stress ratio MC

[00:08:09.270]

is the slope of this line.

[00:08:12.600]

This constant can be calculated

[00:08:14.220]

using the method of least squares.

[00:08:18.300]

Since the failure criteria in the modified Cam Clay model

[00:08:21.210]

is the same as the more cooler model,

[00:08:23.200]

the effect of critical state friction angle five-prime

[00:08:26.190]

is not independent of the critical state stress ratio, MC

[00:08:30.720]

and can be expressed directly in terms of it.

[00:08:37.290]

To demonstrate the calibration procedure

[00:08:39.570]

let us consider three drained tracks yield compression tests

[00:08:43.040]

on Bothkennar clay that was conducted by McGinty in 2006.

[00:08:48.440]

These three tests have been performed

[00:08:50.010]

at different confining pressures.

[00:08:52.490]

The deviator compression stress

[00:08:54.240]

and these tests continued until failure was achieved.

[00:08:58.630]

The critical state line

[00:08:59.780]

that passes through the failure points

[00:09:01.610]

in P prime versus Q space has a slope of 1.36.

[00:09:07.750]

Thus, the critical state ratio MC is 1.36

[00:09:12.150]

and consequently, the effective friction angle

[00:09:14.390]

is calculated to be 33.7 degrees.

[00:09:21.480]

The second step of the calibration procedure

[00:09:23.600]

is to estimate the slope

[00:09:24.790]

of the over consolidation line or kappa.

[00:09:28.530]

For an over consolidated soil

[00:09:30.290]

kappa is the slope of the over consolidation line

[00:09:32.720]

and represents the elastic response of the sample.

[00:09:36.600]

The trends of the measured values of P prime and V

[00:09:39.230]

in this branch of the graph

[00:09:40.530]

can be projected to a straight line.

[00:09:43.280]

The slope of the Y intercept of this line

[00:09:45.400]

can be calculated directly

[00:09:46.910]

using the method of least squares.

[00:09:51.500]

An alternative method for estimating kappa

[00:09:54.160]

is to use the corresponding parameters

[00:09:56.210]

measured during an unloading, reloading process.

[00:09:59.540]

For a normally consolidated soil

[00:10:01.670]

the unloading reloading process

[00:10:03.280]

is required for estimating kappa.

[00:10:06.190]

The method of least squares can again be used

[00:10:08.220]

to calculate the slope and the Y intercept

[00:10:10.790]

of this straight line.

[00:10:15.660]

Let us apply the second calibration step

[00:10:17.680]

to the example, tracks yield test results

[00:10:20.010]

on Bothkennar clay mentioned earlier.

[00:10:23.380]

The over consolidation branch in each of these three curves

[00:10:26.550]

is projected to a straight line.

[00:10:29.700]

The slope of these three lines is almost the same

[00:10:32.650]

So their average 0.084 is used as the constant kappa

[00:10:37.890]

for this type of clay.

[00:10:43.110]

In the third step of the calibration procedure,

[00:10:45.980]

the slope of the normal isotropic consolidation line

[00:10:49.190]

or lambda will be estimated.

[00:10:51.990]

It should be noted that lambda’s the slope

[00:10:53.770]

of the normal consolidation line

[00:10:55.370]

only in an isotropic loading condition.

[00:10:58.520]

For other loading conditions however,

[00:11:00.320]

the normal consolidation branch

[00:11:02.340]

in V versus lawn P prime space is not necessarily linear.

[00:11:07.110]

And so the slope of its curve is obviously

[00:11:09.370]

not equal to lambda.

[00:11:12.630]

Based on the modified Cam Clay framework

[00:11:14.800]

it can be proved that there is an alternative space

[00:11:17.580]

in which the sample response is linear,

[00:11:19.580]

even under normal consolidation.

[00:11:22.110]

The X and Y axes in this space

[00:11:24.080]

are functions of the measured parameters

[00:11:26.040]

and constants estimated in the previous steps.

[00:11:30.640]

The over consolidation and unloading, reloading branches

[00:11:33.660]

are both horizontal in this new space.

[00:11:37.270]

And the normal consolidation branch

[00:11:39.470]

is a straight to sending line.

[00:11:42.390]

The slope of this line represents the difference

[00:11:44.410]

between the isotropic normal consolidation slope, lambda,

[00:11:47.900]

and the over consolidation slope, kappa.

[00:11:52.010]

Given that we already estimated kappa in the previous step,

[00:11:55.400]

the constant lambda can be found by applying

[00:11:57.710]

the method of least squares on the proposed space.

[00:12:04.650]

As shown in this figure,

[00:12:05.720]

the data points corresponding

[00:12:07.220]

to three example tracks yield test

[00:12:09.400]

are plotted in this alternate space.

[00:12:12.470]

The average value of the slopes of these three curves

[00:12:15.270]

in the normal consolidation branch

[00:12:17.080]

indicates the difference between lambda and kappa.

[00:12:20.960]

Since the value of kappa was previously obtained as 0.084

[00:12:25.960]

the constant lambda is estimated here to be 0.332.

[00:12:35.330]

The fourth step of the calibration procedure

[00:12:37.480]

is to calculate the over consolidation ratio

[00:12:39.870]

for each soil sample.

[00:12:42.640]

To do this, it is required to recognize

[00:12:44.960]

the mean effective pressure

[00:12:46.450]

in which the response of the sample changes

[00:12:49.070]

from the over consolidation condition

[00:12:51.170]

to the normal consolidation condition.

[00:12:55.250]

Let us refer to this pressure as the yield pressure

[00:12:57.890]

or P prime Y.

[00:13:00.880]

The over consolidation ratio however,

[00:13:02.790]

is the ratio between the isotropic

[00:13:05.200]

pre consolidation pressure P prime C,

[00:13:08.420]

and the isotropic initial pressure P prime zero.

[00:13:12.730]

As stated earlier the response of the soil changes

[00:13:15.410]

from an elastic or over consolidated state

[00:13:18.580]

to a elasto plastic or normally consolidated state

[00:13:22.090]

only if its stress path touches the yield surface.

[00:13:26.830]

As a result for a stress path that is not

[00:13:29.170]

necessarily isotropic the yield pressure P prime Y

[00:13:33.040]

is less than the isotropic

[00:13:34.600]

pre consolidation pressure P prime C

[00:13:38.240]

these two pressures however, are not independent.

[00:13:43.250]

For example, in a drain tracks yield stress pass

[00:13:45.810]

with a slope of three to one.

[00:13:47.830]

The deviatoric stress at the yield surface is three times

[00:13:50.980]

the difference between the yield and initial pressures.

[00:13:54.570]

So the isotropic pre-consultation pressure P prime C

[00:13:58.563]

can be expressed in terms of yield stresses

[00:14:00.757]

using the yield function of the elliptical surface.

[00:14:05.155]

Finally, the over consolidation ratio

[00:14:07.332]

is estimated as a ratio between

[00:14:09.254]

the isotropic pre consolidation pressure, P prime C,

[00:14:12.980]

and the isotropic initial pressure B prime zero.

[00:14:20.400]

This approach is applied on the Bothkennar clay

[00:14:22.550]

triaxial test data to estimate the over consolidation ratio

[00:14:26.520]

for each of the three samples.

[00:14:29.350]

First of all,

[00:14:30.183]

the yield points of the samples

[00:14:31.580]

in V versus lawn P prime space are detected.

[00:14:35.560]

The values of P prime Y for tests A1, A2 and A3

[00:14:41.090]

are about 83, 107 and 179 KPA respectively.

[00:14:47.630]

According to these yield pressures,

[00:14:49.310]

three yield surfaces are drawn

[00:14:51.060]

and the isotropic pre-consultation pressures

[00:14:53.590]

for three samples have been estimated as 115,

[00:14:58.680]

120 and 201 KPA respectively.

[00:15:04.220]

With this the over consolidation ratios for the samples

[00:15:07.440]

are found to be 2.069, 1.224 and 1.339.

[00:15:16.120]

Therefore the first sample is more over consolidated

[00:15:19.090]

than the other two samples.

[00:15:21.170]

This can also be deduced from the response of the sample

[00:15:23.950]

in V versus lawn P prime space,

[00:15:26.530]

where it has a longer elastic branch than the other samples.

[00:15:31.900]

The last step of the calibration procedure

[00:15:34.140]

for the modified Cam Clay constituent of model

[00:15:36.730]

is to determine the effective Poisson’s ratio, new prime.

[00:15:41.680]

Poissons ratio is defined as the ratio

[00:15:43.930]

of the change in the elements radio strain

[00:15:46.700]

to the change in its axial strain in a drained test.

[00:15:51.030]

In the modified Cam Clay model,

[00:15:52.930]

the Poisson’s ratio is considered only for the elastic

[00:15:56.150]

or over consolidated condition

[00:15:58.250]

and its value is assumed to remain constant during loading.

[00:16:03.230]

Consequently in a drain tracks yield test,

[00:16:06.050]

the method of least squares can be applied

[00:16:08.090]

on the purely elastic or over consolidated part of the curve

[00:16:12.010]

in radial strain versus axial strain space

[00:16:15.280]

to estimate the value of the effective Poisson’s ratio.

[00:16:21.030]

Lets us supply this final step to the Bothkennar clay

[00:16:23.370]

tracks yield test data.

[00:16:26.030]

The yield points of the samples have already been detected

[00:16:28.840]

in the previous steps and are marked with an X

[00:16:31.580]

in these figures.

[00:16:34.230]

As can be seen from the figure on the right

[00:16:36.520]

the sample response in this space is almost linear

[00:16:39.640]

before reaching the yield surface

[00:16:41.720]

while nonlinear behavior begins after yielding.

[00:16:46.430]

If the linear response of all three samples

[00:16:48.570]

was approximated by only one straight line

[00:16:51.040]

passing through the origin,

[00:16:52.800]

the slope of that line would be approximately 0.353.

[00:16:57.860]

This value is an estimation of the effective Poisson’s ratio

[00:17:01.420]

of the Bothkennar clay.

[00:17:06.750]

The results of the calibration procedure

[00:17:08.570]

for the Bothkennar clay can be summarized as follows

[00:17:11.760]

four model constants have been estimated,

[00:17:14.170]

including the slope of the normal

[00:17:15.830]

isotropic consolidation line,

[00:17:18.030]

the slope of the over consolidation line,

[00:17:20.500]

the effective Poisson’s ratio

[00:17:22.090]

and the effective critical state friction angle.

[00:17:25.770]

In addition the sample specific parameters

[00:17:28.010]

for these three tests include initial void ratios,

[00:17:31.360]

which were measured directly in the lab

[00:17:33.820]

and over consolidation ratios,

[00:17:35.770]

which were estimated in the calibration procedure.

[00:17:39.940]

These constants and parameters will be inputted in SIGMA/W

[00:17:43.280]

using the modified Cam Clay material model.

[00:17:49.120]

Now that we’ve reviewed the step-by-step

[00:17:50.700]

calibration procedure for the modified

[00:17:52.530]

Cam Clay material model,

[00:17:54.230]

I will describe how two model attract seal test in SIGMA/W

[00:17:57.830]

and compare the numerical results

[00:17:59.630]

with the previously mentioned laboratory data.

[00:18:02.980]

The numerical model configuration is based on the geometry

[00:18:06.200]

and boundary conditions of the tracks yield test

[00:18:08.440]

conducted in the laboratory.

[00:18:10.970]

A typical track yield test sample has a cylindrical shape

[00:18:14.320]

with a diameter of five centimeters

[00:18:16.250]

and a height of 10 centimeters.

[00:18:18.830]

Due to the axisymmetry shape of this geometry

[00:18:21.280]

with respect to the central vertical axis,

[00:18:24.050]

we can use the 2D axisymmetry geometry type in SIGMA/W.

[00:18:28.930]

The geometry is also symmetric with respect

[00:18:31.270]

to the horizontal axis.

[00:18:33.260]

So I will only model the top half

[00:18:35.010]

of the tracks yield sample.

[00:18:37.940]

An eight node Single element model

[00:18:40.250]

is considered for the resulting rectangle.

[00:18:43.170]

The left and bottom sides of this model

[00:18:45.040]

are fixed in the X and Y directions respectively,

[00:18:48.320]

while loads are applied to the other two sides.

[00:18:53.180]

The next step for setting up our SIGMA/W analysis

[00:18:55.780]

is the material definition.

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This step is performed in the defined materials dialogue.

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The material model is set to modified Cam Clay.

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The sample parameters including the initial void ratio

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and over consolidation ratio

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are entered as discussed earlier.

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It should be noted that the effect of the soil self weight

[00:19:16.430]

can be removed by setting the unit weight to zero.

[00:19:19.720]

While the key note effect can be deactivated

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by specifying Key note and C as one.

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Lastly, the constitutive model constants are entered

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based on the results from the calibration procedure

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for both Cam Clay.

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The simulated tracks yield models are then loaded

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under first, the isotropic confining pressure

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and secondly the deviatoric pressure,

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thus there are two SIGMA/W analysis required

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for each of the triaxial tests.

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The confining pressure analysis acts as the parent

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and its results are used as the initial data

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for the displacement controlled deviatoric analysis.

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These conditions are established

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using the boundary condition

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specified in the defined boundary conditions dialogue.

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For example, in test A1 the constant normal stress

[00:20:12.270]

of 58 KPA is applied on both the right and top sides

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of the model using a normal tan stress boundary type

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for the confining pressure analysis.

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In the deviatoric analysis,

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a displacement type boundary condition

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is applied to the top of the model.

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A displacement of two centimeters that is equivalent

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to 40% strain is applied linearly over time

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using a splined data point function.

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All the analysis are then solved in SIGMA/W

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and the stress, strain, displacement

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and other responses of the model

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can be extracted and interpreted.

[00:20:57.710]

As shown here a 2D axisymmetry geometry

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is used to set up the model domain.

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In the 2D view only one quarter of the cross-section

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running through the center of the tracks yield sample

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is modeled given the symmetry of the domain.

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In the analysis tree, there are three sets of analysis

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each representing attracts yield test

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conducted on the Bothkennar clay samples.

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In each test the confining phase is the parent analysis

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and the deviatoric phase

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that use the results of the previous phase

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is the child analysis.

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The material properties for three soil samples

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were obtained using the outlined calibration procedure.

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The materials are specified

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in the defined materials dialogue.

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The same type of clay

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was subjected to the tracks yield tests.

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Therefore, the Constance of the modified Cam Clay model

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are similar for each sample.

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However, at the initial void ratio

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and over consolidation ratio are not the same

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for each sample

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and so three different materials were defined.

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And isotropic elastic material was used

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during the first phase of the tracks yield simulations,

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because the nonlinear stress strain response

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is inconsequential to establishing the initial stresses.

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The accumulated displacements and strains are reset

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at the start of the loading phase of the simulation.

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The three isotropic elastic materials defined here

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are applied to the corresponding, confining analysis.

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The defined modified Cam Clay materials

[00:22:45.860]

are applied during the deviatoric portion of the tracks

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yield test simulations.

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The boundary conditions representing the confining pressures

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and deviatoric strain are specified

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in defined boundary conditions.

[00:23:08.040]

Three constant confining pressures were created

[00:23:10.710]

for the three tracks yield tests

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using the normal 10 stress boundary type.

[00:23:16.840]

These boundary conditions

[00:23:18.010]

are applied to the corresponding confining analysis.

[00:23:31.600]

The deviatoric strain boundary for the displacement

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control loading phase of the tracks yield test

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uses the force displacement boundary type

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with a displacement function defined

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such that displacement increases

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over the deviatoric strain analysis

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from zero to two centimeters.

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Before solving an analysis

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the final step is to review the finite element mesh.

[00:23:58.070]

In the draw mesh properties dialog

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we see that the global element mesh size is 0.05 meters

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thus, the model domain represents one element.

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This analysis has already been solved

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so I will move to the results view.

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I will go to the first deviatoric analysis

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to investigate the results.

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In the draw graph dialog, I have created graphs

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to illustrate the stress path, stress strain curve,

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and void ratio versus mean effect of stress.

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I can click through the different analysis

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to view the results from each.

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Let us now compare these results

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with the analytical solution

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and also with the corresponding laboratory data.

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The different simulation results of test A1

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are compared here with the corresponding laboratory results.

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Discrete scatter points represent the laboratory results

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and the continuous black lines

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are the SIGMA/W simulation results.

[00:25:12.550]

Analytical results for the modified Cam Clay model

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are also shown in these diagrams as orange dashed lines.

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The full compatibility of the analytical

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and numerical curves shows the reliability

[00:25:25.860]

of the implementation process

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of this material model in SIGMA/W.

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When comparing the laboratory results

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with the constituent of model simulations,

[00:25:35.400]

some of the plots show a better fit than others.

[00:25:38.440]

For instance, a very good match

[00:25:40.210]

can be seen in the first curve

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where the data in V versus lawn P prime space

[00:25:45.640]

is simulated by the modified Cam Clay model.

[00:25:49.450]

However, the results from test A1

[00:25:51.400]

in some of the other spaces

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do not match as nicely as the first curve

[00:25:56.330]

because of the very nature of calibration.

[00:25:59.740]

The calibration procedure highlighted in this webinar

[00:26:02.480]

required multiple samples,

[00:26:04.420]

which each have varying degrees of disturbance.

[00:26:08.010]

For example, during the calibration process,

[00:26:10.880]

the best fit line that was used to determine MC

[00:26:14.140]

was below the A1 and A3 data points,

[00:26:17.610]

but near the A2 data point,

[00:26:19.730]

thus, the simulated deviatoric failure stress

[00:26:22.570]

was underestimated for the A1 sample.

[00:26:26.820]

Meanwhile, the simulated deviatoric failure stress

[00:26:29.660]

better correlates to the laboratory results from test A2

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and underestimates the deviatoric failure stress

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for test A3.

[00:26:39.360]

This demonstrates the nature of the calibration process.

[00:26:42.350]

However, as mentioned for the first test,

[00:26:44.830]

the analytical and numerical results show a perfect match

[00:26:48.100]

verifying that SIGMA/W accurately represents

[00:26:50.540]

the modified Cam Clay material model.

[00:26:55.390]

In this webinar,

[00:26:56.560]

the calibration procedure of the modified Cam Clay

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material model was provided in five straightforward steps.

[00:27:03.740]

The results of the drain tracks yield test,

[00:27:06.030]

where the only laboratory data set required for calibration.

[00:27:10.670]

The identified material constants

[00:27:12.850]

were used in a SIGMA/W numerical model,

[00:27:15.830]

and the simulation results were found to compare favorably

[00:27:19.490]

with both the analytical solution

[00:27:21.340]

and corresponding laboratory results.

[00:27:27.690]

Here are other references discussed in this webinar.

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We’ve now reached the end of the webinar.

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A recording of this webinar will be available

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to view online.

[00:27:43.730]

Please take the time to complete the short survey

[00:27:45.940]

that appears on your screen

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so we know what types of webinars

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you are interested in attending in the future.

[00:27:51.780]

Thank you very much for joining us

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and have a great rest of your day, goodbye.