DISCUSSION OF MODELING FOR ANALYSES OF FULLY SOFTENED LEVEES

DISCUSSION OF MODELING FOR ANALYSES
OF FULLY SOFTENED LEVEES

Danny K. McCook1

ABSTRACT

Levees and embankments constructed of highly plastic clays are susceptible to a special
kind of instability often referred to as surficial or sloughing slides. Highly plastic clay
soils become desiccated over time from repeated drying cycles and develop a pronounced
blocky, open structure. When a heavy rainfall closely follows an extended droughty
period, the cracks in the blocky structured clay become full of water and interfaces
between the blocks in the clay become saturated. The process of repeated wetting and
drying creates what has been termed a “softening” process. The result is a translational
movement of the desiccated zone in the levee.

This phenomenon is particularly severe in southern climates such as Texas, Mississippi,
and Louisiana. The accepted state of the art for modeling the shear strength of these soils
for this condition is to use the fully softened shear strengths. These shear strengths may
be based on either specialized laboratory testing or empirical methods. This paper
discusses the way that empirical methods developed by Stephen Wright, based on the
work done by Stark and Eids, as well as the Stark empirical estimate, can be employed to
obtain safety factors for preliminary analyses. Comparisons are presented for safety
factors obtained by detailed laboratory testing done by the USACE on a project versus
the empirical estimates for several design examples.

The paper also discusses appropriate safety factors and implications of various modeling
assumptions to the design of levees. Factors such as assumed depth of desiccation,
involvement of foundation soils in the model, and others are examined and summarized.
Finally, recommendations are provided on methods that are practical and useful for
designing levees where detailed laboratory testing may not be justified.

INTRODUCTION

Slides in Fissured Clays

Slope instability problems are common where embankments and/or foundation soils have
zones of fissured/blocky structured clays in the cross-section. The slides are often
triggered by sudden increases in pore pressure that occurs when intense rainfall occurs on
a desiccated slope, or a rise in groundwater weakens a structured foundation soil. The
slides are most common when soils consist of relatively high plasticity clays that have a
structure that is variously described as blocky, fissured, or slickensided.

1 Danny K. McCook, McCook Geotechnical Engineering, PLLC, 3221 Rosehaven Drive, Unit 1510, Fort
Worth, TX 76116, [email protected], [email protected]

Analyses of Fully Softened Levees 483

Figures 1 and 2 show a typical slide. This slide occurred in an embankment constructed
of fat clay (CH classification) with a liquid limit (LL) of 78 and a plasticity index (PI) of
52. The embankment cotangent was 2H: 1V. The embankment first slid 27 years after
construction following a 6.3” rainfall event. The slide shown in the figure is one that
recurred in the same location 3 years following repair.

Figure 1. Surficial slide on small dam in Minnesota.

Figure 2. Scarp face of slide shown in Figure 1.
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Figure 3 shows slides that occurred on both slopes of a levee. The USACE has extensive
experience with levee instability on levees in Missouri and Mississippi.

Figure 3. Slides on USACE levee. Photo Credit USACE

Surficial slides are common in excavated slopes in natural materials as well as compacted
as embankments. Figures 4 and 5 show a series of slope failures at a channel project in
the area of Bossier City, Louisiana. Figure 4 shows the blocky structure in the native
soils in the channel banks. The soils were highly plastic clays that were
overconsolidated with a blocky structure that was attributed to desiccation subsequent to
deposition in the alluvium. The structure in the soils was evident at significant depth
below the present surface of the flood plain. The structure is attributable to desiccation of
the layers of sediment subsequent to deposition several thousands of years ago and not
necessarily a result of recent desiccation cycles. Figure 5 shows the slope instability that
occurred when the bottom of the channel was deepened approximately 4 feet. The
excavation was made to provide added flow capacity.

Analyses of Fully Softened Levees 485

Figure 4. Blocky structure in soils. Photo credit NRCS.

Figure 5. Slope failures that occurred following excavation of the channel.
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Figure 6 depicts another example of a slope instability associated with fissured clays.
This instability occurred following a snowmelt episode. During the original construction
of the dam, about 25 years prior to this slide occurring, borrowing at the toe of the slope
caused slides in this same area. This slide occurred following runoff from snow melt.
Soils at this site were weathered shales of high plasticity that had an extremely blocky
structure.

Figure 6. Slide in reservoir rim. Photo credit NRCS.

An engineer who is creating a model to use in the analysis of the stability of levees and
small embankments constructed of highly plastic clays should consider several important
parameters. Factors that may be important in these analyses include:

• The height of the levee
• The cotangent of the levee slope
• The assumed size and shape of the portion of the cross-section that is expected to

develop a blocky structure.
• The shear strength model for the fully softened condition used in the analysis
• The assumed location of the piezometric line.

Some of these parameters and conclusions are presented in following discussions. The
conclusions are primarily based on the experience of the Author in performing numerous
stability analyses.

Analyses of Fully Softened Levees 487

GENERAL CHARACTERISTICS OF SLIDES

General

Slides involving highly plastic fissured clays typically have the following characteristic,
based on the Author’s experience which is primarily with slope failures on embankment
dams.

• Slides frequently occur when a relatively intense precipitation closely follows an
extended period of hot, dry weather. The extended dry period allows large
shrinkage cracks to open in the surface zone of an embankment, and the sudden
rainfall fills the cracks more quickly than it is possible for them to swell shut.

• Slides are typically relatively shallow and have a long radius of curvature.
Shallow failure surfaces are a result of the combination of a very low to zero

effective cohesion and an effective φ' representing the fully softened strength of

the soil.

• The depth of sliding is typically less than 10 feet (measured vertically) based on
the Author’s observations of numerous slides. Branch reported instances of
sliding depths as great as 20 feet. Sills (2011) summarized data from a Corps of
Engineer publication that showed typical depths of from 3.7 to 8.0 feet. In that
study, the depths were measured normal to the slope, with a vertical depth
depending on the slope cotangent according to the sketch shown in Figure 7.

Depth of Slides

Figure 7. Sketch showing relationship between normal and vertical depth of shallow slide.
Z= d
cos(α )

The relationship between d and Z for a common range of the parameters involved is
shown in the following table:

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Table 1. Relationship between vertical depth of slide, d, and normal depth (to slope), z.

Terms defined in Figure 7.

m α, d, feet z, feet m α, d, feet z, feet

degrees degrees

6 6.7 6 6.3

2.0 26.6 8 8.9 3.0 18.4 8 8.4

10 11.2 10 10.5

12 13.4 12 12.6

6 6.5 6 6.2

2.5 21.8 8 6.5 4.0 14.0 8 8.2

10 10.8 10 10.3

12 12.9 12 12.4

Figure 8 is after Aubeny and Lytton (2004) showing the depth of slides they observed in
two high PI clay formations in cut slopes associated with Texas highways.

Figure 8. Depth of slides observed by Aubeny and Lytton

Analyses of Fully Softened Levees 489

Time to Failure
The time between excavation of a cut slope or construction of an embankment and the
first occurrence of a slope failure is highly variable. Some slides have occurred as shortly
as 2 years following construction, and others, not until over 30 years following
construction. Templeton, et al, (1984) reported on slides they observed on Mississippi
river levees that “The slides occur in this weathered zone 20 to 40 years after
construction and appear to be triggered by heavy rainfall.” Aubeny and Lytton gathered
data on slope failures with cut slopes in two geologic formations in Texas, and the data is
summarized in Figure 9. The vast majority of failures occurred in the period of from 15
to 20 years following excavation.

Figure 9. Time to failure of cut slopes in Beaumont and Paris Clay
formations.

The Natural Resources Conservation Service (NRCS) also gathered data from a study of
slope failures on their dams. A report by McCook, (1988), showed the histogram of time
to failure after construction reproduced in Figure 10. This data shows a relatively even
distribution of the time to failure between 5 and 25 years.

490 Innovative Dam and Levee Design and Construction

Figure 10. NRCS embankments time to slope failure
developing subsequent to construction.

Another factor strongly influencing the tendency to develop shallow surface failures
is obviously the plasticity of the soils. The NRCS study (1988) showed that most of
the failures occurred in embankments constructed of soils with LL values greater than
60 and PI values greater than 40. This mirrored the experience reported by the
USACE in a study of slope failures on Mississippi river levees.

Slides are progressive in nature. Excavations into embankments adjacent to an area
where a slide has already occurred have shown precursor development of an incipient
slide. Templeton, et al, showed an example of this phenomenon with the sketch
reproduced from his paper in Figure 11:

Analyses of Fully Softened Levees 491

Figure 11. Incipient slide observed in embankment (after Templeton, et al).

Summary.

Templeton (1984), provides a summary of observations regarding surficial slides on
compacted embankments as follows:

The reduction in strength in the levee embankment results from weathering
effects and strains induced by seasonal shrinking and swelling. During dry
periods, shrinkage cracks open to a depth of 5 to 7 feet. These cracks expose
the interior of the mass allowing desiccation to occur and fissures to form due
to irregular shrinking. Subsequently, water from rainfall percolates through
these cracks and fissures causing the material to swell and slake. … During
dry periods when cracks develop, soil material from the surface is knocked
into the cracks by grazing cattle or surface runoff from rain. These stress
increases are concentrated along discontinuities, and local over-stressing
occurs, forming concentrations of slickensides in zones experiencing the
largest strains. The slough slides appear to be triggered by heavy
rainfall after an extended period of drying. The extensive network of cracks
and fissures developed by years of weathering increases the mass
permeability of the embankment. When these cracks fill with water, the
exposed surfaces along the cracks and fissures soften, reducing the shear
strength along these discontinuities. Piezometric data obtained from this
study indicate that a perched water table forms above the intact clay zone
located below the weathered zone. The increase in driving weight and
concomitant softening of the exposed clay combined with the progressive loss
of shear strength due to long-term seasonal shrinking-swelling effects result
in a slough failure.

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BACKROUND ON PROBLEM

Terzaghi and Peck in 1948 discussed the nature of a fissured clay and how its strength
was far lower than its intact strength after softening occurred. The conclusion at the time
of the writing of the article was that determining the strength was “beyond the scope of
theoretical treatment.”

Almost every stiff clay is weakened by a network of hair cracks or
slickensides. If the surfaces of weakness subdivide the clay into small
fragments 1 inch or less in size, a slope may become unstable during
construction or shortly thereafter. On the other hand, if the spacing of the
joints is greater, failure may not occur until many years after the cut
is made. …If the spacing of the joints in a clay is greater than several
inches, slopes may remain stable for many years or even decades after the
cut is made. The lapse of time between the excavation of the cut and the
failure of the slope indicates a gradual loss of the strength of the soil.
Present conceptions regarding the mechanics of the process of softening
are illustrated by Figure 3 (reproduced below as Figure 12). Before
excavation, the clay is very rigid, and the fissures are completely closed.
The reduction of stress during excavation causes an expansion of the clay,
and some of the fissures open. Water then enters and softens the
clay adjoining these fissures.

Unequal swelling produces new fissures until the larger chunks
disintegrate, and the mass is transformed into a soft matrix containing
hard cores. A slide occurs as soon as the shearing resistance of
the weakened clay becomes too small to counteract the forces of gravity.
Most slides of this type occur along toe circles involving a relatively
shallow body of soil, because the shearing resistance of the clay increases
rapidly with increasing distance below the exposed surface. The
water seems to cause only the deterioration of the clay structure; seepage
pressures appear to be of no consequence... After a slide occurs the
material underlying the newly expose slide begins to soften and the
process continues until another slide occurs… the process does not stop
until the slope angle becomes compatible with the softest consistency the
clay can acquire. Thus the slopes become gentler... The problem
of determining the shear characteristics of such clays for design purposes
has not yet been solved - such clays are beyond the scope of theoretical
treatment.

Analyses of Fully Softened Levees 493

Figure 12. Illustration from Terzaghi and Peck
textbook showing softening process in high PI clay.
Skempton (1977) stated the following in the synopsis of his paper, “Back analysis of
typical long-term slips shows that the strength of the clay at failure corresponds rather
closely to the 'fully softened' condition, or to the fissure strength; and that the field
strength is greater than the residual but smaller than the peak strength, even as measured
on large samples.”
EMPRICAL ESTIMATES OF FULLY SOFTENED SHEAR STRENGTH
Stark and Eid
Based on studies of the fully softened strength as measured by ring shear, direct shear,
and triaxial shear tests on softened soils, Stark and Eid (1997) developed an empirical
relationship between the fully softened shear strength of the soil, and its LL, percent clay
(percent finer than 2 μ), and the normal stress. An empirical relationship was also
developed between the soil’s properties and the residual strength. The empirical
relationships are incorporated into a spreadsheet made available on Stark’s web site, a
screen shot of which is shown in Figure 13.

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Figure 13. Screen shot of Stark spreadsheet. Solution is for LL = 77.

Wright Empirical Equation

Following is some discussion extracted from Wright’s 2007 publication on modeling
shear strength of desiccated high plasticity clays in Texas embankments.

Fully-Softened Shear Strength

The fully-softened shear strength corresponds to the shear strength that many soils,
especially those with a high PI, seem to develop over time. The concept of a fully-
softened strength appears to have been first suggested for natural and excavated slopes
in London Clay by Skempton and his co-workers. Skempton (1977) suggested that the
fully-softened strength was equivalent to the strength of the soil in a normally
consolidated state. Previous research performed for TxDOT and reviewed in Chapter 3
suggests that the fully softened strength may also be applicable to compacted fills
constructed of highly plastic clays. It has been shown that the fully-softened strength as
measured for normally consolidated clay is essentially identical to the strength that the
soil develops after repeated cycles of wetting and drying. Wetting and drying therefore
produces the same type of softening in compacted fills as has been observed in slopes of
natural deposits of London clay.

Analyses of Fully Softened Levees 495

Extension and Modification to Correlations by Stark and Co-Workers.

The relationships for shear strength presented by Stark et al. (2005) and shown in Figure
5.3 are believed to be reasonable for estimating the fully-softened shear strengths of
highly plastic clays. The relationships acknowledge that the Mohr failure envelope is
curved and, thus, the (secant) friction angles vary with the effective normal stress on the
failure plane. Curved failure envelopes are also consistent with the failure envelopes
presented by Kayyal and Wright (1991) for the Beaumont and Paris clays and discussed
earlier in Chapter 3. The relationships developed by Stark et al. can also be simplified
further and expressed by an empirical equation based on related work by Duncan et al.
(1989). Duncan and his co-workers have shown that for cohesionless soils where the
failure envelope is curved, it is convenient to express the shear strength by a secant

friction angle, φ′ secant. The secant friction angle varies with the logarithm of the
effective confining pressure, σ3, which can be expressed by an equation of the form,
where, φ′ secant, is the secant friction angle at an effective confining pressure ( 3) of 1
atmosphere, Δφ′ secant is the change (reduction) in the secant friction angle with each
ten-fold increase in confining pressure, and pa represents atmospheric pressure.
Atmospheric pressure (pa) is used as a convenient reference for stresses, making the

value for Δ φ ′secant independent of the particular units used.

Wright in several reports prepared for the Texas DOT presented some equations for

estimating a non-linear (curved) Mohr-Coloumb envelope for fissured clays. The

equation he presented for the fully softened shear strength of a clay at a given normal

stress is as follows:

'

' 0 −16.70 × log10 (LL) − 60 × log10 (σPf )

φsec ant = 55.3

a

Figrue 14 is a sketch taken after Figure 7.1 in the Wright paper illustrating the definition

of secant friction angle. For a given value of the secant φ′ angle, the shear strength may
be computed at a given value of effective pressure using the Mohr-Coloumb equation as
follows:

τ = σ ′ × tan(φ′ ant )
sec

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Figure 14. Figure 7.1 from Wright's 2007 paper on shear strength of high plasticity clays.

Estimates given by Wright’s equation may be a conservative estimate based on a
comparison to actual tests performed by Wright et al. Figure 15 is extracted from
Wright’s paper, and it shows that higher strengths were measured than are estimated by
the empirical estimation equation for a sample of Beaumont Clay, which had a LL of 73.

Figure 15. Figure from Wright 2007. 497
Analyses of Fully Softened Levees

Using the Wright equation, the data may be plotted using an EXCEL spreadsheet and an
equation obtained that represents the Mohr-Coulomb envelope over the full range of
normal stresses desired. Figure 16 is obtained from such a spreadsheet, showing the
power option for a trendline. It is a perfect (R2 = 1.0) fit for the data. The plot is of
course the same as that shown in the above figure for the assumed LL of 73.

Figure 16. Wright equation plotted and power equation
developed for LL = 73.

Stark, Choi and McCone (2005) recommended against using the normal method of
representing shear strength employing a simplified model of a value for φ′ and c’ in this
article. The recommendation is rather as follows:

The secant residual and fully softened friction angles for a cohesive soil
can be estimated for a particular effective normal stress using the liquid
limit, clay-size fraction, and interpolation between the empirical
relationships presented subsequently. For stability analyses it is
recommended that the secant friction angle corresponding to the average
effective normal stress acting on the slip surface in that particular
material or the entire failure envelope be used to estimate the residual and
fully softened shear strengths.

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A number of slope stability software packages allow the entire failure
envelope to be input using values of shear and normal stress to
incorporate the stress dependency. The empirical correlations can be used
to estimate the stress dependent residual and fully softened failure
envelopes for inclusion in the software.

TESTS TO MEASURE FULLY SOFTENED STRENGTH

Direct Shear Test

Using soil that has been pre-conditioned to a water content near the soil’s liquid limit, a
direct shear test may be performed to measure the fully softened shear strength. At this
date, a standardized procedure for the test has not been developed. However, other than
the sample preparation method, the test is performed basically using the normal
procedure for a direct shear test, ASTM Standard Test Method D3080. The time to
failure must be quite slow, because the soils typically have a very low permeability and
using the standard rule that the time to failure should be equal to or greater than the time
to 50% consolidation will often require a very slow strain rate. Often, the strain rate is
limited by the design of the equipment. The lowest strain rate possible on some machines
is from 7 x 10-5 to 8 x 10-5 in/min. At that rate, the time to 5 % strain for a 2.5 inch size
specimen would from 1,560 - 1,785 minutes.

Preparing a test specimen using this method is shown in Figure 17, copied from an
unpublished USACE Engineering Research and Development Center (ERDC) report.

Figure 17. Molding sample into direct shear test box (left)
and sample after shearing (right)

Analyses of Fully Softened Levees 499

An example of data obtained in this manner is shown in Figure 18. The data is for a soil
with a liquid limit of 77 and a PI of 51

Figure 18. Example of fully softened direct shear test, showing raw data.
Options for Curve Fitting
Several options are available for interpreting the data and using it in a slope stability
analyses model. A commonly used method is to use a spreadsheet such as EXCEL and
develop a best fit correlation line for a linear trendline. The Figure 19 shows the data
from the test shown above with a trendline for a linear best fit option. Using values of
normal stress and shear stress in a lower range of values results in interpreted parameters
of an effective φ' of 22.5°, the arc tangent of 0.415, and an effective c' of 92 psf, the y
intercept. The R2 value is lower for this option than for the trend line determined using
the full range of stresses.

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Figure 19. Linear trend line used to interpret shear test data from fully softened direct
shear test.

This method of interpreting the data results in a simple expression for the relationship
between normal stress and shear stress that is expressed with the slope of the line and the
y-intercept. For this example, the result is an effective φ' of 19.8°, the arc tangent of
0.3599, and an effective c' of 142 psf, the y-intercept.

This method averages the shear strength over the entire range of normal stresses used in
the test. For stability models where a different range of normal stresses may be
appropriate, a different trendline may be developed using only the range of normal
stresses considered appropriate for the particular model. For example, if one uses just the
normal stress versus shear stress plot for a range of normal stresses between zero and
1,500 psf from the data shown in Figure 20, a very different result is obtained, as shown
in the following figure.

Analyses of Fully Softened Levees 501

LL = 77, PI = 51

Figure 20. Linear trend line for low normal stresses for same test shown in Figure above.
Another popular curve-fitting method is the Power Function option. Figure 21 shows the
data for the test shown above with a LL = 77 with the power trend line option used for
best fit of the data. An excellent R2 value of 0.995 is obtained with this option.

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Figure 21. Power function trend line for raw data obtained in direct test on LL = 77 soil.

Discussion of Curve Fitting Options

Traditionally, slope stability analyses have been performed using a simple expression
termed the Mohr-Coulomb equation, given by an effective friction angle, φ' , and a y-
intercept, an effective c' , to represent soils in a model. However, most modern stability
analyses software permits the use of non-linear envelopes relating shear stress to normal
stress. Because this option is readily available and most test data can be manipulated to
develop a best-fit equation such as the power equation, there seems to be little reason for
using the traditional simple effective φ' and effective c' model to represent fully softened
zones in the analyses. These non-linear envelope options are more theoretically correct
and likely to simulate the actual behavior of fully softened zones in the analyses.

Analyses of Fully Softened Levees 503

Ring Shear Test
ASTM Standard test method D7608 at present is the only completely accepted
standardized method for measuring the fully softened shear strength of soils. Figure 22
shows equipment that may be used to perform the test.

Figure 22. Ring shear apparatus. From Wykeham Farrance catalog.
Example data from a laboratory that performs the test, Cooper Testing Laboratory, is
shown in Figure 23. The test results are similar to those for a direct shear test, in that a
non-linear envelope is obtained from which a Power Function equation is obtainable:

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Figure 23. Example ring shear test data.(Cooper Testing Laboratories)
Example soil has LL = 70

Figure 24 has the Cooper labs example ring shear test with the Wright equation for a LL
of 70 overlain on it. The similarity of the curves is remarkable.

Figure 24. Example ring shear test from Cooper Labs (blue line) overlain 505
with Wright's equation for LL = 70.

Analyses of Fully Softened Levees

While this particular set of data shows good agreement with Wright’s equation, one
should not assume that ring shear test data always is in good agreement with direct shear
test data. The equations developed by Wright and Stark consider a correction to ring
shear test data of several degrees to bring the data into agreement with direct shear test
data.
Triaxial Shear Tests
Another method for testing soils to obtain fully softened shear parameters is to use a
triaxial CUbar method. Two sub-sets of this method have been used. First, a sample
may be prepared at about its liquid limit water content, similarly to the preparation of the
direct test discussed previously. The sample is then consolidated using specialized
equipment to the desired consolidation pressure, and then placed in a triaxial cell and its
shear strength measured, for at least 3 specimens. Usually, more than 3 specimens are
used to obtain a more reliable non-linear envelope. This test method is very time-
consuming and requires specialized equipment not available in many laboratories and is
primarily at the present a research method. Wright discusses the test and presents a
typical set of data shown in the first following figure:
A second method for preparation to estimate the fully softened strength of clays is to
prepare samples and then repeatedly wet and dry them before testing in the triaxial
apparatus. This produces a blocky structure intended to simulate the structure of soils in
the field. The second figure below shows the results of a triaxial test on a sample of the
Eagle For shale prepared in this way. Based on a comparison between the test results in
Figures 25 and 26, the wet/dry method appears to result in slightly increased shear
strength.

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Figure 25. Triaxial shear test performed on fully softened sample of Eagle Ford shale
with LL = 88.

Figure 26. Triaxial test subjected to wetting and drying. 507
Same Eagle Ford shale sample as shown in Figure above. LL = 88.

Analyses of Fully Softened Levees

Comparisons between Empirical Methods and an Example Shear Test
Previously, an example direct shear test performed on a fully softened sample of high
plasticity clay, with a LL of 77, was presented. In this section of the paper, this test result
is compared to the empirical estimates provided by Stark’s spreadsheet and the equation
developed by Wright. Figure 27 shows the three plots overlain.

Figure 27. Comparison of Stark and Wright empirical equation estimates
to actual fully softened direct shear test for soil with LL = 77.

For this example, the similarity of test results to the two empirical correlations is
excellent. The Author evaluated about 10 test results from a recent project to determine
if the empirical predictions are typically this coincident with the test results. Following
figures show additional comparisons for two soils with LL values of 85-88, compared to
Stark and Wright empirical estimates. Two plots are shown to illustrate how the
correlations between test data at low normal stresses is better than the estimate extended
over a larger range of normal stresses.
At higher normal stresses, the experimental (actual test) data lies below the Stark and
Wright empirical correlation lines at higher normal stresses, but at low normal stresses,
less than about 2,000 psf, the divergence is much smaller. See the comparisons in
Figures 28 and 29.

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Figure 28. Correlation of Stark and Wright empirical estimates to two fully
softened direct shear tests.

Figure 29. Correlation between Stark and Wright empirical estimates to
fully softened direct shear tests. Smaller scale used.

Analyses of Fully Softened Levees 509

Comparison of Triaxial Shear Test on Wet/Dry Preparation (Desiccated) Sample to
Empirical Estimates
Wright (2009) presents the results of a triaxial CUbar shear test on a sample of clay that
had been prepared by wetting and drying repeatedly to simulate the desiccated structure
that occurs in exposed slopes. Figure 30 shows the plotted envelope for the data shown
in publication 5202.3, Table 8.1:

Figure 30. Triaxial test data for wet/dry preparation specimen
with Wright and Stark empirical curves overlain.

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OPTIONS FOR MODELING STABILITY ANALYSES

Introduction

When developing a model for a stability analyses, one normally attempts to define a two-
dimensional cross-section of the embankment or cut slope being analyzed. The geometry
of the model is developed from a proposed design for a new construction, or for an
existing structure, from knowledge gained from a geotechnical investigation or from
assumptions based on previous experience. In analyzing a site for a potential surficial
slope stability failure, several important parameters have to be considered. Some of the
more important parameters in an analysis are as follows:

• What are the size and configuration of the zones in the cross-section that should
be modeled with fully softened parameters?

• Likewise, what are the size and configuration of zones in the cross-section that
should be modeled with parameters appropriate for soil with no structural features
(non-desiccated zones)?

• What is an appropriate method for modeling the pore water pressures in the
model? Should pore water pressures be modeled with an Ru parameter or should
an assumed piezometric surface be developed?

• What are the appropriate Mohr-Coulomb parameters for each zone in the cross-
section.

• How should the area of the cross-section to be searched be specified? Should
both circular and non-circular surfaces be considered?

Some of the more important assumptions are discussed in following sections.

Size of Fully Softened Zone

For an existing embankment, assumptions on the size and configuration of the desiccated
zone to which fully softened shear parameters are assigned may include the following:

• One may assume a depth of desiccation and apply the fully softened shear
strength to that zone, applying an assumption of intact shear strength below the
zone. The figure below illustrates results for a 30 feet high embankment with 4H:
1V slopes and a desiccated zone assumed to be 10 feet deep.

Analyses of Fully Softened Levees 511

Figure 31. Typical results for assumed desiccated surface zone on embankment.

The critical circle for this set of assumptions is shown in Figure 31. The value of the FS
is quite low, a value of 0.963. However, one should also examine circles that extend
deeper into the cross-section. A relatively low safety factor might be acceptable for an
assumed surficial slide, regarding this occurrence as more of a maintenance problem.
But, a more serious stability problem might be indicated by a deeper failure surface,
which although it has a higher safety factor, might still be lower than generally
considered acceptable. Figure 32 below shows the same cross-section assumed for
Figure 31, but where the failure surfaces were forced deeper in the profile. A safety
factor of 0.963 was obtained for a failure surface limited to a depth of 10 feet (vertical
depth). When a search was allowed to extend into the underlying zone that was assumed
to be intact (not desiccated and not fully softened), obviously, a higher safety factor was
obtained, a value of 1.341. See Figure 32. One might regard a low safety factor as
acceptable for surficial slides such as those represented by the trial with a FS = 0.963, but
would seldom consider the deeper seated failure surface represented by the trial with a FS
= 1.341 as acceptable.

512 Innovative Dam and Levee Design and Construction

Figure 32. Illustrated results for failure surfaces forced below
desiccated zone in embankment.

• A second assumption is that the entire embankment has a structure modeled using
the fully softened shear strength. Figure 33 below illustrates results for a 30 feet
high embankment with 4H: 1V slopes. The entire embankment is assumed to
have the same fully softened shear strength, represented by a power function from
the test on the example soil having a LL of 77 and a PI of 51. The foundation is
assumed to have intact shear strength.

• A third assumption that can be made is that both the embankment and the
foundation have properties that should be modeled with fully softened shear
strength. Figure 34 shows a trial for a 30 feet high embankment resting on a
foundation where both the foundation and the embankment are modeled with a
fully softened power function from the example test on a soil with a LL = 77.

Analyses of Fully Softened Levees 513

Figure 33 Stability results for embankment with 4 to 1 slopes and entire embankment
has fully softened shear strength from power function on Example test with LL = 77.

Figure 34. Stability results for embankment with 4 to 1 slopes and both embankment
and foundation having fully softened shear strength from power function on LL = 77
514 Innovative Dam and Levee Design and Construction

Implications of Assumptions

Using a typical test result on an example soil, very low safety factors are obtained for the
assumption of a fully softened condition in both the embankment and foundation (a FS of
1.100 was obtained. Very flat side slopes would be required to attain safety factors
typically considered desirable, in the range of 1.5. Figure 35 shows the 30 feet high
embankment model where both the embankment and foundation are assumed to be fully
softened, with a side slope of 6 to 1. A safety factor of 1.574 was obtained with this
slope. The depth of sliding was predicted to be about 23 feet by the program.

Figure 35. Stability trial for assumption that both foundation
and embankment have fully softened strength.

Assumptions Regarding Piezometric Line

Several assumptions may be used for the assumed condition of the piezometric surface in
an embankment in a stability analysis. Several possibilities are:

• The embankment may be assumed to be completely saturated when an intense
rainfall falls on a desiccated zone. The cracks in the zone are assumed to be filled
with water represented by a water table or piezometric line coincident with the
surface of the embankment.

Analyses of Fully Softened Levees 515

• A Ru parameter may be assumed. The Ru parameter defines the pore pressure at
the base of each slice as equal to a given fraction of the total stress. For example,
a Ru parameter of 0.5 would mean that the pore water pressure at the base of a
slice would be equal to 50 % of the total weight of the slice. For soils which have
a saturated (total weight) weight of 124.8 pcf, which is double the unit weight of
water, an assumption of an Ru parameter of 0.5 is equivalent to the assumption of
a piezometric surface coincident with the top of the embankment. The User’s
Manual for the SLOPE/W computer program has this caution on the use of the Ru
parameter in analyses:

One of the difficulties with the Ru concept is that the coefficient varies
throughout a slope if the phreatic surface is not parallel to the ground
surface. When the phreatic surface is an irregular distance from the
ground surface, it is necessary to establish Ru at a number of points and
then by some weighted averaging method to calculate one single overall
average value for the slope. The result is that the simplicity of the method
is lost. The variability of Ru within a slope makes it an impractical option
in a product like SLOPE/W. The Ru option is included in SLOPE/W
mainly for historic reasons. Attempting to make use of the option is not
recommended, except in perhaps some simple isolated cases. There are
other better options available.

….Conceptually, Ru is around 0.5 if the phreatic surface is at the ground
surface. This is because the unit weight of water is about half the total unit
weight of the soil. Figure 8-4 Combination of Ru/B-bar with piezometric
pore-water pressures

PARAMETRIC ANALYSES AND DISCUSSION

To evaluate the sensitivity of stability analyses to various parameters involved, a series of
trials were performed. All of the trials assumed an embankment that was 30 feet high,
with a foundation that was 13 feet thick, with the following parameters varied:

• Side slopes of 3H: 1V and 4H: 1V
• Assumed depth of desiccation:

o 15 feet
o 10 feet
o 6 feet
o No restriction
• The following strength assumptions were made for a soil with a test LL of 80
o Test values with linear correlation φ’ = 17.7° and c′ = 92.5 psf
o Test values using Power Curve trendline
o Stark Correlation equation
o Wright Correlation equation

The cross-section analyzed, with one typical trial result are shown in Figure 36.

516 Innovative Dam and Levee Design and Construction

Figure 36. Typical stability analyses cross-section. Side slope is 4H: 1V.
Trial shown is number 13 in Table 2.

Results of the analyses are summarized in the following table.

Analyses of Fully Softened Levees 517

Table 2. Results of Stability Trials

Slope D strength FS Trial Slope D strength Trial
Number FS Number

ERDC Linear 0.83 1 ERDC Linear 1.03 13
15 ERDC Power 0.79 2 14
0.85 3 15 ERDC Power 0.98 15
Stark 0.83 4 Stark 1.05 16
Wright
Wright 1.03

ERDC Linear 0.89 5 ERDC Linear 1.14 17
10 ERDC Power 0.79 6 18
0.80 7 10 ERDC Power 1.01 19
Stark 0.79 8 Stark 1.03 20
Wright
1.11 9 Wright 1.01 21
0.83 10 22
3H: 1V 0.78 11 4H: 1V 23
0.80 12 24
ERDC Linear ERDC Linear 1.43

6 ERDC Power 6 ERDC Power 1.09
Stark
Stark 1.03

Wright Wright 1.05

none ERDC Linear 0.82 29 none ERDC Linear 1.00 25
ERDC Power 0.79 30 ERDC Power 0.97 26
Stark 0.78 31 Stark 1.03 27
Wright 0.79 32 Wright 1.01 28

The stability trials indicate several important points regarding modeling and controlling
the failure surface depths for searches for these models.

• Using the linear trendline for a test often results in a significant cohesion
intercept. When the depth of the fully softened zone is assumed to be relatively
small, higher safety factors result.

• If a shear strength model which has a curved envelope and essentially a zero
cohesion is used, the safety factors are far lower than for a linear trendline with a
significant cohesion intercept when the assumed depth of fully softened zone is
relatively shallow.

• When the depth of failure is not limited and failure surfaces are allowed to pass
into the cross-section as deep as possible, dictated by the program, the trials
which employ a significant cohesion intercept have about the same safety factor
as the trials for shear strength assumptions using curved envelopes through zero.

• The difference between safety factors computed using empirical estimates (Stark
and Wright) are very similar to those using the test data for this set of
comparisons, especially at relatively low values of normal stress.

• Flattening the slope from 3H:1V to 4H:1V increases the safety factor by an
average of 27.5%

• Several trials were performed with 10% increased unit weights and the effect on
the safety factor was about an increase of 0.05.

518 Innovative Dam and Levee Design and Construction

• Using fully softened shear test parameters for a typical soil with a LL=77 (using a
power function as shown in previous Figure 21), a trial was performed with the
water surface at the top of the embankment assuming all the soils in the cross-
section were in a fully softened condition. The results shown Figure 37 illustrate
how similar safety factors are obtained for both shallow and deeper failure arcs.

Figure 37. Output for analysis of cross-section with 4H: 1V side slopes.

Minimum Safety Factor Requirements

Safety factor requirements for stability of levees and embankments are contained in many
Federal and State regulations. Because surficial sliding is a special sub-set of global
stability concerns, some special provisions may be warranted for this type of instability.
As illustrated with previous typical results, using fully softened shear parameters to
represent significant zones of an embankment cross-section typically results in relatively
low safety factor values. Values in the range of 0.9 - 1.0 are common for embankment
cotangents of 3H: 1V to 4H: 1V.

Analyses of Fully Softened Levees 519

To obtain a safety factor of 1.5 which is commonly a requirement for steady seepage
conditions in embankment analyses, would require a side slope on the embankment of
about 6.25H: 1V, as shown in Figure 38. This trial assumes a 30 feet tall embankment
with a depth of fully softened zone of 10 feet. The fully softened strength used is that of
a test soil with a LL = 80 using a power function to fit the data.
Notably, some criteria for slope stability recognize the difference in the nature of shallow
slides for upstream drawdown stability, wher e soils typic ally a re m odeled with a low
cohesion value. Typ ically, safety factors of 1.1 are accepted for this condition (see for
example the NRCS criterion in their design criteria document TR60.

Figure 38. Trial illustrating the side slope of 6.25H: 1V required to obtain a FS = 1.50
for fully softened zone that is 10 feet deep.

If a more severe assumption is made that all of the embankment and the foundation as
well is fully softened, then a side slope of 7H:1V is required to obtain a safety factor of
near 1.50, as shown in Figure 39. The fully softened shear strength used for the trial is
from ERDC data on a soil with a LL = 80.

520 Innovative Dam and Levee Design and Construction

Figure 39. Trial for 30 feet high embankment with 7H: 1V side slopes.

Another trial (not shown here) used an assumed depth of the foundation of 25 feet rather
than the 13 feet shown in the figure above. An almost identical predicted surface with
the same safety factor was obtained. This illustrates that for this very conservative set of
assumptions, for these parameters, the depth of the foundation is not a critical one.

It appears unrealistic to require traditional values of safety factor in the range of 1.50 for
slides modeled with very conservative assumptions using fully softened shear test values
because of the implications. Very flat slopes of at least 7H: 1V would likely be required
to satisfy this requirement for highly plastic soils like those studied.

Analyses of Fully Softened Levees 521

CONCLUSIONS

Major conclusions obtained in the research and background for this paper may be
summarized as follows:

• Empirical equations developed by Wright and Stark provide estimates for the
nonlinear Mohr-Coulomb envelopes for high plasticity clay soils that are in good
agreement with actual fully softened shear tests for one data set available for this
study, particularly at relatively low normal stresses (less than about 2,000 psf).

• At higher normal stresses (above about 2,000 psf) the divergence in shear strength
estimates of the empirical estimates to the test values for the set of data examined
is greater than for low normal stresses.

• The fact that the empirical estimates are significantly higher than the test values at
higher normal stresses is less important when surficial slides are the subject of
interest. For surfaces less than 15 feet deep, the effective normal stresses on the
failure plane are approximately 1,000 psf or less for the unit weights used.

• In general there appears to be good agreement between empirical relationships
such as those developed by Wright and Stark and actual direct shear tests on fully
softened samples, for the available data set examined.

• The lack of standardized test procedures and complicated and lengthy test times
for performing drained tests on highly plastic clays causes test costs to be
significant, which makes the use of empirical estimates attractive for routine
work.

• Using fully softened shear strength parameters to represent the entire embankment
cross-section as well as the foundation of an example embankment showed that
side slopes of at least 7H: 1V would be required to attain normally acceptable
safety factors of 1.5.

• Future criterion statements should consider using a lower required safety factor
for predicted surficial slides less than 10 feet deep. A value of 1.1 is
recommended. Deeper seated failures may justify the normally required value of
1.5 as a criterion.

REFERENCES

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Aubeny, C.P. and R.L. Lytton, “Properties of High Plasticity Clays,” Report 2100-2
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Branch, Al, USACE, Fort Worth, TX, Personal communication October, 2011.

Chandler, R.J. and A.W. Skempton “The design of permanent cutting slopes in stiff
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522 Innovative Dam and Levee Design and Construction

Cooley, Larry A. and Glen R. Andersen, “Slough Slides in Embankments with
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Analyses of Fully Softened Levees 523