elongation criteria and friction loss in ground anchors · evaluation of elongation criteria and...
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Evaluation of Elongation Criteria and Friction Loss in
Ground Anchors
Final Report
Prepared by:
John P. Turner and Benjamin J. Turner
Dan Brown and Associates, PC
Submitted to:
Deep Foundations Institute
Committee on Tiebacks and Soil Nailing
October 16, 2014
1
EXECUTIVE SUMMARY
This report describes a research project for evaluating the applicability of the widely accepted 80 percent
criterion for elongation of ground anchors to anchors with unbonded lengths exceeding 100 feet. This
issue is driven by several recent projects involving ground anchors for landslide stabilization in which a
significant percentage of the anchors did not meet the criterion that requires measured elongation during
proof load testing of at least 80 percent of the theoretical elastic elongation. The projects involved anchor
unbonded lengths in the range of 85 to 220 feet, which is outside the range traditionally used in practice,
although anchors of this length are being used more frequently for landslide stabilization. The principal
objective of this research is to address whether the widely accepted criterion of 80 percent elongation is
applicable for such applications, and whether other factors affect the ability of anchors to meet the
criterion.
Analytical methods for predicting transfer of load along the length of steel strand due to friction loss are
used routinely in the prestressed concrete industry. These analytical expressions provide a rational
framework for quantifying changes in load due to friction along the length of a ground anchor in terms of
a ‘wobble coefficient’ (K) as defined in Aalami (2004). Values of the wobble coefficient for ground anchors
can only be determined by back‐calculating from load tests, i.e., fit the value of K to the appropriate
analytical expression based on the known test load and measured percent elongation. The analytical basis
is first developed and shown to provide a tool for evaluating results of anchor load tests to determine the
magnitude of expected elongation as a function of unbonded length. Next, a database of anchor load
tests is used to back‐calculate values of K for anchors with unbonded lengths in the range typically used
in geotechnical applications (< 100 feet). These values of K are then used to calculate expected friction
loss for anchors with high unbonded lengths (100 to 250 feet) to evaluate whether the 80 percent criterion
is reasonable.
The primary findings of this research are:
Field data data show a general trend of increasing rate of friction loss with increasing unbonded
length, i.e., longer anchors are more likely to fail the 80‐percent minimum elongation criterion.
Shallow anchor inclination appears to be a strong contributor to higher friction loss because it
makes placement of the anchor into the hole difficult, requiring the anchor to be forced in, which
may induce additional curvature and twisting;
Factors that contribute to alignment deviations of the anchor drill hole, such as obstructions,
discontinuities, or alternating hard and soft layers, also contribute to curvature and increase
friction loss;
Factors that result in forcing the anchor into the hole, which for the cases considered involved a
combination of long anchors, shallow inclination, and alignment deviations, increases the
probability of anchor damage. For example, failure of the seal between the bond and unbonded
segments of the anchor may allow grout to penetrate the sheathing, preventing elastic
deformation of the strands.
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Measures that can be taken to mitigate the effects of anchor friction loss include:
Higher inclination angles; if the project conditions allow, use of steeper inclination angles reduces
curvature by allowing gravity to assist in stretching the anchor and making installation easier.
Two‐stage grouting in which the bond zone is grouted and an alignment load is applied to
straighten the unbonded length before it is grouted. This procedure is more time‐consuming and
difficult to perform, and hence not utilized routinely in North American practice, but warrants
consideration where high unbonded lengths (> 100 ft) and shallow inclination angles are required.
Use of instrumentation for: (a) monitoring and correcting for hole alignment, and (b) direct
measurement of load transfer to the bond zone, such as strain gages or direct‐force measuring
devices that can be mounted to the anchor strands. Item (b) allows direct verification of the
change in load over the unbonded length (friction loss) as well as the load transferred to the bond
zone which provides the stabilizing force.
Regardless of whether anchors pass or fail the 80‐percent criterion, slope stability analyses that include
the resisting force of the anchor should only consider the magnitude of load that is expected and specified
to reach the bond zone. If the designer requires more resisting force to reach a target factor of safety,
larger anchors or a higher minimum elongation criteria must be specified. Likewise, anchors that fail the
80‐percent criterion do not necessarily have to be rejected outright if additional slope stability analysis
considering the actual magnitude of load reaching the bond zone can be shown to satisfy the target factor
of safety when supplemental anchors are added. This recommendation is consistent with the PTI
specifications (2004) although it is not typically included in project specifications.
Considering that many anchors from the database with unbonded lengths in the range of 100 to 200 feet
satisfied the 80‐percent criterion, a modified minimum elongation acceptance criterion for long anchors
is not recommended at this time. Additional data will potentially allow us to draw quantitative
conclusions about the influence of specific parameters such as anchor hole inclination and the
manufacturing processes used by various anchor manufacturers, and could lead to more definitive
recommendations in the future. This study should be considered preliminary and the issue of friction loss
in ground anchors should be the subject of additional research.
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1. INTRODUCTION AND PROBLEM STATEMENT
Steel strand used in concrete pre‐stressing applications or in ground anchors for geotechnical applications
exhibit variations in load along the length of the strand during stressing. For strand encased in grease‐
filled plastic sheathing, which is intended to allow the strand to elongate freely, some load can still be
transferred by friction between the strand and the grease and between the grease and sheathing. The
sheathing then transfers load to the surrounding grout and, in the case of ground anchors, to the
surrounding soil or rock. A widely used criterion for ground anchor acceptance based on load testing is
that the measured anchor elongation be required to achieve a minimum value of 80 percent of the
theoretical elastic elongation, based on the well‐known relationship Δ = PL/AE where P = load applied at
the anchor head, L = anchor unbonded length, A = cross‐sectional area of steel strand, and E = modulus
of elasticity of the steel strand. This criterion allows the actual elongation to be 20 percent less than the
theoretical elastic value, presumably because the load over the unbonded length is decreasing with
distance from the anchor head. This decrease in load is referred to as friction loss.
The 80 percent criterion has served the ground anchor industry well. It provides a rational and practical
means to evaluate the ability of an anchor to transfer most of its load (80 percent or more) between the
anchor head and the bond zone. In most applications, a properly manufactured and properly installed
ground anchor will meet the 80 percent elongation criterion easily. However, several cases in recent years
in which anchors being used for landslide stabilization and having unbonded lengths in the range of 85 to
220 feet resulted in unusually high failing rates with respect to the criterion. This raises the question of
whether the 80 percent criterion is applicable to all ground anchors or if it should be limited to anchors
within a certain range of unbonded length. In particular, the question is whether friction loss increases
with unbonded length to a point at which the anchor elongation can be expected to fall below 80 percent
of theoretical elongation. If that is the case, acceptance criteria for anchors with long unbonded lengths,
such as are now being used in landslide stabilization applications, may require modification from the 80
percent criterion.
Section 2 of this report presents the analytical approach for evaluating the change in load along the length
of a pre‐stressing strand, in terms of friction loss. This analysis provides a framework for quantifying
friction loss in ground anchors when load testing is conducted with measurements of elongation. Section
3 introduces the factors having the potential for increasing friction loss in ground anchors. Section 4
presents case histories of anchors not meeting the 80 percent criterion, while Section 5 presents data
from case histories in which anchors met the criterion. These cases are compared in an attempt to identify
the factors that result in less than 80 percent elongation. Anchor unbonded length appears to be a major
factor; however other variables come into play, including anchor inclination (from horizontal), installation
methods, deviation of the drill hole alignment, and subsurface conditions that contribute to drill hole
deviation. Section 6 describes a landslide stabilization project in which long anchors successfully met the
elongation criteria, and identifies the factors that enabled the criterion to be met. Section 7 provides
recommendations on incorporating anchor forces into limit equilibrium slope stability analyses. Finally,
Section 8 summarizes the study and presents recommendations for minimizing friction loss in ground
anchors and suggestions for further research.
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2. ANALYSIS OF FRICTION LOSS IN STRAND ANCHORS The following relationship is often cited (e.g., see AASHTO LRFD Bridge Design Specifications Section
5.9.5.2.2, ACI‐318 Section 18.6.2, or the PTI Post Tensioning Manual) as an approximation of load (P) as a
function of distance (x) from the anchor head:
P(x) = Po e‐[αμ +Kx] (1)
where: P(x) = load in anchor at distance x from anchor head Po = load at anchor head (at x = 0)
α = change in angle of the strands (radians) from the stressing point to distance x
= coefficient of angular friction K = wobble coefficient of friction (radians per unit of length) x = distance from the stressing point
The first term in the exponent, αμ, represents the effect of cumulative change in angle up to a distance x
and is useful for calculating friction losses in pre‐stressing applications where the strand is supported at
known locations in the structure (e.g., the strand is draped over supports in the concrete form). For
prestressed concrete applications, α can be evaluated incrementally over each support interval. For
ground anchors the strand is not supported at constant intervals and the αμ term is not applicable. All
effects of friction loss are lumped into the single parameter, K. Equation 1 reduces to:
P(x) = Po e‐Kx (2)
The parameter K is referred to as the wobble coefficient and is the product of angle change per unit of
length (radians/ft) and the coefficient of angular friction μ for the sheathed strand with grease (Aalami
(2004).
Thus, the normalized load at a distance x from the anchor head is given by:
(3)
Under a tension load, elastic elongation is evaluated according to Hooke’s Law as Δ = PL/AE. Since P varies
over the unbonded length (Lu), anchor elongation must be expressed in its integral form:
∆ (4)
∆ (5)
∆ (6)
5
Solving the integral, the expected elongation with friction loss taken into account is given by:
∆ (7)
evaluated over the interval x = 0 to Lu. The theoretical elastic elongation, assuming no loss due to friction,
is given by:
∆ (8)
The normalized elongation, or ratio of elongation with friction loss taken into account to the theoretical
elastic elongation without friction loss, can be expressed by:
∆
∆
(9)
Or, percent elongation (EL) is given by:
EL = 100% x (10)
Equation (10) provides a tool to evaluate the expected elongation, with friction taken into account, as a
percentage of theoretical elastic elongation. The criterion for ground anchors under proof or performance
load testing in the field is that EL > 80%.
In Figure 1, the percent elongation as calculated by Equation 10 is plotted as a function of anchor free‐
stressing length. Three curves are shown, each representing a different value of K ranging from .001 to
.005 radians per foot. The 80 percent criterion is shown for reference as the blue dashed line. For values
of K in the range of .0025 to .005, the unbonded length beyond which elongation falls below 80 percent
is in the range of 90 feet to 180 feet. These values of unbonded length above which anchors would not
meet the 80 percent criterion are consistent with the sites at which anchors did not meet the criterion,
suggesting a link between anchor unbonded length and friction loss.
Following a discussion of factors that may contribute to anchor friction loss, case histories in which data
from anchor load tests are sufficient to back‐calculate the wobble coefficient K are used to compare cases
with long unbonded lengths in which anchors did not met the 80 percent criterion to cases with anchors
that met the criterion.
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Figure 1. Percent elongation versus free stressing length, for three values of wobble coefficient, K.
3. POTENTIAL CONTRIBUTORS TO FRICTION LOSS
Theoretically, the wobble coefficient K is a function of two physical interactions: (1) friction between the
grease and the steel strand, and between the grease and the sheathing, which are material properties,
and (2) the amount of curvature along the length of the strand. Any aspect of the ground conditions,
construction techniques, or anchor geometry or materials that has the potential to induce unintentional
wobble over the unbonded length of the anchor could therefore contribute to friction loss.
With respect to ground conditions, sedimentary rock sites with bedding planes that are sub‐parallel to the
direction of drilling may cause the drill feed to deviate from its intended path and follow the bedding
surface instead. A similar mechanism is possible at sites with a contact between fill and native soils, planar
foliations, block‐in‐matrix type formations, or any other geologic setting that includes significant changes
in stiffness between adjacent materials and/or planes of weakness.
These effects are likely to be exacerbated for longer anchors due to the increased flexibility of the drilling
feed as its length increases. For example, if a hard inclusion in a soft matrix is encountered 100 feet from
the surface, it is likely that the drill bit will deflect off the inclusion and continue penetrating at an oblique
angle, resulting in a “kink” in the drilled hole. The same inclusion encountered directly beneath the ground
surface may not cause significant deviation from the intended straight path.
Fabrication techniques used by different anchor manufacturers may lead to different amounts of friction
loss for anchors under the same conditions. In particular, different manufacturers use different techniques
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 50 100 150 200 250 300
Elongation as a Percentage of Theoretical Elastic Elongation
Unbonded Length, Lu (ft)
K = .005 rad/ft
K = .0025 rad/ft
K = .001 rad/ft
7
for encapsulating the strand with plastic sheathing over the unbonded length of the anchors, which may
permit more or less shear transfer between the strands and the ground. The major difference is whether
the sheath is extruded over the steel strands or the strands are pulled through the sheath. The type of
grease, and the method of grease emplacement and sealing of the grease inside the sheathing could also
affect friction.
Additionally, placement of the anchors during construction may induce additional unintentional wobble
under certain conditions. An anchor placed in a relatively long hole that is inclined at a shallow angle on
the order of 10 to 15 degrees is difficult to place if any obstruction or deviation from straightness is
encountered over the length of the hole. Anecdotal accounts described in the next section suggest that
in such instances, the contractor is left to force the anchor into the hole using whatever means are
necessary to overcome the resistance. Significant compression placed on the anchor is likely to induce
additional wobble on top of the wobble that may already be present due to curvature of the hole, which
will then be grouted into place prior to stressing.
In contrast to ground anchors used for landslide stabilization, dam tie‐down projects use vertical anchors.
In this application, the anchor self‐weight helps to straighten the strands, and anchor manufacturers
report that tie‐down applications routinely achieve 100% elastic elongation even for very long anchors.
This suggests that anchor inclination is a strong contributor to the potential for unintentional curvature
for ground anchors.
4. CASE HISTORIES OF ANCHORS FAILING THE 80 PERCENT CRITERIA
Two landslide stabilization projects were the impetus for this study, the Togwotee Pass Slide in Wyoming
and the Cuesta Grade Slide in California. In both cases, anchors were rejected by state DOT inspectors for
not passing the 80 percent elongation criterion. Variable geologic conditions, shallow hole inclination, and
forcing of the anchors into the hole may have contributed to the high friction loss for both projects.
Togwotee Pass Landslide
The Togwotee Pass Landslide is located on U.S. Highway 26/287 in northwestern Wyoming. The landslide
is classified as complex, consisting of block, slump, and earthflow components (WYDOT, 2008). The head
scarp of the slide, on the upslope side of the roadway, is 300 ft wide and approximately 20 ft high. The
slide surface is approximately 60 ft below the roadway centerline elevation and extends downslope 970
ft to the Wind River. As part of a roadway widening and reconstruction project in 2008‐09, WYDOT
planned to stabilize the slide using tieback anchors fixed to concrete panels on the upslope side of the
roadway, as shown in Figure 2.
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Figure 2. Installation of anchored panels at Togwotee Pass Landslide, Wyoming
(Photos courtesy of Wyoming Department of Transportation)
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Slide debris above the failure plane at Togwotee Pass consists of a heterogeneous mix of silty to sandy
clay with cobbles and boulders up to 5 ft in diameter. Rock below the slide plane consists of interfingered
lenses of volcaniclastic claystones, siltstones, sandstones, and volcanic breccia of the Eocene Aycross
Formation (WYDOT 2008). Rock strength ranges from extremely weak to medium strong.
The as‐designed stabilization system consisted of two rows of anchor panels with 75 panels per row (150
anchored panels total). All of the anchors were designed with four 7‐wire strands. Each strand is encased
within its own plastic sheath with corrosion‐inhibiting grease and each group of strands is enclosed in an
outer plastic sheath. All anchor lengths were 179 ft, which includes a 30‐ft bond length, 145‐ft unbonded length, and a 4‐ft length between the ground and the jack (tail). All were designed with a batter angle (from horizontal) of 15 degrees. A total of 40 anchors were installed during the fall of
2008. Of these, 32 failed to meet the 80 percent elongation criterion upon the first cycle of proof load
testing. Alignment load was 5 percent of the design load of 126 kips. Proof tests were carried to 133
percent of design load, or 168 kips.
In response to the high failing rate with respect to minimum elongation, several anchors were exhumed
and cut open. It was found at some locations that grout had penetrated into the region between the
plastic sheathing and the strand within the unbonded zone (Figure 3). It was reported that difficulties in
inserting the anchors led to the use of measures involving alternately pulling and pushing the anchors,
which may have ruptured the seal between the bonded and unbonded portions of the anchor, allowing
grout to enter the sheaths, or that plastic sheathing was damaged during installation.
Figure 3. Exhumed anchor at Togwotee Pass Landslide exhibiting grout penetration
(Photo courtesy of Wyoming Department of Transportation)
Grout penetration
10
Work on the Togwotee Pass project was suspended in October 2008 due to winter conditions. As a result
of the grout penetration observed in exhumed anchors, the seal joints were re‐designed and
strengthened, and a plan was developed for avoiding excessive handling forces during anchor insertion.
In June of 2009 an additional 24 anchors were installed, 23 of which were tested. All of the tested anchors
satisfied the 80 percent elongation criterion. Additionally, 25 of the previously installed anchors were re‐
tested for elongation. Of the re‐tested anchors 6 passed the elongation criterion, 3 anchors broke, and
16 did not meet the elongation criterion. In July of 2009 the project was terminated in response to slope
inclinometer measurements indicating activation of a lower slide plane below the bond zone of the
anchors.
Cuesta Grade Slide Repair
Cuesta Grade is located on Highway 101 in central California. The six‐lane roadway is supported on a
wedge of artificial fill that has experienced slip at the fill/native contact, necessitating frequent repair of
cracks in the pavement by Caltrans maintenance crews. An anchored soldier pile wall was designed as a
means to increase stability and control roadway damage. The wall design included 108 soldier piles
consisting of double H‐piles placed in a pre‐drilled hole and backfilled with concrete. Each soldier pile was
anchored with a single tieback extending through the space between the pair of H‐piles, at depths ranging
from 4 to 8 ft below the top of soldier pile. H‐pile sections ranged from HP 8x36 to 12x53. Anchor free‐
stressing lengths varied from 84 ft to 224 ft which includes the unbonded length plus a 4‐ft tail; these
lengths were necessary to extend beneath the existing roadway and to reach suitable bond zone in the
underlying rock. Anchor design loads varied from 34.2 kips to 149.3 kips, requiring from 2 to 5 strands.
Bond lengths, determined by the contractor to meet the design loads, ranged from 15 to 25 ft. All of the
anchors were designed with an inclination angle of 15 degrees.
Subsurface conditions at Cuesta Grade consist of fill overlying the native alluvial soil overlying rock of the
Toro Formation. The alluvium and rock exhibit high degrees of variability. The fill consists predominately
of sandy and gravelly lean clay (CL), stiff to very stiff, with gravel particles up to 1 ¼ inch. The alluvium
varies between very stiff sandy lean clay with gravel (CL) to medium‐dense well graded gravel with silt
and sand (GW‐GM) and contains random sandstone and shale cobbles. The underlying Toro Formation
contains interbedded sandstone and shale that vary widely in hardness, degree of weathering, and degree
of fracturing. The rock also contains slickensides oriented between 15 and 70 degrees from horizontal.
These ground conditions are highly conducive to drill stem deviations because of alternating hard/soft
layers, the presence of obstructions such as cobbles, and the flexibility of the drill stem, especially
considering the low inclination angle. During construction, the contractor reportedly had difficulty drilling
and placing the anchors, and resorted to alternately pushing and pulling the anchors in order to force
them into the hole. Figure 4 shows the Cuesta Grade site during construction.
11
Figure 4. Construction of anchored soldier pile wall at Cuesta Grade
(Photos courtesy of D. Applebaum, Caltrans)
12
Field records from Cuesta Grade show that 24 out of the 108 anchors, or 22%, failed to meet the required
minimum elongation. Unbonded lengths of the anchors that did not meet the required elongation ranged
from 130 to 220 feet. As a percentage of theoretical elastic elongation, those that failed to meet the 80
percent criterion exhibited measured elongations ranging from 59% to 79% of theoretical elastic
elongation, with a mean value of 72%. All of the anchors with unbonded lengths in the range of 80 to 120
feet met the minimum elongation. To account for the failed anchors, an additional thirteen anchors were
installed to increase the stabilizing force required to achieve the target factor of safety. The project was
completed in 2012 and the system has reportedly performed satisfactorily.
The anchor installation contractor at Cuesta Grade removed one of the 5‐strand anchors for inspection
and reported the following observations, which are also shown in Figure 5:
The strands are twisted inside corrugated sheathing, causing friction which did not allow for full
elongation during testing
There was little to no grease inside the PE tubing on 4 of the 5 strands.
On several of the strands, hardened grout was found between the strands and PE tubing
The above observations would be consistent with a broken seal at the bond‐unbonded joint, which would
result in replacement of grease by grout, and with the use of excessive force during anchor installation.
Figure 5. Exhumed anchor at Cuesta Grade exhibiting grout in the outer sheath and lack of grease
In summary, the anchored slide stabilization projects described above, Togwotee Pass in Wyoming and
Cuesta Grade in California, each exhibited a significant number of anchors failing to meet the 80 percent
elongation criterion. Both projects also exhibit the following common features:
Relatively long anchor unbonded lengths (145 ft at Togwotee Pass and up to 220 ft at Cuesta
Grade)
13
Shallow anchor inclination (15 degrees)
Highly variable subsurface conditions conducive to deviations in the anchor alignment, including
cobbles and boulders in a soil matrix, and wide variations in rock hardness and strength. Neither
project utilized instrumentation for monitoring drill hole alignment.
Reportedly excessive force required to install anchors, likely leading to maximum curvature
(wobble) and possibly compromising the seal at the joint between the bond and unbonded
segments of the anchors
5. DATA FROM ANCHOR PROJECTS MEETING THE 80 PERCENT CRITERION
A theoretical or laboratory experimental evaluation of the factors influencing friction loss aimed at
establishing numerical values of K is not likely to produce a practical result for ground anchors.
Laboratory‐scale testing cannot reproduce the field conditions that control friction loss due to wobble,
including anchor unbonded length and factors associated with installation under realistic field conditions
(drill hole deviations during drilling, inclination angle, force required to install a long anchor, etc.).
Numerical modeling requires values of K to be assumed. An empirical approach that could provide useful
insight is to establish back‐calculated values of K from a database of field load tests on ground anchors. K
can be back‐calculated from a proof or performance load test using Equation 10 if the unbonded length
and percent elongation are known from the test. Because K appears in the exponential term in the
numerator and also in the denominator, there is not a closed‐form analytical solution to Equation 10, and
K must therefore be established through an iterative solution approach. The authors developed a
spreadsheet for this purpose that determines K for a given set of results from an anchor load test. The
objective is to back‐calculate K from field load test data to establish (1) a range of “typical” wobble
coefficients for routine projects and (2) the influence of various parameters on the wobble coefficient,
such as anchor inclination, anchor manufacturer, soil/rock conditions, etc.
A database of anchor load tests, summarized in Table 1, was compiled and used to back‐calculate values
of the wobble coefficient, K. The database includes the Togwotee Pass and Cuesta Grade slope
stabilization projects as well as load test data from three additional projects provided by members of the
DFI Tiebacks and Soil Nails Committee. Information such as the project owner and location has been kept
anonymous for these projects at the request of those who provided the data. Relevant load test data for
each anchor in the database in provided as an appendix to this report.
All of the test results used for back‐calculating K were required to include force and elongation
measurements at the alignment load and the maximum test load. Additionally, the test must include
unloading back to the alignment load following the maximum test load so that residual (plastic)
deformation can be separated from the elastic elongation. If data for a given test did not include force
and deformation measurements at the alignment load following the maximum test load, that test was
excluded from the database.
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Table 1: Summary of Anchor Load Test Database Project #
Name No. of Tests
Inclination Angle from Horizontal
Free Stressing Length1
(ft) No. of Strands
Min. Avg. Max. Min. Median Max.
1 Togwotee Pass 20 15° 149 149 149 4 4 4
2 Cuesta Grade 108 15° 84 129 224 2 5 5
3 Anonymous 6 unknown 99 128 158 1 1 1
4 Anonymous 2 45° 115 115 115 6 6 6
5 Anonymous 35 45° to 90° 74 108 138 39 52 58
Total 171 ‐ 74 127 224 1 5 58
1 Free stressing length = unbonded length + tail length
Back‐calculated values of K from the project database are summarized in Table 2 and the individual data
points are plotted versus unbonded length in Figure 6. A general trend of increasing wobble coefficient
with increasing unbonded length is observed. That is to say that the longer anchors in our database were
more likely to have greater total friction loss, but also greater friction loss per unit length over the
unbonded zone. We speculate that the primary factor influencing this trend is that the drill stem becomes
more flexible as it is advanced further into the ground, making it more prone to deviating from a straight
course when an irregularity is encountered.
Table 2: Summary of Wobble Coefficient Values
Project #
Name No. of Tests
Avg. Free Stressing Length (ft)
Average Elongation
K (rad./ft) COV K (%)
Min/Max Mean
1 Togwotee Pass 20 149 83% 0.0005/0.0040 0.0026 39
2 Cuesta Grade 108 129 79% 0.0005/0.0111 0.0038 43
3 Anonymous 6 128 91% 0.0011/0.0022 0.0016 26
4 Anonymous 2 115 94% 0.0006/0.0013 0.0009 53
5 Anonymous 35 108 85% 0.0009/0.0057 0.003 34
Total 171 127 82% 0.0005/0.0111 0.00294 46
15
Figure 6. Wobble coefficient versus unbonded length data. For a given unbonded length, the dashed line shows the maximum wobble coefficient for which achieving elongation of 80% of the theoretical elastic elongation is possible. Data points plotting above this line failed the 80% criterion.
The amount of scatter in the data plotted in Figure 6 does not support development a specific relationship
between friction loss and unbonded length, which is not surprising given the inherent variability in factors
such as subsurface conditions, installation methods, etc. Note that several anchors with unbonded lengths
between 100 and 200 feet did satisfy the 80‐percent criterion. Furthermore, the limited size of the
database does not allow us to quantify the relative influence of parameters such as anchor inclination,
anchor manufacturer, or ground conditions with statistical significance. Nonetheless, designers and
contractors should keep in mind that several parameters are likely to influence the wobble coefficient
even if results currently available are not sufficient to quantify the corresponding amount of friction loss.
Figure 7 shows anchor inclination angle plotted as a function of the back‐calculated values of K. These
data show a trend of decreasing wobble coefficient with increasing inclination angle, suggesting that more
steeply‐inclined anchors are less prone to friction loss resulting from unintentional curvature. A
contributor to this trend is likely that the anchors’ self‐weight makes placement in the hole easier. For
vertical anchors such as those from Anonymous Project #5 that were used as tie‐downs, the anchors’ self‐
weight also helps to straighten the strands prior to grouting.
0 100 200 300Unbonded Length (ft)
0
0.004
0.008
0.012Project (inclination angle)
Togwotee Pass (15 deg.)Cuesta Grade (15 deg.)Project 3 (unknown)Project 4 (45 deg.)Project 5 (45-90 deg.)
16
Figure 7. Wobble coefficient versus inclination angle.
6. A CASE HISTORY WITH DIRECT MEASUREMENT OF FRICTION LOSS
For critical life safety projects or routine projects for which the designer feels that the ground conditions
or other factors may lead to unacceptably large friction loss, engineering controls can be implemented to
reduce the uncertainty with regards to the wobble coefficient and corresponding friction loss. An example
is described here.
As part of a recent slope stabilization project for an adversely‐dipping, weak sedimentary rock slope in
Southern California, two tieback anchors with unbonded lengths of 130 feet were performance tested to
133 percent of design load. Each anchor was instrumented with DYNA Force® elasto‐magnetic sensors,
manufactured by DYWIDAG‐Systems International, mounted directly to the strands over the unbonded
and bonded zones to measure the load‐transfer between the strands and the ground and to determine
where along the length of the anchor the load transfer was occurring. Furthermore, the equipment used
to drill the anchor holes was equipped with a gyroscopic device that measures the deviation of the drill
string from perfectly straight, and anecdotal reports indicated that the device measured less than one‐
percent deviation along the length of the drilled holes. The anchors were inclined at 45 degrees in order
to intersect the potential failure plane, which was assumed to be inclined at a relatively shallow angle of
about five to ten degrees. A crane‐supported dolly was used to mechanically feed the anchors into the
drilled holes, and the contractor did not report any difficulty or blockages during the placement. Figure 8
shows installation and testing of the anchors.
0 30 60 90Inclination Angle (from horizontal; degrees)
0
0.004
0.008
0.012
Togwotee PassCuesta GradeProject 4Project 5
17
Figure 8. Installation and load testing of tieback anchors for mitigation of a recent landslide in
Southern California. Photographs by B. Turner.
Given the reported ease of installation and “straightness” of the drilled holes along with the relatively
steep anchor inclination, it was expected that the 80‐percent criterion would be easily satisfied for these
anchors, and the instrumentation verified that this was the case.
Figure 9 shows normalized load transfer curves for the two test anchors. The behavior illustrated by these
anchors is a textbook example of minimal load transfer over the unbonded length and rapid load transfer
in the bond zone in rock. The two test anchors achieved 93 and 98 percent of theoretical elongation over
their unbonded lengths based on the dial‐gage readings taken at the ground surface. The DYNA Force®
sensors showed that the friction loss that did occur was uniformly distributed over the unbonded zone of
the anchor, suggesting that the loss was due to minor yet unavoidable load transfer through the strand‐
grease‐sheathing‐grout interface as opposed to wobble concentrated in a single zone.
This project provides an illustrative example of how advanced instrumentation can be used to directly
measure friction loss over the unbonded zone of a tieback anchor, reducing uncertainty with regards to
the amount of stabilizing force that is reaching the material behind the potential failure plane. In addition,
the load transfer in the bond zone is directly measured, allowing the designer to verify the design bond
stress and providing a chance to optimize the lengths of the remaining anchors. Because measured friction
loss was relatively low for this project, the performance test results do not shed much light on the factors
that contribute to wobble, other than to suggest that hole‐straightness and relatively steep hole
inclination are conducive to reducing wobble as hypothesized.
18
Figure 9. Normalized load transfer curves for performance test anchors instrumented with DYNA
Force® load sensors.
7. IMPLICATIONS FOR SLOPE STABILITY ANALYSIS
Limit‐equilibrium slope stability analysis is often conducted to estimate the factor of safety of a landslide
or potentially unstable slope and to assess the increased factor of safety that would be obtained by
installing tieback anchors. In such analyses, the engineer specifies a design load in each anchor, and the
computer program determines the corresponding resisting force at the point of intersection of the anchor
with the failure plane and the increased normal stress acting on the soil or rock at this point. The
magnitude of the load in the tieback anchor has a direct impact on the factor of safety computed by the
program.
When these anchors are constructed in the field, if the average friction loss over the unbonded zone is 20
percent of the design load, this means that only 80 percent of the load that was assumed to reach behind
the failure plane in the analysis is actually doing so, and according to typical project specifications this is
acceptable. What is often ignored in practice is that the factor of safety computed during the slope
stability analysis is not actually being achieved in the field when this is the case. Project owners are likely
unaware that the geotechnical report specifies a factor of safety for the slope, while the specifications
effectively allow the project to be constructed with a lower factor of safety. To determine the actual factor
of safety, the engineer would need to re‐run the slope stability analysis using the actual load in the anchor
determined by load testing.
A more practical approach would be to specify a design load that achieves the target factor of safety with
friction loss over the unbonded zone explicitly considered. For example, if a 100 kip anchor load is needed
to achieve the target factor of safety, the engineer should specify a design load for construction of 100
kips/0.8 = 125 kips. There is no rational basis for specifying a target factor of safety and then not enforcing
construction specifications that achieve this factor of safety in the real system.
19
8. CONCLUSIONS AND RECOMMENDATIONS
For this study, we reviewed data from several projects in which tieback anchors were used for either
landslide stabilization or shoring. We used the "wobble coefficient" as a proxy to relate the amount of
unintentional deviation from straightness in the anchor to the amount of friction loss over the unbonded
length.
The data we collected show a general trend of increasing wobble coefficient with increasing unbonded
length, meaning that longer anchors are more likely to fail the 80‐percent minimum elongation criterion.
While we speculate that shallow anchor inclination and certain geologic conditions may lead to higher
wobble, the amount of scatter in our dataset does not allow us to draw specific conclusions about these
effects. Nonetheless, designers and contractors should be aware that the probability of not meeting the
80‐percent minimum elongation criteria goes up with increasing anchor unbonded length.
Shallow anchor inclination appears to be a strong contributor to wobble because it makes placement of
the anchor into the hole difficult, requiring the anchor to be forced in, which may induce additional
curvature. A potential solution to this problem is two‐stage grouting in which the bond zone is grouted
and a small alignment load is applied to straighten the unbonded zone before it is grouted. Although
simple in concept, however, this procedure is time‐consuming and difficult to perform, and hence not
often utilized in North American practice. An alternative is to use more steeply inclined anchors. This
reduces the anchor efficiency in most cases, but could still be more economical than rejecting anchors
and dealing with the remediation that could ensue. Steeply‐inclined anchors will typically be shorter than
anchors with a shallow inclination angle, which further reduces the potential for friction loss.
Methods for directly measuring load transfer between the anchor and the ground are available, such as
strain gages or direct‐force measuring devices that can be mounted to the anchor strands along its length.
Incorporating these measurements into the performance test(s) for critical projects or projects with a
large number of anchors can (1) reduce uncertainty about where friction loss is occurring, which provides
an opportunity to address the problem if excessive loss is occurring in a particular zone, and (2) allows for
a direct measurement of the load transfer in the bond zone, which can be used to optimize the lengths of
the remaining anchors.
Regardless of whether anchors pass or fail the 80‐percent criterion, slope stability analyses that include
the resisting force of the anchor should only consider the magnitude of load that is expected and specified
to reach the bond zone. If the designer requires more resisting force to reach a target factor of safety,
larger anchors or a higher minimum elongation criteria must be specified. Likewise, anchors that fail the
80‐percent criterion do not necessarily have to be rejected outright if additional slope stability analysis
considering the actual magnitude of load reaching the bond zone can be shown to still satisfy the target
factor of safety when supplemental anchors are added. This recommendation is consistent with the PTI
specifications (2004) although it is not typically included in project specifications.
Since many anchors from our database with unbonded lengths in the range of 100 to 200 feet satisfied
the 80‐percent criterion, we do not recommend a modified minimum elongation acceptance criterion for
long anchors at this time. Additional data from field load tests on anchors will potentially allow us to draw
20
quantitative conclusions about the influence of specific parameters such as anchor hole inclination and
the manufacturing processes used by various anchor manufacturers. If more data are submitted for this
effort that provides insightful conclusions, an addendum to this report will be issued.
ACKNOWLEDGMENTS
The authors would like to thank the DFI Committee on Tiebacks and Soil Nails for their generous support
of this project. Mr. Ed Laczynski, Chair, and Mary Ellen Bruce, DFI Technical Activities Manager, provided
valuable review comments on this report as well as guidance and assistance in obtaining field load test
results. The authors wish to acknowledge committee members and others who provided data and
generously shared their insights, including Tom Richards of Nicholson Construction Co., Andy Baxter of
Schnabel Engineering, Chris Allen of Earth Systems, Matthew Niermann of Schnabel Foundation Company,
Lucian Bogdan of DYWIDAG‐Systems International, and Kessi Zicko of Gannett Fleming.
For information pertaining to the Togwotee Pass Landslide project, the authors wish to thank James Dahill,
David Vanderveen, and Cory Rinehart of the WYDOT Geology Program. Dan Applebaum and Ryan Turner,
Caltrans, provided information for the Cuesta Grade Landslide project.
The first author would like to extend a special thanks to Mr. Horst Aschenbroich, President, and Mr. Dan
Maclean, Chief Operating Officer, of Con‐Tech Systems Ltd., for many valuable discussions on the
performance of ground anchors and for providing field load test data for this study.
REFERENCES
Aalami, B.O., 2004. Prestressing Losses and Elongation Calculations, Technical Note Issue T9‐04, ADAPT Corporation, Redwood City, CA, 16 p.
American Association of State Highway and Transportation Officials (AASHTO), 2012. AASHTO LRFD Bridge Design Specifications, Customary U.S. Units, 6th Ed., Washington, D.C.
American Concrete Institute, 2011. ACI 318‐11: Building Code Requirements for Structural Concrete and Commentary, Farmington Hills, MI, 503 p.
Post‐Tensioning Institute, 2006. Post‐Tensioning Manual, 6th edition. Farmington Hills, MI, 354 p.
Post‐Tensioning Institute, 2004. Recommendations for Prestressed Rock and Soil Anchors, 4th edition.
Farmington Hills, MI, 98 p.
Wyoming Department of Transportation (WYDOT), 2008. Geotechnical Baseline Report for the County
Line Landslide [Togwotee Pass Landslide], Cheyenne, WY, 8 p.
21
Appendix:
Tieback Load Test Data and Wobble Coefficient
Computations
Anchor No. / Designation Test Type
Inclination Angle (from horizontal)
Displacement @ Alignment Load at End of Test (i.e.,
Residual Movement)
Displacement @ Max Test
Load
Measured Elastic
Movement (∆e)
Area of Strands
(A)
Elastic Modulus
of Strands
(E)Force @ AL
Force @ TL
Difference btwn AL and TL =
"P0"Unbonded Length (L0)
Theoretical Elongation
(ΔHooke = P0*L0/E*A)
Normalized Elongation (Δe / ΔHooke)
Pass/Fail 80% EL
Criterion
Back-Calculated
Wobble Coefficient,
Kdegrees inches inches inches inches 2 ksi kip kip kip feet inches rad/foot(Project)
Togwotee Pass Slide, WY4 PERF. 15 1.059 9.601 8.542 0.868 28,500 31.5 167.6 136.1 149 9.837 87% PASS 0.0019450 PERF. 15 1.264 10.26 8.996 0.868 28,500 31.5 167.6 136.1 149 9.837 91% PASS 0.001221 PROOF 15 1.752 11.201 9.449 0.868 28,500 31.5 167.6 136.1 149 9.837 96% PASS 0.000542 PROOF 15 1.555 10.669 9.114 0.868 28,500 31.5 167.6 136.1 149 9.837 93% PASS 0.001043 PROOF 15 1.49 10.426 8.936 0.868 28,500 31.5 167.6 136.1 149 9.837 91% PASS 0.001315 PROOF 15 1.306 8.98 7.674 0.868 28,500 31.5 167.6 136.1 149 9.837 78% FAIL 0.003486 PROOF 15 1 05 8 441 7 391 0 868 28 500 31 5 167 6 136 1 149 9 837 75% FAIL 0 004046 PROOF 15 1.05 8.441 7.391 0.868 28,500 31.5 167.6 136.1 149 9.837 75% FAIL 0.004047 PROOF 15 1.481 9.692 8.211 0.868 28,500 31.5 167.6 136.1 149 9.837 83% PASS 0.002508 PROOF 15 1.129 8.62 7.491 0.868 28,500 31.5 167.6 136.1 149 9.837 76% FAIL 0.0038443 PROOF 15 1.37 8.905 7.535 0.868 28,500 31.5 167.6 136.1 149 9.837 77% FAIL 0.0037544 PROOF 15 1.438 9.603 8.165 0.868 28,500 31.5 167.6 136.1 149 9.837 83% PASS 0.0025845 PROOF 15 1.09 8.925 7.835 0.868 28,500 31.5 167.6 136.1 149 9.837 80% FAIL 0.0031846 PROOF 15 1.171 9.415 8.244 0.868 28,500 31.5 167.6 136.1 149 9.837 84% PASS 0.0024547 PROOF 15 1.219 9.437 8.218 0.868 28,500 31.5 167.6 136.1 149 9.837 84% PASS 0.0024948 PROOF 15 1.374 9.078 7.704 0.868 28,500 31.5 167.6 136.1 149 9.837 78% FAIL 0.0034349 PROOF 15 1.125 9.335 8.21 0.868 28,500 31.5 167.6 136.1 149 9.837 83% PASS 0.002505 PROOF 15 1.54 9.548 8.008 0.868 28,500 31.5 167.6 136.1 149 9.837 81% PASS 0.002866 PROOF 15 1.308 9.402 8.094 0.868 28,500 31.5 167.6 136.1 149 9.837 82% PASS 0.002717 PROOF 15 1.31 9.06 7.75 0.868 28,500 31.5 167.6 136.1 149 9.837 79% FAIL 0.003348 PROOF 15 1.315 9.995 8.68 0.868 28,500 31.5 167.6 136.1 149 9.837 88% PASS 0.00172
Cuesta Grade Retaining Wall1 PERF 15 0 312 4 156 3 844 0 444 28 500 3 4 51 2 47 8 99 4 490 86% PASS 0 003221 PERF. 15 0.312 4.156 3.844 0.444 28,500 3.4 51.2 47.8 99 4.490 86% PASS 0.003222 PROOF 15 0.313 4.198 3.885 0.444 28,500 3.4 51.2 47.8 99 4.490 87% PASS 0.003003 PROOF 15 0.438 5.432 4.994 0.444 28,500 3.4 63.7 60.3 99 5.660 88% PASS 0.002584 PROOF 15 0.295 5.538 5.243 0.444 28,500 3.4 63.7 60.3 99 5.660 93% PASS 0.001575 PROOF 15 0.21 5.505 5.295 0.444 28,500 3.4 63.7 60.3 99 5.660 94% PASS 0.001366 PROOF 15 0.564 6.463 5.899 0.666 28,500 3.4 109.2 105.8 109 7.292 81% PASS 0.004047 PROOF 15 1.15 7.668 6.518 0.666 28,500 3.4 109.2 105.8 124 8.296 79% FAIL 0.004068 PROOF 15 0.891 7.41 6.519 0.666 28,500 3.4 109.2 105.8 124 8.296 79% FAIL 0.004069 PROOF 15 1.009 7.021 6.012 0.666 28,500 3.4 109.2 105.8 124 8.296 72% FAIL 0.0055110 PROOF 15 1.111 8.49 7.379 0.666 28,500 3.4 135.7 132.3 134 11.206 66% FAIL 0.0067411 PROOF 15 1.348 10.031 8.683 0.666 28,500 3.4 135.7 132.3 134 11.206 77% FAIL 0.0039812 PROOF 15 1.867 10.72 8.853 0.666 28,500 3.4 135.7 132.3 144 12.042 74% FAIL 0.0045213 PROOF 15 0.57 8.82 8.25 0.888 28,500 3.4 158.9 155.5 154 11.352 73% FAIL 0.0043914 PROOF 15 1.05 10.758 9.708 0.888 28,500 3.4 158.9 155.5 164 12.089 80% PASS 0.0027815 PROOF 15 1.127 11.849 10.722 0.888 28,500 3.4 158.9 155.5 174 12.826 84% PASS 0.0021316 PROOF 15 2 029 10 381 8 352 0 888 28 500 3 4 158 9 155 5 184 13 563 62% FAIL 0 0057816 PROOF 15 2.029 10.381 8.352 0.888 28,500 3.4 158.9 155.5 184 13.563 62% FAIL 0.0057817 PROOF 15 1.05 11.998 10.948 0.888 28,500 3.4 158.9 155.5 199 14.669 75% FAIL 0.0031018 PERF. 15 1.7 13.331 11.631 1.110 28,500 3.4 196.8 193.4 199 14.597 80% FAIL 0.0023819 PROOF 15 0.705 12.705 12 1.110 28,500 3.4 196.8 193.4 204 14.964 80% PASS 0.0022520 PROOF 15 13.545 13.545 1.110 28,500 3.4 196.8 193.4 214 15.698 86% PASS 0.0014121 PROOF 15 2.401 12.31 9.909 1.110 28,500 3.4 196.8 193.4 224 16.431 60% FAIL 0.0049722 PROOF 15 1.9 13.314 11.414 1.110 28,500 3.4 196.8 193.4 224 16.431 69% FAIL 0.00348
23 PROOF 15 1.007 12.878 11.871 1.110 28,500 3.4 196.8 193.4 224 16.431 72% FAIL 0.0030824 PROOF 15 2.335 13.895 11.56 1.110 28,500 3.4 202.3 198.9 224 16.899 68% FAIL 0.0036425 PROOF 15 1.901 11.665 9.764 1.110 28,500 3.4 202.3 198.9 214 16.145 60% FAIL 0.0051726 PROOF 15 2.09 11.989 9.899 1.110 28,500 3.4 196.8 193.4 214 15.698 63% FAIL 0.0047027 PROOF 15 3.085 9.08 5.995 1.110 28,500 3.4 196.8 193.4 214 15.698 38% FAIL 0.0111028 PROOF 15 2.251 10.255 8.004 1.110 28,500 3.4 196.8 193.4 204 14.964 53% FAIL 0.0069429 PROOF 15 1.388 14.757 13.369 1.110 28,500 3.4 223.9 220.5 204 17.064 78% FAIL 0.0025030 PROOF 15 2.1 14.225 12.125 1.110 28,500 3.4 223.9 220.5 204 17.064 71% FAIL 0.0035731 PROOF 15 2 14.623 12.623 1.110 28,500 3.4 223.9 220.5 204 17.064 74% FAIL 0.0031232 PROOF 15 1.59 14.127 12.537 1.110 28,500 3.4 223.9 220.5 194 16.228 77% FAIL 0.0027933 PROOF 15 1.907 12.957 11.05 1.110 28,500 3.4 223.9 220.5 189 15.810 70% FAIL 0.0040534 PROOF 15 1.945 13.522 11.577 1.110 28,500 3.4 223.9 220.5 189 15.810 73% FAIL 0.0034935 PROOF 15 2.0014 13.242 11.2406 1.110 28,500 3.4 223.9 220.5 184 15.391 73% FAIL 0.0036236 PERF. 15 2.085 12.782 10.697 1.110 28,500 3.4 223.9 220.5 184 15.391 69% FAIL 0.0042337 PROOF 15 2.435 12.922 10.487 1.110 28,500 3.4 223.9 220.5 184 15.391 68% FAIL 0.0044838 PROOF 15 1.8 12.367 10.567 1.110 28,500 3.4 223.9 220.5 174 14.555 73% FAIL 0.0039039 PROOF 15 2.62 11.403 8.783 1.110 28,500 3.4 223.9 220.5 174 14.555 60% FAIL 0.0063940 PROOF 15 1.53 13.044 11.514 1.110 28,500 3.4 223.9 220.5 174 14.555 79% FAIL 0.0028141 PROOF 15 2.668 10.585 7.917 1.110 28,500 3.4 223.9 220.5 164 13.718 58% FAIL 0.0074542 PROOF 15 1.085 11.391 10.306 1.110 28,500 3.4 223.9 220.5 149 12.464 83% PASS 0.0026443 PROOF 15 2.193 9.703 7.51 1.110 28,500 3.4 223.9 220.5 134 11.209 67% FAIL 0.0064444 PROOF 15 2.214 9.206 6.992 1.110 28,500 3.4 223.9 220.5 134 11.209 62% FAIL 0.0077045 PROOF 15 1.013 9.758 8.745 1.110 28,500 3.4 223.9 220.5 129 10.791 81% PASS 0.0033846 PROOF 15 1.355 9.779 8.424 1.110 28,500 3.4 223.9 220.5 129 10.791 78% FAIL 0.0040147 PROOF 15 1.635 9.168 7.533 1.110 28,500 3.4 223.9 220.5 129 10.791 70% FAIL 0.0059548 PROOF 15 1.457 9.714 8.257 1.110 28,500 3.4 223.9 220.5 129 10.791 77% FAIL 0.0043549 PROOF 15 2.144 8.992 6.848 1.110 28,500 3.4 223.9 220.5 124 10.373 66% FAIL 0.0072350 PROOF 15 1.085 9.985 8.9 1.110 28,500 3.4 223.9 220.5 124 10.373 86% PASS 0.0025451 PROOF 15 1.685 8.475 6.79 1.110 28,500 3.4 223.9 220.5 124 10.373 65% FAIL 0.0074052 PROOF 15 1.095 9.697 8.602 1.110 28,500 3.4 223.9 220.5 114 9.536 90% PASS 0.0018453 PROOF 15 1.53 9.63 8.1 1.110 28,500 3.4 223.9 220.5 114 9.536 85% PASS 0.0029554 PROOF 15 1.55 8.66 7.11 1.110 28,500 3.4 223.9 220.5 109 9.118 78% FAIL 0.0047755 PROOF 15 1.272 8.922 7.65 1.110 28,500 3.4 223.9 220.5 109 9.118 84% PASS 0.0033256 PROOF 15 1.075 9.097 8.022 1.110 28,500 3.4 223.9 220.5 109 9.118 88% PASS 0.0024057 PROOF 15 1.098 8.608 7.51 1.110 28,500 3.4 223.9 220.5 109 9.118 82% PASS 0.0036858 PROOF 15 1.135 8.785 7.65 1.110 28,500 3.4 223.9 220.5 109 9.118 84% PASS 0.0033259 PROOF 15 1.012 8.617 7.605 1.110 28,500 3.4 223.9 220.5 109 9.118 83% PASS 0.0034460 PROOF 15 1.177 8.785 7.608 1.110 28,500 3.4 223.9 220.5 109 9.118 83% PASS 0.0034361 PROOF 15 1.06 8.906 7.846 1.110 28,500 3.4 223.9 220.5 109 9.118 86% PASS 0.0028362 PROOF 15 0.898 8.799 7.901 1.110 28,500 3.4 223.9 220.5 109 9.118 87% PASS 0.0026963 PROOF 15 0.932 8.705 7.773 1.110 28,500 3.4 223.9 220.5 109 9.118 85% PASS 0.0030164 PROOF 15 1.012 8.418 7.406 1.110 28,500 3.4 223.9 220.5 109 9.118 81% PASS 0.0039665 PROOF 15 1.51 8.208 6.698 1.110 28,500 3.4 223.9 220.5 109 9.118 73% FAIL 0.0059866 PROOF 15 1.302 8.265 6.963 1.110 28,500 3.4 223.9 220.5 109 9.118 76% FAIL 0.0051967 PROOF 15 1.34 8.515 7.175 1.110 28,500 3.4 223.9 220.5 109 9.118 79% FAIL 0.00459,68 PROOF 15 1.234 8.555 7.321 1.110 28,500 3.4 223.9 220.5 109 9.118 80% PASS 0.0041969 PROOF 15 1.37 8.768 7.398 1.110 28,500 3.4 223.9 220.5 109 9.118 81% PASS 0.0039870 PROOF 15 0.985 8.013 7.028 1.110 28,500 3.4 223.9 220.5 109 9.118 77% FAIL 0.0050071 PROOF 15 1.301 8.36 7.059 1.110 28,500 3.4 223.9 220.5 109 9.118 77% FAIL 0.0049172 PERF. 15 1.134 8.684 7.55 1.110 28,500 3.4 223.9 220.5 104 8.700 87% PASS 0.0027973 PROOF 15 1.146 7.581 6.435 1.110 28,500 3.4 223.9 220.5 104 8.700 74% FAIL 0.0061274 PROOF 15 0.9 6.55 5.65 1.110 28,500 3.4 196.8 193.4 104 7.629 74% FAIL 0.00610
75 PROOF 15 0.879 7.18 6.301 1.110 28,500 3.4 196.8 193.4 104 7.629 83% PASS 0.0038076 PROOF 15 0.959 7.305 6.346 1.110 28,500 3.4 196.8 193.4 104 7.629 83% PASS 0.0036677 PROOF 15 0.915 6.707 5.792 1.110 28,500 3.4 196.8 193.4 104 7.629 76% FAIL 0.0055678 PROOF 15 0.905 6.547 5.642 1.110 28,500 3.4 196.8 193.4 99 7.262 78% FAIL 0.0053379 PROOF 15 1.12 7.276 6.156 1.110 28,500 3.4 196.8 193.4 99 7.262 85% PASS 0.0034480 PROOF 15 0.592 7.311 6.719 1.110 28,500 3.4 196.8 193.4 99 7.262 93% PASS 0.0015981 PROOF 15 1.342 7.35 6.008 1.110 28,500 3.4 196.8 193.4 99 7.262 83% PASS 0.0039682 PROOF 15 0.976 6.86 5.884 1.110 28,500 3.4 196.8 193.4 94 6.895 85% PASS 0.0034783 PROOF 15 0.691 6.727 6.036 1.110 28,500 3.4 196.8 193.4 94 6.895 88% PASS 0.0029084 PROOF 15 1.263 6.576 5.313 1.110 28,500 3.4 196.8 193.4 94 6.895 77% FAIL 0.0058185 PERF. 15 0.968 6.402 5.434 1.110 28,500 3.4 196.8 193.4 94 6.895 79% FAIL 0.0052986 PROOF 15 0.79 6.96 6.17 0.888 28,500 3.4 158.9 155.5 94 6.929 89% PASS 0.0025287 PROOF 15 0.874 6.464 5.59 0.888 28,500 3.4 158.9 155.5 89 6.561 85% PASS 0.0037088 PROOF 15 0.958 6.859 5.901 0.888 28,500 3.4 158.9 155.5 89 6.561 90% PASS 0.0024289 PROOF 15 0.785 6.646 5.861 0.888 28,500 3.4 158.9 155.5 89 6.561 89% PASS 0.0025890 PROOF 15 1.055 6.758 5.703 0.888 28,500 3.4 158.9 155.5 84 6.192 92% PASS 0.0019991 PROOF 15 0.792 6.49 5.698 0.888 28,500 3.4 158.9 155.5 84 6.192 92% PASS 0.0020192 PROOF 15 0.818 6.42 5.602 0.888 28,500 3.4 158.9 155.5 84 6.192 90% PASS 0.0024393 PROOF 15 0.66 6.358 5.698 0.888 28,500 3.4 158.9 155.5 84 6.192 92% PASS 0.0020194 PROOF 15 0.949 6.495 5.546 0.888 28,500 3.4 158.9 155.5 84 6.192 90% PASS 0.0026795 PROOF 15 0.784 6.433 5.649 0.888 28,500 3.4 158.9 155.5 84 6.192 91% PASS 0.0022296 PROOF 15 0.855 6.464 5.609 0.888 28,500 3.4 158.9 155.5 84 6.192 91% PASS 0.0023997 PROOF 15 0.84 6.24 5.4 0.888 28,500 3.4 158.9 155.5 84 6.192 87% PASS 0.0033498 PROOF 15 0.063 6.316 6.253 0.666 28,500 3.4 135.7 132.3 84 7.025 89% PASS 0.0028399 PROOF 15 0.562 6.21 5.648 0.666 28,500 3.4 135.7 132.3 84 7.025 80% PASS 0.00540100 PERF. 15 0.325 6.432 6.107 0.666 28,500 3.4 135.7 132.3 84 7.025 87% PASS 0.00341101 PROOF 15 0.38 6.82 6.44 0.666 28,500 3.4 135.7 132.3 84 7.025 92% PASS 0.00210102 PROOF 15 0.211 4.632 4.421 0.444 28,500 3.4 63.7 60.3 84 4.803 92% PASS 0.00200103 PROOF 15 0.134 4.83 4.696 0.444 28,500 3.4 63.7 60.3 84 4.803 98% PASS 0.00054104 PROOF 15 0.307 4.47 4.163 0.444 28,500 3.4 63.7 60.3 84 4.803 87% PASS 0.00349105 PROOF 15 0.378 4.719 4.341 0.444 28,500 3.4 63.7 60.3 84 4.803 90% PASS 0.00245106 PROOF 15 0.22 3.638 3.418 0.444 28,500 3.4 51.2 47.8 84 3.809 90% PASS 0.00263107 PROOF 15 0.491 3.802 3.311 0.444 28,500 3.4 51.2 47.8 84 3.809 87% PASS 0.00342108 PROOF 15 0.28 3.653 3.373 0.444 28,500 3.4 51.2 47.8 84 3.809 89% PASS 0.00296
Anonymous 1Yellow PERF. unknown 1.3125 8.375 7.0625 0.217 28,500 3.3 44.3 41.0 99 7.876 90% PASS 0.00224White PERF. unknown 0.9375 9.0625 8.125 0.217 28,500 3.3 44.3 41.0 110 8.751 93% PASS 0.00137Red PERF. unknown 1.5625 10.1875 8.625 0.217 28,500 3.3 44.3 41.0 121 9.626 90% PASS 0.00185
Green PERF. unknown 0.8125 10.5625 9.75 0.217 28,500 3.3 44.3 41.0 132 10.501 93% PASS 0.00114Blue PERF. unknown 0.9375 11.25 10.3125 0.217 28,500 3.3 44.3 41.0 147 11.694 88% PASS 0.00175Black PERF. unknown 0.75 12.125 11.375 0.217 28,500 3.3 44.3 41.0 158 12.569 90% PASS 0.00129
Anonymous 2C-1 PERF. 45 1.163 11.403 10.10 1.302 28,500 25.8 277.1 251.3 135 10.971 92% PASS 0.00125G-1 PERF. 45 0.871 12.056 10.94 1.302 28,500 16.2 276.5 260.3 135 11.364 96% PASS 0.00057
Anonymous 3yA1 PERF. 90 0.641 6.77 6.129 8.463 28,500 624.0 2537.0 1913.0 74 7.043 87% PASS 0.00385A2 PERF. 90 0.71 8.361 7.651 8.463 28,500 678.0 2534.0 1856.0 93 8.588 89% PASS 0.00253A3 PERF. 90 0.491 9.07 8.579 8.463 28,500 567.0 2570.0 2003.0 104 10.364 83% PASS 0.00376A4 PERF. 90 0.714 9.919 9.205 11.284 28,500 671.0 3163.0 2492.0 114 10.600 87% PASS 0.00254A5 PERF. 90 0.774 9.93 9.156 11.284 28,500 751.0 3270.0 2519.0 112 10.527 87% PASS 0.00255A6 PERF. 90 0.935 9.633 8.698 11.284 28,500 743.0 3139.0 2396.0 113 10.103 86% PASS 0.00272A7 PERF. 90 0.663 9.925 9.262 11.284 28,500 725.0 3223.0 2498.0 114.3 10.654 87% PASS 0.00251
A8 PERF. 90 0.78 10.29 9.51 11.284 28,500 700.0 3193.0 2493.0 115.3 10.726 89% PASS 0.00213A9 PERF. 90 0.967 10.142 9.175 11.284 28,500 729.0 3415.0 2686.0 115.3 11.556 79% FAIL 0.00417A11 PERF. 48 0.715 7.763 7.048 12.586 28,500 691.0 3462.0 2771.0 85.3 7.907 89% PASS 0.00275A12 PERF. 48 0.708 7.773 7.065 12.586 28,500 670.0 3467.0 2797.0 81.3 7.607 93% PASS 0.00184A16 PERF. 48 0.738 7.744 7.006 12.586 28,500 748.0 3803.0 3055.0 87.3 8.922 79% FAIL 0.00578A17 PERF. 48 0.839 8.056 7.217 12.586 28,500 696.0 3445.0 2749.0 88.3 8.121 89% PASS 0.00273A21 PERF. 48 0.818 8.014 7.196 8.463 28,500 577.0 2582.0 2005.0 88.3 8.808 82% PASS 0.00474A22 PERF. 48 0.892 8.009 7.117 8.463 28,500 568.0 2566.0 1998.0 88.3 8.777 81% PASS 0.00493A23 PERF. 48 0.76 8.018 7.258 8.463 28,500 557.0 2555.0 1998.0 88.3 8.777 83% PASS 0.00445A24 PERF. 48 0.885 8.391 7.506 8.463 28,500 597.0 2526.0 1929.0 96.3 9.242 81% PASS 0.00448A28 PERF. 48 0.787 8.475 7.688 8.463 28,500 597.0 2575.0 1978.0 96.3 9.477 81% PASS 0.00451A31 PERF. 48 0.945 8.69 7.745 8.463 28,500 170.0 1829.0 1659.0 98 8.089 96% PASS 0.00089A32 PERF. 90 0.629 11.501 10.872 12.586 28,500 720.0 3437.0 2717.0 131.3 11.934 91% PASS 0.00144A33 PERF. 90 0.875 11.362 10.487 12.586 28,500 690.0 3416.0 2726.0 131.3 11.974 88% PASS 0.00207A34 PERF. 90 0.901 11.987 11.086 12.586 28,500 709.0 3461.0 2752.0 134.3 12.364 90% PASS 0.00166A35 PERF. 48 0.756 9.195 8.439 9.765 28,500 626.0 2840.0 2214.0 105.3 10.052 84% PASS 0.00343A36 PERF. 48 0.753 9.321 8.568 9.765 28,501 623.0 2808.0 2185.0 107.3 10.109 85% PASS 0.00317A37 PERF. 48 0.814 9.599 8.785 9.765 28,502 644.0 2859.0 2215.0 110.3 10.534 83% PASS 0.00340A42 PERF. 48 0.98 10.477 9.497 11.284 28,507 728.0 3266.0 2538.0 118 11.172 85% PASS 0.00283A43 PERF. 48 0.951 10.544 9.593 11.284 28,508 690.0 3219.0 2529.0 118 11.132 86% PASS 0.00259A44 PERF. 48 0.875 10.274 9.399 11.284 28,509 675.0 3245.0 2570.0 119 11.408 82% PASS 0.00337A45 PERF. 48 0.972 10.443 9.471 11.284 28,510 742.0 3163.0 2421.0 120 10.837 87% PASS 0.00230A50 PERF. 45 0.979 9.371 8.392 12.586 28,515 562.0 3411.0 2849.0 104 9.907 85% PASS 0.00329A51 PERF. 45 1.281 10.249 8.968 12.586 28,516 739.0 3563.0 2824.0 114 10.764 83% PASS 0.00331A52 PERF. 45 0.757 10.183 9.426 12.586 28,517 732.0 3541.0 2809.0 114 10.706 88% PASS 0.00228A57 PERF. 45 0.796 10.488 9.692 12.586 28,522 778.0 3541.0 2763.0 121.8 11.250 86% PASS 0.00251A58 PERF. 45 1.195 10.759 9.564 12.586 28,523 470.0 3312.0 2842.0 124 11.780 81% PASS 0.00349A63 PERF. 45 1.153 11.768 10.615 11.284 28,524 318.0 2895.0 2577.0 138 13.259 80% PASS 0.00335