Technical Paper by J.H. Greenwood - IGS - International ...

Technical Paper by J.H. Greenwood
DESIGNING TO RESIDUAL STRENGTH OF
GEOSYNTHETICS INSTEAD OF STRESS-RUPTURE
ABSTRACT: The tensile design strength of geosynthetic reinforcement may be governed
by strain or load and, in the latter case, some design codes base the design strength
on stress-rupture. However, when a factor of safety is applied, this approach can be
over-conservative. By considering the residual or available strength, it is possible to define
a more realistic procedure that can be integrated with the effects of environmental
degradation and mechanical damage.
KEYWORDS: Geosynthetic reinforcement, Creep, Stress-rupture, Partial safety
factor.
AUTHOR: J.H. Greenwood, ERA Technology Ltd., Cleeve Road, Leatherhead,
Surrey KT22 7SA, UK, Telephone: 44/1372-367005, Telefax: 44/1372-367099,
E-mail: john.greenwood@era.co.uk.
PUBLICATION: Geosynthetics International is published by the Industrial Fabrics
Association International, 345 Cedar St., Suite 800, St. Paul, Minnesota 55101-1088,
USA, Telephone: 1/612-222-2508, Telefax: 1/612-222-8215. Geosynthetics
International is registered under ISSN 1072-6349.
DATES: Original manuscript received 19 December 1996, revised version received
24 January 1997 and accepted 27 January 1997. Discussion open until 1 November
1997.
REFERENCE: Greenwood, J.H., 1997, “Designing to Residual Strength of
Geosynthetics Instead of Stress-Rupture”, Geosynthetics International, Vol. 4, No. 1,
pp. 1-10.
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
1 DEFINITION OF UNFACTORED STRENGTH
Design codes such as BS 8006 (1995) prescribe that the design strength of soil reinforcement
should be the load that would lead to failure, or to a maximum acceptable
strain, at the end of the design life. For most materials, failure rather than critical strain
is the dominant design criterion.
The unfactored design strength, T CR , is derived from geosynthetic reinforcement
properties as follows:
S The stress-rupture curve defines the time to failure, t f ,ifaloadT is applied continuously
to the geosynthetic.
S The curve is conventionally plotted as the applied load (or its logarithm) against the
logarithm of time to failure (Figure 1).
S If a design life, t d , is specified, it is then possible by extrapolation of the curve to predict
a load T CR that would lead to failure at the end of the design life (Jewell and Greenwood
1988).
When using partial factors in design, such as prescribed in BS 8006 (1995), the design
load T is obtained by increasing the unfactored load by a partial load factor, f f , that typically
takes on a value of 1.5, and by decreasing the unfactored strength, in this case T CR ,
by a partial geosynthetic material factor, f m , to produce a geosynthetic reinforcement
design strength, T D . At any instant of time during the lifetime of the structure, the applied
load should be less than or equal to T D . The partial geosynthetic material factor,
f m , is for reductions, variations and uncertainties in the properties of the geosynthetic.
Using the definitions in BS 8006 (1995), f m is the product of other partial factors including
the following: f m11 for variations in manufacturing; f m12 for the uncertainty in extrapo-
Stress-rupture curve (experimental)
Extrapolated curve
Load, T
T CR
T D
Unfactored strength
Design load
Log t (time)
Design life, t d
Figure 1.
Stress-rupture diagram.
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
lation; f m21 for installation damage; and f m22 for environmental degradation effects including
ultraviolet light, the hydrolysis of polyester, and the oxidation of polyolefins.
The partial material factor, f m is a single factor that is applied to the unfactored design
strength independently of time.
2 RESIDUAL STRENGTH
In spite of its appearance, the stress-rupture curve does not depict the reduction of
available strength with time in the same manner as, for example, the reduction in
strength due to exposure to weathering. Consider a geosynthetic reinforcement under
sustained load T, after a time t 1 take a sample and increase the load until it breaks, and
then measure the strength. Because of the effect of the continuous load, the strength may
be less than the tensile strength of the virgin geosynthetic, but higher than T. Dothe
same after a longer period time, t 2 , and the strength will have reduced further. Finally,
at a certain time t 3 , the strength will have diminished to as little as T itself, and the geosynthetic
will break spontaneously.
The strengths after times t 1 and t 2 are referred to as the residual (or available) strengths
and will be denoted as T R1 and T R2 . Plotted as in Figure 2, T R1 and T R2 form an envelope
which terminates at the point (t 3 ,T). For each applied load, T 1 ,T 2 ,T 3 and so on, there
is a different, thus far, undefined residual strength curve whose location depends on the
applied load. Each residual strength curve meets the stress-rupture curve where the residual
strength equals the applied load (Figure 3).
Load or strength
T
Applied load
T R1
T R2
T R residual
strength curve
Stress-rupture
point
t 1 t 2 t 3
Log t (time)
Figure 2.
Residual strength as a function of time for a single applied load.
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
Stress-rupture curve
Load or strength
T 3
T 2
T 1
T R3
T R2
T R1
Log t (time)
Figure 3. Residual (available) strength curves, T R1 , T R2 and T R3 , as a function of time for
multiple applied sustained loads T 1 , T 2 and T 3 , respectively.
The residual strength will always be greater than the continuous applied load. Its value
will depend on the mechanism of tensile failure; for example, on the ductile failure
of the remaining cross section of the fibre. It is believed that the residual strength may
remain close to the tensile strength of the geosynthetic for most of the design life, decreasing
only shortly before stress-rupture occurs (Figure 3).
The significance of residual strength was pointed out by Schardin-Liedtke (1990),
who also remarked on the lack of available data. The residual strength of geosynthetics
can be measured as described previously in this section. Place the geosynthetic specimens
under continuous load as in stress-rupture tests and interrupt the tests before the
specimen breaks. Then increase the load as in a normal tensile test to determine the residual
strength of the geosynthetic specimen. Plot the curve of residual strength against
the time before interruption. Do the same for each level of continuous load. Considerable
scatter in the values of the data may be expected, particularly close to the stressrupture
limit.
3 UNDERESTIMATION OF THE DESIGN STRENGTH, T D
It is the purpose of this study to reveal that certain aspects of the traditional design
procedure for soil geosynthetic reinforcement, as described in Section 1, can lead to
over-dimensioning due to an underestimation of T D .
It is first necessary to consider the reason for applying a factor of safety. If it is intended
to guard against miscalculation of T CR , or in other words, if there is a possibility
that the actual load applied to the geosynthetic is in fact T CR , then the traditional method
of a design based on stress-rupture is correct. If on the other hand the purpose of the
factor of safety is to keep some strength in reserve to allow for sudden or short-lived
excess loads, then the partial safety factors should reflect the ratio between the applied
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
load and the available strength. The available strength is equal to the residual strength
as defined in Section 2.
In the following sections of this paper, it is assumed that the load applied is equal to
the design strength, T D . The design strength, T D , was calculated as being equal to T CR /f m
at the design life t d . In fact, the available or residual strength at t d is higher, and equal
to T RD in Figure 4. The effective factor of safety is increased from T CR /T D (= f m )toT RD /T D
(> f m ).
4 THE BRITTLE FRACTURE MODEL
Stress-rupture and residual strength have been described mathematically for polyaramid
fibres (Christensen 1981; Wagner et al. 1986). For polyester fibres, as for polyaramid,
the gradient of the stress-rupture graph plotted on a double logarithmic scale (log
σ against log t, whereσ equals the applied stress) is low in value; for polyester, the
stress-rupture gradient is typically -1/40. If a power law is fitted to the creep curve,
Christensen concludes that the residual strength is insensitive to the previous application
of constant stress so long as the time period of constant stress application is not
close to the ultimate lifetime.
As a simple illustration, let us consider the fibres to be completely brittle, with failure
governed by crack growth alone. The empirical Paris law (Paris and Erdogan 1963) relates
the rate of crack growth to the stress concentration factor as follows:
da
(1)
dt = AKn
Stress-rupture curve
T RD
Residual strength curve
corresponding to T D
Load, T
T CR
Unfactored strength
T D
Design strength or applied load
Log t (time) Design life, t d
Figure 4. Definition of T RD , the residual strength at the end of the design life, t d , under a
sustained load T D (T CR /T D =f m ; T RD /T D > f m ).
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
where: a = crack length; A = a constant; n = index; and, K = stress concentration factor
which is equal to σYa ½ for simple geometries, where σ = applied stress and Y =geometrical
factor (Evans and Wiederhorn 1974). For any value of crack length, a, thereisa
corresponding residual strength σ t with an initial value of σ 0 , corresponding to a critical
value of K=K IC . By expressing σ t as a function of time and integrating, it can be shown
that σ t is given by the following expression:
σ n−2
t
= σ n−2
0
− σ n t B
where B =2/((n - 2) AY 2 K n−2
IC
), omitting any effects of crack growth during tensile testing.
The stress-rupture curve is given by setting σ = σ t which requires solving the following
equation:
(2)
σ n−2
t
= σ n−2
0
− σ n t
t B
Since n is usually large and σ 0 > σ t , Equation 3 can be approximated using the following
expression:
σ n−2
0
= σ n t
t B
which plots as a double logarithmic stress-rupture diagram, and has a gradient of -(1/n).
As mentioned above, for polyester the stress-rupture gradient is of the order of -1/40
and thus n is equal to 40. Thus, if the values σ 0 =1,B =10 - 6 and n = 40 are substituted
into Equation 2, then for an applied load of σ = 0.6 (i.e. 60% of tensile strength), the
time to failure is 748 hours. After 720 hours, the residual strength is 91.7%, after 730
hours it is 90.6%, and after 740 hours it is 88.7%, before reducing to 60% at failure.
This example illustrates how a stress-rupture curve with a low gradient ( -1/n), as observed
in geotextiles, may be associated with a high residual strength over most of the
design life. This index implies that the majority of crack growth takes place just before
failure, and thus the residual strength remains close to the original tensile strength. A
complete model would have to incorporate the processes of primary and secondary
creep, with decreasing and constant strain rates, respectively, as well as the chemical
aspects of the fracture of polymer chains (Horrocks 1996).
(3)
(4)
5 REVISED DESIGN PROCEDURE
5.1 Residual Strength Due to Sustained Load Alone
It is proposed that instead of using the stress-rupture curve directly, the design
strength could be based on the residual strength curve, T R , corresponding to the anticipated
design strength, T D .AvalueofT D must be found such that at the end of the design
life, a factor of safety, f m , will remain between the design strength and the residual or
available strength, T RD , such that T D =T RD /f m (Figure 5). In the absence of an analytical
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
Stress-rupture curve
Residual strength curve at T = TD
Residual strength at t = t d
Load, T
T CR
T D
Unfactored strength
Design strength or applied load
T RD
Log t (time)
Figure 5. Redefinition of T D such that T D =T RD /f m .
Design life, t d
function to describe the residual strength curves, an iterative process will be required
to derive T D .
5.2 Residual Strength Due to Sustained Load, Mechanical Damage and the
Environment
A procedure based on residual strength has the further advantage that it can easily
incorporate degradations due to other effects. Figure 6 shows the residual strength due
to sustained load, mechanical damage and environmental effects individually. If all of
the effects - load, mechanical damage and environmental - apply simultaneously but
without any synergistic effects, such as environmental stress cracking, the degradation
curves expressed as fractions of the initial tensile strength may be multiplied to provide
a set of reduced residual strength curves as shown in Figure 7. The design strength T D
may then be calculated such that, at time t d , T RD /T D =f m in the same manner as shown
in Figure 4 but using the reduced curves.
In dealing with stress-rupture or residual strength, it is important to recognise that
where the geosynthetic reinforcement is under variable load along its length (e.g. due
to interlock with the soil) one should always consider the point of maximum load, as
this is the point where the geosynthetic will break. However, when calculating the total
creep strain, it is necessary to calculate the distribution of load arising from an applied
load T D along the whole load-bearing length of the geosynthetic reinforcement, taking
into account any reduction due to a transfer of load from the geosynthetic reinforcement
to the soil. From this it is possible to derive the total time-dependent strain, which may
then be compared with the criterion for serviceability or maximum strain.
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
Sustained load curves
Mechanical damage
Load, T
Environmental
Stress-rupture curve
Log t (time)
Figure 6. Residual strength curves due to sustained load, mechanical damage and
environmental effects.
Curve for T=T D
Load, T
T RD
T D
Design strength or applied load
Log t (time)
Design life, t d
Figure 7. Combined residual strength curves for sustained load, mechanical damage and
environmental effects; redefinition of T D such that T RD /T D =f m .
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
ACKNOWLEDGMENTS
This paper is an extended version of a discussion contribution made at IS Kyushu
1996. I thank D. Kingston, M. McCreath, W. Voskamp and P. Segrestin for helpful discussions
and the Directors of ERA Technology for permission to publish this paper.
REFERENCES
BS 8006, 1995, “Code of Practice for Strengthened/Reinforced Soils and Other Fills”,
British Standards Institution, London, UK, 170 p.
Christensen, R.M., 1981, “Residual-Strength Determination in Polymeric Materials”,
Journal of Rheology, Vol. 25, No. 4, pp. 529-536.
Evans, A.G. and Wiederhorn, S.M., 1974, “Proof Testing of Ceramic Materials - An
Analytical Basis for Failure Predictions”, International Journal of Fracture Mechanics,
Vol. 10, No. 3, pp. 379-392.
Horrocks, A.R., 1996, “The Effect of Stress on Geosynthetic Durability”, Geosynthetics:
Applications, Design and Construction”, de Groot, M.B., den Hoedt, G. and Termaat,
R.J., Editors, Balkema, pp. 629-636.
Jewell, R.A. and Greenwood, J.H., 1988, “Long-Term Strength and Safety in Steep Soil
Slopes Reinforced by Polymer Materials”, Geotextiles and Geomembranes, Vol.7,
Nos. 1 and 2, pp. 81-118.
Paris, P.C. and Erdogan, F., 1963, “A Critical Analysis of Crack Propagation Laws”,
Transactions of ASME Journal Basic Engineering, Vol. 85, pp. 528-534.
Schardin-Liedtke, H., 1990, “Geotextiles for the Support of Steep Slopes: Approval
Procedure”, Proceedings of the Fourth International Conference on Geotextiles,
Geomembranes and Related Products, Balkema, Vol. 1, The Hague, The Netherlands,
May 1990, pp. 79-85.
Wagner, H.D., Schwartz, P. and Phoenix, S.L., 1986, “Lifetime Statistics for Single Kevlar
49 Filaments in Creep-Rupture”, Journal of Materials Science, Vol. 21, No. 6,
pp. 1868-1878.
NOTATIONS
Basic SI units are given in parentheses.
A = constant (Pa -n m 1-n/2 )
a = crack length (m)
B = 2/((n - 2) AY 2 K n−2
IC )(Pa 2 s)
f f = partial load factor (dimensionless)
f m = partial material factor (dimensionless)
f m11 = partial factors for variations in manufacturing (dimensionless)
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture
f m12 = partial factors for the uncertainty in extrapolation (dimensionless)
f m21 = partial factor for installation damage (dimensionless)
f m22 = partial factor for environmental effects (e.g. ultraviolet light, hydrolysis
of polyester and oxidation of polyolefins) (dimensionless)
K = stress concentration factor = σYa ½ for simple geometries (Pa m ½ )
K IC = initial critical stress concentration factor (Pa m ½ )
n = index value (dimensionless)
T = applied load (N/m)
T CR = unfactored design strength (N/m)
T D = geosynthetic reinforcement design strength (N/m)
T R = residual (or available) geosynthetic strength (N/m)
t = time (s)
t d = design life (s)
t f = time to failure (s)
Y = geometrical factor (dimensionless)
σ = applied stress (N/m 2 )
σ 0 = initial strength (N/m 2 )
σ t = residual strength (N/m 2 )
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Discussion and Closure
DESIGNING TO RESIDUAL STRENGTH OF
GEOSYNTHETICS INSTEAD OF STRESS-RUPTURE
TECHNICAL NOTE UNDER DISCUSSION: Greenwood, J.H., 1997, “Designing
to Residual Strength of Geosynthetics Instead of Stress-Rupture”, Geosynthetics
International, Vol. 4, No. 1, pp. 1-10.
DISCUSSER: S-C.R. Lo, Senior Lecturer, School of Civil Engineering, University
College, University of New South Wales, Canberra, Australia, Telephone:
1/61-6-2688349, Telefax: 1/61-6-2688337, E-mail: srl@octarine.cc.adfa.oz.au.
PUBLICATION: Geosynthetics International is published by the Industrial Fabrics
Association International, 1801 County Road B West, Roseville, Minnesota
55113-4061, USA, Telephone: 1/612-222-2508, Telefax: 1/612-631-9334.
Geosynthetics International is registered under ISSN 1072-6349.
REFERENCES OF DISCUSSION AND CLOSURE: Lo, S-C.R., 1997,
“Discussion of ‘Designing to Residual Strength of Geosynthetics Instead of
Stress-Rupture’ by Greenwood, J.H.”, Geosynthetics International, Vol. 4, No. 6, pp.
673-675.
Greenwood, J.H., 1997, “Closure of Discussion of ‘Designing to Residual Strength of
Geosynthetics Instead of Stress-Rupture’”, Geosynthetics International, Vol. 4, No. 6,
pp. 675-677.
Discussion by S-C.R. Lo
The author of the paper has presented a more rational and less conservative method
for assessing the load carrying capacity of geosynthetics under long term loading. However,
clarifications are needed to ensure the proposed method is applied in a way compatible
with the design conditions and philosophy of the design code used. The latter
cannot be over-emphasised because of the introduction of limit state design codes that
use a series of somewhat confusing partial factors.
In a limit state design code, partial factors are used in lieu of a single factor of safety.
The design strength, T D , is obtained by applying a partial factor f m to T CR , the rupture
strength at the specified design life obtained by extrapolation of test data. In the context
of limit state design, f m is used to cover uncertainties in the determination of T CR and the
loss in effective load carrying area (say, due to construction damage). In BS 8006
(1995), f m is considered as the product of a number of partial factors f m11 , f m12 ,etc.in
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DISCUSSION AND CLOSURE D Designing to Residual Strength Instead of Stress-Rupture
attempt to establish a clear link between partial factors and sources of uncertainties/errors.
But f m is not used to take into account short term overload. However, this does not
invalidate the method proposed by the author because the design reinforcement tension,
T * , which has to be less than or equal to T D , also contains partial load factors. Thus the
sustained reinforcement tension, T S , is always less than T D as evident from the following
fundamental inequality:
T S ≤ T * ≤ T D
(5)
Hence the residual strength curve has to pass through T S instead of T D as illustrated in
Figure 8, and this leads to a higher residual strength. The use ofT S in defining the residual
strength curve will also avoid the duplication of conservatism if the f m value is selected in
a conservative manner. The relevant limit state design equation becomes the following:
T * ≤ T res ∕ f m
(6)
where T res is the residual strength at the design life. However, the determination of T S is
not straight forward. It is important to emphasise that T S may be higher than the unfactored
reinforcement tension, T O , as determined from a simple calculation model. This is
due to: (i) lock in reinforcement tension because of compaction stresses (Enrich and
Mitchell 1994); and (ii) mobilized soil strength parameters lower than those used in the
design calculations. The latter condition is unlikely for a geosynthetic-reinforced soil
wall if the critical state friction angle is specified in the design code, but conceivable if
peak strength parameters are used in the calculation of T O . In the case ofBS 8006(1995),
where peak soil strength parameters are used, it may be adequately conservative to estimate
T S by increasing the unfactored reinforcement tension by approximately 25%. A
Stress rupture line
Residual strength curves
Load or strength
T CR
T D
T S
Greenwood (1997)
Proposed
Design life
Log t (time)
Figure 8. Residual strength curves as a function of time for an applied load and the stress
rupture line.
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DISCUSSION AND CLOSURE D Designing to Residual Strength Instead of Stress-Rupture
lower factor is appropriate if the critical state friction angle, orfactored strength parameters,
are used in the design. Thus the conversion from T * ,orT O ,toT S is code dependent.
The term “overloading” in the context of reinforcement rupture of a reinforced soil
structure really means overloading of the reinforcement elements. As such, an extreme
(hence short lived) increase in surcharge on the wall may only be a minor contributor
to “overloading”. In geotechnical engineering, “overloading” can be long term or short
lived. Long term “overloading” can be caused by soil strength parameters lower than
those assumed in the design and is conceivable if the design is based on unfactored
peak strength parameters. The residual strength method appears to be for short-lived
“overloading”. It is likely that the most severe “overloading” considered in a design
(as specified by a load combination and partial load factors) is short-lived, and the residual
strength method is most appropriate. However, a less severe “overloading” of a
long term nature is still possible. This condition needs to be defined, say, by another
load combination with less severe partial load factors, and be checked using the stress
rupture method.
A related point that needs clarification is how the residual strength needs to be determined.
Figure 2 of the author’s paper and the empirical Equation 4 for polyester appear
to suggest a quick tensile test. In reinforced soil structures, even short-lived “overloading”
is rarely transient in nature but may have a duration of days or weeks. This is because
short-lived “overloading” may be caused by an increase in pore water pressure
(say, due to more severe flooding than that specified) or over-excavation, etc. Hence,
the geotechnical community and code drafting bodies have to agree on a duration for
short-lived “overloading”. Once such an agreement is reached, the residual strength
curve can be determined by maintained load tests where the residual strengths are available
for the specified duration.
REFERENCE
Enrich M. and Mitchell, J.K., 1994, “Working Stress Design for Reinforced Soil
Walls”, Journal of Geotechnical Engineering, Vol. 120, No. 4, pp. 625-645.
Closure by J.H. Greenwood
The intention of the author’s paper was to point out that static load can be treated as a
factor that leads to a gradual reduction in strength in the same manner as ultraviolet light
or a chemical agent. This will lead to partial safety factors that are more realistic than
those obtained by considering the stress-rupture diagram. The discusser is right to point
out that this must be integrated correctly into current codes for designing reinforced
soil. The various load levels, T, should be defined with care and the reason for applying
each individual partial safety factor should be examined.
The following is a simple numerical example to illustrate further the relation between
residual strength and stress-rupture. Suppose that the residual strength T R decreases linearly
with time from an initial value of unity and in proportion to (using the discusser’s
notation) the sustained load T S as follows:
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DISCUSSION AND CLOSURE D Designing to Residual Strength Instead of Stress-Rupture
T R = 1 − T S t ∕ 10
(7)
The result is a group of curves which are plotted against log time, t in Figure 9. The
residual strengths at higher applied loads fall more rapidly than those at lower loads.
Each test ends with rupture when T S =T R ,or:
T R = 1 ∕ (1 + t ∕ 10)
(8)
This is the stress-rupture graph and is plotted as a thick line in Figure 9.
Noting the lack of data, it is now possible to quote the following results. Fifteen specimens
of various polyester yarns had been placed under a constant load at 50% of their
respective tensile strengths for a period of 55700 hours (6.4 years; log t = 4.75) when the
tests were interrupted in August 1997 and the tensile strengths measured (the question
of the duration of short-term overloading was not considered). The creep strain values
ranged between 5.6 and 7.2%. The mean log t value for the same yarns under a sustained
load of 60% of the tensile strength at 20_C was measured as 3.84 (t = 6950 hours).
Greenwood and Yeo (1996) presented the stress-rupture graph of Fortrac geogrid,
which is made from similar yarns, and showed the gradient of the applied load plotted
against log t to be -3.83% of the tensile strength. The sustained load corresponding to
55,700 hours is thus 60 - 3.83×(4.75 - 3.84) = 56.5%; thus, the yarns were exposed at
50÷56.5×100 = 88% of the load that would have led to rupture at the end of the test.
The residual strengths of the yarns are given in Table 1. The test results in Table 1 indicate
that the strength is effectively unchanged under these conditions.
1
0.9
0.8
Percent Tensile tensile strength strength ratio
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
residual strength for applied load 0.1
residual strength for applied load 0.2
residual strength for applied load 0.3
residual strength for applied load 0.4
residual strength for applied load 0.5
residual strength for applied load 0.6
residual strength for applied load 0.7
residual strength for applied load 0.8
residual strength for applied load 0.9
stress-rupture
0.1 1 10 100
Time (hours)
Figure 9. Residual strength and stress-rupture plotted on a logarithmic scale for a
reduction in strength that depends linearly on time and sustained load.
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DISCUSSION AND CLOSURE D Designing to Residual Strength Instead of Stress-Rupture
Table 1.
The residual strengths of yarns after 55,700 hours at 50% tensile strength.
Yarn type Initial strength (N) Residual strength (N) Percent residual strength
Type A 76.6 77.2 100.7
Type B (undamaged) 77.2 75.2 97.3
Type B (damaged) 66.7 64.9 97.4
Type C 75.0 74.4 99.3
Type D 74.0 76.9 103.9
ACKNOWLEDGMENTS
The author of the paper thanks W. Voskamp for permission to publish the test results
reported in Table 1.
REFERENCE
Greenwood, J.H. and Yeo, K.C., 1996, “Assessment of Geogrids for Soil Reinforcement
in Hong Kong”, Earth Reinforcement, Ochiai, H., Yasufuku, N. and Omine K.,
Editors, Balkema, Proceedings of the International Conference on Earth Reinforcement,
Fukuoka, Kyushu, Japan, November 1996, pp. 363-367.
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