Technical Paper by J.H. Greenwood - IGS - International ...
Technical Paper by J.H. Greenwood - IGS - International ... Technical Paper by J.H. Greenwood - IGS - International ...
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 4 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1
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 ). GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1 5
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture<br />
load and the available strength. The available strength is equal to the residual strength<br />
as defined in Section 2.<br />
In the following sections of this paper, it is assumed that the load applied is equal to<br />
the design strength, T D . The design strength, T D , was calculated as being equal to T CR /f m<br />
at the design life t d . In fact, the available or residual strength at t d is higher, and equal<br />
to T RD in Figure 4. The effective factor of safety is increased from T CR /T D (= f m )toT RD /T D<br />
(> f m ).<br />
4 THE BRITTLE FRACTURE MODEL<br />
Stress-rupture and residual strength have been described mathematically for polyaramid<br />
fibres (Christensen 1981; Wagner et al. 1986). For polyester fibres, as for polyaramid,<br />
the gradient of the stress-rupture graph plotted on a double logarithmic scale (log<br />
σ against log t, whereσ equals the applied stress) is low in value; for polyester, the<br />
stress-rupture gradient is typically -1/40. If a power law is fitted to the creep curve,<br />
Christensen concludes that the residual strength is insensitive to the previous application<br />
of constant stress so long as the time period of constant stress application is not<br />
close to the ultimate lifetime.<br />
As a simple illustration, let us consider the fibres to be completely brittle, with failure<br />
governed <strong>by</strong> crack growth alone. The empirical Paris law (Paris and Erdogan 1963) relates<br />
the rate of crack growth to the stress concentration factor as follows:<br />
da<br />
(1)<br />
dt = AKn<br />
Stress-rupture curve<br />
T RD<br />
Residual strength curve<br />
corresponding to T D<br />
Load, T<br />
T CR<br />
Unfactored strength<br />
T D<br />
Design strength or applied load<br />
Log t (time) Design life, t d<br />
Figure 4. Definition of T RD , the residual strength at the end of the design life, t d , under a<br />
sustained load T D (T CR /T D =f m ; T RD /T D > f m ).<br />
GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1<br />
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