Technical Paper by J.H. Greenwood - IGS - International ...
Technical Paper by J.H. Greenwood - IGS - International ... Technical Paper by J.H. Greenwood - IGS - International ...
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. 674 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 6
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: GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 6 675
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DISCUSSION AND CLOSURE D Designing to Residual Strength Instead of Stress-Rupture<br />
attempt to establish a clear link between partial factors and sources of uncertainties/errors.<br />
But f m is not used to take into account short term overload. However, this does not<br />
invalidate the method proposed <strong>by</strong> the author because the design reinforcement tension,<br />
T * , which has to be less than or equal to T D , also contains partial load factors. Thus the<br />
sustained reinforcement tension, T S , is always less than T D as evident from the following<br />
fundamental inequality:<br />
T S ≤ T * ≤ T D<br />
(5)<br />
Hence the residual strength curve has to pass through T S instead of T D as illustrated in<br />
Figure 8, and this leads to a higher residual strength. The use ofT S in defining the residual<br />
strength curve will also avoid the duplication of conservatism if the f m value is selected in<br />
a conservative manner. The relevant limit state design equation becomes the following:<br />
T * ≤ T res ∕ f m<br />
(6)<br />
where T res is the residual strength at the design life. However, the determination of T S is<br />
not straight forward. It is important to emphasise that T S may be higher than the unfactored<br />
reinforcement tension, T O , as determined from a simple calculation model. This is<br />
due to: (i) lock in reinforcement tension because of compaction stresses (Enrich and<br />
Mitchell 1994); and (ii) mobilized soil strength parameters lower than those used in the<br />
design calculations. The latter condition is unlikely for a geosynthetic-reinforced soil<br />
wall if the critical state friction angle is specified in the design code, but conceivable if<br />
peak strength parameters are used in the calculation of T O . In the case ofBS 8006(1995),<br />
where peak soil strength parameters are used, it may be adequately conservative to estimate<br />
T S <strong>by</strong> increasing the unfactored reinforcement tension <strong>by</strong> approximately 25%. A<br />
Stress rupture line<br />
Residual strength curves<br />
Load or strength<br />
T CR<br />
T D<br />
T S<br />
<strong>Greenwood</strong> (1997)<br />
Proposed<br />
Design life<br />
Log t (time)<br />
Figure 8. Residual strength curves as a function of time for an applied load and the stress<br />
rupture line.<br />
674 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 6
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