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 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. 2 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1
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. GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1 3
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GREENWOOD D Designing to Residual Strength Instead of Stress-Rupture<br />
1 DEFINITION OF UNFACTORED STRENGTH<br />
Design codes such as BS 8006 (1995) prescribe that the design strength of soil reinforcement<br />
should be the load that would lead to failure, or to a maximum acceptable<br />
strain, at the end of the design life. For most materials, failure rather than critical strain<br />
is the dominant design criterion.<br />
The unfactored design strength, T CR , is derived from geosynthetic reinforcement<br />
properties as follows:<br />
S The stress-rupture curve defines the time to failure, t f ,ifaloadT is applied continuously<br />
to the geosynthetic.<br />
S The curve is conventionally plotted as the applied load (or its logarithm) against the<br />
logarithm of time to failure (Figure 1).<br />
S If a design life, t d , is specified, it is then possible <strong>by</strong> extrapolation of the curve to predict<br />
a load T CR that would lead to failure at the end of the design life (Jewell and <strong>Greenwood</strong><br />
1988).<br />
When using partial factors in design, such as prescribed in BS 8006 (1995), the design<br />
load T is obtained <strong>by</strong> increasing the unfactored load <strong>by</strong> a partial load factor, f f , that typically<br />
takes on a value of 1.5, and <strong>by</strong> decreasing the unfactored strength, in this case T CR ,<br />
<strong>by</strong> a partial geosynthetic material factor, f m , to produce a geosynthetic reinforcement<br />
design strength, T D . At any instant of time during the lifetime of the structure, the applied<br />
load should be less than or equal to T D . The partial geosynthetic material factor,<br />
f m , is for reductions, variations and uncertainties in the properties of the geosynthetic.<br />
Using the definitions in BS 8006 (1995), f m is the product of other partial factors including<br />
the following: f m11 for variations in manufacturing; f m12 for the uncertainty in extrapo-<br />
Stress-rupture curve (experimental)<br />
Extrapolated curve<br />
Load, T<br />
T CR<br />
T D<br />
Unfactored strength<br />
Design load<br />
Log t (time)<br />
Design life, t d<br />
Figure 1.<br />
Stress-rupture diagram.<br />
2 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NO. 1
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