INTRODUCTION 1.1 General
1.4 Actions and Design input parameters
2.3.2 Rheological and Mathematical Modelling of Geosynthetics Behaviour Several attempts have been made in the past to simulate the behaviour of
2.3.2.4 Zener (Standard Linear Solid) Model
• Strain-Time plots are developed from the data obtained from creep tests for a particular type of geosynthetics at different load levels.
A mathematical model of creep data should describe the structural properties of geosynthetics. Hence a suitable function should be chosen to represent its strain behaviour. The method suggested by Esteve can be briefly outlined step by step as:
In this model the springs and the dashpot are in series and parallel, Figure 2. I2(b).
This model predicts the deformation behaviours for creep, relaxation and recovery, as well. The other forms of the models presented above may be considered as the special cases of this.
In this way, additional elements may be added to simulate the nature of the geosynthetics better but the mathematical solution of the governing equation becomes complex.
• A suitable function is selected to fit in the curve. For the present case, a logarithmic function viz. Y= A Ln (x) +B and power function Viz. Y= A (x) Bare chosen.
• The coefficients A and B are plotted against different load levels and the plots are adjusted by selecting proper functions. For the current case, linear series is found to fit well within the range.
• From these plots, the coefficients A and B are determined for the required load levels.
• These coefficients are substituted in the selected logarithmic and power functions to yield the strain-time plot at the required load levels.
2.4 Strength tests for geosynthetics
2.3.2.6 Boltzmann Superposition Principle
This principle of Boltzmann is explained in detail in the section 3.6 with the aid of figures for the loading history and it's strain response against time. Therefore, it is not felt necessary to elaborate the principle in detail here.
The creep behaviour of geosynthetics to date has assumed that the level of the applied stress is constant, while in service the material may be subjected to a complex pattern of loading and unloading cycles. It may not be feasible to obtain experimental data to cover all possible loading situations for determining the input parameters for design.
For tackling the problem of the sort above, the simplest theoretical model has been presented by Boltzmann to predict the strain response to a complex stress history.
This is referred to as the Boltzmann superposition principle, which proposes that for a linear viscoelastic material, the strain response to a complex loading history is merely the algebraic sum of the strains due to each step in loading. The implication of the idea in this principle is that the behaviour of a geosynthetic is a function of its entire loading history.
There are varieties of test methodologies developed so far to determine the strength of geosynthetics. Depending upon the time and the purpose, an appropriate test may be selected. To be named, they are CRS (constant rate of strain) test, CREEP (Iong- term sustained loading) test, Stress relaxation test and Cyclic tests. These tests utilize different specimen shapes and sizes, loading methodologies, rates ofload application and test temperature for. measuring mechanical behaviour of geosynthetics, Kabir (1984).
Test specimens must be of sufficient size and shape to be representative of the macro-structure of the product, Kabir (1984) and Yeo (1985). However, even when this condition is satisfied, each test may investigate the response of different features of the micro and macro-structures of geosynthetics. Indeed, changing a single test
2.4.1 Constant rate of strain test
This test is very famous and widely performed since it involves very little time. A constant rate of strain is maintained while' applying the load increasingly until the specimen ruptures. Load verses strain is recorded and the ultimate load at the rupture is found out.
condition may result in a change in the load-strain response. For example, for wide width specimens tested at a given test temperature, a change in the rate of strain in monotonic tests has a significant effect on the measured properties of geosynthetics as has changing the test temperature whilst using the same rate of strain has a significant effect, Kabir (1984) and Yeo (1985).
Different standards specify their own rate of strain at which the test is to be performed. For example, BS 6906, Part 5 specifies a rate of strain at 7-13% per minute and the temperature to be (20 :t1)0 C.
The test scheme is shown in Figure 2.13(a) and the qualitative load -strain plot is shown in Figure 2.13(b).
2.4.2 Sustained load creep test
The scheme of test apparatus used in sustained load creep test is shown in Figure 2. 14(a). This test involves very longer period of time compared to CRS test. The specimens are loaded with different weights that are sustained for a long period. The strain verses time at these loads is recorded up to generally 1OOOOhrs.The qualitative plots are shown in Figure 2.14(b). From these plots load-strain curves are developed.
For this test also the test temperature in BS is specified as (20 :t 1)0 C. The test procedure is explained in detail in Chapter Four.
The plots of total strain ET against time for the above loadings are constructed as shown in the Figure 2.16 for elasto-visco-plastic materials following the procedure described below.
2.4.2.1 Isochronous load-strain curves
Each of the test methodologies involves different form of data presentation and for a particular test several forms of data presentation can be used. The most widely applicable form of presenting these data is in the form of Isochronous Load-Strain curves at a constant temperature. Commonly, these are produced from sustained load [creep] test data. However, they can also be produced from most test procedures, for example CRS test. Recently it has been shown by Miiller-Rochholz et al (1994) that the data obtained from cyclic load test can be represented by an equivalent sustained loading. This allows Isochronous Load-Strain curves to be obtained from cyclic load test data as well.
Isochronous curves are the plots of load verses strain at the same temperature from different loading tests such as CREEP (long term sustained load) or CRS (constant rate of strain) tests. In order to obtain isochronous (load-strain) curves the materials (specimens) are subjected to a series ofJoads PI, P2, and p] at time to and sustained as shown in the Figure 2.15, which is a plot ofJoad verses time.
For any time tl, total strain values corresponding to the loads PI, P2, and p] are scaled off from the figures (a) of total strain -time plots. In the same manner for any times t2 and h, corresponding strain values to the loads are obtained from the same figures and marked on the plots of load vs strain. These points corresponding to different times tl, t2 and t], respectively, are joined to produce curves for tl, t2 and t3 respectively. Thus a family of curves is obtained. The typical isochronous curves for elasto-visco_plastic materials are shown in the Figure 2.16(b).
It should be noted that the areas under the Isochronous Load-Strain curves represent the absorbed Strain Energy at the specific time and limiting strain and may be termed as the Isochronous Strain Energy.
2.5.1 Reference Strength
2.5 Design strength of geosynthetics in GRSSs
2.5.1.1 Reference Strength for Single-Stage Actions
The maximum load at rupture of the 'Ex-works' materials under Constant Rate of Strain [CRS] tensile testing is chosen to be the basis of defining the Reference Strength of geosynthetics by DlBt (1998) and AASHTO (1997). To avoid long-term creep rupture, the Reference Strength [PRed, is then obtained by dividing the CRS rupture strength by a Reduction Factor, Figure 2. 17(a). The DlBt and the AASHTO design methods specify 33% per minute and 10% per minute strain rates respectively, for the CRS tests. Kabir (1984) and Yeo (1985) have shown that the CRS test can give different strengths at different test strain rates and temperatures. Therefore, even for a particular type of geosynthetic the same Reduction Factor may not be applicable to all CRS data in order to obtain the long term creep rupture strength, i.e. the Reduction Factor is dependent on the strain rate used in the CRS test.
Troost and Ploeg (1990), BS8006 (1995) and Jewell (1996) have defined the Reference Strength [PRedas the load to cause creep rupture of 'Ex-works' specimens at the end of design life [t.n], Figure 2.17 (b). However, many geosynthetics exhibit a wide range of scatter of creep rupture strains for different sustained [creep] load levels, Fig 2.17 (c). Hence, the Reference Strength [PRed, defined on the basis ofload
In the design of GRSSs, two types of strength have been considered so far, viz.
Reference strength" [PRed and Design Strength [Td]. Various testing techniques have been developed to obtain Reference Strength [PRed. Customarily, Design Strengths [T
d]
for geosynthetics are determined by applying Partial Factors to the Reference Strengths. However, the Partial Factors need to be modified for their appropriate application, khan (1999).The Reference Strength [PRed is obtained from different testing techniques, most often by CRS and CREEP tests. Various design codes and methods define Reference Strength [PRedin different ways for Single-Stage and Multi-Stage Actions.
2.5.1.2 Reference Strength for Multi-Stage Actions
at creep rupture for a specific design life time
[!ctJ],
can be very difficult to select with any certainty related to the strain level developed at creep rupture, McGown et al (1998).Of Multi-Stage Actions, one illustration is sustained loading plus traffic loading that may be applied to the reinforced roads. Although the traffic loads are transient in nature, in most of the design codes, they are calculated as the wheel load divided by the contact area; viz. BS5400 Part2 (1978), and considered as an uniform surcharge load over the whole design life time, GeoguideI (1989), BS8006 (1995) and AASHTO (1997). This implies that these codes permit the Reference Strengths for Single-Stage Actions to be used in designs for sustained loading plus traffic loading.
The external and internal stability analyses for the sustained loading plus traffic loading are carried out for the critical loading combination as outlined in the respective codes.
This way, the Reference Strengths for Single-Stage Actions are defined in two different ways, i.e. on the basis of long term creep rupture strength, and on the basis oflong term creep at a limiting strain.
Some design methods define the Reference Strength [PRed as the load obtained from the Isochronous Load-Strain curves, corresponding to a Performance Limit Strain [Ep], for example the TBW Method (1998) and the HA 68/94 Design Method (1997).
This value is always less than the strength at creep rupture, Figure 2.l7( d). Adoption of the Performance Limit Strain
[!>p]
to define the Reference Strength [PRed for Ultimate Limit State design can be seen to be the quite conservative choice of strength value, Khan (1999).The consideration of wheel contact pressure as a sustained load over the whole design lifetime of the structure does not consider the transient nature of the load which may be economical considering the elasto-visco-plastic behavior of geosynthetics.
Similarly, the performance of seven geosynthetic-reinforced slopes and walls shaken in the Northridge, California earthquake of January 17, 1994, was adequate, particularly compared to the performance of other immediate neighbouring structures, White and Holtz, (1995).
During the Kobe (Hyogo-ken Nanbu), 1995 earthquake with magnitude of 7.2, a great number of RC columns and piers collapsed by shear failure in a brittle manner, in contrast to a number of geogrid soil retaining walls that performed very well. In particular, the geogrid reinforced soil retaining walls with full height rigid facings at Tanata did not collapse despite the site were located in one of the most severely shaken area, Tatsuoka et aI, (1995).
Further illustration of Multi-Stage Actions is sustained loading plus short-term seismic loading. The development of designs for GRSSs involving earthquake forces is presently empirical. Fukuda et al (1994) reported that until 1993, the GRSSs were designed for earthquake on the basis of the procedure for design under ordinary static conditions, as given by Jewell et al (1984). In this procedure the long term creep rupture strength of geosynthetics was used as Reference Strength. The structures, so designed, were found to maintain stability during the Lorna Prieta Earthquake in 1989 having a magnitude of 7.1, Collin et al (1992), and Kushiro Offshore Earthquake in 1993 having a magnitude of7.8, Fukuda et al (1994).
These data indicate that the geosynthetics were actually capable of taking higher
loads applied rapidly, than the long-term creep strength used that time. After the
adequate performance of GRSSs in Lorna Prieta Earthquake (1989) and Kushiro
Offshore Earthquake (1993), it was suggested by Fukuda et al (1994), AASHTO
(1994) and Jones (1996) that the Design Strength of geosynthetic for sustained
loading condition should be increased by 1.5 times when designing for sustained
loading plus short term earthquake loading. In the recent codes/methods, as more
confidence is gained from the performances of GRSSs during recent earthquakes,
factored short term CRS strengths of geosynthetics are suggested for use in designs
against sustained loading plus short term earthquake loading, AASHTO (1997),
2.5.2 Partial Factors and Design Strength
In this regard, it has been also reported by Kupec (2000) about the ability of the geosynthetics to take larger short-term load. The Combined Sustained-Short term loading test results from the series used by him showed that even a load of 80% (1.8 times) the sustained load altered the material only temporarily and that with time this alteration decreases.
NCMA (1997) and DIBt (1998). However, it should be noted that the considerations of higher strengths of geosynthetics, from 1994 to 1998, were all empirical, Khan (1999).
The test results from the Multi stage combined sustained-short term loadings revealed that after the subsidence of the short term load, the strain level in the geosynthetics is likely to be similar to that due to the sustained load alone in course of time, as if there were no occurrence of any earthquake ever, Khan (1999). This further indicates that the geosyntheics are in fact capable of taking larger short-term load.
In the design codes/methods higher strengths of geosynthetics have been suggested, presumably, .on the basis that the earthquake loading would be very transitory, but they do not pronounce any valid technical justification. It is unlikely that the same amount of high strength of geosynthetics may be available over the whole design lifetime of the structure, irrespective of the time of occurrence of an earthquake. If so, current practice of designing GRSSs against earthquake might be unsafe.
a) The Damage Factor; to allow for mechanical damage during construction.
The strengths of the geosynthetics for ULS and SLS analyses require to be modified by applying Partial Factors. Four Partial Factors of major concern have been identified for geosynthetics, Voskamp and Risseeuw (1987), Jewell and Greenwood (1988), Greenwood and Jewell (1989) and Troost and Ploeg (1990) as the followings:
2.6 Design approaches for GRSSs
However, it should be noted that no Partial Factors are given for the combined effec!s of Multi-Stage Actions.
BS 8006 (1995), AASHTO (1997), DlBt (1998) and TBW (1998) suggest that the Partial Factors should be determined by comparing the material strengths of geosynthetics "before" and "after' an event, as obtained from CRS tests.
T =PR,r (2.1)
D fm
b) The Environmental Factor; to allow for the chemical environment and microbiological exposure in the ground.
Conventionally, the Design Strengths for the geosynthetics are determined by applying Partial Factors to the Reference Strengths.
d) The Overall Factor; to allow for the properties of materials not meeting the manufacturer's specification.
c) The Material Factor; to allow for the uncertainty inherent in the e~trapolation of test data, and
Traffic, earthquakes, explosions and variety of intermittent loads result in cyclic or short-term loading to GRSSs in combination with sustained load. Very little is known about the behaviour of these structures under such Multi-stage Actions. Nevertheless, it is appreciated that the duration of the cyclic or the short-term loading during these events has an important influence on the response of the foundation materials and the structures themselves.
The current design approaches to external stability have been founded on classical methods for gravity retaining walls with the appendices of internal stability calculations to take the effect of reinforcements into account. Majority of the design methods for GRSSs is based on Limit Equilibrium Approach. Though Limit State
• Internal Stability
Sliding of the structure at the base Overturning of the structure Bearing failure of the subsoil, and Overall stability of the structure
• External Stability
The method of analysis is based on the assumption that all the constituting elements simultaneously reach their limiting stress conditions. This assumption is not valid for GRSSs, since the limiting stress conditions for soils and geosynthetics may occur at quite different strain levels. This method calls for the following stability analyses to be carried out to ensure the safety of the structures:
principles are included in some desi/,'tl codes and methods, these may be termed as Hybrid Approach as they are based partly on Limit Equilibrium Approach and partly on Limit State Approach. Three, main existing design methods involving these three design approaches are reviewed in the subsequent sections with a special emphasis on Multi-stage actions.