ISOTHERMAL BEHAVIOUR OF SOME GEOSYNTHETICS SUBJECTED TO SINGLE STAGE LOADING
4.2 Test set up and Procedure
ISOTHERMAL BEHAVIOUR OF SOME GEOSYNTHETICS SUBJECTED TO
4.2.1.2 Long-term sustained CREEP test
The test specimen of geogrid or geotextile is cut to the specified shape and size by different standards. One end at top and one at bottom are clamped which are fitted to the CRS testing machine, Figure 2. 13(a). The load is applied hydraulically maintaining the rate of strain at which the test is performed. The lower clamp is fitted with the LTDV. transducers to a programmable data logger. Finally the data are recorded in the computer at specified intervals from which the plots of load and strain are developed, Figure 2.13(b). The test temperature by BS is specified as (20:t I) 0C and the rate of strain as 7-13%.
There are two types of single-stage loading tests, which are commonly employed and widely accepted to determine the strength of geosynthetcs; namely CRS (constant rate of strain) test and long term sustained CREEP test. The procedures for these tests are briefly outlined below.
4.2.1.1 Constant rate of strain (CRS) test 4.2.1 Single-stage action (SSA) tests
(constant rate of strain) and CREEP (long-term sustained) tests are performed in order to determine the strength of geosynthetics.
The scheme of test apparatus used in sustained load creep test is shown in Figure 2.14(a). The specimens are cut to shape and size as specified in different standards.
The upper end is fixed to a clamp that is fixed to the machine. The lower end is fixed to a clamp where it is loaded. Different specimens are loaded with different eights, e.g. 5, 10, 15kN/m and so on. The lower clamp is fitted with the LTDV transducers that transmit the readings to computers. For the first minute the readings are taken at I, 2, 4, 8, 16, 30 and 60 seconds. From Imin to Ihr they are taken at 2, 4, 8, ... minutes and after Ihr they are taken at every 24hrs up to 10000hrs.These data are used to plot strain-time plots from which load strain curves are developed for further usage. The test temperature for this test is similar to that of the CRS test in BS.
Eq4.1 (for power series)
4.3 Extrapolation of CREEP test Data
y=A Ln (x) +B (for logarithmic series)' Eq 4.2
The data from Creep tests perfonned on SS2 and SR80 geogrids are collected for analyses. The Creep tests were undertaken at 20°C on SS2 geogrid at a series ofload levels like 6.9,8.5, lOA and 13.8 kN/m; and similarly that on SR80 geogrid at 5, 10,
15, 20, 25 and 30 kN/m load levels. Figures 4.1 and 4.2 are the total strain-time plots developed from these data.
Mostly GRSSs are designed for an operation period that is greater than the duration of long term CREEP tests. Therefore, it becomes necessary to extrapolate CREEP test data to the required design life of the structure. In the same manner, it also becomes essential to extrapolate CREEP test data at higher load levels other than those employed during the tests. Khan (1999) showed it that the data for much larger duration than the CREEP test could be obtained by extrapolation using best curve fitting technique.
The test data thus obtained from different research works have been modelled using mathematical modelling suggested by Esteves as outlined in chapter two. Two types of equations were found to fit the curves derived as total strain-time plots from the CREEP tests at different load levels, i.e. power series for SS2 and logarithmic series for SR80, Figures 4.3(a) and (b) respectively. The typical forms of the equations are gIVen as:
Thus the parameters A and B were separated and plotted at different load levels where a linear fit was found to represent them, Figures (a) and (b) of4A and 4.5. The equations of both parameters for the geogrids are in the fonn of (y =a x+c). From these linear fits, the parameters A and B have been extrapolated at higher load levels required for the study which upon substitution into the above equations generate the required total strain-time curves at higher load levels. In this way, the CREEP test data were extrapolated at higher load levels viz. 18.8, 23.8, 28.8 and 33.8 kN/m for
4.4 Isochronous load-strain curves and strain
envelopes
SS2; and 37.5, 45.0, 52.5, 60.0, 67.5 and 75.0 kN/m for SR80 geogrids respectively so as to obtain the required loads at different times corresponding to the total strain of 10%
Figures 4.6 and 4.7 are the load-total strain plots derived from the total strain-time plots (Figures 4.1 and 4.2) at 20°C and different load levels for SS2 and SR80 geogrids, respectively, following the procedure described in Chapter 3. Once the Isochronous curves have been derived, the strain at any load level for any time may be found. Alternatively, the load corresponding to a particular strain for any time could be found from these curves.
There are numerous forms in which the data from the strength tests on geosynthetics may be presented. However, the most convenient and broadly accepted form is to present them as Isochronous Curves. These are the load-strain curves for different times at a constant temperature.
Thus the curves for 0.0 I, 0.1, I, 10, 100 and 1000 hrs may be used to obtain the strengths (strain) at various loads up to 1000 hrs. In the same fashion, the curves for larger duration may also be derived. In order to derive the load- locked in strain curves, a set of data from the Unloading tests that were performed at 20°C for the same geogrids at different load levels have been compiled and extrapolated at higher load levels, Figures 4.8 and 4.9, from which the recoverable strain at any load level may be found. Recoverable strain ER is attributed to solely elastic recovery and therefore the value would be constant at a particular load level irrespective of time.
The Figures 4.10 and 4.11 are the load-locked in strain curves, which have resulted from the fact that (EL= ET - ER), i.e. after subtraction of Figures 4.8 and 4.9 from the corresponding Figures 4.6 and 4.7.
For various limiting strains viz. 2%, 5% and 10% the loads are obtained from the Isochronous curves which are then used to find the corresponding recoverable strains and thus the locked in strains. Figures 4.12, 4.13 and 4.14 show the total strains and
4.5 Discussion on test results
their components vs. time for the limiting strains of 2%, 5% and 10%, respectively for SS2 and SR80 geogrids.
In order to reach the strain of 10%, the total strain-time data have been extrapolated at higher loads. These curves exhibit linear extension behaviour. The Isochrones derived from these strain-time plots comply with their general shape. However, more linearity is conspicuous at higher load levels due to extrapolation.
Once the strain components, I.e. ER and EL are obtained, they have been plotted against each other giving rise to the envelopes. Figures 4.15(a) and (b) show the ER- ELplots at 2%, 5% and 10% limiting strains for SS2 and SR80 geogrids respectively.
It should be appreciated that these envelopes have identical linear patterns.
It was identified in Chapter Three that geosynthetics would develop strain upon loading and that this total strain ETat any time comprises of strain components called
"Recoverable Strain" ER and "Locked-in Strain" EL. From the fact that, ET =ER +EL
for any time, the plots of load- locked in strain are developed which are resulted by subtracting Figures 4.8 and 4.9 from the corresponding Figures 4.6 and 4.7. These curves also have similar pattern to the Isochronous curves. Also the strain components ERand EL at 2, 5 and 10 % limiting strains for SS80 and SS2 are obtained using the same relation, i.e. EL =ET - ER and plotted along with ET against log (time) scale, Figures 4.12 through 4.14. These figures show an agreement with the Figure 3.9. From these figures, it may be appreciated that the strain components may combine at any time uniquely to yield the total strain.
The locked in strain EL is seen to be very small at initial stages but increases with time, in contrast with the recoverable strain ER that is reverse. At one point, they are even equal. In other words, if the geosynthetic were to assume a particular strain in a very short period, it would acquire greater ERand a smaller EL. On the other hand, if it
• Isochronous curves 4.6 Summary
were to assume the same strains in a longer dUmtice a sm:aiiEttbut larg,w-fiL.would be acquired. This will become clearer in.the folkw;iDgpmgrapn.
It may be noticed that for each limiting strain, the &R vs. &L plots for SS80 and SS2 show an agreement with Figure 3.14. Again, ifit were to reach the limiting strain in 1 hr, it would acquire a very large &R but small &L; whereas if it were to acquire the same strain in say 1000 hrs, a small &R but very large &L would be required. Thus the geosynthetic may acquire a particular strain with various combinations of &R and &L
depending upon time.
Of many forms, Isochronous curves, which are the load-strain curves for different times at a constant temperature, are the mostly accepted and convenient forms to represent test data. Strain at any load level for different times can be found from these curves, or vice versa.
• Strain components and strain envelope
The total strain in geosynthetics upon loading consists of two components, namely recoverable &R and locked in &L strains. These components combine uniquely for different times to yield a particular strain at isothermal conditions and when the plotted against each other they result in a strain envelope for a particular strain.
750 1000
500 Time (hrs) 250
FIGURE 4.1 Total strain vs time plot from creep test for SS2 at 200C
o o
-.- 6_9kN/m
-.- 8.5kN/m
-.-IOAkN/m -y
y-
-Y-13.8kN/m ~
12
~~
/Y
//
•
9
1
~~~;;.
/
~
.s-
o:
/ .--. • •
-03
tl
'IS
6 ~.----
~
".---- •
/ • .' . - - . •
/ --- .-
3
3000 3500 -.-5kN/m -e-10kN/m -~-15kN/m -9'-20kN/m -,-25kNlm -+-30kN/m
2000 2500 Time (hrs) 1500
500 1000
FIGURE 4.2 Total strain vs time plot from creep test for SR80 at 20.C
12
.5 kN/m 1lII10kN/m lJ.15kN/m X20kN/m J:25 kN/m .30 kN/m
4000 -e-S.5 kN/m -.!>- 104 kN/m
~13.8kN/m
y ~ 0.0461Ln(x) +0.5946 y ~ 0.1 093Ln(x) +1.3223 y ~ 0.IS95Ln(x) +2.2216 y ~ 0.2621 Ln(x) +3.0376 y ~ 0.3367Ln(x) +3.5049 y ~ 0.35Ln(x) +4.7414
3000 y ~ 2.5398xO.1494 y ~ 2.9628xO.1584 y~4.512xOI595 trend lines
Logrithmic series trend lines
o ----,-- -- ---(-- - --~----'---'
o
ZOO 4()0 600 800 \000 1200Time (hrs) 16. ----
14 -
;? 12
"---'~ 10
~ 8
S 6
f-0
4 2
(a) For SS2
(b) For SR80
Figure 4.3 Curve fitting into total strain-time plots
15
y
=
0.0124x - 0.0073 Load kN/mo - ---~-~~---.----.
o
5 100.4 0.35 0.3 -
«:
E 0.25 -
"
.0 0.2
!Ei
"
0 0.15U
0.1 . 0.05 - 0
0 5 10 15 20 25 30 35 40 45
Load kN/m 5
4
«:
E 3 -
"
.<3
!Ei 2
"
u0
(b) For SR80
Figure 4.4 Deriving the coefficient A for extrapolation
15