Large scale triaxial machine is used to examine ballast in this project, as its function cycle loading is used to simulate reality train loading condition. The load cell of the GDS Large Diameter Cyclic Triaxial Testing System (LDCTTS) is operated by a powerful hydraulic unit, so it's possible for testing any large size of particles such as railway ballast (GDS, 2009). It is suitable to examine samples with height of 450mm and diameter of 300mm. According to work of Mitchell (2009), the 2:1 height to diameter ratio of sample suggested by Bishop & Green (1965) can achieve minimum friction effects between sample and platen. However, the problem of this ratio is not able to achieve the required "oil flow" in order to simulate reality train loading. To achieve the same minimum friction end effect with shorter sample height (height to diameter ratio 1.5:1), silicone grease is applied to the membrane on the top and bottom platen.
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Figure â€Ž3â€‘1: Schematic of LDCTTS components (Aursudkij, 2007)
Sample is sat in the inner cell, surrounding by water that gives confining pressure. The sample is enclosed with membrane, it is used for retaining its cylinder shape and preventing water reaches the sample. Air pressure is also applied to the outer cell to maintain the test condition.
Once the equipments have been set up, water is pumped to the inner cell. Water level is allowed to reach the top neck of the inner cell, and then cross drained valve is opened to allow water enters the reference tube. Once the water in the inner and reference tube reach about the same level, water valve and cross drained valve are closed.
After the water is settling down to a stable level, test sequences are then needed to be inserted to the computer logging system in order to activate the triaxial machine.
Sample under repeated loading will be slightly deformed; these small changes will be detected by differential pressure transducer in order to calculate volume change of the sample. Axial load is measured by a 100kN external load cell at the crosshead of the triaxial machine. Axial strain is detected by an LVDT (Linear Variable Differential Transformer) which is attached to the actuator and it is able to measure a maximum axial strain of 100mm.
Uncertainty factor of the test is the volume change measured by differential pressure transducer: the dynamic loading causing momentum to the water, it's possible to make water overtopping at the neck of the inner cell. Water level must be checked regularly and any volume of overtopping water must be recorded. In some stages, the bottom ram is moved upward causing displacement of water level and this should be accounted in the value of volume change.
3.1.2 Computer logging system
LDCTTS is a computer controlled system, which allows users to set up the test procedures and collect output data. The software used in this system is called GDSLAB and it is developed by triaxial machine manufacturer GDS.
Test sequences are needed to be inserted in order to control the loading condition of triaxial machine.
This software is also used as data collector: axial displacement, axial stress, volume change, deviator stress and duration of each stage are all recorded in a file with ".gds" formal and it can be assessed by Microsoft Excel.
3.1.3 Ballast sample
Recycled ballast is examined in this project. They are smaller size, worn, dirty and poor quality crushed rocks. It is believed that the recycled ballast is collected from railway trackbed and it has been used for a long period of time. Unlike other mount sorrels, their shape are rounder and more easily to be broken.
Since there is no universal specification for railway ballast, it's free to choose any reasonable ballast grading, but the selection of grading is necessary to represent the size proportion of the raw ballast. It is also restricted to the available sieving pans in laboratory. According to the ballast's physical size and aims of this project, a smaller sample grading specification is chosen. There is a total weight of 55kg specimen for one test.
Table â€Ž3â€‘1 Sample grading specification
Square Mesh Sieve (mm)
Cumulative mass passing for one sample (kg)
Cumulative percentage by mass passing (%)
Always on Time
Marked to Standard
Figure â€Ž3â€‘2: Ballast size distribution curve
3.1.4 Geogrid Reinforcement
There are 4 types of geogrid testing in this project. The main type is the triangular shape geogrid called TriAx; the other one is the diamond shape geogrid which is made by removing one rib between two triangle apertures. Both geogrids are examined with two different sizes: TX160 and TX 130, they have different aperture sizes but they have the same tensile strengths of 20kN/m.
Figure â€Ž3â€‘3: TriAx Geogrid (Tensar TriAxTM, 2010)
Triangular design providing high strength and stiffness.
Stress is equally distributed to six ribs with isotropic property.
Giving aperture /particle size ratio of 1.12:1 for smaller size and 1.82:1 for larger size.
Figure â€Ž3â€‘4: Diamond Geogrid
Diamond shape design providing larger aperture size to give better interlocking ability to greater size of particle.
Stress distribution become unbalance as ribs were removed.
Tensile strength is possibly reduced.
Giving aperture /particle size ratio of 2.5:1 for smaller and 4:1 for larger size.
3.2.1 Sample preparation
3.2.1.A Ballast Sieving
Before any tests begin, ballast must be sieved into the correct grading specification by using a sieving machine. This machine contains several different aperture size of sieving pans and it is capable to vibrate itself with a timing ability.
Raw sample from Lafarge Aggregate contains 1 tonne of recycled ballast, these samples are manually carried to the sieving machine and sieved to the correct particle grading. Ballast is then put in the brackets and labelled, then they will be mixed together in correct proportions according to the sample specification as stated in table 3-1. To ensure well-distribution of sample, mixing is taken place on the floor using a shove. Weighting is done after the mixing process to ensure no significant weight loss.
Plate â€Ž3â€‘2: Sieving machine
3.2.1.B Building a specimen
After the ballast sieving, the sample is then filled in a metal mould (450mm height x 304 diameter) with a membrane (2mm thickness) encloses to the inner side. The mould is carried by a lifter fork to the top of a vibrating table and ready for vibrations. Sample vibration is divided into 3 stages; this is done by the ballast is filled to 1/3, 2/3 and top of the total height, vibrating table is activated and a surcharge of 20kg is placed on the top of specimen to enhance the compaction. This process allows particles to be compacted and settled. The purpose is to reduce void ratio in the specimen and maximise the initial sample density. After the final vibration, ballast in the top layer may be removed or replaced for a level surface. Not all of the 55kg sample is used for the specimen, excess materials are weighted and subtract from the initial mass to get the final mass of specimen. Finally a top platen with two circular membrane sheets is placed on the top to seal the specimen.
Specimen and the mould are then carried to the triaxial workshop. The next process is sealing the specimen, orings are fastened the membrane on the top and bottom pedestal. It is then sealed by both fastening tape and clips on these orings.
Vacuum is applied to the specimen through the drainage tube. This removes air pressure in the specimen and allows the membrane to support the sample itself. After 15 minutes of suction, the mould can be removed and allows to check any damages and punctures on the membrane.
The inner cell is then placed over the specimen and bolted to the base. Following the inner cell, the outer cell is carried by a lift fork and is placed over the inner cell and bolted. The process must be done by 2 people or more for carefully positioning not to cause any damage to inner cell.
Plate â€Ž3â€‘3: Inner cell
Lift fork then carries the entire cell base to the loading rig. Lower the crosshead on the top and connect to the loading ram. At the same time, all the connections must be done including the water pipe, transducer, air supply and bolts at the rigs. Vacuum can now be replaced by the air supply. The air supply in the test is 30kPa.
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The test is now ready and it is left for a whole night to allow everything is settled down and operate the test in the next day.
Plate â€Ž3â€‘4 Outer cell and connections
3.2.1.C Water supply and final check
As stated in section 3.1.1, water is filled to the inner cell. A drained tube is directly connected to specimen. Any water leaks into the specimen will come out from the drained tube. The membrane failure causes the water leaks in and contaminates the sample. Water contamination would make the sample less stiffness and totally alter the results. For this reason, drain tube is necessary to be checked regularly during the test.
3.2.2 Sample Testing
A 1kN of seating load applying to the specimen in order to let the loading ram touching the specimen. Let the water level reaches the scale at the neck of the inner cell and waits for the reference tube reaches approximate the same level, then close the cross drained valve and differential pressure transducer will be activates. Zero the value of volume change and axial displacement in GDSLAB. Test is ready to begin.
Insert the test sequences in GDSLAB and then LDCTTS is operated. Test sequences in this project follow the work of Ferguson (2008) and Mitchell (2009). All data is set to be collected in every 5 seconds. Test sequences of this project are found in Appendix 3. A brief description of the test stages is stated as following:
The test starts with load cycles 1 to 5 and cycles 6 to 30, these two stages are relatively slow and it's frequency only allows the system to be run as advance loading with a sinusoidal control instead of dynamic loading. From cycles 31-100, 181-200, 481-500, 981-1000, 4981-5000, 9981-10000 and 49981-50000, each stage contains only 20 cycles. These stages have a loading frequency of 0.2Hz which allows the volume change to be stabilised, as suggested by Aursudkij (2007). Following the slower stages, load cycles 101-180, 201-480, 501-980, 1001-4980, 5001-9880 and 10001-49980 are relatively faster stages with a loading frequency of 4Hz. Each stage contains more cycles. A higher frequency allows more load cycles to be run in a possibly shorter period of time.
According to Aursudkij (2007), axial displacement of the specimen should not excess 12% of its original height. Otherwise, the specimen could possibly touch the inner cell wall causing collapse of the inner cell.
3.3 Results and Analysis
Data in the test is collected in every 5 seconds, but not all of the data is used for analysis. Only cycles 10, 20, 50, 100, 200, 500, 1000, 5000, 10000 and 50000 are plotted in the figures. Load cycles can be found by calculating time spend on one cycle for each stage. There are 5 specimens examined in the project: 2 unreinforced samples (Unreinforced 1 and Unreinforced 2), 1 small TriAx, 1 large TriAx and 1 small diamond. The geogrids in these samples are located in the 150mm and 300mm of the specimen height (450mm). Initially it is planned that there will be 7 tests in total, but accidentally the inner cell of the triaxial machine broke after 5 tests and it's not possible to continue. The other two non-examinable samples are 1 large diamond and 1 for the best performance geogrid to be placed in the mid depth.
3.3.2 Sample density
It's not possible to keep sample density consistent for each test, it's because of the irregular particles shape and different particle arrangement.
Figure â€Ž3â€‘5: Effect of initial sample density on total permanent axial strain
Figure â€Ž3â€‘6: Effect of initial sample density on permanent axial strain from cycles 100 - 50000
Figure â€Ž3â€‘7: Void ratio against sample density
The figure 3-5 shows the effects of initial sample density on total axial strain, as seen in the figure, it's not possible to see any linear relationship as Unreinforced 1 has the peak total permanent strain. This is because the figure is not purely shown the relationship between permanent strain and sample density, geogrid reinforcement also has influence on the permanent strain.
The figure 3-6 shows the effects of initial sample density on permanent strains from cycles 100-50000. By ignoring the first 100 cycles, a roughly linear relationship is shown; The smaller the sample density, the greater the permanent strain is.
The figure 3-7 shows a perfect linear relationship between void ratio and sample density.
3.3.3 Deviator stress and axial strain
Figure 3-8 is a figure of deviator stress against axial strain for small TriAx shape geogrids. As shown in the figure, hysteresis loops are formed for each load cycle. Area under the hysteresis loop represents the energy loss during the loading, and this energy is used to make strain. The figure also indicates that the size of hysteresis loops getting smaller for the subsequence load cycles. This shows that energy loss in the earlier cycles are greater than the later cycles so that earlier load cycles contribute greater permanent strain.
Figure â€Ž3â€‘8: Multi-hysteresis loops for Small TriAx geogrid
3.3.4 Permanent strain
Figure 3-9 shows the total permanent strain against number of cycles for 5 different specimens. It clearly indicates that Unreinforced 1 and Unreinforced 2 have greater total permanent strain than other samples with geogrids reinforcement.
Figure 3-10 shows the same graph with logarithmic scale, each sample roughly has linear relationship after the cycles 100. For further analysing, figure 3-12 is plotted by ignoring the effects made by the first 100 load cycles.
Figure â€Ž3â€‘9: Total permanent axial strain against the number of cycles
Figure â€Ž3â€‘10: Total permanent axial strain against the number of cycles in logarithmic scale
Figure â€Ž3â€‘11: Total permanent axial strain against the number of cycles for geogrid-reinforced samples
Figure â€Ž3â€‘12: Permanent axial strain from cycles 100 to 50,000 against number of cycles in logarithmic scale
Figure â€Ž3â€‘13: Total permanent axial strain against aperture size/particle size ratio
Figure â€Ž3â€‘14: Total permanent radial strain against the number of cycles in logarithmic scale
3.3.5 Resilient Modulus
To calculate resilient modulus: the values of volume change, axial strain, volumetric strain and axial force are required. However, the loading ram motion at the inner cell is also needed to be taken account. The calculation steps are followed the work of Mitchell (2009) to work out the resilient modulus.
1) Calculate the volume change with the effect of loading ram:
= the adjusted value of volume change which takes account of the loading ram moving up (m3)
= the values of volume change from differential pressure transducer (m3)
= the cross sectional area of loading ram (m2)
= axial displacement of the specimen (m)
2) Calculate the axial and volumetric strain of the specimen:
= absolute axial strain (%)
= axial displacement of the specimen (m)
= initial height of the specimen (m)
= absolute volumetric strain (%)
= adjusted values of volume change (m3)
= initial volume of the specimen (m3)
3) Calculate maximum, minimum and average values for axial strain and volumetric strain for cycles 10, 20, 50, 100, 200, 500, 1000, 5000, 10000 and 50000:
= resilient axial strain
= maximum absolute axial strain
= minimum absolute axial strain
= resilient volumetric strain
= maximum absolute volumetric strain
= minimum absolute volumetric strain
4) Calculate Resilient Modulus:
Mr = Resilient Modulus (MPa)
Favg = Average axial force in a load cycle (N)
A0 = initial cross sectional area of specimen
= average axial strain in a load cycle
= average volumetric strain in a load cycle
Figure 3-15 shows the trend of resilient modulus for all 5 specimens. Apart from Unreinforced 1, other specimens are more consistent, they are more likely falling into a small range. As figure shows, resilient modulus has became consistent as more load cycles applied to the sample.
Figure 3-16 shows the relationship of resilient modulus and total permanent axial strain. Sample with lower total permanent strain is likely to have a greater resilient modulus.
Figure â€Ž3â€‘15: Resilient Modulus against the number of cycles
Figure â€Ž3â€‘16: Resilient Modulus against total permanent axial strain
3.3.6 Poisson's Ratio
Poisson ratio can be calculated by using the following formula:
Figure 3-17 shows the trend of Poisson's ratio for 5 specimens. The results of 5 specimens are within -0.5 to 0.5, they are falling into the range apart from the Unreinforced 1 in which there may be mistakes made in the test.
Figure â€Ž3â€‘17 Poisson's ratio against the number of cycles
3.4 Discussion of Results
This section will analysis the results from pervious section, as figures shows, the output results are reliable and definitely can demonstrate the performance of different types of geogrids. Apart from the results of Unreinforced 1, which is more likely a trial test, is not reliable. However, results of Unreinforced 2 is more reasonable and it can represent unreinforced sample. The following content will discuss the behaviour of ballast with and without geogrids under repeated loading.
3.4.1 Behaviour of ballast under repeated loading
184.108.40.206 Permanent deformation
220.127.116.11.A Permanent Axial Strain
Permanent axial strain of the sample is caused by ballast re-orientation (particles slipped) and ballast breakage. Figure 3-9 shows the permanent axial strain against the number of load cycles. It can be seen that permanent strain increased with more applications of load cycle, but the scale of x-axis is too great to see the trend developed before load cycles of 10000.
For this reason, figure 3-10 and figure 3-12 show the same results with logarithmic scale, and it can be seen that there is a linear relationship between the permanent axial strain and number of cycles after 1000th load cycle. The results agree with the work of Mitchell (2009). If the specimens can be examined for further load cycles up to the maximum of 100,000. It is predicted that the output results will follow the same pattern.
18.104.22.168.B Permanent Radial Strain
Figure 3-14 shows the total radial strain against the number of cycles in logarithmic scale, and it can be seen that there is a roughly linear behaviour. This is because the particles under repeated loading are re-orientated themselves, larger size of particle tries to squeeze in a smaller gap between other particles. This action causes more particles re-orientation and these particles are forced to push outward against membrane to result more radial strain.
3.4.2 Resilient Behaviour and Poisson's ratio
22.214.171.124 Resilient Modulus
Figure 3-8 shows deviator stress against permanent strain with a line represents a load cycle. It is clearly to see that hysteresis loops are formed in the figure. Area within the loop represents energy loss during the load cycles, the energy used in load cycles results to permanent strain. It can be seen that the area within the loop is smaller as more applications of load cycles.
Figure 3-15 shows resilient modulus against number of load cycles. It can be seen that resilient modulus is increased with more load cycles before the 100th cycle. After that, resilient modulus becomes consistent and this agrees with Hicks (1971).
More plastic strains are resulted from the beginning where the condition is less resilient modulus, but as more application of load cycles, the samples become more elastic. Therefore, resilient modulus increases and this parameter can be regarded as the indicator of the elastic property of granular materials.
Figure 3-16 shows resilient modulus against total permanent strain of 5 samples. Apart from the result of Unreinforced 1, it can be seen that the greater permanent strain results in lower value of resilient modulus. As suggested before, lower value of resilient modulus means that the material is behaving plastically and resulting more permanent unrecoverable axial strain.
It is summarised that there are many factors can affect the results of resilient modulus, as proven by Lekarp et al. (2000a): stress level, sample density, number of load cycles, confining stress, aggregate type and particle size & distribution. However, in this project, the application of geogrid in the sample also gives influence on the resilient modulus.
126.96.36.199 Poisson' ratio
Poisson's ratio, v can be represented by the following formula:
is the radial strain of the specimen
is the axial strain of the specimen
Poisson's ratio is the ratio of radial strain to axial strain, Gercek (2007) states that the value of Poisson' ratio of a stable and elastic behaviour should have a range between -1.0 to 0.5. The results of Poisson's ratio in the project agrees the statement of Gercek (2007) but have conflict with Mitchell (2009). The values of Poisson's ratio from each specimen are consistent throughout the test.
3.4.3 Sample density
Figure 3-5 shows that there isn't any linear relationship between sample density and total permanent axial strain. However, this figure cannot be used to determine the influence of sample density on permanent strain. It's because every test has different geogrid reinforcement which it also has influence on the permanent axial strain. Therefore, figure 1 cannot fully represent the relationship.
Figure 3-6 shows the same results but ignoring the first 100th load cycles, as the early load cycles are treated as "bedding in" stage, suggested by Mitchell (2009) and Ferguson (2008). It is said that specimens become more stable after this stage, and the results are more reliable to be used for comparison. It can be seen that looser sample density has higher permanent strain.
Figure 3-7 shows void ratio against sample density. It is observed that they have a perfect linear relationship, higher void ratio means more gaps between particles. Therefore, the number of particle contact points is decreased, then less stress path means there is a higher stress level apply to each particle contact point. This action is resulting more particles breakage and re-orientation in the specimen.
3.4.4 Geogrid reinforcement
Both figure 3-9 and figure 3-10 show total permanent axial strain against number of load cycles with and without geogrid reinforcement. It can be clearly seen that specimens with geogrid reinforcement definitely have lower total permanent axial strain than unreinforced specimens.
As suggested before, sample density could influence the results, so figure 3 is produced to reinforce this statement by plotting permanent axial strain against load cycles of 100 to 50,000, as the first 100th cycles are regarded as "bedding in" stages. Apart from Unreinforced 1 which it may be regarded as wrong results, it can be seen that Unreinforced 2 has the highest permanent axial strain of all.
The results agree the works of Mitchell (2009) and Ferguson (2008), both works state that geogrids have efficiently improve the long term settlement in ballast layer. However, the results slightly disagree the statement of Mitchell (2009) and McDowell & Stickley (2006) which is "geogrids offers minor improvement on weaker materials".
As figure 3-10 shows, the best performance of geogrid gives at least 4% of axial strain reduction on total permanent axial strain and gives 0.15% of axial strain reduction from load cycles 100 to 50,000. This is because Unreinforced 1 and Unreinforced 2 have higher total permanent strain, so any improvements from geogrid are marked. However, further tests are required to support this argument.
Figure 3-14 also supports the results, geogrid has effectively improved radial strain of the specimens. Geogrid-reinforcement is successfully stopping particle re-orientation.
The best performance of geogrid is small diamond shape. The effects of geogrid shape and aperture size will be discussed later in this section.
3.4.5 Aperture size of geogrid reinforcement
Figure 3-11 shows total permanent axial strain against aperture/particle size ratio for 3 geogrid-reinforced specimens. It can be seen that they have linear relationship and diamond shape geogrid with 2.5:1 of aperture/particle size ratio has offered the best improvement. Due to the equipment failure, no further tests can be done. But the results of Mitchell (2009) states that aperture/particle size ratio of 2:1 is better than 3.4:1. This suggests that any larger aperture size will not have any better improvement than the ratio around 2.
Specimen with small diamond geogrid, has the highest initial sample density and lowest permanent axial strain in the test. It can be said that this geogrid offers the best improvement because of the contribution of the highest sample density. However, this statement does not being supported by figure 3-12 with the removal of the strain gained in the first 100th load cycle. It is believed that after "bedding in" stage, samples are being compressed into a more stable state. In figure 3-12, it can be seen that Small Diamond has the lowest rate of permanent strain increment.
3.4.6 Number / Position of geogrids
Due to equipment failure, it's not possible to examine specimens with geogrid-reinforced in the mid layer. According to the work of Mitchell (2009), specimens with two layers of geogrid reinforced in 1/3 and 2/3 height have better improvement of axial strain and radial strain than specimens reinforced in the mid layer. Further tests are required to carry out to support this statement for weaker sample.
The initial objective of this project is to use LDCTTS (Large Diameter Cyclic Triaxial Testing System) to investigate the influence of geogrid-reinforcement on railway ballast under repeated loading. The results from this project are used to compare with the work of Audley (2010), Mitchell (2009) and Ferguson (2008) with sample grading and geogrid. Sample used in this project is worn, small and weak ballast, and it is predicted that geogrid will offer minor improvement on weaker material. Initial sample density, different shape & aperture size of geogrid and position / number of geogird will also being investigated. However, equipment failure after 5 tests of weak materials and it's not possible to continue any further tests. Conclusion can be only made from 5 tests.
3.6 Results and Summary
Initial sample density has great influence on total permanent axial strain: Dense samples have less permanent axial strain and loose samples have higher permanent axial strain. This results also agree after "bedding in" stages.
The rate of permanent strain gains in the first 100th load cycles (bedding in stages) is higher than the rest. Permanent axial strain has linear relationship with number of cycles after 1000th load cycle in logarithmic scale.
Unreinforced specimens in this project have higher total permanent axial strain than other materials.
Samples with geogrid reinforcement have lower permanent axial strain than unreinforced samples. It is shown that placing geogrids in the specimen has significant improvement on the samples. It is also found that geogrid has also improved radial strain.
Small diamond shape of geogrid has the best performance of the others. It has aperture / particle size of 2.5:1, which is better than small TriAx with ratio of 1.12:1 and large TriAx with ratio of 1.82:1.
Resilient modulus represents the elasticity of the materials. Samples with higher resilient modulus behave more elastically. Resilient modulus increases initially as more applications of load cycles, then this value will become consistence after load cycles of 1000. Higher resilient modulus results in less plastic strain. This cannot apply to Unreinforced 1 as the values of volume change for this specimens are likely incorrect.
Poisson's ratio sits between -0.5 and 0.5. These values are consistence through the application of load cycles except the results of Unreinforced 1.
It is concluded that results in this project cannot be used to compare the work of Audley (2010), Mitchell (2009) and Ferguson (2008). It's because these three projects used different ballast and different grading specification. Additionally, there are only 5 tests performed in this project. Conclusion is restricted to limit number of tests. The only possible conclusion is geogrid with small diamond shape has the best performance on poor quality ballast (mount sorrel) with grading stated in table 3-1.