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Factors Controlling Deformation Under Repeated Loading .1 Influence of Loading Conditions (level, sequence, frequency)



2.4.7 Factors Controlling Deformation Under Repeated Loading .1 Influence of Loading Conditions (level, sequence, frequency)

There is enough evidence to show that both the residual deformation (ORE, 1970;

Knutson, 1976; Siller, 1980; Stewart and Selig, 1984; Shenton, 1985) and the resilient modulus of granular media (Hicks and Monismith, 1971; Kalcheff and Hicks, 1973;

Brown 1974; Thompson, 1989; Zaman et al., 1994; Kolisoja, 1997) are highly dependent on stress. The use of test devices providing a higher confinement level during the tests resulted in a lower rate of development of plastic deformation (Knutson, 1976; Raymond and Davies, 1978; Jeffs and Marich, 1987). It was reported that for similar test conditions, confining pressures and number of load repetitions, the higher the ratio between the applied repeated stress and failure stress from monotonic tests the

Chapter 2: Critical review of granular media with special reference to railway ballast

higher the rate of accumulation of residual strains (Olowokere, 1975; Knutson, 1976;

Raymond and Davies, 1978, Profillidis, 1995). Shenton (1985) also reported that the remanent strain after the first load application was always larger if the applied stress was higher. These correlate with the field observations by Feng (1984), Bathurst and Raymond (1994) and Sato (1995) that an increase in the axle load resulted in higher maintenance costs.

Research by Yeaman (1975) and Zaman et al. (1994) showed that the resilient modulus was mostly affected by the level of bulk stress. Other research (Seed et al., 1962;

Brown, 1974; Stewart, 1982; Janardhanam and Desai, 1983; Selig and Waters, 1994) reported that the resilient characteristics of various types of particulate media were also affected by the level of cyclic deviator stress and shear reversal to which the specimens were subjected, as presented in Figure 21. This contradicts the findings of Chan and Brown (1994) that the rotation of principal planes associated with shear stress reversal did not affect the resilient behaviour. However, an earlier study by Yandell (1966) reported that at higher levels of confining pressure the variation of resilient modulus with the cycled shear stress was minimal.

Shenton (1975), Siller (1980) and Stewart and Selig (1984) demonstrated that full load removal between the load cycles was associated with a higher rate of plastic strains development (Fig. 22.a, 22.b). It was also established by Stewart and Selig (1984) that if the tests were conducted with shear stress reversal, the plastic strain at the end of the first cycle was always less than without reversal, as shown in Figure 22.c.

Furthermore, O’Reilly and Brown (1991) showed that after each stress reversal the material stiffness increased dramatically and subsequently decreased (Fig. 23). At the

Figure 21. Effect of degree of unloading on resilient modulus (after Selig and Waters, 1994)

Figure 22. Strain development: (a), (b) variation of accumulation rate for tests with and without shear stress reversal; (c) representation of stress-strain curves

(after Stewart and Selig, 1984) (b)



Chapter 2: Critical review of granular media with special reference to railway ballast

Figure 23. The effect of stress reversal on soil stiffness (after O’Reilly and Brown, 1991)

particulate scale, this phenomenon could be reproduced by a model of sliding blocks linked by springs, as proposed by O’Reilly and Brown (1991) and shown in Figure 24.a. The increase in stiffness upon reversal of stress was explained by the ‘locked-in forces’ at the interparticle contacts. The higher the reversal level the higher the force unlocked, and therefore the lower the stiffness. As a consequence, during the stress cycle the specimen exhibits hysteresis, i.e. the stress sustained at any strain level of the unloading phase is lower than that at the corresponding strain during loading, the excess energy being dissipated in the form of interparticle friction (Fig. 24.b). It should be mentioned that the capacity of ballast to suppress its own vibration by absorbing energy is very important for the railway environment. Moreover, it was also found that the resilient modulus increased with the increase of stress ratio, as depicted in several models to be described in a later section (Shackel, 1973; Brown and Pappin, 1985;

Johnson et al., 1986; Tam and Brown, 1988; Uzan, 1992; Wong, 1992). Furthermore, Hicks (1970) found that the direction of resilient strain (or direction of Poisson’s ratio) was dependent on the applied stress ratio and the type of confining stress (constant or variable) findings confirmed later by Allen and Thompson (1974) and Brown and Hyde (1975).

(a) (b) Figure 24. Simple model of the behaviour of granular materials under cyclic loading: (a) conceptual model; (b) typical results (after O’Reilly and Brown, 1991)

The railway track environment is subjected to varied amplitude loads due to the complex traffic profile (passengers, freight) but also due to occasional higher dynamic loads induced by rolling-stock defects (wheel-flats). By employing multi-stage cyclic loading tests, research has shown that it is the largest applied load that controls the magnitude of ballast settlement (Birman, 1975; Klugar, 1975; Shenton, 1975; Stewart and Selig; 1984; Diyaljee, 1987). In addition, Stewart and Selig (1984) showed that, for any confining pressure, the sequence of applied stress did not affect the final value of permanent strain provided that the total number of load cycles was about the same as that of a larger load applied (Fig. 25). The additional settlement produced by the smaller loads was almost insignificant. Furthermore, Bathurst and Raymond (1994) and Selig and Waters (1994) indicated that plastic deformation after a given cumulative load (rather than number of cycles) was proportional to the peak cyclic load up to a certain breakpoint, after which the deformation increased greatly.

Studies on road base by Edwards (1986) established that the ratio of the number of cycles of a standard axle load (80 kN) to the number of cycles of another axle load

Chapter 2: Critical review of granular media with special reference to railway ballast

Figure 25. Permanent strain accumulation for different loading sequences (after Stewart and Selig, 1984)

producing the same damage was almost proportional to the axle load ratio to the fourth power. Stewart (1986) and Ford (1995) described a procedure that enabled correlation between the level of ballast settlement produced by one load to an equivalent number of cycles produced by another load. A similar method is currently implemented in Australia to estimate the cumulative number of equivalent axle load that would cause the fatigue failure of flexible pavements (Wardle, 1989, 2003).

It was suggested from field measurements on both heavy haul and high speed lines that the range of recorded frequencies could be divided into two groups depending upon their source: quasi-static values or lower frequency range up to 25 to 30 Hz which are mainly generated by the axle spacing of the bogies, and dynamic values or the structure born noise with frequencies in the 50 to 120 Hz range (Maree, 1989; Ford, 1992;

Eisenmann et al., 1994). Furthermore, Eisenmann et al. (1994) demonstrated that only the higher range of frequency specific to high-speed lines (speed > 225 km/h) would

affect the settlement of ballast. Similar conclusions were reached from experimental work on railway ballast by Shenton (1975), Jeffs and Marich (1987), Jeffs and Martin (1994) and Raymond and Bathurst (1994). In addition, studies on sand reported by Timmerman and Wu (1966) showed that the strain increased faster in the lower range of frequency (2.5 Hz) than in the higher range of frequency of load application.

Additional work by Hicks (1973) and Kalcheff and Hicks (1973) showed that the resilient modulus was insensitive to frequency and load duration, whereas Janardhanam and Desai (1983) argued that these did affect to some degree the resilient behaviour of ballast. Though, with regard to the sequence of the stresses there is a general consensus between researchers that it has little effect on the resilient behaviour of cohesionless materials (Hicks, 1973; Kalcheff and Hicks, 1973; Janardhanam and Desai, 1983).

It was also reported by Hicks (1970) and Brown (1974) that the number of load applications had little effect on the resilient behaviour of granular materials, a finding later confirmed by Boyce et al. (1976). However, work by Shenton (1975) and later by Alva-Hurtado (1980) showed that the resilient modulus increased gradually with the number of load cycles. It should be mentioned that the early findings were from well-graded road base aggregates, whereas the later research was carried out on railway ballast. Influence of Initial Density

It is well established that in addition to the applied stress, the initial density of ballast also affects the residual strain development (ORE, 1970; Olowokere, 1975; Shenton, 1975; Knutson, 1976; Raymond and Davies, 1978, Alva-Hurtado and Selig, 1981). The

Chapter 2: Critical review of granular media with special reference to railway ballast

resistance to accumulation of plastic deformation (especially in the initial stage of loading) was found to be greatly improved when high (compacted) densities were achieved (Shenton, 1975; Jeffs and Marich, 1987; Brown, 1996).

Tam (1986) showed that for dry sand, the recorded plastic volumetric strain increased in proportion to the elastic cyclic strain. Raymond (1992) and Raymond and Bathurst (1994) reported that in ballast box tests, the use of a stiffer subgrade reduced the elastic cyclic strains and resulted to lower levels of ballast settlement.

On the other hand, it was reported that the effect of density on material resilient characteristics is minimal (Brown and Selig, 1991; Selig and Waters, 1994; Zaman et al., 1994). Worth noting that these findings were of qualitative nature and the effect of density on the magnitude of the resilient modulus was indirectly accounted for.

Kolisoja (1997) expressed the density of tested materials in terms of porosity. The reported results showed that for a given material and the same set of test conditions there is a linear relationship between the concentration of solids (1-n) and the magnitude of resilient modulus. This agrees with earlier reports by Raymond (1992), Raymond and Bathurst (1994) and Sharpe (1996) and warrants the use of porosity in the estimation of plastic deformation (ORE, 1970). Influence of Material Properties

Brown and Selig (1991) stated that the intrinsic properties of materials influence the mechanical properties of a compacted layer of granular material. Earlier research by Janardhanam and Desai (1983), Thompson (1989) and O’Reilly and Brown (1991) also showed that the resilient behaviour of ballast is affected to some extent by the gradation

and grain shape, size and texture.

From repeated triaxial tests on railway ballast at a low confining pressure (35 kPa), Raymond and Diyaljee (1979) concluded that, as the maximum grain size was increased the measured shear strength increased and a lower level of plastic strains was displayed.

Selig (1985) argued that for the same type of ballast, the settlement increased as the average particle size increased. Kolisoja (1997) showed that the magnitude of the resilient modulus increased linearly with the equivalent or average particle size (Dekv) defined as:

3 D D

Dekv D10 + 50 + 90

= (2.13)

verifying earlier findings by Janardhanam and Desai (1983), although they correlated the resilient modulus to the median particle size (D50), as shown in Figure 26.

However, Zaman et al. (1994) reported a contradictory finding, that a finer gradation (eg. smaller Dmax) gave slightly higher values of resilient modulus for specimens of same size. It was also reported that a reduction in the test specimen size resulted only in a slight increase in the magnitude of the resilient modulus.

Johnson (1985) and Klassen et al. (1987) reported that broader gradations were associated with longer ballast life and lower rate of settlement. However, it was emphasized that these gradations were susceptible to rapid fouling as a result of smaller voids and a lower void ratio.

Chapter 2: Critical review of granular media with special reference to railway ballast

0 10 20 30 40

Mean grain size, D50 (mm)

0 50 100 150 200 250 300

Resilient modulus, (MPa)

σ3 = 68.9 kPa σ3 = 103.4 kPa σ3 = 137.8 kPa σ3 = 206.7 kPa

Figure 26. Variation of resilient modulus with grain size (after Janrdhanam and Desai, 1983)

Thom and Brown (1988) reported that for an uncompacted dolomitic limestone road base, it was the uniform grading which gave least plastic strains, while for the heavily compacted specimens the gradation had little influence on settlement accumulation. It was also suggested that a very high fine content could lead to sudden failure. However, according to Jeffs and Marich (1987), if the amount of fines (1-9.5 mm) added to an initially uniform gradation of railway ballast was limited to 20 %, a considerable reduction of the permanent deformations was observed. Futhermore, Ravitharan and Martin (1996) showed that, independent of ballast type, a direct correlation existed between the settlement rate and the proportion of flaky particles.

Jeffs and Marich (1987) reported from repeated loading tests performed in a semi-confined device that the recorded settlement was lower for fresh ballast containing

rough surfaced particles when compared with worn railway ballast. In addition they showed that the fine-grained, hard-mineral aggregates were associated with lower plastic deformations, results confirmed later by Greene (1990). Thom and Brown (1989) arrived at a similar conclusion that crushed road base displayed lower plastic deformation than that comprised of naturally occurring sands and gravels.

Later, research by Kolisoja (1997) showed that the resilient modulus was higher for crushed rock in comparison with crushed gravel and natural gravel, provided that the gradation and the tests conditions were the same. This agreed with earlier reports by Yeaman (1975), Thom and Brown (1988, 1989) and Thompson (1989), which showed that the stiffness of specimens increased with increasing angularity of the grains.

Furthermore, Brown and Selig (1991) correlated the increase in surface friction between angular particles with the increase in the stress ratio at failure and higher magnitude for the resilient modulus. Using this observation, Zaman et al. (1994) quantified the effect of the angle of internal friction together with other factors on the resilient modulus. In addition, Zaman et al. (1994) reported that, provided that the gradation and test conditions were the same, a significant increase (20-50%) of resilient modulus was observed as the type of material varied, ie. the lowest values were recorded for sandstone gravel, and the highest for limestone gravel with granite and rhyolite displaying intermediate values. Kolisoja (1997) confirmed that the rock type had a significant effect on the resilient characteristics of the material.

2.4.8. Empirical Models for the Strength and Deformation of Granular Media