Experimental Observation of Shakedown Behaviour in the

The test results from experimental observations by various investigators which involved a series of direct repeated wheel load or repeated load tests have shown the existence of the shakedown behaviour in pavement materials. When the applied load on the pavement surface was above the shakedown limit, the vertical surface deformation increased rapidly and caused rutting or failure on the pavement surface after a lower number of load repetitions. However, when the applied load was below the shakedown load, the vertical surface deformed initially and remained constant for a large number of load repetitions. For design purposes, this implies that the maximum shakedown limit must be known and then not exceeded, thus uncontrolled permanent deformations can be prevented.

A list of observations that involved repeated load triaxial tests and are related to the shakedown response of various types of pavement materials is shown in Table 2.1. A comparison of the deformation data under repeated stresses and the maximum compressive stresses of the test materials (s max) shows that the shakedown limit may be significantly lower than s max (see Table 2.1).

These experimental observations relate the test results with the soil compressive strength only. Therefore, the objective of the research is to compute the shakedown based numerical model that uses the soil shear

strength as an input parameter and compare the computational results with the experimental results which involves a series of direct wheel tracking tests.

Table 2. 1 Summary of experiments using repeated load triaxial apparatus associated with shakedown concept

Researches Types Observation using Repeated Load Triaxial load triaxial tests with a constant confining pressure for all the tests.

 Compacted

Lashine (1971) Varying the deviator stress under undrained cyclic

Larew and Leonards (1962) did a series of undrained repeated load tests on Piedmont Micaceous silt and coastal plain sandy clay in which the deviator stress for each test was varied and the confining pressure was constant. They only reported there was a critical value for sandy clay but no further information regarding the exact critical limit or the range for the critical limit.

However, from the plot of the deformation against number of load repetition curves for sandy clay, it seemed that the critical limit for sandy clay is ranging from 0.98 to 1.11 of _smax.

Sangrey et al. (1969) found, for various consolidation histories of saturated clay such as overconsolidated, isotropic and anisotropic normally consolidated, that the shakedown behaviour existed and varied for any consolidation history.

An extensive work on prediction of permanent deformation in soils and granular materials has been carried out in Nottingham University. Typical forms of the permanent deformation curves versus logarithmic scale of number of load applications are presented in Figures 2.3 and 2.4.

Figure 2. 3 Variation of Permanent Vertical Deformation with Number of Load Applications for the Rutting Tests carried out in the Slab Test

Facility (after Chan, 1990)

Figure 2. 4 Variation of Permanent Vertical Deformation with Number of Passes of Wheel Load for the Rutting Tests carried out in Pavement Test

Facility (after Chan, 1990)

Werkmeister et al. (2001) working on repeated load tests on granular materials reported the results by plotting the permanent vertical strain rate against permanent vertical strain accumulations. Based on the plot (see Figure 2.5), they categorised the response of the granular materials to three regions which

are region A, B and C. The granular materials with the shakedown response are categorised as in region A or the plastic shakedown range. Meanwhile, the regions B and C represent the intermediate response or plastic creep and incremental collapse respectively. Region A is for all the responses that are related to the elastic response which is initially plastic indicating the compaction period. After the post-compaction period the response becomes purely resilient. When the load increases to a certain level, the response in region B is initially plastic, then elastic for a certain number of cycles and then continues with plastic behaviour. At the region C, the response is always plastic and further load repetitions increase the permanent strain and lead to failure.

Figure 2. 5 Cumulative permanent strain versus strain rate of Granodiorite, with 3 = 70kPa (after Werkmeister et al., 2001)

Werkmeister et al. (2005) proposed a model to define the boundary of each

 3 [kPa] confining pressure (minor principal stress),

 [kPa] material parameter,

 [-] material parameter.

According to Werkmeister et al. (2005), the material parameters,  and , were likely to depend on the grading, particle shape, degree of compaction, and the moisture content of the materials.

Instead of performing the repeated load triaxial tests and measuring the permanent vertical strain, Radovsky and Murashina (1996) conducted a full-scale experiment to prove the applicability of the shakedown concept in soil under repetitive loads. The full-scale experiment was conducted on the road between Kiev and Kharkov in the Ukraine. The residual horizontal stresses were measured using pressure cells which were installed below the subgrade surface at various depths as illustrated in Figure 2.6a. Silty loam as a sub-grade layer with an initial dry density and moisture content of 1.52Mg/m³ and 15%

respectively was compacted, using a semitrailer roller with five tyres and a wheel weight of 14.8kN, to a final dry density of 1.72 Mg/m³. From the measurement results (see Figure 2.6b), they found that the residual stress

increased with the number of repetitions and reached a constant value after a few dozen repetitions. The maximum residual horizontal stress did not occur immediately below the loaded area. A comparison of the residual horizontal stresses within the soil sub-grade from the full-scale experiment measurements and a theoretical analysis model shows that the shakedown theory may apply to describe the behaviour of sub-grade soils. The theoretical analysis developed by Radovsky and Murashina (1996) will be reviewed in section 2.2.2.

Figure 2. 6 Horizontal stress distribution from full scale experiment (after Radovsky and Murashina, 1996)