Figure 2.3 illustrates the general stress regime experienced by an element of material in or below a pavement structure as a result of a moving wheel load within the plane of the wheel track, that is, the longitudinal plane. There are pulses of vertical and horizontal stress accompanied by a double pulse of shear stress with a sign reversal on the vertical and horizontal planes. Figure 2.4 shows the associated pattern of principal stresses illustrating the rotation of principal planes which takes place. Performance tests in the laboratory are those which attempt to reproduce the field situation. Clearly, for pavements this would demand complex test facilities. The Repeated Load Triaxial (RLT) (Shaw, 1980), hollow cylinder (Chan 1990) and k-mould (Semmelink et al, 1997) apparatuses can in various degrees simulate pavement loading on soils and granular materials.
Repeated Load Triaxial tests typically involve a repeated load to simulate many vehicle passes. Tests in the laboratory are usually element based where one set of stress conditions can only be tested at any one time. Therefore, to cover the full spectra of stresses that occur within the pavement many performance tests at different stress conditions are required. Wheel tracking and full scale accelerated pavement tests are also considered performance tests, but only triaxial type tests are discussed in this section.
2.5.1 Repeated Load Triaxial (RLT) Apparatus
The RLT apparatus tests cylindrical samples of soils or granular materials. Figure 2.9 illustrates a typical Repeated Load Triaxial apparatus test set up. For RLT tests the axial load supply is cycled for as many cycles as programmed by the user. The axial load type is usually programmed as a sinusoidal vertical pulse with a short rest period. Although possible for some RLT apparatuses, in this study the cell pressure was not cycled simultaneously with vertical load, but held constant. Two types of repeated load tests are usually conducted, being either a resilient or permanent deformation test. The most recent standard currently used for triaxial testing is the prEN 13286-7 (2004) Unbound and hydraulically bound
mixtures – Test methods – Part 7: Cyclic load triaxial test for unbound mixtures.
However, as triaxial testing is a research tool with the aim to simulate as closely as possible the range of conditions that will be experienced in a pavement it is common for a researcher to vary from this standard to assess material characteristics at other loading and environmental conditions expected in-service.
The resilient test determines the resilient (or elastic) modulus and Poisson’s ratio (only possible if radial strains are measured in the test) for a full range of vertical and horizontal (cell pressure) combinations.
In a RLT test the principal stress in the x and y direction is the cell pressure and in the z direction the principal stress is the cell pressure plus the applied axial stress (as cell pressure acts all over the specimen including the top). Figure 2.10 shows the stresses acting on a RLT specimen during a test. The resilient test provides the elastic parameters needed for mechanistic pavement design (Section 2.2.2).
During a RLT test vertical stress, cell pressure, radial and vertical displacement on the specimen are recorded. The difference between the maximum and minimum displacement divided by the length over which this occurs gives the strain. Two types of strain are recorded: elastic/resilient (Equation 2.21); and permanent/plastic (Equation 2.22).
Resilient or elastic strain (ε) is defined by:
( ) ( )
(
1)
01− − ∆ = N p N L L ε ε Equation 2.21Permanent strain (εp) is defined as:
( ) 0 L LTotal p ∆ = ε Equation 2.22 where,
L0 = original specimen length (height or diameter);
∆L(Total)= total plastic change in specimen length or difference in length from original length;
∆L(N) = resilient/elastic change in specimen length for N cycles; and
N = number of cycles.
Resilient modulus is then calculated by dividing the applied vertical deviator stress by the resilient strain for a constant cell pressure test (Equation 2.23). The Poisson’s ratio is defined by Equation 2.24. Noting the minimum axial strain after each load cycle gives the permanent axial strain result for a test in which σd changes. Resilient Modulus: a d r M ε σ = Equation 2.23 Poisson’s ratio: a r ε ε υ = − Equation 2.24 where,
σd = maximum cyclic deviator axial stress
εr = radial strain; and
εa = axial strain.
The resilient modulus of a material according to 3-D Hooke's law equation is given by:
(
)(
)
(
d d)
r d r d d d d r M 3 3 3 1 1 3 1 3 1 2 2 σ ε σ σ ε σ σ σ σ − + + − = Equation 2.25 where,Mr = calculated equivalent E-modulus (MPa);
ε1r = measured axial resilient strain (µm/m);
ε3r = measured radial resilient strain (µm/m);
σ1d = difference in maximum and minimum principal axial stress (kPa); and
σ3d = difference in maximum and minimum principal radial stress (kPa).
This assumes the material behaves linear-elastically for any individual stress stage.
For unbound granular materials it is usual to report resilient modulus versus bulk stress as the material’s stiffness is highly stress-dependent. Established research (Hicks and Monismith, 1971) suggests a general relationship between these parameters as defined by Equation 2.27 (Section 2.7).
For a permanent deformation test at least 50,000 loading cycles are applied at one set of vertical and horizontal (cell pressure) combination. The amount of permanent strain versus load cycles is plotted. Currently, there is no standard method to interpret the result of the permanent strain test. Often a judgement is made as to whether the result is acceptable or not for the test stress level.
A major step towards implementation of the Repeated Load Triaxial test has been the standardisation of the test by various organisations worldwide such as CEN (2004), Australia Standards (1995) and AASHTO (1994). These test methods give a description of equipment, specimen preparation procedures and testing procedures.
The limitations of the RLT test are that only two of the maximum of six stress components are varied independently for complete general conditions (Hyde, 1974; Pappin, 1979; Chan, 1990). Only the vertical and horizontal stresses can be applied and this simulates the situation when the load is directly above the element. Principal stress rotation (Section 2.4.1) that occurs in a pavement from a passing wheel load cannot be duplicated in the Repeated Load Triaxial apparatus and is therefore a limitation of its ability to fully simulate vehicle loading.
2.5.2 K-mould Apparatus
The K-mould apparatus is the same as the RLT apparatus described in Section 2.5.1 except the confinement is achieved by elastic springs. Springs push cell walls against the cylindrical specimen with the effect that the lateral restraint increases as the granular specimen is being loaded vertically. Material parameters such as stress dependent elastic modulus and Poisson’s ratio, cohesion and friction angle are determined from a single test specimen (Semmelink and de Beer, 1995). Springs containing the specimen give a controlled elastic modulus (or spring constant) in the horizontal or radial direction, E3 and confining stress (σ3) is determined by multiplying the elastic modulus by radial strain (ε3):
σ3 = - E3 ε3 Equation 2.26
2.5.3 Hollow Cylinder Apparatus
The Hollow Cylinder Apparatus (HCA) is similar in principle to the Repeated Load Triaxial apparatus accept this device rotates principal stresses and as such better simulates actual stresses in the pavement under vehicle loading. Confining stress and an axial deviator stress can be applied in the same way as the RLT test (Section 2.5.1). However, it is also possible to apply a torque and vary the pressure in the centre of the cylinder from that outside the cylinder (Thom, 1988; Chan, 1990). Application of a torque generates shear stresses on the horizontal and vertical planes in the wall of the cylinder, whereas variation of internal pressure imposes variation in circumferential stress (Figure 2.11). While this improves the reproduction of the pavement stress state, it makes for a much more complex and expensive test. Also, as the wall thickness of the cylinder is 28mm this limits the maximum particle size to 4mm. Thus, tests cannot be carried out on most pavement materials at their normal gradings. However, Thom and Dawson
(1996) found that particle size did affect the magnitude of the strain but the form of the behaviour was similar.