Abstract
Resilient modulus, , is an important parameter for designing pavements. However, its determination by resorting to cyclic triaxial tests is tedious and time consuming. Moreover, empirical relationships, correlating to various other material properties (namely, California Bearing Ratio, CBR; Limerock Bearing Ratio, LBR; R-value and the Soil Support Value, SSV), give vast variation in the estimated results. With this in view, an electronic circuitry, which employs bender and extender elements (i.e., piezo-ceramic elements), was developed. Details of the circuitry and the testing methodology adopted for this purpose are presented in this paper. This methodology helps in determining the resilient modulus of the material quite precisely. Further, it is believed that this methodology would be quite useful to engineers and technologists for conducting quality check of the pavements, quite rapidly and easily.
1. Introduction
Resilient modulus, , generally corresponds to the degree to which a material recovers from external shock or disturbance. This property of the material is actually an estimate of its modulus of elasticity, . In case of slowly applied load, slope of the stress-strain curve in linearly elastic region yields , whereas, for rapidly applied loads (e.g., load experienced by pavements), this would yield . The resilient modulus can be expressed as where is the applied stress and is the recoverable axial strain.
describes the mechanical response of a pavement base or subgrade to the applied cyclic (traffic) load, and, hence it is considered to be an essential parameter for pavement design. By knowing the resilient modulus for the subgrade soil and the pavement material, the structural behavior of the pavement against traffic loading can be ascertained.
However, obtaining is a very difficult task, and it can only be determined by laboratory testing of the material [1β3]. As such, the Long Term Pavement Test Protocol (LTTP) P46 is widely used [1, 4, 5] for determining , which in turn requires dynamic triaxial testing on cylindrical cores. Several other (modified) methodologies such as National Highway Research Program (NCHRP) 1-28A method and Federal Highway Administration (FHWA) method (1) are also employed for determining . Various empirical relationships, correlating to other material properties (namely, California Bearing Ratio, CBR; Limerock Bearing Ratio, LBR; -value and the Soil Support Value, SSV) can also be employed to estimate . However, these relationships give vast variation between the estimated and experimental results [4β6]. In addition to the material properties, value depends upon many of the testing parameters like preparation technique, loading amplitude, sequence of loading cycle and the confining pressure. However, not much attention has been paid by the earlier researchers to corroborate laboratory results vis-Γ -vis field conditions. This necessitates development of a methodology that would yield in a convenient way without compromising the field conditions. Under these circumstances, application of a nondestructive methodology, which is based on propagation of mechanical waves, seems to be a better choice [1, 7]. In recent years, it has been found that some of the nondestructive testing methods (namely, the laser technique, ground-penetrating radar, falling weight deflectometers, mini- or portable lightweight cone penetrometers, GeoGauge, and infrared and seismic technologies) can be successfully employed for the prediction of and for the purpose of quality control and acceptance of flexible pavement construction [8]. However, some researchers [6, 9β11] have found that , determined from the laboratory testing, differs from the nondestructive testing based analysis.
With this in view, attempts were made to determine the resilient modulus of asphaltic concrete cores by employing piezoceramic elements and an electronic circuitry developed by the researchers at the Indian Institute of Technology Bombay, India [12, 13]. In addition, complete characterization of these cores was done as a part of the proposed method for determining . The result obtained from this method was then compared with that obtained from the triaxial loading testing, and it was concluded that piezoceramic elements can be successfully employed for determining resilient modulus in pavement designing.
2. Experimental Investigations
2.1. Characterization of Asphaltic Concrete Cores
DAC (Dense Asphaltic Concrete) and SDAC (Semi-Dense Asphaltic Concrete) cylindrical core samples for this study were obtained from the airfield pavements of the two runways of an airport in India. These cores were extracted from the wearing and binder courses of the pavements of these runways. Density-void analysis, Marshall Stability, and Flow value tests were carried out on these cores as per ASTM D6927 [14], and the results are depicted in Table 1.
The Marshall Stability value of the DAC and SDAC specimens, when tested at 60Β°C, were found to be 765βkg and 725βkg, respectively. The flow value of the SDAC specimens was found to be on the higher side as compared to that for DAC samples. The average bulk density of the DAC and SDAC specimens was found to be 2.36 and 2.33βg/cc, respectively. The stiffness modulus of the mix was determined based on the parameters of the mix (namely, density, air voids, aggregate voids filled with bitumen, and bitumen content), the properties of the bitumen (namely, penetration, softening point, temperature susceptibility, penetration index, and specific gravity), and the properties of aggregates (namely, specific gravity) by using the Shell nomograms [15], as listed in Table 1. The gradation curves for the samples are depicted in Figure 1.
2.2. Measurement of Shear and Compression Wave Velocities
To determine the shear and compression wave velocities ( and , resp.), a simple and cost-effective bender element setup developed by the authors [12, 13] was employed. Signal interpretation and analysis of the results has been done in accordance with the information available in the literature [16β18]. The block diagram of the test setup for measuring and in the cylindrical asphaltic concrete cores has been depicted in Figure 2. As depicted in the figure, on both ends of the specimen, piezoceramic elements (the pair of a transmitter and a receiver) can be fitted. The transmitter is excited with a single-cycle sine wave of certain amplitude, which is generated from a function generator. The receiver is connected to a filter/amplifier circuitry, which in turn is connected to a digital oscilloscope that also receives a direct sine wave or a step signal from the function generator.
Bender elements used in this study were procured from the Centre for Offshore Foundation Systems, The University of Western Australia. These elements were constructed by bonding two piezoceramic materials together in such a way that a voltage applied to their faces causes one face to expand while the other face to contracts. This causes the entire element to bend and generation of a voltage and vice versa. As depicted in Figure 3, the receiver and transmitter bender elements consist of series and parallel bimorph configurations, respectively. The bender elements in Figures 3(a) and 3(b) were subsequently used as extender element, thus producing , by inter changing the wiring configurations and direction of polarization, as shown in Figures 4(a) and 4(b).
(a)
(b)
(a)
(b)
For determining the time delay introduced in the measurements due to the electronics, ceramics, and coating materials of the bender element, calibration of the complete system was conducted. This was achieved by placing the tips of the two bender elements in direct contact with each other and measuring the calibration time between the electrical pulse sent to the transmitter and received by the receiver. It was found that the magnitude of is very small (=5βΞΌs). In addition to this, for an aluminum rod (160βmm Γ 25βmm Γ 25βmm), a thermocol (82βmm diameter and 62βmm length) and a M-30 grade concrete (50βmm diameter and 67βmm length), was also measured [11]. To achieve this, thin slits (about 1.6βmm wide and 11βmm long) were created at the centre of each of the two planes, which are perpendicular to the length of the aluminum bar or concrete block. Later, in these slits, which are parallel to each other, bender elements were fitted. For these materials, was found to be 3217βm/s, 280βm/s and 1500βm/s, respectively, which match very well with the values reported in the literature [19]. Moreover, and were measured on some standard materials. Using (2), [20, 21], Poissonβs ratio, , when computed for rubber, stainless steel, and cork was found to be 0.5, 0.29, and 0, respectively, matching well with the results in literature [22β24] where is ratio between and .
Later, and in the DAC and SDAC specimens were measured. A typical waveform obtained for the DAC specimen is depicted in Figure 5.
2.3. Loading Test
A Humboldt, USA, made master loader system (HM 3000) was used for determining . This setup facilitates microprocessor-based stepper motor speed control and consists of analogue-to-digital converter with real-time data acquisition; the motor speed can be selected between 0 to 75βmm/min, with RS-232 interface.
Load was applied on the specimens with the help of computer-controlled user defined test setup program. Before loading the specimens, strain rate was set to 25βmm/min and stop condition was set to: βload exceeding 18βkN,β which is based upon the possible elastic modulus values for these samples. Deformation undergone by the specimens was recorded every 1βs by employing a Linearly Variable Differential Transducer (LVDT), connected to the computer controlled user defined setup. Each load cycle followed a time lag of 10βs during which unloading was done. A total nos. of 35 loading cycle was applied to each specimen.
3. Results and Discussions
Low strain shear modulus, , and elastic modulus, , in the specimens were computed as follows [20, 21]: Where is the mass density of the specimen. for the samples was obtained from (2) by using and .
A typical stress-strain curve obtained for a DAC specimen is depicted in Figure 6(a). Figure 6(b) exhibits the variation of stress and strain during the loading process. It can be observed from these figures that the variations in these parameters are quite similar to the variation of load and deformation, with time [25]. It must be noted that this concept is widely used for determining resilient modulus by dynamic triaxial testing and applying a haversine pulse loading. Hence, it is believed that the resilient modulus determined by this method would represent the same situation when axle load passes over the pavement.
(a)
(b)
Recoverable axial strain for the specimens was determined as depicted in Figure 6(b) and using this value, the resilient modulus was determined by using (1). The value of shear, elastic, and resilient modulli are listed in Table 2.
The relationships between with and has been depicted in Figure 7. As suggested by earlier researchers [20, 26], / and, hence, , for a particular type of material (namely, asphaltic concrete, cement concrete or a particular type of rock) remain the same. Hence, can be correlated to both and , as these two parameters are interrelated by , which is a function of and (ref. (2)). The relationships obtained between these parameters can be expressed as
(a)
(b)
This indicates that in an asphaltic concrete pavement can be predicted easily with the help of piezoceramic element by measuring and .
4. Conclusions
This paper presents details of a novel methodology, which employs piezoceramic elements for determining resilient modulus of the dense and semi-dense asphaltic concrete blocks. It has been demonstrated that this methodology yields results in a very short duration and also without employing costly paraphernalia. The results obtained are found to be quite close to those obtained from conventional cyclic tests. However, extension of this methodology to in-situ conditions requires further investigations.
Nomenclature
| : | elastic modulus |
| : | shear modulus |
| : | low-strain shear modulus |
| : | resilient modulus |
| : | calibration time |
| : | shear wave velocity |
| compression wave velocity | |
| : | recoverable axial strain |
| : | mass density |
| : | applied stress |
| : | Poissonβs ratio. |