Introduction

Road networks are one of the key components for the economic growth of any developed nation. The Ministry of Road Transport and Highways [1] proposes to develop various mega projects by connecting expressways/access-controlled/strategic, coastal and port connectivity highways, economic corridors, and border roads. Quality control and Quality Assurance (QC and QA) are the important criteria in order to ensure quality of construction, minimal maintenance, and long-term performance of pavements. The required degree of compaction needs to be achieved by controlling the process of geomaterials compaction in the field. Typically, this process involves the use of periodic in-situ monitoring of density and moisture, generally obtained by using destructive tests such as sand cone test, core cutter test and rubber balloon test as well as non-destructive tests (NDT) such as Moisture Density Indicator (MDI) and Electrical Density Gauge (EDG) which are tedious, time-consuming, laborious and sometimes not feasible to perform in accordance with the specifications, whereas Nuclear Density Gauge (NDG) releases gamma radiation, which causes a potential hazard to the user and frequency response of the Soil Density Gauge (SDG) will be influenced by the soil gradation (refer Table 1). Hence, the importance and usage of non-destructive test (NDT) devices based on stiffness/modulus has been increased and the success rate is in the range of 64–86%, compared to the density-based devices [2].

Table 1 Comparison of in-situ density-based devices
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The Stiffness/modulus-based NDT devices are Briaud Compaction Device (BCD), Clegg Hammer (CH), Dynamic Cone Penetrometer (DCP), and Soil Stiffness Geo-Gauge (SSGG). In addition, various deflectometer devices are available for measuring the deformation modulus of the compacted geomaterials. Those are, dropping weight deflectometer (DWD), Heavyweight deflectometer (HWD), Falling weight deflectometer (FWD), Rolling weight deflectometer (RWD), and Lightweight deflectometer (LWD). According to Ebrahimi and Edil [3], the usage of lightweight deflectometer (LWD) has been increased to evaluate the quality of any compacted geomaterial for its ease of use, portability, without interrupting the construction activities and suitable for all types of geomaterials.

In 1981, a portable dropping weight deflectometer (DWD) was first invented and developed by the Federal Highway Research Institute (FHRI) and Headquarters of Magdeburger Prufgeratebau (HMP) Company [4]. However, research within European countries has been focused on demonstrating the usefulness and reliability through field trials. The LWD currently uses technology that is similar to trailer mounted-FWD equipment, with the reduced load pulse duration and reduced maximum applied force being the first compromise in the development of the LWD device to convert into portability. An extensive study has been carried out using the LWD device on pavement structures for QC for the past three decades. The utilization of LWD device is more reliable as it provides consistent correlation and measurements [5]. A general comparison of conventional in-situ density-based devices and stiffness/modulus-based devices are listed in Tables 1 and 2 respectively. A detailed description of the LWD operating principles, strengths and limitations, has been reported in the literature [6,7,8,9]. The main focus of this study is to present the various research works carried out by using the LWD device.

Table 2 Comparison of in-situ stiffness/modulus-based devices
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Description of LWD device and operating procedure

Figure 1 shows the schematic view of LWD device with the components. The major components of the LWD device are drop weight, loading plate, and accelerometer. Initially, place the loading plate on top of the compacted geomaterials, release the drop weight along the guide rod by ensuring a standard drop height. The drop weight is allowed to drop on buffers made of either rubber pads or steel springs and deformation of the loading plate is measured with the help of an accelerometer. The first three drops are allowed for seating to enhance the intact contact between the loading plate and compacted geomaterials. The next three consecutive drops are used to evaluate the average deformation. Finally, the deformation modulus (ELWD) can be calculated by using the well-known Boussinesq’s elastic solution (Eq. 1) for the case of a rigid or flexible base resting on an elastic half-space. Table 3 presents various LWD devices and specifications which were manufactured by various agencies.

$${\mathrm{E}}_{\mathrm{LWD}}=\frac{q r (1-{\upsilon }^{2}){f}_{r}}{w}$$
(1)

where ELWD = Deformation modulus of compacted geomaterial (MPa), r = Radius of loading plate (mm), υ = Poisson’s ratio of the compacted geomaterial, fr = Plate rigidity factor (Fig. 3), w = Deformation of the loading plate measured at its center (mm), and q = Maximum contact pressure (MPa);


where;

$$\mathrm{q}=\frac{\mathrm{Applied Force }(\mathrm{F})}{\mathrm{Area of loading plate }(\mathrm{a})}$$
(2)

F = Applied force (N) and a = area of loading plate (mm2).

Fig. 1
figure 1

Schematic view of Lightweight Deflectometer (LWD)

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Table 3 Summary of specifications of the LWD devices.
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Theoretically, the applied force on a surface cannot be constant, because it clearly depends on the stiffness of the buffer material on which the load is applied (Eq. 3):

$$\mathrm{F}= \sqrt{2\mathrm{mghc}}$$
(3)

where; F = Applied force (N), m = mass of falling weight (kg), g = acceleration due to gravity, 9.81 (m/s2), h = drop height (m), and c = material stiffness constant (N/m).

Factors influencing the deformation modulus

Various parameters that influence the deformation modulus of compacted geomaterials are diameter of loading plate, plate rigidity, plate contact stress, loading rate, buffer type, location, and type of deformation transducer [7, 9]. Further details on the various factors influencing the deformation modulus (ELWD) are discussed in the following sections.

Diameter of loading plate

The diameter of loading plate is in the range of 100–300 mm (refer Table 3). Researchers (Deng-Fong Lin et al., Chaddock and Brown [6, 10]) concluded that the selection of the diameter of loading plate is a significant factor that influences deformation modulus due to the reason of depth of influence. Generally, the depth of influence is equal to 1.0–1.5 times the diameter of the loading plate. In the literature, it is reported that the decrease in diameter of the loading plate leads to an increase in the deformation modulus, due to the reason of increase in contact stresses of loading plate. Chaddock and Brown [10] conducted tests on crushed rock base and subbase materials over compacted clay materials. The deformation modulus for the 200 mm diameter loading plate was found to be 1.3–1.5 times that of a 300 mm diameter loading plate. Deng-Fong Lin et al. [6], performed field studies using the LWD device on a natural sand soil deposit and found that the estimated ELWD from a 100 mm diameter loading plate was found to be 1.5–1.6 times that of a 300 mm diameter loading plate. Vennapusa and White [9] recommended 300 mm, 200 mm, and 100 mm diameter of loading plates, for the range of ELWD < 125 MPa, ELWD between 125 and 170 MPa, and ELWD > 170 MPa respectively.

Plate rigidity

The plate rigidity factor depends on the rigidity of loading plate and type of compacted geomaterials as shown in Fig. 2. Mooney and Miller [8] reported that it might be the tendency of a soil to attain a failure where the stress distribution is uniform. Das [14] stated that it may imply some consequences of the plate rigidity, but theoretically, a flexible plate shows uniform stress distribution for a loaded clayey subgrade and a true rigid plate should not deform under a load. Various thickness of plates (refer Table 3) and their materials, which cause variations in their rigidity. Plate rigidity factors (fr) under the loading plate vary with the stiffness of the plate and compacted geomaterials. Borowicka [11] proposed an analytical solution to evaluate the relative rigidity of the plate (Eq. 4).

$$\mathrm{K}= \frac{{\mathrm{E}}_{\mathrm{p}}\left(1-{{\upupsilon }_{p}}^{2}\right)}{6{\mathrm{E}}_{\mathrm{s}}\left(1-{{\upupsilon }_{s}}^{2}\right)}{\left(\frac{{t}_{p}}{\mathrm{r}}\right)}^{3}$$
(4)

where; K = Relative rigidity of the loading plate, Ep and Es = Modulus of elasticity of the loading plate and compacted geomaterial respectively (MPa), υp and υs = Poisson’s ratio of the loading plate and compacted geomaterial respectively, tp = Thickness of the loading plate (m) and r = Radius of the loading plate (m).

Fig. 2
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Schematic view of Plate Rigidity (shape) factors (fr) [12,13,14]

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For K = 0, the contact stress distribution under the loading plate is uniform and it is considered as a flexible plate, K > 0, the contact stress distribution at the edges increases to infinity and varies at the center of loading plate, and K = ∞, the contact stress at the center of the loading plate is half of the applied stress and it is considered as a perfectly rigid plate.

Plate contact stress

The contact stress between the loading plate and the compacted geomaterials is assumed to be uniform or that of a parabolic and inverse parabolic for a rigid plate on an elastic half-space (as shown in Fig. 2). The applicability of linear elastic half-space theory to the LWD device, as well as the nature of the contact stress between the loading plate and the compacted geomaterials, must be assessed. The impact force and diameter of the loading plate are designed to deliver a peak contact stress in the range of 100–200 kPa, simulating the approximate stress pulse on a typical sub-grade or base layer caused by traffic loading on top of a finished pavement [9, 15, 17]; Nazzal et al. [16].

Most of the studies indicated that the measured deformation modulus increases with higher applied contact stress and it depends on the type of compacted geomaterials. For dense and compacted granular materials, ELWD increases with higher applied contact stress and for the materials with cementitious properties and soft subgrade soils are not influenced by change in the contact stress stated by Vennapusa and White [9]. Fleming et al. [18] found that the measured ELWD with a 300 mm diameter loading plate was increased by 1.15 times by increasing the plate contact stress from 35 to 120 kPa. Similar studies on very stiff crushed aggregate and stabilized aggregate materials shown no significant difference in the plate contact stress from 140 to 200 kPa [19].

The contact stress for the 100 mm diameter loading plate was 8–9 times that of a 300 mm diameter loading plate [6]. Bilodeau and Dore [20] conducted an experiment with both 100 mm and 300 mm diameter loading plate on Ultra High Molecular Weight Polyethylene (UHMWP) plastic material (properties similar to granular soils). The higher stresses were recorded with the 100 mm diameter loading plate. However, the contact stress distribution for the 100 mm loading plate shows flattening and/or increasing stresses near the plate edge. The assessment of contact stress under the LWD loading plate was found to be affected by the diameter of the loading plate. Hence, the contact area has a significant impact on the ELWD.

Loading rate and buffer type

The rate of loading can be regulated by changing the spring rigidity of the buffer between the drop weight and the contact loading plate and thus can affect the measured deformation modulus. Lenngren and Lukanen [21] reported that by using stiffer buffer for the case of asphalt concrete pavements, the load pulse time history was shortened and the resulting ELWD is increased by 10–20%. Lenngren and Lukanen [21] also indicated that the shape of the load pulse, its peak, and time history affects the magnitude of the measured deformations to some extent. Fleming [18] reported that a comparatively lower stiffness buffer provides more efficient load transfer and better simulates static plate loading conditions. Deng-Fong Lin et al. [6] also evaluated the effect of drop heights, concluding there was a very low impact of different drop heights on stiffness buffers.

The effect of buffer temperature and loading pulse was evaluated by Adam and Kopf [22]. ELWD was measured on the rigid laboratory floor for a fixed drop weight and height at different temperatures. Data for 10 repetitive loading has been recorded with two buffers. The applied impulse load varied approximately 30% with a change in the buffer temperature from 0 to 30 °C because the rubber buffers are slightly softened when heated due to repetitive loading because of the impact of load on the loading plate is independent of the surrounding and equipment temperature. However, it remains constant for a steel-spring buffer. Hence, the researchers recommend to using the steel spring buffers (Larsen BW et al. 2008) [23].

Location and type of deformation transducer

The various LWD manufacturers provide various transducers and their built-in position. For instance, the spring-loaded geophone is used in direct contact with the compacted geomaterial through a hole in the center of the loading plate to measure the velocity of the compacted geomaterial in Keros, Dynatest, Prima, and TFT devices as shown in Fig. 3a. Whereas, the Zorn device has an accelerometer built into the loading plate (Vennapusa and White 2009) [9] from which the readings are twice integrated to calculate deformation of the loading plate as shown in Fig. 3b. These differences seem to contribute to differences in the evaluation of loading plate deformation. The contact area of the geophone is very disturbed due to the narrow foot of the geophone, and has a relatively stiff spring buffer inside the housing to maintain contact between the geophone and the compacted geomaterials, which results in disturbance (Fleming et al. 2007) [18]. This disturbance is common on softer subgrades and some granular compacted geomaterials. However, it is not clear about the quantifying of recorded permanent deformation during the impact and effect of disturbance on ELWD. The contact area of the accelerometer loading plate has not reported any such disturbances under it, as it is built into the loading plate.

Fig. 3
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Schematic sketch of the location and type of transducer: a Geophone measures velocity and is located on the compacted material, b Accelerometer measures vibrations and is located in the plate

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Correlations and ranges of deformation modulus (ELWD)

Since LWD tests are easy and rapid to conduct, the testing period can be significantly shortened [24]. Hence, researchers proposed the correlations (refer Table 4) between measured ELWD and other parameters like density, unconfined compressive strength, California bearing ratio, etc. The deformation of modulus range varies based on the type of LWD device used and type of material. Based on available data, the typical deformation modulus reported for various types of subgrades, subbase, base layers, granular layers, and backfilling materials are listed in Table 5.

Table 4 Correlations between LWD and other devices for various compacted geomaterials
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Table 5 Typical range of deformation modulus (ELWD) for various compacted geomaterials
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Application of lightweight deflectometer

The LWD device is a new evolution through the use of its best practice and simple operating principle, moreover internationally recognized and widely accepted for infrastructural applications in recent years after being used over 34 years in European countries (i.e., Germany, United Kingdom, United States, Australia and New Zealand on a performance design basis). The several advantages of the methods are likely to benefit the sectors, such as monitoring of compaction activities of earthworks, pavements, runways, embankments, retaining walls, mechanically stabilized earth walls (MSE), landfills, compressibility of waste or contaminated land, marine works, treated and untreated soil, canal construction. In addition, a new testing procedure has been implemented to obtain direct measurements of resilient modulus (MR) of a compacted geomaterials using a simple technique and it was designed for both laboratory and in-situ testing [37]. Recent studies have been carried out based on the forward and back-calculation solutions, which are formulated as an inverse problem to match the predicted deformations to the observed deformations by using most existing techniques such as static back-calculations use regression equations that are fitted to a database of deformations by using artificial neural network system (ANNS) [38] and by employing gradient search or genetic algorithm iterative methods to minimize an objective function of any set of independent variables (i.e., thicknesses and layer moduli) [39].

The instant results of the compacted geomaterials obtained from LWD makes it an effective device and an ideal replacement, saving time and minimizing the cost. The deformation modulus value depends on various factors such as the diameter of the loading plate, drop height, contact stress, and flexural rigidity. Hence, researchers recommend that the range of deformation modulus values need to be exercised for a selected geomaterials by constructing a test pad before proceeding to the actual construction.

Conclusions

The lightweight deflectometer (LWD) device is an internationally recognized and widely used technique in infrastructural applications. The long-term performance of any project depends on the characteristics of the compacted geomaterials. This study provides a state-of-the-art resource for contractors and engineers by focusing on evaluation of deformation modulus by using various LWD devices and discussed the influence of various factors on deformation modulus. Several correlations between deformation modulus and other engineering properties of geomaterials like dry density, UCS, and CBR. Range of deformation modulus values were presented for various geomaterials. Infield, it is necessary to construct a test pad for evaluating the range of deformation modulus values for the corresponding geomaterials. It is concluded that the lightweight deflectometer (LWD) is a valuable and very effective device for monitoring the quality of construction as it is versatile, portable, can reduce duration, running cost of major projects, and it is suitable for all construction geomaterials. The LWD has to be deploy in India and other developing countries by the consultants, geomaterial specifiers, contractors, and clients to play a major role in QC/QA in ensuring the safe and solid system of transportation and long-term pavement performance along major road network corridors.