Indirect diagnosis of pavement structural damages using surface GPR reflection techniques

Journal of Applied Geophysics 62 (2007) 107 – 123 www.elsevier.com/locate/jappgeo

Indirect diagnosis of pavement structural damages using surface GPR reflection techniques A. Benedetto ⁎, S. Pensa Department of Sciences of Civil Engineering, University of Roma Tre, via Vito Volterra 60, 00146, Rome – Italy Received 7 November 2005; accepted 1 September 2006

Abstract The safety and operability of road networks is, in part, dependent on the quality of the pavement. It is known that pavements suffer from many different structural problems which can lead to damage to the pavement surface. To minimize the effect of these problems programmed policies for pavement management are required. Additionally a given local anomaly on the road surface can affect the safety of the road to various degrees according to the category of the road, so it is possible to set up different programmes of repair according to the different standards of road. Programmed policies for pavement management are required because of the wide structural damage which occurs to pavements during their normal operating life. This has consequences for the safety and operability of road networks. During the last decade, road networks suffered from great structural damage. The damage occurs for different reasons, such as the increasing traffic or the lack of means for routine maintenance. Many forms of damage, originating in the bottom layers are invisible until the pavement cracks. They depend on the infiltration of water and the presence of cohesive soil greatly reduces the bearing capacity of the subasphalt layers and underlying soils. On the basis of an in-depth literature review, an experimental survey with Ground Penetrating Radar (GPR) was carried out to calibrate the geophysical parameters and to validate the reliability of an indirect diagnostic method of pavement damage. The experiments were set on a pavement under which water was injected over a period of several hours. GPR travel time data were used to estimate the dielectric constant and the water content in the unbound aggregate layer, the variations in water content with time and particular areas where rate of infiltration decreases. A new methodology has been proposed to extract the hydraulic permittivity fields in sub-asphalt structural layers and soils from the moisture maps observed with GPR. It is effective at diagnosing the presence of clay or cohesive soil that compromises the bearing capacity of sub-base and induces damage. © 2006 Elsevier B.V. All rights reserved. Keywords: Ground penetrating radar; Pavement damage; Pavement management; Water content; Hydraulic permittivity

1. Introduction All over the world, in industrialized as well as in developing countries, the road networks suffer from significant structural damages for a variety of reasons, such as the increasing traffic and the lack of means for ⁎ Corresponding author. Tel.: +39 06 55173543; fax: +39 06 55173441. E-mail address: [email protected] (A. Benedetto). 0926-9851/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jappgeo.2006.09.001

routine maintenance (i.e. Shahin, 1994; Aultman-Hall et al., 2004; Robinson and Thagesen, 2004). This fact has important consequences as far as driving safety is concerned, since the damage of pavements creates significant risks for drivers (PRIN, 1999; Tighe et al., 2000; Guell et al., 2003). Several recent initiatives were therefore taken in order to recover the functionality of the road network both in the EU, in the USA and many industrialized countries.

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The traditional approach to the Pavement Management System (PMS) consists of the ability both to determine the current condition of a pavement network and to predict its future performance. The use of the Pavement Condition Index (PCI) has received wide acceptance and has been formally adopted as standard procedure by many agencies worldwide (Cuvillier et al., 1987; Shahin, 1994). However, because PCI was originally developed to describe the structural condition of pavement and road, it totally neglects the effect of pavement damage on driving safety. This is also the case with other similar diffused “mechanically based” approaches. As will be later discussed, new trends have been developing that take into consideration the fact that pavement damage is not critical by itself but only if it becomes dangerous for driving. For example, the damage is dangerous when rutting is so deep that, during a period of rain, the water film is so thick that skid resistance drastically decreases. Moreover, the same damage can be dangerous on motorway and secure on an urban road because the operating speeds are different. These facts are usually neglected under a traditional PCI approach. The current limits of PCI can be summarized as follows: (i) it gives aggregated information about the pavement condition unless considering a specific type of damage, (ii) it provides no information on the causes of the damage, (iii) it cannot suggest any rehabilitation action, but only the need for rehabilitation, (iv) it can assume the same value for damaged pavements that are visually similar but that can be distressed in completely different ways and for completely different causes, (v) it does not predict the evolution of the pavement performance, (vi) it does not consider the effect of damage on driving safety. Other quantitative indexes have been proposed, such as the International Roughness Index (IRI) or the Skid Number (SN), in order to quantify specific defects of the pavement. They seem to be more useful to identify the impact on safety and the best rehabilitation action, although they only measure the effect of the defect and give no information about the causes. Road damage reveals itself in several ways. Superficial anomalies are clearly visible, yet damage that begins from deep layers, such as sub-base, becomes visible only later when the pavement has completely failed. These phenomena are always irreversible and appropriate repairs are expensive. Structural damage in road pavements is frequently directly connected with the percentage of moisture in its deepest layers or in the sub-grade soils. Water infiltration and clayey soil pumping is one of the most important cause of the decrease of bearing capacity of the unbound

layers (Kelley, 1999; Rainwater et al., 2001; Al-Qadi et al., 2004; Zuo et al., 2004, Diefenderfer et al., 2005). Bearing capacity can be defined as the ability to carry a defined number of repetitions of a set load. Rational design methods are used in order to understand the stress and strain conditions due to the action of loads and temperature changes. In fact, the entity of strain generates the rate of onset of fatigue and the phenomenon of the accumulation of permanent strains. To characterize the elastic behaviour of the subasphalt unbound layers, pavement engineers usually refer to the resilient modulus. The resilient modulus only considers the completely given strain; this is the ratio between the stress applied and the strain returned (i.e. Hicks, 1970; Rahim and George, 2005). Since the status of stress in the aggregate layer varies in relation to the bearing capacity of the sub-grade, programmed policy could be inadequate or useless if we do not assess the effectiveness accurately. Road engineers have tools for local diagnostics (such as core sampling). Yet these diagnostic tools are destructive, expensive and slow, and Administration Agencies cannot manage the local road network using these destructive tools alone, especially when studies have to be repeated periodically to update database and covering areas of thousands of km. The most commonly used non destructive method to estimate the bearing capacity of a sub-grade is the Falling Weight Deflectometer (FWD), which is used to assess the elastic modulus of the sub-grade and the aggregate layers (Mehta and Roque, 2003). Measurement of soil water content is also important because as it increases, stiffness decreases, therefore the strains increase. A widely used method to measure soil water content, bulk electrical conductivity, and deformation of rock is based on Time Domain Reflectometry system (TDR). TDR measurements are non destructive and offer excellent accuracy and precision: it is the analysis of a conductor (wire, cable, or fiber optic) by sending a pulsed signal into the conductor, and then examining the reflection of the pulse (Weiler et al., 1998). FWD and TDR methods for inspection of wide roads are not generally efficient in terms of time and cost. Moreover, as moisture in sub-grade is not spatially homogeneous, these methods are limited because they provide only local measurements and cannot be used in wide areas. On the contrary, GPR systems are suitable to the aim, in fact they are non destructive and quick if used large scale. To obtain significant measurements non-local studies are needed. This is because moisture conditions change

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continuously both spatially and temporally. GPR allows quick measurements and obtains data that reflect the real physical conditions of the sub-grade soil. This paper aims to provide a tool that can directly aid the planning of an optimum maintenance regime for roads. 2. GPR inspection GPR is a diagnostic non destructive technology based on the transmitting/receiving of a given frequency electromagnetic signal. The analysis of phase, frequency and amplitude differences between the transmitted and the received signal gives information about the electromagnetic properties of the media through which the signal is transmitted, reflected or scattered. The electromagnetic property most commonly measured is the dielectric constant (ε). The reflected impulse is received through antenna(s). The radar impulse is reflected or scattered by any electric anomaly that is present in pavement and subasphalt layers. Analytically the received signal y(t) can be modelled in time domain as the sum of multiple scaled and delayed replicas of the transmitted pulse signal plus noise. The considered model follows the general equation (Wu et al., 1999): yðtÞ ¼

I X

ai hðt−si Þ þ eðtÞ

ð1Þ

i¼1

where h(t) is the transmitted signal, y(t) is composed of I replicas of h(t) with different amplitudes {ai}i=1,I and delays {τi}i=1,I and e(t) is the random noise. Numerical processing (generally in frequency domain) removes the spurious reflections' noise and extracts information about the phase and frequency of each replica. The time delays depend on the layer thickness, according to Eq. (2). So layer thickness (r) can be computed from the delays (Δt), while the frequencies of the replicas (radar cross section variation) give information about the shape of the interface (Benedetto et al., 2004). Assuming the velocity v for signal transmission in a generic dielectric media, Eq. (2) computes the layer thickness: r¼

md Dt 2

ð2Þ

where v can be estimated with the following equation: c m ¼ pffiffiffi ε

ð3Þ

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where ε is the dielectric constant and c is the free space electromagnetic wave propagation velocity. GPR (see Davis and Annan, 1989; Daniels, 1996 for a comprehensive introduction to the subject) is used often to infer the volumetric water content of soils in unsaturated porous media. Unbound layers of a pavement are composed of such a media. It is a mixture of three phases (solid, water and air), which are characterized by significantly different dielectric constant (or relative permittivity) ε. Air has a dielectric constant of 1, aggregate from 3 to 8 and water 81 (Daniels, 1996). Thus, the dielectric constant of the mixture is highly sensitive to water content, that explains the success of GPR inspection. GPR non-invasive measures of water content in soils have many applications in civil and environmental engineering, such as the characterization of hydraulic parameters in environmental, engineering, and agricultural subsurface investigations (Hubbard and Rubin, 2000, Serbin and Or, 2003) and in soil characteristics interpretation for the classification of pavement damage in roads management (Smith and Scullion, 1993; Saarenketo et al., 1994; Scullion et al., 1994; Maser, 1996; Saarenketo and Scullion, 2000; Benedetto and Benedetto, 2002; Hubbard et al., 2002; Grote et al., 2002, 2003, 2005), to cite a few. The relation between the dielectric constant of soils and their volumetric water content has been extensively studied in the past and various empirical relations have been proposed. Topp et al. (1980) suggested one among the more commonly used ones, which is supposed valid for any mineral soil material. However, the relationship is not entirely appropriate for moisture estimation in unbound layers of a pavement, because it was developed and validated on different soils and in approximately uniform moisture distributions: h ¼ 4:3d10−6 e3 −5:5d10−4 e2 þ 2:92d10−2 e−5:3d10−2

ð4Þ

where θ is the volumetric water content in soil and ε is the dielectric constant. A more theoretical approach to relate soil water content and permittivity is based on dielectric mixing models, which use the volume fractions and the dielectric permittivity of each constituent soil to derive an approximate relationship (e.g., Alharthi and Lange, 1987; Roth et al., 1990; Du and Rummel, 1994; Greaves et al., 1996; Van Overmeeren et al., 1997; Saarenketo, 1998; Friedman, 1998; Huisman et al., 2003; Robinson et al., 2003). More recently the EMA (Effective Medium Approximation) model has been experimentally validated by Fiori et al.

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(2005) and it is here assumed together with Topp equation. EMA equation here follows h¼

ðew þ 2eef Þtðea þ 2eef Þðeef −es Þ þ 3eef Wðes −ea Þb 2eef ð2eef þ es Þðew −ea Þ ð5Þ

The three phases j are characterized by dielectric constants εs, εw, εa: εs is the dielectric constant of the solid, εw of water and εa of air. εef is the dielectric constant of the mixture of phases, generally denoted as the effective dielectric constant or the effective permittivity. The relative volume fractions are ns = 1 − ψ (solid volumetric fraction), nw = θ (water volumetric content), na = ψ − θ (air volumetric fraction); ψ is the soil porosity, and θ is the water content, defined as volume of water per bulk volume. 3. Framework for an innovative method to diagnose early pavement damage Pavement structural damages are often not visible until pavement cracks or fails. Often damage affects the sub-base from the bottom and the structural failure propagates to the top. When the pavement finally cracks the cost of repair increases while the efficiency of repair decreases. It is not easy to diagnose the cause of the damage when it is visible. In fact the same damage can be generated by several different causes. If the cause is not correctly diagnosed any rehabilitation could be ineffective or effective for only a short time period as they only treat the symptoms rather than the cause. The type of damage investigated here is structural damage, generated by water and plastic soil infiltration in sub-asphalt layers. This kind of damage, known in pavement engineering as pumping, is frequent in pavement designed on clay soils or on soils with clay fractions. A methodology is proposed to predict this damage before it becomes visible and to diagnose the most probable cause of it. By detecting the damage early, this strategy increases the efficiency and the effectiveness of the repair. The proposed method is based on Ground Penetrating Radar inspection and considers two-dimensional analysis of moisture distribution under pavement. The methodology, its accuracy and reliability has been experimentally tested. Road unbound materials have to have very good mechanical characteristics to bear the repeated heavy set load. This implies that clay and plastic soil fractions

have to be absent from soils. Then, the hydraulic permittivity of sub-base and sub-grade after compaction is generally good and water infiltrates both as a pure infiltration of gravitational water and as suction by capillary forces. It is generally accepted that moisture content variation depends on the cycles of repeated loads increasing the pore water pressure. Generally, drying and wetting should not impact on bearing capacity of unbound layers and in this sense it has to be clear that high or low permeability of layers does not influence the bearing capacity of the structure. In any case it may happen that clay or fine soil fractions are transported by water in the unbound layers, causing a high risk of plastic deformation under repeated cycles of loading. This damage becomes visible only after a wide corruption of the road structure and pavement. This produces unsafe driving conditions and consequently the cost of repair gets high. Briefly the philosophy behind this method can be summarized as follows: It is known that: – structural damage of pavement is frequently caused by water and plastic soil infiltration in sub-asphalt layers, – structural damage is not visible until the pavement cracks and consequently repair costs get high, – groundwater and rain infiltration depend on the permeability of sub-asphalt layers, pavement permeability, initial conditions (i.e. initial moisture, initial hydraulic permittivity) and boundary conditions (i.e. hydraulic permittivity of soils and pavement, drainage systems, rain intensity), – infiltration can be studied according to the hydraulic laws If we assume that: – all the boundary and initial conditions are known, – the spatial distribution of moisture under pavement is known at a specific time instant Therefore – it is possible to invert the hydraulic laws of infiltration to extract the spatial distribution of the hydraulic permittivity from the moisture distribution, – knowing the hydraulic permittivity distribution characteristic of the unbound layer, it is possible to diagnose accurately if cohesive soil has penetrated the sub-asphalt layers.

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The hypotheses may be expressed by the following formal equation: Hðx; y; tj Þ ¼ F½Hi ðx; yÞ; Ki ðx; yÞ; Kðx; y; tÞ; IðtÞ; RðtÞ; Dðx; yÞ

ð6Þ

where the spatial distribution of moisture Θ(x,y,tj) (averaged in depth z, for a thickness comparable to the thickness of sub-asphalt layers, i.e. sub-base and sub-grade) at the time tj depends on the initial moisture Θi(x,y), the initial hydraulic permittivity Ki and the permittivity K(t) at the time t; it also depends on the infiltration I(t) from the bottom and on the rain R(t) from the top as well as on the drainage system D(x,y). The thesis is formally expressed by the following equation, that is the inversion of Eq. (6): Kðx; y; tÞ ¼ F −1 ½Hðx; y; tj Þ; Hi ðx; yÞ; IðtÞ; RðtÞ; Dðx; yÞ ð7Þ Two points have to be considered before problem solving: (1) the distributions of moisture at the time tj and at the initial time have to be known as do the infiltration, rain and configuration of drainage system, (2) the function F has to be defined and it must be invertible. As discussed in chapter 2 the prediction of moisture in soil from GPR inspection has been investigated and numerous models to calculate water content from di-

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electric permittivity have been developed and validated. Here two models will be considered: the Topp equation (Topp et al., 1980) and the EMA (Fiori et al., 2005). The function F can be analytically defined only in very particular conditions, such as a homogeneous and isotropic domain, validity of Darcy hypotheses (Darcy, 1856). Also, if a defined function F exists, it is not always possible to invert it. This makes the solving of the problem difficult and in most cases impossible through traditional mathematical processes. Here a methodology is suggested utilising the Monte Carlo process (Von Neumann and Ulam, 1945; Metropolis and Ulam, 1949; Von Neumann, 1951). The basic idea is to assume numerous different values for the function K(x,y,t) and, knowing the boundary and initial conditions, to simulate the water infiltration in sub-asphalt layer. If we assume N values Ki(x,y,t) the outcomes of simulation yield N values for Θi(x,y,tj). Defining an objective function OF as the absolute value of the difference between simulated moisture field and observed moisture field, the problem is now to find the minimum of OF: OFk ¼ jjHk ðx; y; tÞ−Hðx; y; tÞjj

ð8Þ

The hydraulic permittivity field Km(x,y,t) for which OFm is minimum is assumed as the best approximation of the real field of permittivity. If the number of different functions N tends to infinity the numeric solution is a field of permittivity that is compatible with the observed moisture field and it is assumed to be a good approximation of the real one.

Fig. 1. Conceptual procedure for structural damage detection using GPR and inverting the moisture distribution.

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A standard software package was used for simulation of two-dimensional infiltration of water in soil. This software will be discussed later. The conceptual procedure is illustrated in Fig. 1. 4. Experimental approach After much laboratory research designed to assess the reliability of moisture prediction using GPR (Benedetto, 2004; Benedetto and Benedetto, 2002), three different experiments in real scale have been developed and are presented here. Two were developed to calibrate the methodology and the other was developed to validate the procedure. The first two experiments were performed on the same existing pavement assuming different conditions of water injection. The final experiment was developed on another existing pavement to check the applicability and reliability of the procedure.

The calibration experiments were performed on an existing pavement which had been used for a long time as a store for industrial works with heavy vehicles, loading and unloading blocks of granite causing substantial dynamic stresses and strains. The road has no hydraulic protection (gutters and other systems of drainage). For the calibration models two different hydraulic loading conditions have been considered. Firstly an injection of water in one point at constant hydraulic load and secondly an injection of water at multiple points at constant hydraulic load. The injection schemes will be described later. The validation experiment was performed on an analogous pavement where the condition following rainfall was assessed. The main difference being this pavement had hydraulic drainage to a manhole and an urban sewer. For validation the condition after a rainfall has been assessed. Details follow in next chapter.

Fig. 2. Scheme of the survey grid for calibration experiments and location of the 10 drilled cores.

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Fig. 3. Section of the pavement interested with the calibration survey and a core sample.

4.1. Experimental configuration For calibration experiments a section of pavement 2 m × 4 m has been identified and a regular grid with a step of 0.5 m has been traced (Fig. 2). After the experiment the pavement was cored in 10 points to provide a reliable assessment of the layers (Fig. 2). The layers thicknesses are not perfectly homogeneous over the section of pavement and the average vertical profile is shown in Fig. 3. The pavement has, on average, 20 mm of asphalt overlay, 60 mm of asphalt bound binder layer, 100 mm of

asphalt bound base and a maximum 100 mm of unbound base of gravel and sand (loose soil), which has a permeability about 10− 1 mm/s. The sub-grade is an alluvial soil which has a permeability about 5·10− 4 mm/s. Grading of sub-base material and sub-grade material is shown in Fig. 4. 4.1.1. First calibration experiment First of all a radial symmetric domain has been investigated. The scheme of the infiltration system is shown in Fig. 5a. Some measurements were made before starting

Fig. 4. Sub-asphalt grading: sub-base (k = 10− 1 mm/s) and sub-grade (k = 10− 4 mm/s).

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Fig. 5. a and b : Schemes of infiltration system of the two calibration experiments.

the experiment to test the ability of GPR to collect accurate data about the pavement's stratification: three longitudinal and five transversal measurements were made. The infiltration system consists of an 18 mm diameter hole, approximately 150 mm deep, drilled through the whole first layer to the permeable layer, where the water was injected. The water was injected at a constant hydraulic head of 0.7 m (Fig. 6a). The GPR thickness prediction corresponded with the cores and the error was always less than 5%. According to previous results (Fernando and Maser, 1991; Roddis et al., 1992) the reliability depends on the thickness and the constituent material of the layers. 4.1.2. Second calibration experiment The infiltration system consisted of five 18 mm diameter holes, approximately 150 mm deep, drilled through the whole first layer to the permeable layer, where water is injected at a total head of 2 m, to ensure that water reached every hole. A breather pipe was created to remove any surplus air from the holes. The

holes were drilled on a longitudinal line of the grid. The scheme of infiltration system is shown in Fig. 5b. This configuration is not symmetrically radial but it simulates the infiltration of water from a linear bound. This experiment accurately simulated the infiltration of surface water through a cracked, damaged pavement layer by means of five simultaneous points of injection and enabled us to study the consequences of this phenomenon into sub-grade, sub-base and base. We set up the grid using some pipe-unions to create an infiltration system starting from the tank, that represents the main fuel pump again. This survey is set up as the first one: there is an electronic balance to control the weight of the tank as infiltration goes on, but the observation points have been set on four transversal scan lines, parallel to the infiltration line, as shown in Fig. 6b. 4.1.3. Validation experiment The validation experiment was carried out at a different site. The pavement profile and sub-grade was approximately the same of the calibration experiments. The GPR survey was carried out on a pavement area

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Fig. 6. a and b: Infiltration system configuration and flow direction in the two calibration experiments.

8 m × 6 m wide. A regular 2 m square grid was traced. The radar scan followed this grid to test 6 transversal sections and 4 longitudinal sections. The road is located within the University campus. Fig. 7 shows the map of the site. The boundary conditions are characterized by a vegetated pervious slope on one side of the road, the other side is impervious and a manhole of urban sewer is located approximately next to the side of the area for the drainage of surface and ground water.

4.2. Experimental procedures: data acquisition and processing Ground-coupled Radar antennas (RIS/MF system produced by IDS S.p.A., Italy) were used for GPR analysis (Fig. 8). GPR operates with two antennas with central frequencies about 600 and 1600 MHz (Benedetto et al., 2004). GPR measurements are developed using 4 channels, 2 mono-static and 2 bi-static. The received signal is sampled in the time domain at dt =

Fig. 7. Map of the validation experiment site (direction of sub-asphalt expected hydraulic flow).

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Fig. 8. GPR on the work site.

7.8125 × 10− 2 ns. GPR data were collected at 600 MHz frequency, while 1600 MHz frequency to verify the thickness of the thinnest layers. 4.2.1. First calibration experiment In the first experiment GPR measurements have been ordered as follows: – – – – –

Initial scanning before infiltration (t = 0) After 5 min from the start of infiltration: holes 1 to 8 After 10 min from the start of infiltration: holes 1 to 16 After 15 min from the start of infiltration: holes 1 to 8 After 20 min from the start of infiltration: holes 1 to 16 – After 25 min from the start of infiltration: holes 1 to 8 – After 30 min from the start of infiltration: holes 1 to 22

And so on through the whole experiment, repeating the same sequence.

4.2.2. Second calibration experiment Scans were carried out every 10 min, which was the minimum time step for a continuous scan over the entire grid, as shown by the scheme in Fig. 6b. This time step makes it possible to have a more complete collection of data. On every transversal line nine main points have been selected, with a 0.25 m spatial gap between them. After the first transient hour from the start, it was realized that soil was soaking a constant flow, which is a volume of 0.5 L/10 min. During the 5 h of infiltration the soil had absorbed about a hundred litres of water, which indicates a high permeability soil. 4.2.3. Validation experiment Finally in the case of the validation experiment no forced injection of water was developed, but “natural” infiltration of rain from the boundary was considered. The pavement was surveyed using GPR before and after 2 days of intense rain (about 25 mm). The variation of the moisture field on the grid has been calculated.

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4.3. Experimental results Data processing led to very interesting results, as shown here. 4.3.1. Calibration experiments Fig. 9 shows the different radargrams obtained on the same road section at different time after starting the injection of water. As water content in sub-base layer increases the average dielectric permittivity increases. The effect is that the propagation velocity of the electromagnetic wave in the layer is lower as the infiltration proceeds. The consequence is that the delay in time of signal reflection increases, and the layer appears thicker. Of course it is not a real effect but apparent because the thickness is constant the factor that changes is ε. Dielectric permittivity can be calculated by inverting Eqs. (2) and (3). Water content is calculated from the average value of permittivity using Eqs. (4) and (5). Maps in Figs. 10 and 11 clearly prove the ability of GPR to detect the presence of water within the subasphalt layer and to follow its path as infiltration proceeds. The scale shows the moisture percentage reached within the layer compared to the initial configuration, therefore it can be seen how water distribution is changed during the surveys in the two calibration experiments. Each figure is relative to a different time t from the start: a section of the plan of the experimental grid is shown,

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where the points are the injection points. Axes represent the distance expressed in meters. 4.3.2. Validation experiment Maps in Fig. 12 show the moisture field before and after the rain. A significant increase (about 10% on the average) of water content in sub-base is evident. The spatial distribution of moisture remains the same. As discussed later, this constant spatial distribution depends on the fact that the boundary conditions are also constant. 4.4. Inverting the moisture map As discussed in Section 3, the final problem is the solution of Eq. (7). According to the methodology presented in Section 3, VS2DTI software (Model for simulating water flow and solute transport in variably saturated porous media) has been used to simulate the infiltration in sub-asphalt layer of the pavement, under numerous different distributions of hydraulic permittivity. VS2DTI is a graphical user interface for simulating water and solute transport through variably saturated porous media with the computer program VS2DT (Healy, 1990; Lappala et al., 1987). It is a finite-difference model to simulate water and solute movement through variably saturated porous media. It has been applied in a variety of fields (for

Fig. 9. Radargrams of the same road section at different time during water injection (second calibration experiment). It is clear as the radar signal delay increases to the final Δt. The variation of ε can be calculated inversing Eqs. (2) and (3) as ε = (0.5 Δtc / r)2 and moisture from Eqs. (4) and (5).

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Fig. 10. Spatial distribution of variations of moisture in sub-base layer from the beginning of the experiment (t = 0) to the end of water injection (first calibration experiment); the grey scale shows a variation of moisture from 0 to about 2%.

example, McCord et al., 1997; Halford, 1997) and it can be assumed as an international standard. The approximating equations solved by VS2DT are based on Richard's equation (Richards, 1931) for flow and the advection–dispersion equation for transport. The adopted procedure to solve Eq. (7) is developed in four main steps. First of all the two-dimensional domain of investigation has been numerically generated in terms of boundary conditions, initial conditions, soil characteristics (porosity, grading, etc.). The soil characterization is defined according to the proven ground from soil cores. Secondly a set of hydraulic permittivity functions Ki(x,y) has been synthetically generated assuming the expected value of Ki(x,y) according to the soil type and the data from literature. The set used for simulation is 200 different fields of permittivity. Third 200 simulations have been implemented to calculate the field of moisture under the pavement Θi(x,y,tj).

Finally the value of the objective function OFi from Eq. (8) has been computed for the 200 outcomes and the most approximated field of hydraulic permittivity results. The most approximated field of hydraulic permittivity applies to the minimum value OFmin = min {OFi}. The case of the best approximated solution is shown in Fig. 13. Fig. 13 shows the values of observed moisture extracted from GPR maps and calculated averaging the value from Eqs. (4) and (5) over 16 points versus the simulated moisture values obtained using VS2DT, for the same points. The difference between simulated and observed data is always less than 10% and it decreases with time when the values of moisture increase to a homogeneous field. 5. Discussion and conclusions These experiments have shown that GPR can be used as the main technique for an innovative method in

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Fig. 11. Spatial distribution of variations of moisture in sub-base layer from the beginning of the experiment (t = 0) to the end of water injection (second calibration experiment); the grey scale shows a variation of moisture from 0 to about 6.5%.

pavement diagnostics. In detail, the experiments proved that it is possible to estimate the volumetric water content in sub-asphalt layer with a high resolution in space (10− 1 m) and in time (101 ÷ 2 s). Using a Monte Carlo procedure it is possible to simulate the infiltration from the top and from the bottom of the pavement considering numerous fields of hydraulic permittivity. Boundary and initial conditions are imposed according to the known site conditions and the soil characteristics can be determined from samples. Extracting the most approximated field of hydraulic permittivity is essential to diagnose the presence of plastic soil intrusion or discontinuity of the sub-asphalt layer characteristics. A discontinuity of hydraulic permittivity

is likely to identify a decrease of the potential bearing capacity that can evolve to cause damage to the pavement. In fact after compaction unbound layers generally have a homogeneous porosity and a homogeneous hydraulic permittivity (values from 10− 4 to 10− 1 mm/s are frequent). If permittivity locally decreases it is likely due to the consequence of fine soil intrusion such as clay or silt (permittivity decreases to 10− 6 mm/s or less), this intrusion of cohesive material may cause reduction of bearing capacity. In other cases it can also happen that hydraulic permittivity locally increases, generally as the consequence of larger voids or cracks (permittivity increases to 10 mm/s or more), this also has a significant impact on bearing capacity.

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Fig. 12. Validation experiment: absolute moisture fields before and after the rainfall; the grey scale shows a variation of moisture from 15 to about 40%.

The results of the calibration experiments show conclusively that through GPR inspection the water infiltration path can be followed with time. In the first experiment (Fig. 10) infiltration proceeds following a diagonal path with a relatively slow effective horizontal speed (approximately 1 m/2 h). In the second experiment, the water follows the same diagonal direction confirming a partially, heterogeneous, distribution of hydraulic permittivity (Fig. 11). The effective horizontal speed of water in the sub-asphalt layer is approximately the same as the first experiment. Moreover the second experiment shows zones in which infiltration speeds decrease and moisture does not change significantly. The sampled cores show a variation of thickness for pervious sub-asphalt layer about 10− 2 m in agreement with the observed moisture fields. In particular, along the diagonal direction of flow the pervious layer (k =

10− 1 mm/s) between asphalt base and sub-grade (k = 10− 4 mm/s) is about 10 mm thicker rather than the orthogonal direction. It is of great importance to note that knowing the moisture distribution in the sub-asphalt layer is not a sufficient condition to diagnose an eventual anomaly of soil characteristics. In fact, the moisture distribution is the final consequence of both the hydraulic permittivity distributions and of the boundary and initial conditions. According to Eq. (6) moisture content depends on permittivity, both as rainfall, as infiltration and the boundary conditions. The same moisture field in the sub-base layer can be the consequence of a particular permittivity distribution associated to particular boundary conditions and hydraulic forcing. It may also be the consequence of a different permittivity distribution associated to a different boundary conditions or hydraulic forcing.

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Fig. 13. Comparison between observed (from GPR) and simulated (from VS2DT) moistures during time in calibration experiments.

For example, a confined dry zone under pavement (1) can be the consequence of the intrusion of clay that defines an impervious section where water infiltrates very slowly and the zone appears to GPR as dry, or (2) it can be the consequence of a very pervious area located under the sub-asphalt layer that drains down rapidly. Analogously a confined wet zone under pavement (1) can be the consequence of the intrusion of clay that determines an impervious section where water stays for long time before drying and the zone appears to GPR as wet, or (2) it can be the consequence of a very pervious area located under the sub-asphalt layer where the water drains faster through it rather than around it. The validation experiment (Section 4.3.2) is very interesting from this point of view. In fact the moisture field both before and after rain is not homogeneous but a drier zone is well diagnosed. This anomaly is present both before and after rainfall, notwithstanding the fact that the absolute value of water content increases over all the domain. The simulation identified that this particular distribution of moisture should be expected due to the presence of a manhole of the urban sewer which drains in a privileged direction the water coming from the pervious slope on one side of the road. According to this boundary condition the most approximated solution obtained with Monte Carlo procedure for the hydraulic permittivity field is largely homogeneous. The implications on pavement management are relevant. It is important to point out that the application of this technique on large scale, extended to the road network level, introduces efficiency in planning the rehabilitation actions. In fact, the application of the presented method along hundreds kilometres of road network needs

only the time of survey at traffic speed (from 40 to 90 km/ h) and the time of numerical processing of maps, to extract the values of dielectric constant, to map the moisture field and consequently, to diagnose unexpected variations of the value of hydraulic permittivity. Assuming that the unexpected variation of hydraulic permittivity can be induced by plastic soil intrusion in unbound layers, it is considered as a possible early warning of bearing capacity reduction. Under such an assumption, this process makes possible to select the road sections which should be considered as critical. Destructive analysis and traditional point located measurements can be implemented only to the selected road sections with two main benefits. Firstly a relevant financial benefit considering that the traditional measurements are much more expensive and the survey duration is enormously longer, and secondly a more significant result because GPR investigation can be considered continuous whereas the traditional measures are discrete. Such an approach based on detection of critical sections of the road and assuming those sections as candidate for successive in depth investigations has been evaluated in previous researches and the effectiveness has been calculated and discussed (Benedetto et al., 2004). The financial resources for pavement management are usually underestimated in many countries. This implies the need for a selection of priorities. The proposed method identifies probable critical conditions of road and it greatly helps the management agencies to allocate the main expenditures for more expensive in depth analysis and successive rehabilitation. This approach is also effective for damage that cannot yet be seen at the surface. This is crucial to prevent cracks, holes and other defects on the road surface that could be unsafe for driving.

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Although this proposed method appeared to work well in three experimental cases, for the application on a large scale (road network surveying) some considerations follow. For large scale surveying, the procedure should not be considered as a deterministic method to accurately investigate the sub-asphalt layer and consequently to diagnose structural damages. It is instead a method to identify over hundreds kilometres of roads the site where damage is most likely. However it may be used to constrain the locations of traditional tests to those locations where a probable critical situation has been diagnosed. Secondly, for a survey of hundreds kilometres of road, the problem solving of Eq. (7) cannot be efficiently approached under a Monte Carlo procedure. It means that empirical models for estimation of expected moisture distributions under specific boundary conditions have to be implemented. In general, if the boundary conditions are known (for example drainage systems configuration, road section and profile, side slopes and permeability, etc.), these models are not complicated and the expected distribution of water content in sub-asphalt layers can be easily predicted coherently by the hydraulic laws. Finally a more adequate configuration of GPR should be implemented as suggested also by Grote et al. (2005). In particular the use of a single, lower frequency antenna instead of a multi-frequency one is suggested. It may cause a little decrease of accuracy but a significant increase of the speed of data collection and a better depth penetration. Acknowledgements This work has been carried out also thanks to Romana Conglomerati Bituminosi s.r.l., that supported the authors for the destructive measurements, and Ingegneria dei Sistemi S.p.A., that supports and cooperates with the authors for GPR surveys. Special thanks to Spartaco Cera, who greatly and very generously supported the authors during all the experimental phases. The authors are particularly grateful to Prof. Carlo Benedetto and Prof. Maria Rosaria De Blasiis, who contributed to the success of this research indicating the most interesting and promising applications. Special thanks to Alex Lee for assisting with the translation and organization of the paper. Finally the authors thank Prof. Aldo Fiori for the interesting discussions during the development of this study. References Alharthi, A., Lange, J., 1987. Soil water saturation: dielectric determination. Water Resour. Res. 32, 591–595.

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