Transportation Geotechnics 1 (2014) 21–30

Contents lists available at ScienceDirect

Transportation Geotechnics

journal homepage: www.elsevier .com/ locate/ t rgeo

Estimating the coefficient of at-rest earth pressure in granularpavement layers

http://dx.doi.org/10.1016/j.trgeo.2014.01.0012214-3912/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +972 829 2809; fax: +972 829 5706.E-mail addresses: elevenbe@technion.ac.il (E. Levenberg), navneet.

garg@faa.gov (N. Garg).1 Tel.: +1 609 485 4483; fax: +1 609 485 4845.

Eyal Levenberg a,⇑, Navneet Garg b,1

a Technion – Israel Institute of Technology, Faculty of Civil and Environmental Engineering, Transportation Infrastructure Laboratory, Technion City, Haifa32000, Israelb Federal Aviation Administration, Airport Technology R&D Branch, William J. Hughes Technical Center, Atlantic City International Airport, NJ 08405, United States

a r t i c l e i n f o

Article history:Available online 21 January 2014

Keywords:Unbound granular materialAt-rest earth pressure coefficientInstrumented pavementInverse analysisLayered viscoelasticity

a b s t r a c t

Compaction of pavement layers composed of unbound granular materials increases the at-rest earth pressure coefficients. These coefficients influence the stress-state in the materialand are therefore important for modeling pavement behavior; they may also serve as indi-cators, alongside densities, of compaction quality. Given the inability of geotechnical toolsto directly measure the coefficient of at-rest earth pressure in granular pavement layers thepaper offers an estimation approach that is computational in nature. The scheme is basedon solving a multi-objective inverse problem and requires a pavement instrumented withimplanted sensors, preferably monitoring a wide variety of response types. It also requireslaboratory resilient modulus information of granular specimens compacted to in situ den-sities. In order to demonstrate the computations, a simplified version of the method isapplied to an airport pavement system tested in an accelerated loading facility. Post-construction at-rest earth pressure coefficients of the base and subbase layers arequantified and evaluated for reasonableness. It is concluded that the approach, even inits simplified form, is capable of producing realistic estimates.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Pavement layers made of unbound granular materials(UGMs) are mechanically compacted in-place by heavyvibratory rollers in relatively thin lifts. As a result, desiredstrength parameters and suitable (overconsolidated)stress–strain behavior are developed. In addition to densi-fication, compaction operations increase the coefficient ofat-rest earth pressure (K0), defined as the ratio of lateralto vertical effective stress under the condition of zero lat-eral deformation (Bishop, 1958). Over time, the value ofK0 may evolve further because of permanent deformations

induced by traffic loads in combination with changingenvironmental conditions. The prevailing K0 values ingranular layers are of engineering importance as bothshear resistance and resilient modulus depend upon thestress-state within the compacted mass; as such they serveas basic modeling input for simulating pavement re-sponses to loadings. Even so, compaction quality is mainlygauged with density measurements that characterize thetightness level of the aggregate packing in comparisonwith some target value; the as-built K0 levels are neitherquantified nor considered as an indicator for pavementconstruction quality (Talbot, 2011).

Based on controlled compaction experiments of granu-lar soils against instrumented non-yielding walls (Duncanand Seed, 1986; Duncan et al., 1991; Filz and Duncan,1996; Chen and Fang, 2008; El-Emam, 2011), it is reportedthat post-construction K0 values approach passive

22 E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30

conditions for layers close to the surface. With modernvibratory rollers such conditions can be expected to reachdepths of the order of 1000 mm (Broms, 1971; Ingold,1979). These studies are relevant to pavements becausein most typical structural designs UGMs are placed withinthe top 1000 mm, and are compacted in large horizontalmats that restrict lateral deformations. This indicates thatrelatively high K0 values should be developed under typicalpavement construction operations. In the classic geotech-nical literature (Jaky, 1948; Mayne and Kulhawy, 1982;Mesri and Hayat, 1993), the coefficient of at-rest earthpressure in granular soils is usually related to the effective(peak) internal friction angle /0 and to the overconsolida-tion ratio (OCR):

K0 ¼ K0ðncÞðOCRÞn ð1Þ

in which K0(nc) denotes the normally consolidated at-restearth pressure coefficient, traditionally taken as 1�sin /0

(Jaky, 1948), and the power n is positive, statistically foundto equal sin /0 when OCR <15 and /0 <45� (Mayne and Kul-hawy, 1982). This equation is phenomenological in nature,and degrades in predictive ability with increasing OCR lev-els (Hanna and Al-Romhein, 2008). Also, it is fundamen-tally deficient because of the interdependence between adeformation parameter (K0) and a strength parameter(/0) (Feda, 1984; Michalowski, 2005). More in-depth re-search, based on laboratory investigations, suggest thatother influencing factors should be considered, e.g., soilfabric, constant volume friction angle, initial relative den-sity, void ratio, stress-state, and deformation time-history(Youd and Craven, 1975; Pruska, 1978; Al-Hussaini,1981; Guo and Stolle, 2006; Wanatowski and Chu, 2007;Mesri and Vardhanabhuti, 2009; Guo, 2010; Northcuttand Wijewickreme, 2013). Neither the classic relationsnor any of the more advanced models is useful for pave-ments as many of the governing factors are not known orcannot be monitored in-place.

The geotechnical literature mentions techniques forin situ evaluation of K0 (Hamouche et al., 1995). Testing de-vices with the most potential in this connection includethe self-boring pressuremeter (Da Cunha, 1994; Schnaid,2009) and the flat dilatometer (Marchetti, 1980; Smith,1993; Yu, 2006; Choi et al., 2011). The use of these devicesis based on the possibility of inserting them into the testedmedium, and with very little disturbance. For pavements,it is impractical to comply with such preconditions be-cause of the large aggregate sizes and high compaction lev-els. Another potential method for estimating K0 is based onin situ seismic testing (Fioravante et al., 1998; Pan andLiou, 2004; Cai et al., 2011). The approach assumes thatwave velocities in a granular assembly are a function ofstress-state and therefore suggests that K0 may be esti-mated from the ratio of horizontal to vertical wave veloci-ties. While the method seems promising, fieldinvestigations have shown that variations in soil fabricand anisotropy mask stress effects (Sully and Campanella,1995).

The purpose of this study is to suggest and explore ascheme for estimating the coefficient of at-rest earth pres-sure in compacted UGM layers. The focus is on asphalt

pavements although the approach can be potentially ap-plied to other pavement types. The method is computa-tional in nature, based on solving an inverse problem forinferring K0. A simplified version of the scheme is demon-strated by application to an airport pavement system in anaccelerated loading facility. Inferred post-construction K0

values in a base layer and in a subbase layer are quantifiedand discussed.

Estimation scheme

The proposed scheme requires the presence of embed-ded sensors in the pavement system, preferably at differ-ent locations. These sensors should be capable ofmeasuring a variety of mechanical response-traces (stres-ses, strains, displacements, velocities, accelerations) gener-ated by traffic loads traveling over the finished surface. Inaddition, the scheme is based on the availability of labora-tory test results that characterize the relationship betweenthe resilient UGM properties and the stress-state for the at-tained compaction level.

Subsequently, the idea calls for modeling the behaviorof the pavement system under the influence of a movingload and adjusting each of the layer properties until bestmatch is achieved between all computed and measured re-sponses. During the backcalculation process, the resilientmodulus constants for the UGMs are not freely adjustedbut taken from the laboratory investigation leaving as un-known only the value of K0 for each granular layer. Essen-tially, K0 controls the initial stress-state in a given UGMelement and therefore defines its modulus level whenthe loading is far relative to the element location. At closerdistances, although the loading alters the stress-state inthe element, the modulus is still influenced by K0. It is pre-sumed that these effects can be captured by the embeddedinstrumentation accurately enough to be resolved by sub-sequent modeling.

The procedure entails the execution of a multi-objectiveoptimization procedure in order to: (i) resolve conflictingsituations where improvements in matching the readingsfrom one sensor degrade the reproducibility of another;and (ii) balance the matching of distinct responses havingdifferent magnitudes or units (or both). The versatilemechanical information provided by the different sensorsreduces the number of acceptable solutions for the inverseproblem, minimizes systematic errors due to simplified(incorrect) modeling, and therefore increases the confi-dence of inferring an unbiased estimate for K0.

Simplified version

The above described estimation scheme is computa-tionally intensive; it requires an efficient ‘forward solver’that calculates response-traces due to a moving vehiclewhile taking into account both the time-dependence inthe mechanical properties of the asphaltic lifts and alsothe nonlinear behavior of the UGM layers. Even if the otherpavement layers (e.g., capping, subgrade, cement stabi-lized, etc.) are assumed linear and time-independent, theglobal pavement response is fundamentally non-linear

E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30 23

viscoelastic. The use of superposition is hence invalid, andthe simulation task becomes challenging and lengthy(Wang, 2011).

Motivated by practicality, a simplified scheme is there-fore offered. It has the same overall requirements and com-putational approach as described above except that thepavement modeling is restricted to linear behavior. Lineartheories are being used for design and analysis of pave-ment systems despite the fundamentally nonlinear behav-ior exhibited by pavement materials in laboratoryexperiments. The main incentive for retaining a linearframework is the ability, in many practical cases, to rea-sonably reproduce observed transient responses resultingfrom traffic loads (Sanders et al., 1993; Levenberg et al.,2009). Additional advantages when working with a lineartheory include: (i) improved calculation speed because ofthe possibility of employing analytical or semi-analyticalsolutions, (ii) greater ease in simulating the interaction ofmultiple loads because of the ability to take advantage ofsuperposition, and (iii) a relatively small set of modelparameters which is especially attractive for inverse anal-ysis applications.

Demonstrative application

Demonstrated hereafter is the estimation of K0 in an un-bound granular base layer and in a subbase layer. Thepavement under investigation was built in the FAA’s Na-tional Airport Pavement Test Facility (NAPTF) during thefirst construction cycle (CC1) (Garg and Hayhoe, 2008).The primary objective of this facility is to generate experi-mental data for validation and extension of airfield pave-ment design procedures. It consists of: (i) prototype-scale

Fig. 1. Cross-section of instrumented pavement system (left) and p

test sections built under tight construction quality control,(ii) a heavily instrumented structure and subgrade withstate-of-the-art measurement gear, (iii) laboratory charac-terization for the different materials, and (iv) controlledloading parameters and closely monitored environmentalconditions. Hence, the work and data produced by thisfacility are ideally suited for the current estimation task.The specific test section considered is the south lane ofthe so-called LFC section (Garg and Hayhoe, 2008); theLFC code refers to a conventional flexible pavement struc-ture built over a low-strength subgrade. This section wastraversed by a Boeing 777 landing gear (north side) andin parallel (south side) by a Boeing 747 configuration.The analysis herein focuses of the south LFC lane loadedby a single B747 pass.

Pavement system

The LFC pavement system included five layers as shownin Fig. 1 (left side). The structural items were per FAA stan-dard specifications (Federal Aviation Administration,2011). Following is a description of the design arrange-ment (top to bottom): (i) 127 mm of hot mix asphalt (ItemP-401); (ii) 197 mm unbound granular base (Item P-209);(iii) 925 mm unbound granular subbase (Item P-154); (iv)2405 mm of controlled low-strength subgrade classifiedas CL-CH (known as Dupont Clay); and (v) natural sandysoil classified as SW-SM extending to a large depth.

The LFC section was asphalted during March 1999,paved in two lifts. The mixture was a 19 mm Marshall de-signed surface with 5.4% binder content (on average). Post-construction coring showed that actual layer thicknessesvaried from 122 to 143 mm (130 mm on average). The

lan view of loading configuration relative to sensors (right).

24 E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30

as-constructed air voids ranged between 2.8 and 8.1% (4.8%on average). Aggregate base and subbase layers were com-pacted with single-drum vibratory rollers. The base wascompacted in a single lift while the subbase was com-pacted in six lifts. Relative to modified Proctor (dry) densi-ties, the average as-constructed base density was 101%. Asimilar average compaction degree was achieved in thesubbase across all lifts. In this connection it is noted thatthe first subbase lift had the lowest density (97.5% on aver-age), indicating difficulties in achieving good compactiondirectly over a low-strength support.

Laboratory characterization

As part of the CC1 study, triaxial shear tests and resil-ient modulus tests were performed on compacted UGMspecimens. As reported in Kim and Tutumluer (2005), ra-pid triaxial shear tests gave a base friction angle (/0B) of62� and a subbase friction angle (/0SB) of 44�; the associatedcohesion levels were 0.1 and 0.2 MPa, respectively.

Resilient modulus (MR) results for the base and subbaseare shown in Fig. 2 plotted against the applied bulk stress(h), i.e., the sum of principal stresses. Data for producingthis plot were taken from the NAPTF database (www.air-porttech.tc.faa.gov/naptf/cc1.asp, 2013). The ordinate(moduli) varies between 50 and 450 MPa and the abscissa(bulk stress) varies between 50 and 700 kPa. Circularmarkers, solid for base and hollow for subbase, indicateraw test data; each point gives the measured modulusfor a specific combination of confining pressure and devia-tor stress. Testing was done under five different confine-ment levels (between 21 and 138 kPa) and a range ofdeviator stresses (between 18 and 250 kPa). The showndata include two base compaction levels: 98% and 100%,and one subbase compaction level: 103%. The smoothcurves seen passing through the data points, either solid

Fig. 2. Resilient modulus test result

or dashed, are fitted power law expressions (h in kPa andMR in MPa). As can be seen, the data are narrowly spreadaround these curves indicating that the resilient modulusis governed by the bulk stress. Also noteworthy is thatthe base moduli levels are consistently higher than thesubbase moduli across all tested stress conditions. No dis-tinction was made here between total and effective stres-ses because suction effects (due to the presence ofmoisture) are assumed negligible.

Instrumentation

Various instruments were installed in the CC1 pave-ments, either during construction or immediately after.The instrumentation pertinent to this investigation in-cludes: (i) multi-depth deflectometers (MDDs), (ii) asphaltstrain gauges (ASGs), (iii) subgrade pressure cells, and(iv) temperature probes. All employed devices were off-the-shelf commercial products; their naming conforms tothat used in the NAPTF database. It is noted that not all im-planted sensors were utilized herein; this is mainly be-cause not all were active during the analyzed pass, andalso because some gave questionable readings, especiallyin relation to their reported location within the pavement.

The MDD design used in the NAPTF study consisted of aribbed flexible tube made of plastic. Each MDD tube wasvertically embedded (post-construction) inside an auger-drilled borehole. To ensure adherence of the tube to theborehole sides and base, and to eliminate any gaps, Ben-tonite was poured and a hydraulic anchor was inflated atthe bottom. Subsequently, the installed MDDs were ex-pected to deform together with the surrounding medium,i.e., shorten or elongate as needed. Rigid ‘snap’ rings insideeach tube were preinstalled at different elevations; eachring, as well as the bottom anchor point, served as ‘plat-form’ for one carbon-graphite rod extending towards the

s for base and subbase UGMs.

E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30 25

surface, passing freely through holes in the other rings onthe way up. In effect, the vertical displacement of eachrod reproduced the (relative) movement of its associatedring or anchor. These displacements were monitored byan array of potentiometers located in a metallic ‘headassembly’ that was fixed to the pavement surface. The spe-cific MDD addressed herein was installed on the west sideof the south LFC lane. This so-called SW MDD was about3.2 m long (see Fig. 1), and monitored displacements rela-tive to the head assembly at seven depths: 311, 1257,1302, 1454, 1683, 1988, and 3162 mm. For example, read-ings from MDD1 measured the change in vertical distancebetween the pavement surface and a point 3162 mm deep;readings from MDD7 measured the combined thicknesschanges in the asphalt and base layers.

The ASGs were fastened to the bottom of the asphaltlayer at a depth of 114 mm, targeting horizontal strains ineither the travel direction (longitudinal) or crosswise(transversely). Each ASG was H-shaped with end flangesconnected by a round polyester bar (Garg and Hayhoe,2001). The active measuring component was fixed at mid-length on the polyester bar and consisted of four straingauges, two axial and two transverse (rotated by 90�). Thisgauge array was connected in a full Wheatstone bridgecircuit so that only the longitudinal strain of the bar issensed. Three specific ASGs are analyzed herein, as shownin Fig. 1 (right hand side): LSC11 and LSC12 (longitudinal)and LSC8 (transverse). Subgrade pressure cells targeted ver-tical stresses at the so-called formation level (or bottom ofsubbase). These sensors were disk-shaped, 51 mm in diam-eter and 13 mm thick, filled with liquid. Their measurementmechanism is based on the assumption that verticalstresses are transferred to the internal liquid in the formof pressure increase because the volume is confined. Thepressure changes are detected by a transducer housed with-in the cell. Specifically, readings from the LCSW cell are ad-dressed; this sensor was located along the same line as theSW MDD and the longitudinal strain gauges (refer to Fig. 1).

Loading and response data

The loading event addressed herein included a B747landing gear traveling once over the finished pavementalong a straight line at constant speed of 8.05 km/h(5 mph). In the NAPTF database the investigated pass isidentified as Event #31 which took place on February 14,2000 (around 11 AM). This specific pass was selected foranalysis because of two main reasons: (i) the pavementsystem was in pristine condition so that K0 should reflectpost-construction conditions, and (ii) the resulting pave-ment response was reliably captured by the aforemen-tioned sensors. The recorded asphalt layer temperatureduring the pass was relatively low: 5.7 �C (42.3 F) at adepth of 64 mm (2.5 in.). This fact is also advantageous be-cause it lessens base and subbase nonlinearity as a result ofthe improved load spreadability of the surface layer due toits higher average ‘stiffness.’

The landing gear had four tires, each 482.6 mm (19 in.)wide, inflated to 1.3 MPa (188 psi) and loaded (vertically)to 200 kN (45,000 lb). The gear configuration is shown inFig. 1 (right hand side) by circles numbered 1–4, each

representing the tire-pavement contact. A right-handedCartesian coordinate system is included in the figure; theorigin of this system coincides with the surface such thatthe x-axis is parallel to the travel direction, the y-axis isperpendicular to it, and the z-axis (not shown) pointsdownward into the pavement. The gear moved relative tothis system in the positive x-axis direction; this axis de-notes the travel path as it ‘splits’ the wheel arrangementin the middle such that y = +559 mm for wheels 1 and 2and y = �559 mm for wheels 3 and 4. Fig. 1 also showsthe different sensors used for the inverse analysis and theiroffset relative to the travel path. As can be seen, the sub-grade pressure cell, the MDD array, and the longitudinalASGs are all located along the y = 292 mm line; thetransverse ASG is located 698 mm to the left of the maininstrumentation line (along y = �406 mm).

Measurements from the transverse strain gauge (LSC8)and from the vertical stress gauge (LSCW) are shown asdashed lines in Fig. 3. The strain ordinate (on the left)ranges between 50 and �250 microstrains with negativestrains indicating tension; the stress ordinate (on theright) ranges between �0.02 and 0.06 MPa. The abscissafor the curves denote the offset along the travel direction(i.e., along the x-axis) in the range of ±5000 mm betweeneach of the sensors (separately) and the gear center point(a virtual point equidistant from all wheels). An offset ofzero represents the closest distance between the sensorand the gear center. This alignment is approximate be-cause data acquisition and gear location were only roughlysynchronized in CC1 (Donovan, 2009). As can be seen, bothresponses increase as the gear approaches their embed-ment location, and diminish as the loading recedes. Smallhumps near the peak response indicate the individual ef-fects of tires 2 and 4 (offset � �500 mm) and later the ef-fects of tires 1 and 3 (offset � +500 mm).

Fig. 4 depicts the response of the two ASGs that mea-sured longitudinal (horizontal) strains along they = 292 mm line (LSC11 and LSC12). The strain ordinateranges between 80 and �200 microstrains; as before theabscissa represents the approximate gear-center off-set along the travel direction relative to the gauge location.Referring to the dashed curves, it can be seen that com-pressive (positive) strain is produced as the gear ap-proaches the measurement point; the strain changes totension as the wheels get closer, then reverts back to com-pression in-between the front and rear tires, then back totension, and again to compression before fading towardszero as the gear retreats. The effect of the front and reartires is clear and much more pronounced compared withthe response in Fig. 3. Also noteworthy is the difference be-tween the two gauges that were expected to measure iden-tical strain response. This is not an uncommon observationfor instrumented pavements (Levenberg et al., 2009); it isindicative of structural heterogeneity in combination withsensor embedment differences.

The MDD measurements vs. gear-center offset areshown in Fig. 5 by the dashed lines, each correspondingto a different measurement depth. It can be seen thatdeformations were mostly compressive indicating shorten-ing of the MDD tube. As expected, the smallest reading,with a peak of about 0.15 mm, was recorded by MDD7

Fig. 3. Response trace for top-of-subgrade vertical stress and transverse horizontal asphalt strain (refer to Fig. 1).

Fig. 4. Response trace for longitudinal horizontal asphalt strain (refer to Fig. 1).

26 E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30

(z = 311 mm) which spanned the joint thickness of the as-phalt and base layers. The maximum MDD response(MDD1) reached a peak of about 2.7 mm representing thecompression of the entire structure and most of the con-trolled subgrade up to z = 3162 mm. Across all MDD levelsthere is a clear asymmetry in the response: (i) the recedingbranch (positive offsets) is noticeably more gradual thanthe approaching branch (negative offsets), and (ii) the peakresponse is higher for the rear wheels. Both effects are

manifestation of time-dependent properties in certain lay-ers. Also, by comparing MDD readings between the startand end of a loading event, permanent deformation maybe observed. The accumulation of permanent deformationsin the MDD readings due to multiple gear passes was stud-ied by different researchers (Garg and Hayhoe, 2001, 2008;Kim and Tutumluer, 2005; Donovan, 2009), but thesedeformations are ignored here because only a single passis investigated.

Fig. 5. Multi-depth deflectometer response history (refer to Fig. 1).

Table 1Layer properties of the pavement model.

# Description (density, t/m3) Thickness Mechanical properties

Pre-assigned From inverse analysis

1 Asphalt (q1 = 2.46) 127 mm m1 = 0.30

E01 = 40,000 MPa

E11 = 150 MPa

sD = 1185 snD = 0.685

2 Aggregate base (q2 = 2.50) 197 mm m2 = 0.35 E2 = 160 MPa3 Aggregate subbase (q3 = 2.20) 925 mm m3 = 0.35 E3 = 120 MPa4 Controlled subgrade (q4 = 1.91) 2405 mm m4 = 0.40 E4 = 40 MPa5 Natural soil Semi-inf. m5 = 0.40 E5 = 140 MPa

E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30 27

Pavement modeling

The LFC pavement system was modeled as a stratifiedhalf-space composed of five fully bonded homogenousand isotropic (weightless) layers. The layers were num-bered sequentially with the top asphaltic layer being layer1. The upper four layers were of finite thickness, represent-ing the pavement structure and controlled subgrade (seeFig. 1); the lowest layer was semi-infinite, representingthe underlying natural sandy soil. The asphaltic layer wastaken as time-dependent linear viscoelastic with a con-stant Poisson’s ratio m1 = 0.30 and uniaxial relaxationtime-function E1(t) shaped as a sigmoid (Levenberg, 2013):

E1ðtÞ ¼E11 þ E11 ðt=sDÞnD

ðt=sDÞnD þ ðE11 =E01Þ

ð2Þ

in which E01 is the instantaneous modulus and E11 is the

long-time equilibrium modulus (units of stress). The con-stants sD (units of time) and nD (unitless) control the ‘tran-sition’ of E1ðtÞ between the two extreme moduli E0

1 and E11 .The unbound granular pavement layers (layers 2 and 3) for

which K0 is sought were taken as linear elastic with moduliE2 and E3; the Poisson’s ratios were pre-assigned:m2 = m3 = 0.35. The controlled subgrade and underlying soilwere also assumed linear elastic with moduli E4 and E5

respectively, and with m4 = m5 = 0.40. A summary of thepavement model and layer parameters is provided inTable 1. The columns (from left to right) report: layernumbering, description (and density), thickness, andmechanical properties (either pre-assigned or inferred).

The B747 loading was modeled by four identical circu-lar areas arranged as shown in Fig. 1, each representingthe tire contact with the pavement. Radius of contactwas taken as half the tire width, i.e., 241.3 mm (9.5 in.),contact stresses were presumed uniformly distributedand in the vertical (z-direction) only, and contact stressintensity was taken as 1.10 MPa to conform to the200 kN wheel loads. As opposed to equating the contactstress intensity with tire inflation pressure, the chosencontact conditions better capture the effects of tire rigidityobserved in full-scale tests (Airbus, 2013). Mechanical re-sponses produced by the moving B747 gear were simu-lated quasi-statically, neglecting inertia effects. This is

28 E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30

justified because a travel speed of 8.05 km/h is consider-ably less than the velocities of all stress-wave types inthe medium. In general terms, the computations werebased on the elastic–viscoelastic correspondence principleas done in a recent study (Levenberg, 2013). The derivationemployed Schapery’s direct Laplace transform-inversiontechnique for improved computational speed (Schapery,1962) combined with the ELLEA1 code (Levenberg et al.,2009) as a layered elastic kernel.

In order to simulate the gear movement, the modelpavement was ‘loaded’ for a short duration and then ‘un-loaded’ along the travel path. This was done sequentiallyover 201 stationary points at 100 mm intervals withinthe offset range ±10,000 mm. Each load-unload eventlasted about 0.0447 s so that a travel speed of 2.22 m/s(i.e., 8.05 km/h) was attained on average. While stationary,the viscoelastic pavement response (in time) was com-puted at several locations of interest within the system.The computations targeted the implanted sensors in theNAPTF experiment (refer to Fig. 1) in terms of their posi-tion relative to the loading point, and in terms of theirmeasured response type (i.e., horizontal strain, verticalstress, etc.). To generate a viscoelastic solution for a sta-tionary loading event, the responses of interest were com-puted in ELLEA1 for a range of E1 values between E0

1 and E11with all other moduli kept constant. By inverting Eq. (2) toisolate t, the dependence of the computed response uponE1 was converted to a dependence upon time. The outcomegives the sought after viscoelastic solution; this is the so-called quasi-elastic approximation. For the same stationarypoint and response, an unloading event need not be com-puted as it is identical in shape to a loading event but witha negative sign.

With the availability of viscoelastic solutions for sta-tionary events covering 201 successive points along thegear travel path, hereditary superposition was employedto generate a solution for the entire movement (i.e., withinthe offset range ±10,000 mm). The basic underlyingexpression is:

RveðtÞ ¼X

a

Z t

s¼0Rve

a ðt � sÞdIaðsÞ ð3Þ

in which RveðtÞ is the viscoelastic response trace of interest,Rve

a ðtÞ is the stationary viscoelastic response of the pave-ment to loading (or unloading) event at point a along thetravel path (a ¼ 1;2; ::201), and s is a time-like integrationvariable. The function IaðtÞ contains the timing informationof each of the a loading–unloading events; it is zero every-where except for 0.0447 s during which it attains a value ofunity.

Inference of K0 and discussion

With an initial set of layer properties, response traceswere computed for all abovementioned sensors. A multi-objective inverse problem was subsequently carried outto calibrate the layer properties guided by the requirementto best match the measurements. The min–max approach(Osyczka, 1978) was employed to resolve conflicting situa-tions and produce a well-balanced solution. Because of the

difficulty to infer the values of E01 and E11 from a single pass,

both were pre-assigned as follows: E01 = 40,000 MPa,

approximately the elastic modulus of a mature Portlandcement concrete, and E11 = 150 MPa, roughly the character-istic modulus of a well compacted high quality unboundgranular base. In effect, properties were determined usingthe MDD measurements while the stress and strain sensorsserved as validation for the calibrated model. It is impor-tant to note that the MDD anchor was not assumed fixed,but allowed to deflect in the analyses (Scullion et al., 1988).

The optimal layer properties are given in Table 1 (right-most column), and the calibrated model responses aregraphically superposed over the sensor measurements inFigs. 2–4 (solid lines). As can be seen, even though diverseresponse types are involved, a relatively good match wasachieved with the linear theory. The model is seen to becapable of reproducing both the shape of the responsetraces as well as their magnitudes. Moreover, the inferredmoduli values appear consistent from an engineeringstandpoint: the base layer (E2 = 160 MPa) is stiffer thanthe subbase (E3 = 120 MPa) by about 40%, and the subbaseis 2.8 times stiffer than the controlled subgrade. The latter,with a modulus of 40 MPa, classically conforms to themeasured average CBR of 4% (www.airporttech.tc.faa.gov/naptf/cc1.asp, 2013; Heukelom and Klomp, 1962).

As indicated by the solid arrows in Fig. 2, a base modu-lus of 160 MPa is associated with a bulk stress of 145 kPa.From self-weight (only), vertical stress (rz) in the midheight of the base layer (z = 225.5 mm) is 5.5 kPa. Thismeans that the horizontal stresses (rx ¼ ry) are about70 MPa in order to generate h = 145 kPa. Therefore, theestimated value of K0 for the base layer is 13 (=70/5.5).Similarly, a subbase modulus of 120 MPa is associated witha bulk stress of 125 kPa (dashed arrows in Fig. 2). Fromself-weight, rz in the mid height of the subbase layer(z = 786.5 mm) is 18 kPa. This means that the horizontalstresses are about 53 MPa and that the estimated subbaseK0 is about 3 (=53/18).

No benchmark information or test results exist to di-rectly evaluate the accuracy level of the obtained K0 values.Hence, their reasonableness can only be assessed indi-rectly. First, it is noted that a K0 value cannot exceed aphysically permissible upper limit defined by the coeffi-cient of passive earth pressure Kp. Based on the measuredinternal friction angles, /0SB = 44� and /0B = 62�, thecompacted subbase is associated with Kp = 5.6 and thecompacted base with Kp = 16.1. Therefore, the estimatedpost-construction conditions are deemed legitimate.Second, from an engineering standpoint it is expected thatthe subbase should have a lower at-rest earth pressurecoefficient than the base. One reason for this is the differ-ences in material quality (subbase being inferior); anotherreason is the difficulty in achieving effective compactionover a weak subgrade. Backing for this latter argumentcan be gained from evaluating the ratio K0/Kp. This ratiois indicative of compaction effectiveness because it mea-sures the induced (or mobilized) ‘stress-reinforcement’ ina layer as a percentage of its potential. As anticipated,K0/Kp � 50% for the subbase and K0/Kp � 80% for the base.The realized OCR level in each layer is also related to com-paction intensity. Based on Eq. (1), an OCR � 27 is found for

Fig. 6. Variation of K0 across the subbase thickness assuming constant E3 (left), and variation of E3 across the subbase thickness assuming constant K0

(right).

E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30 29

the subbase and an OCR � 207 is found for the base. Whilethese values are outside the usable range of Eq. (1), theynonetheless provide additional indication that the basewas more effectively compacted. A third indication forthe correctness of the results was attained by reapplicationof the entire scheme; this was carried out with measure-ments taken from a different MDD (SE MDD) and also withtwo other B747 passes (Event #26 and Event #28) in whichdifferent paths were traveled (relative to the instrumenta-tion). Essentially similar at-rest earth pressure coefficientswere obtained.

The subbase in the modeling was treated as a singlelayer that is 925 mm thick. If the attained subbase stiffness(of 120 MPa) is truly uniform over the entire layer thick-ness then a specific K0 profile, consistent with its stress-dependency, must be built into the material. This conditionis depicted in Fig. 6 (left chart) by the dashed line; it showsthe coefficient of at-rest earth pressure decreasing fromtop to bottom, from K0 = 7.5 (unrealistic consideringK0 = 5.6) to a value of K0 = 1.8. The solid circular markersuperposed over the dashed line designates the inferred(optimal) result of K0 = 3 at a depth of 786.5 mm fromthe surface, i.e., middle of the subbase layer. Alternatively,if the inferred K0 = 3 is taken as constant across the entiresubbase layer then a particular stiffness profile must bebuilt into the material. This situation is depicted by thedashed line in Fig. 6 (right chart); it shows modulus levelsincreasing with depth, from 74 to 157 MPa. In this case thesolid circular marker designates the optimal (analysis) re-sult of E3 = 120 MPa at mid-thickness of the subbase layer.

In order to assess which of the two scenarios is bettertuned to the measured pavement response, the entire anal-ysis was repeated, but this time with the subbase dividedinto two sublayers: an upper part with a thickness of425 mm and a lower part with a thickness of 500 mm.The respective moduli were kept fully adjustable while aPoisson’s ratio of 0.35 was pre-assigned for both. At(new) optimum, all other layer properties did not deviatefrom their earlier levels (Table 1) by more than 3%. How-ever, the moduli of the upper and lower subbase partsdid deviate from 120 MPa; the upper part received a mod-ulus level of 98 MPa and the lower part a modulus level of

140 MPa. These are graphically shown in Fig. 6 (right chart)by the two hollow circular markers, located at the mid-thickness of their respective sublayers. This outcomeclearly favors the constant K0 scenario and therefore rein-forces the analysis findings.

Summary and conclusions

Layers composed of UGMs are aggressively compactedby heavy rollers during pavement construction. In additionto densification, this activity considerably increases K0 lev-els. Quantifying at-rest earth pressure coefficients in com-pacted UGMs is not directly possible with the currentgeotechnical tools. Therefore, an indirect method was sug-gested in the paper for estimating K0. The scheme is basedon multi-objective inverse analysis of an instrumentedpavement and requires the availability of laboratory resil-ient modulus test results. These preconditions essentiallylimit the approach to controlled full-scale research facili-ties where wired instrumentation is usually installed,accompanied by thorough laboratory investigation. None-theless, as more live projects are constructed with instru-mentation, and as new wireless pavement sensors arebeing developed, the approach could enjoy a more wide-spread application in the future.

It is currently deemed impractical to model nonlinearbehavior as well as time-dependence in conjunction withmulti-objective inverse analysis. For this reason a simpli-fied version of the scheme, assuming linear response, wasalternatively proposed. It is well recognized that theassumption of linearity produces only a first order approx-imation; linearity is not consistent with actual material re-sponse as seen in laboratory characterization and thereforeintroduces bias into the analysis. However, for high K0 val-ues, pavement layers are practically ‘stress-reinforced’ andtherefore exhibit near-linear mechanical behavior. Also,systematic errors from incorrect constitutive treatmentare minimized because parameters are obtained from thesimultaneous matching of several (preferably distinct) re-sponse traces.

The simplified version was applied to demonstrate therequired calculations and quantify K0 values in a case

30 E. Levenberg, N. Garg / Transportation Geotechnics 1 (2014) 21–30

study. A flexible pavement test section (LFC) from the firstconstruction cycle in the NAPTF (CC1), loaded by a B747landing gear, was chosen for this purpose. The estimationeffort targeted post-construction K0 levels in the unboundgranular structural layers. A K0 value of 3 was obtained forthe subbase and a K0 value of 13 was obtained for the base.The accuracy level of these values was confirmed indirectlythrough a series of modeling and engineering evaluations.It is concluded that the offered scheme, even in its simpli-fied form, is capable of estimating realistic K0 levels. Appli-cation of the approach to other situations is advocated forenriched explanation of mechanical behavior and as addi-tional indication, together with densities, of compactionquality.

References

Airbus SAS. High tire pressure test: technical report, referencex32rp0926801, issue 1.0, airbus.com/fileadmin/media_gallery/files/tech_data/Pavement/HTPT_final_report_Aug2010.pdf [accessed12.25.13].

Al-Hussaini M. Comparison of various methods for determining K0. In:Yong RN, Townsend FC, editors. ASTM STP 740; 1981. p. 78–93.

Bishop AW. Test requirements for measuring the coefficient of earthpressure at rest. In: Proceedings of the Brussels conference on earthpressure problems, vol. 1. Brussels, Belgium; 1958. p. 2–14.

Broms BB. Lateral earth pressure due to compaction of cohesionless soils.In: Proceedings of the 5th Budapest conference on soil mechanics andfoundation engineers, Budapest, Hungary; 1971. p. 373–84.

Cai G, Liu S, Puppala AJ, Tong L. Assessment of the coefficient of lateralearth pressure at rest (K0) from in situ seismic tests. Geotech Test J2011;34(4):1–11.

Chen TJ, Fang YS. Earth pressure due to vibratory compaction. J GeotechGeoenviron Eng 2008;134(4):437–44.

Choi SK, Lee MJ, Choi YM, Lee W. Evaluation of K0 of granular soils usingDMT indices. Mar Georesour Geotechnol 2011;29(2):117–30.

Da Cunha RP. Interpretation of selfboring pressuremeter tests in sand,Ph.D. Dissertation, University of British Columbia; 1994.

Donovan PR. Analysis of unbound aggregate layer deformation behaviorfrom full scale aircraft gear loading with wander, Ph.D. Dissertation,University of Illinois at Urbana-Champaign; 2009.

Duncan JM, Seed RB. Compaction-induced earth pressures under K0-conditions. J Geotech Eng 1986;112(1):1–22.

Duncan JM, Williams GW, Sehn AL, Seed RB. Estimation earth pressuresdue to compaction. J Geotech Eng 1991;117(12):1833–47.

El-Emam M. Experimental and numerical study of at-rest lateral earthpressure of overconsolidated sand. Adv Civil Eng 2011;2011:1–12.

Feda J. K0-coefficient of sand in triaxial apparatus. J Geotech Eng1984;110(4):519–24.

Federal Aviation Administration. Standards for specifying construction ofairports, advisory circular no. 150/5370-10F; 2011.

Filz GM, Duncan JM. Earth pressures due to compaction: comparison oftheory with laboratory and field behavior. J Transportat Res Board1996;1526:28–37.

Fioravante V, Jamiolkowski M, Lo Presti DCF, Manfredini G, Pedroni S.Assessment of the coefficient of the earth pressure at rest from shearwave velocity measurements. Géotechnique 1998;48(5):657–66.

Garg N, Hayhoe GF. Asphalt concrete strain responses at high loads andlow speeds at the national airport pavement test facility (NAPTF). In:Proceedings of the ASCE airfield pavements specialty conference,Chicago, IL; 2001.

Garg N, Hayhoe GF. Permanent deformation behavior of the granularlayers tested at the FAA’s national airport pavement test facility. In:Proceedings of the 3rd international conference on acceleratedpavement testing 11(4), Madrid, Spain; 2008.

Guo P. Effect of density and compressibility on K0 of cohesionless soils.Acta Geotech 2010;5:225–38.

Guo PJ, Stolle DFE. Fabric and particle shape influence on K0 of granularmaterials. Soils Found 2006;46(5):639–52.

Hamouche KK, Leroueil S, Roy M, Lutenegger AJ. In situ evaluation of K0 ineastern Canada clays. Can Geotech J 1995;32(4):677–88.

Hanna A, Al-Romhein R. At-rest earth pressure of overconsolidatedcohesionless soil. J Geotech Geoenviron Eng 2008;134(3):408–12.

Heukelom W, Klomp AJG. Dynamic testing as a means of controllingpavement during and after construction. In: Proceedings of the 1stinternational conference on the structural design of asphaltpavements, Ann Arbor, Michigan; 1962. p. 667–79.

Ingold TS. The effects of compaction on retaining walls. Géotechnique1979;29:265–84.

Jaky J. Pressure in silos. In: Proceedings of the 2nd internationalconference on soil mechanics and foundation engineering, vol. 1.Rotterdam, Netherlands; 1948. p. 103–7.

Kim T, Tutumluer E, Permanent deformation behavior of airport flexiblepavement base and subbase courses, center of excellence for airporttechnology (COE), report no. 28, University of Illinois at Urbana-Champaign; 2005.

Levenberg E. Inverse analysis of viscoelastic pavement properties usingdata from embedded instrumentation. Int J Numer Anal MethGeomech 2013;37:1016–33.

Levenberg E, McDaniel RS, Olek J. Validation of NCAT structural test trackexperiment using INDOT APT facility: final report, joint transportationresearch program, report FHWA/IN/JTRP-2008/26, Purdue University;2009.

Marchetti S. In situ tests by flat dilatometer. J Geotech Eng1980;106(3):299–321.

Mayne PW, Kulhawy FH. K0-OCR relationships in soil. J Geotech Eng1982;108(6):851–72.

Mesri G, Hayat TM. The coefficient of earth pressure at rest. Can Geotech J1993;30(4):647–66.

Mesri G, Vardhanabhuti B. Compression of granular materials. CanGeotech J 2009;46:369–92.

Michalowski RL. Coefficient of earth pressure at rest. J GeotechGeoenviron Eng 2005;131(11):1429–33.

Northcutt S, Wijewickreme D. Effect of particle fabric on the coefficient oflateral earth pressure observed during one-dimensional compressionof sand. Can Geotech J 2013;50(5):457–66.

Osyczka A. An approach to multicriterion optimization problems forengineering design. Comput Methods Appl Mech Eng1978;15:309–33.

Pan YW, Liou JC. K0 estimation in level granular soil from anisotropicwave velocities on the basis of micromechanics. Int J Numer AnalMeth Geomech 2004;28:1401–25.

Pruska L. At-rest lateral earth pressure coefficient of a granular medium.Soil Mech Found Eng 1978;15(1):56–61.

Sanders PJ, de Beer M, du Plessis HW. Characterization of the elasticproperties of existing pavements: state of the art, research report 91/012. South Africa: National Department of Transport; 1993.

Schapery RA. Approximate methods of transform inversion forviscoelastic stress analysis. In: Proceedings of the ASME 4th U.S.national congress on applied mechanics, vol. 2. Berkeley, California;1962. p. 1075–85.

Schnaid F. In situ testing in geomechanics: the main tests. NewYork: Taylor & Francis; 2009.

Scullion T, Uzan J, Yazdani JI, Chan P. Field evaluation of the multi-depthdeflectometers, texas transportation institute research report 1123–2. Texas: College Station; 1988.

Smith MG. A laboratory study of the Marchetti dilatometer, Ph.D.Dissertation, Oxford University; 1993.

Sully JP, Campanella RG. Evaluation of in situ anisotropy from crossholeand downhole shear wave velocity measurements. Géotechnique1995;45(2):267–82.

Talbot J. Quality control of soil compaction using ASTM standards, manual70. West Conshohocken, Pennsylvania: ASTM International; 2011.

Wanatowski D, Chu J. K0 of sand measured by a plane-strain apparatus.Can Geotech J 2007;44(8):1006–12.

Wang H. Analysis of tire-pavement interaction and pavement responsesusing a decoupled modeling approach, Ph.D. Dissertation, Universityof Illinois at Urbana-Champaign; 2011.

www.airporttech.tc.faa.gov/naptf/cc1.asp [accessed 12.25.13].Youd TL, Craven TN. Lateral stress in sands during cyclic loading. J

Geotech Eng 1975;101:217–21.Yu HS. In situ soil testing: from mechanics to interpretation. Geomech

Geoeng 2006;1(3):165–95.