Improved Characterization Model for Granular Bases

Transcription

1 128 TRANSPORTATON RESEARCH RECORD 1227 mproved Charateriation Model for Granlar Bases ROBERT P. ELLOTT AND LOURDESNATHAN DAVD Laboratory resilient modls tests ere ondted on granlar materials at stress states exeeding the materials' stati shear strengths. The test reslts sho that, above the stati strength, the modls dereases ith inreasing stress levels. These data ere sed to develop a harateriation model that is a modifiation of the ommonly sed k-theta-11 model. The modifiation onsists of the addition of a stress ratio (stress/strength) parameter. The stress ratio model as sed in the finite element program LLl-PAVE to analye typial flexible pavement setions. The analysis reslts are ompared ith similar analyses sing the Mohr Colomb stress adjstment model normauy sed ith LLl-PAVE. The omparison shos that similar stress and strain patterns are predited by both models bt that the stresses predited in the granlar base by the stress ratio model appear to be more realisti. Also, the stress ratio model provides a means for analying the strtral effets of granlar materials having different shear strength harateristis n reent years, pavement design researh has emphasied the development of mehanisti analysis proedres. The objetive of the development is to establish a rational method of design that is based on load-inded stresses and strains in eah pavement layer. Material ombinations and thiknesses are seleted on the basis of the effet the stresses and strains have on eah material's behavior as a part of the pavement system. Perhaps the most signifiant eakness in the mehanisti analysis proedres that have been developed to date is the inability to model the behavior of nbond granlar layers realistially. The granlar base models rrently in se typially predit stress states that exeed the strength of the material. For example, tensile radial stresses are freqently predited at the bottom of the granlar layer of a onventional flexible pavement. This paper presents the reslts of a stdy sponsored by the National Siene Fondation. The objetive of the stdy as to establish an improved strtral harateriation model for granlar base material. An analysis of laboratory test data has been sed to propose a harateriation model hih is a modifiation of the model that is rrently sed by most pavement analysts. PAVEMENT STRUCTURAL MODELS To mathematial models are sed in mehanisti analyses to represent the pavement system: the elasti layered theory Arkansas Highay and Transportation Researh Center, Department of Civil Engineering, University of Arkansas, Fayetteville, Ark model and the finite element model. The elasti layered model is sed most freqently. By the elasti layered theory, the pavement system is represented as a series of layers of linear elasti material. Eah layer is represented by a single elasti modls and Poisson's ratio. The single modls provides a reasonable representation for asphalt onrete and other stabilied materials; hoever, it is not a good representation for nbond granlar layers. Nmeros stdies have demonstrated that the elasti behavior of nbond granlar materials is stress dependent. That is, the apparent modls of the granlar material hanges as the applied stress state hanges. The typial behavior is shon by the data plotted in Figre 1. The resilient (elasti) modls of the materials inreases as the stress state (sm of the prinipal stresses) inreases. This stress dependeny an be inorporated into an elasti layered analysis throgh the se of iterative tehniqes. An initial modls is assigned and stresses are allated. A ne modls is assigned for the next iteration on the basis of the stress state of the rrent iteration. An obvios limitation to this approah is the fat that a single modls mst still be assigned for the entire layer. The stress state ill not be onstant throghot the layer. t ill be higher diretly belo the load and derease as the distane from the load inreases. Conseqently, the modls shold not be onstant throghot the layer. n this respet, the finite element model provides a sperior pavement representation. The finite element model treats the pavement as a series of interonneted elements. Eah element an be assigned a different modls and Poisson's ratio. As a reslt, the inflene of stress variation on the modls an be represented in both the vertial and horiontal diretions. Nevertheless, as rrently sed, neither model provides a realisti representation of the stresses and strains ithin an nbond granlar layer. Both pavement models (elasti layered and finite element) freqently predit stress states that exeed the strength of the material. For the finite element model, this problem might be alleviated ith an appropriate material harateriation model. LL-PA VE (a pavement analysis program provided by the Transportation Failities Grop, Department of Civil Engineering, University of llinois at Urbana-Champaign) is a finite element model that attempts to ompensate for the problem by adjsting the predited stresses so that they do not violate the Mohr-Colomb failre envelope. Hoever, the adjsted stresses are sed only to allate the modls vales to be sed in the next iteration. As a reslt, the final stresses in the

2 Elliott and David (./) :::::> :::::> ""'' S 1 = Callated Major Prinipal Stress Sadj = Adjsted Stress for Material Having Shear Angle.p Sdj = Adjsted Slress for Material Hoving Shear Angle </>' Note : For <P <.p' Sadj > Sdj 8 =S +2Sadj.". Bsetter < BPoorer 1-1 (./) ::: 1 FGURE 1 Typial stress dependeny relationship for a granlar base material. 1 FGURE 2 Mohr-Colomb stress adjstment sed in LL PAVE (5). granlar layer ontine to be qestionable and freqently exeed the material strength. GRANULAR LA YER CHARACTERZATON MODELS The harateriation model most ommonly sed for nbond granlar materials is based on data sh as that shon in Figre 1. The resilient modls is determined sing ylindrial speimens in a triaxial ell. The speimen is sbjeted to a onstant onfining pressre. A repeated, dynami deviator load (stress) is applied vertially, and the vertial resilient or rebond deformation (strain) is measred. The harateriation model is M, = k" (1) here M, = the resilient modls ( deviator stress/resilient strain), k and n regression oeffiients determined from the laboratory data, and sm of the prinipal stresses ( deviator stress + 3 * onfining pressre). A more omplex model as proposed and sed by Bron and Pappin (1,2). This model is referred to as the ontor model. t appears to have some analytial advantages bt as not investigated in this stdy bease of the omplex laboratory testing reqired to develop the material parameters that are sed. Uan (3) examined these and other granlar harateriation models. From his analysis, he sggested se of a modifiation of Eqation 1: here ad eqals the deviator stress and a eqals the regression oeffiient determined from laboratory data. This model as sggested to aont for trends of dereasing resilient mod- (2) ls ith inreasing deviator stress at onstant onfining pressres. Both Uan (3) and Bron and Pappin (J) reported that se of their models reslted in tensile stresses being predited for at least some pavement onfigrations. Bron and Pappin stated that this as de to some inaray in their model and as an indiation of a eak pavement. Uan arged that the tensile stresses ere small and ere offset by residal ompressive stresses inded by ompation dring pavement onstrtion. The finite element program LL-PAVE ses the Eqation 1 model ith its Mohr-Colomb stress-adjstment proedre. This ill be referred to as the Mohr-Colomb model. Elliott and Thompson ( 4) noted that one problem ith the Mohr-Colomb model as that it did not properly differentiate beteen poorer and better granlar material. As illstrated in Figre 2, for eqal predited stress states, the higher phi angle of the better material ill reslt in a loer adjsted stress. As a reslt, theta ill also be loer and the resilient modls for the next iteration ill be loer. There is another problem ith the Mohr-Colomb model. The stresses are adjsted bt are not redistribted. Conseqently, the adjsted stresses are not in eqilibrim and tre onvergene of the iterative approah is not ahieved. LABORATORY TESTNG Three aggregates ere tested to develop data to be sed in developing an improved harateriation model. The tests ere ondted in aordane ith AASHTO T-274 exept that some tests ere performed at deviator stresses that exeeded the materials' stati shear strengths. The failrestate tests ere performed to examine the resilient modls stress dependeny nder stress states approahing those predited by the rrently sed models. The failre state tests ere ondted in sh a manner that a ne test speimen as reqired for eah onfining pressre in hih tests ere performed beyond failre. After the tests at the standard onfining pressre and deviator stress

3 13 ombinations ere omplete, the test as ontined at a onstant onfining pressnre ith the rleviator stress heine; inreriserl Testing ontined at higher and higher deviator stresses ntil a signifiant amlation of permanent deformation made frther testing meaningless. For to of the aggregates, failre-state testing as performed at only one level of onfining pressre (Figres 3 and 4). The thirrl aggregate as tested in failre states at three onfining pressres (Figre 5). (The nonfailre reslts shon on Figres 3, 4, and 5 that have theta vales greater than those of failre tests represent tests at higher onfining pressres.) No speifi effort as made to examine the repeatability of the failre-state tests. Hoever, the onsisteny of reslts obtained for the aggregate tested at three onfining pressres sggests a reasonable degree of repeatability. Regression eqations onforming to Eqation 1 ere developed sing only the nonfailre data. These eqations are shon on the figres. By observing the data points and the R 2 vales, it an be seen that Eqation 1 provides a good representation of the behavior at stresses belo failre. Hoever, at stresses exeeding failre, the resilient modls dereases as the deviator stress (and, therefore, theta) inreases. This behavior ontrasts ith the effet of the Mohr- en 4.::.t. 1 (J) O:'. / TRANSPORTATON RESEARCH RECORD 1227 LURE STATE TESTS Con Press. 3 psi " 5 psi 7 psi 1 1 FGURE 5 Resilient modls test reslts for a dense-graded gravel. Colomb adjstment model. As illstrated in Figre 2, the stress adjstment inreases thetri, hih in trn innerises the modls. D D D - 4 " UJ _y =i =i 2 1 (}>' FGURE 3-4 en.:::l ::J ::J!=:! O O:'.'. ")-.-r-...--r-r-r-.--, ,..., 1 1 Resilient modls test reslts for a rshed stone. 1 Failre State Tests FGURE 4 Resilient modls test reslts for a lo fines gravel. 1 MODEL DEVELOPMENT The data displayed in Figres 3, 4, and 5 ere stdied to develop a ne harateriation model. To fats ere noted. First, the Eqation 1 model provided an exellent representation of the data belo failre. Seond, above failre, there appeared to be a need to inorporate a failre term. These fats sggested that the general form of Eqation 1 shold be modified by inorporating a failre term. The failre term shold have little or no impat ntil failre is approahed. Several models ere investigated. The one fond to provide the best fit modifies Eqation 1 by adding a stress/strength ratio as the failre term. The model seleted is M, = k"/1a (3) here A m R mr3, regression oeffiient determined from laboratory data, and stress/strength ratio (de via tor stress divided by the failre deviator stress). The failre deviator stress is determined on the basis of the onfining pressre and the stati triaxial shear test. This model (Eqation 3) is referred to hereafter as the stress ratio model. Analysis of all the data shon in Figre 5 sing the stress ratio model proded the regression eqation shon in Figre 6. The plots of the regression eqation at the three onfining pressres for hih failre-state tests ere ondted sho a good fit beteen the model and the test reslts. Analyses ere also performed on the data for the other to aggregates. These proded similar regression eqations. Hoever, bease the other aggregates ere tested at only one onfining pressre, the reslts are not as meaningfl and are not shon.

4 Elliot/ and David :::) :::) 2 1 ::::::i et:: M, = /1 5 (RJ. R 2 =.88 FALURE STATE TESTS Conf. Press, 3 psi " 5 psi 4 7 psi 3 en ClJ _ UJ <t m \-- () 12 8 ; <lj Q_ E " ' Mohr-Colomb Model Stress Rotio Model 1 1 FGURE 6 Plot of stress ratio model verss test reslts for a dense-graded gravel RAD AL STRESS, p s i FGURE 7 Comparison of predited radial stresses in the base for the 1-in. (25-mm) srfae pavement. MODEL COMPARSON A omparison of the stress ratio model and the Mohr-Colomb model as developed sing LL-PA VE. This reqired reating a modified version of LL-PAVE that inorporated the stress ratio model in lie of the Mohr-Colomb model. Three pavement setions ere analyed sing the to models. The setions ere idential exept for the thikness of the asphalt srfaing. Eah setion had a 12-in. (35-mm) granlar layer. The srfaing thiknesses ere 1 in. (25 mm), 3 in. (76 mm), and 6 in. (152 mm). A modls of 5, psi (3447 Mpa) as sed for the asphalt onrete; and the sbgrade as represented as having a breakpoint resilient modls of 6, psi (41.4 MPa). The material parameters determined for the aggregate tested most extensively in the stdy ere sed for the granlar layer. For the Mohr-Colomb model, the phi angle (48.6 degrees) determined by the triaxial shear strength test as sed for the stress adjstment, and the stress dependeny as h arateried sing the regression eqation developed from the belo failre data and shon on Figre 5. The stress ratio model sed the regression eqation developed from all the data and shon on Figre 6. Stresses and strains ere determined for a standard 9,- pond ( 4-kN) heel load and an 8-psi (552-kPa) ontat pressre. Five analysis iterations ere speified so that both the final analysis reslts anj the program onvergene old be ompared. The radial stresses predited by the to models are shon in Figres 7, 8, and 9 for the 1-in. (25-mm), 3-in. (76-mm), and 6-in. (152-mm) srfae pavements, respetively. The stress patterns predited by the models are seen to be similar, ith both models prediting tensile stresses at the bottom of the base for the 1-in. (25-mm) and 3-in. (76-mm) srfae pavements. Hoever, the tensile stresses are loer ith the stress ratio model. Program onvergene and the base orse modls vales sed are ompared in Figre 1 for.the 6-in. (152-mm) srfae pavement. Both models onverged in feer than five iterations, ith the stress ratio model onverging in three iterations and the Mohr-Colomb model onverging in for. The modls vales sed ere similar to the stress ratio model, sing [f) QJ _ <( rn :r:: f- Q_ '\ r r :.Q : ' Mohr-Colomb Model Stress Ratio Model f-- "' -5 5 RAD AL STRE SS, psi FGURE 8 Comparison of predited radial stresses in the base for the 3-in. (76-mm) srfae pavement. [f) QJ _ <( 12 8 rn 4 1:' (l_ :r:: 1-- E Q_ <lj f-- Mohr-Colomb Model Stress Ratio Model RAD AL STRE SS, p s i FGURE 9 Comparison of predited radial stresses in the base for the 6-in. (152-mm) srfae pavement.

5 132 TRANSPORTATON RESEARCH RECORD => => et: ' \ \ \ Mohr-Colomb Model '.3Lr "'' R Li Mel tial strain is a better (i.e., longer expeted servie life) pavement. Using these riteria, Table 1 shos that the Mohr Colomb model ranks the pavements inorretly by prediting loer defletion and asphalt strain for the pavement ith the eaker base orse (loer phi angle). With the stress ratio model, the pavements are ranked orretly, bease the pavement ith the eaker base is predited to have higher defletion and higher asphalt strain. Exept for the relative rankings, the differenes in predited pavement response are not signifiant for pratial engineering prposes ith either model. Hoever, the fat that the stress ratio model ranks the pavements in the proper order is important and enoraging. o J 4 TERATON NUMBER FGURE 1 Comparison of onvergene and resilient modls vales sed for the 6-in. (152-mm) srfae pavement. slightly loer vales. Similar patterns of modls vales ere noted for the other srfae thiknesses; hoever, neither model onverged in feer than five iterations. COMPARSON OF GRANULAR MATERALS Bease of the problems in modeiing the behavior of granlar materials, mehanisti analyses to date have not been able to examine the relative inflene of aggregate bases of different qality. The stress ratio model provides an approah that makes sh examinations possible. To demonstrate this, the 3-in. (76-mm) srfae pavement as also analyed assming a eaker base material. For this analysis, a base shear strength phi angle of 4 degrees as sed. This hanged both the stress adjstment of the Mohr Colomb model and the failre deviator stress in the stress ratio model. All other parameters in the harateriation models ere left nhanged so that the phi angle effet old be demonstrated. The pavement response parameters most ommonly sed in mehanisti pavement analysis are srfae defletion at the enter of loading, radial strain at the bottom of the asphalt, and vertial strain at the top of the sbgrade. The inflene of hanges in base orse phi angle is shon by the reslts of the analyses displayed in Table 1. n general, a pavement that exhibits a loer srfae defletion, a loer asphalt radial strain, and a loer sbgrade ver- CONCLUSONS On the basis of the testing and analyses reported in this paper, the folloing onlsions have been made, relative to the strtral harateriation of granlar base materials. 1. The k-theta-n model (Eqation 1) provides a good representation of the laboratory stress-dependent behavior of granlar material as long as the stress onditions are less than failre, as determined by the stati triaxial test. 2. The stress ratio model (Eqation 3) provides a good representation of the laboratory stress-dependent behavior of granlar material both belo and above stati failre stresses. 3. The stress, strain, and defletions predited sing the stress ratio model in the LL-PA VE finite element program are similar to those predited sing the Mohr-Colomb model. Hoever, the predited tensile stresses in the granlar base are loer, appearing to be more realisti. 4. The stress ratio model provides a means for analying the strtral effets of granlar materials having different shear strength harateristis. 5. Althogh additional testing and analysis are needed, the stress ratio model appears to offer a signifiant improvement in the ability to analye the strtral behavior of granlar base flexible pavements. ACKNOWLEDGMENTS This researh as part of a stdy, Development of an mproved Strtral Model for Granlar Pavement Layers, sponsored by the National Siene Fondation. The stdy as ondted by the Arkansas Highay and Transportation Researh Center at the University of Arkansas, Fayetteville. TABLE l COMPARSON OF STRESS RATO AND MOHR-COULOMB MODELS N EVALUATNG EFFECT OF GRANULAR BASE SHEAR STRENGTH Pavement Response Parameter Srfae defletion (in.) A\, rarfoil strain Sbgrade vertial strain Effet of Phi Angle ( ) by Strtral Model Mohr-Colomb Stress Ratio nmrn ()()n18()

6 Elliott and David REFERENCES 1. S. F. Bron and J. W. Pappin. Analysis of Pavements ith Granlar Bases. n Transportation Researh Reord 81, TRB, National Researh Conil, Washington, D.C., S. F. Bron and J. W. Pappin. Modeling of Granlar Materials in Pavements. n Transportation Researh Reord 122, TRB, National Researh Conil, Washington, D.C., J. Uan. Charateriation of Granlar Material. n Transportation Researh Reord 122, TRB, National Researh Conil, Washington, D.C., R. P. Elliott and M. R. Thompson. Mehanisti Design Conepts for Conventional Flexible Pavements. Trnnsportation Engineering Series No. 42, University of llinois at Urbana-Champaign, The opinions, findings, and onlsions expressed in this paper are those of the athor and not neessarily those of the National Siene Fondation. Pbliation of this paper sponsored by Committee on Strength and Deformation Charateristis of Pavements. 133