A new algorithm for back-calculating flexible pavement layer moduli

Size: px

Start display at page:

Download "A new algorithm for back-calculating flexible pavement layer moduli"

Lesley O’Neal’
6 years ago
Views:

1 ndian Journal of Engineering & Materials Sciences Vol. 10, June 2003, pp A new algorithm for back-calculating flexible pavement layer moduli Mehmet Saltan* Suleyman Demirel University, Engineering and Architectural Faculty, Civi l Engineering Department, 32260!sparta, Turkey Received 17 June 2002; accepted 28 March 2003 n thi s paper, a new algorithm for backcalculating pavement layer moduli from pavement deflection basin is presented. The algorithm uses SDUFEM finite element based backcalculation program in the iterative process and adopts backcalculating pavement layer moduli at fixed Poisson's ratios. After forward calculation for surface deflections at specific points is made with known elastic properties, fl exible pavement layer moduli are backcalculated usi ng new algorithm. n recent years, highway and transportation agencies have an increased responsibility for the maintenance and rehabilitation planning for flexible pavements. Knowledge of the structural condition of pavements is essential in order to assess the need for rehabilitation and the nature of required treatment, wich may be a strengthening overlay, or partial and complete reconstruction. n order to determine structural capacity of pavements, a non-destructive testing (NOT) equipment is preferred among highway agencies. These are mainly Benkelman Beam, Road Rater, Dynaflect and Falling Weight Deflectometer (FWD). Since the FWD simulates the wheel loading and its dynamic feature, many countries use the FWD. Backcalculating pavement layer moduli are wellaccepted procedures for the evaluation of the structural capacity of pavements. Deflections obtained from the FWD are used to backcalculate the layer material properties which are elastic modulus, Poisson's ratio and layer thicknesses. n order to determine the material properties, linear elastic theories and finite element methods (FEM) are used. Backcalculating the structural capacity of flexible pavements from non-destructive test data is one of the most efficient and economical methods. n order to simulate the truck loading on the pavement, a circular plate is dropped on the pavement from a certain height. The height is adjusted according to the desired load level. Underneath the circular plate, a rubber pad is mounted to prevent the shock loading. Seven geophones or sensors are generall y mounted on the trailer (the number of geophones or sensors can change). When the vertical *For correspondence ( load is applied on the pavement, the geophones collect the data in a byte form. Using the calibration factors, the bytes can be converted to the real deflections. Benkelman Beam and Dynaflect, which were mostly used in developing countries, only give the pavement information about underneath the circular plate. The FWD gives information about other six points which are away from the circular plate. Therefore, the effect of the wheel loading can also be seen in other points. Calculation of load-related pavement surface deflections at specific points using material properties of pavement layers (modulus, Poisson's ratio, thickness), is well established. Backcalculation of pavement layer moduli is a reversed procedure. Pavement layer moduli are calculated using loadrelated pavement surface deflection measurements (actual deflection bowl) and making assumptions for Poisson' s ratios 1 The use of models to backcalculate layer moduli from deflection bowl appears to be a promising method of determining the performance of in-service pavements 2 The finite-element method (FEM) has been widely used in numerous engineering problems 3. This method takes into account the complexity in the geometry and material properties. So, we can model the complex problems using FEM. Pavement layers are vertically layered. But, stiffness characteristics and material properties can be varied at horizontal directions as well as the vertical directions. Since the finite-element method is best suited for such circumstances, a number of researchers have used it in pavement analysis 4. FEM has been efficiently used in the structural capacity analysis of flexible pavements 5. There are a number of finite-element computer

SALTAN: A NEW ALGORTHM FOR BACK-CALCULATTNG FLEXTBLE PAVEMENT LAYER MODUL 203 programs available to compute pavement response to surface loading.

2 SALTAN: A NEW ALGORTHM FOR BACK-CALCULATTNG FLEXTBLE PAVEMENT LAYER MODUL 203 programs available to compute pavement response to surface loading. n this paper, SDUFEM finiteelement program developed by the present author 6 has been used. soparametric elements are used in SDUFEM. Theoretical SDUFEM has been developed 6 in The first estimation of material properties, or seed values are provided as input data by the user. Pavement response (surface deflection basin) is then calculated using FEM and compared with the measured response. f the calculated response is significantly different from the measured one, the new algorithm is used to generate new trial values of material properties. The following relative error square summation, RSS, defi nition is employed: 2 RSS = s ( d m _ d" ] = s ( d " ] dm dm t = l i 1= l i where d/' = calculated deflections m i 1 " d;" = measured deflections in i () geophone; geophone, and s=sensor number from i to s. The Poisson's ratio values for all layers are assumed to be fixed throughout the iteration process. After fi nite element mesh is generated using mesh generator routine, the software requires as input seed layer moduli and measured deflection values. t provides information on moduli, error in the calculated deflections, stresses and strains in the pavement concerned. FEM can be efficiently used for backcalculating pavement layer moduli 5. The accuracy of the method makes it possible to analyse the structural capacity of the pavements in a realistic manner. f necessary, software provides stresses and strai ns at nodal points of the finite element mesh for each iteration. SDUFEM program The algorithm presented in this paper is being implemented in the computer program named SDUFEM. User can easily activate the different backcalculation algorithms in the SDUFEM. The program can also make forward calculations fo r computing the deflections by using finite element technique. The program is very user-friendly. The problem in usi ng any finite element program is to prepare mesh data. n order to facilitate the mesh preparation, a mesh generator was developed and mounted in the SDUFEM. Finite element method in analysing flexible pavements Solutions of problems with complex geometry are very difficult. n order to solve this kind of problems, numerical methods are often used, one being FEM 7. FEM is efficiently used for modelling the objects with complex geometry. Different material properties for different layers can be easi ly defined using finite element method for multi-layered systems. n addition, nonlinear material behaviour, especially granular material behaviour, can be simulated using FEM as reported by Duncan et a/. 8 Material descriptions are simple for user 9. Boundary conditions are easily applied using FEM as reported by Siddharthan et a/. 10 (Fig. 1). Layered elastic theory was used fo r analysing flexible pavements for simplicity. Especiall y material behaviours are not modelled realistically using layered elastic theory. But use of FEM exterminates this drawback 11 Pavement systems and loading conditions are axiall y symmetric. So, displacements of pavement system only occur in vertical and radial directions (Fig. 2). '*' '-1 ::-... ""' ::-... "' :::::J.. '1' ("" 1'1 ", llrr t.rr Mr ll n Arr Fig.!- Typical finite element mesh used in SDUFEM

204 NDAN J. ENG. MATER. SC., JUNE 2003 LOAD! i Fig. 3-Deflection basin under loading Fig. 2- Finite element idealisation of axially symmetric system CF = 1 _ def/ -def/ defa.

3 204 NDAN J. ENG. MATER. SC., JUNE 2003 LOAD! i Fig. 3-Deflection basin under loading Fig. 2- Finite element idealisation of axially symmetric system CF = 1 _ def/ -def/ defa... (2) Backcalculation Backcalculation process is to find the beginning from results of a problem. n highway pavements, deflections are measured at the pavement surface using non-destructive testing equipment. Pavement properties are backcalculated using surface deflections. n this problem, typical applied load and surface deflection values are known (Fig. 3). But, in order to evaluate the pavement structural condition and to estimate the residual life of the pavement, elastic moduli values of each layer of a pavement must be determined. The basis of the backcalculation process is to compare the in situ measured and calculated deflection values of a pavement and to change the elastic moduli values of each layer until differences between measured and calculated deflection values reach a tolerance value 6. The new algorithm adopts a new iterative technique to backcalculate the elastic moduli of the layer in the pavement. Fig. 4 shows the flow chart of the iterative process used in the algorithm. The first estimated values of the moduli are input by the user and the moduli values are then corrected after each iteration until difference between measured and calculated deflection bowl is minimum. The principle for calculating a correction factor to correct a layer modulus after each iteration is based on a relationship between the elastic modulus and the deformation of the layer concerned. The elastic modulus of a layer is inversely proportional to the deformation of the layer. The deformation of the layer can be easily calculated using FEM. The correction factor of the calculated modulus value for a layer used in the n 1 h iteration can be expressed in terms of the calculated layer deformation and the actual layer deformation as: where def/' and def/ are the actual and calculated deformations respectively of layer i in the pavement. New moduli values for the next iteration (n+ 1) 1 h can be calculated as: "+ 1 = E" CF... (3) Eq. (2) can also be expressed in terms of surface deflections usmg relationship between layer deformations and surface deflections. The deformation in each layer is found by observation to reduce with increasing radial distances and become effectively zero at a distance named the "critical radial distance", rc, computed as follows: rc =a+ t.... (4) where l; is the equivalent depth to bottom of the layer i and a is the radius of the loading plate of FWD. For a multi-layer system, the equivalent thickness of the upper layers with respect to the modulus of the bottom layer can be expressed using the following. 13 equation :... (5) where l; S the equivalent thickness for radial distance measured deflection concerned, f is the correction coefficient for this equation changing between 0.8 and 1.0. n this algorithm, it is considered that a layer affects a measured deflection value at a

4 SALT AN: A NEW ALGORTHM FOR BACK-CALCULATNG FLEXBLE PAVEMENT LAYER MODUL 205 Measured deflections, load quantity, loading plate diameter Layer thicknesses (h), Poisson ratios(v), Material unit weights (y) Seed elastic moduli values (E) Material model descriptions and model parameters JDONG=JDONG+l Computing of surface deflections at certain radial distances using finite element method Detennination of deflection bowl fonn using least squares Correction of layer elastic moduli values (new algorithm) No No Output of backcalculated elasticity moduli and measured and computed deflection values Fig. 4-Backcalculation algorithm used in the program radial distance from loading center. This critical radial distance can be determined using equivalent thickness equation for each layer in the pavement. n order to estimate critical radial distance affected from a layer from loading center, the equivalent thickness to bottom of the layer must be computed. Numerical example n order to check the new algorithm, backcalculation process is applied for a four-layer-pavement (Fig. 5). Layer characteristics of the pavement, load quantity, loading plate radius and layer thicknesses are given in Fig. 5. After surface deflection values are obtained using FEM throughout forward calculation, the pavement layer moduli values are backcalculated using new algorithm. Different elastic moduli values from actual ones are attained as seed moduli values; and near moduli values to actual ones are obtained using new algorithm (Table 1 and Fig. 6). Comparison between deflections used for backcalculation and deflections using elastic moduli obtained from new algorithm is shown in Fig. 7.

206 NDAN 1. ENG. MATER. SC., JUNE 2003 H 15 em. q-550 kpa... Bituminous Layer - 1000 MPa y=().j5 F2.4 kglm 3!Oem. Base Course - 600 MPa y=().j5 r=2.2 kglm 20 em. Subbase -400 MPa v-0.40 r=2.

5 206 NDAN 1. ENG. MATER. SC., JUNE 2003 H 15 em. q-550 kpa... Bituminous Layer MPa y=().j5 F2.4 kglm 3!Oem. Base Course MPa y=().j5 r=2.2 kglm 20 em. Subbase -400 MPa v-0.40 r=2.2 kglm 3 20 em. OOS' 0,0 111 "' oou 0086 A O J.a4.:; OC!? Subgrade -200 MPa v-=0.45 r=2.0 kglm half spaee Ot7 Fig. 5-Pavement system for checking new algorithm "00, , D Actu l Saoo.c.a lc ul t ed Fig. 7- Comparison of deflection values calculated by using results in Table 1 Table!- Actual and backcalculated elastic moduli values Elastic moduli Bituminous Base Subbase Subgrade values (MPa) Layer course course Actual Backcalculated Fig. 6-Compari son of actual and backcalculated elastic modu li values Conclusions The backcalculation process is a complicated but powerful tool and is based on empirical evidence. An algorithm based on the FEM is presented for the backcalculation of pavement layer properties from measured surface deflections. The method is capable of backcalculating pavement layer moduli and has been implemented in the backcalculation program named SDUFEM. Until now, in computing the critical radial distance to loading center, loading radius was added to layer thickness. But, this is not realistic. n the new algorithm, loading radius is added to equivalent layer thickness and equivalent thickness for each layer is re-computed for each iteration. This condition affects the backcalculated layer elastic moduli values. For this numerical example, the critical radial distance is 30 em according to Vuong's algorithm, while it is em for the new algorithm. This difference affects the backcalculated layer elastic moduli values. So, it can be concluded that critical radial distance from loading center is extremely important in backcalculating pavement layer moduli. References Noureldin A S, New scenario for backcalculation of layer moduli of flexible pavemellfs, Transportation Research Record 1384, USA, Vuong B, Aust Road Res, 19( ) (1989) Zienkiewicz 0 C & Taylor R L, The finite element method, Vol. (McGraw-Hill Book Company, London), Siddharthan R, Yao J & Sebaaly PE, Field verification of moving load model for pavemellf response, Transportation Research Record No. 1540, U.S.A., Tseng K H, A finite element method for the performance analysis of flexible pavements, Ph.D. Thesis, Texas A&M University, U.S.A., Saltan M, Analytical Evaluation of Flexible Pavemems, Ph.D. Thesis,!sparta, Turkey, Gi.inay D, Basis of finite element method for enginee rs (in Turkish), (Sakarya University, Sakarya, Turkey), Duncan J M, Monismith C L & Wilson E L, Finite element analysis of pavements (U.S.A.), Highway Research Record No. 228, Stock A F, Flexible pavement design, Ph.D. Thesis, University of Nottingham, U.K, Siddharthan R, Norri s G M & Zafir Z, Pavement material properties using non-destructive testing, Proc Third lnt Conf Constitut Laws Eng Mater: Theory Applicat, Tuscon, Arizona, USA, ( 199 1) Ong C L, Newcomb D E & Siddharthan R, Comparison of dynamic and static backcalculation modulus for three layer pavements (Transportation Research Board 70 1 h Annual Meeting, Washington, D.C.), January 13-17, 1991, Paper No.9!. 12 Clough R W & Rashid Y, 1 Eng Mech Div ASCE, USA, 91, (EMl) (1965) Ullidtz P, Pavement analysis (Elsevier Science Publishing Company, nc., Netherlands), 1987.

THE DEVELOPMENT OF AN ANALYTICAL OVERLAY DESIGN PROCEDURE BASED ON THE ASPHALT INSTITUTE 83 METHOD. Djunaedi Kosasih. Civil Engineering Department

THE DEVELOPMENT OF AN ANALYTICAL OVERLAY DESIGN PROCEDURE BASED ON THE ASPHALT INSTITUTE 83 METHOD Djunaedi Kosasih Civil Engineering Department Faculty of Civil Engineering and Environment Institute of