DETERMINATION OF STRESS-DEPENDENT MATERIAL ...

DETERMINATION OF STRESS-DEPENDENT MATERIAL PROPERTIES WITH THE FWD, FOR USE IN THE STRUCTURAL ANALYSIS OF PAVEMENTS USING FINITE ELEMENT ANALYSIS TECHNIQUES S.J. Bredenhann1 and K.J. Jenkins2 1

Entech Consultants (Pty) Ltd PO Box 413, 7600 Stellenbosch, South Africa. E-mail: [email protected]. Currently TUDelft, Section of Structural Mechanics, Stevinweg 1, 2628 CN Delft, The Netherlands. E-mail: [email protected] 2 SANRAL Chair in Pavement Engineering University of Stellenbosch, Private Bag X2, Matieland, 7602 South Africa. E-mail: [email protected]

ABSTRACT The stress-dependent and nonlinear behaviour of granular pavement materials is well known. It is however expensive and time consuming to determine the properties of such materials in a laboratory. It has been shown that, as part of pavement investigation, the drop sequence of the Falling Weight Deflectometer (FWD) measurements can be successfully adjusted and used in the determination of material characteristics. Experience from an investigation of pavements on highly trafficked roads is used to demonstrate the role of a FWD in the determination of material properties to describe the nonlinear and stress-dependent material behaviour of insitu pavement materials. FWD deflections were measured at four different load levels, with five drops at each load level. Back-calculation of layer moduli for each load level gave an indication of the stress-dependent behaviour of each layer. The pavement response at each load level, and therefore the stress condition for each layer, was calculated using a linear-elastic method. Material characteristics for the pavement layers were determined from the relationships developed by comparing the back-calculated moduli with the calculated pavement responses. This method of determining material characteristics proved to be very cost-effective. Material models describing the stress-dependent behaviour of each layer as determined from the material characteristics and pavement response is applied in a structural analysis of the pavement using Finite Element Analysis techniques. From the finite element analysis firstly the required cement treated subbase thickness is calculated and secondly the resulting stress condition in the foamed bitumen treated base course is calculated. It is shown that the FWD can be used to extract more information out of an existing pavement than is currently the case. Different falling weight loads allow stress dependent models to be cost-effectively developed. Stress ratios in granular and foamed bitumen treated layers determined using stress dependent analyses of pavement structures incorporating these layers, should be used for pavement design. Keywords: Stress-dependent, back-analysis, FWD, foamed bitumen

Proceedings of the 8th Conference on Asphalt Pavements for Southern Africa (CAPSA'04) ISBN Number: 1-920-01718-6 Proceedings produced by: Document Transformation Technologies cc

12 – 16 September 2004 Sun City, South Africa

8th CONFERENCE ON ASPHALT PAVEMENTS FOR SOUTHERN AFRICA

1. INTRODUCTION An investigation of a pavement on a highly trafficked route was carried out for rehabilitation design purposes. The road is in a remote part of South Africa with a limited availability of quality road base material. The finite element analysis on test results from one test pit is presented in this paper as an example of how the structural analysis involving a foam treated layer can be approached. Bredenhann et al (2002) showed that, as part of pavement investigation, the drop sequence of the Falling Weight Deflectometer (FWD) deflection measurements can be successfully adjusted and used in the determination of material characteristics. FWD deflections were measured at four different load levels, with five drops at each load level. Back-calculation of layer moduli for each load level gave an indication of the stress-dependent behaviour of each layer. The pavement response at each load level, and therefore the stress condition for each layer, was calculated using a linear-elastic finite element analysis method. Material characteristics for the pavement layers were determined from the relationships developed by comparing the back-calculated moduli with the calculated pavement responses. This method of determining material characteristics proved to be very cost-effective. Material characteristics for the foam bitumen treated material were determined with three types of triaxial tests, namely: monotonic tests; short dynamic tests; and repeated load dynamic tests to determine the shear parameters (Cohesion C and angle of internal friction (φ)) and resilient stiffness (MR), respectively. Stress dependent models for resilient stiffness and permanent deformation developed by Jenkins (2000) were used to design the pavement in such a way that safe stress ratios in the foam treated base are not exceeded. Finite Element Analysis techniques were used in the analyses. Jenkins showed that the ratio of critical deviator stress in a layer, as determined through pavement modelling, relative to the ultimate deviator stress under the same confining stress, as determined by the shear parameters of the material (from lab tests), will define the permanent deformation behaviour of a “granular type” material. The stress ratio approach was shown to be applicable to foamed bitumen treated materials (Jenkins, 2000) and granular materials (van Niekerk, 2002). The choice of the cemented subbase thickness is very important. Experience has shown that the pavement life is usually determined by the cemented subbase strength and this again proved to be true with this design.

2. EXISTING PAVEMENT AND MATERIAL PROPERTIES The road under review is located in the Western Cape in a semi-arid (dry) climate with a Weinert N-value > 5, indicating that weathering is caused by physical breakdown. The specification for the existing pavement structure is as follows (COLTO, 1994): •

19 mm Cape Seal, a seal with a single 19 mm stone on a tack coat with two applications of slurry.

•

200 mm G1 base layer of sandstone, a graded crushed stone layer conforming to grading requirements, i.e. Grading Coefficient n = 0,45.

•

150 mm G5 subbase layer of sandstone gravel, a natural or crushed gravel with CBR > 45% and grading requirements specified with GM 1,5 to 2,5.

•

250 mm G7 selected layer, natural material with CBR > 15% and GM 0,75 to 2,7. Grading Modulus (GM) is defined in COLTO (1994).

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In total 26 test pits were excavated on the road, roughly one every kilometre. Results of field tests of the test pit at km 2,0 are shown in Table 1. Only these field test results are shown as the foam bitumen designs were done on material from this test pit. Material on this project was rather uniform and the results shown in Table 1 are fairly representative of the material on the project. Table 1. Properties of Layers in Pavement Structure at km 2,0.

Notes: 1. Base course material must comply with a very stringent grading and compaction specification. These specifications were not in use yet when this road was built some thirty years ago. 2. The CBR values shown for base, subbase and SSG layers are at 98%, 95% and 93% compaction as per specification.

From Table 1, it is observed that the Atterberg Limits comply with the specified parameters for a G1 material, as could be expected from sandstone. The CBR at 98 % of modified AASHTO density is 140 %, which is higher than the specified minimum CBR of 80 % for a G1 material. The modified AASHTO density of the base layer sample is 2 200 kg/m³, which is typical for a sandstone material. In-situ density exceed 98 % of modified AASHTO density, with a density of 100,5 %. The in-situ moisture contents of all the layers were found to be close to the Optimum Moisture Content (OMC) of the material, which is high for the region. An equilibrium moisture content of approximately 70% of OMC would have been expected. Local influences such as seasonal climatic effects and surface cracking could have influenced these results. The grading of the base material does not conform to well-graded, high density graded crushed G1 specifications (COLTO, 1996). The fractions passing the 4,75 mm up to the 19,0 mm sieves are too coarse, up to 10 % in the case of the 13,2 mm sieve as is shown in Figure 1. This result in a higher percentage voids in the layer, and can possibly be linked to the high in-situ moisture content of the base. From Table 1 it is also observed that the Atterberg limits comply with the specified parameters for an untreated G5 subbase material, but the CBR value of the sub-base layer is substantially lower than the specified 45 % at 95 % modified AASHTO compaction. The CBR of the subbase material of 40 % at in-situ compaction is still lower than the specified requirement. The subbase is thus clearly the weak link in the pavement and it will be shown later that the FWD deflections also show the subbase as the weak layer. It is clear from table 1 that the selected layer exhibits properties of a high quality material with a CBR value well in excess of the specified 15 % at 93 % of modified AASHTO.

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Figure 1. Grading of base material.

3. REHABILITATION DESIGN It was shown that the subbase do not comply with specifications. While base material does comply with Atterberg and other indicator specifications it fails the G1 grading specifications. Various options to rehabilitate the pavement were investigated (i.e. thick asphalt overlay, concrete overlay and granular overlay, all with a lightly cemented subbase), but only the foamed bitumen in combination with a lightly cemented subbase is discussed in this paper. It is proposed that the surfacing and 200 mm base layer be reworked in a single milling operation, with the addition of make-up material, and modified with 2,0 % cement to a 300 mm thickness C3 quality subbase with Unconfined Compressive Strength (UCS) of 1 500 MPa minimum. A new foamed bitumen treated sandstone base, 150 mm thick, will be added on top of the C3 subbase giving adequate protection to the weak existing subbase layer.

4. TRAFFIC LOADING The predicted traffic loading for the pavement under consideration is 8,0 to 17,1 x 106 ESALs for a 20-Year Structural Design Period for axle load factors varying from 0,6 to 0,8.

5. METHODOLOGY A finite element analysis was done using the computer program PaveFEL, an axi-symmetric finite element analysis program developed by the main author and based on the linear-elastic finite element program Felipe. Eight-noded quadrilateral elements are used with four integration points per element. The mesh utilised for the finite element analysis of the road pavement is summarised in Table 2. The total finite element mesh is 896 elements and 2 809 nodes. Nodes at the bottom are assumed to be fixed in both directions with nodes at the side assumed fixed in the horizontal direction only. A comparison of the results from PaveFEL in the linear-elastic mode compares well with multilayer linear-elastic programs such as mePADS.

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8th CONFERENCE ON ASPHALT PAVEMENTS FOR SOUTHERN AFRICA Table 2. Division of existing pavement layers for finite element mesh.

The use of finite element method in the structural analysis of pavements is highly recommended. Most material response parameters are deduced from deflection analysis (as is the case in this paper) while the actual pavement design is done at a totally different stress condition, i.e. when a cemented layer is introduced the stress below the cemented layer will reduce drastically and subsequently the modulus. Finite element analysis also brings other benefits such as the possibility to model variation in contact pressure.

6. LOADS Only single loads are analysed with PaveFEL, reducing the problem to an axi-symmetric one. The loaded area is divided into six elements of equal dimension of 25 mm. Since the existing 200 mm base course is also divided into 25 mm elements in the horizontal direction, the elements directly underneath the loaded area are square elements of 25 mm x 25 mm. The load is then distributed uniformly over the six elements underneath the load, with equivalent loads being applied at each node as determined by numerical integration.

7. MATERIAL MODELS FOR GRANULAR MATERIAL Five material models for granular materials were implemented in PaveFEL.

7.1 Bulk Stress ( K − θ ) Model Resilient moduli (MR) of granular materials are characterized with the K-θ model. The mathematical representation of the K-θ model is shown in Equation 1 and Equation 2 in log-log and semi-log format respectively.

Μ R = k1θ k 2 Μ R = k1e k sθ

(Eq.1) (Eq.2)

Where θ = σ1 + σ2 + σ3, with k1, k2 and k3 as material constants. This model is demonstrated in Figure 2. The behaviour of the log-log and semi-log models are totally different, especially at low and high stress levels. The semi-log model can accommodate negative bulk stress levels, while adjustments must be made to the bulk stress for the log-log model. Since the semi-log model grows exponentially with high bulk stresses the model implemented makes provision for a maximum value of MR. Paper 041


1800

Resilient Modulus (MPa)

1600 1400 1200 1000

Log-Log

800

Semi-Log

600 400 200 0 -1000

-500

0

500

1000

1500

Bulk Stress θ (kPa)

Figure 2. K-θ model for granular materials.

7.2 Huurman-Van Niekerk Model The most recent developed model to characterize the material behaviour of granular materials is the Huurman-van Niekerk Model, as shown in Equation 3 (Huurman (1997), van Niekerk (2002)). The model is an extension of the bulk stress K – θ model and relates resilient modulus to the ratio of the main principal stress σ1 to the principal stress at failure σ1,f.

M R = k1θ

σ 1, f =

k2

⎡ ⎛ σ ⎢1 − k 3 ⎜ 1 ⎜σ ⎢ ⎝ 1, f ⎣

⎞ ⎟ ⎟ ⎠

k4

⎤ ⎥ ⎥ ⎦

(Eq.3)

(1 + Sinφ )σ 3 + 2c ⋅ Cosφ 1 − Sinφ

(Eq.4)

Resilient Modulus MR (MPa)

Huurman-van Niekerk’s Model is illustrated in Figure 3, showing the material behaviour at different confinement stress levels. 2500 2000

σ3 = 75 kPa σ3 = 125 kPa

1500

σ3 = 175 kPa 1000

σ3 = 225 kPa σ3 = 500 kPa

500 0 0

500

1000

1500

2000

2500

3000

3500

4000


Figure 3. Huurman-Van Niekerk model for granular material.

The Huurman-van Niekerk Model is a more comprehensive model than the K-θ model and describes the material behaviour of granular materials better. Paper 041


7.3 Uzan Model Uzan (1992) published a uniform approach for the characterization of pavement materials and is shown in Equation 5. k3 M R = k1θ k 2 τ OCT

(Eq.5)

The Uzan Model is applicable for both granular stress-hardening and cohesive stresssoftening materials, making it very attractive for computer applications.

7.4 Thompson and Elliot Bilinear Model Resilient moduli (MR) of cohesive soils are specified in terms of deviator stress through a bilinear model Harichandan et al (2000) and the mathematical representation of the bilinear model is shown Equation 6.

Μ R = K 2 + K 3 (K 1 − σ d ) when σ d ≤ K 1

(Eq.6)

K 2 + K 4 (σ d − K 1 ) when σ d > K 1

where σd = σ1 - σ3 with K1, K2, K3 and K4 constants of the model. Thompson and Elliot (1999) found through extensive laboratory testing, non-destructive pavement testing and pavement analysis and design studies at the University of Illinois that the bilinear model is adequate for the material modelling of cohesive materials. The Bilinear Model is illustrated in Figure 4, with a comparison with the Uzan Model to show that the Uzan Model can be used instead of the Bilinear Model. The Uzan Model is a continuous function enabling easier computer iteration. 200 Resilient Modulus t (MPa)

180 160 140 120

Uzan

100

Thompson

80 60 40 20 0 0

20

40

60

80

100

120

Deviator Stress σ d (kPa)

Figure 4. Bilinear model for cohesive materials (Harichandran et al, 2000).

Typical values for K1, K2 and K3 are shown in Table 3 Huang (1993). Table 3. Typical values for material constants in bilinear model (Huang, 1993).

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8. MEASURED DEFLECTIONS Deflection measurements were done at four load levels at each test pit position. Five drops were done at each load level (a total of 20 drops), which was normalised and averaged for every load level in an effort to eliminate standard and random errors normally incurred with deflection measurements. Normalized measured deflections at different load levels for the test pit at km 2,0 are shown in Table 4. Table 4. Measured deflections at different load levels.

9. DETERMINATION OF MATERIAL PARAMETERS THROUGH BACK-CALCULATION The back-calculation will be done with the following three methods: Conventional multilayer linear-elastic method Linear-elastic finite element method Linear-elastic finite element method with stress-dependent models The conventional multilayer linear-elastic method is included as demonstration only as the main purpose of this paper is to concentrate on the finite element method. Geostatic (gravity) stresses in both the vertical and lateral directions must be included in the models. Since an axi-symmetric problem is analyzed in this paper the vertical and horizontal geostatic stresses will coincide with the principal stress directions.

9.1 Conventional Multilayer Linear-Elastic Back-Calculation As a demonstration the K – θ Bulk Stress Model is determined using the multilayer linear-elastic method. Back-calculation is done in a conventional manner for every load level after which the stresses, including geostatic stresses, are calculated. The material model is then determined with regression analysis as is shown in Figure 5. Stress-dependent models obtained with this method can only be applied in multi-layer linear-elastic analysis. It can be used as a guideline for the determination of model parameters in the finite element analysis, but it cannot be used directly. The multi-layer linear-elastic method is especially extremely helpful in determining whether a material has a stress-hardening or a stress-softening behaviour.

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Figure 5. K - θ bulk stress model for base course based on multilayer linear-elastic method.

As a further demonstration it is shown in Figure 6 that the model can be improved by using the semi-log bulk stress model.

Figure 6. Semi-log bulk stress model for base course based on multilayer linear-elastic method.

In Figure 7 the bilinear model for the subgrade is illustrated. It should be noted from Figure 7 that k1 material constant is approximately 45 kPa and that the slope of the σd < k1 line is positive.

Figure 7. Bilinear model for subgrade based on multilayer linear-elastic method. Paper 041


9.2 Linear-Elastic Back-Calculation with Finite Element Method A comparison of the back-calculated moduli with the two linear-elastic models is given in Table 5. Table 5. Comparison of back-calculation with linear-elastic multilayer and finite element methods for normalized 40 kN load level.

The back-calculated deflection basin with the finite element method is shown in Figure 8.

Figure 8. Back-calculation with linear-elastic finite element method.

It should be noted from Figure 8 that a very good fit was obtained for the deflection value at the 200 mm offset. Normally with linear-elastic back-calculations the fit at the 200 mm geophone is poor and almost impossible to improve. Factors such as annular stress distribution in the circular load (rubber buffer) and local effects in the 50mm zone outside the FWD loading plate (where the 200mm offset geophone is located), also play a role. This is in addition to the lateral stress distribution limitations inherent in non-FEA linear-elastic modelling.

9.3 Back-Calculation with Stress-Dependent Linear-Elastic Finite Element Method The existing pavement structure was analysed as an 8-layer system and back-calculations done with PaveFEL (i.e. finite element methods) with back-calculated material constants shown in Table 6. The K – θ material model were used for layers 1 to 4 and the bilinear model for layers 5 to 8.

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8th CONFERENCE ON ASPHALT PAVEMENTS FOR SOUTHERN AFRICA Table 6. Back-calculated stress-dependent material models for existing layers.

Although the other material models, i.e. Huurman-van Niekerk and Uzan were also used in alternative calculations, but only the K – θ and bilinear models are reported here due to limited space. The back-calculated deflection basins for the four load levels are shown in Figure 9. 0.0

0.3

0.6

0.9

1.2

1.5

1.8

0.0

DEFLECTION (mm)

-0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

OFFSET (m) Calculated

Measured

Figure 9. Back-calculation results with FEM.

The best results were obtained with the 40 kN and 50 kN load levels with a very good fit on all the deflections at all load levels, except for the maximum deflections. It will be noted that the calculated maximum deflections at 30 kN and 60 kN are respectively lower and higher than the measured one. A semi-log model for the base course was tested, based on the experience gained with the linear-elastic results in Figure 6, but the model gave erroneous results due the exponential nature of the model. It was decided that a bulk stress model with a k2 = 0,66 is representative of the base course (remember that the existing base course will be reworked so that the base course model will not be used in the design). As far as stress-dependent back-calculation is concerned the following should be noted: With stress-dependent back-calculation the material parameters, i.e. k1, k2, etc. are backcalculated rather than the E-moduli as in the linear-elastic case. It is only really possible to back-calculate one parameter at a time, therefore one parameter is selected and the second parameter is back-calculated. Paper 041


A complicated model like the Huurman-van Niekerk model has many parameters and a prior knowledge of the material, or similar materials, is beneficial in estimating some parameters. Even with the K-θ model it is suggested that the parameter k2 is based on experience with similar materials and only k1 is back-calculated. The procedure followed in the back-calculation was to back-calculated the material parameters for the 40 kN load level initially and then use the same parameters in the 30 kN, 50kN and 60 kN load levels. If the fit is not good in the other load levels adjustments can be made. When making adjustments it should be kept in mind what the specific parameter represents. As an example, in the K-θ model k1 is an indication of material quality and density, while k2 is an indication of the stress dependency of the material. Therefore, as an example, once k1 in the K-θ model is back-calculated for a certain k2 at 40 kN, the fit is checked at the other three load levels of 30 kN, 50 kN and 60 kN and k2 adjusted and the whole process is repeated. The model parameters are not mutually exclusive and normally there is a relation between parameters, therefore the parameter sets are not unique. It should, however, be kept in mind that a model of the pavement is built and that this model must represent the pavement in the conditions it will be used. It is not suggested that back-calculated material parameters should replace laboratory procedures such as triaxial testing. It is rather suggested that deflection measurements is used to augment laboratory work with laboratory work being concentrated on the upper layers.

10. COMPARISON OF DIFFERENT MODELS A brief comparison of the different models is given below, mainly to compare the implementation of and performance of the models in the finite element method.

10.1 Bulk Stress Model The bulk stress model is easy to implement and gave consistent good results. It is, however, necessary to implement some safety precautions in the finite element model as the bulk stress becomes very low in elements far away from the load or deep down in the pavement. A minimum modulus was therefore introduced in the program, related to a minimum bulk stress. It must also be realised that the bulk stress model does not give an accurate representation of the actual material behaviour as is determined in the triaxial equipment (Huurman, 1997).

10.2 Semi-Log Bulk Stress Model The semi-log bulk stress model gives good results in multi-layer linear-elastic analysis where parameters are obtained directly through regression analysis. In finite element analysis one needs to cap the model by specifying a maximum modulus as the exponential nature of the model will predict very high moduli due to the high stress in the elements just below the load. This capping exercise results in reduced accuracy and unpredicted behaviour of the model in finite element analysis.

10.3 Huurman-Van Niekerk Model The Huurman-van Niekerk Model is a more comprehensive model than the K-θ model and describes the material behaviour of granular materials better. Actual behaviour as determined with triaxial tests is described accurately. Computer implementation of the Huurman-van Niekerk Model is, however, difficult due to its complexity and instability in the finite element program can occur easily. Assumptions must be made for at least three parameters and one parameter back-calculated at a time. This becomes a very time consuming operation. It was Paper 041


possible to build a model for the base course but implementation in more layers at once becomes too complicated. Further investigation is required in the application of this model as it is felt that this model is essential for detailed analyses. Alternative models exist (Huurman, 1997) that do not rely on the bulk stress and promise to be more stable in finite element analysis.

10.4 Uzan Model The Uzan Model is a uniform model that is applicable for both stress-hardening and stress-softening behaviour of materials. It is easy to implement in the finite element method and it is not required to make adjustments for low bulk stress conditions as the octahedral shear stress component will take care of that situation.

10.5 Bilinear Model The Bilinear Model is a well tested model. Its effect was, however, not important in this study as the subgrade moduli are high. The variations in moduli due to a stress condition in the pavement therefore have been small. The model will prove to be important if one should investigate the situation where the subgrade becomes wet and therefore softer, i.e.

11. MATERIAL MODELS FOR PAVEMENT LAYERS The following material models were implemented for each of the pavement layers.

11.1 Material Model for Foam Treated Base Course Material Three types of triaxial tests were carried out on the foamed treated material, namely: monotonic tests; short dynamic tests; and repeated load dynamic tests to determine the shear parameters Cohesion C, angle of internal friction (φ) and resilient stiffness (MR) of the foam bitumen treated base, respectively. Two material models, shown in Figure 10 and Figure 11 respectively, were investigated for the foam treated material. The MR – θ - τOCT model is essentially the Uzan model. 12000

(σ3)0.385 MR

10000 8000 6000 4000 MR = 139.54θ0.599σ3-0.385

2000

R2 = 0.99

0 0

200

400

600

800

1000

1200

1400

1600

Bulk Stress θ (kPa) Figure 10. MR - θ - σ3 material model for foam treated material.

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12000

(τoct)0.385 MR

10000 8000 6000 4000 MR = 77.901θ0.681τoct -0.385

2000

R2 = 0.53

0 0

200

400

600

800

1000

1200

1400

1600


Figure 11. MR - θ - τOCT material model for foam treated material.

From Figure 10 and Figure 11 it is clear that the MR – θ - σ3 material model fits the laboratory data best. This model is defined in Equation 7 and shown graphically for different confinement stress values in Figure 12.

M R = 139 .54θ 0.599 σ 3−0.385

(Eq.5)

Resilient Modulus M R (MPa)

1500 1400 1300 1200 1100

100 kPa

1000

150 kPa

900

260 kPa

800 700 600 500 0

500

1000

1500

2000

Bulk Stress θ (kPa) Figure 12. resilient modulus for a foam treated base as determined with triaxial testing (COLTO, 1994) and MR – θ –σ3 material model.

11.2 Material Model for Cement Treated Subbase Material The long-term behaviour of cemented C3 Subbase is described in COLTO (1994) and shown schematically in Figure 13. Initially the cemented subbase is in the pre-cracked phase with a very high E-modulus. The duration of this is relatively short after which the cemented layer moved into a phase of effective fatigue life where the life of the layer is determined by the horizontal strain at the bottom of the layer. At the end of the effective fatigue life the pavement Paper 041


moves into an equivalent granular state. Based on research and experience certain material parameters are suggested in COLTO (1994), i.e. an E-modulus of 1 500 MPa for the effective fatigue phase and 300 MPa for the equivalent granular phase. The cemented subbase was modelled in two phases along these guidelines.

Figure 13. Long-term behaviour of cemented subbase (Colto, 1994).

A linear-elastic material model for both the effective fatigue and equivalent granular phases of the cemented material was implemented. The pre-cracked phase normally represents a very short period in the total pavement life and was not modelled.

11.3 Material Models for Supporting Layers Material models for the supporting layers were developed from back-calculated E-moduli at different load levels reported in Table 6. Principal stresses, incorporating geostatic stresses, were calculated for each set of load level and E-moduli. The model parameters for the pavement layers are summarized in Table 7. Table 7. Model constants and material properties for nonlinear material models.

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Effective fatigue phase Equivalent granular phase Cohesion and ø for existing layers, shown in Table 7, is based on experience with similar materials specified in COLTO (1994).

12. PAVEMENT RESPONSE The pavement’s life entirely depends on the cement treated subbase as is shown in Figure 14.

Pavement Life (E80 Axles)

1.00E+08

1.00E+07

1.00E+06 200

220

240

260

280

300

Layer Thickness (mm) Nf

Ll

Lu

Figure 14. pavement life based on cemented subbase.

From Figure 14 it is deduced that a pavement with a cement treated subbase thickness of approximately 235 mm to 285 mm will ensure that the required pavement life is achieved. It should be noted that the pavement life shown in Figure 14 is based on the results of a single test pit, presented here as an example. In a complete pavement design the variability of the measured deflections would have been accounted for in a statistical approach resulting in a thicker layer thickness. In conclusion it is clear that the required rehabilitation measure for this road will be reworking the existing base and adding make-up material to a achieve a 300 mm CTSB and add a new 150 mm foam treated base course with a 50 mm asphalt surfacing. The calculated stress condition in the foam treated base course layer for a 40 kN load and 700 kPa contact stress, is shown in Table 8. In this case the stress ratio that has been determined is the ratio of Major Principal Stress resulting from the load relative to the maximum Major Principal Stress that the particular material can sustain (using C and φ). Jenkins (2000) and van Niekerk (2002) also use the deviator stress to determine this ratio, which is a more consistent parameter as it does not create anomalies at high Minor Principal Stresses in materials with low φ values, as experienced by the former model. In this analysis, the former ratio i.e. Major Principal Stress Ratio, is consistent and suffices. Table 8 shows that the stress ratio in the foam treated base never exceeds 0,3 indicating that very little permanent deformation can be expected (Jenkins, 2000), as it is significantly less than the critical value of 0,4 to 0,45. It is interesting to note that the stress ratio in the base decreases as the CTSB loses stiffness. This occurs because, without adequate support, the Paper 041


stress dependent base is unable to attract high stresses and generate a higher resilient modulus. In effect, in the equivalent granular phase the load spreading by the base and subbase will reduce and the stresses from the wheel load will be transferred deeper into the pavement structure, causing an increase in deformation at depth. Table 8. Stress condition in foamed base on a 300 mm thick CTSB.

The effect of the cemented subbase layer on the stress condition in the foam treated base course layer can be seen in Table 8. As soon as the cemented subbase layer’s modulus reduced to its equivalent granular state, tension develops in the base course layer. This aspect will be addressed in further research as the tension can be attributed more to the theory used than the actual situation.

13. CONCLUSION It has been shown that the FWD can be used to extract more information out of an existing pavement than is currently the case. Parameters describing the characteristic material behaviour of insitu pavement material were successfully determined by adjusting the FWD drop sequence. Material parameters for the foam treated material were determined through triaxial tests in the laboratory. The combination of FWD measurements and laboratory testing proved to be an economical way to develop more sophisticated pavement design models. All the material models investigated could be implemented in a finite element model. As for back-calculation the bulk stress model proved to be the easiest to use as only two parameters need to be estimated. However, it was possible to obtain good results with other models as well, but certain knowledge and experience is required in the estimation of parameters the more sophisticated the model becomes. Experience gained form the work done so far indicates that the sophisticated like the Huurman-van Niekerk model should be used for new layers and material parameters should be determined in a laboratory. Stress ratios in granular and foamed bitumen treated layers determined using stress dependent analyses of pavement structures incorporating these layers, should be used for pavement design. The use of finite element analysis in pavement design is highly recommended. Due to different stress conditions in the pavement during its lifetime (new pavement) as compared to the situation when the deflection measurements were taken it is necessary to extrapolate from Paper 041


one stress condition to the other. This can only be done with stress-dependent models, preferably implemented in finite element methods as these can then be used in nonlinear analysis as well as elasto-plasto type analyses.

14. ACKNOWLEDGEMENT The South African National Roads Agency Ltd is thanked for permission to publish this paper. Riaan Burger, PhD student and Lee-Ann Mullins, MSc (Eng) student at the Stellenbosch University and Paul Faria, engineer at Entech Consultants (Pty) Ltd, are thanked for work they did. The cooperation of V&V Consultants (Pty) Ltd, as Joint Venture Partners on the project, is also acknowledged.

15. REFERENCES Bredenhann, SJ, Jenkins, KJ and Bester AJ (2002). A Practical Approach To Non-Linear Structural Analysis Of Pavements Using Finite Element Analysis Techniques. 3rd International Symposium on 3D Finite Element for Pavement Design and Research. Amsterdam. April 2002. COLTO (1994). The South African Mechanistic Design Method. Committee for Land Transport Officials. Pretoria. 1994. COLTO (1996). Structural Design of Flexible Pavements for Interurban and Rural Roads. Committee for Land Transport Officials. Draft TRH4. Pretoria. 1996. Harichandan, RS and Baladi, GY (2000). Michpave User’s Manual (Version 1.2). Michigan State University. Michigan. January 2000. Haricahndran, RS and Ming-Shan Y (1998). Flexible Boundary in Finite-Element Analysis of Pavements. Transportation Research Record 1207. TRB. Washington. 1998. Huang YH (1993). Pavement Analysis and Design. Prentice- Hall International UK, London. Huurman M (1997). Permanent Deformation in Concrete Block Pavements. Doctoral Dissertation. Delft University of Technology, Netherlands. Jenkins KJ and van de Ven MFC (1999). Investigation of the performance properties of the Vanguard drive road, recycled with foamed bitumen and emulsion respectively and analysed using accelerated pavement testing and triaxial testing. ITT Report 9-1999 for Stewart Scott Inc., University of Stellenbosch. Jenkins KJ, van de Ven MFC, Derbyshire R and Bondietti M (2000). Investigation of Early Performance of a Pavement Recycled with Foamed Bitumen and Emulsion through Field Testing. South African Transport Conference (SATC) Pretoria, Session 2C. Jenkins KJ (2000). Mix Design Considerations for Cold and Half-warm Bituminous Mixes with an Emphasis on Foamed Bitumen. Doctoral Dissertation. University of Stellenbosch. Thompson MR and Elliott RP (1985). ILLI-PAVE-Based Response Algorithms for Design of Conventional Flexible Pavements. Transportation Research Record 1043. TRB. Washington. 1985. Van Niekerk AA (2002). Mechanical Behaviour and Performance of Granular Bases and Sub-bases in Pavements. Doctoral Dissertation. Delft University Press. Delft Universoty of Technology. Delft. The Netherlands. Uzan J (1992). Resilient Characterization of Pavement Materials. International Journal for Numerical and Anallytical Methods in Geomechanics. Vol. 16.

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