Design And Construction Of Continuously Reinforced Concrete Pavement (Crcp) And Jointed Plain Concrete Pavement (Jpcp)

The master thesis studies the state of art of CRCP and JPCP construction and design. Special focus is the design of such concrete pavements with respect to traffic load, climatic impact and other relevant loading. JPCP is the standard concrete pavement design used for road traffic infrastructure in Germany, documented by actual specifications. Nevertheless some road sections using CRCP had been built during the last decade to study applicability, performance and potential benefits for German road infrastructure. Other national standards are using CRCP, e.g. Belgium based on good long-term behavior. Because of the significant economic impact a critical approach is needed to decide on future pavement systems.

Main work/scope of master's thesis:
The following four steps are the main scope of this thesis:
Studying the actual regulations, design procedures (models, tools to calculate stresses, deformations ') and literature dealing with experiences of concrete pavements based on JPCP and CRCP principles.
Performing a comparative design analysis using analytical tools. Loading of such pavements given by combination of different loads, which are traffic, climate and others, will be determined and evaluated.
Analyzing the designs with respect to expected failure modes.
And concluding on future relevance of such concrete pavements.
Table of Contents
1. Introduction 1
1.1 Flexible and Rigid Pavements 1
1.2 Continuously Reinforced Concrete Pavement (CRCP) 2
1.3 Jointed Plain Concrete Pavement (JPCP) 5
2. Pavement Types and Materials 7
3. Structural Design Methods of Rigid Pavements JPCPs and CRCPs 8
3.1 AASHTO Design for Rigid Highway Pavements 9
3.1.1 AASHTO Thickness Design for Rigid Highway Pavements 9
3.1.2 Longitudinal Reinforcement Design for CRCP 17
3.2 The German Design Method (Empirical) 23
3.3 The Analytical Dutch Design Method 26
3.3.1 Traffic loadings 27
3.3.2 Climate 28
3.3.3 Substructure 28
3.3.4 Concrete 29
3.3.5 Traffic load stresses 30
3.3.6 Slab Thickness of JPCP and CRCP 31
4. A Comparative Design Analysis of Design Methods of JPCPs and CRCPs 34
4.1 Modulus of Substructure Reaction (K) 35
4.2 Traffic Loadings 40
4.3 Conclusion 49
5. Determination and Analysis of Failure Modes in Design Methods 51
6. Suggestions and Conclusions 52
7. References 53

List of figures
Figure '1.1: A typical cross section of flexible pavement including load transmission 2
Figure '1.2: A typical cross section of rigid pavement including load transmission 2
Figure '1.3: A typical CRCP cross section 3
Figure '1.4: Application of CRC pavements in Roundabouts and Tram-Bus lanes in Belgium 5
Figure '1.5: A typical scheme of JPCP 6
Figure '3.1: Rigid pavement thickness design chart 10
Figure '3.2: Chart for estimating composite K 12
Figure '3.3: Chart for k as a function of bedrock depth 13
Figure '3.4: Correction of effective modulus of subgrade reaction for potential loss of subbase support 14
Figure '3.5: Minimum percent reinforcement to satisfy crack-spacing criteria 18
Figure '3.6: Chart for estimating wheel load tensile stress sw 20
Figure '3.7: Minimum percent steel reinforcement to satisfy crack-width criteria 21
Figure '3.8: Minimum percent reinforcement to satisfy steel'stress criteria 22
Figure '3.9: Standard JPCP structures in the German Guidelines RStO 12 24
Figure '3.10: Flow chart of the structural design of jointed plain/reinforced concrete pavements according to the VENCON2.0 design method 27
Figure '4.1: Definition of the 'modulus of substructure reaction' k 35
Figure '4.2: Indicative relationship between "K0" and CBR for various types of subgrades 37
Figure '4.3: Nomo graph for the determination of the k-value on top of a 38

List of Tables
Table '3.1: Typical Ranges of Loss of Support (LS) Factors for Various Types of Materials 15
Table '3.2: Recommended Value of Drainage Coefficient, Cd, for Rigid Pavement Design 16
Table '3.3: Recommended Load Transfer Coefficient for Various Pavement Types and Design Conditions 16
Table '3.4: Shrinkage and Thermal Coefficient of Portland Cement Concrete 19
Table '3.5: Allowable Steel Working Stress, ksi 22
Table '3.6: Default temperature gradient frequency distribution 28
Table '3.7: Mechanical properties of (Dutch) concrete grades for concrete pavement structures 30
Table '4.1: AASHTO ESAL factors for rigid pavements 44
Table '4.2: Recommended percentage of ESAL on design lane by AASHTO 44
Table '4.3: Directional factor as a function of the number and the width of carriageways 46
Table '4.4: Percentage of heavy vehicles on design traffic lane as a function of the number of traffic lanes per direction 46
Table '4.5: Default axle load frequency distributions for different types of roads in the Netherlands 47
Table '4.6: Value of parameter b (equation 76) for different types of tyre 48

Introduction
Pavements are designed to provide perdurable surfaces for the people and goods. They should guarantee safety and speedy movement with an acceptable level of comfort for the users.
Thus careful considerations must be made in many aspects during design and construction phases. The considerations in the aspects of pavement selection type, selection of materials for pavement layers, structural thickness design of the pavement layers and the drainage design for the pavement systems must be done while constructing a pavement.
Pavements are categorized into two types of flexible pavements and rigid pavements. The focus of this study is on the rigid pavements (Continuously Reinforced Pavement and Jointed Plain Concrete Pavement).
The introduction of flexible and rigid pavements in terms of load distribution will be presented in this first update of the research. The report will be followed by presenting different regulations and specifications introduced by different organizations for design of CRCPs and JPCPs.
Flexible and Rigid Pavements
The classification of pavements into flexible and rigid pavements is on the basis of the mechanism in which the load is transmitted to the subgrade soil through the pavement structure.
The load distribution in flexible pavements is through a multilayer structure and the pavement provides sufficient thickness for that. In these types of pavements the stresses and strains in the subgrade soil layers are within the required limits. The strength of subgrade soil would have a direct bearing on the total thickness of the flexible pavement. The magnitude of stresses decreases as the depth of the pavement increases in flexible pavements (Fwa, 2002).
Figure '1.1 shows a typical cross section of flexible pavement including load transmission though the depth.

Figure '1.1: A typical cross section of flexible pavement including load transmission
Source: (Fwa, 2002)
The scenario of load distribution in rigid pavements is different from the one in flexible pavements. The rigid pavement has the ability to effect the slab action to spread the wheel load over the entire slab area. The bearing capacity of the rigid pavement is greatly provided by the slab itself. Comparing rigid and flexible pavements, the effect of subgrade soil properties on the slab thickness is much less important in rigid slabs (Fwa, 2002).
Figure '1.2 also shows a typical cross section of rigid pavement including load transmission though the depth.

Figure '1.2: A typical cross section of rigid pavement including load transmission
Source: (Fwa, 2002)
Continuously Reinforced Concrete Pavement (CRCP)
Continuously reinforced concrete pavements (CRCP) as rigid pavements contain continuous longitudinal reinforcement and do not have transverse joints.
Exceptions for having transverse joints are when necessary for construction purposes such as end-of-day construction header joints or at bridge approaches or transitions to other pavement structures.
Unlike jointed plain concrete pavements (JPCP), where the number and location of transverse cracks are managed by sawing or constructing joints, in CRCP the continuous reinforcement allows transverse cracks to occur relatively close together and holds them tightly closed for maximum aggregate interlock. As a result, load transfer between pavement slabs is maximized, and flexural (bending) stresses due to traffic loads and curling and warping are minimized (Rasmussen, et al., 2011).
Longitudinal joints may be used to relieve concrete stresses in the transverse direction, for example when the paving width exceeds 14 ft. (4.3 m). To hold any longitudinal cracks that may form tightly closed, CRCP commonly contains transverse reinforcement as well. Figure '1.3 shows a typical CRCP cross section.

Figure '1.3: A typical CRCP cross section
Source: (Rasmussen, et al., 2011)
The bearing capacity of CRCP has made it a very suitable pavement solution for heavily loaded and traveled roadways. Also the excellences of CRCP are:
1. There will be no joint maintenance cost for all over the life of the pavement. This will be beside the more satisfaction of the users of the pavement.
2. The consistency of transfer of shear stresses from heavy wheel loads results in consistently quiet ride and less distress development at the cracks in CRCP.
CRCP also can be expected to provide over 40 years of very good performance with minimal maintenance (Rasmussen, et al., 2011).
The first practice of constructing CRCP was formed in 1921 by the Bureau of Public Roads on Columbia Pike in Arlington, Virginia (Ha, et al., 2012). 17 years later in 1938, the first significant experimental highway using CRCP was built in a distance of five miles in Indiana as a result of a good performance of the first test section. This was followed in 1947 by two additional experimental projects in Illinois and New Jersey, and then many experimental miles in California, Maryland, Pennsylvania, and other states in the early 1950s. Nowadays, over 28,000 lane-miles of CRCP have been built in the U.S in more than 35 states, at least on a trial basis (Rasmussen, et al., 2011).
So far, Germany doesn't have much experience in CRCP. JPCP is the standard concrete pavement design used for road traffic infrastructure in Germany. However Germany has performed CRCP construction in three road sections namely A5 highway close to Darmstadt, B56 federal road close to D??ren and A94 close to Munich, while the CRC pavements are increasingly being used in neighboring countries such as Belgium based on good long term behavior (Eck, 2012).
In Belgium, the first CRCP practice performed in 1950 in National Road 8 Brussels - Tournai in Leuze-en- Hainaut. The project was 584 meter long and still is in service covered with asphaltic wearing course.
Construction of CRCP continued in Belgium by constructing:
Zonhoven, a 1200 meter tank track, Ministry of Defense in 1958
Stockem, a 350 meter tank track, Ministry of Defense in 1961
Brussels - Charleroi 3700 meter (Frasnez-les-Gosselies) in 1964
Velaine,1028 meter municipal road in 1965 and
The 1400 meter Bierwart roadway in 1968.
In 1968, a team of Belgian engineers consisting engineers from the Ministry of Public Works, Belgium Cement Research Centre and Steel Research Centre made a study tour to U.S.A. with the objective to collect all required information related to design, construction and behavior of CRCP. American CRCP design and construction technologies were adapted to Belgium and used to construct a large portion of the Belgian motorway network in the1970s. Having a look to the history of road pavement in Belgium shows a great increase of using CRCP (Rens & FEBELCEM, 2011).
This type of pavement is also being used for Tram-Bus and Roundabouts in Belgium. (Figure '1.4)

Figure '1.4: Application of CRC pavements in Roundabouts and Tram-Bus lanes in Belgium
Source: (Rens & FEBELCEM, 2011)
Jointed Plain Concrete Pavement (JPCP)
Unlike CRCPs, Jointed plain concrete pavements (JPCP) are concrete pavements without any reinforcement (neither Longitudinal nor transversal) and thus the least expensive concrete pavement to construct.
By means of longitudinal and transverse contraction joints the concrete pavement is divided into slabs with horizontal dimensions usually not exceeding 5 m. More or less square slabs are applied, i.e. the ratio of length and with is limited to about 1.25. (For slabs with joint spacing greater than 6 m, steel reinforcements have to be provided for crack control) (Houben, 2009).
These types of pavements use contraction joints to control cracking. A typical JPCP is constructed with the following components (Figure '1.5):
Concrete Slabs (i.e. 5 m x 5 m)
Joints (both transverse and longitudinal)
Tie bars
Base layer
Subbase layer (if required)
And Subgrade

Figure '1.5: A typical scheme of JPCP
Source: (Rasmussen, et al., 2011)
Natural actions such as shrinkage or curling cause the concrete slabs to crack randomly. Thus, joints are very important components introduced into JPCPs in order to control cracking and horizontal movements of the slabs. Longitudinal contraction and construction joints and transverse contraction and construction joints are the joints in JPC pavements.
Transverse joint spacing is selected such that temperature and moisture stresses do not produce intermediate cracking between joints. Dowel bars are applied in the transverse joints for better load transfer across the joints and for better longitudinal evenness at long term. Tie bars are applied in the longitudinal joints to limit the joint width. Even with JPCPs, incorrectly placed or poorly designed joints will result in premature cracking. The joints are mostly sealed, although for minor roads for reasons of costs sealing is not always done. Jointed plain concrete pavements (JPCP) are most widely applied in Europe and also for highways worldwide. In general, compared to JPCP, the CRCP investment costs are higher and the maintenance costs are lower. Therefore in practice the application of CRCP is limited to heavily loaded pavements.

Pavement Types and Materials
Structural Design Methods of Rigid Pavements JPCPs and CRCPs
The design of the rigid pavements contains of the determination of the slab thickness plus the determination of the amount of reinforcement. Today two major forms of thickness design method are being used.
The first one relies on empirical relationships derived from performance of full-scale test pavements and in-service pavements. The design procedure of AASHTO [1993] (American Association of State Highway and Transportation) and the German concrete pavement design method are examples of mainly empirical methods.
The second form develops relationships in terms of the properties of pavement materials as well as load-induced and thermal stresses and calibrates these relationships with pavement performance data. The PCA [1984] (Portland Cement Association) and the FAA [1978] (Federal Aviation Administration) methods of design adopt this approach (Fwa, 2002).
A recent survey on CRCP design practices in the US indicated that most States that commonly use this pavement type use the AASHTO design procedure published in 1986 and later in 1993. One exception is Illinois, which uses a modified version of this method (Rasmussen, et al., 2011). Also the thickness design method for CRCP and JPCP are more or less the same in many investigated regulations.
In Europe, although the majority of the European countries are united in the European Union (EU) neither a standard European Design Method for Concrete Pavements nor a European Code of Practice for concrete pavements does exist. Each country in fact has its own design method and most of these methods are mainly based on experience. Exceptions are the analytical design procedures in France and the Netherlands. Construction practice is however more or less the same throughout the continent (Houben, 2009).
Based on the investigated design methods in US and the European countries, in this chapter the design regulations of AASHTO from US will be presented followed by regulations introduced by Germany as examples of a mainly empirical design methods. Next, as an example of a mainly analytical design method, the Dutch design method will be explained.
Then in the next chapter (Chapter 4) different aspects of the design of concrete pavements such as the traffic loadings, the concrete grade, the substructure and a comparison of the required concrete pavement thickness in design methods will be compared to each other.
AASHTO Design for Rigid Highway Pavements
The AASHTO design for rigid pavements consist of the thickness design for the rigid pavements and the reinforcement required for using in CRC pavement. In the following sections the thickness design of the rigid pavements according to AASHTO 1993 guidelines will be presented and then the procedure of the determination of the required reinforcement will be addressed.
AASHTO Thickness Design for Rigid Highway Pavements
The AASHTO design procedure (AASHTO, 1993) was developed based on the findings of the AASHO road test (Highway Research Board, 1962). Determination of the concrete thickness with the AASHTO Thickness Designs method involves number of variations. Figure '3.1 is being used to determine the thickness of the rigid pavement.

Figure '3.1: Rigid pavement thickness design chart
Source: (AASHTO, 1993)
In order to determine the appropriate thickness from Figure '3.1 the following variables must be calculated and considered in design procedure:
Reliability
For uncertainties in traffic prediction and pavement performance AASHTO guide has introduces a factor called Reliability factor and is being shown in percent (R %). With the probability of R%, the pavement may not reach the terminal serviceability level before the end of the design period. For example, the AASHTO considers the ranges of R% are 85 to 99.9% for urban interstates, 80 to 99% for principal arterials, 80 to 95% for collectors and 50 to 80% for local roads. Also the overall standard deviation, so, for flexible and rigid pavements developed at the AASHO road test is 0.45 and 0.35, respectively (Fwa, 2002).
Serviceability
The AASHTO defines pavement performance in terms of the present serviceability index (PSI), which varies from 0 to 5. The PSIs of newly constructed flexible pavements and rigid pavements were found to be about 4.2 and 4.5, respectively. For pavements of major highways, the end of service life is considered to be reached when PSI = 2.5. A terminal value of PSI = 2.0 may be used for secondary roads (AASHTO, 1993). Serviceability loss, given by the difference of the initial and terminal serviceability, is required as an input parameter.
Pavement Material Properties
The elastic modulus Ec and modulus of rupture Sc of concrete are required input parameters. Ec is determined by the procedure specified in ASTM C469. It could also be estimated using the following correlation (Fwa, 2002):

Where fc = the concrete compressive strength in psi as determined by AASHTO T22, T140 (AASHTO, 1989) or ASTM C39 (ASTM, 1992)
Sc is the mean 28-day modulus of rupture determined using third-point loading as specified by AASHTO T97 (AASHTO, 1989) or ASTM C39 (ASTM, 1992)
Modulus of Subgrade Reaction
The value of modulus of subgrade reaction k to be used in the design is affected by the depth of bedrock and the characteristics of the subbase layer, if used (AASHTO, 1993). Figure '3.2 is first applied to account for the presence of subbase course and obtain the composite modulus of subgrade reaction. Figure '3.3 is next used to include adjustment for the depth of rigid foundation. It is noted from Figure '3.2 that the subgrade soil property required for input is the resilient modulus Mr.
It is common practice to estimate Mr through empirical correlation with other soil properties. Equation below is one such correlation suggested by AASHTO for fine-grained soils with soaked CBR of 10 or less:


Figure '3.2: Chart for estimating composite K
Source: (AASHTO, 1993)

Figure '3.3: Chart for k as a function of bedrock depth
Source: (AASHTO, 1993)
Effective Modulus of Subgrade Reaction
An effective k must be computed to represent the combined effect of seasonal variations of k. The relative damage u is now computed as:

Depending on the type of subbase and subgrade materials, the effective k must be reduced according to Figure '3.4 to account for likely loss of support by foundation erosion and/or differential soil movements. Suggested values of LS in Figure '3.4 are given in Table '3.1 (Fwa, 2002).

Figure '3.4: Correction of effective modulus of subgrade reaction for potential loss of subbase support
Source: (AASHTO, 1993)

Table '3.1: Typical Ranges of Loss of Support (LS) Factors for Various Types of Materials
Source: (AASHTO, 1993)
Drainage Coefficient
To allow for changes in thickness requirement due to differences in drainage properties, pavement layers, and subgrade, a drainage coefficient Cd was included in the design. Setting Cd = 1 for conditions at the AASHO road test, Table '3.2 shows the Cd values for other conditions (Fwa, 2002). The percentage of time during the year that the pavement structure would be exposed to moisture levels approaching saturation can be estimated from the annual rainfall and the prevailing drainage condition.

Table '3.2: Recommended Value of Drainage Coefficient, Cd, for Rigid Pavement Design
Source: (AASHTO, 1993)
Load Transfer Coefficient
Load transfer coefficient J is a numerical index developed from experience and stress analysis. Table '3.3 presents the J values for the AASHO road test conditions. Lower J values are associated with pavements with load transfer devices (such as dowel bars) and those with tied shoulders. For cases where a range of J values applies, higher values should be used with low k values, high thermal coefficients, and large variations of temperature (Fwa, 2002). When dowel bars are used, the AASHTO guide recommends that the dowel diameter should be equal to the slab thickness multiplied by 1/8, with normal dowel spacing and length of 12 in. and 18 in., respectively.

Table '3.3: Recommended Load Transfer Coefficient for Various Pavement Types and Design Conditions
Source: (AASHTO, 1993)
Longitudinal Reinforcement Design for CRCP
The design of longitudinal reinforcement for CRCP is an elaborate process. The amount of reinforcement selected must satisfy limiting criteria in the following three aspects: (a) crack spacing, (b) crack width, and (c) steel stress.

(a) CRCP Reinforcements Based on Crack Spacing: (Pmin) 1 and (Pmax) 1.
The amount of steel reinforcement provided should be such that the crack spacing is between 3.5 ft. (1.1 m) and 8 ft. (2.4 m). The lower limit is to minimize punchout and the upper limit to minimize spalling (Fwa, 2002). For each of these two crack spacings, Figure '3.5 is used to determine the percent reinforcement P required, resulting in two values of P that define the range of acceptable percent reinforcement: (Pmax)1 and (Pmin)1. The input variables for determining P are the thermal coefficient of Portland cement concrete ac, the thermal coefficient of steel as, diameter of reinforcing bar, concrete shrinkage Z at 28 days, tensile stress sw due to wheel load, and concrete tensile strength ft at 28 days. Values of ac and Z are given in Table '3.4. A value of as = 5.0 * 10^-6 in./in./??F may be used. Steel bars of 5/8- and 3/4-in. (AASHTO, 1993) diameter are typically used, and the 3/4-in. bar is the largest practical size for crack-width control and bond requirements. The nominal diameter of a reinforcing bar, in inches, is simply the bar number divided by 8. Meanwhile, sw is the tensile stress developed during initial loading of the constructed pavement by either construction equipment or truck traffic. It is determined using Figure '3.6 based on the design slab thickness, the magnitude of the wheel load, and the effective modulus of subgrade reaction. Likewise, ft. is the concrete indirect tensile strength determined by AASHTO T198 or ASTM C496. It can be assumed as 86% of the modulus of rupture Sc used for thickness design.

Figure '3.5: Minimum percent reinforcement to satisfy crack-spacing criteria
Source: (AASHTO, 1993)

Table '3.4: Shrinkage and Thermal Coefficient of Portland Cement Concrete
Source: (AASHTO, 1993)

Figure '3.6: Chart for estimating wheel load tensile stress sw
Source: (AASHTO, 1993)
(b) CRCP Reinforcements Based on Crack Width: (Pmin)2.
Crack width in CRCP is controlled to within 0.04 in. (1.0 mm) to prevent spalling and water infiltration (AASHTO, 1993). The minimum percent steel (Pmin)2 that would produce crack widths of 0.04 in. can be determined from Figure '3.7 with a selected bar size and input variables sw and ft .

Figure '3.7: Minimum percent steel reinforcement to satisfy crack-width criteria
Source: (AASHTO, 1993)
(c) CRCP Reinforcements Based on Steel Stress: (Pmin)3
To guard against steel fracture and excessive permanent deformation, a minimum amount of steel (Pmin)3 is determined according to Figure '3.8 Input variables Z, sw, and ft have been determined earlier. For the steel stress ss, a limiting value equal to 75% of the ultimate tensile strength is recommended. Table '3.5 gives the allowable steel working stress for grade 60 steel meeting ASTM A615 specifications. The determination of (Pmin)3 also requires the computation of a design temperature drop given by (AASHTO, 1993)

Where
TH = the average daily high temperature during the month the pavement is constructed
TL = the average daily low temperature during the coldest month of the year


Figure '3.8: Minimum percent reinforcement to satisfy steel'stress criteria
Source: (AASHTO, 1993)

Table '3.5: Allowable Steel Working Stress, ksi
Source: (AASHTO, 1993)
Reinforcement Design:
Based on the three criteria discussed above, the design percent steel should fall within Pmax and Pmin given by:

If Pmax is less than Pmin, a design revised by changing some of the input parameters is required. With Pmax greater than Pmin, the number of reinforcing bars or wires required, N, is given by Nmin <= N <= Nmax, where Nmin and Nmax are computed by (Fwa, 2002):

Where
Ws = the width of pavement in inches
D = the slab thickness in inches
f = the reinforcing bar or wire diameter in inches
The German Design Method (Empirical)
Germany has a long term experience in concrete design (Mostly JPCP). More numerical analysis especially into the effects of temperature gradients on design and performances of JPC pavements have been done by Prof. Eisenmann in Technical University of Munich In seventies and eighties (Houben, 2009).
The structural design guidelines for JPCP are published since 1925 in Germany and are being revised regularly. The most recent guidelines, the so-called RStO 12, have been published in 2012. RStO 12 contains standard JPCP structures as a function of the traffic loading and the type of base material (Figure '3.9)

Figure '3.9: Standard JPCP structures in the German Guidelines RStO 12
Source: (Houben, 2009)
Having a look to the RStO 12, there exist 7 types of roads ranging from SV (most heavily loaded roads, such as motorways) to VI (very lightly loaded rural roads and residential streets).
The second row in Figure '3.9 indicates the Total cumulative no of equivalent 100 kN(10 Tones) standard axle loads on design traffic lane in design period.
The first column (Zelle) indicates the types of base. 1.1, 1.2 and 1.2 stand for the cement bound base relatively from high to low quality. The asphalt base in being shown by 2 and granular base by 3.
The third row show the required total thickness (in cm) of non-frost susceptible materials (dependent on location, i.e. in the north of Germany there is a relatively mild sea climate while in the east and south there is a colder land climate).
The numbers below the pavement structure are the minimum thicknesses (in cm) of the non-frost susceptible sub-base to fulfill the requirement given in the third row of Figure '3.9.
The numbers at right side of the pavement structure in Figure '3.9 indicate the thicknesses of concrete pavement, the base, and the concrete plus base respectively from up to down.
The numbers at the left side of the structure (i.e. 45 and 120) are the required minimum values of the deformation modulus 'Ev2' at top of subgrade level and top of subbase level respectively. This Ev2 is an equivalent modulus for all the underlying layers. One general requirement is that Ev2 should have a value of at least 45 MPa at the top of the subgrade (RSTO, 2012).
A so-called Static Plate Loading Test will determine the Ev2 value. A circular steel plate will be loaded slowly to a specified level and then will be unloaded repeatedly (Houben, 2009).

Where:
Ev2 = deformation modulus (MPa)
p = applied maximum stress (MPa)
a = radius of circular plate (= 150 mm)
y = measured rebound (elastic) deformation (mm) during unloading at the 2nd load cycle
While the pavement is being constructed, the Ev2 is also measured. If the value of the Ev2 does not fulfill the requirements, the contractor has to perform some measurements (i.e. compaction or stabilization of the layer) so that the required Ev2 value is reached. The slabs in the motorways usually are performed in a 5m length x 4m width. The length of the slabs must be smaller than 25 times the thickness of the slabs and it also should not exceed 7.5 m to control the temperature gradient stresses. This limitation to slab length will limit joint width variations due to temperature changes and increases the lifetime of the joint filling material.
In transverse contraction joints, non-profiled steel dowel bars (diameter 25 mm, length 500 mm) is being used in mid-depth slab. The spacing of the bars usually is 250 mm in order to achieve a better load transfer.
In longitudinal contraction joints, profiled steel tie bars (diameter 25 mm, length 500 mm) is being used at 2/3 of concrete depth to limit the width of longitudinal joints. The bars are placed 3 per slab length with a plastic coating at the central 1/3 part (Houben, 2009).
The Analytical Dutch Design Method
A software package called VENCON2.0 was released early 2005 by CROW and the current Dutch method for the structural design of jointed plain concrete pavements (JPCP) and continuously reinforced concrete pavements (CRCP), subjected to normal road traffic is available in this software package.
A fatigue strength analysis in being performed for different critical locations on the pavement i.e. transverse joint in the center of the wheel track, longitudinal joints etc. the structural design of the JPCP is based on this fatigue analysis.
The traffic load stresses calculated by Westergaard equation and the temperature gradient stresses calculated by a modified Eisenmann theory are included in the analysis.
For designing the thickness of the CRCP, the pavement is being considered as JPCP with modified horizontal slab dimensions and a greater load transfer over the relatively small transverse cracks. After determination of concrete thickness, the required longitudinal reinforcement of the pavement will be determined in a way to control the crack width (Houben, 2009).
Figure '3.10 briefly illustrates the procedure of the VENCON2.0 design method.

Figure '3.10: Flow chart of the structural design of jointed plain/reinforced concrete pavements according to the VENCON2.0 design method
Source: (Houben, 2009)
A brief introduction of the variables used for the design of rigid pavement is being presented in the following.
Traffic loadings
The traffic loading is calculated as the total number of axles per axle load group (> 20 KN) on the design traffic lane during the desired life of the concrete pavement.
Different types of tire are also included in the VENCON2.0 design method (i.e. single tires, dual tires, wide base tires and extra wide base tires. As the Westergaard equation for calculation of the traffic load stresses uses a circular contact area and because every tire contact area is assumed to be rectangular, thus the equivalent radius a of the circular contact area of the tire is calculated by (Houben, 2009):

Where:
b = parameter dependent on the type of tire
P = average wheel load (N) of the axle load group
Climate
The temperature gradient on a stretch of the newly build motorway A12 near Utrecht in the center of the Netherlands has continuously been measured in 2000 and 2001. Based on these measurements it was decided to include the default temperature gradient frequency distribution shown in Table '3.6 in the current design method (Houben, 2009).

Table '3.6: Default temperature gradient frequency distribution
Source: (Houben, 2009)
Substructure
The substructure consists of the bas, subbase and the subgrade layers. To obtain the modulus of substructure reaction k at the top of the base, the following equation has to be applied for each layer (Houben, 2009): (first the sub-base, then the base)

Concrete
In accordance with the Eurocode 2, in the VENCON2.0 design method the mean flexural tensile strength (fbrm) after 28 days for loading of short duration is defined as a function of the thickness h (in mm) of the concrete slab:

The mean flexural tensile strength is used in the fatigue analysis. The stiffness (i.e. Young's modulus of elasticity) of concrete is also important for the structural design of concrete pavements. The Young's modulus of elasticity of concrete depends to some extent on its strength. According to NEN 6720 (10) the Young's modulus of elasticity Ec can be calculated with the equation (Houben, 2009):

Where:
f'ck = characteristic cube compressive strength (N/mm??) after 28 days for loading of short duration
h = concrete thickness (mm)
Table '3.7 shows some strength and stiffness values for the two concrete grades used in concrete pavements in Netherlands. The Poisson's ratio and the coefficient of linear thermal expansion are the other important values showed in the tables.

Table '3.7: Mechanical properties of (Dutch) concrete grades for concrete pavement structures
Source: (Houben, 2009)
Traffic load stresses
The tensile flexural stress due to a wheel load P at the bottom of the concrete slab along a free edge, along a longitudinal joint, along a transverse joint (jointed plain concrete pavements) and along a transverse crack (continuously reinforced concrete pavement) is calculated by means of the 'new' Westergaard equation for a circular tire contact area (Houben, 2009):

The load transfer W at edges/joints/cracks is incorporated in the design of concrete pavement structures by means of a reduction of the actual wheel load P to the wheel load Pcal (to be used in the Westergaard equation) according to (Houben, 2009):

The values of W are different depending on free edge, longitudinal joints and transverse joints and cracks.
Slab Thickness of JPCP and CRCP
Fatigue strength analysis will be performed in the following critical locations in JPCP on a 2-lane road (Houben, 2009):
1. The wheel load just along the free edge of the slab;
2. The wheel load just along the longitudinal joint between the traffic lanes;
3. The wheel load just before the transverse joint,
In the case of a multi-lane road (e.g. a motorway) the strength analysis is also done for:
1. The wheel load just along every longitudinal joint between the traffic lanes;
2. The wheel load just along the longitudinal joint between the entry or exit lane and the adjacent lane.
For CRC pavements the strength analysis will be done in two locations:
1. The wheel load just before a transverse crack 2. The wheel load just along a longitudinal joint
The flexural tensile stress at the bottom of the concrete slab due to the wheel load (Pi) in each of the mentioned locations is calculated by Westergaard equation.
Also the flexural tensile stress at the bottom of the concrete slab due to a positive temperature gradient (??Ti) in each of the mentioned locations is calculated by the relative equations(the equations have not been included in this report)
The length L and width W are predefined in JPC pavement. For CRCPs, the width W of the slab is predefined but length L of the slab is taken as 1.35*W arbitrarily, with L ' 4.5 m (Houben, 2009).
Also the structural design of both CRCP and JPCP is based on a fatigue analysis for all the mentioned locations of the pavement. The following fatigue equation is used:


The Palmgren-Miner fatigue damage rule is the Design criterion which is applied on all of the above-mentioned CRCP and JPCP (Houben, 2009):


A Comparative Design Analysis of Design Methods of JPCPs and CRCPs
So far, the German rigid pavement design method, the rigid design method of AASHTO in United States and the current Dutch design method of rigid pavements including CRCPs and JPCPs were discussed.
A comparative design analysis between the parameters used in the design process of AASHTO and Dutch method will be presented in this chapter. After a comparison between the essential parameters such as the traffic loadings, the concrete grade and the substructure for these two design methods, the total designs procedures including the final results obtained from each of methods will be compared to each other in this chapter.
Each of these design methods has its own criteria in designing of the thickness of JPC pavements.
For design of CRCPs, In the Dutch design method the pavement is being considered as a JPC pavement, however with modified horizontal slab dimensions (As there exist transverse cracks in CRCPs instead of transverse Joints in JPCPs) and a great load transfer at these cracks as they are very narrow. After finding the thickness of the concrete based on the concrete strength criterion, the required longitudinal reinforcement (to control the crack pattern) is determined (Houben, 2009).
Also in AASHTO after determination of the slab thickness then the designed longitudinal reinforcement for CRCP must satisfy the following three criteria (Fwa, 2002):
crack spacing
crack width
steel stress
We will first perform a comparative analysis between the input parameters used for the thickness design of the rigid pavements (JPCPs) by both methods (K value and traffic loading determination).
The comparative design analysis regarding the procedures resulting the determination of slab thickness for JPCP and CRCP and also the required reinforcement for CRC pavements will be presented next.
Modulus of Substructure Reaction (K)
Generally the bearing capacity of the substructure is being shown as a so-called value 'Modulus of Substructure Reaction K' which is defined as the following equation (Figure '4.1).

Figure '4.1: Definition of the 'modulus of substructure reaction' k
Source: (Houben, 2009)
K = p/w

Where:
K = modulus of substructure reaction (N/mm3)
p = ground pressure (N/mm2) on top of the substructure
w = vertical displacement (deflection) (mm) at the top of the substructure

The whole substructure is modeled as a dense liquid so that no shear stresses can occur in the substructure (Houben, 2009).
The modulus of substructure reaction has to be determined in situ by the so-called plate bearing test. This test is so costly and time consuming costing from $1,000 to $5,000 per test in 1981 according to TRC 67 and thus the use of the test is not common and the K value is calculated by means of indirect ways (Thornton, 1983).
Each standard of design has its own indirect way to calculate the K value and these indirect ways will increase the possibility of inaccuracy in determination of K value.
The modulus of substructure reaction K which is used in the Dutch design method of concrete thickness is resulted from an increase in the modulus of subgrade reaction "K" _"0" . This increase is because of the presence of other layers i.e. subbase and base above the subgrade (Houben, 2009).
The value of modulus of substructure reaction K to be used in the AAHTO design method is affected by the characteristics of the subbase layer including the depth of bedrock, while there is no direct consideration of the depth of bedrock for determination of the K value in the Dutch design method (Fwa, 2002).
Also AASHTO uses a term 'Effective modulus of subgrade reaction K' as it is discussed before.
Determination of K in AASHTO is in a different way than in Dutch method. Given the resilient modulus of a subgrade "M" _"r" (psi), AASHTO suggests to determine the K value by means of the following equation (AASHTO, 1993):

This equation indicates that there is a linear relationship between "M" _"r" and K.
If a CBR of a soil is given, then AASHTO also suggests to determine "M" _"r" (psi) by mean of the following equation:

This correlation suggested by AASHTO for fine-grained soils with soaked CBR of 10 or less. CBR (California Bearing Ratio) is determined for each specific groups of soils by a so-called CBR test which is described by AASHTO. The smaller the CBR of a soil is, the poorer is the strength of the subgrade. On the contrary the harder the surface, the higher the CBR rating. The above mentioned equations indicate that if the CBR of a soil is given, then one can derive the K value by means of these equations suggested by AASHTO.
The K value then has to be modified to achieve the effective modulus of subgrade reaction used in the procedure of concrete thickness determination.
On the other hand, when the CBR value of a subgrade is known, then an indication of the "K" _"0" value can be obtained by means of Figure '4.2 based on the Dutch design method.

Figure '4.2: Indicative relationship between "K" _"0" and CBR for various types of subgrades
Source: (Houben, 2009)
There exists also a correlation between CBR and the dynamic modulus of elasticity "E" _"0" used in Dutch method. The CBR can be obtained from the following equation:

The dynamic modulus of elasticity "E" _"0" in the above mentioned equation has to be expressed in (N/mm2). After determination of "K" _"0" value in Dutch design method and by knowing the static modulus of elasticity "E" _"f" and thickness "h" _"f" of base or subbase, then one can refer to the Figure '4.3 and read the respective modulus of substructure reaction K at the top of base or subbase layer.

Figure '4.3: Nomo graph for the determination of the k-value on top of a
(sub-) base layer
Source: (Houben, 2009)
The corresponding formula of the Figure '4.3 to determine the K-value on top of the base or subbase layer and its relative parameters are already discussed before ( ).
The big difference in determination of K value in these two methods is firstly shown in the determination of "K" _"0" value. If we divide "M" _"r" by 19.4, the "K" _"0" value will be achieved according to the AASHTO specification.
Now assume dividing "M" _"r" by 1500; by doing so, the CBR value will be achieved according to the AASHTO definition.
Then if go to Figure '4.2 to determine the "K" _"0" value, the result which we get from this chart is totally different with the result achieved by dividing "M" _"r" by 19.4.
This is while we expect to read a "K" _"0" from the chart close to the value which we get by dividing "M" _"r" by 19.4.
For Example, assume a subgrade with a resilient modulus value "M" _"r" of 7000 psi (48.23 N/mm2).
The "K" _"0" value specified by AASHTO is:
"K" _"0" = 7000 psi/19.4 = 360.82 pci (0.098 N/mm3).
Also the CBR value according to AASHTO is achieved as follows:
CBR = 7000/1500 = 4.67 %
By referring to Figure '4.2 and assuming this CBR value we get a "K" _"0" value equal to around 0.038 N/mm3 from Dutch method, which is completely incomparable to 0.098 N/mm3 achieved from AASHTO!!!
It is important to note that the American Concrete Pavement Association ACPA has developed a new method for calculation of K value from the resilient modulus of subgrade "M" _"r" . An applet of this method is available in the website of ACPA under the link http://apps.acpa.org/apps/kValue.aspx .
In this method, the American Concrete Pavement Association indicates that the conversion from resilient modulus of the subgrade to k-value was updated in the fall of 2011 to better reflect published test results. It also indicates that the constant conversion factor of 19.4 as suggested in the AASHTO guide for design of pavement structures 1993 is no longer used. This will result in a totally different K value achieved from AASHTO.
For example entering a value of 7000 psi for "M" _"r" in the applet of ACPA, we get a value of 161 pci (0.043 N/mm3) for "K" _"0" value, while AASHTO gives a value of 360.82 (0.098 N/mm3) by dividing 7000 by 19.4.
Also there is a possibility to calculate the "M" _"r" and "K" _"0" from a given value of CBR in the ACPA applet. For example for a given CBR value equal to 4.67%, AASHTO gives a value of 7000 psi (48.23 N/mm2) for "M" _"r" and a value of 360.82 pci (0.098 N/mm3) for "K" _"0" . But entering this CBR value to the applet of ACPA, we get "M" _"r" = 5014 psi (34.45 N/mm2) and "K" _"0" = 120 pci (0.033 N/mm3) as result.
Also the Dutch design method gives a "K" _"0" value of around 0.038 N/mm3 for a given CBR equal to 4.67%.
It is clear that the result achieved form ACPA is more convergent to the result achieved from Dutch method for calculation of "K" _"0" value.
As mentioned above, the K value used in the thickness design of concrete pavement by AASHTO is the effective modulus of subgrade reaction.
The calculation of effective modulus of subgrade "K" _"eff" is discussed before. Also depending on the type of subbase and subgrade materials, the effective K must be reduced to account for likely loss of support by foundation erosion and/or differential soil movements.
The Dutch method however does not consider the effects of loss of support, depth of bedrock and the relative damage 'u' directly, but by means of other parameters ("C" _"1" , "C" _"2" , "C" _"3" , "C" _"4" and "C" _"5" ) and also by means of using the natural logarithm of "K" _"0" and "E" _"f" ("ln" ''"K" _"0" ' and "ln" ''"E" _"f" ') in the calculation of these parameters. Using the natural logarithm of "K" _"0" and "E" _"f" means that the Dutch design method has considered the concept of time in the calculation of K that could be translated to the effect of loss of support which is considered directly in AASHTO design method.
It is to note that in the structural design of concrete pavements for motorways the Dutch State Highway Authorities use a k-value of 0.105 N/mm3. This K value is obtained for a 150 mm thick lean concrete base, with "E" _"f" = 6000 N/mm2, on a sand sub-base and sand subgrade (Houben, 2009).
Traffic Loadings
For the traffic loadings, two aspects namely the number of applications and the magnitude of each load type are of concern in the structural design of highway pavements. Although it is convenient to describe the design life of a pavement in years, it is the total traffic loading during service that determines the actual design life of the pavement. For example a pavement which is designed for 40 years with an assumed traffic growth of 4% will reach to the end of its life sooner if the traffic growth is greater than 4%. In this section the difference of expressing the traffic information in two design methods of AASHTO and Netherlands will be presented.
The combined loading effects of different axle types on pavements cannot be easily analyzed.
AASHTO has presented the term ESAL ("W" _"18" ) to provide equivalency factors to convert all given kinds of axles (single axels and tandem axles) to equivalent passes of one 18 kip (80 KN) single axle load (AASHTO, 1993). The single axle load of 18 kip is chosen arbitrarily in AASHTO, with a damaging effect equal to 1 and then the ESAL factor of any other axle is being determined based on the relative damaging effect of that axle load. Table '4.1 presents the ESAL factors of axle loads for different thicknesses of rigid pavements with a terminal serviceability index ("P" _"t" ) of 2.5.

Table '4.1: AASHTO ESAL factors for rigid pavements
Source: (Fwa, 2002)
The traffic volume information from a highway is normally being reported as the flows for all lanes in both directions (Fwa, 2002). Thus the total traffic must be multiplied by factors to reach the design traffic loading on the design lane. The factor for the directional split ("f" _"D" ) and the factor for the lane distributions ("f" _"L" ).
In case of an unequal directional split, the pavements are designed based on the heavier directional traffic loading.
For the split of traffic in order to determine the respective traffic on design lane, AASHTO introduces the following factors (Table '4.2):

Table '4.2: Recommended percentage of ESAL on design lane by AASHTO
Source: (AASHTO, 1993)
When the ESAL of initial year ('"ESAL" '_"0" ) is known and a constant growth rate of r% per year is predicted, then the design ESAL ('"ESAL" '_"T" ) for an analysis period of n years is calculated as (AASHTO, 1993):



After calculation of ESAL ("W" _"18" ), AASHTO then uses this value in its charts for the thickness design of a rigid pavement.
It is to note that AASHTO presents an empirical formula to design the thickness of rigid pavements which will be discussed later.
The above mentioned was the way of estimation that AASHTO uses to estimate the design traffic loading for rigid pavements.
On the other hand, the Dutch design method does not involve the calculation of ESAL. The process of expressing the traffic loadings in Dutch design method involves the calculation of total number of axles per axle load group on the design lane during the designed life of the pavement. The axle load groups are such that only the heavy vehicles such as trucks and busses are taken into account (axle load more than 20 KN). The desired life of the pavement usually is taken as 20 to 40 years (Houben, 2009).
Only the working days of a year (usually between 260 and 300 days) is taken into account in the design process of a pavement in Dutch design method for a desired life of the concrete pavement.
The same as the directional split factors in AASHTO, Dutch design method also split the total two directional traffic stream. For roads having one carriageway, the directional factor depends on the width of the carriageway. Also for roads having two carriageways the directional factor is taken as 0.5. Table '4.3 shows the directional factors used in the current Dutch design method.

Table '4.3: Directional factor as a function of the number and the width of carriageways
Source: (Houben, 2009)
Similar to AASHTO factors for split of the traffic for determination of the respective traffic on design lane, Dutch design method uses the factors which are presented in Table '4.4:

Table '4.4: Percentage of heavy vehicles on design traffic lane as a function of the number of traffic lanes per direction
Source: (Houben, 2009)
In years 2000 and 2001 axle load measurements was done in many provincial roads of the Netherlands. From that measurements, an axle load frequency in the roads of the Netherlands is achieved that can be used in design of a new pavement for a certain type of a road in case that there exist no real axle load data available.
This default axle load frequency distribution is given in Table '4.5.

Table '4.5: Default axle load frequency distributions for different types of roads in the Netherlands
Source: (Houben, 2009)
It is to note that the Dutch design method introduces different types of tyres for the vehicles. Four different types of tyres are presented by Dutch design method namely single tyre, dual tyre, wide base tyre and extra wide base tyre. The last group of the tyres (Extra wide tyre) are the ones that in future will be allowed for driven axles (Houben, 2009).
The contact area of a tyre is assumed to be rectangular but the Westergaard formula for calculation of the flexural tensile stress due to traffic loading considers the contact area as a circular area. So the equivalent radius of the circular contact area of a tyre is calculated by means of the following equation given by Dutch design method:

Also the value of b in the equation is presented by Dutch design method as Table '4.6 shows.

Table '4.6: Value of parameter b (equation 76) for different types of tyre
Source: (Houben, 2009)
Now after explanation of the traffic loadings determination by the two methods of AASHTO and the Dutch method, it is clear that these two standards have big differences in determination of the term 'Traffic Loading'.
One of the important differences is that AASHTO uses 365 days of a year for its calculations of the pavement thickness while the Dutch method considers only the working days (between 260 and 300 days).
This is obvious that the traffic stream per day is not a constant value during a year. It could be that the traffic stream of heavy vehicles is less in holidays than it is in working days. The Dutch design method thus considers this issue and reduces the value of 365 to a less value. This makes the AASHTO design method more conservative than the Dutch design method.
Another important issue is that the Dutch design method does not consider the 'Actual wheel load "P" _"act" ' as the wheel load used in Westergaard formula for the calculation of traffic loading stresses.
The Dutch method reduces the actual wheel load "P" _"act" by means of the following equation (Houben, 2009):

W (the 'joint efficiency') in the formula is due the load transfer at the joints.
The larger the joint efficiency value the better the load transfer at the joint.
The detailed descriptions about how to calculate this parameter will be given in the next steps of the work.
On the other hand, AASHTO does not reduce the wheel loadings due to the joint efficiency while calculating the traffic loading parameter (ESAL).
With this different in these two methods and even by knowing this fact that AASHTO does not reduce the "P" _"act" , we cannot conclude that AASHTO is more conservative because of considering greater traffic loading values.
This could be because there is no direct calculation of the flexural tensile stresses in the AASHTO design method. Thus, in this case we cannot comment about the conservativeness of one method.
Another difference is that the Dutch design method uses each group of the axle load separately to calculate the fatigue analysis. This means that the calculation of "??" _"v" and allowable number of repetitions "N" _"i" including the "n" _"i" / "N" _"i" must be done for each group of the axle loads at the critical points of a slab one by one. This is necessary for the fatigue analysis.
On the other hand, AASHTO takes the single axle load of 18 kip (80 KN) as its benchmark with a damaging effect of 1, and convert by means of factors each of the other groups of axle loads to the equivalent number of 18 kip single axle load. At the end AASHTO presents one value as the equivalent single axle load of 18 kip (ESAL) by summing up all the converted axle loads of each group. But as discussed before, the Dutch design method does not have any standard axle load as a benchmark in order to convert the other loads to this benchmark.
Subsequently the Dutch method doesn't present only one value for the ultimate traffic loadings (as AASHTO does) but analyze the stresses used in fatigue analysis for each group of the axle loads.
Conclusion
The differences in determination of the traffic loadings and also in determination of the K value in AASHTO and Dutch design method show that there can be many significant differences in the parameters used by these two standards but this could be because of different methodologies used for designing a pavement.
Since there would be some parameters in one standard that the other standard does not consider it directly to its method of design, so it would be so difficult to compare the parameters used by two standards respectively. For some parameters in a standard we cannot find the corresponding parameter in another standard because a corresponding parameter does not basically exist in the other design method. Thus the effort is to analyze the corresponding parameters where it is possible.
The structure of the work in short term will be to have a comparative analysis between the parameters used in different design standards and at the end analyze the outcome of the design methods which will be the calculated slab thickness, the determined reinforcement etc. Analysis of the final results of the standards will give us a wider view of different considerations in different standards.
Determination and Analysis of Failure Modes in Design Methods
Suggestions and Conclusions
References
AASHTO, 1993. AASHTO Guide For Design of Pavement Structures. Washington, D. C.: American Association of State Highway and Transportation Officials.
Eck, C., 2012. Pioneering work in road construction: HeidelbergCement tests innovative concrete construction methods on the A 94 motorway, s.l.: HeidelbergCement AG.
Fwa, T. F., 2002. Highway and Airport Design. In: W. F. Chen & J. Y. R. Liew, eds. The Civil Engineering Handbook. 2nd ed. Boca Raton: CRC Press LLC, p. Chapter 62.
Ha, S. et al., 2012. Develop Mechanistic-Empirical Design for CRCP, Texas: Texas Tech University.
Houben, L. J. M., 2009. European Practice on Design and Construction of Concrete Pavements, Delft: Delft University of Technology.
Rasmussen, R. O., Rogers, R. & Ferragut, T. R., 2011. Continuously Reinforced Concrete Pavement Design and Construction Guidelines, s.l.: FHWA and CRSI .
Rens, L. C. E. & FEBELCEM, C. E., 2011. History of Design and Construction Practice of CRCP in Belgium, Buenos Aires: EUPAVE.
RSTO, 2012. Guidelines for the Standardisation of Surfaces of Road Traffic Areas, Cologne: FGSV Verlag GmbH.
S??derqvist, J., 2006. Design of Concrete Pavements ' Design Criteria for Plain and Lean Concrete, Stockholm: Royal Institute of Technology and Swedish Cement and Concrete Research Institute (CBI).
Thornton, S. I., 1983. CORRELATION OF SUBGRADE REACTION WITH CBR, HVEEM STABILOMETER, OR RESILIENT MODULUS, Arkansas: University of Arkansas.

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