Abstract
Roller compacted concrete (RCC) is a type of rigid pavement that is designed in a similar way to conventional concrete pavements reflecting its mode of failure. The thickness design of RCC pavements is based on keeping the flexural stresses and fatigue damage in the pavement caused by wheel loads within allowable limits. As in all jointed concrete pavements, there is a greater effect from loads placed along edges and less at interior locations in the pavement. Joints in RCC pavement are clearly critical areas and form weak points. RCC is typically constructed with saw-cut joints to prevent random cracking, improve the appearance of the pavement surface, and maintain the highest possible load transfer across the joints. This paper presents an approach to designing the thickness of a two-layer RCC with induced cracks (i.e., joints) based on load transfer stiffness and fatigue damage, using the KENSLAB program to obtain pavement life, predict joint deterioration, and pavement damage.
Keywords
In recent years, roller compacted concrete (RCC) has become an increasingly viable type of concrete pavement, especially in urban areas. RCC contains the same ingredients as conventional concrete: well-graded aggregates, cementitious materials, and water. The main difference between RCC and traditional concrete is the mixture proportions and the function of the compaction method used ( 1 – 3 ).
RCC is becoming increasingly attractive as an alternative pavement type because of its construction expediency, reduced material and construction costs, sustainability benefits, and overall structural capacity. Current RCC pavement mix design procedures are based on select mix constituents and proportions depending on strength requirements, workability, and field density ( 4 ). RCC does not represent either a new paving technique or a new material, but it combines the construction procedure used for asphaltic concrete or cement-treated base with the final product of Portland cement concrete (PCC) ( 5 , 6 ). This technique allows a large amount of concrete to be placed quickly and continuously without forms, dowels, or reinforcing steel. The absence of dowels and tie bars in this pavement makes it economical and construction time efficient ( 5 ).
Multiple lifts have typically been used for RCC pavements when the thickness exceeds about 250 mm to ensure adequate compaction of each lift, with the intention of developing sufficient bonds at the interface between lifts so that the RCC can be considered monolithic ( 7 ). The bottom layer is often thicker and serves as the main structural component of the composite slab, while the top lift is generally constructed with higher quality constituent materials for improved surface characteristics such as noise and skid resistance as well as durability ( 8 , 9 ).
Joints in RCC pavement are clearly critical areas and form weak points. RCC is similar to conventional concrete pavements in that it can have different types of joints such as construction joints and sawn (contraction) joints. Longitudinal and transverse construction joints are generally a practical necessity. Longitudinal and transverse joints, sawn through only part of the layer thickness, are normally used to control random cracking and to provide a mechanism to control the spacing of cracks ( 9 , 10 ). Because neither dowel bars nor steel reinforcement is used, load transfer across the cracks of unjointed RCC is carried out mainly through aggregate interlocking, while the base layer stiffness provides a minimum load transfer. The shear capabilities induced by aggregate interlock across the cracks depend on the magnitude of the crack opening, cracked surface roughness, and aggregate size ( 11 , 12 ). Sok et al. ( 12 ) found that using aggregate gradation with a 19-mm maximum aggregate size in RCC pavement (RCCP) provides better load transfer efficiency than using a 13-mm maximum aggregate size.
RCC is designed as a rigid pavement similar to conventional concrete pavements reflecting its mode of failure, which is fatigue resulting from repeated tensile stress. Generally, the inputs to the design process are the stiffness of the subgrade, the type and thickness of the subbase, the flexural tensile strength (or modulus of rupture) of the RCC, and the type and frequency of loading ( 13 , 14 ).
The thickness design of both conventional concrete and RCC pavements is based on keeping the flexural stresses, and therefore fatigue damage, in the pavement, caused by wheel loads within allowable limits. Stresses and fatigue damage are greatly influenced by wheel load placement, which leads to a greater effect from loads placed along edges and joints and less at interior locations in the pavement ( 7 ).
An important characteristic of concrete pavement joints in the design procedure is load transfer (or joint efficiency). Load transfer refers to the ability of a joint or crack to transfer load from one slab to an adjacent slab, thereby reducing the amount of load and therefore stress which must be borne by an individual slab. Joint efficiency is a measure of load transfer, being the proportion of deflection caused by a load on one slab that is transferred to an adjacent slab through the joint. Load transfer is best across narrow cracks or joints and is therefore improved by limiting the spacing between joints ( 4 , 15 ) since thermally induced expansion and contraction will be less concentrated. Load transfer significantly affects the performance of concrete pavement. Load transfer in RCCP mainly depends on shear transfer capabilities induced by aggregate interlocks and base stiffness ( 12 ).
Concrete pavements undergo stress and strain from a variety of sources during their service life. These include self-weight, thermal loads, wheel loads, and shrinkage, some of these varying with time. To predict the service life of a pavement, the damage ratio, which is the ratio between the predicted and allowable number of repetitions, is computed for different load groups at different times and summed over a year. The service life of concrete is then defined as the number of years before the damage ratio adds up to 1 ( 16 ).
Thickness design procedures for RCC pavements for certain applications such as ports and multimodal terminals have been developed by the Portland Cement Association (PCA) and U.S. Army Corps of Engineers (USACE) ( 10 ). These design approaches involve the assumption that the pavement structure can withstand loads of certain magnitudes at certain repetition levels without failing. Following previous studies ( 7 , 8 , 13 ), the critical stresses in RCC relating to flexural fatigue are used for thickness design. The stress ratio, as typically used in fatigue predictions, is the ratio of flexural stress under load to flexural strength ( 7 ). In RCC thickness design, either the pavement thickness, the strength of the concrete, or the foundation stiffness is increased until the stress ratio is reduced sufficiently to provide adequate fatigue performance ( 10 ). On the other hand, the U.S. Army Corps of Engineers (USACE) has argued there is a difference between designing the thicknesses of RCC and PCC pavement related to the assumptions of load transfer at joints, which directly affects the design stress and therefore the thickness of the pavement. Thus, they concluded that the assumption of 25% load transfer at joints in open storage areas and airfields constructed of plain concrete might not be valid for RCC pavement thickness design. Therefore, their approach was to base the thickness design of RCC pavement on zero load transfer at the joints by assuming all joints and cracks give a free edge condition ( 7 , 10 , 17 ).
Theoretical Analysis of Two-Layer RCC Pavement
In this study, the finite-element computer program KENSLAB has been used to investigate the influence of several common variables in concrete pavement. Huang ( 18 ) at the University of Kentucky developed the program to calculate stresses and deflections in jointed rigid pavements. It can analyze a series of slabs with aggregate interlock (or dowels) as load transfer devices. The KENSLAB program is based on the finite-element method, in which the surface area of the slabs is divided into rectangular finite elements with many nodes. Both wheel loads and subgrade reactions are applied to the slab as vertical concentrated forces at the nodes ( 18 – 20 ).
For this investigation, the maximum tensile stress in a two-layer RCC pavement has been examined assuming various aggregate joint efficiencies, slab depths, and differential temperatures. Longitudinal surface profiles have been determined so that the vertical deflections on either side of a loaded and unloaded crack or joint could be compared.
According to previous information and based on laboratory test data, a design method will be presented, and recommendations made as to how two-layer RCC pavement performance may be designed in practice.
Basis of Design
Methodology
The aim of this paper is to design a two-layer RCC with joints, based on different load transfer stiffnesses, representing the joint efficiency caused by aggregate interlock, using KENSLAB. In addition, this study will investigate the prediction of joint deterioration and fatigue damage. It focuses on the effect of two design factors on the performance of two-layer RCC with joints, namely the load transfer stiffness and fatigue characteristics. Design criteria are defined to evaluate the pavement performance.
Two distinct types of mixture were used in this investigation of two-layer systems. The lower layer incorporated crushed carboniferous limestone aggregate, sourced primarily from Tunstead quarry in Derbyshire (UK), with a maximum particle size of 20 mm. For the upper layer, crushed granite aggregate sourced from Bardon Hill quarry in Leicestershire was employed, with a maximum particle size of 10 mm. These materials were selected based on their availability within the UK. The decision to use granite aggregate for the upper layer was motivated by its superior skid resistance and abrasion resistance properties. Conversely, limestone was chosen for the lower layer because of its cost-effectiveness and high strength characteristics.
Figure 1 shows a flowchart of the methodology for two-layer RCC pavement design depending on parameters such as slab thickness, modulus of subgrade reaction, chosen according to concrete pavement design procedures in Huang ( 18 ), the stiffness of each layer, and load transfer stiffness. From these inputs, tensile stresses were obtained and the fatigue life was calculated by KENSLAB to check the sensitivity to each input parameter. Then, recognizing that load transfer stiffness will tend to deteriorate during the life of the pavement, an incremental damage approach has been taken based on equations for both concrete fatigue and joint deterioration.
Design flowchart for two-layer roller compacted concrete (RCC) pavement.
Key Inputs
Fatigue Cracking
Fatigue cracking under repeated flexure is an important aspect of pavement design. For this study, a four-point bending test was carried out on samples with dimensions 60 × 60 × 305 mm (2.4 × 2.4 × 12 in.) of the two RCC layers to check the relationship between stress ratio and number of cycles to failure. Figure 2 presents the results for both the upper and the lower layers. See Mohammed ( 21 , 22 ).
Fatigue test data for the upper and lower roller compacted concrete (RCC) layers.
Load Transfer Stiffness
Load transfer stiffness was measured based on a laboratory test described by Mohammed ( 21 ), namely a cyclic shear test with varying crack width (0.2 mm, 0.5 mm, and 1 mm) (0.008 in., 0.02 in., 0.04 in.) and shear stress magnitude. Based on these tests, equation 1 was formulated to describe the joint deterioration:
where
load transfer stiffness (LTS) is (MN/m3),
τ is the shear stress (kPa),
MOR is the modulus of rupture (kPa),
W is the crack width (mm), and
Ni is the number of cycles.
Figure 3 illustrates predictions of load transfer stiffness from equation 1 against the number of cycles for 200 kPa (0.03 kips per square inch [ksi]), shear stress, and a stress ratio of 0.3.
Results of load transfer stiffness against number of cycles at 200 kPa shear stress.
KENSLAB Model
The two-dimensional mesh used in the finite-element analysis is shown in Figure 4, following the example in Haung ( 18 ). It was analyzed as a linear elastic system. Four slabs were analyzed with the same four load transfer stiffnesses between them to cover the most critical situation. In this analysis, a single wheel load was applied as a uniform load placed directly on a rectangular area on the edge of the surface near a transverse joint at 1.5 m (5 ft) from the pavement edge; it was considered the most critical point as it has the highest stress. Figure 5 shows the profile of the two-layer RCC.
The finite-element grid for the two-layer roller compacted concrete (RCC) pavement analysis wheel position is shown in black.
Depth profile of two-layer roller compacted concrete (RCC).
The constant parameters were wheel load (F = 41.5 kN, 9,217 lb) and tire pressure (P = 690 kPa, 0.1 ksi), following Huang ( 18 ); RCC stiffness as measured in the laboratory (E for surface layer = 31,530 MPa, 4.6 × 106 pounds per square inch [psi] E for base layer = 33,470 MPa, 4.8 × 106 psi); modulus of rupture 5 MPa, (725 psi); and modulus of subgrade reaction (k = 50 MPa/m, 200 pounds per cubic inch [pci]). These values are chosen from the American Concrete Institution (ACI) design charts in accordance with previous studies of RCC design ( 4 , 6 , 11 ).
The input variables were: slab depth in mm (D = 150, 175, 200, and 250) (6 in., 7 in., 8 in., and 10 in.) chosen to cover a wide range of slab thicknesses but always with an upper layer thickness of 50 mm, (2 in.); slab length in m (L = 3.6, 4.5) (12 in.,15 in.). LTS in MN/m3 (LTS = 100, 1000, 10,000) (368.4 pci, 3,684 pci, 36,840 pci), representing very low, medium, and very high load transfer efficiency depending on Thompson ( 23 ). The number of cycles to failure was calculated based on the stress ratio and fatigue equation derived from laboratory testing.
Procedure for Using KENSLAB in RCC pavement design:
Foundation selection: choose “liquid foundation”
Contact type: select “full contact”
Mesh size: set according to Figure 4
Joints configuration: input the number of joints and their stiffnesses
RCC layers properties: enter the stiffness values of the RCC layers ○ specify the dimensions (thickness and other relevant dimensions) of each layer
Slabs and nodes: define the number of slabs ○ input the number of nodes.
Load type and units: select the type of load ○ choose the units.
Run analysis: execute the program
Review outputs: ○ maximum deflection ○ maximum RCC tensile stress ○ maximum joint shear stress
Results and Discussion
Results of Stresses in Two-Layer RCC Pavement
Traffic load is the major cause of stresses and deflections in a concrete pavement slab. Thermal warping or curling could also be significant in some circumstances as when there is a difference in temperature between the top and bottom surfaces of a concrete slab. The most critical stresses are found to be along the edge of the slab near the joint in the bottom layer under the load. Figure 6 presents the relationship between tensile stress and slab thickness for a slab length of 4.5m. It can be seen from these results that the joint stiffness and slab thickness both have a significant effect on the tensile stresses in the lower layer of the RCC pavement. The effect of slab length has not been shown since it was relatively minor, only 2.66% difference in stress for example between slab lengths of 3.6 m and 4.5 m at 1,000 MN/m3 joint stiffness and 200 mm slab thickness.
Results for tensile stress at different slab thicknesses with different joint stiffnesses and slab length 4.5 m.
The reduction in stress is about 25% when the joint stiffness increases from 100 MN/m3 to 10,000 MN/m3 for a slab thickness of 200 mm. This agrees well with Thompson’s ( 23 ) work on cement-bound material. The reduction in stress is 48% when the slab thickness is increased from 150 mm to 250 mm at 1,000 MN/m3 joint stiffness.
Shear stresses across the transverse joint were also obtained from KENSLAB analysis; see Figure 7 for an example. It can be observed that increasing load transfer stiffness increases the shear stress. The increase in shear stress, when the load transfer stiffness increased from 100 MN/m3 to 10,000 MN/m3, was a factor of about 3.5 depending on slab thickness. As with concrete stress, the effect of the slab length was found to be minor. And, as expected, shear stress was also found to be roughly proportional to the inverse of slab thickness.
Results for shear stress at different slab thicknesses with different joint stiffnesses and slab length 4.5 m.
Results of Deflections for Two-Layer RCC Pavement
The highest deflection is under the load adjacent to the joint, and unsurprisingly the load transfer stiffness has a significant effect on deflection.
Results for deflection with different slab thicknesses and load transfer stiffnesses at 4.5 m slab length.
It can be seen from Figure 8 that the maximum deflection of a RCC pavement along the transverse joint for different slab thicknesses, the maximum deflection was reduced with increasing load transfer stiffness, reducing by 40% to 50% when changing the load transfer stiffness from 100 MN/m3 to 10,000 MN/m3.
Increasing slab thickness from 150 mm to 250 mm reduced the deflection by up to 50%, while the slab length was again found to have only a small effect on deflection. Therefore, it is important to have adequate load transfer stiffness with reasonable slab thickness to reduce the deflections.
Pavement Design Sensitivity Analysis
Evaluation of the performance of the two-layer RCC pavement was initially carried out according to fatigue life based on the tensile stresses obtained, without reference to joint deterioration. Previous sections showed that the maximum tensile stresses occurred at the bottom of the base layer of the RCC, which means that these are the stresses appropriate for design purposes. The fatigue equation, based on Figure 2, used in calculating the life of the pavement is shown below:
where Nf is the number of cycles to failure and SR is the stress ratio
Figure 9 shows the predicted number of cycles to failure against slab thickness for load transfer stiffness between 100 MN/m3 and 10,000 MN/m3, and a slab length of 4.5 m.
Relationship between number of cycles to failure and slab thicknesses depending on load transfer stiffness at 4.5 m slab length.
Road Deterioration Prediction
From KENSLAB analysis and the LTS equation, road deterioration has been predicted. Deterioration is expressed as a damage ratio, in effect the proportion of the fatigue life that has been used at any given time. Failure occurs when the total damage ratio reaches the value 1, although a damage ratio of 1 actually indicates that the probability of failure is 50%, that is, that 50% of the area will experience fatigue cracking ( 18 ). Therefore, the theoretical end of service life does not mean 100% failure.
The damage ratio (Dr) is expressed by using the Miner ( 15 ) equation, which is given by:
where ni = the number of load repetitions that have been applied in increment i, and Nf = the number of load repetitions to failure (from analysis related to that increment).
Figure 10 shows an example of predicted pavement deterioration using an incremental damage approach. In this case, damage increments of 0.1 were used. The computed tensile stress allowed the calculation of Nf in each increment, giving Ni = 0.1 × Nf. The computed shear stress across the crack or joint was then used in the load transfer stiffness equation to give the equivalent number of load applications to have reached the current load transfer stiffness under the current shear stress; increasing this by Ni then gives the load transfer stiffness to be used in the next increment. Figure 10 shows a reduction in load transfer stiffness with the increasing number of cycles while the damage ratio increased, and the shear stress reduced.
Relationship between load transfer stiffness, shear stress, damage ratio, and number of cycles.
Figure 10 is based on 200 mm of concrete with a crack width of 0.2 mm and a modulus of rupture of 5 MPa under a wheel load of 41.5 kN, and shows cumulative non-linear damage increase over nearly two million load applications, but this is clearly just one example. Of particular interest is the effect of crack width which, according to the equation presented in this paper, is inversely proportional to load transfer stiffness, and will be affected by joint spacing as explained clearly by Mohammed et al. ( 24 ).
Thus, for example, a 3-m joint spacing would lead to an increased prediction of pavement life simply as a result of the narrower cracks induced. It should also be appreciated that crack width will vary with pavement temperature and so a complete prediction should really take much smaller damage ratio increments and sum up effects through summer and winter possibly day and night to arrive at a realistic prediction for a particular climate and traffic combination.
Conclusions
This paper has presented computations of stresses and deflections in a two-layer roller-compacted concrete slab with induced joints, as a function of load transfer stiffness. It has also presented an equation to predict the rate of deterioration of load transfer. Continuing these inputs with an appropriate concrete fatigue law has led to the conclusion that rational prediction of the life of an RCC system is possible. This has been demonstrated by means of an example and it opens the door to the scientific evaluation of the effect of crack width, and therefore joint spacing, as well as other key pavement variables. It shows the importance of incorporating the effect of load transfer stiffness on the design thickness of layers and therefore on fatigue life. The deterioration of pavement is expressed as a cumulative non-linear damage increase over nearly two million load applications. This paper recommends that future work include the effect of differential temperature on crack width and therefore on pavement damage.
Footnotes
Acknowledgements
The support from the Higher Committee of Education Development (HCED) in Iraq by providing a scholarship for this research is gratefully acknowledged. The author also acknowledges the support of the technical staff of the Nottingham Transportation Engineering Centre (NTEC) at the University of Nottingham.
Author Contributions
The authors confirm contribution to the paper as follows: study conception and design: Haneen Mohammed, Nick Thom, Zainab Hacham; data collection: Haneen Mohammed; analysis and interpretation of results: Haneen Mohammed; draft manuscript preparation: Haneen Mohammed, Nick Thom, Andrew Dawson. All authors reviewed the results and approved the final version of the manuscript.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
