Hello, I am looking for someone to write an article on Rigid pavement design. It needs to be at least 250 words. The movement of people and goods throughout the world is primarily dependent upon a transportation network consisting of roadways. The surface of these roadways is the pavement that must have sufficient smoothness to allow a reasonable speed of travel as well as ensuring the safety of people and cargo. Types of pavements can be categorized as rigid, flexible, and composite pavement. This paper focuses on the rigid pavement and it describes the layers under Portland Cement Concrete (PCC) slap. Also, it gives a brief description of the main types of rigid pavement, which are Jointed Plain Concrete Pavement (JPCP), Jointed Reinforced Concrete Pavement (JRCP), and Continuously Reinforced Concrete Pavement (CRCP). The joints in PCC slab help in reducing the stresses due to subgrade moisture variation, temperature variation, and shrinking of concrete based on AASHTO, 1993. Moreover, to determine the slab thickness of concrete pavement, there are equation and parameters have to be taken into account. Design, Analysis, and Rehabilitation of Windows () is a software program used to evaluate the pavement structure in terms of the expected performance under design traffic loadings and given climatic environments. The rigid pavement can resist a variety of conditions for a long time and requires less maintenance provided that it is professionally laid. . However, the need for repair is sometimes very crucial in the case of any distress. Every strategy comes with a cost and by performing an economical analysis of the alternative strategies, the cost of each strategy can be roughly estimated. The life cycle cost analysis (LCCA) is the most effective method used to approximate the cost.
In the twentieth century, the cars took the lead as the main means of transport. After the Second World War, the growth in traffic, tire pressures, loads, and the higher speeds necessitated the development of pavement technology beyond designs based on experience only. Functional performance had to be defined, predicted and understood to the basis of the service that is provided to the road users in relation to the cost. Nevertheless, this performance required a structural behavior and pavement distress knowledge in relation to the time. However, this motivated the American Association of State Highway Officials (AASHO) road test.
A pavement is a structure composed of structural elements, whose functions are to protect the natural subgrade, distribute the applied vehicle loads to the subgrade, and carry the traffic safely and economically. The essential aim of pavement is to ensure that the transmitted stresses due to wheel load are sufficiently reduced, so that they will not exceed bearing capacity of the subgrade. Additionally, the pavements can be classified based on the structural performance into three major types, which are flexible pavements (upper layer of asphalt), rigid pavements (upper layer of concrete), and composite pavements. This paper gives an overview of rigid pavement layers, types, and functions. Also, this paper describes the design procedures and design input variables based on AASHTO (1993) Design Guide. There are multiple factors in the design and construction of a pavement system and this paper addresses those factors having a significant effect on the pavement life and serviceability.
The objective of this paper is to provide a brief explanation on the use of AASHTO (1993) design equation for rigid pavements designas well as developing a good qualified rigid pavement system by taking into consideration some factors such as: pavement materials, traffic loads, subgrade, and drainage coefficient.
2.0 Rigid Pavement
Rigid pavements are well known because the pavement structure deflects very little under loading due to the high modulus of elasticity of their surface course. Rigid pavement is defined as a pavement structure that depends upon tensile beam strength of a Portland Cement Concrete slab (PCC) for the support of traffic loads. A rigid pavement structure is composed of a PCC (surface course) built on top of either the subgrade or an underlying base course. The pavement structure distributes loads over a width of the underneath layers because of its relative rigidity. Figure (1) describes rigid pavement load distribution.
2.1 Basic Structural Elements
A typical rigid pavement structure consists of the surface course and the underlying base and subbase courses (if used). The stiffest layer that provides the majority of strength is the concrete slab (surface course). The base course is the layer immediately below the surface course and consists of aggregate or stabilized subgrade. Subbase courses that are the layers under the base layer are often be removed as they are not very essential. The underlying layers are less stiff than the concrete slab but make significant contributions to pavement drainage, frost protection as well as providing a working platform for construction equipment. Due to the high modulus of elasticity of the Portland Cement Concrete material, the rigid pavement is considered stiffer than flexible pavement. The reinforcing steel of rigid pavements is generally used to handle thermal stresses in order to eliminate or reduce joints, and maintain tight crack widths. Figure (2) shows a typical section for a rigid pavement.
2.1.1 Surface Course
The surface course consists of Portland Cement Concrete slab (PCC) and it is the stiffest layer. It is considered the layer in contact with traffic loads. Smoothness, friction, drainage, and noise control are some of characteristics that a surface course has. The surface course layer is considered as a waterproofing layer to the underlying base, subbase and subgrade. The thickness is typically between 6.0 inch (150 mm) for light loads and 12 inch (300 mm) for high traffic and heavy loads. Figure (3) shows a rigid pavement slab 300 mm (12 inch) surface course thickness. This top structural layer of material is sometimes subdivided into two layers:
2.1.2 Base Course
The base course is the second layer after Portland Cement Concrete (PCC) slab (surface course). It improves the drainage and frost resistance, additional load distribution and stable platform for construction equipment, and uniform support to the pavement. In addition, this layer prevents subgrade soil movement due to pumping.
2.1.3 Aggregate Interlock
Aggregate interlock .is the mechanical locking which forms between the fractured surfaces along the crack below the joint saw cut. Some secondary road systems and low volume rely entirely on aggregate interlock to provide load transfer. Therefore, it is not adequate to provide long term load transfer for high traffic volumes. Dowel bars are often used to provide the majority of load transfer. .Aggregate interlock is ineffective in cracks wider than about 0.035 inches (0.9 mm).
2.1.4 Dowel Bars
The short steel of dowel bars establish a mechanical connection between slabs .without restricting horizontal joint movement. .Dowel bars can help in increasing the efficiency of load transfer through allowing the leave slab to assume some of the load before the load is actually over it. Dowel bars are typically 1.25 – 1.5 inches (32 – 38 mm) in diameter, 18 inches (460 mm) long and spaced 12 inches (305 mm) apart. . At mid slab depth, Dowel bars are usually inserted and then coated with a bond breaking substance in order to prevent bonding to the PCC. . In addition, the dowels help transfer the load as well as enabling adjacent slabs to expand and contract independent of each other. See Figure (4) and (5).
2.1.5 Reinforcing Steel
Reinforcing steel is used to provide load transfer and the transverse contraction joints are usually removed when reinforcing steel is used. As a result, the PCC cracks on itsself and the reinforcing steel provides load transfer across these cracks since there are no joints. Unlike dowel bars, reinforcing steel is bonded to the PCC on either side of the crack in order to hold the crack tightly together. Rigid pavement reinforcing steel consists of grade 60 (yield stress of 60 ksi) No. 5 or No. 6 bars. . The steel constitutes .about 0.6 – 0.7 % of the pavement cross sectional area and is typically placed at slab mid depth. . At least 2.5 inches (63 mm) of PCC cover should be maintained over the reinforcing steel to minimize the potential for steel corrosion.
2.1.6 Tie Bars
Tie bars are used to hold the faces of abutting slabs in contact either deformed steel bars or connectors are used. In addition, tie bars provide some minimal amount of load transfer and they are not designed to act as load transfer devices and should not be used as such. The are typically used between an edge joint and a curb, shoulder or at longitudinal joints. Tie bars are typically about 0.5 inches (12.5 mm) in diameter and between 24 and 40 inches long.
2.2 Types of Rigid Pavement
Almost all types of rigid pavement are made with Portland Cement Concrete (PCC). Rigid pavements are categorized into three major types by their means of crack control:
2.2.1 Jointed Plain Concrete Pavement (JPCP)
JPCP is the most common type of concrete pavement. Jointed Plain Concrete Pavement uses contraction joints to control cracking by dividing the pavement into individual slabs and separating it by contraction joints. It does not use any reinforcing steel and it just uses tie bars and dowel bars. Slabs are usually one lane wide and between 12 ft (3.7 m) and 20 ft (6.1 m) long. Transverse joint spacing is used such that temperature and moisture stresses do not produce intermediate cracking between joints.  .Tie bars .are usually used at longitudinal joints and dowel bars .are usually used at transverse joints to assist in .load transfer. Figure (6) shows a typical section of Jointed Plain Concrete Pavement (JPCP). 2.2.2 Jointed Reinforced Concrete Pavement (JRCP)
To control cracking on this type of rigid pavement, contraction joints and reinforcing steel should be used. Transverse joint spacing in JRCP is longer than transverse joint spacing in Jointed Plain Concrete Pavement JPCP and it is between 25 ft (7.6 m) to 50 ft (15.2 m). Moisture and temperature stresses are expected to cause cracking between joints, therefore, reinforcing steel is used to prevent these cracks. Dowel bars .are typically used at transverse joints to assist in .load transfer .while the reinforcing steel assists in load transfer across cracks. Figure (7) shows a typical section (JRCP).
2.2.3 Continuously Reinforced Concrete Pavement (CRCP)
CRCP is a rigid pavement constructed through continuously longitudinal reinforcement. It does not require any contraction joints, which means it provides joint free design. CRCP is allowed to develop random transverse cracks but the reinforcing steel holds the cracked sections together. The maximum allowable design crack width is about 0.02 inches (0.5 mm) to protect against spalling and water penetration. The spacing of the cracks is affected by the percentage of reinforcing steel used. Reinforcing steel usually constitutes about 0.6 to 0.7 percent of the slab cross-section area and is located near mid depth in the slab. Figure (8) shows a typical section of Continuously Reinforced Concrete Pavement.
2.3 Joints in Rigid Pavement
Joints are the discontinuities in a rigid pavement Portland Cement Concrete (PCC) slab and help in reducing the stresses due to subgrade moisture variation, temperature variation and shrinking of concrete. According to (AASHTO, 1993), the most common types of rigid pavement joints are:
1. Contraction Joints
The most common type of joint in concrete pavement is a contraction joint. The spacing and the method of load transfer of contraction joints define the contraction joints itself. Using the contraction joints can regulate the cracking location caused by dimensional changes in the concrete slab. On the other side, water inflation and unaccepted rough surface can be resulted from unregulated cracks.
2. Expansion Joints
The purpose of expansion joint is to allow the pavement expansion without damaging adjacent structure or the pavement itself, the expansion joint must be placed at a specific location. Expansion joints were common practices in the U.S. in 1950s and today due to their progressive closure, they are not used.
3. Isolation Joints
This type of joint is used to lessen compressive stresses that develop at ramps, building foundations, T-intersections, drainage inlets, manholes, and any differential movement between the pavement and structure.
4. Construction Joints
It is a joint between slabs that results from placing the concrete at different time. This type of joint can be categorized into transverse and longitudinal construction joints. Longitudinal construction joints also allow slab warping without appreciable separation or cracking of the slabs.
2.3.1 Joint Sealing
Once a joint is cut or made, it must be sealed to minimize water and incompressible material entry. In addition, sealants reduce dowel bar corrosion by reducing entrance of deicing chemicals. The followings are three different types of joint sealants:
1. Hot Pour Liquid Sealants:
These sealants are heated up to decrease their viscosity and then poured. As soon as the sealant has cooled, joints will be ready for traffic. Approximately, 25 % of roadway agencies use hot-pour liquid sealants in transverse contraction joints. Moreover, most hot-pour liquid sealants are used in longitudinal joints and low traffic PCC pavements. Figure (9) shows joints filled with hot-pour sealant.
2. Compression Seals:
These are preformed rubber compounds placed into a joint under compression. After rubber compounds are placed, they form a seal by pushing against each side of the joint and are immediately ready for traffic. Compression seals are used by about 21 % of roadway agencies in transverse contraction joints.
3. Silicone Sealants:
These types of sealants are silicone polymer compounds that are poured into joints at ambient temperatures. It takes about 30 minutes for them to harden and make the joint ready for traffic. About 52 % of roadway agencies use silicone sealants in transverse contraction joints.
3.1 AASHTO (1993) Pavement Structures Design Guide
In 1972, The American Association of State Highway and Transportation Officials (AASHTO) pavement design guide was first published as an interim guide. In 1986 and 1993, the updates to the guide were subsequently published. The AASHTO design procedure is based on the results of the American Association of State Highway Officials (AASHO) Road Test conducted from 1958-1960 in Ottawa, Illinois. The AASHTO (1993) Rigid Pavement design procedure is the only method used to design rigid pavements. It is available in nomograph or automated .form. Automated procedures include the (TSLAB 86) .program and the AASHTO .() program. The AASHTO guide also contains design procedures for rehabilitation of rigid pavements, including PCC overlays rigid pavements or asphalt concrete overlays.
3.2 AASHTO Design Equation for Rigid Pavement
3.2 Design Considerations for the AASHTO (1993) Rigid Pavement Design
Traffic is one of most important factors in pavement design. Every effort should be made to collect accurate data specific to each project. The evaluation of initial traffic volume, traffic type, directional distribution, and traffic growth are the requirements of traffic analysis. The AASHTO Design Guide is based on cumulative 18 kip equivalent single-axle loads (ESALs). However, ESALs may be estimated using the following equation:
It is defined as the statistical probability that a pavement will meet its design life. It must account for uncertainties in environmental conditions, traffic loading, and construction materials. The AASHTO design method accounts for these uncertainties by incorporating a reliability level .(R) to provide a factor of safety into the pavement design and thereby increase the probability that the pavement will perform as intended over its design life. Table (1) summarizes the levels of reliability that recommended by AASHTO for various classes of roads.
The reliability level in the AASHTO design equation is not included directly. It is used to determine the value of standard normal deviate (ZR). Values of standard normal deviate (ZR) corresponding to selected levels of reliability are summarized in the following Table
Standard Deviation (S0)
The AASHTO design equation requires specification of the overall standard deviation (S0). Standard Deviation (S0) is defined as the amount of statistical error present in the design equation resulting from construction, variability in materials, and traffic. The standard deviation (S0) Values for rigid pavement typically ranges between 0.3 and 0.45, and the commonly used value for design is 0.35.
The serviceability is defined as its ability to serve the type of traffic (trucks and automobiles), which use the facility. The Present Serviceability Index (PSI) is the primary measure of the serviceability. PSI is determined on a strictly objective basis by applying the users rating scale to sections of roads featuring different states of distress. This scale allows users to rate the pavement’s state in terms of its service quality. The scale rates pavements from 0.0 (very poor / impossible road) to 5.0 (very good / perfect road) see Figure (10) demonstrates Present Serviceability Index (PSI) scale rate. The following equation should be applied to define the total change in serviceability index:
Selection of the terminal serviceability index or the lowest allowable (PSI) is based on the lowest index that will be tolerated before resurfacing, rehabilitation, or reconstruction becomes necessary. For rigid pavement, a typical value of . .is 4.4 and a terminal serviceability index of 2.5 or higher is recommended for design of major highways. Therefore, a typical allowable serviceability loss due to traffic for rigid pavements can be listed as:
Performance (Analysis) Period
The time that a pavement design is intended to last before it needs rehabilitation is called Performance period. It is equivalent to the time elapsed as a reconstructed, new or rehabilitated pavement structure deteriorates from its initial serviceability to its terminal serviceability . The term of analysis period refers to the overall duration that the design strategy must cover. However, the desired analysis period could be required by the realistic performance limitations, in which case, the performance period may encompass multiple performance periods. Performance period in this context is synonymous with design life in the 1993 AASHTO Guide. AASHTO recommendations for analysis periods for different types of roads are summarized in Table (3).
Modulus of Subgrade Reaction
The design modulus of subgrade reaction (k) is a computed quantity that is a function of the subgrade resilient modulus (MR), thickness of granular subbase (DSB), resilient modulus of granular subbase (ESB), depth to bedrock (DSG) and loss of Service (LS). Other layer properties include the elastic modulus (Ec) and modulus of rupture (Sc) for the PCC slabs, the subbase drainage coefficient (Cd), and an empirical joint load transfer coefficient (J). The PCC parameters (Ec) and (Sc) are standard material properties and the mean values should be used for the pavement design inputs. The joint load transfer coefficient (J) is a function of the shoulder type and the load transfer condition between the shoulders and pavement slab.
Drainage Coefficient ()
The drainage coefficient () is used to account the expected level of drainage a rigid pavement is to encounter over its design life. Drainage coefficient () is dependent on the quality of drainage and the percent of time during the year. Table (4) describes the quality of drainage and the time to remove water from the pavement.
After obtaining the quality of drainage from Table (4), the recommended values of drainage coefficient () for rigid pavement design according to AASHTO are provided on Table (5).
Load Transfer Coefficient
Term of load transfer is used to describe the distribution or transfer load across discontinuities such as cracks or joints. The loaded and unloaded slabs will deflect when a wheel load is applied to a joint or crack. The deflecting amount of unloaded slab is related to joint performance. Both the loaded and unloaded slabs deflect equally, if a joint is performing perfectly. The following equation defines the load transfer efficiency:
The load transfer efficiency equation depends on several factors including number and magnitude of load applications, the presence of mechanical load transfer devices, temperature, foundation support, aggregate particle angularity, and joint spacing. Figure (11) illustrates the extremes in load transfer efficiency.
The aim of the AASHTO 1993 model in the pavement thickness design process is to calculate the Required Slab Thickness (D) of the concrete pavement. This is the depth of the concrete pavement that must be constructed to carry the mixed vehicle loads to the roadbed soil while providing satisfactory serviceability during the design period. This process is applicable to all reconstruction and new construction projects. The Accumulated (18 kip) Equivalent Single Axle Loads (ESAL), the Modulus of Subgrade Reaction (k), and Reliability (R) are the steps to consider when determining the required slab thickness of the concrete pavement. To determine the Required Slab Thickness (D) the computer program, the tables provided by AASHTO 1993 Design Guide should be used. Each table uses a different Reliability (R) value and relates the Accumulated (18 kip) Equivalent Single Axle Loads (ESAL) to the Required Slab Thickness (D) for multiple Modulus of Subgrade Reaction (K) values.
Computer Software Tools
The empirical design equations for rigid pavement design equation are implicit relationships between the Required Slab Depth (D) and Structural Number (SN). The AASHTO 1993 Design Guide provides monographs for the graphical evaluation of rigid pavement design equation. It can also be evaluated by using a spreadsheet via the Solver tool in Microsoft Excel. Design, Analysis, and Rehabilitation for Windows () is a computerized pavement design tool based on the AASHTO 1993 Design Guide of pavement structures. is much more than an online presentation of the design methodology in the AASHTO design guide. In addition to providing an accurate and comprehensive means of performing pavement designs, performs a wide range of analyses and calculations. Moreover, is easy to use, fast, and can streamline many repetitive tasks.
3.3 Rigid Pavement Design Process The following figure summarizes the rigid pavement design process.
4.0 Life Cycle Cost Analysis (LCCA) in Pavement Design
5.0 The advantages and disadvantages of rigid pavement
A pavement is an arrangement consisting of elements structured to function as protective sub grade, disseminate the load to the vehicles, economically and transport it safely. The essential aim of is to facilitate transported stresses to the wheel to limit bearing the capacity of the load. Then also they can be grouped on performances, flexibility and duration.
Normal standardize pavement, should have the capabilities of draining water without hitches. These allow water to follow smoothly to different drainage systems. Stagnation of water is as a result of poor pavement systems. This might lead to damaging and cutting the age of the structure. Their safety is also at risk since they can also lead to avoidable accidents, especially slippery bit of it.
Service levels are enabled by its muscles to serve trucks and automobiles using the structure. This can be done by applying scales to different section of the roads in different condition. Durability will enhance efficient and effective in its purpose. Pavements should be made by proper analyzing of the truck and automobiles that will be using the facility in day to day operation. This enable to calculate the weight exerted on them by b movement of trucks.
The structures should be managed. This can be done through, defining the stock, inspecting, assessment, predication, analyzing and planning of the structures .This swill keep and maintain the structures to be reliable and durable. Just like any structure in an organization, pavements should be well managed and inspected after a certain duration, to validate their capabilities of carrying trucks and automobile with larger loads.