Establishing stress boundaries for various loading and pavement configuration

This article is aimed to understand the relationship between stress and pavement components and finding the boundaries of the vertical and lateral stress distribution. It is carried out on four-layer pavement structure to understand the load distribution behavior through different type of materials in each layer with different resilience modulus values and different thickness. This analysis supports us to improve the pavement design accuracy and realistic, which will reduce the road maintenance cost and increase the pavement service life. Several simplifying assumptions regarding tire load applied location has been used. Therefore, 25,000 different vertical stress values in form of 125 different set of data (difference loading and pavement configuration) under five different loading conditions were analyzed using the KENPAVE software (using mechanistic empirical design method). Conclusions from the data and plot analysis show that pavement layer load distribution is affected unevenly as the effect of thickness is greater than the impact of the strength of the layer. Moreover, the results showed that there is a theoretical boundary for load distribution in the lateral direction at the bottom of the surface layer between (8 in - 14.5 in), bottom of base layer (10 in - 19.5 in) and bottom of sub-surface layer (12 in - 22 in). The stress distribution might be used as an indicator for engineers to determine the pavement behavior under an applied load.


Introduction
Expansion of the heavy industry sectors have resulted in more changes in terms of the characteristics of the heavy vehicles types and configurations. The changes are to cope with the increase rate in economic and industrial activities, heavy goods and construction materials movements and the individuals travelling demands Truck traffic also is a major factor in pavement design because truck loads are the primary cause of pavement distress. Different axle configurations of track give a different level of pavement damage [1].
Highways are constructed in a series of layers of different materials to distribute high surface stresses to relatively low bearing subgrades. Generally, the highest quality materials are located near the surface, the load carrying capacity of such a highway is dependent upon the load-distributing characteristics of the layered system. To create a rational economical design of a layered pavement system it is necessary to understand the load-distributing characteristics of the system.
Most pavements consist of a surface course, a base course, a subbase course and a subgrade. The thickness of layers, types of materials and other variables offer an infinite number of possible combinations [2]. IOP Publishing doi:10.1088/1757-899X/1075/1/012027 2 A Number of simplifying assumptions must be made in order to arrive at a theoretical mathematical description of the stresses induced in the components of a roads by tire loads on the surface. Under such idealized assumptions a highway pavement can be symbolized by a layered system. Therefore, unparalleled expansion of major expressway systems makes imperative the development and use of adequate methods for evaluation, design and construction control of flexible pavement systems. The problem to be solved by the engineer in roads design or airport construction deals mainly with layered soil deposits.
In foundation engineering, serious difficulties are encountered, where a soft compressible clay layer is sandwiched at some depth between an upper layer of sand and underlying layer of sand or rock.
Whether the surface layer is stronger or weaker than the underlying layer, Road foundation design of most important structures in civil engineering deals with the evaluation of stresses and strain in multilayered systems.
This investigation was undertaken to provide a general analysis of stresses and strain distribution through a multi-layered system for the engineer. The analysis is intended as a useful tool which can be directly applied to the analysis of actual conditions encountered in layered soil structures [3].
Therefore, by using various types of loads and layer configuration and using Kenpave program (which use Mechanistic-Empirical Methods) the results will give better prediction for the load behavior and effect (stress, strain and distribution boundaries) through the pavement layers. Also, the results will be more accurate when size of data increase.
Therefore, the investigation builds on 25000 value of stress and strain. Then the stress results plotted in tables and figure to be analyzed and extract the lateral distribution boundary for each set of data.

Objectives
This investigation was undertaken to provide a general analysis of stresses and strain of a multi-layered system, for civil engineers. The analysis is intended as a useful tool which can be directly applied to the analysis of actual conditions encountered in pavement layered structure, Numerical evaluation for these data of certain cases is given in a form of influence curves of practical problems. This investigation used Kenpave software as the analyzing program for the pavement therefore area of study will be affected by the limitation of the software.

Methodology
Kenpave software was developed by Yang H. Huang [4]. It is a Microsoft-windows based version that combines the old KENLAYER flexible pavement software and KENSLABS rigid pavement software [5]. This software allows the use of linear elastic, nonlinear and viscoelastic properties of the materials for the different layers. The software can handle up to 19 layers and performs damage analysis. The interface between the different layers can be specified as either un bounded or fully bonded.

coordination (vertical and horizontal) (in)
For this study lateral and vertical coordination has been entered for analyzing: The pavement divided to 8 vertical locations: 1-At the top of each layer 2-At the bottom of each layer 3-At the middle of each layer Moreover, at each vertical location there will be 25 different points in the lateral direction the distance between each point and the next is ¼ contact radius. Table 1 show The thicknesses for each layer obtained from JKR [6] and AASHTO [7] limits for layer thickness for The Structural Design of Flexible Pavement. Subgrade is the natural layer in pavement IOP Publishing doi:10.1088/1757-899X/1075/1/012027 3 structure and has infinity thickness. Therefore, the input data for subgrade thickness in KENLAYER should be "infinity".

Elastic Modulus (psi)
The modulus of elasticity is stress divided by strain for a slowly applied load. In kenpave computer program, each layer has unique number of modulus of elasticity. The elastic modulus for each layer is obtained as follow: 1-Asphalt concrete elastic modulus E is between (450000 -250000) psi 2-Crushed aggregate base elastic modulus E is between (45400 -32000) psi -CBR(100-60) 3-Granular sub-base elastic modulus E is between (32000 -15000) psi -CBR(60-20) 4-Subgrade elastic modulus E is between ((0.07 -0.03) x E for surface layer) psi

Traffic loading
In this study for simplification of the analysis, the dual wheels are converted into an equivalent 70-80-90-100-120 kN single axle load (ESAL). The contact area is important to be determined so the axle load can be assumed to be uniformly distributed. In this study, single axle with dual tires need to be considered and each tire is assumed to have circular contact area. The tire spacing is assumed with a typical distance between dual tires of 30 cm (distance between center lines of tires) [8] . The contact pressure in this study is (80 psi) and contact radius is calculated as follows: Where are: a-radius. P-Total load on the tire. q-tire pressure.

Output Parameters of Kenpave
The output from this program are stress, strain and displacement. For a single and multiple load groups, a maximum of nine and ten responses can be obtained respectively. Only the vertical stress and vertical strain values are used for this study.

Analyzing the results using excel
All data were tabulated and used to plot relationship graphs between vertical stress and vertical strain against the lateral distribution distance in order to observe the ultimate distance the stress or strain will reach at the interconnecting point between the two tangential drown between curves. After all the lateral distance values has been measured, a new relationship will was created using Excel analyzing tools in order to understand how each variable will affect the stress distribution between pavement layers.

Test results and discussion
The results had tabulated into five deferent tables depending on deferent arrangement of layer, resilience modulus and layers thickness.
Each table is divided into four main columns, column one shows the load value in KN which is similar in all tables 70,80,90,100 and 120kn.
Second column shows the thickness in (inches) of layers and it is divided into 3 miner columns (surface layer, Base-layer, Sub-Base layer).
third column show the strength of material or resilience modules in Psi and contain four miner column for each layer (surface layer, base layer, subbase layer and subgrade ).

Relationships between pavement layer thickness and the stress lateral distribution distance in comparison to the relationship between resilience modules and the stress lateral distribution distance
According to the relationship graphs (Figures 1,2,3,4,5 and 6) between (resilience modulus, layer thickness) vs lateral stress distribution distance in 'inches' under 80&120 kN load for the pavement layers (Surface layer, Base layer, Sub-base layer), it can be concluding that the lateral distribution distance increase by increasing the layer thickness and the resilience modules moreover, the plots show that the distribution distance is significantly affected by the thickness under high load values.     Figure 7 which show the relationship between LOAD in KN at Y-axis and Lateral distribution distance X-axis for (surface layer and Base layer and Sub-base layer ) it can be seen that the lateral distribution distance increase by increasing the applied load value on the pavement.

Summary and conclusion
The study was built on 125 sets of data for three main variables applied load, layer thickness and strength of material which presented as (resilience modulus) and CBR for the sub-grad. Therefore, after using Kenpave software (linear method of analysis) to get values for stress and strain, the result was presented in 25,000 values for different point location. the finding has been tabulated and plotted in-different type