SYSTEMIC DESIGN AND THE ELEMENTS OF
OPTIMIZATION OF AIRPORT CONCRETE
PAVEMENTS
Nita P.
Instytut Techniczny Wojsk Lotniczych, Warsaw, Poland
Abstract: The computer-based methods are nowadays commonly in use in the dimensioning of
airfield concrete pavements. Therefore, it is possible to make use of techniques of mathematical modelling and optimisation of solutions throughout this process. The system approach to the design process takes account of principles of future operational use of the pavement. It is also intended to determine relations between actual and design operating conditions. Mathematical models make formalisation of design tasks a practice.
1. Systemic conditions of airport concrete pavements design
The use of computers in pavement design allows the employment of mathematical modelling methods and the optimization of those structures. Design solutions should strictly comply with the possibilities of technical and technological execution of works. At the same time, the systemic approach to pavement construction should allow for the conditions of its future operation as well as the actual conditions of work in relation to the presupposed assumptions (load calculation, traffic intensity, etc.)
Taking into account the interaction of all elements of the system and the influence of various interactions on pavement reliability and durability allow the optimization of structural solutions. This process, which allows for the principles of systemic construction, includes the following stages: preparation of the assumptions, model construction, preparation of the calculation method, execution of the calculation on the basis of already known or self-designed computer programs, analysis of the achieved solutions and their implementation. Model construction makes it possible to present it in the form of mathematical formulas. A model serves to work out calculation and informatics schemes, and to define the functional and computational relations among the systems in use. By defining optimization criteria it is possible to analyse their structure and calculationalgorithms. What also undergoes the analysis is the goal function in the field of its applications. As a result, it is possible to suggest task optimization function in the form of:
x
x Gf max ;
min (1)
where: x – a standard element of space, which defines a natural model;
G – area defining f(x) that may have manifold models defining their structure and the features of the task under analysis.
In many design tasks it is necessary to find an optimal, and, at the same time, practical and realistic solution. After the analysis is carried out, the designer chooses the solution that is the most applicable under the given conditions. The functioning of the system may be shown as a process or a model which complies with various reactions and certain characteristic features, e.g. pavement wear and tear function. The main system consists of a certain number of subsystems, i.e.: theoretical-computational, structural, realization, economic and maintenance subsystems. Among the most important ones are:
a subsystem for index calculation of operational reliability of pavement work,
a subsystem for the evaluation of operational reliability of subsoil work according to deformation characteristics according to the limit state method,
a subsystem for forecasting the state in relation to air traffic load in the overall period
of structure operation,
a subsystem for structure analysis with reference to the established model,
implementation of the calculation process according to the established calculation methods, e.g.: according to the finite element method,
defining the physiomechanical properties of construction materials and their changes
in the pavement operation process.
In order to obtain unambiguous results it is essential to examine the methodology of the approach, e.g. by checking the dimensions of concrete paving slabs. In this process it is necessary to know a significant number of coefficients which interact, and, at the same time, are very important in the process of durability evaluation. Design and operational experiments concerning concrete pavements make it possible to define a set of parameters that directly influence durability. Among those parameters are: modulus of elasticity of concrete Eb, tensile strength and bending tensile strength Rs and Rzg, apparent density γ,
Poisson’s ratio μ, deformation size in relation to the location εp, heat conductivity and the
dimensions of a slab, i.e. its thickness, width and length. What is taken into account here are the factors related to physical and mechanical properties of concrete and their influence on its durability, which is determined by air temperature and air humidity. This relation is of a functional character ψ=f(t,w). Pavement work is influenced by the kind of joints between slabs which conditions their cooperation in load transfer. According to the systemic approach to pavement design it is essential to consider summary temperature loads (slow-changing and forced) and the intensity of aerial operations.
The systemic approach to pavement construction and optimization has to allow for permissible – standard differences between a design and itsactual execution. A systemic approach allowing for the above-mentioned factors and the phenomena accompanying pavement work should be presented as a model, with a possibility of computer analysis, which would distinguish criteria for pavement reliability and durability with the possibly low expenditures on their implementation and maintenance. The structure of factors that are possible to distinguish in the systemic approach has been illustrated in figure 1. The above-mentioned statements have been based on the suggestions presented in the study [2].
In fact, it is not enough to choose a pavement structure only on the basis of its strength (load capacity). Loadbearing layers, which may be durable during the construction, may turn out to be not enough traffic durable and result in accelerated pavement failure. It may also turn out that those pavement structures that are very durable are at the same time very expensive. That is why the aim is to work out global systems of pavement design which would allow for all technical and economic factors. It is commonly acknowledged that pavement design should go according to the following stages:
Stage 1 consists in the collection of the data about materials concerning traffic, ground and climatic conditions. What is also considered as the input data are the assumed pavement durability, the structure (the number and kind of layers), costs of construction and maintenance.
Stage 2 consists in assuming certain variant solutions such as defining the thickness of layers, materials, maintenance technology and rehabilitation cost.
Stage 3 consists in the analysis, comparison, evaluation and optimization of the established solutions.
In the process the forecast of pavement changes is taken into account. Next, after optimization research is carried out, it is possible to choose a variant. Optimization can be carried out from the viewpoint of costs, durability or pavement quality. This system takes into account all conditions of save work of the structure. It is possible to complicate the structure of the model, however, one should bear in mind the possibility of model analysis and the practical advantages arising from this analysis. After the pavement is constructed, the data collected from the construction, from test sections, from pavement operation are stored in the pavement data bank. These data are compared with the assumed design and analysed, next, complementary research is carried out, and on the basis of these analyses it is possible to adjust the norms and criteria. What is here taken into account are reconstruction, resurfacing, and maintenance. Pavement design is not a one-off achievement but continuous work. A reliable, developed data base is a necessary condition of reasonable management of resources which are necessary in particular building projects. A systemic, optimum airport artificial (concrete) pavement design is a current issue in this branch of construction. In the process of design it is appropriate to present several variant solutions. In modern pavement design it is possible to distinguish the following principles:
1. variety of solutions consisting in the analysis of various structural solutions, the possibility of the execution of the road works, and taking into account strucutre
durability and reliability factors in the overall period of structure operation. The period for this kind of structure should not be shorter than 30 years,
2. optimization of structural solutions, which should include not only the structure itself but also the execution stage in the given conditions,
3. choice of appropriate calculation methods which should allow for the changing soil-hydrological conditions of the construction area, with special attention paid to the possibility of the appearance of extremely difficult conditions,
4. modelling of pavement operation conditions which allow for working, geometrical and many other conditions,
5. evaluation of the security of the designed pavements aims in the first place to define the influence of the effect of operational factors on the pavement, dynamic effect of aircrafts on the pavement. In the operation process may appear the changes in the physiomechanical properties of the construction materials of which the pavement has been built,
6. possibility of the change of structural solutions of the task being designed; this pertains to unusual situations, which are difficult to predict,
7. The systemic design is a process of a high degree of complexity; it consists of a number of subsystems, i.e.:
Computational structural, which determines durability parameters at the moment when the pavement is put into operation, and cost constituents,
Operation and maintenance, which allows for the changes in the pavement structure
connected with the operating period of the structure,
Economic, which evaluates the efficiency of investments, the dynamics of changes
in expenditure on maintenance and repairs, and other characteristics.
2. Optimization criteria in pavement design
The systemic approach to pavement design uses the term ‘optimization criteria’ which deal with the goal function. Optimization criteria are a value expressed as structure parameters: design parameters, which allow for the geometric sizes of the structure, the volume of the structure and of construction materials, work consumption and costs of construction. It is necessary to determine those concepts and their values in terms of criteria and a goal function. A many-criteria optimization is also possible. In the design of transport structures one often assumes a cost criterion in which the costs concern all the constituents of a building project during the construction and operation. The load carrying capacity of concrete pavements is a complex function of many variables which have been determined in relation:
Φ = f (P, q, x, y, Ni, m, kd, η, Eb, μ, k, Rs, Rzg, h, λ, L, B) (2)
where: P – the load on the gear leg; q – pressure quantity in tyres; x,y – coordinates of the application of force on a slab; Ni – the number of wheels in the gear leg; m – coefficient of
pavement work conditions; kd – dynamic coefficient; η – overload factor; Eb – modulus of
compressive strength of concrete after 28 days; Rz – bending tensile strength of concrete
after 28 days; h – thickness of a slab; λ – radius of relative stiffness of a slab; L, B – dimensions of a slab.
When analysing the constituents of interrelation (2), one should stress that a number of the above-mentioned variable parameters are a function of specific arguments, e.g. the values
E
b, R
zg, R
s, which depend on the temperature and the humidity of concrete. The value ofthe coefficient of subgrade reaction k changes significantly, depending on the season of the year. The value of the parameter m depends on many factors; first of all, climatic conditions, load structures and pavement maintenance procedures. The above-mentioned factors may be grouped as follows:
I – those characterizing load conditions,
II – those characterizing physical and mechanical properties of materials.
The factors grouped under point I can be assumed as quasi-stationary and relatively stable. The factors grouped under point II are changeable in specific intervals, and provide basis for the search of multi-variant structural solutions for pavement. General conditions including the elements of the optimization of concrete pavement structure pertain to:
the differences between the thicknesses of slabs executed as single-layered concrete
and reinforced concrete structures, with the distinction of physical and mechanical characteristics of constituent materials,
the optimum choice of e.g.: reinforcement percentage for steel reinforced pavements.
The structure optimization principles are especially useful for multilayer composite structures. At this stage the chosen mathematical model includes a set of information concerning the optimized structure, the relations between them and the goal function. The calculation model includes calculation comparisons and indices complying with the current norms. It is possible to distinguish two groups of variables: variables which can assume various values and significantly influence the result of optimization, e.g.: a type of the surface course of the concrete pavement (concrete or reinforced concrete) WP1, the
thickness of a concrete surface course h1, the grade of concrete of a surface course MB1,
the grade of concrete of the lower layer of the pavement MB2, bending tensile stress of
concrete Rzg, the coefficient of natural or improved subgrade reaction C1, C2, the thickness
of the layers of a natural or improved subgrade h01, h02. Other variables in the process of
choosing a solution are in fact expressed as the slab thickness function h1.
In other cases one should identify an assumed load, a slab prop scheme, and the intensity of aerial operations on the pavement. This information is known as input data, which are determined at the stage of structure design. What is assumed are: literal-digital codes of an airport or a runway, a basic type of the aircraft to be operated, and the traffic intensity on the pavement, a kind of subgrade soil, a climatic zone and the assumed period of safe operation.
Technological parameters are: climatic conditions with load conditions, the minimum thickness and the maximum thickness of the pavement hminab and hmaxab , the minimum thickness and the maximum thickness of the upper and the lower layer of the structure h
min
1 , h1max, hmin2 , hmax2 , and, if need be, the minimum thickness and the maximum thickness of an improved subgrade hocmin, hocmax, treated as single- or double-layered.
Technological parameters characterize the area of the goal function mainly with reference to the thickness of the layers. The area of the goal function can be presented as the relation:
hab, WP1, MB1, h1, MB2, h2, Rzg, hoc, C1, h01, C2, h02
(3) The goal function is defined by the relation:
F
C (4)
The area D for goal function F
depends on technical, technological, structuralconditions and traffic restraints.
Technological restraints mainly concern the thickness of pavement layers and appear as undefined events, the occurrence of which causes pavement damage.
During the assumed operation period it is essential to take into account the use of appropriate materials for the respective layers of the pavement and the subgrade:
The attempt at the optimization of concrete pavement structure may be presented as follows:
F D x _ min min arg (5)The minimized goal function may be presented as:
F C D min min (7)where: Cmin– the assumed minimum summary costs or its close value, C pr - the designed goal function which allow determining complementary optimization criteria, such as: reliability, durability, etc. Function F
is linear for variables hab, h1, h2, hoc,h01, h02, and is discrete for variables MB1, MB2, Rzg, C1, C2. In other cases function
F
is not linear. When analysing area D which defines function area F
, one should takeinto account the relation between the values of moments Mr and Mobl. Further restraints are
composite, just like the meaning of variables assumed for discrete and necessary values. Iterative changes in the thickness of layers may lead to composite states. In this way the task of the optimization of rigid airport concrete pavements becomes a non-linear task
which is discrete and of a composite type. The goal function also appears as non-linear and discrete.
3. Goal function in pavement design
What is usually applied in mathematical design are the concepts of optimization criteria, connected with the concept of goal function. Optimization criteria are those concepts which pertain to the mass volume of structures under construction and of materials, work consumption in structure preparation, its value, etc. These criteria are expressed by the geometric parameters of the structure, variants of structural solutions of the design, the type of technology. Objective criteria allow the choice of the best solution. What is often applied in order to distinguish the best solution is a many-criteria optimization [3]. When designing airport pavement systems one should determine the value of the structure under construction. For those structures, by means of the cost comparison method, one should allow for the scope of planned operation and maintenance procedures, and determine the function of the decrease in technical capability of the structure, the so-called loss function. By comparing variants according to the summary task method, in the assumed period of time it is possible to state the relation:
T K K K S K S 0 (18)
where: S - the summary loss value; K0 – the loss value that is assumed during the
construction of a pavement unit, S – the value of investments and buildings; KK - major
repair costs of a pavement unit, KT - specific costs of current maintenance procedures per
pavement unit.
What should be considered as the main optimization criterion is the minimum loss value C → min together with the assumed criteria including the criterion of safety and technical reliability of all the elements of the system of roads and airport surfaces.
4. Summary
Pavement design is a complex issue. There are a very large number of variables and parameters, hence the existence of many variant solutions and structure optimization are obvious. Many countries have their own systems which are applicable in the conditions of those particular countries. Yet, such systems have not been used in the domestic pavement construction. Bearing in mind that pavement design has ceased to be merely a craft and turned into an art, it should be based on scientific principles.
References
1. Rolla S.: Projektowanie nawierzchni. Wydawnictwo Komunikacji i Łączności, Warsaw, 1987.
2. Głuszkow G.I.: Żostkije pokrytia awtomobilnych dorog. Wydawnictwo Transport, Moscow, 1987.
3. Nita P.: Betonowe nawierzchnie lotniskowe. Teoria i wymiarowanie konstrukcyjne. Wydawnictwo Instytutu Technicznego Wojsk Lotniczych, Warsaw, 2005.
