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Евразийский Союз Ученых (ЕСУ) #1 (34), 2017\ ТЕХНИЧЕСКИЕ НАУКИ
ТЕХНИЧЕСКИЕ НАУКИ
REFINEMENT OF CALCULATION MODEL OF ASPHALT CONCRETE
PAVEMENT
Jafarov N.D.
Baku, ASOIU
Аннотация
Уточнение модели расчета асфальтобетонного покрытия
Джафаров Н.Д. - к.т.н., доцент (Баку, АГУНП)
Ключевые слова: асфальтобетон, дорожное покрытия, поры, критическое состояние.
В данной статье предложено модели расчета асфальтобетонного покрытия с учетом существование поры. В рамках предложенного модели определены предельные состояния и величина осадки асфальтобетонного покрытия.
Summary
Refinement of the model calculation of asphalt concrete pavement
Jafarov N. D - PhD, docent (ASOIU)
Key words: asphalt-concrete, pavement, pores, critical condition
In this article the calculation model of asphalt concrete pavement, taking into account the existence of pores is proposed. Under the proposed model, the marginal status and value of deposits of asphalt concrete pavement has been identified.
Introduction. Transportation of greater volume of freight makes argent to increase freight traffic ability of roads. Therefore, construction and broading of new roads, renewal of old ones are principal problems of our day. This time the roads are covered with relatively hard new asphalt. That is, by covering the roads, such factors as the load-carrying capacity of vehicles, increase of their speed, and change of constitution of exhausted gases should be taken into account. Indeed, it is known from the structure of asphalt-concrete and its placement technique that such pavements have pores. The less is the volume of pores the less settlement and the hard pavement. It should be noted that the settlement consists of two addends: settlement caused bydeformation of asphalt-concrete particles and settlement caused by change of the volume of pores. The quality of asphalt-concrete pavement is characterized by small volumes of pores. The goal of this paper is to determine the settlement of asphalt-concrete pavement.
Problem statement. Let us consider a prism of length L , cross section F and made of the material of asphalt-concrete pavement. Assume that one of its ends is rigidly built - in, the another end is under the action of the force T that longitudinally compresses the prism. Suppose that the material of the asphalt-concrete pavement consists of hard particles connected with binder [2]. This time, since the binder doesn't fill the space between hard particles, the asphalt-concrete pavement has pores. We denote the porosity factor being one of the parameters of the asphalt-
V
concrete pavement by Ш-
пор
where Vnop is
the volume of pores, V is the total volume of the isolated prism.
Assume that behavior of the prism is described within theory of rods. Then, in special case the parameter ® is independent of transversal coordinate. In the general case, as the binder possesses rheological properties, then on the whole the prisma's material demonstrates its rheological property. But one can assume that the compression process may occur in the asphalt-concrete pavement at a moment as well. Therefore, in the prism, rheological processes are not considered.
It is known that by taking into account the pores, two types of stresses are considered: the stress: G3 that belongs to the cross section F , and the stress Gs that belongs to the entire part of the cross section without pores, i.e. the stress Fs = F(1 — ©) is considered. From the loading condition we get
T
a.
F
a s —
T
T
— a,
1
Fs F (1 -ш) э 1 -ш
(1)
Under the real stress, hard particles connected with the binder are deformed. As a result of this deformation, the volume of pores changes. Thus, the considered deformation reduces to longitudinal displacement, in particular for a loaded one to displacement, i.e. to settlement.
Евразийский Союз Ученых (ЕСУ) # 1(34), 2017 | технические науки
51
Problem solution. From the equilibrium equa- is determined by experiments. We generalize (4) and
T n
tion we get < — — = P — const. Under the
g 3 F
stress <s the longitudinal deformation of hard particles and the binder occurs. In some cases it is accepted that hard particles are not deformed. Furthermore, since the binder is similar to viscous fluid it works only for slippage. As a result, from these assumptions we get that by compressing the asphalt-concrete sample in the prismatic form, the thread consisting of hard particles is not deformed longitudinally, they displace with respect to each other. The longitudinal displacement occurs only because of change of volume of pores. This displacement scheme is approximate.
Determine the value of the parameter © depending on the value of the applied load P . From the definition of the parameter © we get:
/m Vo — Vs (0) du du
©(p) _ 0 sv / + _ ©o + __ . (2)
dx
dx
Here Vs is the volume of the hard particle, Vq is the initial volume of the prism, U is longitudinal displacement, ©q is the initial relative value of the volume of pores. Assume that the pavement's material «on the whole» manifests its nonlinearity property i.e.
du (
Tx = f (a ') = -f
P
1 -©
(3)
here f is a nonlinear function characterizing
physical state of the material. Then according to (2) we get:
( P A
© —©q — f
V1 -©v
(4)
In the general case, the quantity © is characterized not only by the function f. Dependence of © on P has a relatively complex character and mainly
X = X
P 1 E 1 - ©
= 2 xx
get:
d© dP
Ф
P
v Ï-©/
; © = ©0 ; for P = 0.
Here © ^ is any function of nonlinearity. This relation is similar to the kinetic equation of damages in theory of damages [3]. Similar to this theory, we can accept the physical relation in the following form:
ds J P } du
dP
= Ф
1 -©
s = 0; s = — ; for
dx
P _ 0.
Note that replacement of a nonlinear algebraic equation by a first order ordinary differential equation simplifies the solution of the problem.
Analyses of the obtained solution. For analyzing the settlement quantity, we accept f as a linear
function and simplify equation (4). In equation (4), the determining term in small values of load is linear. So instead of (4) we get the following relation:
© = ©0
1 P E 1 - ©
(5)
E is the modulus of elasticity. © is a positive quantity, then relation (5) is valid for 0 < P < Pcr,
here Pcr = E©o. P =Pcr corresponds to closure of pores [4]. After transformations, from equation (5)
we get:
© =
x = (©0 - ©)(1 - ©); 1 + ©-j(1 -©0)2 + 4x
_ P := E •
For T = 0 the sign in front of the square root is chosen subject to the condition © = ©o . From equation (3) and from the boundary condition for a prism: for X = 0 from the rigidly built - in condition, i.e. for X = 0 as U = 0 we get:
©o +1 + 7 (1 -©0)2 + 4t j"1.
The obtained quantity determines the problem's solution. Let us determine the settlement quantity, i.e. for X _ L the displacement for loaded one:
S _ 2t
- ©0 + 1 + j(1 - ©0)2 + 4x I ; S
Г ; S=
u ( L)
(6)
For 0 < I < Tcr _ ©0, as a result we get
0 < S < Scr where Scr — ©q . It is seen from
the expressions of i and Icr that this quantity is small. We expand relation (6) in Taylor series and for the linear term get:
c 1
Sl —— . (7)
1 — ©0
At the given values of the parameter ©q , for
the values ©q — 0.05, ©q — 0.1, the comparison of calculation results of the linearized solution and nonlinear solution was given in figure 1.
It is seen from the comparison of the curves that the difference between nonlinear and linear solutions increases at the mentioned value of i .
It is clear from the problem statement that at the mentioned value of the load, the greater is settle-
_52_Евразийский Союз Ученых (ЕСУ) #1 (34), 2017\ ТЕХНИЧЕСКИЕ НАУКИ
ment, the greater is the volume of pores, i.e. in this case the quality of the pavement is not good. Note that
the limit values of the settlement ипр and of the load Тпр correspond to their critical values.
Fig.1. Comparison of computation results of nonlinear and linearized solution.
1. for ©o = 0.05, 2. for ©o = 0.1 (nonlinear case); 3. for ©0 = 0.05, 4. for ©0 = 0.1 (linear case).
Knowing the thickness of the asphalt-concrete
O ci
road, we get S =-. So, S = ©0 , then
L
1
©0 — — U . The found value of ©q characterizes
L
quality of the asphalt-concrete pavement. The less ©0, the higher quality of the pavement.
Conclusion. Subject to existence of pores, a model of behavior of motion of asphalt-beton pave-
ment of roads was suggested. Within the suggested model critical case and settlement quantity of the asphalt-concrete pavement characterized by closure of pores was determined.
References
1. Deformative ability of asphalt pavements and foundations. VNITI, 1975, 38, pp. 1-29.
2. Glushko I.M. and others. Road building materials. M. Transport, 1983, 383 p.
3. Rabotnov Yu.N. Deformable solid mechanics. M. Nauka, 1979, 744 p.
4. Rustamov T.A. Compression of a porous material made bar with regard to large displacements. Mekhanics, Machine-building. Ministry of Education of the Republic of Azerbaijan. Baku, 2006, №1, pp. 22- 23.
РАЗРАБОТКА КОНЦЕПЦИИ ОПРЕДЕЛЕНИЯ АМОРТИЗАЦИОННОГО
СРОКА СЛУЖБЫ АВТОМОБИЛЯ
Мосикян К.А. к.т.н. доцент Барсегян М. С.
к.т.н.
Национальный аграрный университет Армении
Аннотация
В статье рассмотренны вопросы определения срока службы автомобиля в условиях эксплуатации, на основе изменения качественных показателей автомобиля и обеспечения положительного сальто баланса экономической составляющей.
Приведены конкретные данные для разных концепций формирования и подержания списочного числа автомобильного парка, показаны количественные оценки технических и экономических показателей.
