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Fundamentals of Penneability in Aspbalt Mixtures

By

Baoshan Huang Research Associate

Louay N. Mohammad, Ph.D., Corresponding Author Assistant Professor and Manager

Amar Raghavendra Research Associate

Chris Abadie, P,E. Asphalt Research Supervisor

Louisiana Transportation Research Center 4101 Goumer Lane

Balon Rouge, LA 70808 Phone: (504) 767·9126 F",: (504) 767-9108

E-mail: Louaym@Ltrc.Lsu.Edu

Submined to:

The Annual Meeting of the Association of Asphalt Paving Technologist March 8 - 10, 1999 Chicago, Illinois

FUDdameDtab .fPermeability iD Asphalt Milium

Baoshan Huang', Louay N. MohammaJ. Amar Raghavendra, Chris Abadie Louisiana Transportation Research Center

4101 Gourrier Ave .• Balon Rouge, LA 70808

ABSTRACT

Permeability is an important characteristic of asphalt mixtW'CS. However, there is much confusion regarding the measured value of coefficient of penneability obtained from different sources. II is not W'iCOmmon that reported values for similar materials have up to 100 limes difference. A study has been conducted at the Louisiana Transportation Research Center (LTItC) to investigate the drainability of five different types of asphalt mixtures that arc used for pavement surface layers as well as base course layers. These mixes include: I) a traditionaJ design of Louisiana Type 8 dense·graded mixture, 2) 19mm Superpave wearing course mixtures, 3) a traditional open-graded Louisiana Type 501 asphalt treated base mixture and, 4) a newly developed open graded large slone asphalt mixture (LSAM). A dual mode fleltible wall permcameler has been developed for the purpose of measuring the waler penneability or the hydraulic conductivity of asphalt minuees. This device works on both constant head and falling bead principles. It is also capable of determining the materials' hydraulic conductivity when the common Darcy's Law is no longer valid, a situation the authors found 10 be true for the studied drainable asphalt mixtures (Type 501 asphalt treated base mixture and open graded LSAM). A statistical model to predict the hydraulic conductivity has been developed for the drainable asphalt mixtures in the range of materials of this study,

INTRODUCTION

Penneability or hydraulic conductivity is an important characteristic of pavement materials. A dense graded asphalt mix will prevent water from passing through the layer so thaI the pavement structure will not be sarurated. On the other hand, an open graded asphalt treated based is designed to have the maximum drainability so that waler will not stay in the pavement structure.

The common design procedures require drainability characteristics of the paving materials in tenus of hydraulic conductivity and effective porosity [1). Hydraulic conductivity is generally considered the same as the coefficient of permeability as defined in the famous Darcy's l.aw, in which fluid 's discharge velocity is directly proportional to hydraulic gradient [2], The validity of Darcy's Law depends on the flow condition. It is only valid when the fluid travels at a very low speed in the porous media and no turbulence should occur. Such a flow is called a laminar flow. Unfortwlately.

1 Research A!SOCiIIC, Louisiana Tnruponllion Rcsurch Center, 41 01 Gouoier, B.IOII Rougc, LA 70808, e-mail: !lJosban@I]!tt ISl!NIL Tel: 22S-767-9164, f .... : 22S-767-9108. I COITcsponding author, AssiSllnl profcuor. Louisiana Transportation RCSCIKh Ccnter, l.ouiliana SIIiC University, 41 01 Gounier. l»lon Rouge, LA 70108, e-mail: !ouJym@ltrdsu_edu, Tel: 225-767·9126, f .... : llS-767·9108.

pavement engineers often forget to check for this important criterion when applying Darcy's Law to characterize paving materials.

When characterizing the penneability of drainable (living materials, confusion often arises for the measured values of coefficient of penneability. According to lbou, et al., the reported coefficient of penneability for untreated permeable base from different state DOTs varies from 0.7 mmlsec (200 ftJday) to 70 mmlsec (20,000 I\Jday) [3]. One of the important factors for this variation is the different test conditions under which the coefficient of penneability being reported. Tan et al. (4] reported that for the open graded coarse mixture in their study, Darcy's law was no longer valid.

This paper reports the results of. drainabil ity study of several asphalt mixtures used or proposed by the Louisiana Department of Transportation and Development (LAOOTD). The fundamentals of hydraulic conductivity has betn reviewed and the validity of Darcy's Law has betn discussed. A dual mode penneability testing device has betn developed for this study, and a statistical model to predict the hydraulic conductivity has betn developed for the drainable asphalt mixtures in the range of materials of this study.

FUNDAMENTALS OF HYDRAULIC CONDUCTIVITY

Darcy'S 1.11''' In 18S6, Henry Darcy investigated the flow of water in vertical homogenous sand

filters in connection with the fountains of the city of Oijon, France. He concluded that the rate of flow, Q, is (a) proportional to the cross-sectional area A, (b) proportional to water head loss, (hi - hl). and (cl inversely proportional to the length L. When combined, these conclusions give the famous Darcy's Law

Q - K A (hl - h2) I L or v· · Ki

(I) (2)

where K is the proportional factor called hydraulic conductivity (or coefficient of penneabilily), v,. Q I A is the discharge velocity and, i- iJWen.. is the hydrawic gradient.

: Q j - i

UJ ~ ra ~

! IUD ,-I

Figure I. Darcy's EIptrimenf

,

Later researchers., having further developed Darcy's basic ideas. determined the dependence of conductivity on the parameters of the transported fluid [5]. They found that hydraulic conductivity is proportional to the ratio of specific weight (y) and dynamic viscosity (Il) of the fluid, which is the acceleration due to gravity (g) divided by the kinematic viscosity (v) of the fluid. Thus, the hydraulic conductivity as defined by Darcy's Law can further be defined as:

(3)

where k is a factor that depends only on the properties of the solid matrix of the porous medium, and is called intrinsic penneability, matrix permeability or sometimes only permeability. The dimension for K is [Lrl] and k, [L'].

Theoretical Determination of Darcy's Hydraulic Conductivity Having understood the basic equation of Darcy's Law as well as the definition of

hydraulic conductivity and intrinsic penneability, it is not difficult to relate the hydraulic conductivity with geometric characteristics of porous media. The following derivations are excerpted from the translation of the original work of G. Kovacs [5].

••

Figure 2. Symbols used For Deriving PoiseulJe 's Equalion

Assuming that the irregularly connected channels fonned by the pores of porous medium can be simplified into a bundle of small straight pipes and assuming only two main forces influence the laminar movement (i.e. gravity and friclion), their equilibrium can be expressed in a mathematical fonn from a model pipe with a diameter of do. Poiseuille's equation can be derived in this way. The equilibrium of a cylinder concentric about the axis of the pipe having a radius r and a length of I, gives the following equation:

(4)

J

where 11 is the viscosity of the fluid (Pa sec).

After solving this differential equation with a boundary condition, where the velocity at the wall of the pipe is uro (v = 0 at r = ro), the velocity at a point at a distance of r from the axis can be detennined by:

(S)

Integrating the product of the velocity and an elementary area (ciA) along the total surface of the cross section, the flow-rate through one pipe with a radius of ' 0 can be obtained by:

(6)

Dividing Equation (6) by the total area, we have the mean velocity,

() iT 1 ~ = s ,, _,

A 811 I (1)

The number of pipes in the model system crossing the unit area of the sample is known, and thus, the total discharge and the virtual seepage velocity can be calculated as follows:

Q ;T z v =-= Q.N:-~ • A, 3211 I

(I)

where A, is the total cross-sectional area of the sample, n is the porosity of the medium and N is the total nwnber of pipes which is given by:

.. N~-,

d, ' (' )

where do is the average diameter of the model pipe (do " 2ro) and it is related to the effective particle diameter I\ through the following equation:

d_·" .D. o- J- " a

where a is the coefficient of shape factor.

(10)

Substitute Equation (10) into Equation (8), the following relationship can be detennined:

,

v ::_L __ .::t ., I III (D)' , 21/(1 _ 11)1 a

(II)

Hydraulic conductivity of the mooel pipes with constant diameter calculated from Equation (II) is greater than the actual value detennined by since the actual pipe diameter is not a constant. Kovacs suggested that the right hand side of Equation (II) being multiplied by a factor ofOA. The theoretical value of ofhydrawic conductivity can therefore be determined, which agrees with the dynamic analysis and includes all the effects of the influencing factors.

(\2)

From Equation (12). it can be concluded that hydraulic conductivity is detennined by three factors: • The fluid characteristics (rill, or using the kinematic viscosity \Al/p, the equivalent

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