Virtual Pervious Concrete: Microstructure, Percolation, and Permeability – Dale P. Bentz

Virtual Pervious Concrete: Microstructure, Percolation, and Permeability presents various virtual pervious concrete microstructural percolation characteristics and computed transport properties to those of real world pervious concretes. Of the various virtual pervious concretes explored in th is study, one based on a correlation filter three dimensional reconstruction algorithm clearly provides a void structure closest to that achieved in real pervious concrete.

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Virtual Pervious Concrete: Microstructure, Percolation, and Permeability – Dale P. Bentz

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Nội dung Text: Virtual Pervious Concrete: Microstructure, Percolation, and Permeability – Dale P. Bentz

- ACI MATERIALS JOURNAL TECHNICAL PAPER

Title no. 105-M35Virtual Pervious Concrete: Microstructure,

Percolation, and Permeability

by Dale P. BentzAs the usage of pervious concrete continues to increase dramatically, available experimental data. A successful microstructural

a better understanding of the linkages between microstructure, model should prove useful for assisting in the design of

transport properties, and durability will assist suppliers in mixture pervious concrete mixtures and also for examining durability

proportioning and design. This paper presents various virtual aspects of pervious concretes, such as clogging and freezing-

pervious concrete microstructural models and compares their

and-thawing durability. To aid in this objective, the

percolation characteristics and computed transport properties to

those of real world pervious concretes. Of the various virtual computational programs used to create 3D microstructures

pervious concretes explored in this study, one based on a correlation and to compute percolation and transport properties have

filter three-dimensional reconstruction algorithm clearly provides been documented4,5 and are being made freely available to

a void structure closest to that achieved in real pervious concretes. the public from the National Institute of Standards and

Extensions to durability issues, such as freezing-and-thawing Technology (NIST) anonymous ftp site: ftp://ftp.nist.gov/

resistance and clogging, that use further analysis of the virtual pub/bfrl/bentz/permsolver and ftp://ftp.nist.gov/pub/bfrl/

pervious concrete’s void structure are introduced. garbocz/FDFEMANUAL.Keywords: freezing-and-thawing; microstructure; percolation; permeability; RESEARCH SIGNIFICANCE

pervious concrete; void. Pervious concrete is one of the fastest growing markets of

concrete construction. As emphasis on environmental

INTRODUCTION protection and building green is continuing to increase, the

In the first years of the twenty-first century in the U.S., demand for pervious concrete will increase as well. A better

renewed interest has been expressed in pervious concrete understanding of the relationships between the microstructure

pavements, mainly due to environmental issues.1 According and transport properties of pervious concretes will allow for

to Reference 1, these materials have actually been used for better mixture proportioning and materials selection. The

over 30 years in England and the U.S. and are also widely demonstration of a virtual pervious concrete that captures the

used in Europe and Japan as a roadway surface course to percolation and transport properties of the real in-place

reduce traffic noise and improve skid resistance. Basically, a material will also allow an extension to computational-based

pervious concrete is simply produced by removing the fine durability studies of pervious concrete, considering issues

aggregates from a concrete mixture and often using a much relevant to freezing-and-thawing resistance and clogging,

narrower distribution of coarse aggregates, leading to an for example.

increased voids content, typically on the order of 15 to 30%.

These voids are at least partially connected (percolated) so COMPUTER MODELING

that the pervious concrete not only has dramatically Microstructural models

increased permeability to allow water penetration and filtration Various microstructural models have been investigated to

but also lower strength and potentially lower durability. As assess their suitability for creating virtual pervious concrete

the volume of pervious concrete placed in service increases microstructures. First, the NIST hard core/soft shell (HCSS)

dramatically, research on this material and technology model was examined.6 It consists of a 3D continuum model

transfer activities are also increasing.1-3 For example, ACI for a three-phase material. Hard core spherical particles are

Committee 522, Pervious Concrete, was formed in 2001 to surrounded by a soft shell and placed within a third bulk

“develop and report information on pervious concrete,” and phase. Whereas the hard core particles cannot overlap, the

ASTM International’s Subcommittee C09.49, Pervious soft shells can freely overlap with one another and even with

Concrete, was recently formed to deal exclusively with the hard cores. Such a model seems a likely candidate to

pervious concrete issues. represent pervious concrete, if one considers the hard cores

Some of the efforts within ASTM International will center as the coarse aggregates, the soft shells as the (surrounding)

on the development of standard test methods for unit weight cement paste, and the leftover bulk phase as the voids within

and fluid permeability, as well as standard consolidation the pervious concrete structure. Because this model is based

methods for preparing cylindrical specimens for further on the random placement (parking and not packing) of the

testing. Whereas previous studies have focused mainly on hard cores,6 however, even when the particles were placed in

experimental measurements of the strength and flow properties order from largest to smallest, for realistic (for example,

of pervious concretes,1-3 herein the focus will be on so-

called virtual pervious concrete. The goal will be to develop ACI Materials Journal, V. 105, No. 3, May-June 2008.

MS No. M-2007-109.R1 received March 15, 2007, and reviewed under Institute

a realistic three-dimensional (3D) computer microstructural publication policies. Copyright © 2008, American Concrete Institute. All rights reserved,

model to represent pervious concrete and to compute its including the making of copies unless permission is obtained from the copyright proprietors.

Pertinent discussion including authors’ closure, if any, will be published in the March-

percolation and transport properties for comparison against April 2009 ACI Materials Journal if the discussion is received by December 1, 2008.ACI Materials Journal/May-June 2008 297

- Percolation

ACI member Dale P. Bentz is a Chemical Engineer in the Materials and Construction

Research Division, National Institute of Standards Technology (NIST), Gaithersburg, The porous virtual pervious concrete microstructures were

MD. He is a member of ACI Committees 231, Properties of Concrete at Early Ages; first evaluated with respect to their percolation characteristics,

236, Materials Science of Concrete; and 308, Curing Concrete. His research interests namely, the degree of connectivity of the voids in 3D space.

include experimental and computer modeling studies of microstructure and performance of

cement-based materials. He was a co-recipient of the 2007 ACI Wason Medal for A 3D burning algorithm developed previously for 3D digital

Materials Research. images10 was employed to determine the fraction of total

void voxels that are part of a continuous pathway from one

narrow) pervious concrete aggregate size distributions, face of the microstructure to the opposite face, for each of the

the maximum achievable aggregate volume fraction three principal directions (x, y, and z). One of the key micro-

remained below 40%, far below that of the 55 to 65% typical structural parameters influencing transport (in addition to

overall porosity and pore size) is the connectivity of the 3D

of real materials.

void system. It is reported that for pervious concretes, based

Next, a hybrid model was considered. First, a simple on permeability measurements for various void fractions, the

computational algorithm to drop (and roll) spherical particles percolation threshold for the voids is somewhere in the range

of a specified size distribution into a 3D rectangular of 10 to 15%.1,2

parallelepiped continuum volume was used.7 This model

employs periodic boundaries on the faces parallel to the Conductivity

direction in which the spheres are being packed. The central Next, the electrical conductivities of the virtual pervious

portion (in the direction of the dropping) of such a loosely concretes were computed using the C programming

packed particle system was then used as direct input to language version of a previously published finite difference

provide the particle center locations required by the HCSS computer program (dc3d.c).5 Here, for comparison against

computer program. The HCSS code was then used to experimental data,3 the voids were considered to have a

surround each of these aggregates with a user-specified conductivity of one unit, with the remaining solids (paste and

uniform thickness layer of cement paste varying between 0.1 aggregates) considered to have a conductivity of 0. The

and 1.0 mm (0.004 and 0.04 in.), each thickness corresponding program then returns the computed conductivity of the

to a separate 3D virtual pervious concrete. Once again, the composite microstructure in each of the three principal

remainder of the 3D volume was considered to be occupied directions. These values can be conveniently compared with

by voids. With this hybrid model, it was easily possible to the experimental data of Neithalath, Weiss, and Olek,3 who

obtain realistic volume fractions of aggregate particles, and recently measured the electrical impedance properties of a

thus 3D virtual pervious concretes that matched their real wide variety of pervious concretes.

counterparts in terms of volume fractions of aggregates,

cement paste, and voids. For example, one model consisting Permeability

of equal volume fractions of aggregates of diameters 4.75, Finally, the permeabilities of the virtual pervious

concretes were computed using a linear Stokes solver.4,11,12

7.25, and 9.5 mm (0.187, 0.285, and 0.374 in.) was used with

The permeability computer program applies a pressure

various thicknesses of paste shells to create virtual concretes gradient in one of the three principal directions and

with 62% by volume aggregates and voids contents ranging computes the resulting velocity vector field within the

from 4 to 32% by volume. Each continuum microstructure, porosity. The Darcy equation11 is then used to compute the

100 mm (3.94 in.) on a side, was digitized into a 300 x 300 x equivalent permeability for the microstructure. A user’s manual

300 voxel cubic volume for subsequent computation of for this code is available4 and the codes are also available for

percolation and transport properties. Thus, each voxel download at ftp://ftp.nist.gov/pub/bfrl/bentz/permsolver.

was 1/3 or 0.333 mm (0.013 in.) in dimension. The ability The computed permeabilities can be compared with experi-

of these models to capture the percolation and transport mental measurements previously performed on a wide

characteristics of real pervious concretes will be variety of pervious concretes.1-3 The permeability codes have

presented in the results that follow. been validated previously by computing the permeabilities

Finally, as the study progressed, it became clear (refer to of both circular and square tubes;4,13,14 for a square tube

the Results and Discussion section) that a microstructural 25 voxels on a side, the error between computed and theoretical

model with a higher percolation threshold for the void phase permeabilities was only approximately 0.01%, whereas for a

was needed. Thus, a 3D reconstruction algorithm (computer circular tube with a diameter of 25 voxels, it was less than

program rand3d.c on the ftp site) based on filtering a 3D 2%.4 In addition to being used for computing the permeabilities

of virtual materials as demonstrated in the present study,

image of Gaussian noise with a measured correlation

these transport property computer codes are equally applicable

function8 was employed to generate a set of 300 x 300 x 300

to real 3D microstructures obtained from tomography data,15

voxel digitized virtual pervious concretes, with void volume for instance.

fractions ranging between 12 and 32%. In this case, the needed

correlation functions were obtained from two-dimensional

RESULTS AND DISCUSSION

(2D) images from the hybrid HCSS virtual microstructures Microstructures

of similar porosity. These virtual digital image microstructures Representative 2D slices from the 3D microstructural

were also characterized with respect to their percolation and models are provided in Fig. 1 and 2 for the hybrid HCSS and

transport properties. It should be emphasized that the micro- the filtered correlation reconstruction models, respectively.

structural models presented herein do not specifically In the former case, all three phases (aggregates, cement

consider the gradients in vertical porosity distributions that paste, and voids) are identifiable, whereas in the latter case,

may be produced during the compaction of pervious only the solids (aggregates and paste) and voids are delineated.

concrete specimens in the field.9 To the human eye, the void space in the hybrid HCSS model298 ACI Materials Journal/May-June 2008

- appears to consist of larger and somewhat more connected

pores. Because the two microstructural models are clearly

visually different, the next step was to undertake a quantitative

analysis of their 3D percolation characteristics.Percolation and transport properties

The 3D burning algorithm was applied to the various

virtual pervious concretes and the results are presented in

Fig. 3, which plots the fraction of the total porosity that is

part of a percolated pathway versus the total porosity.

Clearly, the two models exhibit vastly different percolation

characteristics. Previously, the percolation threshold for the

void space in the case of totally overlapping spheres has been

determined to be 3.2 ± 0.4%,16 and the hybrid HCSS model

is observed to exhibit a similar value of approximately 4%.

On the other hand, the correlation filter reconstruction

algorithm yields a set of microstructures with a void perco-

lation threshold near 10%, closer to the commonly quoted

value for actual pervious concretes.1,2 Thus, from a percolation

standpoint, the reconstruction-based model appears to be

more consistent with real pervious concretes than the hybrid

HCSS model. Fig. 2—Two-dimensional images from 3D virtual pervious

Next, the electrical conductivity and permeability of the concrete microstructures based on correlation filter recon-

virtual microstructures were considered. The computed struction algorithm. Aggregates and cement paste are white

relative electrical conductivities for the virtual pervious and voids are black. Porosities are: (a) 27.4%; (b) 22.3%;

concretes as a function of void fraction are presented in Fig. 4. (c) 17.9%; and (d) 14.1%. Images are 100 x 100 mm (3.94 x

In Fig. 4, the experimental data from Neithalath et al.3 are 3.94 in.) in size.

included; the actual values in Fig. 4 were obtained by multi-

plying the experimentally measured void fractions by their

measured pore connectivity factors. According to the equations

and definitions presented in Neithalath et al.,3 this should be

equivalent to the relative conductivity for the case where the

pores are filled with a solution with a conductivity of one

unit and the solids have a conductivity of 0 (in agreementFig. 3—Percolation plots for two virtual pervious concrete

microstructural models.Fig. 1—Two-dimensional images from 3D virtual pervious

concrete microstructures based on hybrid HCSS model.

Aggregates are grey circles, surrounding cement paste is Fig. 4—Model and measured relative electrical conductivities

white, and voids are black. Porosities are: (a) 27.3%; (b) for pervious concretes as function of porosity (void fraction).

22.4%; (c) 18.0%; and (d) 14.1%. Images are 100 x 100 mm Experimental data are calculated from values provided by

(3.94 x 3.94 in.) in size. Neithalath et al.3ACI Materials Journal/May-June 2008 299

- with the conditions used in the simulations). Once again, the generally fall near the middle of the range of experimental

agreement between experimental data and virtual data is data for any given porosity in the range of 12 to 32%.

clearly superior for the correlation filter reconstruction- The results in Fig. 3 to 5 have demonstrated that the virtual

based microstructures. pervious concrete based on the correlation filter reconstruction

A similar comparison is observed for the permeability algorithm produces a simulated void microstructure whose

predictions, as shown in Fig. 5. Once again, clearly, the percolation characteristics and transport properties are quite

permeability values computed for the correlation filter close to those reported for various pervious concretes. Such

reconstruction-based microstructures are in far better a model could be used to predict the permeability, or conduc-

agreement with the experimental values taken from the tivity, of a pervious concrete a priori. Another possibility

literature1-3 than are the ones computed for the microstructures would be to obtain a real 2D image of a pervious concrete,

based on the hybrid HCSS model. Not surprisingly, the extract the voids, measure their correlation properties, and

microstructure model that better captures the percolation use this information to model a 3D pervious concrete whose

characteristics of real pervious concretes also provides transport properties could be computed, instead of making

estimates of conductivity and permeability that are in good the corresponding physical measurements.

agreement with those measured experimentally. Because Additionally, the existence of a realistic 3D microstructure

permeability is also strongly dependent on (entryway) pore model should allow for the virtual examination of degradation

size,7,8,11 the correlation filter reconstruction algorithm appears potentials. For example, with regard to freezing-and-thawing

to be adequately capturing that aspect of the real pervious durability, one can envision that in some pervious concretes,

concrete microstructures. Whereas there is significant vari- there exists a subset of the void space that fills with water,

ability amongst the experimental values presented in Fig. 5, but does not drain. This accessible but not percolated porosity

the reconstruction model produces permeability values that can be easily quantified by using the burning algorithm

mentioned previously. Figure 6 provides a plot of both the

accessible and the percolated void (porosity) fractions for

virtual pervious concretes with various total porosities. The

difference between these two would indicate porosity that is

accessible, but perhaps not drainable. As the total porosity

falls below approximately 20%, there exists a measurable

(1% or more) fraction of such porosity that can easily fill

with water but is not part of a connected pathway for

drainage. This causes concerns with frost durability in this

subset of pervious concretes.

Clogging potential is another possibility that can perhaps

be examined using the virtual pervious concrete. Computa-

tionally, an algorithm similar to a mercury intrusion experiment

can be used to examine the accessibility of the 3D porosity

Fig. 5—Model and measured permeabilities for pervious as a function of entryway pore size.17 By equating this entryway

concretes as function of porosity (void fraction). Experimental pore size to the size of the particles causing the clogging, the

data are taken from indicated references.1-3 Uncertainty clogging potential of various pervious concretes might be

estimates provided in references are as follows: for data of assessed. An example of this analysis is provided in Fig. 7 in

Montes and Haselbach,2 repeatability in experimental values which various diameter spherical particles (templates) have

was within ±10% for a particular sample, whereas for data been intruded into the voids of two different virtual pervious

of Neithalath et al.,3 coefficient of variation for three concretes based on the correlation filter reconstruction

repeated measurements was on order of 20%. Permeability algorithm and one based on the hybrid HCSS model. For

conversion: 1 m2 = 1.01 × 1012 darcy.Fig. 6—Percolated and accessible percentages of total voids

as function of porosity (void) fraction for virtual pervious Fig. 7—Intruded volume fraction versus entryway pore

concrete microstructures based on correlation filter diameter for virtual pervious concretes with different void

reconstruction algorithm. fractions and based on two different microstructural models.300 ACI Materials Journal/May-June 2008

- both of the correlation filter-based virtual pervious 3. Neithalath, N.; Weiss, J.; and Olek, J., “Characterizing Enhanced

concretes, the infiltration of particles 1 mm (0.0394 in.) in Porosity Concrete Using Electrical Impedance to Predict Acoustic and

Hydraulic Performance,” Cement and Concrete Research, V. 36, No. 11,

diameter or greater could lead to considerable clogging, as 2006, pp. 2074-2085.

indicated by the low intrusion volumes. For smaller particles 4. Bentz, D. P., and Martys, N. S., “A Stokes Permeability Solver for

(for example, 0.333 mm [0.013 in.] in diameter), the 14% Three-Dimensional Porous Media,” NISTIR 7416, U.S. Department of

porosity virtual pervious concrete should be more susceptible Commerce, 2007, 110 pp.

to clogging than the 27% one. The clogging results for the 5. Garboczi, E. J., “Finite Element and Finite Difference Programs for

virtual pervious concrete based on the hybrid HCSS model Computing the Linear Electric and Elastic Properties of Digital Images of

indicates a much larger critical pore size, consistent with this Random Materials,” NISTIR 6269, U.S. Department of Commerce, 1998.

model’s higher permeability values in comparison with the 6. Bentz, D. P.; Garboczi, E. J.; and Snyder, K. A., “A Hard Core/Soft

reconstructed and real pervious concretes. With both a more Shell Microstructural Model for Studying Percolation and Transport in

Three-Dimensional Composite Media,” NISTIR 6265, U.S. Department of

percolated void network and a larger critical pore size, it Commerce, 1999, 51 pp.

would naturally be expected that the virtual pervious 7. Schwartz, L. M.; Martys, N.; Bentz, D. P.; Garboczi, E. J.; and

concretes based on the hybrid HCSS model would have a Torquato, S., “Cross Property Relations and Permeability Estimation in Model

much higher permeability, as illustrated in Fig. 5. Porous Media,” Physical Review E, V. 48, No. 6, 1993, pp. 4584-4591.

8. Bentz, D. P., and Martys, N. S., “Hydraulic Radius and Transport in

CONCLUSIONS Reconstructed Model Three-Dimensional Porous Media,” Transport in

The successful development of a virtual pervious concrete Porous Media, V. 17, No. 3, 1994, pp. 221-238.

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3D void structure that exhibits percolation characteristics 10. Bentz, D. P., and Garboczi, E. J., “Percolation of Phases in a Three-

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future, they may be obtained directly from 2D images of 1994, pp. 403-408.

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Springer-Verlag, New York, 1983, 358 pp.

sets are available from actual pervious concretes,1 the

13. Middleman, S., Fundamentals of Polymer Processing, McGraw-Hill,

presented percolation and transport property computation New York, 1977, 525 pp.

codes may be conveniently used to compute percolation, 14. Sisavath, S.; Jing, X.; and Zimmerman, R. W., “Laminar Flow

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exploring durability issues such as freezing-and-thawing 15. Bentz, D. P.; Quenard, D. A.; Kunzel, H. M.; Baruchel, J.; Peyrin, F.;

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